ISSN: 1402-1544 ISBN 978-91-7583-XXX-X Se i listan och fyll i siffror där kryssen är
DOCTORAL T H E SIS Giuseppe Caprolu Evaluation of Splitting Capacity Bottom Rails in Partially Anchored Timber Frame Shear Walls
Department of Civil, Environmental and Natural Resources Engineering Division of Structural and Construction Engineering Evaluation of Splitting Capacity of Bottom ISSN 1402-1544 ISBN 978-91-7583-149-7 (print) ISBN 978-91-7583-150-3 (pdf) Rails in Partially Anchored Timber Frame Luleå University of Technology 2014 Shear Walls
Giuseppe Caprolu
Evaluation of Splitting Capacity of Bottom Rails in Partially Anchored Timber Frame Shear Walls
Giuseppe Caprolu
Luleå University of Technology Department of Civil, Environmental and Natural Resources Engineering Division of Structural and Construction Engineering – Timber Structures
Printed by Luleå University of Technology, Graphic Production 2014
ISSN 1402-1544 ISBN 978-91-7583-149-7 (print) ISBN 978-91-7583-150-3 (pdf) Luleå 2014 www.ltu.se Abstract I
ABSTRACT The horizontal stabilization of timber frame buildings is often provided by shear walls. Plastic design methods can be used to determine the load-carrying capacity of fully and partially anchored shear walls. In order to use these methods, a ductile behaviour of the sheathing-to-framing joint must be ensured. If hold-downs are not provided, the vertical uplifting forces are transferred to the substrate by the fasteners of the sheathing-to-framing joints. Since the forces in the anchor bolts and the sheathing-to-framing joints do not act in the same vertical plane, the bottom rail will be subjected to bending in the crosswise direction, and splitting of the bottom rail may occur. If the bottom rail splits the applicability of the plastic design method for partially anchored shear walls is questionable. This doctoral thesis addresses the problem of brittle failure of the bottom rail in partially anchored timber frame shear walls. The first part of the study comprised of two basic experimental programs, for single-sided and double-sided sheathed shear walls. The aim was to evaluate the different failure modes and the corresponding splitting capacity of the bottom rail. Two brittle failure modes were observed: (1) a crack opening from the bottom surface of the bottom rail; and (2) a crack opening from the side surface of the bottom rail along the line of the fasteners of the sheathing-to-framing joints. It was found that the distance between the washer edge and the loaded edge of the bottom rail has a decisive influence on the type of failure mode and the maximum failure load of the bottom rail. Two theoretical models for the load-carrying capacity for each type of failure mode based on a fracture mechanics approach are studied and validated. The two analytical closed-form solutions are in good agreement with the test results. The fracture mechanics models seem to capture the essential behaviour and to include the decisive parameters of the bottom rail. These parameters can easily be determined and the fracture mechanics models can be used in design equations for bottom rails in partially anchored shear walls. Also, an extended fracture mechanics model for the load-carrying capacity for each type of failure mode is presented and evaluated. The present study discusses the splitting behaviour of the bottom rail and provides methods to determine the splitting capacity for two brittle failure modes, splitting of the bottom surface (mode 1) and of the side surface of the rail (mode 2). By these means brittle failure of the bottom rail can be avoided and the full plastic load-carrying capacity of the sheathing-to-framing joints can be utilized.
Sammanfattning III
SAMMANFATTNING Horisontalstabiliseringen av byggnader med trästomme sker ofta via skivverkan. Plastiska dimensioneringsmetoder kan användas för att bestämma bärförmågan för fullt och partiellt förankrade skjuvväggar. För att kunna använda dessa metoder, måste ett duktilt beteende hos förbandet mellan skiva och stomme säkerställas. Om förankringsjärn inte används, kommer de vertikala lyftkrafterna att överföras till underlaget via förbindare mellan skiva och stomme. Eftersom krafterna i förankringsbultarna och förbindarna mellan skiva och stomme inte verkar i samma vertikala plan kommer syllen att utsättas för böjning vinkelrätt fibrerna och uppsprickning av syllen kan resultera. Om syllen spricker är det tveksamt om en plastisk dimensioneringsmetod kan användas för partiellt förankrade skjuvväggar. Den första delen i studien innehöll två experimentella delstudier, en för enkelsidig och en för dubbelsidiga skivor. Syftet var att utvärdera olika brottmoder och tillhörande kapacitet för syllen. Två spröda brottmoder observerades: (1) en spricka längs syllen öppnas från botten på syllen och uppåt och (2) en spricka längs syllen öppnas från sidan på syllen och propagerar i huvudsak horisontellt längs förbindarna mellan skiva och stomme. Avståndet mellan brickans kant och den belastade änden av syllen har en avgörande påverkan på brottmod och maximal last för syllen. Två teoretiska modeller för bärförmågan för varje brottmod har härletts, båda baserade på brottmekanik. De två analytiska lösningarna överensstämmer väl med testresultaten. De brottmekaniska modellerna fångar det grundläggande beteendet hos syllen och innehåller de avgörande parametrarna. Dessa parametrar kan enkelt bestämmas och brottmekaniska modeller kan användas i dimensioneringssituationen av syllen i partiellt förankrade skjuvväggar. En vidareutveckling av de brottmekaniska modellerna med förfinad modellering presenteras och utvärderas också. Studien diskuterar uppsprickning av syllen och visar på metoder för att bestämma bärförmågan för två spröda brott: uppsprickning av undersidan på syllen (mod 1) och av sidan på syllen (mod 2). Genom att använda metoderna kan spröda brott i syllen undvikas och full plastisk bärförmåga hos förbanden mellan skiva och stomme utnyttjas.
Acknowledgements V
ACKNOWLEDGEMENTS First of all I would like to express my sincere gratitude to my supervisors, Professor Ulf Arne Girhammar and Associate Professor Helena Lidelöw for their support during these five years. I would also like to thanks Professor Bo Källsner for sharing his broad knowledge in timber structures and to Professor Barbara De Nicolo and Professor Massimo Fragiacomo for helping me to start this journey. Many thanks to all my colleagues at the University, for all I learned from them and for their help. I would like also to thank the staff working at the laboratory at Umeå University and SP laboratory in Stockholm, where I performed all my experimental studies. I take this chance to thank the Sardinian Region for its financial support with the PhD scholarship program “Master and Back” that gave me the idea and possibility to do this experience. Finally I would like to thank my family for their mental support and all friends and people I have met during these five years, you are too many to be mentioned one by one, but I have to mention my best friends Nicola and Damiano, you made my stay in cold Luleå warmer.
Giuseppe Caprolu Luleå, November 2014
List of publications VII
LIST OF PUBLICATIONS The thesis is based on studies presented in the following publications: I. Caprolu G., Girhammar U. A., Källsner B. and Lidelöw H. (2014) Splitting capacity of bottom rail in partially anchored timber frame shear walls with single-sided sheathing. Published in The IES Journal Part A: Civil & Structural Engineering, 7:83 – 105. II. Caprolu G., Girhammar U. A. and Källsner B. (2014) Splitting capacity of bottom rail in partially anchored timber frame shear walls with double-sided sheathing. Published online in The IES Journal Part A: Civil & Structural Engineering, November 2014. III. Caprolu G., Girhammar U. A. and Källsner B. (2014) Analytical models for splitting capacity of bottom rails in partially anchored timber frame shear walls based on fracture mechanics. Submitted to Engineering Structures in November 2014. IV. Jensen J. L., Caprolu G. and Girhammar U.A. (2014) Fracture mechanics models for brittle failure of bottom rails due to uplift in timber frame shear walls. Submitted to Structural Engineering and Mechanics in November 2014. V. Caprolu G., Girhammar U. A. and Källsner B. (2014) Comparison of models and tests on bottom rails in timber frame shear walls experiencing uplift. Submitted to Material and Structures in November 2014. In addition to the publications listed above, conference contributions have been written during the project: x Caprolu G., Girhammar U. A., Källsner B. and Johnsson H. (2012) Tests on splitting failure capacity of the bottom rail due to uplift in partially anchored shear walls. In Proceedings of the 12th World Conference on Timber Engineering, Auckland, New Zealand. x Caprolu G., Girhammar U. A., Källsner B. and Vessby J. (2012) Analytical and experimental evaluation of the capacity of the bottom rail in partially anchored timber frame shear walls. In Proceedings of the 12th World Conference on Timber Engineering, Auckland, New Zealand.
Table of contents IX
TABLE OF CONTENTS ABSTRACT ...... I SAMMANFATTNING ...... III ACKNOWLEDGEMENTS ...... V LIST OF PUBLICATIONS ...... VII PART I ...... XI NOTATIONS AND SYMBOLS ...... 1 1 INTRODUCTION ...... 3 1.1 BACKGROUND ...... 3 1.2 AIMS AND SCOPE ...... 7 1.3 LIMITATIONS ...... 8 1.4 OUTLINE OF THE THESIS ...... 8 2 THEORETICAL CHAPTER ...... 11 2.1 MODELLING OF SHEAR WALLS ...... 11 2.1.1 Elastic models ...... 13 2.1.2 Finite element models ...... 17 2.1.3 Plastic models ...... 18 2.1.4 Design method according to Eurocode 5...... 20 2.2 FRACTURE MECHANICS ...... 21 2.2.1 Strain energy release rate ...... 23 3 EXPERIMENTAL STUDIES...... 27 3.1 SPLITTING CAPACITY OF BOTTOM RAIL ...... 27 3.1.1 Material properties ...... 27 3.1.2 Test programmes ...... 27 3.1.3 Test set-up ...... 28 3.2 MATCHING TESTS OF BRITTLE FAILURE OF BOTTOM RAIL, FRACTURE ENERGY AND TENSILE STRENGTH PERPENDICULAR TO THE GRAIN ...... 30 3.2.1 Bottom rail experimental program ...... 32 3.2.2 Fracture energy ...... 33 3.2.2.1 Material properties ...... 33 3.2.2.2 Test program ...... 33 3.2.2.3 Test set-up ...... 34 3.2.3 Tensile strength perpendicular to the grain ...... 35 3.2.3.1 Material properties ...... 35 3.2.3.2 Test program ...... 35 3.2.3.3 Test set-up ...... 35 4 ANALYTICAL MODELS ...... 39
X Table of contents
4.1 FAILURE MODE 1 ...... 39 4.2 FAILURE MODE 2 ...... 41 5 RESULTS ...... 43 5.1 BOTTOM RAIL TEST RESULTS ...... 43 5.1.1 Failure modes ...... 43 5.1.2 Load-time curves and crack development ...... 46 5.1.3 Failure loads ...... 48 5.2 MATCHING TESTS OF BRITTLE FAILURE OF BOTTOM RAIL, FRACTURE ENERGY AND TENSILE STRENGTH PERPENDICULAR TO THE GRAIN ...... 57 5.2.1 Bottom rail ...... 57 5.2.2 Fracture energy ...... 58 5.2.3 Tensile strength perpendicular to the grain ...... 60 6 ANALYSIS AND DISCUSSION ...... 61 6.1 BOTTOM RAIL EXPERIMENTAL PROGRAMMES ...... 61 6.1.1 Distance s ...... 61 6.1.2 Pith orientation ...... 62 6.2 BOTTOM RAIL ANALYTICAL MODELS ...... 63 7 CONCLUSIONS ...... 69 8 FUTURE WORK ...... 73 REFERENCES ...... 75 PART II Appended papers PAPER I PAPER II PAPER III PAPER IV PAPER V
PART I
Notation and symbols 1
NOTATIONS AND SYMBOLS A area of the crack [mm2] C compliance [mm/N] DOF degree of freedom DS double-sided E modulus of elasticity [MPa] FEM finite element method G shear modulus [MPa]
Gc critical fracture energy [N/m]
Gf fracture energy [N/m] LEFM linear elastic fracture mechanics LR longitudinal-radial crack orientation LT longitudinal-tangential crack orientation NLFM nonlinear fracture mechanics Ø diameter [mm] P bottom rail failure load [kN]
Pu failure load of a loaded elastic body [kN] PD pith downwards PU pith upwards R radial direction R2 coefficient of determination RL radial-longitudinal crack orientation RMSE root mean square error RT radial-tangential crack orientation SS single-sided T tangential direction TL tangential-longitudinal crack orientation TR tangential-radial crack orientation XFEM extended finite element method a crack length [mm] b width of the bottom rail [mm]
2 Notations and symbols
bcrack1 distance between a vertical crack and the loaded edge of the bottom rail [mm] bcrack2 length of a horizontal crack before change to the vertical direction [mm] be “cantilever span” for the geometry used to derive formulas for failure mode 1 [mm] c additional cantilever length [mm] d thickness of the fracture energy specimen [mm] e depth of the tensile strength perpendicular to the grain specimen [mm] ft,90 tensile strength perpendicular to the grain [MPa] h depth of the bottom rail [mm] hc distance between the notch and the upper edge of the fracture energy specimen [mm] he depth of the “cantilever beam” used to derive formulas for failure mode 1 [mm] l length of the bottom rail [mm] s distance between the edge of the washer and the loaded edge of the bottom rail [mm] t depth of the fracture energy specimen [mm] u width of the tensile strength perpendicular to the grain specimen [mm] v thickness of the tensile strength perpendicular to the grain specimen [mm] į deflection of the loading point [mm]
įb contribution from bending to the deflection of the loading point [mm]
įr contribution from shear to the deflection of the loading point [mm]
įv contribution from rotation to the deflection of the loading point [mm]
Introduction 3
1 INTRODUCTION
This chapter outlines the motivation for this thesis followed by the aim of the research, its limitations and outline of the thesis structure.
1.1 Background Timber frame building systems are a commonly used solution in timber housing construction. Timber frame buildings are made up by a frame of timber joists and studs, sheathed with panels joined to the wood elements. Wood-based panels, such as plywood, OSB, fibre- board or chipboard, are commonly used in timber frame buildings. Gypsum panels or similar products are also widely used in combination with timber, mainly to provide fire resistance. The timber frame concept is also competitive for multi-storey and multi-residential buildings (Thelandersson and Larsen 2003). In Figure 1.1 examples of multi-storey timber frame house are shown.
a) b) Figure 1.1 Examples of multi-storey timber frame buildings built in Stockholm (Sweden): (a) 2011; and (b) 2009. (Lindbäcks Bygg). One of the main issues to ensure when designing timber frame buildings is the horizontal stability. Since timber structures are light- weight, due to the high strength to weight ratio of wood, actions of horizontal force as wind and earthquake can cause high load concentrations and large deformations in timber structures. With increasing number of storeys the issue becomes more severe, as the self-weight of the structure is not sufficient to provide the necessary
4 Introduction stabilising force to counteract overturning, Thelandersson and Larsen (2003). The stabilisation of timber frame building is often provided by shear walls. Shear walls are structural elements designed to transmit forces in its own plane. They carry wind or other horizontal forces, called racking loads, in the plane of the wall (shear loads) in addition to the vertical loads and lateral pressure on their surface. They are composed of a frame made of vertical elements, studs, connected to two horizontal elements, top and bottom rail, and sheathed with panels. In Figure 1.2 the behaviour of a shear wall subjected to wind load and its typical construction details are shown.
Figure 1.2 Typical shear wall behaviour: (a) the building is loaded by wind load and one half of the total wind load is transferred to the roof level; (b) the roof diaphragm, acting as a deep horizontal beam, transmits the load to the shear wall; (c) the shear wall transfers the load to the foundation; and (d) construction details of the shear wall structure.
Introduction 5
The lateral wall, Figure 1.2a, is considered to be simply supported at roof and foundation, transferring one half of the total wind load to the roof level. Then the roof diaphragm, acting as a deep horizontal beam, transmits the load to the shear wall, Figure 1.2b. In turn, the shear wall transfers the load to the foundation, Figure 1.2c. The structural behaviour of shear walls is to a large extent determined by the sheathing-to-framing joints and by the connection between walls and the surrounding structure. Of particular importance is the anchoring of the shear wall to the floor/foundation. Sometimes tie-down devices are used for anchorage of the end studs of the shear wall. On other occasions only the bottom rail is anchored to the floor foundation, Källsner and Girhammar (2009). As pointed out by Prion and Lam (2003) it is important to understand the difference in the anchorage systems: anchor bolts and hold-downs, Figure 1.3.
a) b) Figure 1.3 Different ways to anchor a shear wall: (a) the anchor bolt provides horizontal shear continuously between the bottom rail and the foundation; and (b) the hold-down serves as a vertical anchorage device between the leading stud and the foundation. Anchor bolts provide horizontal shear continuity between the bottom rail and the foundation. Hold-downs serve as vertical anchorage devices between the vertical end studs and the foundation. In fully anchored shear walls, where both of them are provided, the vertical loads are directly transferred to the substrate, resulting in a concentrated force at the end of the wall, as shown in Figure 1.4a. The notation fully anchored means that the bottom rail fully interacts with the substrate and that there is no uplift of the studs of the walls, especially of the leading stud. When hold-downs are not provided, in
6 Introduction partially anchored shear walls, the corresponding tying-down forces may be replaced by vertical loads from dead-weight or anchorage forces transferred from transverse walls. The bottom row of nails transmits the vertical forces in the sheathing to the bottom rail (instead of the vertical stud) where the anchor bolts will further transmit the forces to the foundation. This results in a distributed force, as shown in Figure 1.4b.
Figure 1.4 Two principal ways to anchor timber frame shear walls subjected to horizontal loading: (a) fully anchored shear wall – concentrated anchorage of the leading stud, i.e. using a hold-down; and (b) partially anchored shear walls – distributed anchorage of the bottom rail through the sheathing-to-framing joints. Since the forces in the anchor bolts and the sheathing-to-framing joints do not act in the same vertical plane, the bottom rail will be subjected to crosswise bending and shear, and splitting of the bottom rail may occur, as shown in Figure 1.5.
a) b) Figure 1.5 Examples of splitting failure of the bottom rail in partially anchored timber frame shear walls: (a) splitting failure along the bottom side of the rail; and (b) splitting failure along the edge side of the rail. For both cases the left pictures refers to a bottom rail with single-sided sheathing and the right pictures to a bottom rail with double-sided sheathing. Nowadays, in Europe, two design methods of shear walls exist. They are given in Eurocode 5 (2008): (1) method A, with a theoretical background, can only be applied to shear walls with a tie-down at the loaded leading stud in order to prevent uplift; and (2) method B (together with the test protocol according to EN 594, 2008), which is a soft conversion of the procedure developed in the United Kingdom for racking strength given in BS 5268 (1996), (Porteous and Kermani, 2007), which can be used to design shear walls where the corresponding stud is free to move vertically and the bottom rail is anchored to the substrate. Method A corresponds to a fully anchored
Introduction 7 shear wall, while method B corresponds to a partially anchored shear wall. Brittle failure of the bottom rail is not taken into account in Eurocode 5 (2008). Despite method B is used also for partially anchored shear walls, no recommendation is given on how to avoid possible bottom rail splitting. Vessby (2011) pointed out that both methods are to be considered as plastic methods, but if the bottom rail fails in a brittle manner, the applicability of plastic methods can be questioned. It is important to avoid brittle failure of the bottom rail in order to enable the development of the force distribution shown in Figure 1.4b and hence be able to apply plastic methods. 1.2 Aims and scope The aim of this research is to identify the main factors influencing the splitting of the bottom rail in partially anchored timber frame shear walls. Further, the aim is to evaluate different developed models for calculating the splitting failure capacity of the bottom rail. First, the splitting capacity of the bottom rail in partially anchored timber frame shear walls was measured in two experimental programs for single- and double-sided sheathing. Data was collected about the failure modes and failure loads of the bottom rail. Then theoretical models for the load-carrying capacity of the bottom rail, based on a fracture mechanics approach, were studied and validated. Two of the main parameters in the studied fracture mechanics models were the fracture energy and the tensile strength perpendicular to the grain values. Due to the orthotropic characteristics of wood, it was difficult to find values in literature for the same timber used in our studies and for the same crack orientation. It was then decided to carry out an additional matching experimental program, with bottom rail tests after which both fracture energy and tensile strength perpendicular to the grain were evaluated with specimens cut from the bottom rail specimen used in the tests. Then really explicit values were collected and used to compare model predictions to test results. Specific questions addressed by the work presented in this thesis are: ¾ How do the varied parameters during the bottom rail tests, distance between the washer edge and the loaded edge of the bottom rail and the pith orientation of the bottom rail, influence the failure mode and load of bottom rail in partially anchored timber frame shear walls? ¾ Which of the evaluated models, based on a fracture mechanics approach, show the best fit with the experimental results, in terms of failure load, from the tests of bottom rail subjected to uplift in partially anchored timber frame shear walls?
8 Introduction
1.3 Limitations The research has several limitations. All tests performed during the study were short-term tests. No full size shear wall has been tested; however, data has been collected from previous studies. The cross section of the bottom rail used in the experiment was always the same: 120×45 mm. The species was spruce (Picea Abies). Only hardboard sheathing 8 mm from Masonite AB was used in the tests. During the bottom rail tests a small distance, 25 and 50 mm, between the nails in the sheathing-to-framing joints was used. This distance was applied, despite it is not a distance used in reality, in order to have a strong sheathing-to-framing joint and obtain splitting as the failure mode of the bottom rail. Finally, all models derived and validated in this study are 2D models that do not take into account that the anchor bolts were discretely placed along the bottom rail and are based on linear elastic fracture mechanics, even if a nonlinear approach is recommended for wood. 1.4 Outline of the thesis This thesis is divided in two parts: part I gives a summary of the research carried out, while part II collects all journal articles written. In part I some additional information not included in part II are included; a literature review on shear wall modelling. Part I This part is divided in eight chapters. Chapter 2 gives a literature review on shear wall modelling and the fracture mechanics concepts used in the thesis are included. Chapter 3 gives a background on the experimental studies. Chapter 4 collects the models evaluated for calculating the splitting failure capacity of the bottom rail. Chapter 5 collects the test results. Chapter 6 is a collection and discussion of the main findings of the study while chapter 7 summarizes the main conclusions. Finally chapter 8 gives suggestions about the future work. Part II Paper I “Splitting capacity of bottom rail in partially anchored timber frame shear walls with single-sided sheathing” by Giuseppe Caprolu, Ulf Arne Girhammar, Bo Källsner and Helena Lidelöw was published in The IES Journal Part A: Civil & Structural Engineering in May 2014, 7:83 – 105. Giuseppe Caprolu’s contribution to this paper was participating and performing the bottom rail tests, evaluating the test results and carrying out the analysis suggested by the senior authors. Furthermore, the introduction, the experimental part of the paper including test results presentation, was
Introduction 9 written by Caprolu. The experimental purpose was to study the influence of the distance between the edge of the washer and the loaded edge of the bottom rail and of the pith orientation on the failure mode and the failure load of the bottom rail with single-sided sheathing subjected to uplift in partially anchored timber frame shear walls. Paper II “Splitting capacity of bottom rail in partially anchored timber frame shear walls with double-sided sheathing” by Giuseppe Caprolu, Ulf Arne Girhammar and Bo Källsner was published online in The IES Journal Part A: Civil & Structural Engineering in November 2014. Giuseppe Caprolu’s contribution to this paper was participating and performing the bottom rail tests, evaluating the test results and carrying out the analysis. Furthermore, the introduction, the experimental part of the paper including test results presentation, the analysis and the discussion were mainly written by Caprolu. The experimental purpose was to study the influence of the distance between the edge of the washer and the loaded edge of the bottom rail and of the pith orientation on the failure mode and on the failure load of the bottom rails with double- sided sheathing subjected to uplift in partially anchored timber frame shear walls. Paper III “Analytical models for splitting capacity of bottom rails in partially anchored timber frame shear walls based on fracture mechanics” by Giuseppe Caprolu, Ulf Arne Girhammar and Bo Källsner was submitted to Engineering Structures in November 2014. Giuseppe Caprolu’s contribution to this paper was to provide the experimental background and performing the analysis. Furthermore, the introduction, the experimental background of the paper, and part of the analysis and the discussion was written by Caprolu. The purpose was to present and validate analytical models based on a fracture mechanics approach, able to predict the splitting capacity of bottom rails. Paper IV “Fracture mechanics models for brittle failure of bottom rails due to uplift in timber frame shear walls” by Jørgen L. Jensen, Giuseppe Caprolu and Ulf Arne Girhammar was submitted to Structural Engineering and Mechanics in November 2014. Giuseppe Caprolu’s contribution to this paper was to provide the experimental background. Furthermore, the experimental part of the paper including test results presentation was written by Caprolu. The purpose was to present and validate additional analytical models based on a fracture mechanics approach, able to predict the splitting capacity of bottom rails.
10 Introduction
Paper V “Comparison of models and tests on bottom rails in timber frame shear walls experiencing uplift” by Giuseppe Caprolu, Ulf Arne Girhammar and Bo Källsner was submitted to Material and Structures in November 2014. Giuseppe Caprolu’s contribution to this paper was participating and performing the bottom rail, the fracture energy and the tensile strength perpendicular to the grain tests, evaluating the test results and carrying out the analysis. Furthermore, the introduction, the experimental part of the paper including test results presentation, the analysis and the discussion were mainly written by Caprolu. The purpose was to have explicit values for evaluating tests and analytical results in order to be able to state which of the previously presented models show the best fit with the bottom rail test results.
Theoretical chapter 11
2 THEORETICAL CHAPTER
The chapter starts with a literature review of modelling of shear walls. Due to the high number of studies in this area, the most important studies are chosen on basis of the number of citations. Studies relative to seismic action are not taken into account. The review is grouped based on the modelling used for their derivation: (1) elastic; (2) plastic; and (3) finite element. Where possible, the derived equation for the load-carrying capacity of shear walls is presented. The two official design methods given in Eurocode 5 (2008) are explained. The purpose of the literature review was to highlight strong, weak and missing points of the different methods and also to show the simplicity of plastic methods, which, if the splitting of the bottom rail can be avoided, could be applied to partially anchored shear walls. Finally, a theoretical background for linear elastic fracture mechanics (LEFM), used to derivate the failure load models presented for the bottom rail, is explained. The notation used in this chapter does not follow the general thesis notation.
2.1 Modelling of shear walls Wood shear walls have been a research subject since the 1920’s with activities focused both on experimental and theoretical modelling approaches, Källsner and Girhammar (2009). Dolan and Foschi (1991) pointed out that the construction of timber buildings today is not the same as decades ago. Multifamily structures are larger. In addition, concrete overlayments on floors, concrete tile on roofs, and other new, heavier materials are used in the upper stories for fire protection, sound control, aesthetics, and reduced cost. Due to these and other changes to the construction of timber buildings, the assumption of past experience proving the reliability of timber structures is questionable. Therefore, modelling of wood shear walls has evolved over the last three decades from simple equations for the prediction of strength, stiffness and deformation to complex nonlinear finite element models detailed enough to include nonlinear elements for each fastener, van de Lindt (2004). Models have been developed both for hand calculation and computer based numerical models, usually based on the finite element method. These are based both on linear elastic and nonlinear elastic properties. They are applicable to fully and, in a few cases, to partially anchored shear walls, both for shear walls with and without openings and both for static and dynamic loads. Further, models have been developed considering the influence of vertical loads and lateral walls.
12 Theoretical chapter
Some of the simplest, and most used, models for analysis of the capacity of shear walls are based on the theory of elasticity, Vessby (2011). The basic assumptions for the elastic models are: rigid framing and sheathing, framing members connected by frictionless hinges and bottom rail assumed to interact fully with the foundation. The results in these models are determined using the elastic approach where the shear wall capacity is based on the most loaded fastener. The plastic approach has the potential to specify more realistic load paths than is the case in an elastic analysis. The fasteners are assumed to reach their maximum capacity and, except for the corner ones, carry the full design load. The framing members are assumed to be completely flexible, which implies that the force distribution from the fasteners will become parallel with the framing members. This can be of great importance for load levels approaching the ultimate capacity as the load transferred by a single fastener changes both in terms of magnitude and direction. According to the assumptions above, plastic design methods are the only method that may be used to design partially anchored timber frame shear walls, on condition that a ductile behaviour of the sheathing-to-framing joint is provided and splitting of the bottom rail avoided. Källsner et al. (2001) pointed out that the elastic model and the plastic lower bound model give almost the same load-carrying capacity for the shear wall. However the distribution of the fastener forces is fairly different, as shown in Figure 2.1. F F
a) b) c)
Figure 2.1 (a) A shear wall unit built up of a timber frame and a sheet; (b) forces acting on the sheet according to a linear elastic model; and (c) forces acting on the sheet according to a plastic lower bound model. Källsner et al. (2001) highlighted that at ultimate limit state the force distribution according to the plastic lower bound model can be justified for different reasons. One reason is that the joints between the timber members often tend to yield, which means that the force components perpendicular to the length direction of the timber members cannot be fully built up. Another reason is that at high loads some bending deformations in the timber members can almost always be seen, that also lead to reduced force components perpendicular to the timber members.
Theoretical chapter 13
2.1.1 Elastic models In this section, where possible, equations derived in the presented studies are shown. The parameters in the equations refer to Figure 2.2.
Figure 2.2 Sheet dimensions and nail patterns. Tuomi and McCutcheon (1978) developed a method based on the energy formulation where linear elastic nails absorb the internal energy and the external energy is given by the racking load. The model is able to predict the racking load of frame panels. The input data required are the panel geometry, the number and spacing of nails, and the lateral resistance of a single nail. Both small-scale and full-scale tests were run to verify the accuracy of the model. The theoretical results were found to give close agreement with experimental data for two panel sizes. The total racking strength F of a panel is computed by:
F rªº K K wK22 cK wK 2 cK 2 (2.1) ¬¼n mp na nb ma mb f where the subscripts p and f are the contribution of the perimeter and field nails, respectively, r is the individual nail resistance, wHH f , cBB f , according to Figure 2.2, and Kn , Km , Kna , Knb , Kma , and Kmb are given in Tuomi and McCutcheon (1978). The model is elastic and fully anchored to the foundation. McCutcheon (1985) highlighted that this method assumes a linear load-displacement relationship for a single nail, while in reality it is highly nonlinear, hence it cannot adequately predict the real behaviour of the wall. Further, as pointed out by Källsner and Girhammar (2009), the applicability of this model is limited by the hypothesis chosen. In fact the corner fasteners are supposed to displace along the diagonals of the sheathing, but this is
14 Theoretical chapter true only if the same number of fastener spacings are used in the rails and in the studs. Itani et al. (1982) presented a methodology for calculating the racking performance of sheathed wood-stud walls with and without door and window openings. In their model each sheet is replaced by a pair of diagonal springs, with the stiffness of each spring calculated from the stiffness of an individual nail of the sheathing-to-framing joint. The stiffness of the diagonal springs K is calculated according to:
22 knªº21§·22 m 1 Knm «»¨¸cosEE sin (2.2) 43¬¼©¹nm where k is the nail slip modulus, n, m, and ȕ are given in Figure 2.2. An equation was then used to fit the load F to the slip of the nails. The equation was based on unpublished experimental data collected at the U.S. Forest Products Laboratory. The model is based on Tuomi and McCutcheon (1978), hence the same objections about the linear behaviour of the fasteners may be made. Further, when calculating the stiffness, only the perimeter fasteners of the sheathing-to-framing joints are considered, while internal ones are neglected. However, this may be a good approximation since they contribute with only 5% of the total stiffness. The connection between bottom rail and foundation is modelled with linear springs. Finally, the model does not take into account the load carried by the parts above and below the openings. In Rainer et al. (2008), where three mechanics-based models were compared, it was found an increase of calculated load-carrying capacity between 20% and 34% when the panels above and below the openings were added to the prediction. Easley et al. (1982) derived equations for the sheathing fastener forces, for the linear shear stiffness of a wall and for the nonlinear shear load-strain behaviour of a wall. The equations were based on deformation patterns observed during testing, which were verified using linear and nonlinear finite element analyses. For the 2D finite element model the sheets were modelled as plane stress isotropic element with eight nodes. The frame was also modelled with eight- nodes and a linear isotropic material. Two springs were used to model the sheathing-to-framing connection, one in each perpendicular direction. They concluded that their equation for sheathing forces should only be applied in the linear range, with the exception of the side and maximum end fastener force, which is accurate well into the nonlinear range. The model is elastic and fully anchored to the foundation. Further, as pointed out by Källsner and Girhammar (2009), the fasteners along the vertical studs were assumed to be loaded only in
Theoretical chapter 15 the vertical direction. This assumption is an approximation. Due to the number of equations, they are not presented here. Gupta and Kuo (1985) presented a simple numerical model, based on a generalized coordinate approach to derive equilibrium equations, to represent the shear behaviour of shear walls. Nonlinear properties were used for the sheathing-to-framing joints. The model includes the bending stiffness of the stud and shear stiffness of the sheathing. The model was compared to a finite element model and shear wall tests performed by Easley et al. (1982) and Foschi (1982). The comparison showed the adequacy of the model. They concluded that their model was accurate and simple enough to be used in repetitive analysis, e.g. nonlinear dynamic analysis. This model considers only fully anchored shear walls. Further, Robertson (1980) indicated that the shear strength per unit length of wall increases with the increase in the vertical loading on the wall and with the increase in the length of the wall. This dependence of the shear strength on the vertical load and the wall length cannot be explained by the model of Gupta and Kuo (1985). At a later stage, Gupta and Kuo (1987a) made a modification of the model, taking into account the uplift of the studs (assuming fully anchored bottom rail). The proposed model had five degrees of freedom (DOF) for a single-storey wall and two additional DOF for walls of two or more stories. The studs were modelled as continuous through all stories and each storey had a separate sheet. In Gupta and Kuo (1987b) an analytical three-dimensional model of a complete house was presented. A major part of the effort went into perfecting the shear wall behaviour suitable for house analysis. The model was extended in order to consider uplift of the bottom rail, in addition to that of the stud. The model prediction was compared to the test results from a full scale house, presented in Tuomi and McCutcheon (1974), giving results that were in good agreement with the experimental results. The derived equations are given in matrix form and hence they are not presented here. Mallory and McCutcheon (1987) extended a previous elastic model for shear wall performance developed by McCutcheon (1985), to model the nonlinear racking load-displacement behaviour of fully anchored shear walls sheathed on both sides with dissimilar materials. Four types of curves were used to model the fastener load slip: power, logarithmic, hyperbolic and asymptotic, with the latter found to give the best agreement with test results. The model prediction was compared to the results of numerous small wall tests, and predicted the racking behaviour well. The derived equation for the racking load F was:
16 Theoretical chapter
§·Q2' FS ¦¨¸f (2.3) ©¹ZQ'f
where Q is the wall horizontal racking displacement, ȴf is the fastener slip and S and Z are constants. Schmidt and Moody (1989) developed a simple structural analysis model to predict the nonlinear deformations of three-dimensional light frame buildings under lateral load. Openings are not included in the model. The model is based on the energy method and is an extension of the previous work of Tuomi and McCutcheon (1978), which is combined with nonlinear load-slip curves for fasteners presented by Foschi (1977) and McCutcheon (1985). A comparison of the predicted behaviour to the results from two full-scale house tests, Tuomi and McCutcheon (1974) and Boughton and Reardon (1984), reveals reasonable agreement with the test results. The derived equations are given in matrix form and they are not given here. Filiatrault (1990) developed a simple structural analysis model to predict the behaviour of timber shear walls under lateral static loads and earthquake excitations. The model is restricted to two-dimensional shear walls with arbitrary geometry of the framing, sheathing and connections, and wall discontinuities, i.e. openings. Nonlinear load-slip characteristics of the fasteners are used in a displacement-based energy formulation to develop the static and dynamic equilibrium equations. The model was verified with full-scale shear wall racking and shaketable tests, and was found to be accurate. The derived equations are given in matrix form not given here. Källsner and Girhammar (2009) presented an analysis of fully anchored light-frame timber shear walls. The analysis was based on an elastic model with the assumption of a linear elastic load-slip relation for the sheathing-to-framing joints. Only static loads were considered. Equations both for the load-carrying capacity and the deformation of the shear walls for ultimate and serviceability limit state were derived. Openings in the shear walls were not considered. Forces and displacements of the fasteners and sheathing were also derived. Other influences discussed were: discrete point or continuous flow per unit length modelling of the fasteners, effect of different patterns and spacing of the fasteners, influence of flexible framing member and shear deformations in the sheets and also the effect of vertical loads. The model was compared to the results from an experimental study and reasonable agreement was found. The equation proposed for the horizontal load-carrying capacity F of the wall unit was:
Theoretical chapter 17
r F (2.4) 22 ªºªº xyˆˆcorner corner H «»«»nn «»«»xyˆˆ22 ¬¼¬¼¦¦ii 11ii where r is the shear capacity of the fastener, H as given in Figure 2.2 and xˆ and yˆ are the fastener coordinates referring to the new coordinate axes, which are referred to the centre of gravity of the fasteners. 2.1.2 Finite element models Foschi (1977) presented a structural analysis for wood diaphragms based on finite element model. Four different structural elements were considered in the analysis: the sheet, assumed to be elastic and orthotropic, the frame, represented by linear beam elements and the connections between frame members and sheet-frame connections, assuming a nonlinear behaviour. A comparison was made with experimental results on 6×18 m plywood and decking roof diaphragms. The comparison showed that the analysis gives reliable estimates for diaphragm deformations and is capable of providing an approximation for ultimate loads based on connection yielding. Falk and Itani (1989) presented a two-dimensional finite element model for analysing the nonlinear load displacement of vertical and horizontal wood diaphragms. Their formulation included a nonlinear finite element model that accounted for the distribution and stiffness of fasteners connecting the sheet to the framing. A parametric study was performed and it showed that both nail stiffness and nail spacing, the latter with a greater effect, influenced the diaphragm stiffness. Blocking was shown to increase the diaphragm stiffness due to the greater number of nails used with blocking and the increased frame action provided. A comparison of the model results with experimental tests reported in Falk and Itani (1987) indicated a good prediction. This model is a respond to the finite element model proposed by Itani and Cheung (1984) for the static analysis of wood diaphragms. That model needed a large number of DOF when modelling large diaphragms. The model presented by Falk and Itani (1989) require fewer DOF and gives a better representation of the distributed fasteners if larger ceiling and floor diaphragms have to be analysed. A numerical model, based on a finite element analysis procedure for nonlinear static analysis of wood shear walls was developed by Dolan and Foschi (1991). The model is an improved version of that developed by Foschi (1977) and the improvements are the possibility to include: (1) nonlinearities in the sheathing due to bending and
18 Theoretical chapter buckling of the sheathing; (2) modification of the fastener in the sheathing-to-framing joint in order to include three directions of movement and the ultimate capacity of the connector; and (3) the bearing between adjacent sheathing elements. The model has been verified by comparison with the load-deflection curves from full-scale shear wall tests presented by Dolan (1989) and good prediction was found. The authors conclude that their model is general and capable of modelling irregular shapes as well as adhesive connections. In order to reduce the total number of DOF Kasal and Leichti (1992) developed a two-dimensional model that was equivalent to a detailed three-dimensional model. The equivalent model was formulated using equivalent energy concepts, and yielded the global behaviour of the structure in reasonable time. The model can treat a wall with or without openings. 2.1.3 Plastic models In Ni and Karacabeyli (2000; 2002) one mechanical-based method and one empirical method were developed to account for effects of vertical loads and perpendicular walls on the performance of shear walls with and without hold downs. The methods were found to be in reasonable agreement with test data from a previous study. The proposed equation to calculate the lateral capacity F for the mechanical-based method is given as:
FfL 12IJ J2 J p (2.5)
Where fp is the plastic capacity of a panel per unit length,I PfHRp, where PR is the uplift restraint force on the end stud of a shear wall segment H is given in Figure 2.2, and J HL, where L is the full wall length. The mechanical-based option has been adopted in Canada in the CSA-O86 (2001) Standard for wood design and in the Wood Design Manual. Eq. (2.5) was then changed by simply introducing the hold down effect reduction factor Jhd, to Eq. (2.5). The reduction factor is calculated as:
2 Pij §·HH Jhd 1 2 ¨¸ d 1.0 (2.6) VBBhd ©¹
With Pij and Vhd as given in Ni and Karacabeyli (2002) and H and B as given in Figure 2.1.
If the shear wall is fully anchored Jhd is considered as being unity, otherwise it is determined using Eq. (2.6). The model is not able to take into account openings in the shear wall.
Theoretical chapter 19
Later, Källsner et al. (2001; 2002), developed a plastic lower bound method, meaning that the force distribution was chosen in order to fulfil the conditions of force and moment equilibrium. The method is able to calculate the load-carrying capacity of fully and partially anchored timber frame shear walls at ultimate limit state. The model covers only static loads and can only be applied when mechanical fasteners with plastic characteristics are used. The influence of vertical loads is also taken into account. Only walls without openings were dealt with in this study. Many equations have been presented depending on the anchorage system and external loads acting on the shear walls. Due to the number of equations, they are not presented here. In Källsner and Girhammar (2004) a plastic lower bound method was presented to study the influence of the stud-to-rail joint on the load-carrying capacity of partially anchored timber frame shear walls. The calculations showed that considering this, the load-carrying capacity can be increased by 10 to 15%. In this method the full vertical shear capacity of the wall was utilized, which not fully fulfil the conditions of equilibrium. The calculated load-carrying capacity was equal or slightly higher than the method presented in Källsner et al. (2001; 2002), but it was much easier to calculate. In Källsner and Girhammar (2005) this theory was presented in a simple format and it was shown that the theory can also be applied to shear walls with openings. Vertical point and distributed loads acting on the wall were considered. The model assumptions were: x The model covers only static loads; x The sheathing-to-framing joints in the vertical studs and top rail are assumed to transfer only shear forces parallel to the timber members; x The sheathing-to-framing joints in the bottom rail are assumed to transfer forces both parallel and perpendicular to the bottom rail; x The framing joints can transfer tensile or shear forces; x Compressive forces can be transferred via contact between adjacent sheets and in the framing joints.
This analytical model has different advantages. It is able to calculate the load-carrying capacity of shear walls with and without openings. It can be used in design of shear walls with different sheet materials, sheathing-to-framing joints, geometric layout, anchoring conditions and load configurations. The main problem has been that the shear
20 Theoretical chapter walls are fastened to the substrate in different ways in different countries. This fact must be reflected in national codes but it is not. The model can be applied to shear walls that are fully or partially anchored to the substrate, giving a solution to this problem. The authors derived easy used closed form equations for the wall configurations needed by a designer. They are presented in Källsner and Girhammar (2005). 2.1.4 Design method according to Eurocode 5 In Eurocode 5 (2008) two methods are given for the design of shear walls, method A and method B. Method A is based on a theoretical background, while method B is a soft conversion of the procedure developed in the United Kingdom for racking strength and given in BS 5268 (1996), (Porteous and Kermani, 2007). In both models, the design racking load-carrying capacity is based on the lateral design capacity of the individual fasteners in the sheathing-to-framing joints. The capacity of the single fastener is then multiplied by the number of spacings between these connections and the design load-carrying capacity of the wall panel is obtained. If the wall assembly is composed of several wall panels, the total load-carrying capacity is given by the sum of their single load-carrying capacities. In method A, the capacity of areas around door and window openings in the wall panels are not considered to contribute to the total load-carrying capacity, while in method B no mention is made concerning this. The fastener spacing is constant along the shear wall perimeter and all fasteners are considered to reach their maximum lateral load capacity. It should be noted that the two methods have different boundary conditions: method A corresponds to a fully anchored shear wall while method B corresponds to a partially anchored shear wall, meaning that the studs are allowed to separate from the bottom rail when subjected to uplift and that the bottom rail can be subjected to transverse bending. It is obvious that the two methods are not consistent with one other, except in the case where vertical loads of sufficient magnitude to stabilize the wall are applied in method B. As already highlighted, the structural behaviour in the case of partially anchored shear wall introduces different failure modes than the fully anchored, for example splitting failure of the bottom rail could happen. However, no recommendations are given with respect to this. Vessby (2011) pointed out that both methods are to be considered as methods based on theory of plasticity since they assume the same load (magnitude) being transferred by all the fasteners. However, no recommendations are given on any larger scale than parts of walls, i.e. single shear walls. Much of the benefits of an overall plastic analysis,
Theoretical chapter 21 with possibilities to e.g. include the effects of lateral walls, are not indicated and thus not regulated in Eurocode 5 (2008). 2.2 Fracture mechanics Aicher et al. (2002) pointed out that when a body made of a solid material is loaded it will ultimately respond by undergoing large deformations or fracture. Fracture is the loss of contact between parts of the body resulting in a creation of two new surfaces and it is the topic of interest in fracture mechanics. The concern is partly with the microscopic mechanism, which govern the separation and partly with predictions from a macroscopic point of view. Of prime concern is the development of criteria and methods by which it is possible to predict the load-carrying capacity of structural members based on knowledge about the material properties. The factors that govern fracture are: loading conditions, material properties, size and shape of body and defect in material or body. Fracture mechanics is a branch of mechanics of materials. It is used in situations where large stress or strain concentrations arise, such as close to holes or notches. Serrano and Gustafsson (2006) highlighted that the geometrical features of timber structures, including the ultra- structure of the wood material, are such that flaws, cracks or sharp corners always induce stress or strain singularities. The presence of knots, drying cracks and other anomalies in timber also represent stress or strain concentrations, which can be considered as crack equivalents. Consequently, traditional approaches based on stress and strain criteria, can give poor predictions of the load-carrying capacity in many cases, and a fracture mechanics approach can give better predictions. Three basic types of loading and fracture are defined for a body, as shown in Figure 2.3. Mode I is the opening mode, mode II is the in- plane shear mode and mode III the out-of-plane shear mode. Usually the bodies are not loaded in only one mode but in a combination of them, giving a mixed mode loading.
22 Theoretical chapter
Figure 2.3 The three modes of loading and fracture. Since wood is an orthotropic material, the three directions (longitudinal, radial and tangential) give six possible orientations of the crack, as shown in Figure 2.4. The possible orientations are: RL, TL, LT, RT, LR and TR. In this notation the first letter indicates the direction normal to the crack plane while the second letter indicates the direction of the crack growth.
Figure 2.4 Crack orientations in wood. Since there are three loading modes for crack orientation, there are a total of 18 crack situations, with different values of the crack resistance. Fracture mechanics theory is divided in two branches, linear elastic fracture mechanics (LEFM) and nonlinear fracture mechanics (NLFM). In LEFM the material under consideration is assumed to exhibit linearly or very nearly linearly elastic behaviour right up to the point where fracture occurs and it is supposed that all the available strain
Theoretical chapter 23 energy goes into propagating a crack. However, in almost all materials there are several microstructural mechanisms that are capable of dissipating energy strain energy. If these microstructural mechanisms are taken into account NLFM should be used. The influence of the microstructural mechanisms depend on the size of the body compared to the fracture process zone. In Smith and Vasic (2003) a work aimed at identifying the crack evolution in softwood, including any restraining mechanisms due to bridging and micro-cracking at crack tips was reported. It was shown that behind the crack tip partially delaminated longitudinally oriented cells (tracheids) bridged the crack. This fibre bridging provided crack closure forces proportional to the local crack opening displacement. Bridging was found to be the main mechanism of crack tip shielding in spruce and presumably other softwood species. It has an influence on the fracture energy. Obviously, there is no contribution to the fracture energy from the bridging stresses prior to the crack initiation and evolution, but once established, the bridging zone was found to contribute with about 10% to the total fracture energy release rate. When activated, they decrease the strain energy G in the sense that not all strain energy is used for the crack growth but a part of it will be dissipated by the microstructural mechanism and will increase the crack resistance R in the sense that the fibres will tend to counteract crack opening. Since the size of the fracture process zone is essentially invariant, its influence changes with the size of the specimen. Larger specimens will have behaviour closer to LEFM and smaller specimens closer to NLFM. 2.2.1 Strain energy release rate The main point in fracture mechanics is to find a criterion that can be used in order to predict when a crack present in a body starts to propagate. Griffith (1921) made a study in order to provide a quantitative criterion for crack growth. His approach was to consider the thermodynamic equilibrium of a system with a crack. The total energy 3 of a loaded system can be written as:
3 ULW (2.7) where U is the elastic strain energy stored in the body loaded by an external force, L is the negative work of load due to the change in the potential energy of the system and W is the surface energy associated with the crack formation. The Griffith criterion for crack growth can then be written as:
ddW LU (2.8) ddAA
24 Theoretical chapter
where dA is the incremental change in the crack area. The left-hand side of Eq. (2.8) is commonly referred to as the strain energy release rate G, while the right-hand side of Eq. (2.8) is commonly referred to as the crack resistance R. Therefore G is interpreted as the energy available to grow a crack of unit area, while R is interpreted as the energy required for propagating a crack of unit area. Hence G = R is considered as the critical condition for the crack propagation. The critical strain energy, Gc, is the value of G when the crack starts to propagate and it is often used as a condition for crack growth. The value of G depends on the mode of loading, but in case of mixed mode fracture G = GI + GII + GIII, where the subscript refers to the mode of loading. This quantity can be measured by test of an elastic body subjected to a load, and it is given by the area under the load-displacement curve. The load can be either an applied load or a result of displacement control, but since it is important to have stable crack growth, displacement control is suggested. Serrano and Gustafsson (2006) pointed out that in order to avoid catastrophic failure upon and after reaching the maximum stress, the amount of strain energy released during the course of fracture must be less than or equal to the amount of energy needed to continue the fracture softening process. Smith et al. (2003) showed that a stable crack growth is possible only if displacement control is applied. If the compliance C is introduced and defined as the reciprocal of the slope of the load-displacement curve, it has been shown that G becomes:
1dC GP 2 (2.9) 2dba for both load and displacement control. In Eq. (2.9) b is the thickness of the specimen, P is the value of the force which cause the crack growth and a is the crack length. The failure load can then be obtained as:
2 P c (2.10) dCA dA where A is the area of the crack considered. The area can be calculated using the initial crack length ac according to Eq. (2.11) given in Serrano and Gustafsson (2006):
E c ac 2 (2.11) S ft
Theoretical chapter 25
where E is the modulus of elasticity and ft is the tensile strength.
Experimental studies 27
3 EXPERIMENTAL STUDIES
Three different types of experiments were carried out: 1. Splitting capacity of bottom rail in partially anchored timber frame shear walls with single- and double-sided sheathing; 2. Fracture energy of spruce (Picea Abies) in the RT and TR plane; 3. Tensile strength perpendicular to the grain of spruce (Picea Abies) in tangential and radial direction.
3.1 Splitting capacity of bottom rail 3.1.1 Material properties The details of the test specimens were as follows: x Bottom rail: spruce (Picea Abies), C24 according to EN 338 (2009), 45×120 mm; x Sheathing: hardboard, 8 mm (wet process fibre board, HB.HLA2, EN 622-2 (2004), Masonite AB); x Sheathing-to-framing joints: annular ringed shank nails, 50×2.1 mm (Duofast, Nordisk Kartro AB). The joints were nailed manually and the holes were pre-drilled in the sheets, Ø 1.7 mm; x Anchor bolt: Ø 12 (M12). The holes in the bottom rail were pre-drilled, Ø 13 mm. 3.1.2 Test programmes The splitting capacity and failure mode of the bottom rail was studied varying the distance between the edge of the washer and loaded edge of the bottom rail, distance s according to Figures 3.1c and 3.1d. This distance was varied using different washer sizes and moving the anchor bolt of the bottom rail along the width of the bottom rail, for specimens with single-sided sheathing, and by the variation of the washer size for specimens with double-sided sheathing (for this case, the anchor bolt was located at the middle). Two experimental programs were run, at different times, for specimens with single- and double-sided sheathing. Here they are called study A and study B. The influence of pith orientation of the bottom rail, with the major effort in study B, was also studied. In study A, a total of 89 and 40 specimens were tested for single- and double-sided sheathing, respectively, whilst
28 Experimental studies for study B, a total of 144 and 64 specimens for single- and double-side sheathing were tested, according to Table 3.1. Table 3.1 Test programmes of study A and B. PD = pith downwards, PU = pith upwards, SS = single-sided specimens, DS = double-sided specimens, b = width of rail (notations as in Figure 3.1).
Study A Study B a)
Number Number Number Number b) s of tests of tests of tests of tests bolt Size of Anchor washer position position Distance Distance SS DS SS DS Set Series PD PD PD PD PD PU PU PU PU PU PU [mm] [mm] [mm]
1 8 2 10 - 8 8 8 8 b/2 40×40 40 2 8 2 8 2 8 8 8 8 60×60 30 1 60 mm 3 8 2 7 3 8 8 8 8 from 80×70 20 4 8 2 10 - 8 8 8 8 sheathing 100×70 10 1 8 2 7 7 3b/8 40×40 25 2 2 8 2 - 8 8 - 45 mm 60×60 15 from 3 8 2 8 8 sheathing 80×70 5 1 9 1 8 8 b/4 40×40 10 3 - - 30 mm 2 8 1 8 8 from 60×60 0 sheathing a) The depth of all washers was 15 mm. b) Distance from the washer edge to the loaded edge of the bottom rail. The studies have been presented in detail in Paper I and Paper II. 3.1.3 Test set-up The test set-up is shown in Figure 3.1, both for single- and double- sided sheathing. The bottom rail was fastened to a supporting welded steel structure by two anchor bolts. The distance between the bolts was 600 mm and the distance between the bolt and the end of the bottom rail was 150 mm. A rigid square- or rectangular-shaped washer was inserted between the bottom rail and the bolt head throughout all tests. The thickness of the washer (15 mm) was chosen so that there would not arise any visible bending in the washers. A hydraulic piston (static load capacity 100 kN) was attached to a steel bar, which was connected to the upper panel using C-shaped steel profiles and four bolts Ø16. Different boundary conditions were used in the two studies: in study A, the vertical load was transferred to the C-shaped steel profiles via a welded connection; introducing some bending moments in the test specimens (cf. Figure 3.1a). The bracing bars reduced the rotation of
Experimental studies 29 the specimen. Since it was argued that this arrangement did not render full rotational restraint and, also, to simulate the behaviour in practice closer (believed to be more “uneven”, failure starting at one end), it was decided to have more clearly defined boundary conditions in study B by removing the inclined bars and only using the hinge according to Figure 3.1b. There were few differences between the two studies for specimens with single-sided sheathing: in study A, the distance between the nails in the sheathing-to-framing joint was 25 mm with a few exceptions where the distance was 50 mm. The main reason to have such a small distance was to have a strong joint in order to avoid a ductile failure of the fasteners, because the aim of the experimental study was to study the possible brittle failure modes of the bottom rail. In study B, the distance was kept constant in all series at 50 mm. Other differences were the torque moment used to tighten the bolts, 40 Nm in study A and 50 Nm in study B, and the displacement rate, 2 mm/min in study A and, by mistake, 10 mm/min in study B for specimens with single-sided sheathing. The influence of this difference in displacement rate has not been evaluated. However, as a rule of thumb, a tenfold increase of rate gives a 10% increase of strength. Regarding specimens with double-sided sheathing the only difference between the two studies was the boundary conditions. For both of them a nail distance of 50 mm, a torque moment of 50 Nm to tighten the bolts and a displacement rate of 2 mm/min were used. For each specimen, the moisture content and density of the bottom rail were measured after the test, according to ISO 3130 (1975) and ISO 3131 (1975), respectively.
30 Experimental studies
Figure 3.1 The test set-up and boundary conditions of sheathed bottom rails subjected to single- and double-sided vertical uplift. (a) Boundary conditions of study A; (b) boundary conditions of study B; (c) section of the single-sided specimen: the distance s is the distance between the washer edge and the loaded edge of the bottom rail; and (d) section of the double-sided specimen: the distance s is the distance between the washer edge and the edge of the bottom rail. 3.2 Matching tests of brittle failure of bottom rail, fracture energy and tensile strength perpendicular to the grain This experimental program was composed of three tests: (a) bottom rail tests; (b) fracture energy; and (c) tensile strength perpendicular to the grain. The aim was to have fracture energy and tensile strength perpendicular to the grain measured from the same specimen already tested in the bottom rail experimental program in order to have comparable material properties.
Experimental studies 31
The board from where the specimens were cut initially had a length of about 5 m and a cross section of 120×45 mm. Each board was cut in four parts; then two parts were used to build bottom rail specimens with possible failure mode 1 and the other two to build bottom rail specimens with possible failure mode 2, according to Figure 3.2. Figure 3.3 from Paper I was used to foresee what failure mode that would occur in the bottom rail. It refers to study A of Paper I. In that study, the distance between nails in the sheathing-to-framing joint was 25 mm, which was chosen also here. For the bottom rail experimental program, the same characteristics as in study A of Paper I were used.
The plan was to test 15 specimens for Gf tests for side crack and 33 for bottom crack, and 15 specimens for ft,90 in radial direction and 33 in tangential direction. According to Figure 3.3, one can predict a bottom crack failure mode for the rails in Series 1, Set 1, 2 and 3 and a side crack failure mode for rails in Series 2, Set 3 and Series 3, Set 1 and 2.
Figure 3.2 Scheme of the way the cut and selection of the boards for the specimens were made (PU = pith upwards, PD = pith downwards). The left pair of specimens were used for failure mode 1 and these boards were selected for tests for Gf in TR direction and ft,90 in tangential direction. The right pair of specimens were used for failure mode 2 and these boards were selected for test for Gf in RT and TR direction and ft,90 in radial and tangential direction. For the bottom rail with possible failure mode 2, it was decided to test the fracture energy in both RT and TR orientations and the tensile strength perpendicular to the grain in both radial and tangential direction. This was done in order to evaluate the influence of any of these orientations on the failure modes and loads of the bottom rail.
32 Experimental studies
9 8 7 6 5 4 3 2 Mode 3 1 Mode 2 0 Mode 1 Set 3 (5)* PD 3 (5)* Set PU 3 (5)* Set PD 2 (0)* Set PU 2 (0)* Set Set 1 (40)* PD 1 (40)* Set PU 1 (40)* Set PD 2 (30)* Set PU 2 (30)* Set PD 3 (20)* Set PU 3 (20)* Set PD 4 (10)* Set PU 4 (10)* Set PD 1 (25)* Set PU 1 (25)* Set PD 2 (15)* Set PU 2 (15)* Set PD 1 (10)* Set PU 1 (10)* Set 40** 60** 80** 100** 40** 60** 80** 40** 60** Serie 1 (b/2)*** Serie 2 (3b/8)*** Serie 3 (b/4)*** Figure 3.3 Recorded failure modes for the different test series and sets belonging to study A of Paper I (PD = pith downwards, PU = pith upwards). *Distance from washer edge to loaded edge of the bottom rail [mm]; **size of washer [mm]; and ***bolt position. 3.2.1 Bottom rail experimental program The material properties and test set-up were according to section 3.1 above. A total of 54 specimens, according to Figure 3.1, were tested. The boundary conditions were according to Figure 3.1b. The test program is listed in Table 3.2. Table 3.2 Test program for bottom rail tests. PD = pith downwards, PU = pith upwards, b = width of rail (notations as in Figure 3.1).
Series Set Number of Anchor bolt position Size of Distance tests washer sa) PD PU [mm] [mm] 1 3 3 40×40×15 40 b/2 2 3 3 60×60×15 30 1 60 mm from 3 3 3 80×70×15 20 sheathing 4 3 3 100×70×15 10 1 3 3 3b/8 40×40×15 25 2 2 3 3 45 mm from 60×60×15 15 3 3 3 sheathing 80×70×15 5 1 3 3 b/4 40×40×15 10 3 30 mm from 2 3 3 60×60×15 0 sheathing a) Distance from washer edge to loaded edge of the bottom rail.
Experimental studies 33
3.2.2 Fracture energy 3.2.2.1 Material properties x Specimen: from the same wood board as for the bottom rail tests; x Glue (two different glues were used for the specimens): (1) Wood Glue PU Light 421 1-component moisture-curing polyurethane adhesive, water resistant according to EN 204 (2001) and EN 205 (2003) class D4; and (2) CASCO Adhesive, Adhesive 1711 + Hardener 2520 (Phenol Resorcinol). 3.2.2.2 Test program The two brittle failures found for the bottom rail correspond to an opening failure mode with orientation TR, for crack opening from the bottom surface of the bottom rail, and RT, for crack opening from the edge surface of the bottom rail along the line of the sheathing-to- framing joints. Figure 3.4 shows the two crack orientations. The dotted line shows the part of the rail that was cut for the fracture energy specimen.
Figure 3.4 Crack orientation for the two brittle failure mode of the bottom rail. The dotted line shows the part of the rail that was cut for the fracture energy specimen. (a) Crack from the bottom of the bottom rail, orientation TR; and (b) crack from the edge side of the bottom rail, orientation RT. A total of 48 specimens according to Table 3.3 were tested.
Table 3.3 Test program of Gf tests (notations as in Figure 3.5).
Series Crack orientation Specimen size [mm] Number of tests t d 1 RT 45 45 15 2 TR 45 45 33
34 Experimental studies
3.2.2.3 Test set-up The test set-up was chosen according to NT BUILD 422 (1993) and it is shown in Figure 3.5. The specimen was glued to two pieces of timber, according to Figure 3.5a. The dimension of the specimen and of the two timber pieces was chosen according to Figure 3.5a and 3.5b. The test specimens were simply supported at both ends by two steel cylinders, as shown in Figure 3.5f, and loaded at midpoint through a cone connected to the load cell, according to Figure 3.5e. A 1 mm thick rubber layer was placed between the wood test specimen and the supports. The same was done between the wood test specimen and the cone connected to the load cell. The machine used for the tests was a universal testing machine UTM “Alwetron” TCT 50. The displacement was recorded electronically at the tip of the cone as the movement of the hydraulic piston.
Figure 3.5 Test set-up of the fracture energy tests. (a) Specimen glued to two pieces of timber; (b) dimensions of the test specimen; (c) annual ring orientation for specimens tested in the RT crack orientation; (d) annual ring orientation for specimens tested in the TR crack orientation; (e) details of the test set-up; and (f) details of the test set-up. The tests were performed under displacement control and a compression load was applied by a hydraulic piston with a rate of 1.30 mm/min until failure. The displacement rate was decided according to NT BUILD 422 (1993), where it is suggested that it shall be adjusted so that collapse is obtained in about 3±1 minutes. Some trial tests were performed in order to find the right displacement rate. The fracture energy is calculated as the area below the load vs. deflection curve of the test. In order for the test to be valid, the softening part of the load vs. deflection curve must be stable, as shown in Figure 3.6. However,
Experimental studies 35 during the trial tests the behaviour was found to be unstable. As a solution, the length of the notch was increased by 3 mm using a razor blade, according to Figure 3.5e.
Figure 3.6 Example of stable load vs. deflection curve for fracture energy test. 3.2.3 Tensile strength perpendicular to the grain 3.2.3.1 Material properties The same materials, wood type and glue, were used as for the fracture energy discussed above. However for these tests fiberglass was used, applied with CASCO Adhesive, to reinforce the glued bond. The dimensions of the specimen were: 45×70×45 mm and 45×70×120 mm for radial and tangential direction, respectively. 3.2.3.2 Test program A total of 48 specimens, according to Figure 3.7, were tested: 15 for the radial direction and 33 for the tangential direction. The test program is shown in Table 3.4.
Table 3.4 Test program of ft,90 tests (notations as in Figure 3.7).
Series Direction Specimen size [mm] Number of tests
u v e 1 Radial 70 45 45 18a) 2 Tangential 70 45 120 34b) a) 15 tests were planned but the three trial tests have been added. b) 33 tests were planned but one of the three trial tests has been added. 3.2.3.3 Test set-up The tests were run according to EN 408 (2010). However, as for fracture energy tests, due to the experimental study purpose, it was not possible to follow all the requirements given, i.e. the dimensions of the specimens. For the details the reader should refer to Paper V.
36 Experimental studies
The test set-up is shown in Figure 3.7. The specimen was glued to two pieces of timber, according to Figures 3.7a and d. The dimensions of the specimen and of the two timber pieces were varied according to Figure 3.7a, b, d and e, depending on the direction tested. The specimen was then connected to steel bars which in turn were connected to the testing machine by dowels, as shown in Figure 3.7g. The machine used was the same as for fracture energy tests. The tests were performed under displacement control and a tensile load with a rate of 10 mm/min until a load of 20 N and then 0.5 mm/min until failure was applied by a hydraulic piston. The displacement rate was decided according to EN 408 (2010), where it is suggested that it shall be adjusted so that maximum load is reached within (300 ± 120) seconds. Some trial tests were performed in order to find the right displacement rate. During the trial tests the failure occurred in the glued interface instead of within the specimen. Two actions were then taken. The volume of the specimen was reduced by two half circles having a diameter of 18 mm. They were positioned at the middle of the specimen depth in the edges, as shown in Figures 3.7a and 3.7d. For the specimens tested in radial direction, since the tensile strength perpendicular-to-grain was found to be higher than that found for the tangential direction, the addition of the two half circles was not enough in order to have the failure in the specimen. The glued surface was then strengthened by addition of fiberglass (this was made also for a few specimens in the tangential direction), as shown in Figures 3.7c and 3.7f.
Experimental studies 37
Figure 3.7 Test set-up of the tensile strength perpendicular to the grain tests. (a) Specimen glued to two pieces of timber for tests in the radial direction; (b) dimensions of the test specimen in radial direction; (c) fiberglass reinforcement for specimens tested in radial direction; (d) specimen glued to two pieces of timber for tests in the tangential direction; (e) dimensions of the test specimen in tangential direction; (f) fiberglass reinforcement for specimens tested in tangential direction; and (g) the connection between the specimen and the steel bars connected to the hydraulic piston.
Analytical models 39
4 ANALYTICAL MODELS
During the experimental studies on the splitting capacity of bottom rail two brittle failure modes were found: (a) splitting along the bottom side of the rail; and (b) splitting along the edge side of the rail. Based on LEFM theory, the compliance method has been used to derive formulas to calculate the load- carrying capacity for each failure mode. One of the points of this study was to validate these formulas through experimental studies. The derived models and a summary of the used assumptions are listed in the two following subsections, one per failure mode. For their derivation the reader should refer to Papers III and IV.
4.1 Failure mode 1 The model in Figure 4.1 has been presented in Serrano et al. (2012), and evaluated in Paper III. The figure shows the bottom rail considered as a cantilever beam fully clamped at the crack position. Using Eq. (4.1) below, the failure load P can be calculated.
2G P c (4.1) u dCA dA The compliance has been calculated considering both flexural and shear deformations. Eq. (4.2) is then obtained. Simplified versions of Eq. (4.2) may be obtained if the initial crack length a is considered small, assuming that bending deformations can be ignored (G/E ĺ 0) or assuming both small crack length and that bending deformations can be ignored.
2Gb ce Plha 2 (4.2) G §·be 12 ¨¸ Es Eha©¹
Figure 4.1 Geometry used to derive the first model in Paper III for failure mode 1. Using the same geometry as in Figure 4.1, another equation has been derived in Paper IV. In this case it is assumed that the cantilever is
40 Analytical models not completely rigidly clamped at the end, but that some finite rotation occurs. The deflection of the loading point, į, is then given by į = įb + įv + įr where įb is the contribution from bending of the cantilever, įv is the contribution from shear of the cantilever, and įr is the contribution from a rotation at the clamped end of the cantilever. If the compliance is chosen as in Paper IV, Eq. (4.3) is obtained. Simplified versions, shown in Paper IV, may be obtained if the initial crack length is not considered, or assuming negligible bending deformations or both small crack length and insignificant bending deformations.
2/GbG Plha ce (4.3) G b 12 e E Eh a s The third model, also presented in Paper IV, has been derived using the end-notched beam model, Gustafsson (1988), according to Figure 4.2. The cantilever has been assumed fixed to a rotational spring in exactly the same way as in the previous model. The compliance of the spring was in Gustafsson (1988) chosen as to result in a simple expression for the failure load. However, since the crack propagation considered in Gustafsson (1988) makes the length of the cantilever increase, while the crack considered here propagates so that the length of the cantilever is constant but its depth decreases, the influence of crack propagation becomes different in the two cases, and thus different expressions for the spring compliance optimize the simplicity. If the same spring compliance as given in Paper IV is used, Eq. (4.4) is obtained for the failure load in our case.
Figure 4.2 Geometry used to derive the third model in Paper IV for failure mode 1.
2/GbG Plh D ce (4.4) 2 3 GG§·bbee18 4 3DD 12 ¨¸Es Eh©¹DD5 E 11DD 3 h
Analytical models 41
As for the previous models, if the initial crack length is not considered, and if the deformations from bending are assumed to be negligible as compared to the shear deformations and for small crack length and negligible bending deformations, simplified versions of Eq. (4.4) may be obtained. 4.2 Failure mode 2 The model in Figure 4.3 has been derived by professor Bo Källsner and was first presented at the CIB-W18 meeting in 2011 (see Serrano et al. 2011). As the model in Eq. (4.2) for failure mode 1, the compliance has been calculated considering both flexural and shear deformations. Eq. (4.5) is then obtained and a simplified version may be obtained if the initial crack length a is considered as small.
2Gh ce Pl 2 (4.5) Ga§· 12 ¨¸ Es Eh©¹e
Figure 4.3 Geometry used to derive the first model in Paper III for failure mode 2. In Gustafsson (1988), splitting failure of an end-notched beam as shown in Figure 4.2 was considered. While the previous model presented in Paper III assumes that only shear and bending deformations of the cantilever beam shown in Figure 4.3 give contributions to the compliance, the model derived in Gustafsson (1988) also takes into account contributions from the part of the beam with depth h and from additional rotation of the cantilever due to the fact that the stiffness of the beam with depth h cannot be fully activated in the immediate vicinity of the corner of the notch. The solution given in Gustafsson (1988) if used on a bottom rail as considered in Figure 4.3, gives a failure load according to Eq. (4.6). Simplified versions may be obtained in the special case of a small crack or if assuming that the bending deformations are negligible as compared to the shear deformations.
42 Analytical models
GGc Plh h (4.6) 3 11D aG§· 5 61¨¸3 DDhE©¹ In Jensen (2005), a beam loaded perpendicular to the grain by a bolt located close to the edge and close to the end was considered. Figure 4.4 defines the geometry. The general expression for the failure load is not simple, but for small crack lengths (a ĺ 0), a simple solution was obtained. The horizontal crack in a bottom rail may be considered a special case of that solution, namely for (be ĺ 0), which leads to Eq. (4.7). In van der Put and Leijten (2000), a linear elastic fracture mechanics model was derived for a simply supported beam loaded perpendicular to grain by a single load at mid-span. For that model, if a small edge distance (he/h ĺ 0) is considered, the failure load P = P0, with P0 from Eq. (4.8). P0 may therefore be considered as a special case of the van der Put and Leijten (2000) model. A semi-empirical generalized version of Eq. (4.7) may be proposed, as in Eq. (4.10).
1 PP (4.7) 0 22] 1
PlCh01 2 e (4.8)
5 CG G (4.9) 1 3 c
h PlC 2 e (4.10) 1 h 1 e h
Figure 4.4 Geometry used to derive the third model in Paper IV for failure mode 2.
Results 43
5 RESULTS
In this chapter the main findings and test results of all experimental programmes are summarized. The results from the tests on the bottom rail have been presented in detail in Paper I and Paper II, for single- and double-sided sheathing, respectively, while those from matching tests of bottom rail, fracture energy and tensile strength perpendicular to the grain are presented in Paper V.
5.1 Bottom rail test results 5.1.1 Failure modes During the experiments three failure modes were found: x Splitting along the bottom of the rail, according to Figure 5.1a; x Splitting along the edge side of the rail according to Figure 5.1b; x Yielding and withdrawal of the nails in the sheathing-to-framing joints according to Figure 5.1c. The first two failure modes are considered brittle, while the third one is ductile. Failure mode 1 is due to crosswise bending of the bottom rail, introducing tension perpendicular to the grain. Failure mode 2 is due to vertical shear forces in the nails of the sheathing-to- framing joints, causing splitting failure along the edge of the bottom rail. Finally, failure mode 3 is due to yielding and withdrawal of the nails in the sheathing-to-framing joints. The first and third column of Figure 5.1 refers to bottom rails with pith downwards (PD = N) for both single- and double-sided sheathing, respectively, while the second and fourth column with pith upwards (PU = U) for both single- and double-sided sheathing, respectively. The picture of specimens 441 U and 446 U indicate a mixed failure mode. However, since the first noted failure mode for these specimens were number 2 and 3, respectively, it was assumed that these modes were the decisive ones.
44 Results
a) Mode 1
b) Mode 2
c) Mode 3 Figure 5.1 (a) Splitting failure along the bottom side of the rail; (b) splitting failure along the edge side of the rail; and (c) yielding and withdrawal of the nails in the sheathing-to-framing joints. In Figures 5.2 and 5.3 the number of observations of the three different failure modes is graphically shown for the series in study A and study B, respectively, with single-sided sheathing.
Mode 1 Mode 2 Mode 3 9 8 7 6 5 4 3 2 1 0 Set 3 (5)* PD Set 3 (5)* PU Set 2 (0)* PD Set 2 (0)* PU Set 1 (40)* PD Set 1 (40)* PU Set 2 (30)* PD Set 2 (30)* PU Set 3 (20)* PD Set 3 (20)* PU Set 4 (10)* PD Set 4 (10)* PU Set 1 (25)* PD Set 1 (25)* PU Set 2 (15)* PD Set 2 (15)* PU Set 1 (10)* PD Set 1 (10)* PU 40** 60** 80** 100** 40** 60** 80** 40** 60** Serie 1 (b/2)*** Serie 2 (3b/8)*** Serie 3 (b/4)***
Figure 5.2 Recorded failure modes for the different test series and sets belonging to study A (PD = Pith downwards, PU = Pith upwards). *Distance from washer edge to loaded edge of the bottom rail [mm]; **size of washer [mm]; and ***bolt position. Specimens with single-sided sheathing.
Results 45
It is noted that in study A only two specimens failed in mode 3. This is a consequence of the small nail distance used in the sheathing-to- framing joint in study A, 25 mm, instead of 50 mm as in study B.
Mode 1 Mode 2 Mode 3 8 7 6 5 4 3 2 1 0 Set 3 (5)* PD Set 3 (5)* PU Set 2 (0)* PD Set 2 (0)* PU Set 1 (40)* PD Set 1 (40)* PU Set 2 (30)* PD Set 2 (30)* PU Set 3 (20)* PD Set 3 (20)* PU Set 4 (10)* PD Set 4 (10)* PU Set 1 (25)* PD Set 1 (25)* PU Set 2 (15)* PD Set 2 (15)* PU Set 1 (10)* PD Set 1 (10)* PU 40** 60** 80** 100** 40** 60** 80** 40** 60** Serie 1 (b/2)*** Serie 2 (3b/8)*** Serie 3 (b/4)***
Figure 5.3 Recorded failure modes for the different test series and sets belonging to study B (PD = Pith downwards, PU = Pith upwards). *Distance from washer edge to loaded edge of the bottom rail [mm]; **size of washer [mm]; and ***bolt position. Specimens with single-sided sheathing. It seems that the distance s has a decisive influence on the failure mode. In fact, failure mode 1 is the only failure mode when s DQG 20 mm, for study A and B, respectively. When the distance s was decreased, failure modes 2 and 3 also appeared. The same result was found to be valid also for specimens with double-sided sheathing, as shown in Figures 5.4 and 5.5. In this case the limit between failure modes was found to be s PP
46 Results
10 9 8 7 6 5 4 3 Mode 3 2 1 Mode 2 0 Mode 1 Set 1 (40)* PD 1 (40)* Set PU 1 (40)* Set PD 2 (30)* Set PU 2 (30)* Set PD 3 (20)* Set PU 3 (20)* Set PD 4 (10)* Set PU 4 (10)* Set 40** 60** 80** 100** Bolt position (b/2) Figure 5.4 Recorded failure modes for the different sets belonging to study A (PD = pith downwards, PU = pith upwards). *Distance from washer edge to loaded edge of the bottom rail [mm]; and **size of washer [mm]. Specimens with double- sided sheathing.
8 7 6 5 4 3 2 1 0 Mode 3 Mode 2 Mode 1 Set 1 (40)* PD 1 (40)* Set PU 1 (40)* Set PD 2 (30)* Set PU 2 (30)* Set PD 3 (20)* Set PU 3 (20)* Set PD 4 (10)* Set PU 4 (10)* Set Set 1-BC(A) (40)* PD (40)* 1-BC(A) Set PU (40)* 1-BC(A) Set 40** 40** 60** 80** 100** Bolt position (b/2) Figure 5.5 Recorded failure modes for the different sets belonging to study B (PD = pith downwards, PU = pith upwards). *Distance from washer edge to loaded edge of the bottom rail [mm]; and **size of washer [mm]. Set 1-BC(A) had boundary conditions as in study A. Specimens with double-sided sheathing. 5.1.2 Load-time curves and crack development The displacements of the specimens were not recorded, but since the displacement was applied with a constant rate, it was possible to obtain fictitious load-displacement curves by plotting load versus time.
Results 47
Some examples of load-time curves recorded during the experiments are shown in Paper I and Paper II. The curves show different behaviour depending on the failure mode. For failure mode 1, the crack usually starts from one end of the bottom rail and it develops toward the other end. Analysing the bottom of the bottom rail, it was noted that the crack was divided in three parts: (1) it develops from one end to the closest anchor bolt; (2) between the anchor bolts; and finally (3) from the other end to the closest anchor bolt. In the curves for failure mode 1, three drops of loads are depicted, which are believed to represent the drop of load when the crack appear and develops in each of these parts. In curves for specimens that failed in mode 2, there is only one crack and drop in the load. Finally in curves for failure mode 3, it is possible to observe ductile behaviour when the failure happens. Since these tests were a data collection for a fracture mechanics approach, the crack development was studied in detail. For failure mode 1, the crack position along the width of the bottom rail cross section was found to be dependent on the distance s and the anchor bolt position. When the anchor bolt was moved towards the edge or when big washers were used, the crack appeared closer to the edge. In this failure mode the crack always started from the bottom of the bottom rail and then developed in the vertical direction in different ways: (1) straight; (2) changing its direction toward the pith, in case of pith upwards; or (3) following the annual ring orientation. For failure mode 2 the crack appeared at the loaded edge in the line of the nails of the sheathing-to-framing joints and then developed horizontally for a certain length, usually between 15 and 20 mm, and then in a more vertical direction following the annual ring orientation or across them. In Paper I and Paper II, the distance between the vertical crack and the loaded edge of the rail, called bcrack1, and the length of the horizontal crack before it changes direction for failure mode 2, called bcrack2, were measured and listed. Figure 5.6 shows a few examples for each failure mode and the distances bcrack1 and bcrack2.
48 Results
bcrack1 bcrack1
a)
bcrack2 bcrack2 bcrack2
b) Figure 5.6 Crack development for the bottom rail. In the left column only specimens with single-sided sheathing and in the right column only specimens with double-sided sheathing. (a) Example of mode 1 crack development in a straight line or in a straight line for a certain length and then following the annual ring orientation; and (b) example of mode 2 crack development, starting horizontally and then propagating vertically along the annual ring orientation. 5.1.3 Failure loads The failure load for the two brittle failure modes 1 and 2 is defined as the load at which there is a first distinct decrease in the load carrying capacity due to a propagating crack in the bottom rail. For failure mode 3 the failure load is defined as the maximum load. The results of the different tests of the two studies are summarized in Tables 5.1 and 5.2, for specimens with single-sided sheathing, and in Tables 5.3 and 5.4, for specimens with double-sided sheathing. The failure load of the two studies is presented with respect to the pith orientation in Tables 5.1 and 5.3 (pith upwards) and in Tables 5.2 and 5.4 (pith downwards). Mean failure load is presented for all specimens tested, independently of the failure mode, but also with respect to it.
Results 49
Table 5.1 Results from testing of specimens with the pith oriented upwards (PU) and specimens with single-sided sheathing.
Mean failure load per failure mode Number of tests per failure All (1) (2) (3) mode Number
Set Set of tests Series Series
Mean Stddev Mean Stddev Mean Stddev Mean Stddev (1) (2) (3)
[kN] [kN] [kN] [kN] [kN] [kN] [kN] [kN] Study A 1 2 12.6 1.34 12.6 1.34 - - - - 2 0 0 2 2 11.3 0.54 11.3 0.54 - - - - 2 0 0 1a) 3 2 17.0 5.73 12.9 - 21.0 - - - 1 1 0 4 2 24.1 0.35 24.3 - 23.8 - - - 1 1 0 1 2 21.5 0.47 - - 21.5 0.47 - - 0 2 0 2 2 2 21.2 0.85 - - 21.2 0.85 - - 0 2 0 3 2 28.9 2.50 30.6 - 27.1 - - - 1 1 0 3 1 1 19.9 - - - 19.9 - - - 0 1 0 2 1 27.1 - - - 27.1 - - - 0 1 0 Study B 1 8 9.49 2.59 9.49 2.59 - - - - 8 0 0 2 8 10.6 2.04 10.5 2.04 - - - - 8 0 0 1 3 8 17.1 2.77 16.8 3.12 - - 18.7 - 7 0 1 4 8 19.4 2.68 19.4 3.10 18.1 - 20.1 - 6 1 1 1 7 12.2 2.42 12.2 2.42 - - - - 7 0 0 2 2 8 16.9 2.56 16.6 2.87 17.5 2.38 - - 5 3 0 3 8 22.6 4.07 23.2 5.21 22.2 3.87 - - 3 5 0 1 8 18.6 2.23 17.9 - 18.6 2.62 18.9 - 1 6 1 3 2 8 21.3 2.66 - - 21.4 2.77 20.8 3.24 0 6 2 a) Series 1 of study A had a nail distance of 50 mm instead of 25 mm as the other two series of study A.
50 Results
Table 5.2 Results from testing of specimens with the pith oriented downwards (PD) and specimens with single-sided sheathing.
Mean failure load per failure mode Number of tests per failure All (1) (2) (3) mode Number Set Set
Series Series of tests
Mean Stddev Mean Stddev Mean Stddev Mean Stddev (1) (2) (3)
[kN] [kN] [kN] [kN] [kN] [kN] [kN] [kN] Study A 1 8 12.0 1.77 12.0 1.77 - - 8 0 0 2 8 13.5 2.51 13.5 2.51 - - 8 0 0 1a) 3 8 17.4 1.76 17.4 1.76 - - 8 0 0 4 8 22.8 4.42 22.1 4.40 28.6 20.7 6 1 1 1 8 16.0 2.24 16.0 2.24 - - 8 0 0 2 2 8 20.7 2.61 20.3 2.53 23.6 - 7 1 0 3 8 29.1 2.87 30.3 3.07 28.0 - 4 4 0 3 1 9 21.6 3.09 21.7 2.21 23.1 15.1b) 4 4 1 2 8 29.2 1.91 28.6 0.55 29.5 - 3 5 0 Study B 1 8 10.3 1.84 10.2 1.84 - - - - 8 0 0 2 8 13.5 2.06 13.5 2.06 - - - - 8 0 0 1 3 8 18.2 1.47 17.9 0.92 16.7 - 19.0 2.00 4 1 3 4 8 21.8 1.65 23.5 2.12 20.7 - 21.4 1.32 2 1 5 1 7 14.0 2.84 14.0 2.84 - - - - 7 0 0 2 2 8 17.9 4.48 19.3 1.94 7.70c) - - - 7 1 0 3 8 23.7 3.16 23.5 - 25.6 3.26 21.3 1.83 1 4 3 1 8 18.1 2.32 15.9 2.53 19.5 0.62 19.4 0.35 3 3 2 3 2 8 23.8 2.50 - - 25.4 1.40 22.1 2.38 0 4 4 a) Series A of study A for both single- and double-sided sheathing had a nail distance of 50 mm instead of 25 mm as the other two series of study A, except for one specimen in series 3 where the distance was 50 mm by mistake. b) This specimen, by mistake, had a nail distance of 50 mm instead of 25 mm as the other specimens of the same series. This is the reason for ductile failure. c) Not taken into account. Probably this specimen had some defect since if we compare with the same series in Table 5.1 the failure load is too low.
Results 51
Table 5.3 Results from testing of specimens with the pith oriented upwards (PU) and specimens with double-sided sheathing.
Mean failure load per failure mode Number of tests per failure All (1) (2) (3) mode Set Set Mean Mean Mean Mean Series Series Stddev Stddev Stddev Stddev Stddev (1) (2) (3) Number of tests [kN] [kN] [kN] [kN] [kN] [kN] [kN] [kN] Study A 1 ------2 2 25.0 2.55 25.0 2.55 - - - - 2 - - 1a) 3 3 30.8 5.83 30.8 5.83 - - - - 3 - - 4 ------Study B 1- BC(A)b) 8 17.0 3.20 17.0 3.20 - - - - 8 - - 1 8 17.6 1.78 17.6 1.78 - - - - 8 - - 1 2 8 19.5 2.31 19.5 2.31 - - - - 8 - - 3 8 34.0 1.79 33.4 1.32 35.8 2.33 - - 6 2 - 37.8 3.86 6 2 4c) 8 39.5 5.37 - - 44.5 7.78 - (39.5) (5.37) (8) (0) a) Series 1 of study A had a nail distance of 50 mm instead of 25 mm as the other two series of study A. b) Set with boundary conditions as in study A. c) For two specimens with double-sided sheathing of this set it was difficult to establish if the failure mode was mode 2 or 3. The results without parenthesis refer to the case of six failure mode 2 and two failure mode 3, while the results in parenthesis refer to the case of eight failure mode 2.
52 Results
Table 5.4 Results from testing of specimens with the pith oriented downwards (PD) and specimens with double-sided sheathing.
Mean failure load per failure mode Number of tests All (1) (2) (3) per failure mode Set Set Mean Mean Mean Mean Series Series Stddev Stddev Stddev Stddev Stddev (1) (2) (3) Number of tests [kN] [kN] [kN] [kN] [kN] [kN] [kN] [kN] Study A 1 10 22.1 1.41 22.1 1.41 - - - - 10 - - 2 8 29.2 2.05 29.2 2.05 - - - - 8 - - 1a) 3 7 38.6 4.38 39.0 4.62 - - 35.9 - 6 - 1 4 10 39.7 3.58 39.3 3.55 43.4 - - - 9 1 - Study B 1- BC(A)b) 8 22.6 1.53 22.6 1.53 - - - - 8 0 0 1 8 20.5 3.29 20.5 3.29 - - - - 8 0 0 1 2 8 28.0 1.94 28.0 1.94 - - - - 8 0 0 3 8 39.1 5.41 39.5 4.84 38.0 9.19 - - 6 2 0 4c) 8 45.8 1.98 45.4 - 47.1 0.78 44.2 2.20 1 4 3 a) Series A of study A had a nail distance of 50 mm instead of 25 mm as the other two series of study A. b) Set with boundary conditions in study A. Comparing the Tables 5.1 and 5.2, and 5.3 and 5.4, the results show a higher load-carrying capacity for the bottom rail with the pith oriented downwards, as compared to the bottom rail with the pith oriented upwards. When calculating the ratios between the two pith orientations, the different number of specimens tested within the same set regarding the pith orientation of the bottom rail should be kept in mind. Especially, it should be noted that very few specimens were tested with pith upwards in study A. Also, some failure modes in both studies only appear in a few cases. However, a general conclusion might be possible to give the saying that the load-carrying capacity is about 5%-10% higher if the pith in the bottom rail is oriented downwards, for specimens with single-sided sheathing, and 15%-30% for specimens with double-sided sheathing. One of the main reasons for that is the cupping shape of the bottom rail that occurs after drying. Also, by comparing the two studies A and B in Tables 5.1-5.4, it is found that the load-carrying capacities of the specimens from study A are generally higher than the corresponding ones found in study B. This effect of increased failure load is in the order of 10%-20%. For specimens with PU, it should be remembered the different number of specimens tested in the two studies. For specimens with PD, the higher load-carrying capacity for study A is confirmed. An exception is set 4 for specimens with single-sided sheathing and, to a minor extent, set 1-
Results 53
BC(A) and 3 for specimens with double-sided sheathing. The results in set 4 for specimens with single-sided sheathing could be regarded as exceptional or less accurate due to the different number of specimens that failed in the same mode. The difference in failure load between the studies refers only to the brittle failure modes 1 and 2, and not to the ductile failure mode 3. The fact that the load-carrying capacity in general is found to be higher in study A than in study B for the splitting modes may be due to the difference in: (1) boundary conditions; (2) moisture content; (3) nail distance; (4) planeness of the bottom rail; and (5) loading rate. The more rigid boundary conditions in study A will render higher failure loads, because the straining of the bottom rail is more equally distributed along its whole length. This is a natural effect for brittle failure loads, but not for ductile ones. For small nail distances, failures in mode 3 will be reduced or even eliminated, but instead failures in mode 2 (splitting along the edge side of the rail) will increase. More ductile failures (mode 3) in study B, especially for series 2 and 3, as observed from Table 5.2, will lower the mean values for the other failure modes 1 and 2. The un-planeness or the cupping shape of the bottom rail due to drying will cause initial cracking at the bottom side of the rail when the anchor bolts are tightened to the bottom rail if the pith is oriented upwards. This will decrease the failure load for mode 1 and also make the bottom rail more flexible. In both studies the bottom rails were fairly plane, but if there was any difference, the planeness in study B was higher. The higher load or displacement rate in study B will increase the failure loads relative to those in study A. From Figures 5.7-5.10 the relationship between failure load and distance s from washer edge to the loaded edge of the bottom rail is shown for studies A and B, respectively, for specimens with single- sided sheathing. The results are grouped with respect to the position of the anchor bolts along the bottom rail width (b) and are separated with respect to the pith orientation.
54 Results
35 35 Centre b/2 3b/8 Failure mode 1 and 2 Only failure mode 1 30 30 b/4 Trend R2 = 0.67 25 Trend R2 = 0.81 25 Trend R2 = 0.70 20 X2 Trend R2 = 0.81 20
15 15 Centre b/2 3b/8
Failure load [kN] Failure load [kN] b/4 10 10 Trend R2 = 0.68 Trend R2 = 0.65 5 5 2 Failure mode 1, 2 and 3 Only failure mode 1 Trend R = 1 X2 Trend R2 = 0.73 0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] Figure 5.7 Failure load versus distance Figure 5.8 Failure load versus distance s from washer edge to loaded edge of s from washer edge to loaded edge of bottom rail. All test results from study A bottom rail. All test results from study A (pith oriented downwards). The vertical (pith oriented upwards). The vertical line shows the border between failure line shows the border between failure modes. modes.
35 35 Centre b/2 Centre b/2 3b/8 3b/8 30 30 b/4 b/4 Trend R2 = 0.87 Trend R2 = 0.75 25 Trend R2 = 0.56 25 Trend R2 = 0.67 Trend R2 = 0.61 Trend R2 = 0.26 20 X2 Trend R2 = 0.71 20 X2 Trend R2 = 0.71
15 15 Failure load [kN] Failure load [kN] 10 10
5 5 Failure mode 1, 2 and 3 Only failure mode 1 Failure mode 1, 2 and 3 Only failure mode 1
0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] Figure 5.9 Failure load versus distance Figure 5.10 Failure load versus distance s from washer edge to loaded edge of s from washer edge to loaded edge of bottom rail. All test results from study B bottom rail. All test results from study B (pith oriented downwards). The vertical (pith oriented upwards). The vertical line shows the border between failure line shows the border between failure modes. modes.
It should be noted that Figure 5.8 is based on very few data and, therefore, a statistical treatment of the data is not reliable and for some data not even meaningful. In each graph four different curves are visible: three linear trend lines, one per series tested, and a polynomial regression type of second
Results 55 order for all data tested. For all cases, good correlation is obtained between the distance s and the failure load. This is highlighted by a coefficient of determination R2 ranging from 0.71 to 0.81, for a polynomial regression type of second order. Looking at each group, the linear models also give good statistical results, R2 values ranging from 0.56 to 0.87, except for series 3 in Figure 5.10, where R2 = 0.26 was found, probably due to data points that fall close to a horizontal line or a small variation of the data along the x-coordinate. From Figures 5.11-5.13 the same relationship is shown for specimens with double-sided sheathing. Due to too few specimens tested with pith upwards for study A, these results are not presented. R2 ranged from 0.81 to 0.89 for the linear trend lines and a coefficient of determination R2 ranging from 0.85 to 0.89 for a polynomial regression type of second order was found for specimens with pith downward in Figures 5.11 and 5.12. The same good correlation is noted in Figure 5.13 for specimens with pith upwards, highlighted by a coefficient R2 = 0.84 for the linear trend lines and R2 = 0.85 for a polynomial regression type of second order. It is evident that for a given anchor bolt position, the failure load increases when the distance s decreases.
56 Results
50
45
40
35
30 Failure mode 1, 2 and 3 25
20 Washer 40 mm Failure load [kN] 15 Washer 60 mm Washer 80 mm Only failure mode 1 10 Washer 100 mm 2 5 Trend R = 0.81 X2 Trend R2 = 0.85 0 0 5 10 15 20 25 30 35 40 Distance s [mm] Figure 5.11 Failure load versus distance s from washer edge to edge of the bottom rail. All test results from study A (pith oriented downwards). The vertical line shows the border between failure modes.
50 50
45 45
40 40
35 35
30 30 Failure mode 1, 2 and 3 Failure mode1 , 2 and 3 25 25
20 Washer 40 mm1) 20 Washer 40 mm1) Washer 40 mm Washer 40 mm Failure load [kN] Failure load [kN] 15 Washer 60 mm 15 Washer 60 mm Washer 80 mm Only failure mode 1 Washer 80 mm 10 10 Washer 100 mm Washer 100 mm 2 2 Only failure mode 1 5 Trend R = 0.89 5 Trend R = 0.84 X2 Trend R2 = 0.89 X2 Trend R2 = 0.85 0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] Figure 5.12 Failure load versus Figure 5.13 Failure load versus distance distance s from washer edge to edge of s from washer edge to edge of the the bottom rail. All test results from bottom rail. All test results from study B study B (pith oriented downwards). The (pith oriented upwards). The vertical vertical line shows the border between line shows the border between failure failure modes. 1) These results are not modes. 1) These results are not included included in the trend lines since these in the trend lines since these tests had tests had different boundary conditions different boundary conditions than the than the others. others.
Results 57
5.2 Matching tests of brittle failure of bottom rail, fracture energy and tensile strength perpendicular to the grain 5.2.1 Bottom rail The results regarding the bottom rail tests of this experimental program are explained in less detail than the previous bottom rail studies. The general behaviour is the same and it is not repeated here. The specimens failed in mode 1 and 2. Failure mode 3 was not found, due to the small distance between nails in the sheathing-to-framing joint, 25 mm. Failure mode 1 was the only failure mode for distance s PP7KHIDLOXUHORDGLVVXPPDUL]HGLQ7DEOH Table 5.5 Results from bottom rail tests. Failure modes: (1) splitting along the bottom side of the rail; and (2) splitting along the edge side of the rail.
Mean failure load per failure mode Number of tests per Number All Stddev (1) Stddev (2) Stddev failure Set
Series of tests mode Mean Mean Mean (1) (2) [kN] [kN] [kN] [kN] [kN] [kN] Pith down 1 3 10.8 2.74 10.8 2.74 - - 3 - 2 3 12.1 4.09 12.1 4.09 - - 3 - 1 3 3 17.1 1.40 17.1 1.40 - - 3 - 4 3 21.6 1.51 21.6 1.51 - - 3 - 1 3 12.3 2.66 12.3 2.66 - - 3 - 2 2 3 15.8 2.07 15.8 2.07 - - 3 - 3 3 27.4 2.83 27.4 2.83 - - 3 - 1 3 22.9 2.17 22.9 2.17 - - 3 - 3 2 3 26.7 6.10 28.9 - 22.5 - 2 1 Pith up 1 3 8.62 1.14 8.62 1.14 - - 3 - 2 3 12.1 3.39 12.1 3.39 - - 3 - 1 3 3 15.5 5.39 15.5 5.39 - - 3 - 4 3 18.0 4.25 18.0 4.25 - - 3 - 1 3 11.4 2.91 11.4 2.91 - - 3 - 2 2 3 11.7 1.43 11.7 1.43 - - 3 - 3 3 24.5 2.83 25.2 - 23.2 - 2 1 1 3 17.5 2.12 16.4 - 19.7 - 2 1 3 2 3 23.1 2.30 - - 23.1 2.30 0 3
58 Results
5.2.2 Fracture energy For the test to be valid it is required that the load deflection response is stable, meaning that it is a completely continuous curve. During this experimental program it was difficult to obtain a stable curve for the post peak behaviour. Three types of curves have been identified, according to their post peak behaviour: x Stable curve, according to Figure 5.14a; x Almost stable curve, according to Figure 5.14b; x Unstable curve, according to Figure 5.14c.
100 80 60 40
a) [N] Load 20 0 02468 Displacement [mm]
100 80 60 40
b) [N] Load 20 0 0246810 Displacement [mm]
200 160 120 80
c) [N] Load 40 0 0 5 10 15 Displacement [mm]
Figure 5.14 Examples of load-deflection curve. (a) Stable curve; (b) almost stable curve; and (c) unstable curve.
Results 59
The curve in Figure 5.14a shows a completely continuous curve, i.e. the curve is stable. The curve in Figure 5.14b shows a drop of load after the peak load, where the curve is discontinuous. In this case the curve has been defined as almost stable since the drop of the load is small and the curve becomes stable again. In Figure 5.14c, the curve is clearly unstable. For specimens with TR orientation most of the curves were unstable, Figure 5.15b. A reason for this could be the annual ring orientation. In Figure 5.15a the crack for specimens with RT orientation is shown. In this case most of the curves were found to be stable or almost stable. The stability is probably due to the annual ring orientation since the crack is able to develop following the annual ring shape in a plane between them. The difference in the crack path is noted with respect to RT orientation, since in this case the crack develops perpendicular to the annual ring “jumping” from one annual ring to another.
a)
b) Figure 5.15 Examples of crack growth during the fracture energy tests. (a) RT orientation of the crack; and (b) TR orientation of the crack. The results of the tests are summarized in Table 5.6. The results are presented with respect to the direction tested. Mean failure load and mean fracture energy are presented.
60 Results
Table 5.6 Results from fracture energy testing in RT and TR direction.
Failure load Fracture energy Gf Type of curve
Mean Min. Mean Min. and and Series stable Direction Max Stable Stddev Stddev Max Almost Unstable Number of tests [N] [N] [N] [N/m] [N/m] [N/m] 60.0 190 1 RT 15 98.0 ÷ 27.4 322 ÷ 86.7 6 4 5 169 476 69.0 196 2 TR 33 123 ÷ 29.7 303a) ÷ 66.5 2 6 25 192 432 a) Result calculated with 31 specimens. 5.2.3 Tensile strength perpendicular to the grain The displacement was directly recorded by the testing machine. All curves were found to show a similar stiffness and a brittle failure load, typical for timber loaded by a tensile load perpendicular to the grain. The results are presented in Table 5.7 with respect to the direction tested. Mean failure load, defined as the maximum load reached during the test and mean tensile strength perpendicular to the grain are presented. Table 5.7 Results from testing of specimens in tensile strength perpendicular to the grain. R = radial direction, T = tangential direction.
Failure load Tensile strength perpendicular to the grain
ft,90 Mean Min. Stddev Mean Min. Stddev Series
Direction and and
Number of tests Max Max [kN] [kN] [kN] [MPa] [MPa] [MPa] 1 R 18 4.73 3.26 ÷ 6.45 0.83 2.28 1.54 ÷ 3.10 0.40 2 T 34 3.63 1.98 ÷ 6.11 0.88 1.79 0.98 ÷ 2.84 0.39
Analysis and discussion 61
6 ANALYSIS AND DISCUSSION
The appended papers of the thesis present different analyses. The aim of these analyses was to evaluate the failure load of a bottom rail subjected to uplift in a partially anchored timber frame shear wall. Since three failure modes were found during the experimental programmes, different models were needed to predict the failure load of each failure mode. In Paper I and II an analysis based on a material strength approach, was carried out for failure mode 1 and 3. In Paper III and IV failure modes 1 and 2 were analysed, with models based on an LEFM approach, using different assumptions. Finally in Paper V the analysis carried out in Paper III and IV was repeated together with a new experimental programme, which was organised in order to match bottom rail tests and tests of the material properties needed as input values in the analysis: fracture energy and tensile strength perpendicular to the grain. By this, the formulas, one per failure mode, showing the best fit between calculated and observed splitting failure of the bottom rail could be chosen. In order to keep the analysis simple, some influencing parameters such as the friction under the bottom rail, the friction between the rail and the washer, the effect of the pretension force and the discretely placed washers are not taken into account. The purpose of this chapter is not to repeat the analysis but to show and discuss the main findings from: (1) the experimental studies; and (2) from the analysis carried out in the appended papers, giving an overview of how the models were tested and evaluated with respect to the tests results, and the procedure used to choose the models, one per failure mode, giving the best fit between calculated and observed splitting failure capacity.
6.1 Bottom rail experimental programmes The main findings from the experimental programmes of the bottom rail are listed in Paper I and II, for specimens with single- and double-sided sheathing, respectively. The varied parameters during the experimental studies were the distance between the washer edge and the loaded edge of the bottom rail, distance s, and the pith orientation. The main findings are summarized as follows. 6.1.1 Distance s The failure mode and load of the bottom rail have been found to be strongly dependent on the distance s. For s PPIDLOXUHPRGH was the only failure mode, while for s PPIDLOXUHPRGHDQG also appeared. The failure load was found to increase when decreasing the distance s.
62 Analysis and discussion
6.1.2 Pith orientation The experimental results show that the load-carrying capacity of the specimens with the pith oriented downwards is higher than the capacity of the specimens with the pith oriented upwards: 5%-10% for specimens with single-sided sheathing and 10%-20% for specimens with double-sided sheathing. The reason for this effect with respect to the pith orientation is probably caused by the initial cupping due to the anisotropic shrinkage from drying as shown in Figure 6.1, but may also be an effect of the anisotropic material properties in the radial- tangential plane of the timber. When the anchor bolt in Figure 6.1a is tightened the washer will rest on its edges creating a bending moment with compression stresses at the level of the pith. When the anchor bolt in Figure 6.2b is tightened the timber will rest on its edges creating a bending moment with tensile stresses at the bottom of the rail. Combining these cross- wise bending stresses with the bending stresses caused by the sheathing- to-framing fasteners it becomes obvious that it is more favourable to orient the pith downwards than upwards. Figure 6.1 shows specimens with single-sided sheathing, but the same conclusions can be stated for specimens with double-sided sheathing.
a) b) Figure 6.1 Effect of shrinkage due to the drying for specimens with pith oriented: (a) downwards; and (b) upwards. Further, pre-cracks in the bottom rail can occur at the time of tightening of the bottom rail to the foundation, due to the cupping shape of the rail caused by drying. Cracks occur on the bottom side of the rail when the pith is oriented upwards independent of the size of the washer but cracks on the upper side of the rail can also occur when the pith is oriented downwards if the washer is big. However, in Paper
Analysis and discussion 63
II it is shown that pre-cracks on the bottom side of the rail do not adversely affect the final failure capacity of the bottom rail. 6.2 Bottom rail analytical models Failure mode 1 was the splitting along the bottom side of the rail. The derived models, independently of the used approach, consider a part of the bottom rail as a cantilever beam clamped at the crack position. A general model for this approach is shown in Figure 6.2.
Figure 6.2 General example of the geometry assumed when deriving models for failure mode 1.
When considering the “cantilever span” be of the model it is noted that an additional length, c, has to be added to the distance s. In Paper I and II four values of c were hypothesized, c = 15; 20; 25 and 30 mm, whilst in Paper III the c value was calculated using the root mean square error (RMSE) method, where a distance c ranging from 0 to 60 mm was tested in the equation, and the value giving the best fit (lowest RMSE) between formula and results was chosen. The results gave c- values ranging from 19.8 to 47.0 mm, depending on the formula and the material properties used. In general a value of c = 20 mm has been used for the analysis, and this value seems to give a good agreement between the calculated failure load and the test results. The test results have shown that failure load and failure modes depend on the distance s. When comparing the derived models with the experimental results, all the plots used were failure load versus distance s. The equations were used for both single- and double-sided sheathing. In the latter case, the result of the equation was multiplied by a factor 2. Further, in Paper III, the presented formulas were tested considering the timber as both orthotropic and isotropic material, in order to evaluate how much material characteristics influence the calculated load-carrying capacity. The varied parameters, between orthotropic and isotropic material, were the modulus of elasticity, E, and the shear modulus, G. When orthotropic was considered E was chosen as the direction of the “cantilever span” in Figure 6.2, hence in
64 Analysis and discussion tangential direction and G in the radial-tangential plane. In literature E = 500 MPa and G = 50 MPa were found, while for isotropic E = 400 MPa and G = 70 MPa. Since the values of these parameters do not change too much between the two hypotheses above, the influence was found to be negligible. An example of failure load versus distance s graphs is shown in Figure 6.3. Figure 6.3a shows the failure load versus distance s graph using the analysis of Paper I for specimens tested in study A with single-sided sheathing, pith downwards and failed in mode 1, whilst Figure 6.3b shows the failure load versus distance s graph using the analysis of Paper III for specimens with both single- and double-sided sheathing, pith downwards and failing in mode 1. It is noted how well the trend of the curves fit with the experimental results, which indicates that the models are capable of capturing the splitting behaviour.
50 50 Centre b/2 Single-Sided 45 3b/8 45 Double-Sided b/4 Ortho, a 40 40 b = 15 + s Ortho, a = 0 e Iso, a 35 b = 20 + s 35 e Iso, a = 0 b = 25 + s 30 e 30 b = 30 + s e 25 25
20 20
Failure load [kN] 15 Failure load [kN] 15
10 10
5 5
0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] a) b) Figure 6.3 Failure load versus distance s graph for specimens of study A with pith downwards failing in mode 1. (a) Specimens with single-sided sheathing and curves from the analysis in Paper I; and (b) specimens with both single- and double-sided sheathing and curves from the analysis in Paper III. Figure 6.3b, with curves from a fracture mechanics approach and c = 20 mm show really good agreement between the formulas and the mean test results. The models derived for failure mode 2, in Paper III and IV, are independent of the distance s. When plotting the results in a similar graph they give a constant value. However they still show a rather good agreement with the test results. Even if it was found that also for failure mode 2 the failure load increases when the distance s is decreased, failure mode 2 appears only for small distances s and the difference in failure load with respect to the distance s is not evident as
Analysis and discussion 65 for failure mode 1. For some models derived for failure mode 1, when the distance s tends to zero, the failure load tends to infinity or increases much above the test results. In Paper III, the limit between failure mode 1 and 2, with respect to the distance s, was presented. The limit depends mainly on the strength properties and the size of the bottom rail. In Figure 6.4 this limit is shown using the models of Paper III (the corresponding curves and limits can be evaluated for all models presented in this thesis). Figure 6.4 present a curve representing the plot for failure mode 1 connected to a horizontal line representing the plot for failure mode 2. In Figure 6.4a the orthotropic properties of the wood have been considered and the formulas including the initial crack length used, whilst in Figure 6.4b isotropic wood properties have been considered and the formulas neglecting the initial crack length used. The values used are listed and discussed in Paper III. It seems that the dominating part of the results for failure mode 2, occur for small s- values below the limit, whilst the results of failure mode 1 are found for all distances s, but however more dominating for s-values above the limit. Further it is noted that using orthotropic properties and including the initial crack length tend to give better predictions compared to the mean values of the tests.
35 35 Failure mode 1 Failure mode 1 Failure mode 2 Failure mode 2 30 30
25 25
20 20 15
Failure load [kN] 15 Failure load [kN] 10
10 5
5 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] a) b) Figure 6.4 Limit between failure mode 1 and 2. (a) Results from study A and B and analysis with orthotropic values and formulas with initial crack length; and (b) results from study A and B and analysis with isotropic values and formulas without initial crack length. A further evaluation was conducted in Paper IV, as shown in Figure 6.5. The formula for failure mode 1 presented in Paper III, was plotted versus the crack length a using five be-values. With the “cantilever span” expressed as be = s + c, with the s-values ranging between s 40 mm, and choosing the distance c equal to c = 20 mm, five curves
66 Analysis and discussion are plotted in Figure 6.5. A corresponding for failure mode 2 (with the formula from Paper III) is also shown in the figures. In Figure 6.5a orthotropic properties have been used, whilst in Figure 6.5b isotropic.
30 30 Mode 1 - b = 60 mm Mode 1 - b = 60 mm e e Mode 1 - b = 50 mm Mode 1 - b = 50 mm 25 e 25 e Mode 1 - b = 40 mm Mode 1 - b = 40 mm e e Mode 1 - b = 30 mm Mode 1 - b = 30 mm e e 20 Mode 1 - b = 20 mm 20 Mode 1 - b = 20 mm e e Mode 2 Mode 2
15 15
Failure load [kN] 10 Failure load [kN] 10
5 5
0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Crack length a [mm] Crack length a [mm] a) b) Figure 6.5 Failure load versus crack length a. (a) Curves plotted using orthotropic values; and (b) curves plotted using isotropic values.
From these graphs it is noted that for be 50 mm in case of orthotropic properties and for be 0 mm for isotropic properties, respectively, the failure load curves for mode 1 are below the curve for failure mode 2, meaning that for a distances s PPIRU orthotropic and for s PPIRUisotropic conditions, respectively, failure mode 1 is the only failure mode. This agrees with the test results. The analysis carried out in Paper III and IV show that almost all the derived models have good agreement with the experimental results. Since the models in these papers were tested using values found in the literature, in Paper V they were tested using the values of the matching experimental study: fracture energy and tensile strength perpendicular to the grain found in the experimental study and compared to the bottom rail test results of the same study. For the evaluation the root mean square error (RMSE) method, as defined in Paper V, was used. The RMSE value was calculated for: (1) by using the individual values for Gf and ft,90 for each specimens tested; and (2) by using the mean values of for Gf and ft,90. The formulas giving the best fit with the test results, i.e. the smallest RMSE-values, were then chosen. For failure mode 1 the formula was:
Analysis and discussion 67
2/GbG Plh fe (6.1) G b 12 e E Eh s given in Paper IV, while for failure mode 2 the formulas giving best agreement were:
h PlC J e 1 h 1 e h (6.2)
5 11C1 G CG1f 3 G ;;10J] 21] fEht,90 e
also given in Paper IV. In Paper V the chosen equations were plotted versus the test results from bottom rail tests using the mean values of fracture energy and tensile strength perpendicular to the grain found in the tests. Regarding the fracture energy both orientations tested gave results close to the value given in literature and used in Papers III and IV, even if a small difference was found between RT and TR orientation. Regarding the tensile strength perpendicular to the grain the values were found to be smaller than the one found in literature and different for the two tested directions. For radial direction, failure mode 1, it was ft,90 = 1.80 MPa, while for tangential direction, failure mode 2, it was ft,90 = 2.30 MPa. This could be a reason also for the higher number of specimens that failing in mode 1 than in mode 2. Eqs. (6.1) and (6.2) seem to be promising for calculating the splitting failure capacity of bottom rail in partially anchored timber frame shear walls. They seem to include the main parameters needed for the calculation.
Conclusions 69
7CONCLUSIONS
The purpose of this research project was to identify the main factors influencing the splitting of the bottom rail in partially anchored timber frame shear walls and to evaluate different developed models for calculating the splitting failure capacity of the bottom rail in order to find those that show the best fit with the test results. The general conclusions and main findings that can be drawn from the appended papers and this thesis are summarized below in the form of answers to the research questions posed in Chapter 1.
¾ How do the varied parameters during the bottom rail tests, distance between the washer edge and the loaded edge of the bottom rail and the pith orientation of the bottom rail, influence the failure mode and load of bottom rail in partially anchored timber frame shear walls? The tests results show that the distance s between the edge of the washer and the edge of the bottom rail has a significant impact on the load-carrying capacity of the bottom rail and on the failure mode, while the pith orientation has some impact on the load-carrying capacity. Three primary failure modes were found during the tests: x Splitting of the bottom side of the rail due to cross-wise bending of the bottom rail. This brittle type of failure occurs when a large value of the distance s (s PP is used; x Splitting along the edge side of the bottom rail due to the sheathing-to-framing joints. This brittle failure mode occurs for small s-distances; x Yielding and withdrawal of the nails in the sheathing-to- framing joints. This is the favourable failure mode presupposed for using the plastic design method. This ductile failure mode occurs in this study when the distance s is small or when the plastic capacity of the joints was lower than the splitting capacity. The splitting capacity of the bottom rail can be increased by decreasing the distance s or by locating the pith downwards. Further findings of the experimental studies were that the surfaces of the bottom rail should be planed carefully after drying to avoid the formation of a cupped shape of the rail, which could cause pre-crack on the bottom rail when tightening the anchor bolt.
70 Conclusions
The load-carrying capacity of the bottom rail with double-sided sheathing was observed to be about twice of that observed for single- sided sheathing. ¾ Which of the evaluated models, based on a fracture mechanics approach, show the best fit with the experimental results, in terms of failure load, from the tests of bottom rail subjected to uplift in partially anchored timber frame shear walls? The different formulas were evaluated with respect to whether derived models were able to reproduce the general behaviour of the bottom rail in addition to the magnitudes of the failure loads that could observed during the tests. Almost all analytical models for determining the load-carrying capacity give results that are in good agreement with the observed load-carrying capacity. The influence of using orthotropic properties and including the initial crack length was evaluated. The range and limit between failure mode 1 and 2 with respect to the distance s from the edge of the washer to the sheathing were also evaluated. The following analytical models have been shown to fit best with respect to both the general behaviour and the load-carrying capacity of the bottom rail compared to the test results (cf. primarily Paper V). These models seem to include the main parameters needed to predict the capacity of the bottom rail in partially anchored shear walls. The load-carrying capacity to avoid splitting according to failure mode 1 is given by
2/GbG Plh fe (7.1) G b 12 e E Eh s
Figure 7.1 Geometry used for the derivation of Eq. (7.1). For failure mode 2 it is given by
Conclusions 71
h PlC J e 1 h 1 e h CG 5 G ; 1f3 (7.2) 1 J ; 21] C G 1 ] 1 10 fEht,90 e
Figure 7.2 Geometry used for the derivation of Eq. (7.2). The model of Eq. (7.2) assumes a ĺ 0.
It is noted that Eq. (7.1) includes be = s + c, where c is an empirically added length for the “cantilever” illustrated in Figure 7.1 to account for the fact that fully clamping conditions at the edge of washer cannot practically be assumed. Both of them were found to be decisive for calculating the load-carrying capacity. The parameter c has been empirically evaluated to c = 20 mm. It also noted that Eq. (7.2) does not include the distance s. It takes the effect of the total depth of the bottom rail into account and predicts infinitely high failure loads for he/h ĺ 1, i.e. horizontal splitting according to failure mode 2 is not an issue if the nails are placed sufficiently close to the bottom surface of the bottom rail. By using these formulas it is possible to design the bottom rail in partially anchored shear walls in such a way that splitting of the bottom rail can be avoided and the plastic capacity of the sheathing-to-framing joints can be utilized and the plastic design method can be used.
Future work 73
8 FUTURE WORK
This section collects suggestions on what are the next steps that should be taken to continuing this study.
The models derived and evaluated during this research do not consider some influencing factors as the friction under the bottom rail, the friction between the rail and the washer, the effect of the pretension force in the anchor bolts and the fact that the washers are discretely placed along the bottom rail length. The inclusion of friction would result in a higher prediction of load-carrying capacity. The effect of the pretension force depends on its magnitude, the cupping shape and orientation of the bottom rail. The models presented are 2D, meaning that the anchoring of the bottom rail is assumed to be continuous along its whole length. As future work it is suggested to study the influence of especially the third dimension, in order to confirm the applicability of the simple 2D models here presented. A means to do this could be to continue an already started analysis based on the extended finite element method (XFEM). XFEM is a numerical technique that extends the classical finite element method (FEM), by adding a part that allows it to treat discontinuities and singularities. An advantage using XFEM is that the location of the crack initiation and its propagation path do not need to be known in advance. Also, the crack propagates inside the elements and re-meshing is not needed for most crack growth problems.
References 75
REFERENCES Aicher S., Gustafsson P. J. (ed), Haller P. and Petersson H. (2002) Fracture Mechanics Models for Strength Analysis of Timber Beams with a Hole or a Notch. – A Report of RILEM TC-133. Report TVSM- 7134, Lund University, Division of Structural Mechanics, Lund, Sweden. Boughton G. N. and Reardon G. F. (1984) Simulated Wind Tests on the Tongan Hurricane House. Technical Report No. 23, James Cook Cyclone Structural Testing Station, Townsville, Queensland, Australia. BS 5268 (1996) The Structural Use of Timber. British Standards Institution. CSA-O86 (2001) Engineering Design Wood. Canadian Standards Association, 178 Rexdale Boulevard, Etobicoke, Ontario. Dolan J. D. (1989) The Dynamic Response of Timber Shear Walls. Doctoral Thesis, The University of British Columbia, Vancouver, British Columbia, Canada. Dolan J. D. and Foschi R. O. (1991) Structural Analysis Model for Static Lads on Timber Shear Walls. Journal of Structural Engineering, 117:851-861. Easley J. T., Foomani M. and Dodds R. H. (1982) Formulas for Wood Shear Walls. Journal of the Structural Division, 108:2460-2478. EN 204 (2001) Classification of Thermoplastic Wood Adhesives for Non- Structural Applications. European Committee for Standardization, Brussels, Belgium. EN 205 (2003) Adhesives – Wood Adhesives for Non-Structural Applications – Determination of Tensile Shear Strength of Lap Joints. European Committee for Standardization, Brussels, Belgium. EN 338 (2009) Structural Timber – Strength Classes. European Committee for Standardization, Brussels, Belgium. EN 594 (2008) Timber Structures – Test Methods – Racking Strength and Stiffness of Timber Frame Wall Panels. European Committee for Standardization, Brussels, Belgium. EN 622-2 (2004) Fibreboards – Specifications – Part 2: Requirements for Hardboard. European Committee for Standardization, Brussels, Belgium. EN 408 (2010) Timber Structures – Structural Timber and Glued Laminated Timber – Determination of Some Physical and Mechanical Properties. European Committee for Standardization, Brussels, Belgium. Eurocode 5 (2008) Design of Timber Structures – Part 1-1: General – Common Rules and Rules for Building. prEN 1995-1-1, European Committee for Standardization, Brussels, Belgium.
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Kasal B. and Leichti R. J. (1992) Nonlinear Finite-Element Model for Light-Frame Stud Walls. Journal of Structural Engineering, 118:3122-3135. Källsner B., Girhammar U. A. and Wu L. (2001) A Simplified Plastic Model for Design Partially Anchored Wood-Framed Shear Walls. In: Proceedings CIB-W18 Timber Structures Meeting, Venice, Italy, Paper 34-15-1. Källsner B., Girhammar U. A. and Wu L. (2002) A Plastic Design Model for Partially Anchored Wood-Framed Shear Walls with Openings. In: Proceedings of CIB-W18 Timber Structures Meeting, Kyoto, Japan, Paper 35-15-2. Källsner B., Girhammar U. A. and Wu L. (2004) Influence of Framing Joints on Plastic Capacity of Partially Anchored Wood-Framed Shear Walls. In: Proceedings of CIB-W18 Timber Structures Meeting, Edinburgh, UK, Paper 37-15-3. Källsner B. and Girhammar U. A. (2005) Plastic Design of Partially Anchored Wood-Framed Wall Diaphragms with and without Openings. In: Proceedings of CIB-W18 Timber Structures Meeting, Karlsruhe, Germany, Paper 38-15-7. Mallory M. P. and McCutcheon W. J. (1987) Predicting Racking Performance of Walls Sheathed on Both Sides. Forest Product Journal, 37:27-32. McCutcheon W. J. (1985) Racking Deformations in Wood Shear Walls. Journal of Structural Engineering, 111:257-269. Ni C. and Karacabeyli E. (2000) Effect of Overturning Restraint on Performance of Shear Walls. In Proceedings from the 6th World Conference on Timber Engineering WCTE 2000, British Columbia, Canada. Ni C. and Karacabeyli E. (2002) Capacity of Shear Wall Segments Without Hold-Downs. Wood Design Focus, 12:10-17. NT BUILD 422 (1993) Wood: Fracture Energy in Tension Perpendicular to the Grain. Porteous J. and Kermani A. (2007) Design of Stability Bracing, Floor and Wall Diaphragms. In Structural Timber Design to Eurocode 5, edited by J. Porteous and A. Kermani 338 – 371, Blackwell. Prion H. G. L. and Lam F. (2003) Shear walls Diaphragms. In Timber Engineering, edited by S. Thelandersson and H. J. Larsen 383 – 408, John Wiley & Sons Ltd. Rainer H., Ni C. and Karacabeyli E. (2008) Mechanics-Based Model for Seismic Resistance of Conventional Wood-Frame Walls. In Proceedings from the 10th World Conference on Timber Engineering WCTE 2008, Miyazaki, Japan.
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Robertson A. (1980) Discussion of “Racking Strength of Light-Frame Nailed Walls,” by R. L. Tuomi and W. J. McCutcheon. Journal of the Structural Division, 106:1981-1985. Schmidt R. J. and Moody R. C. (1989) Modeling Laterally Loaded Light- Frame Buildings. Journal of Structural Engineering, 115:201-217. Serrano E. and Gustafsson P. J. (2006) Fracture Mechanics in Timber Engineering – Strength Analyses of Components and Joints. Material and Structures, 40:87-96. Serrano E., Vessby J., Olsson A., Girhammar U. A. and Källsner B. (2011) Design of Bottom Rail in Partially Anchored Shear Walls Using Fracture Mechanics. In: Proceedings of CIB-W18 Timber Structures Meeting, Alghero, Sardinia, Italy, Paper 44-15-4. Serrano E., Vessby J. and Olsson A. (2012) Modeling of Fracture in the Sill Plate in Partially Anchored Shear Walls. Journal of Structural Engineering, 138:1285-1288. Smith I. and Vasic S. (2003) Fracture Behaviour of Softwood. Mechanics of Materials, 35:803-815. Smith I., Landis E. and Gong M. (2003) Principle of Fracture Mechanics. In Fracture and Fatigue in Wood, edited by Smith I., Landis E. and Gong M. 67 – 97, John Wiley & Sons Ltd. Thelandersson S. (2003) Timber Engineering – General Introduction. In Timber Engineering, edited by S. Thelandersson and H. J. Larsen 1 – 11, John Wiley & Sons Ltd. Tuomi R. L. and McCutcheon W. J. (1974) Testing of a Full-Scale House Under Simulated Snowloads and Windloads. U.S. Forest Product Laboratory Research Paper, FPL 234. Tuomi R. L. and McCutcheon W. J. (1978) Racking Strength of Light- Frame Nailed Walls. Journal of the Structural Division, 104:1131- 1140. van de Lindt J. W. (2004) Evolution of Wood Shear Wall Testing, Modeling, and Reliability Analysis: Bibliography. Practice Periodical on Structural Design and Construction, 9:44-53. van der Put T. A. C. M., Leijten A. J. M. (2000) Evaluation of Perpendicular to Grain Failure of Beams Caused by Concentrated Loads of Joints. In: Proceedings of CIB-W18 Timber Structures Meeting, Delft, The Netherlands, Paper 33-7-7. Vessby J. (2011) Analysis of Shear Walls for Multi-Storey Timber Buildings. Doctoral Thesis, Linnaeus University, Växjö, Sweden.
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Doctoral and licentiate theses Timber Structures Luleå University of Technology
Doctoral theses
2001 Nils Olsson: Glulam Timber Arches – Strength of Splices and Reliability-Based Optimisation. 2001:12D. 2004 Helena Johnsson: Plug Shear Failures in Nailed Timber Connections – Avoiding Brittle and Promoting Ductile Failures. 2004:03D. 2004 Max Bergström: Industrialized Timber Frame Housing – Managing Customization, Change and Information. 2004:45D. 2005 Andreas Falk: Architectural Aspects of Massive Timber – Structural Form and Systems. 2005:41D. 2005 Ylva Sardén: Complexity and Learning in Timber Frame Housing – The Case of a Solid Wood Pilot Project. 2005:43D. 2006 Anders Björnfot: An Exploration of Lean thinking for Multi- Storey Timber Housing Construction – Contemporary Swedish Practices and Future Opportunities. 2006:51D. 2008 Matilda Höök: Lean Culture in Industrialized housing – A study of Timber Volume Element Prefabrication, 2008:21D. 2008 Tomas Nord: Prefabrication strategies in the timber housing industry - A comparison of Swedish and Austrian markets, 2008:51D. 2009 Elzbieta Lukaszewska: Development of prefabricated timber- concrete composite floors, ISBN 978-91-86233-85-3. 2010 John Meiling: Continous improvement and experience feedback in off-site construction – Timber-framed module prefabrication, ISBN 978-91-7439-180-0. 2011 Gabriela Tlustochowicsz: Stabilising system for multi-storey beam and post timber buildings, ISBN 978-91-7439-339-2. 2012 Susanne Engström: Managing information to unblock supplier- led innovation in construction – Barriers to client decision-
80
making on industrialized building in Sweden, ISBN 978-91- 7439-407-8. 2012 Martin Lennartsson: The transition of industrialised house- building towards improved production control, ISBN 978-91- 7439-458-0. 2013 Erika Hedgren: Overcoming organizational lock-in in decision making – Construction clients facing innovation, ISBN 978-91- 7439-572-3. 2013 Gustav Jansson: Platforms in industrialised house-building, ISBN 978-91-7439-758-1. 2014 Jarkko Erikshammar: Supply chain integration for small sawmills in industrialized house-building, ISBN 978-91-7439-934-9. 2014 Martin Haller: Design iteration control framework for offsite building projects, ISBN 978-91-7583-123-7.
Licentiate theses
2001 Helena Johansson: Systematic Design of Glulam Trusses. 2001:07L. 2003 Ylva Fredriksson: Samverkan mellan träkomponenttillverkare och stora byggföretag – en studie av massivträbyggandet. 2003:14L. 2003 Sunna Cigén: Materialleverantören i byggprocessen – en studie av kommunikationen mellan träkomponentleverantören och byggprocessens övriga aktörer. 2003:69L. 2004 Anders Björnfot: Modular Long-Span Timber Structures – a Systematic Framework for Buildable Construction. 2004:34L. 2005 Henrik Janols: Communicating Long-Span Timber Structures with 3D Computer Visualisation. 2005:30L. 2005 Tomas Nord: Structure and Development in the Solid Wood Value Chain – Dominant Saw Milling Strategies and Industrialized Housing. 2005:57L. 2005 Matilda Höök: Timber Volume Element Prefabrication – Production and Market Aspects. 2005:65L. 2008 Annicka Cettner: Kvinna i byggbranschen – Civilingenjörers erfarenheter ur genusperspektiv. 2008:05L.
81
2008 John Meiling: Product Quality through experience feedback in industrialised housing, 2008:36L 2009 Martin Lennartsson: Modularity in Industrial Timber Housing – A Lean approach to develop building service systems, ISBN 978-91-7439-047-6. 2010 Erik Söderholm: Applicability of Continuous Improvements in Industrialised Construction Design Process, ISBN 978-91-7439- 086-5. 2010 Erika Levander: Addressing Client Uncertainty – A Swedish property owners´ perspective on industrial timber framed housing and property, ISBN 978-91-7439-109-1. 2010 Gustav Jansson: Industrialised Housing Design Efficiency, ISBN 978-91-7439-138-1. 2011 Jarkko Erikshammar: Collaborative product development – a purchasing method in small industrialized house-building companies, ISBN 978-91-7439-329-3. 2012 Martin Haller: Critical design activities in house-building projects – an industrial process perspective, ISBN 978-91-7439- 383-5. 2014 Gustav Nordström: Use of energy-signature method to estimate energy performance in single-family buildings, ISBN 978-91- 7583-023-0
PART II
Paper I
The IES Journal Part A: Civil & Structural Engineering, 2014 Vol. 7, No. 2, 83–105, http://dx.doi.org/10.1080/19373260.2014.898558
TECHNICAL PAPER Splitting capacity of bottom rail in partially anchored timber frame shear walls with single-sided sheathing Giuseppe Caprolua*, Ulf Arne Girhammara,BoK€allsnerb and Helena Lidelow€ a
aDivision of Structural and Construction Engineering – Timber Structures, Lulea University of Technology, SE-971 87 Lulea, Sweden; bSchool of Engineering, Linnaeus University, 351 95 Vaxj€ o,€ Sweden (Received 28 January 2014; accepted 24 February 2014)
Plastic design methods can be used for determining the load-carrying capacity of partially anchored shear walls, where hold-downs are not provided. In order to use these methods, a ductile behaviour of the sheathing-to-framing joints must be ensured. Since the forces in the anchor bolts and the sheathing-to-framing joints do not act in the same vertical plane, the bottom rail will be subjected to bending and shear in the crosswise direction, and splitting of the bottom rail may occur. In this article, results of two experimental programmes on the splitting capacity of the bottom rail due to uplift in partially anchored shear walls are presented. Two brittle failure modes occurred during testing: (1) a crack opening from the bottom surface of the bottom rail; and (2) a crack opening from the edge surface of the bottom rail along the line of the sheathing- to-framing joints. The results show that the distance between the edge of the washer and the loaded edge of the bottom rail has a decisive influence on the maximum load and the failure modes of the bottom rail. Keywords: timber shear walls; partially anchored; sheathing-to-framing joint; bottom rail; crosswise bending; splitting of bottom rail
1. Introduction 1.2. Background 1.1. Actions on the bottom rail Shear walls are structural elements designed to transmit In Figure 1, the difference in structural behaviour of fully horizontal and vertical forces in their own plane. Shear and partially anchored shear walls is shown. In fully walls are used, together with roof and floor diaphragms, anchored shear walls, the leading stud is anchored to the to stabilise timber-framed buildings against external substrate by hold-downs. This will result in a concentrated loads. In Eurocode 5 (2004), two parallel methods for the force at the end of the wall (Figure 1(a)). The notation design of shear walls are given: one analytical method fully anchored means that there is no uplift of the studs of with a theoretical background, method A, which can be the wall, especially of the leading stud. In partially applied only to shear walls with a tie-down at the loaded anchored shear walls, where hold-downs are not provided, leading stud in order to prevent uplift, and one with an the uplift is resisted by the sheathing-to-framing joint experimental approach using a test protocol according to along the bottom rail (Figure 1(b)). In this case, there is EN 594 (2008), method B, where the corresponding stud some uplift of the studs of the wall. Hence, it is important is free to move vertically and the bottom rail is anchored that the bottom rail is anchored to the substrate by anchor to the substrate. bolts and, therefore, is able to transmit the distributed Method A corresponds to a fully anchored shear wall, force to the structure below. In general, the anchor bolts while method B corresponds to a partially anchored shear are always subjected to shear forces, and in this case of wall, where the bottom rail can be subjected to transverse partially anchored shear walls, also to tensile forces. Since bending as discussed in this paper. It is obvious that the the forces in the anchor bolts and the sheathing-to-framing two methods are not consistent with each other, except in joints do not act in the same vertical plane, the bottom rail the case where vertical loads of sufficient magnitude to will be subjected to crosswise bending and shear, and stabilise the wall are applied in method B. € splitting of the bottom rail may occur. It is important to Kallsner and Girhammar (2005) have presented a new avoid a brittle failure of the bottom rail in order to enable plastic design method of wood-framed shear walls at an the development of the force distribution shown in ultimate limit state. This method allows the designer to Figure 1(b). calculate the load-carrying capacity also for partially
*Corresponding author. Email: [email protected]
Ó 2014 The Institution of Engineers, Singapore 84 G. Caprolu et al.
Figure 1. Two principal ways to anchor timber frame shear walls subjected to horizontal loading: (a) fully anchored shear wall – con- centrated anchorage of the leading stud, i.e. using a hold-down; and (b) partially anchored shear walls – distributed anchorage of the bot- tom rail through the sheathing-to-framing joints (freely adapted from Girhammar and K€allsner [2009]). anchored shear walls where the leading stud is not fully nine tests, splitting along the edge side of the bottom rail anchored against uplift. The model covers only static occurred. When square washers were used, splitting along loads and the sheathing-to-timber joints are presupposed the edge side of the bottom rail was the dominating failure to show a plastic behaviour. The plastic design method mode. In one of the three tests, the sheathing-to-framing leads to more economic structures with great flexibility in joints of the top rail failed. Thus, big square washers sup- the placement and arrangement of anchorage devices. press the bottom rail cross-grain failure mode. These Prion and Lam (2003) pointed out the importance to specimens also showed an increased peak load. understand the differences between hold-downs and Two experimental studies, Girhammar and Juto anchor bolts. Anchor bolts provide horizontal shear conti- (2009) and Caprolu (2011), have been carried out, called nuity between the bottom rail and the foundation. Hold- study A and study B. The first study has partly and prelim- downs serve as vertical anchorage devices between the inarily been evaluated and discussed in Girhammar and vertical end studs and the foundation. When hold-downs K€allsner (2009) and Girhammar, K€allsner, and Daerga are not provided, the corresponding tying-down forces (2010). In that study, it was concluded that the distance may be replaced by vertical loads from dead-weight or between the edge of the washer and the loaded edge of the anchorage forces transferred from transverse walls. In the bottom rail is a decisive parameter for the capacity and case of no hold-downs, the bottom row of nails transmits the failure modes of the bottom rail. It was also found that the vertical forces in the sheathing to the bottom rail the pith orientation had an influence on the results. Study (instead of the vertical stud) where the anchor bolts will A was extended to study B in order to investigate the further transmit the forces into the foundation. Because of behaviour in more detail and to include more influential the eccentric load transfer, transverse bending is created parameters. The two studies also differ with respect to the in the bottom rail and splitting may occur. Brittle failure boundary conditions of the test set-ups. The second study modes in the bottom rail, especially with respect to the was preliminarily presented recently by Caprolu et al., bottom surface, can be avoided using large washers at the “Tests on the Splitting Failure” (2012). In Girhammar and anchor bolts. The size and the position of the washer influ- K€allsner (2009) and Girhammar, K€allsner, and Daerga ence the eccentricity moment in the bottom rail. (2010), the capacity of the anchored bottom rail was eval- Ni and Karacabeyli (2002) developed two methods, uated empirically, while the test results presented in one empirical and one mechanics-based to account for Caprolu et al., “Tests on the Splitting Failure” (2012) effects of uplift restraint on the performance of shear were followed by an analytical comparison using fracture walls without hold-downs. In order to quantify effects of mechanics with acceptable agreement (see Caprolu et al., overturning restraints on the performance of wood-frame “Analytical and Experimental Evaluation,” 2012). shear walls, full-scale shear wall specimens were tested under horizontal load. In the NAHB (2005) report, an experimental study is 1.3. Aim presented. Four types of partially anchored shear walls The aim of this research is to evaluate the splitting failure with varying nail size and spacing, and with small round capacity and failure modes of the bottom rail, in order to or big square washers, were tested under tensile loading be able to design against the problem of splitting of the (perpendicular to the bottom rail) with three samples per bottom rail and apply the plastic design method. The pur- type of configuration. Splitting along the bottom side of pose of this study (study B) is also to extend, deepen and the bottom rail was the predominant failure mode for compare the test results with those obtained at an earlier shear walls with small round washers, but in two of the study (study A) and to form the basis for an analytical The IES Journal Part A: Civil & Structural Engineering 85 evaluation using fracture mechanics models. The experi- different series with respect to the position of the anchor mental results are presented in such a way as to facilitate bolt in the width direction “b” of the bottom rail a subsequent analytical modelling and evaluation. (Figure 2(d)) and each series into different sets with regard to the washer size. Knowing the anchor bolt posi- tion and the washer size, the distance between the washer 2. Materials and methods edge and the edge of the bottom rail at the loaded side, s, 2.1. Test specimens and material properties as shown in Figure 2(d), is defined. The depth of the bot- tom rail is defined as h, as shown in Figure 2(d). The specimens were built by hand using rails of length The test programme of study A is specified in Table 1. 900 mm with a cross section of 45 120 mm, fastened to Study B (according to Figure 2(b)): a total of 142 a hardboard sheet of 900 500 mm by nails of 50 specimens were tested. As in study A, the specimens were 2.1 mm. divided into three different series (with regard to the posi- The details of the test specimens are as follows: tion of the anchor bolt), and each series was divided into different sets (with respect to the washer size and pith ori- Bottom rail: spruce (Picea Abies), C24 according to entation). The test programme of study B is specified in EN 338 (2009),45 120 mm. Table 2. Sheathing: hardboard, 8 mm (wet process fibre board, HB.HLA2, EN 622-2 (2004), Masonite AB). 2.3. Test set-up Sheathing-to-timber joints: annular ringed shank The test set-up is shown in Figure 2. nails, 50 2.1 mm (Duofast, Nordisk Kartro AB). The bottom rail was fastened to a supporting welded The joints were nailed manually and the holes were steel structure by two anchor bolts. The distance between pre-drilled, only in the sheet, 1.7 mm. the bolts was 600 mm and the distance between the bolt Anchor bolt: Ø 12 (M12). The holes in the bottom and the end of the bottom rail was 150 mm. A rigid rails were pre-drilled, 13 mm. square- or rectangular-shaped washer was inserted between the bottom rail and the bolt head throughout all tests. The thickness of the washer (15 mm) was chosen so 2.2. Test programme that there would not arise any visible permanent deforma- When evaluating the tests results in study A (Girhammar tions in the washers. A hydraulic piston (static load capac- and Juto 2009), it was found that more parameters than ity 100 kN) was attached to a steel bar, which was originally planned for had an influence on the results, e.g. connected to the upper panel using C-shaped steel profiles the pith orientation. As a consequence, it was decided to and four bolts Ø16, according to Figure 2(e). vary these parameters and perform an additional experi- As mentioned, different boundary conditions were mental investigation, study B (Caprolu 2011). These two used in the two studies: in study A, the vertical load was experimental studies differ with respect to the boundary transferred to the C-shaped steel profiles via a welded conditions of the test set-ups. In study A, the rotation of connection, introducing some bending moments in the the sheathing relative to the bottom rail was restrained by test specimens (cf. Figure 2(a)). The bracing bars reduced using two bracing bars (Figure 2(a)). The purpose of this the rotation of the specimen, but since it was believed that arrangement was to have a uniform displacement of the this arrangement did not render full rotation restraint and, sheathing perpendicular to the bottom rail. In study B, the also, to simulate more the behaviour in practice (believed sheathing was free to rotate by transmitting the applied to be more “uneven”, starting failure at one end), it was load through a hinge (Figure 2(b)). Also, in study B, the decided to have more clearly defined boundary conditions pith orientation was systematically studied and the evalua- in study B by removing the inclined bars and only using tion of the test results was much more detailed to observe the hinge according to Figure 2(b). and measure the crack propagation as a basis for a future In study A, the distance between the nails in the fracture mechanics study. sheathing-to-timber joint was 50 mm for series 1 and In study A, 10 specimens were tested for each set; all 25 mm for series 2 and 3 (except for one specimen in tests were planned with the pith orientation of the bottom series 3, where the distance was 50 mm by mistake). The rail downwards (PD), but by mistake two of them had pith main reason to change it and have a so small distance was oriented upwards (PU). The results seemed to show a sys- to have a strong joint in order to avoid a ductile failure of tematic difference for the two pith orientations. Hence, in the fasteners, because the aim of the experimental study study B, 16 specimens were tested for each set, 8 with was to study the possible brittle failure modes of the bot- pith upwards and 8 with pith downwards. tom rail. In study B, the distance was kept constant in all Study A (according to Figure 2(a)): a total of 89 speci- series as 50 mm, because it is a more realistic distance to mens were tested. The specimens were divided into three use in practice. 86 G. Caprolu et al.
Figure 2. Test set-up and boundary conditions of sheathed bottom rails subjected to single-sided vertical uplift. (a) Boundary condi- tions of study A: the two diagonal bars prevent rotation of the specimen; (b) boundary conditions of study B: the two diagonal bars have been removed and a hinge is created that allows the specimen to rotate; (c) view from above of the specimen; (d) lateral view of the spec- imen: the distance s is the distance between the washer edge and the loaded edge of the bottom rail; (e) the connection between the spec- imen and the steel bar connected to the hydraulic piston.
Other differences were the torque moment used to 3. Results tighten the bolts, 40 Nm in study A and 50 Nm in study B, 3.1. Failure modes and the displacement rate, 2 mm/min in study A and, by Three primary failure modes were found during the tests: mistake, 10 mm/min in study B. The influence of this dif- ference in displacement rate has not been evaluated. How- (1) Splitting along the bottom side of the rail accord- ever, as a rule of thumb, a tenfold increase of rate gives a ing to Figure 3(a) 10% increase of strength. (2) Splitting along the edge side of the rail according For each specimen, the moisture content and density to Figure 3(b) of the bottom rail were measured after the test, according (3) Yielding and withdrawal of the nails in the sheath- to ISO 3130 (1975) and ISO 3131 (1975), respectively. ing-to-framing joints according to Figure 3(c) The IES Journal Part A: Civil & Structural Engineering 87
Table 1. Test programme of study A.
Number of tests a Anchor bolt position Size of washer Distance s Series Set PD PU [mm] [mm] [mm]
1182b/2 60 mm from sheathing 40 40 15 40 28 2 60 60 15 30 38 2 80 70 15 20 4 8 2 100 70 15 10 21823b/8 45 mm from sheathing 40 40 15 25 28 2 60 60 15 15 38 2 80 70 15 5 3191b/4 30 mm from sheathing 40 40 15 10 28 1 60 60 15 0
PD ¼ pith downwards, PU ¼ pith upwards, b ¼ width of rail (notations as in Figure 2). aDistance from the washer edge to the loaded edge of the bottom rail.
The first two failure modes are brittle and the third is due to withdrawal of the nails in the sheathing-to-framing ductile and the consequence of them is quite different. joint. This failure mode happens without any visible crack The brittle failure modes need to be eliminated, but it is along the bottom rail. not critical in the ultimate limit state that the ductile fail- In Figures 4 and 5, the number of observations of the ure occurs. (However, in the serviceability limit state, the three different failure modes is graphically shown for the slip should be limited.) Failure mode (1) is due to cross- series in study A and study B, respectively. It is noted that wise bending of the bottom rail, introducing tension per- the predominant failure mode is failure mode (1), splitting pendicular to the grain. The failure is developed as a failure along the bottom side of the rail. It is also possible vertical crack propagating from the middle of the bottom to note an influence between distance s and failure mode. side of the rail. When the anchor bolt is moved towards For small values of distance s, failure modes (2) and (3) the sheathing-to-framing joints or when big washers are dominate, while failure mode (1) dominates for large s- used, the crack usually appears closer to that edge. Once values. the crack appears, it develops from one end to the other It is noted that there were only two specimens with end of the bottom rail. Failure mode (2) is due to vertical withdrawal failure in study A. This is of course a conse- shear forces in the nails of the sheathing-to-framing joints, quence of the small nail distance. One specimen was in causing splitting failure at the edge of the bottom rail. The series 1, where a nails distance of 50 mm was used. The crack usually starts from the line of the nails propagating second specimen, although was in series 3, by mistake in the horizontal direction and finally changing to a more had a nails distance of 50 mm. vertical direction. The crack usually starts at one end and then propagates longitudinally along the bottom rail, but never reaches the other end. Sometimes a horizontal crack 3.2. Load–time curves and crack development appears also in the other end, but that is a separate crack The displacements of the specimens were not recorded, independent of the first one. Finally, failure mode (3) is but since the displacement was applied with a constant
Table 2. Test programme of study B.
Number of tests a Anchor bolt position Size of washer Distance s Series Set PD PU [mm] [mm] [mm]
1188b/2 60 mm from sheathing 40 40 15 40 28 8 60 60 15 30 38 8 80 70 15 20 4 8 8 100 70 15 10 21773b/8 45 mm from sheathing 40 40 15 25 28 8 60 60 15 15 38 8 80 70 15 5 3188b/4 30 mm from sheathing 40 40 15 10 28 8 60 60 15 0
PD ¼ pith downwards, PU ¼ pith upwards, b ¼ width of rail (notations as in Figure 2). aDistance from the washer edge to the loaded edge of the bottom rail. 88 G. Caprolu et al.
Figure 3. (a) Splitting failure along the bottom side of the rail; (b) splitting failure along the edge side of the rail; and (c) yielding and withdrawal of the nails in the sheathing-to-framing joints. The left column of pictures refers to bottom rails with pith upwards (PU ¼ U) and the right column with pith downwards (PD ¼ N). rate, it is possible to obtain fictitious load–displacement to be to a large extent linked to the displacements of the curves by plotting load versus time. Typical load–time sheathing-to-framing joints (compression deformations in curves, from study B, are shown in Figure 6. the wood and sheathing material around the nails). It Figure 6(a) shows the influence of a splitting failure might also be caused by some embedding deformations along the bottom side of the rail, mode (1). For this type of the bottom rail in the compressed area under the of failure, the crack usually was initiated at one end of the washers. bottom rail and then developed until it reached the other Sometimes the crack seems to appear at both ends at end. This behaviour is visible in Figure 6(a) for some the same time. In these cases, the load versus time curves specimens tested failing in the same way. The first abrupt show two drops instead of three, as shown in Figure 6(b). decrease in the load, point 2, is caused by a crack propa- The first decrease in the load, point 2, is then caused by a gating from one end of the bottom rail to the anchor bolt. crack propagating from each end of the bottom rail to the The second decrease in load, point 3, is probably caused nearest anchor bolt. The second decrease in load, point 3, by a crack propagating between the two anchor bolts. The is probably caused by a crack propagating between the third drop of the load, point 4, occurs when the crack two anchor bolts. As mentioned before, the crack stop can propagates from the anchor bolts to the other end. Instead also be caused by knots. of the crack stopping at the anchor bolt positions, it can Figure 6(c) shows the influence of splitting along the stop propagating at some knots. edge side of the rail, failure mode (2), for some specimens Point 1 in Figure 6 depicts the inflection point in all tested failing in the same way. As is evident from the curves. It represents some non-linearity and is believed figure, the crack behaviour is different from that of failure The IES Journal Part A: Civil & Structural Engineering 89
Figure 4. Recorded failure modes for the different test series and sets belonging to study A (PD ¼ pith downwards, PU ¼ pith upwards). Notes: Distance from the washer edge to loaded edge of the bottom rail [mm]; size of the washer [mm]; bolt position. mode (1) (Figure 6(a)). For failure mode (2), there is only testing are shown. It is interesting to analyse the behaviour one crack and drop in the load, point 2. of the different cracks relative to the washer dimension, Finally, in Figure 6(d), some examples of the charac- bolt position and pith orientation. ter of the load–time curve are shown for failure mode (3), The formation of cracks is mainly dependent on the yielding and withdrawal of the nails in the sheathing-to- position of the washer, the orientation of the pith and the framing joints. Here it is possible to observe a ductile annular ring pattern. Typical examples of crack propaga- behaviour after point 2, where the failure happens. tions are shown in Figure 7 for bottom rails with pith ori- In Girhammar and Juto (2009) and Caprolu (2011), ented upwards (PU) and in Figure 8 with pith orientation photos of almost all the cracks that appeared during the downwards (PD). For bottom rails with the pith oriented
Figure 5. Recorded failure modes for the different test series and sets belonging to study B (PD ¼ pith downwards, PU ¼ pith upwards). Notes: Distance from the washer edge to loaded edge of the bottom rail [mm]; size of the washer [mm]; bolt position. 90 G. Caprolu et al.
Figure 6. Examples of measured load–time curves. Point 1 depicts an inflection point in all curves. (a) Failure mode (1) (crack from the bottom side of the rail). Point 2 is caused by a crack propagating from one end of the bottom rail to the closest anchor bolt. Point 3 is probably caused by a crack propagating between the two anchor bolts. Finally, point 4 depicts a crack propagating from the anchor bolt to the other end. (b) Failure mode (1) (crack from the bottom side of the rail) for specimens with a crack appearing at the same time at both ends. Point 2 is caused by a crack propagating from each end of the bottom rail to the closest anchor bolt. Point 3 depicts a crack propagating between the anchor bolts. (c) Failure mode (2) (crack from the edge side of rail). Point 2 is caused by the horizontal crack propagating along the longitudinal direction of the bottom rail. (d) Failure mode (3) (yielding and withdrawal of fasteners). Point 2 depicts the withdrawal of fasteners. upwards, four typical types of crack formations are shown For mode (2), the crack is initiated at the side of the in Figure 7, three for failure mode (1) (Figure 7(a)–(c)) bottom rail along the line of the nails in the sheathing-to- and one for failure mode (2) (Figure 7(d)). framing joints and develops in the horizontal direction for For mode (1), the crack is initiated at the bottom side about 20 mm and then changes direction in a more vertical of the bottom rail and always starts to propagate vertically direction, often across the annular rings towards the pith, across (more or less perpendicular to) the annular rings sometimes directly to a vertical crack, as shown in and then continues either (1) in the same or somewhat Figure 7(d). The location where the crack changes direc- deviating direction heading towards the pith location tion, the distance bcrack2, is presented in Table 3. (Figure 7(a) and (b)), or (2) by changing direction to prop- For bottom rails with the pith oriented downwards, the agate along a certain annular ring (Figure 7(c)). (The dis- crack development is similar to that for bottom rails with tance up to where the crack starts to change direction pith oriented upwards. Typical examples of crack forma- seems to be of the same order in the experiments.) It is of tions are shown in Figure 8, three for mode (1) (Figure 8 interest to note the location of the crack initiation, the dis- (a)–(c)) and one for mode (2) (Figure 8(d)). With the pith tance bcrack1, somewhere between the middle of the width oriented downwards, it seems to be a tendency for the and the edge of the washer, as presented in Table 3.Itis crack in mode (1) to be initiated at the bottom side of the obvious that for bolts closer to the loaded edge or for big- rail closer to the pith than when the pith is oriented ger washers, the crack initiates closer to the loaded end. upwards (Figure 8(a) and 8(b)). Also, as is evident from Note also the exception shown in Figure 7(b), the left- Figure 8(c), the crack can be initiated and propagate along hand photo, where the pith is located near the loaded end; an annular ring and then change direction more or less per- the crack propagates to the left towards the pith (cf. the pendicular to the annular rings, in a more vertical direction opposite in Figure 7(b), the right-hand photo). pointing backwards to the pith. The distance, bcrack1,is The IES Journal Part A: Civil & Structural Engineering 91
Figure 7. Crack development for the bottom rail with pith oriented upwards (PU). (a) Mode (1) crack developed in a straight line, starting and propagating vertically in the middle of the bottom rail; (b) mode (1) crack developed in an oblique line, starting at a location close to the edge of the washer and propagating towards the pith; (c) mode (1) crack developed in a straight line for a certain length and then fol- lowing the annual ring shape; and (d) mode (2) crack development, starting horizontally and then propagating vertically towards the pith. given in Table 4. For mode (2) in Figure 8(d) with pith decrease in the load-carrying capacity due to a propagat- downwards, it is obvious that the horizontal crack changes ing crack in the bottom rail. For failure mode (3), the fail- directly to a vertical crack or deviates to follow an annular ure load is defined as the maximum load. The results of ring before changing to a vertical crack. The distance, the different tests of the two studies are summarised in bcrack2,isgiveninTable 4. Tables 5 and 6. Since the pith orientation turned out to be Since there are ongoing theoretical studies based on a an important parameter at the evaluation of the test fracture mechanics approach (see, for instance, Caprolu results, the failure load of the two studies are presented et al., “Analytical and Experimental Evaluation,” 2012; with respect to this parameter in Table 5 (PU) and Table 6 Serrano, Vessby, and Olsson 2012), it is interesting to give (PD). Mean failure load and mean density are presented a few details of the crack characteristics. In Tables 3 and 4, with respect to failure mode. The dry density, defined as the distance between the vertical crack and the loaded edge the ratio between the mass of the specimen after drying of the bottom rail, for failure mode (1), and the length of and the volume of the specimen before drying at v mois- the horizontal crack before it changes direction, for failure ture content, indicated as r0,v, is shown in Tables 5 and 6 mode (2), are given. The data are presented with respect to as the mean value per set and failure mode. The mean pith orientation for study A and study B. moisture content per set, indicated as v, is also shown in Tables 5 and 6. 3.3. Failure loads From Tables 5 and 6, it is evident that the overall val- The failure load for the two brittle failure modes 1 and 2 is ues for the density in the two studies are comparable, but defined as the load at which there is a first distinct there is a clear difference in moisture content. In study A, 92 G. Caprolu et al.
Figure 8. Crack development for the bottom rail with pith oriented downwards (PD). (a) Mode (1) crack developed in a straight line, starting and propagating vertically in the middle of the bottom rail; (b) mode (1) crack developed in an oblique line, starting at a location close to the pith and propagating towards the loaded edge of the bottom rail; (c) mode (1) crack developed following the annual ring shape and then in a straight line; and (d) mode (2) crack development, starting horizontally and then propagating vertically. the moisture content is, essentially through all tests, different modes given in the tables do not represent the true higher than in study B. This might have an overall influ- values we want to determine. The type of data described ence on the failure mode and load-carrying capacity. Dry here are said to be “censored” and can be handled using the timber is probably more sensitive to crack initiation and maximum-likelihood method. An evaluation using this tech- propagation. The moisture content also influences the cre- nique will result in slightly larger mean values. ation of initial cracks in connection with nailing in the Comparing Tables 5 and 6, the results show a higher wood (mode (2) cracks due to the sheathing-to-framing load-carrying capacity for the bottom rail with the pith joints). The very few failures in mode (3) observed in oriented downwards, as compared to the bottom rail with study A are mainly due to the fact that the centre distance the pith oriented upwards (see Table 7), where the ratios between the nails in the bottom rail was 25 mm compared between the load-carrying capacity for specimens with to 50 mm in study B. This is also confirmed by the fact PD and PU are presented for study A and study B, respec- that the only two failures in mode (3) happened in speci- tively. In viewing the ratios, the different numbers of mens where the nail distance was 50 mm. specimens tested within the same set regarding the pith At the evaluation of the failure loads (mean, standard orientation of the bottom rail should be kept in mind. deviation and coefficient of variation) of the different Especially, it should be noted that the results given in the modes in Tables 5 and 6, it has not been considered that column for study A are very uncertain due the very small the capacity of each test specimen is determined by the number of tests with pith oriented upwards in that study. failure mode exhibiting the lowest capacity value of the Also, some failure modes in both studies only appear in a three possible failure modes. Thus, the failure loads of the few cases. However, a general conclusion from Table 7 The IES Journal Part A: Civil & Structural Engineering 93
might be possible to give the saying that the load-carrying capacity is about 5%–10% higher if the pith in the bottom rail is oriented downwards. One of the main reasons for End 1 End 2 that is the cupping shape of the bottom rail that occurs after drying. For further details, see Section 5 below. 3/23.1 2/24.5 3/18.5 2/17.0 2/23.0 2/23.0 2/19.3 2/21.9 2/27.1 20 Failure mode/ load Also, by comparing the two studies A and B in Tables 5 and 6, respectively, it is found that the load-car- rying capacities of the specimens from study B are gener- ally somewhat lower than the corresponding ones found End 1 End 2 in study A (see Table 8). The general comments regarding
) is given. For failure mode (2), the length Table 7 with respect to the number of tests also apply to 2/20.3 2/19.9 11 2/23.0 Failure mode/ load this table (especially concerning the last column in crack1 b Table 8). The difference in failure load between the stud- 12 3/18.9 22 2/16.5 12 il ( ies refers only to the brittle failure modes 1 and 2, and not to the ductile failure mode (3). The fact that the load-car-
End 1 End 2 rying capacity in general is found to be higher in study A than in study B for the splitting modes may be due to the 1/22.0 23 37 2/17.1
Failure mode/ load difference in: (1) boundary conditions; (2) moisture con- tent; (3) nail distance; (4) planeness of the bottom rail; 18 2/25.5 17 1/18.6 44 60 2/18.8 and (5) loading rate. The more rigid boundary conditions in study A will
End 1 End 2 render higher failure loads, because the straining of the bottom rail is more equally distributed along its whole 1/21.1 37 15 2/19.7 22 2/17.1 1/14.9 49 28 2/17.2 2/20.6 16 14 1/30.6 46 length. This is a natural effect for brittle failure loads, but Failure mode/ load not for ductile ones. The lower moisture content in study B will increase the tendency for splitting failure and, therefore, lower the failure load. For small nail distances,
End 1 End 2 failures in mode (3) will be reduced or even eliminated, Study B Study A but failures in mode (2) (splitting along the edge side of
the rail) will increase. More ductile failures (mode (3)) in 1/14.8 63 41 2/20.1 1/7.93 42 70 1/17.4 63 46 2/22.2 1/11.8 58 1/11.9 1/10.8 45 48 1/13.8 41 35 2/26.3 26 13 2/16.2 1/14.7 48 44 1/15.5 35 31 1/28.9 69 64 1/17.9 2/21.2 22 27 2/21.8 20 16 2/27.1 5 1/13.5 45 40 2/15.4 2/21.9 16 Failure mode/ load study B, especially for series 2 and 3, as observed from Table 8, will lower the mean values for the other failure modes 1 and 2. The un-planeness or the cupping shape of the bottom rail due to drying will cause initial cracking at End 1 End 2 the bottom side of the rail when the anchor bolts are tight- ened to the bottom rail if the pith is oriented upwards; for 3/20.1 1/18.2 1/19.2 2/18.1 1/21.0 1/22.4 57 52 1/21.8 Failure mode/ load further details, see Section 5 below. This will decrease the
53 1/24.3 67 failure load for mode (1) and also make the bottom rail more flexible. In both studies, the bottom rails were fairly ) is given. End 1 and End 2 indicate the two bottom rail ends, but no distinction is made here between them. All distances and crack lengths are given plane, but if there was any difference, the plainness in End 1 End 2
crack2 study B was higher. In general, a clear difference between b 8.7 the ratios for PD and PU cannot be observed in Table 8. 1/19.7 3/1 1/21.1 1/14.3 1/15.5 1/12.1 1/17.7 Failure mode/ load The higher load or displacement rate in study B will Series 1 Series 2 Series 3
56 1/17.4 53 58 1/14.0 increase the failure loads relatively to those in study A. From Table 8, it is obvious that the failure load, essen- tially in all tests, is higher in study A than in study B. This End 1 End 2 effect of increased failure load of the order of 10%–20% is then due to the more rigid boundary conditions, the 1/10.2 1/11.0 1/14.3 1/11.8 1/10.8 1/7.22 1/9.30 Failure mode/ load higher moisture content, and the smaller nail distances used in study A in series 2 and 3. In fact in series 1, where a nails distance of 50 mm as used in study B was consid- Set 1 Set 2 Set 3 Set 4ered, the Set 1 series average Set 2 was quite close Set 3 to a value Set 1 of 1. Set 2
End 1 End 2 However, this effect is smaller than it would have been if the same low displacement rate had been used in study B Specimens related to both study A and study B are shown. For failure mode (1), the distance between the vertical crack and the loaded edge of the bottom ra 1/9.98 63 47 1/9.73 1/9.71 1/10.2 1/9.77 1/5.14 1/13.6 62 35 1/10.9 57 57 1/12.9 Failure mode/ load 1/12.3 1/12.5 1/11.7 60 55 1/11.7 58 54 2/21.0 15 13 2/23.8 12 of the horizontal crack before it changes direction ( Table 3. Measured crack data for specimens with the pith oriented upwards (PU). in mm, whilst the failure load is given in kN. 1/6.31 as in study A. Even if it is not possible to tell, the main 94
Table 4. Measured crack data for specimens with the pith oriented downwards (PD).
Series 1 Series 2 Series 3
Failure Set 1Failure Set 2Failure Set 3Failure Set 4Failure Set 1Failure Set 2Failure Set 3Failure Set 1Failure Set 2 mode/ mode/ mode/ mode/ mode/ mode/ mode/ mode/ mode/ load End 1 End 2 load End 1 End 2 load End 1 End 2 load End 1 End 2 load End 1 End 2 load End 1 End 2 load End 1 End 2 load End 1 End 2 load End 1 End 2
Study A 1/8.43 57 43 1/11.4 65 47 1/17.2 44 70 1/21.3 63 1/12.5 66 56 1/21.5 45 31 2/31.4 22 3/15.1 2/28.2 1/10.5 55 68 1/12.8 64 40 1/14.8 58 60 3/20.7 1/14.5 63 51 1/24.0 54 35 1/33.2 66 70 1/18.6 2/26.9 1/12.4 57 64 1/15.9 45 1/19.6 49 1/19.9 38 1/19.3 56 54 1/21.6 36 33 1/31.9 71 37 2/20.5 11 1/28.8 17 17 1/12.4 51 53 1/11.9 48 60 1/18.6 28 1/23.4 56 1/17.3 61 65 1/17.2 68 51 1/29.8 58 1/23.7 30 12 1/13.6 50 62 1/13.4 58 64 1/18.5 50 1/29.9 24 1/17.1 56 88 1/18.9 46 1 2/27.1 13 1/22.5 64 60 2/33.4 18 1/12.3 54 47 1/12.9 42 65 1/18.7 60 2/28.6 1/17.9 60 60 2/23.6 20 1/26.2 49 30 2/23.7 2/29.5 10 1/12.7 63 47 1/18.4 56 50 1/15.4 55 54 1/20.5 62 1/15.3 54 45 1/21.7 49 53 2/27.8 17 2/24.5 1/28.0 15 30 Caprolu G. 1/13.9 1/10.9 61 1/16.1 46 58 1/17.1 60 60 1/14.4 48 61 1/17.4 54 2/25.6 31 2/23.9 2/29.4 17 1/22.3 21 21 1/29.1 34 Study B 1/8.61 1/11.5 1/18.9 2/20.7 21 1/22.5 41 2/24.5 39 3/19.7 2/26.5
1/10.9 1/14.8 1/17.8 1/22.0 1/15.7 25 54 2/7.70 21 2/28.8 22 1/18.3 2/26.7 al. et 1/12.9 1/13.2 3/20.1 3/22.0 1/16.7 43 1/17.3 44 39 2/27.5 18 2/19.4 3/24.8 1/8.71 1/11.6 1/18.1 3/21.4 1/13.2 44 1/17.4 24 44 2/21.5 37 1/13.3 3/22.5 1/9.10 1/12.5 2/16.7 1/25.0 1/16.2 41 53 1/18.5 29 44 1/23.5 43 2/18.9 2/24.8 1/12.6 1/11.8 1/16.7 3/25.2 1/11.7 48 1/21.0 53 62 3/21.6 3/19.2 3/22.0 1/8.24 1/15.6 3/20.2 3/20.0 1/9.01 45 49 1/18.4 61 57 3/23.0 1/16.1 2/23.8 1/10.9 50 63 1/17.0 58 3/16.7 3/20.2 1/15.6 50 58 1/20.2 61 3/19.4 2/20.2 3/19.2
Specimens related to both study A and study B are shown. For failure mode (1), the distance between the vertical crack and the loaded edge of the bottom rail (bcrack1 ) is given. For failure mode (2), the length of the horizontal crack before it changes direction (bcrack2 ) is given. End 1 and End 2 indicate the two bottom rail ends, but no distinction is made here between them. All distances and crack lengths are given in mm, whilst the failure load is given in kN. Table 5. Results from testing of specimens with the pith oriented upwards (PU).
Mean failure load per failure mode
All failure modes (1) (2) (3) r Number of tests per 0,v mean value per 3 failure mode failure mode [kg/m ] v
Number Mean Stddev CoV Mean Stddev CoV Mean Stddev CoV Mean Stddev CoV mean Engineering Structural & Civil A: Part Journal IES The Series Set of tests [kN] [kN] [%] [kN] [kN] [%] [kN] [kN] [%] [kN] [kN] [%] (1) (2) (3) All (1) (2) (3) value [%]
Study A 1a 1 2 12.6 1.34 10.6 12.6 1.34 10.6 2 0 0 394 394 13.9 2 2 11.3 0.54 4.82 11.3 0.54 4.82 2 0 0 368 368 12.2 3 2 17.0 5.73 33.8 12.9 21.0 1 1 0 365 365 365 13.1 4 2 24.1 0.35 1.46 24.3 23.8 1 1 0 397 376 418 13.1 2 1 2 21.5 0.47 2.17 21.5 0.47 2.17 020426 426 13.5 2 2 21.2 0.85 4.01 21.2 0.85 4.00 020398 398 13.1 3 2 28.9 2.50 8.67 30.6 27.1 1 1 0 427 424 430 13.4 3 1 1 19.9 19.9 010312 312 12.1 2 1 27.1 27.1 010380 380 12.7 All Mean value 385 373 403 13.0 Study B 1 1 8 9.49 2.59 27.3 9.49 2.59 27.3 8 0 0 397 397 11.9 2 8 10.6 2.04 19.2 10.5 2.04 19.4 8 0 0 390 390 10.9 3 8 17.1 2.77 16.2 16.8 3.12 18.5 18.7 7 0 1 409 412 384 10.7 4 8 19.4 2.68 13.8 19.4 3.10 16.0 18.1 20.1 6 1 1 422 428 415 394 11.1 2 1 7 12.2 2.42 19.8 12.2 2.42 19.8 7 0 0 405 405 9.61 2 8 16.9 2.56 15.1 16.6 2.87 17.3 17.5 2.38 13.6 5 3 0 360 370 343 12.4 3 8 22.6 4.07 18.0 23.2 5.21 22.5 22.2 3.87 17.4 3 5 0 416 420 419 11.6 3 1 8 18.6 2.23 12.0 17.9 18.6 2.62 14.0 18.9 1 6 1 379 363 382 375 11.6 2 8 21.3 2.66 12.5 21.4 2.77 12.9 20.8 3.24 15.5 0 6 2 402 401 406 12.2 All Mean value 398 398 392 390 11.3
Failure modes: (1) splitting along the bottom side of the rail; (2) splitting along the edge side of the rail; (3) yielding and withdrawal of the nails in the sheathing-to-framing joints. r0, v ¼ dry density with respect to volume at v ¼ moisture content. aSeries 1 of study A had a nails distance of 50 mm instead of 25 mm as the other two series of study A. 95 96
Table 6. Results from testing of specimens with the pith oriented downwards (PD).
Mean failure load per failure mode
All failure modes (1) (2) (3) r Number of tests per 0,v mean value per failure mode failure mode [kg/m3] Number Mean Stddev CoV Mean Stddev CoV Mean Stddev CoV Mean Stddev CoV v mean Series Set of tests [kN] [kN] [%] [kN] [kN] [%] [kN] [kN] [%] [kN] [kN] [%] (1) (2) (3) All (1) (2) (3) value [%]
Study A 1a 1 8 12.0 1.77 14.8 12.0 1.77 14.8 8 0 0 418 418 13.2 2 8 13.5 2.51 18.6 13.5 2.51 18.6 8 0 0 372 372 12.6 3 8 17.4 1.76 10.1 17.4 1.76 10.1 8 0 0 380 380 12.9 4 8 22.8 4.42 19.4 22.1 4.40 19.9 28.6 20.7 6 1 1 398 394 432 388 12.4 2 1 8 16.0 2.24 14.0 16.0 2.24 14.0 8 0 0 424 424 13.0
2 8 20.7 2.61 12.6 20.3 2.53 12.4 23.6 7 1 0 389 391 372 12.5 Caprolu G. 3 8 29.1 2.87 9.85 30.3 3.07 10.1 28.0 2.49 8.90 4 4 0 419 420 417 13.4 3 1 9 21.6 3.09 14.3 21.7 2.21 10.2 23.1 1.80 7.77 15.1b 4 4 1 348 359 351 288 12.6 2 8 29.2 1.91 6.54 28.6 0.55 1.92 29.5 2.43 8.24 3 5 0 420 414 424 13.1 All Mean value 396 397 399 388 12.9 Study B al. et 1 1 8 10.3 1.84 18.0 10.2 1.84 18.0 8 0 0 392 392 12.2 2 8 13.5 2.06 15.3 13.5 2.06 15.2 8 0 0 383 383 10.9 3 8 18.2 1.47 8.08 17.9 0.92 5.13 16.7 19.0 2.00 10.4 4 1 3 426 428 461 411 10.9 4 8 21.8 1.65 7.57 23.5 2.12 9.05 20.7 21.4 1.32 6.18 2 1 5 406 430 391 399 10.9 2 1 7 14.0 2.84 20.3 14.0 2.84 20.2 7 0 0 397 397 9.00 2 8 17.9 4.48 25.0 19.3 1.94 10.0 7.70c 7 1 0 397 386 345 12.7 3 8 23.7 3.16 13.3 23.5 25.6 3.26 12.8 21.3 1.83 8.56 1 4 3 415 417 416 413 11.6 3 1 8 18.1 2.32 12.8 15.9 2.53 15.9 19.5 0.62 3.17 19.4 0.35 1.80 3 3 2 364 378 345 369 11.4 2 8 23.8 2.50 10.5 25.4 1.40 5.52 22.1 2.38 10.3 0 4 4 414 424 404 11.9 All Mean value 399 401 397 399 11.3
Failure modes: (1) splitting along the bottom side of the rail; (2) splitting along the edge side of the rail; (3) yielding and withdrawal of the nails in the sheathing-to-framing joints. r0, v ¼ dry density with respect to volume at v ¼ moisture content. aSeries A of study A had a nails distance of 50 mm instead of 25 mm as the other two series of study A, except for one specimen in series 3 where the distance was 50 mm by mistake. bThis specimen, by mistake, had a nails distance of 50 mm instead of 25 mm as the other specimens of the same series. This is the reason for a ductile failure. cNot taken into account. Probably, this specimen had some defect since if we compare with the same series in Table 7, the failure load is too low. Not included in Table 8. The IES Journal Part A: Civil & Structural Engineering 97
Table 7. Ratio between the load-carrying capacities of specimens with different pith orientations of the bottom rail within study A and study B, respectively.
Study A: ratio Study B: ratio PD/PU per failure mode PD/PU per failure mode
Series Set Washer size [mm] Bolt position Distance s [mm] All (1) (2) (3) All (1) (2) (3)
1140 40 15 b/2 40 0.95 0.95 1.08 1.08 260 60 15 b/2 30 1.19 1.19 1.28 1.28 380 70 15 b/2 20 1.02 1.35 1.07 1.07 1.02 4 100 70 15 b/2 10 0.94 0.91 1.20a 1.13 1.21 1.14 1.06 Series average 1.03 1.10 1.20 – 1.14 1.16 1.14 1.04 2140 40 15 3b/8 25 0.74c 1.14 1.14a 260 60 15 3b/8 15 0.98 1.11 1.06 1.16 0.44b 380 70 15 3b/8 5 1.01 0.99 1.03 1.05 1.01 1.15 Series average 0.91 0.99 1.07 – 1.08 1.12 1.15 – 3140 40 15 b/4 10 1.09 1.09 0.97 0.89 1.05 1.03 260 60 15 b/4 0 1.08 1.09 1.12 1.19 1.06 Series average 1.09 1.09 1.09 – 1.05 0.89 1.12 1.05 Total average 1.01 1.06 1.12 – 1.10 1.06 1.14 1.05
PD ¼ pith downwards, PU ¼ pith upwards. aThese two values (series 1, set 4 and series 2, set 1) are more accurate than the others, because the number of specimens that failed in the same mode is equal for PD and PU. bThis exceptional value is not included in the average value. cAlso, this value could be regarded as exceptional, but it is still included in the average value. One reason for these exceptional values could be the very different numbers of specimens tested within the same set. reason for the observed load increase might be the differ- example, the linear trend line for group “b/4” in the figure ence in boundary conditions. is based only on two data and, therefore, the value R2 ¼ 1 From Figures 9–12, the relationship between failure is not meaningful. In each graph, four different curves are load and distance s from the washer edge to the loaded visible: three linear trend lines, one per series tested, and edge of the bottom rail is shown for study A and study B, a polynomial regression type of second order for all data respectively. The results are grouped with respect to the tested. For all cases, a good correlation is obtained position of the anchor bolts along the bottom rail width between the distance s and the failure load. This is (b) and are separated with respect to the pith orientation. spotlighted by a coefficient of determination R2 ranging It should be noted that Figure 10 is based on very few from 0.71 to 0.81, for a polynomial regression type of sec- data and, therefore, a statistical treatment of the data is ond order, meaning that there is a strong influence of the not reliable, and for some data, not even meaningful. For parameter s on the final failure load. Looking at each
Table 8. Ratio between the load-carrying capacities of specimens from study A compared to study B for different pith orientations.
Ratio study A/study B Ratio study A/study B (PD) for failure mode (PU) for failure mode
Series Set Washer size [mm] Bolt position Distance s [mm] All (1) (2) (3) All (1) (2) (3)
1140 40 15 b/2 40 1.17 1.17a 1.33 1.33 260 60 15 b/2 30 1.00 1.00a 1.07 1.07 380 70 15 b/2 20 0.95 0.95 1.00 0.77 4 100 70 15 b/2 10 1.04 0.94 1.38a 0.97 1.24 1.25 1.31a Series average 1.04 1.02 1.38 0.97 1.16 1.11 1.31 – 2140 40 15 3b/8 25 1.14 1.14 1.76 260 60 15 3b/8 15 1.16 1.05a 1.25 1.21 380 70 15 3b/8 5 1.23 1.29 1.09a 1.28 1.32 1.22 Series average 1.18 1.16 1.09 – 1.43 1.32 1.22 – 3140 40 15 b/4 10 1.19 1.36 1.18 0.78 1.07 1.11a 260 60 15 b/4 0 1.23 1.16 1.27 1.27 Series average 1.21 1.36 1.17 0.78 1.17 1.11 1.27 – Total average 1.14 1.18 1.21 0.88 1.25 1.18 1.27 –
PD ¼ pith downwards, PU ¼ pith upwards. aThese seven values (series 1, sets 1, 2 and 4; series 2, sets 2 and 3; and series 3, set 1) are more accurate than the others, because the number of specimens that failed in the same mode is equal for PD and PU. 98 G. Caprolu et al.
Figure 9. Failure load versus distance s from the washer edge Figure 11. Failure load versus distance s from the washer edge to loaded edge of the bottom rail. All test results are from study to loaded edge of the bottom rail. All test results are from study A (PD). The vertical line shows a border between failure modes. B (PD). The vertical line shows a border between failure modes. group, the linear models also give good statistical results, additional parameter could be the size of the washer. In spotlighted by a coefficient of determination R2 ranging Figure 13, the relationship between failure load and dis- from 0.56 to 0.87, except for series 3 in Figure 12, where tance s is shown, but in this case, the results are grouped a coefficient of determination R2 of 0.26 was found, prob- with respect to the washer size. ably due to data points that fall close to a horizontal line It is evident from Figures 9–13 that for a given anchor or a small variation of the data in the x-coordinate. Due to bolt position, the failure load increases when the distance a small number of tests, it is not possible to state the same s decreases. conclusions (Figure 10). The overlap of the four curves in In Table 9,theR2 and the standard error of the esti- the graph is considered as a signal that the distance s could mate (SEE) values for each trend line showed in Figures 9– be used as a unique parameter for giving good predictions 12 are summarised. of the failure load. This is not the case for Figure 11, where the data seem to belong to three separate groups, 4. Analysis meaning that in this case the correlation between the dis- Two types of analyses are here presented, one evaluating tance s and the failure load is not so strong and an addi- the failure load of the bottom rail for modes (1) and (3) tional parameter is needed to predict the failure load. This based on a strength-of-materials approach, and one basic
Figure 10. Failure load versus distance s from the washer edge Figure 12. Failure load versus distance s from the washer edge to loaded edge of the bottom rail. All test results are from study to loaded edge of the bottom rail. All test results are from study A (PU). The vertical line shows a border between failure modes. B (PU). The vertical line shows a border between failure modes. The IES Journal Part A: Civil & Structural Engineering 99
Figure 13. Failure load versus distance s from the washer edge to loaded edge of the bottom rail. All test results are from study B (PD). The vertical line shows a border between failure modes. statistical evaluation concerning the significance of deci- sive parameters for determining the failure load.
4.1. Analytical failure load For failure mode (1), the bottom rail is modelled as a can- Figure 14. Cantilever beam used as a model for mode (1) failure. tilever beam fixed at the crack position, as shown in Figure 14. The failure load (P) for bending and shear fail- general applicable to cantilevers with such a small span- ure is then given by to-depth ratio and that in Equation (1) the tensile strength, not the bending strength, is used. 2 Lh For ft,90 a value of 2.5 MPa was used, according to P ¼ ft;90; ð1Þ 6le Serrano et al. (2011), and for fv a mean value of 6.0 MPa 2 was used, calculated according to JCSS (2006). P ¼ Lhf ; ð2Þ 3 v The results of the analysis for failure mode (1) are shown in Figures 15–18 for study A and study B and for where ft,90 is the tensile strength perpendicular to the grain different pith orientations. Note that in these figures all of the timber, fv is the shear strength of the timber, L is the test results are included, regardless of the failure mode. length of the bottom rail; h is the depth of the bottom rail Four different values of le were used as in Caprolu et al., and le is the cantilever span relative to failure mode (1) “Analytical and Experimental Evaluation” (2012), rang- according to Figure 14. Note that the Euler–Bernoulli ing from le ¼ 15 þ s to le ¼ 30þs (unit in mm), indicating beam theory, that these equations are based on, is not in that the “free” distance s, which takes into account both
Table 9. R2 and SEE values for the trend lines of the relationship between failure load and distance s showed in Figures 9–12.
R2 and SEE values for linear trend lines per series tested R2 and SEE values for polynomial regression b/2 3b/8 b/4 type of second order per study
Study R2 SEE R2 SEE R2 SEE R2 SEE
Study A (PD) 0.67 2.92 0.81 2.68 0.70 2.61 0.81 3.08 Study A (PU) 0.68 3.51 0.65 2.68 1.00 – 0.73 3.38 Study B (PD) 0.87 1.73 0.56 3.59 0.61 2.41 0.71 2.78 Study B (PU) 0.75 2.55 0.67 3.07 0.26 2.45 0.71 2.81
PD ¼ pith downwards, PU ¼ pith upwards. Values based on few data and on only two x-values; therefore, a statistical treatment of the data is not reliable. 100 G. Caprolu et al.
Figure 15. Results of the analysis for failure mode (1). Results Figure 18. Results of the analysis for failure mode (1). Results are from study A (PD). are from study B (PU).
the bolt position and the washer size, needs to be increased by 15–30 mm in order to represent the position of the clamped end, i.e. represent the “real” cantilever span. It seems that the shape of the curves in Figures 15–18 agrees reasonably well with the test results, especially for larger values of s, indicating that other failure modes are dominant for small s-values. It is noted that the test results in Figure 16 with respect to pith oriented upwards in study A are very few. There is a better agreement for study A (Figure 15) and a greater scatter for the results in study B (Figures 17 and 18). The best fit concerning the “increased span length” is about 20–25 mm for study A and 25– 30 mm for study B. The failure load due to a possible shear failure would be of the order of 160 kN. Even though the model is not Figure 16. Results of the analysis for failure mode (1). Results quite realistic, it is evident that this failure mode can be are from study A (PU). excluded. For failure mode (3), the Johansen (1949) theory is used. The decisive failure mode is a plastic hinge in the nail in the bottom rail, for which the failure load is given by "#sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f ; t d 4bð2 þ bÞM P ¼ h s s 2bð1 þ bÞþ y b þ P : þ b 2 rope 2 fh;sdts ð3Þ
If we assume a plastic hinge also in the sheathing, the failure is given by sffiffiffiffiffiffiffiffiffiffiffi 2b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ¼ 2M f ; d þ P ; ð4Þ 1 þ b y h s rope
Figure 17. Results of the analysis for failure mode (1). Results where ts is the sheathing thickness, fh,s and fh,w are the are from study B (PD). embedment strength of the hardboard sheathing and of the The IES Journal Part A: Civil & Structural Engineering 101
CoV ¼ 12.4% based on 17 results with PD, and umean ¼ 11:0 mm and CoV ¼ 13.0% based on five results with PU. Note that in study A, the boundary conditions were partially fixed according to Figure 2(a), and in study B, they were hinged according to Figure 2(b). The angle then becomes, respectively,
14:6 a ; ¼ arctan ¼ 52:3 ; ð7Þ A PD 8:49 þ 2:80 11:8 a ; ¼ arctan ¼ 46:3 ; ð8Þ B PD 8:49 þ 2:80
11:0 a ; ¼ arctan ¼ 44:3 ; ð9Þ B PU 8:49 þ 2:80
where the subscripts A and B refer to the studies, and PD Figure 19. A simple model for estimating the rope effect. and PU to the pith orientation. The contribution from the rope effect then becomes, respectively, wood, respectively, d is the fastener diameter, My is the 3 fastener yield moment My ¼ fyd /6, b ¼ fh,w/fh,s is the ratio between the embedment strengths of the members and Prope;A;PD ¼ sinð52:6 ÞFax ¼ 0:79Fax; ð10Þ Prope is the load attributable to the rope effect (withdrawal Prope;B;PD ¼ sinð46:3 ÞFax ¼ 0:72Fax ð11Þ of the fastener). The following mean values have been used: (1) with respect to the sheathing: thickness ts ¼ Prope;B;PU ¼ sinð44:3 ÞFax ¼ 0:70Fax; ð12Þ 3 8 mm, density rs ¼ 900 kg/m , embedment strength fh,s ¼ 2 83.6 N/mm ; (2) with respect to the bottom rail: where F ¼ f dt is the axial withdrawal capacity of ¼ r ¼ 3 ¼ ax ax pen tw 42 mm (nail length in wood), w 420 kg/m , fh,w the fastener, where t ¼ 30.5 mm is the point side pene- 2 ¼ pen 27.6 N/mm ; and (3) with respect to the nail: d 2.1 mm, tration length or the length of the threaded part in the point ¼ 2 fy 900 N/mm . According to Figure 19, a plastic hinge side member. According to Traeinformation (2009), the is formed in the sheathing and, therefore, Equation (4) characteristic axial withdrawal capacity for annual ringed will be used in the evaluation of the test results. nails is expressed as The contribution from the rope effect can in a simpli- fied way be estimated as follows. Consider Figure 19 r 2 k 3 where a plastic hinge is formed both in the bottom rail f ; ¼ 6 MPa; r in ½kg=m ; ð13Þ ax k 350 k and in the sheathing at a distance xw and xs, respectively. The displacement of the sheathing (u) can be approxi- where 350 kg/m3 is the reference value for the characteris- mated as equal to the stroke of the head of the testing tic density. machine (this is an upper limit value). This displacement Note that this value might be reduced for laterally a causes a withdrawal of the nail and an angle to be deformed cases as shown in Figure 19, where plastic embed- formed between the two plastic hinges. According to ding displacements take place, i.e. in the area between xw Bijtka and Blass (2002), the locations of the two plastic and xs, cf. Bijtka and Blass (2002). moments are given by In order to compare with our results, we transform this sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi equation to give mean values. In Equation (13) the refer- ence density represents wood of quality C24. To get the ¼ 4Myfh;s ; ð Þ xw 5 mean value for the withdrawal capacity corresponding to ðfh;w þ fh;sÞfh;wd Equation (13), both the factor and the density expression fh;w in the equation need to be changed. The density expres- xs ¼ xw: ð6Þ fh;s sion is changed so that both the numerator and denomina- tor refer to mean values. The factor is changed as follows. 3 3 With My ¼ fyd =6 ¼ 900 2:1 =6 ¼ 1389 Nmm, we If there is a large data series behind the formula, then the obtain xw ¼ 8:49 mm and xs ¼ 2:80 mm. The mean value statistical coefficient is kp ¼ 1.64, and if we assume a for the displacement u at maximum load in study A was rather large scatter, the coefficient of variation is CoV ¼ umean ¼ 14:6 mm and CoV ¼ 3.87% based on two test 20%. Then, the mean value could be calculated as results with PD, and in study B, umean ¼ 11:8 mm and xmean=xk ¼ 1=ð1 kp CoVÞ 1:5 and the mean 102 G. Caprolu et al.
capacity becomes
r 2 mean 3 f ; ¼ 9 MPa; r in ½kg=m : ð14Þ ax mean 420 mean
The analytical results are then given by Panal,mean,PD ¼ 17.0 kN for study A with PD, and Panal,mean,PD ¼ 16.3 kN and Panal,mean,PU ¼ 16.1 kN for study B with PD and PU, respectively. The results of the analyses for failure mode (3) are shown in Figures 20–22 together with the test results. The mean value of the test results of study A with PD (Figure 20) is Ptest,mean,PD ¼ 17.9 kN. The corresponding values for study B with PD (Figure 21)isPtest,mean,PD ¼ 21.0 kN, and with PU (Figure 22), Ptest,mean,PU ¼ 19.9 kN. Figure 20. Results of the analysis for failure mode (3). Results are from study A (PD). 4.2. Statistical significance of decisive parameters determining the failure load In study A we observed that the distance s was the decisive parameter, but also that the pith position had an influence. To verify these findings, study B was conducted. Here we will, from a statistics point of view, evaluate the significance of these influencing parameters determining the failure load. According to Tables 1 and 2, the experimental pro- grammes contain the variation of mainly two parameters, the distance s with eight variations (bolt position and washer size) and the pith orientation with two variations (PD and PU). According to Montgomery (2009), this type of experiment is well suited for a statistical analysis based on factorial design in order to evaluate the possible influ- ence of those parameters and their interaction on the fail- ure load. The effect of a parameter (a so-called factor) is defined to be the change in response produced by a change Figure 21. Results of the analysis for failure mode (3). Results are from study B (PD). in the variation (or the so-called level) of the parameter. Here, a significance level of a ¼ 0.05 was used. The so-called P-value was used in order to evaluate if a factor had an influence or not on the outcomes. The P-value may be formally defined as the smallest level of significance that would lead to rejection of the null hypothesis. The null hypothesis is rejected when the P-value is less than the predetermined significance level a, which in our case is 0.05. The null hypothesis for this test was that the distance s, the pith orientation and the interactions of these factors did not have any influence on the failure load. The software MINITAB was used in order to carry out the analysis. Regarding study A, the statistical analysis rendered a P-value of 0.000. For the distance s, P ¼ 0.81 for the pith orientation and P ¼ 0.33 for the influence of the interac- tion of these two parameters on the failure load. Thus, in this study, the only influencing parameter was the distance 2 Figure 22. Results of the analysis for failure mode (3). Results s and this influence was validated by a basic R -value of are from study B (PU). 85% for the linear model used. The IES Journal Part A: Civil & Structural Engineering 103
Regarding study B, the corresponding results were may also be caused by the anisotropic material properties P ¼ 0.000 (distance s), P ¼ 0.002 (pith orientation) and in the radial–tangential plane of the timber. P ¼ 0.92 (interaction). In this study, both distance s and When the anchor bolt in Figure 23(a) is tightened, the pith orientation have an influence on the failure load washer will rest on its edges, creating a bending moment (R2-value ¼ 75%). with compression stresses at the level of the pith. When the anchor bolt in Figure 23(b) is tightened, the timber will rest on its edges, creating a bending moment with ten- sile stresses at the bottom of the rail. Adding these initial 5. Discussion crosswise bending stresses with the bending stresses In Figures 4 and 5, the percentage of the three different caused by the sheathing-to-framing fasteners, it becomes failure modes is graphically shown for the series tested obvious that orienting the pith downwards is more favour- for study A and study B, respectively. It is noted that the able than orienting upwards. failure modes are strongly dependent on the distance s Another observation is that, for the test series with the from the washer edge to the loaded edge of the bottom pith oriented downwards, the measured load-carrying rail. For s 25 mm, only failure mode (1) occurs. The capacities of the specimens from study B are generally reason for this failure mode is that the bottom rail is sub- somewhat lower than the corresponding ones found in jected to crosswise bending giving rise to tensile stresses study A. This is quantified in Table 8. For the bottom rail along the bottom side of the rail. For small values of the with pith oriented downwards, the difference in load-car- distance s, failure mode (2) (splitting along the edge side rying capacity is about 20% higher for specimens of study of the rail) and mode (3) (yielding and withdrawal of the A for the splitting modes (1) and (2), but lower for ductile sheathing-to-framing joints) dominate. failure mode (3). The same seems to be true for bottom The results show that the splitting failure of the bot- rails with the pith oriented upwards (but the small number tom rail can be avoided by using a proper distance s, i.e. of tests in study A makes this conclusion uncertain). It is using an appropriate bolt position and washer size. If no noted that the larger nail spacing in study B caused more splitting takes place and only failure mode (3) occurs, the yielding and withdrawal failures in study B than in study plastic design method is valid. A. This fact indicates that the average failure loads for the As seen for the experimental results, the load-carrying splitting failure modes are higher than given by the test capacities of the specimens with the pith oriented upwards results and, thus, would reduce the difference between the are somewhat lower than the capacities of the specimens two studies. It is also observed that the rigid test rig in with the pith oriented downwards. This is quantified in study A induced more uniformly distributed stresses in Table 7. In general, for splitting mode (1), the failure load the nails along the bottom rail than those of study B, lead- is about 5% higher for bottom rails with the pith oriented ing to loading sharing between the nails and, therefore, a downwards than those with the pith oriented upwards. For higher load-carrying capacity. Also, the higher moisture splitting mode (2), the corresponding ratio is more than content level in study A may reduce the tendency for split- 10%. This effect with respect to the pith orientation is ting compared to that of study B. The larger initial cup- probably caused by the initial cupping due to the aniso- ping due to shrinkage in study A than in study B may also tropic shrinkage from drying, as shown in Figure 23, but have had an influence. However, it is also noted that the
Figure 23. Effect of shrinkage due to drying for specimens with pith oriented (a) downwards and (b) upwards. 104 G. Caprolu et al. loading rate was five times higher in study B than in study Three primary failure modes were found during the A, which rendered higher failure loads in study B than tests: what would have been the case if the same loading rate as in study A had been applied. This implies that the differ- Splitting of the bottom side of the rail due to cross- ence would have been even higher if this effect had not wise bending of the bottom rail. This brittle type of been present. failure occurs when a large value of the distance s is In Girhammar and K€allsner (2009), Girhammar, used. K€allsner, and Daerga (2010), Caprolu et al., “Tests on the Splitting along the edge side of the bottom rail due Splitting Failure” (2012) and Caprolu et al., “Analytical to the sheathing-to-framing joints. This brittle fail- and Experimental Evaluation” (2012), it was found that ure mode occurs for small s-values. the parameter s, denoting the distance from the washer Yielding and withdrawal of the nails in the sheath- edge to the loaded edge of the bottom rail, could be used ing-to-framing joints. This is the favourable failure for giving good predictions of the failure load. The effect mode presupposed for using the plastic design of the distance s on the failure load is evident from Fig- method. This ductile failure mode occurs in this ures 9–13. This observation, together with the influence of study when the distance s is small or when the plas- the pith orientation on the failure load according to tic capacity of the joints was not so high. (This fail- Table 7, is also confirmed by the statistical analyses. ure mode was planned to be avoided as much as However, in study A, the analysis gives only the distance possible.) s as a factor influencing the failure load and not the pith orientation. This is, from a statistical point of view, due As a result of the study, the distance s can be chosen the fact that in study A most of the specimens had the pith small enough so that brittle failures due to splitting of the oriented downwards and just a few upwards. In study B, bottom rail can be avoided. Then, the plastic design on the other hand, there were equal number of specimens method is applicable without using any hold-downs. Note with pith oriented downwards and upwards, respectively also that the load-carrying capacity of the bottom rail can and, hence, the analysis in study B gave the result that be enhanced by locating the pith downwards or being both the distance s and the pith orientation are influencing careful to plane the bottom rail surfaces and, thereby, factors for the failure load. eliminate the cupping shape. It is obvious that the distance s is the most decisive parameter, but from Figures 9–13, it can also be observed that the bolt position (Figures 9–11) and the washer size 7. Future work (Figure 13) have an influence, because the individual lines The experimental results are presented in such a way as to are separated in different ways from the trend line. How- facilitate a subsequent analytical modelling and evalua- ever, in Figure 12, it is observed that this effect is negligi- tion. A theoretical study based on a fracture mechanics ble. In study B, there were several failures due to yielding approach for the two failure modes is ongoing. There is a and withdrawal of the sheathing-to-framing fasteners, need of some additional tests to validate the theory. especially for small s-values; it is possible that this may be one of the explanations for some of the differences found in the two studies. Acknowledgements The authors declare that there are no conflicts of interest of any personal or institutional kind, and between them and the funding 6. Conclusions bodies below. Tests on the splitting failure mode and capacity of the bot- tom rail in partially anchored shear walls have been con- Funding ducted. The anchored rail was sheathed on one side and This work was supported by the County Administrative Board in was subjected to an uplifting force applied on the Norrbotten [grant number 303-2602-13 (174311)]; the Regional sheathing. Council of V€asterbotten [grant number REGAC-2013-000133 The test results show that the distance s between the (00179026)]; the European Union’s Structural Funds – The edge of the washer and the edge of the bottom rail has a Regional Fund [grant number 2013-000828 (174106)]. significant impact on the load-carrying capacity of the bottom rail and the failure mode, but also to some degree References the pith orientation of the bottom rail. Decreasing the dis- tance s increases the failure load and the pith should be Bejtka, I., and H. J. Blass. 2002. “Joints with Inclined Screws.” Paper presented at the Annual CIB-W18 Timber Structures oriented downwards. The bolt position and the size of the Meeting, Kyoto, September (Paper 35-7-4). washer also seem to influence the behaviour, but to a Caprolu, G. 2011. Experimental Testing of Anchoring Devices much less extent. for Bottom Rails in Partially Anchored Timber Frame Shear The IES Journal Part A: Civil & Structural Engineering 105
Walls (Technical Report, ISBN 978-91-7439-302-6). Lulea: ISO 3130. 1975. Wood – Determination of Moisture Content for Lulea University of Technology. Physical and Mechanical Tests. Caprolu, G., U. A. Girhammar, B. K€allsner, and H. Johnsson. ISO 3131 1975. Wood – Determination of Density for Physical 2012. “Tests on the Splitting Failure Capacity of the Bottom and Mechanical Tests. Rail Due to Uplift in Partially Anchored Timber Shear JCSS. 2006. Probabilistic Model Code: Part 3: Resistance Models. Walls.” Paper presented at the 12th World Conference on Johansen, K. W. 1949. “Theory of Timber Connections.” Paper Timber Engineering, Auckland, July 16–19. presented at the International Association of Bridge and Caprolu, G., U. A. Girhammar, B. K€allsner, and J. Vessby. 2012. Structural Engineering, Bern. “Analytical and Experimental Evaluation of the Capacity of K€allsner, B., and U. A. Girhammar. 2005. “Plastic Design of Par- the Bottom Rail in Partially Anchored Timber Shear Walls.” tially Anchored Wood-Framed Wall Diaphragms with and Paper presented at the 12th World Conference on Timber without Openings.” Paper presented at the annual CIB-W18 Engineering, Auckland, July 16–19. Timber Structures Meeting, Karlsruhe, August (Paper 38-15-7). Eurocode 5. 2004. Design of Timber Structures (prEN 1995-1- Montgomery, D. C. 2009. “Factorial Experiments.” Chap. 5 in 1:2003 Part 1-1: General – Common Rules and Rules for Design and Analysis of Experiment. New York: Wiley. Building). NAHB. 2005. Full-Scale Tensile and Shear Wall Performance EN 338. 2009. Structural Timber – Strength Classes. Testing of Light-Frame Wall Assemblies Sheathed with EN 594. 2008. Timber Structures – Test Methods – Racking Windstorm OSB Panels (Test Report 4105-008). Upper Strength and Stiffness of Timber Frame Wall Panels. Marlboro, MD: NAHB Research Center. EN 622-2. 2004. Fibreboards – Specifications – Part 2: Require- Ni, C., and E. Karacabeyli. 2002. “Capacity of Shear Wall Seg- ments for Hardboard. ments Without Hold-Downs.” Wood Design Focus 12 (2): Girhammar, U. A., and H. Juto. 2009. Testing of Cross-wise Bend- 10–17. ing and Splitting of Wooden Bottom Rails in Partially Prion, H. G. L., and F. Lam. 2003. “Shear Walls Diaphragms.” Anchored Shear Walls [in Swedish] (Technical Report, Lulea, In Timber Engineering, edited by S. Thelandersson and H. J. Sweden 2014 [originally presented as an internal report, Umea Larsen, 383–408. New York: Wiley. University, 2009]). Lulea:LuleaUniversity of Technology. Serrano, E., J. Vessby, and A. Olsson. 2012. “Modeling of Girhammar, U. A., and B. K€allsner. 2009. “Design Aspects on Fracture in the Sill Plate in Partially Anchored Shear Walls.” Anchoring the Bottom Rail in Partially Anchored Wood- Journal of Structural Engineering 138: 1285–1288. Framed Shear Walls.” Paper presented at the annual CIB- Serrano, E., J. Vessby, A. Olsson, U. A. G. Girhammar, and B. W18 Timber Structures Meeting, Dubendorf,€ Switzerland, K€allsner. 2011. “Design of Bottom Rail in Partially August (Paper 42-15-1). Anchored Shear Walls Using Fracture Mechanics.” Paper Girhammar, U. A., B. K€allsner, and P. A. Daerga. 2010. presented at the CIB-W18 Timber Structures Meeting, “Recommendations for Design of Anchoring Devices for Alghero, Sardinia, August–September (Paper 44-15-4). Bottom Rails in Partially Anchored Timber Frame Shear Traeinformation. 2009. Eurocode 5 – Beregning af Forbindelser Walls.” Paper presented at the 10th World Conference on [in Danish]. (ISBN: 978-87-90856-90-8, Traeinformation, Timber Engineering, Riva del Garda, June 20–24. Lyngby, Denmark).
Paper II
The IES Journal Part A: Civil & Structural Engineering, 2014 http://dx.doi.org/10.1080/19373260.2014.952607
TECHNICAL PAPER Splitting capacity of bottom rails in partially anchored timber frame shear walls with double-sided sheathing Giuseppe Caprolua*, Ulf Arne Girhammara and Bo K€allsnerb
aDepartment of Civil, Environmental and Natural Resources Engineering, Lulea University of Technology, Lulea, Sweden; bDepartment of Building Technology, Linnaeus University, Vaxj€ o,€ Sweden (Received 5 June 2014; accepted 5 August 2014)
In partially anchored shear walls, the leading stud is not fully anchored against the uplift; hence the uplifting force is resisted by the sheathing-to-framing joint along the bottom rail. These joint forces will introduce crosswise bending and shear in the bottom rail leading to possible splitting failures. To design partially anchored shear walls, plastic design methods can be used and, therefore, the bottom rails must not fail in a brittle manner. In this paper, results of two experimental programmes with respect to the splitting capacity of bottom rails with double-sided sheathing due to uplift in partially anchored shear walls are presented. This was evaluated varying the distance between the washer edge and the edge of the bottom rail, and the pith orientation of the bottom rail. The experimental results show two brittle failure modes for the bottom rail: (1) a crack opening from the bottom surface of the bottom rail and (2) a crack opening from the edge surface of the bottom rail. The results indicate that the distance from the edge of the washer to the edges of the bottom rail has a decisive influence on the load-carrying capacity and failure modes of the bottom rail. Keywords: timber shear walls; partially anchored; sheathing-to-framing joint; bottom rail; crosswise bending; splitting of bottom rail
1. Introduction sided sheathing has earlier been presented by Caprolu Shear walls are structural elements designed to resist the et al. (2014). For a more detailed background on this effects of lateral loads, like wind and seismic loads, acting topic, the reader is referred to that paper. on a building. In Eurocode 5 (2004), two parallel methods The detailed experimental background for this study is for the design of shear walls are given: one analytical found in Girhammar and Juto (2009), here called study A, method with a theoretical background, which can only be and Caprolu (2012), called study B. The two studies differ applied to fully anchored shear walls, and one with an with respect to the boundary conditions of the test set-ups. experimental background using the test protocol accord- Study A has been partly and preliminary evaluated in Gir- € € ing to EN 594 (2008), where the boundary conditions cor- hammar and Kallsner (2009) and Girhammar, Kallsner, respond to partially anchored shear walls. and Daerga (2010), where it was found that the distance In fully anchored shear walls, the uplift of the leading between the edge of the washer and the loaded edge of the stud is prevented by some kind of hold down, while in bottom rail has a decisive influence on the capacity and partially anchored shear walls, the stud at the loaded end the failure mode of the bottom rail. It was also found that of the wall is free to move vertically and the bottom rail is the pith orientation had an influence on the results. In anchored to the substrate. order to take into account these results and investigate the In order to be consistent, a unified design method is behaviour in more detail, the study B was conducted. The needed. K€allsner and Girhammar (2005)havepresenteda test results of study B were preliminary presented by Cap- new plastic design method for shear walls in the ultimate rolu et al. (2012a). As already mentioned, a corresponding limit state, which can be applied to both fully and partially study for shear walls with single-side sheathing has earlier anchored shear walls. The model covers only static loads been presented in Caprolu et al. (2014). and can be used only if the plastic behaviour of the sheath- The aim of the present study is to evaluate the splitting ing-to-framing joints is ensured. The plastic design method capacity and failure modes of the bottom rail in double- leads to economic structures with great flexibility concerning sided light-frame shear walls, in order to be able to design the placement and arrangement of anchorage devices. against the problem of splitting of the bottom rail. The In this paper, shear walls with double-sided sheathing purpose of this study (study B) is also to extend and com- are studied. A parallel study on shear walls with single- pare the test results with those obtained in an earlier study
*Corresponding author. Email: [email protected]
Ó 2014 The Institution of Engineers, Singapore 2 G. Caprolu et al.
Figure 1. Test set-up and boundary conditions of sheathed bottom rails subjected to double-sided vertical uplift. (a) Boundary condi- tions of study A: the two diagonal bars partially prevent rotation of the specimen; (b) boundary conditions of study B: the two diagonal bars have been removed and a hinge is created that allows the specimen to rotate; (c) view from above of the specimen; (d) lateral view of the specimen; (e) the connection between the specimen and the steel bars connected to the hydraulic piston. In Figure 1d, the distance s is the distance between the washer edge and the edge of the bottom rail, b is the width of the bottom rail and h is the depth of the bottom rail.
(study A). The aim of the experimental studies is also to with hardboard sheets of 500 £ 900 £ 8 mm on both form the basis for a future analytical evaluation of the sides. They were usually assembled 12 24 hours before splitting capacity of the bottom rail. testing. For study B, the rails were stored in the laboratory (20 C) under plastic cover for about three months before testing. They were already cut in pieces and supplied with 2. Materials and methods a length of 900 mm; therefore, it was impossible to choose 2.1. Test specimens and material properties rails cut from the same board in order to have rails with The specimens were built by hand using rails of length similar density. The surfaces of the rails were considered 900 mm and with a cross section of 45 £ 120 mm, joined as acceptable, from a visual point of view, with regard to The IES Journal Part A: Civil & Structural Engineering 3
flatness; hence we did not consider it necessary to plane with respect to crack propagation as a basis for future the rails in order to eliminate any influence of cupping fracture mechanics studies. and possible pre-cracking, when tightening the anchor In study A, 10 specimens were planed and tested for bolts. However, the bottom rails were stored in the labora- each set; the intention was to orient the pith downwards tory for another three months and, unfortunately, we for- (PD) for all tests, but by mistake 2 specimens in set 2 and got to observe that some cupping had occurred. 3 specimens in set 3 had the pith oriented upwards (PU). Therefore, we could observe that some pre-cracks The results indicated a systematic influence of the two occurred when the bolts were tightened, which means that pith orientations. Hence in study B, 16 specimens were a small visible vertical crack was created at the end of the tested for each set, 8 with PU and 8 with PD. bottom rail. This was observed in sets 3 and 4 of study B. In study A, a total of 40 specimens were tested. The The details of the test specimens were as follows: specimens were divided into four different sets, according to the washer size. Knowing the anchor bolt position and Bottom rail: Spruce (Picea Abies), C24 according to the washer size, the distance between the washer edge and EN 338 (2009), 45 £ 120 mm. the edge of the bottom rail, s, as shown in Figure 1(d), is Sheathing: Hardboard, 8 mm (wet process fibre defined. The width “b” and depth “h” of the bottom rail board, HB.HLA2, EN 622-2 (2004), Masonite AB). are also defined in Figure 1(d). Sheathing-to-timber joints: Annular ringed shank The test programme of study A is specified in Table 1. nails, 50 £ 2.1 mm (Duofast, Nordisk Kartro AB). In study B, a total of 80 specimens were tested. As for The joints were nailed manually and the holes were study A, the specimens were divided into sets with respect pre-drilled, only in the sheet, at 1.7 mm. to the washer size. For each set, 16 specimens were tested, Anchor bolt: ; 12 (M12). The holes in the bottom 8 with PD and 8 with PU. However, for set 1, two subsets rails were pre-drilled at 13 mm. were tested: one with boundary conditions as in study A according to Figure 1(a), noted set 1-BC(A), and one with boundary conditions according to the regular ones for study B (Figure 1(b)) noted set 1. 2.2. Test programme The test programme of study B is specified in Table 2. When evaluating the tests results in study A (Girhammar and Juto 2009), it was found that more parameters than originally planned for had an influence on the results, e.g. 2.3. Test set-up the pith orientation. As a consequence, it was decided to The test set-up is shown in Figure 1. vary these parameters and perform an additional experi- The bottom rail was fixed to a steel plate simulating mental investigation, study B (Caprolu 2012). These two the foundation which in turn was welded to a steel struc- experimental studies differ with respect to the boundary ture. The connection between the specimen and the steel conditions of the test set-ups. In study A, the rotation of plate was made by two anchor bolts. The distance between the sheathing relative to the bottom rail was partly the bolts was 600 mm and the distance between the bolt restrained by using two bracing bars (Figure 1(a)). The and the end of the bottom rail was 150 mm. To tighten the purpose of this arrangement was to have a uniform dis- bolts a torsional moment of 50 Nm was applied resulting placement of the sheathing perpendicular to the bottom in a pretension force of about 25 kN. A square or rectan- rail. In study B, the sheathing was free to rotate by trans- gular washer of high rigidity, thickness 15 mm, was mitting the applied load through a hinge (Figure 1(b)). inserted between the bottom rail and the bolt head. Its size Also, in study B, the pith orientation was systematically and shape varied for the set tested, according to Tables 1 varied and the measurements were much more detailed and 2.
Table 1. Test programme of study A.
Number of tests Anchor bolt position Size of washer Distance sa Set PD PU (mm) (mm) (mm)
110 b/2 40 £ 40 £ 15 40 2 8 2 60 mm 60 £ 60 £ 15 30 3 7 3 from 80 £ 70 £ 15 20 410 sheathing 100 £ 70 £ 15 10
Note: PD D pith downwards, PU D pith upwards, b D width of rail (notation as in Figure 1). aDistance from the washer edge to the edge of the bottom rail. 4 G. Caprolu et al.
Table 2. Test programme of study B.
Number of tests Anchor bolt position Size of washer Distance sa Set PD PU (mm) (mm) (mm)
1-BC(A)b 88 b/2 40 £ 40 £ 15 40 18860mm40£ 40 £ 15 40 2 8 8 from 60 £ 60 £ 15 30 3 8 8 sheathing 80 £ 70 £ 15 20 4 8 8 100 £ 70 £ 15 10
Note: PD D pith downwards, PU D pith upwards, b D width of rail (notation as in Figure 1). aDistance from the washer edge to the edge of the bottom rail. bSet with boundary condition as in study A.
The tests were conducted under displacement control The first two failure modes are brittle while the third applying a tensile load by a hydraulic piston (static load one is ductile. The brittle failure occurs when there is a capacity of 100 kN) using a displacement rate of sudden drop of the load (due to a crack). In the test results 2 mm/min. The hydraulic piston was connected to a steel presented here, there are some “small” brittle failures in bar which in turn was connected to two load-distributing the beginning of the loading process (cf. e.g. Figure 22), C-shaped steel profiles attached to the specimen by eight but still the load increases after the small drops of the bolts of ; 16, four per sheet, according to Figure 1(e). The load. The final brittle failure occurs when there is a sub- two C-shaped steel profiles were connected together by a stantial drop of the load and the capacity of the bottom welded steel profile. rail is more or less exhausted. Failure mode 1 occurs due As mentioned, different boundary conditions were to crosswise bending of the bottom rail introducing ten- used in the two studies. In study A, the vertical load was sion stresses perpendicular to the grain. A crack usually transferred to the C-shaped steel profiles via a welded starts from the centre of the underneath surface of the bot- connection, introducing some bending moments in the tom rail propagating in the vertical rail cross section. Fail- test specimens (cf. Figure 1(a)). The bracing bars reduced ure mode 2 is due to vertical shear forces in the nails of the rotation of the specimen, but since it was believed that the sheathing-to-framing joints, causing splitting failure at this arrangement did not render full rotation restraint and, the edge of the bottom rail. The crack usually arises in also, to simulate more the behaviour in practice (believed line with the nails and propagates in the horizontal direc- to be more “uneven”, starting failure at one end), it was tion for a certain length and then changes in a more verti- decided to have more clearly defined boundary conditions cal direction. In longitudinal direction, the crack in study B by removing the inclined bars and only using propagates for a certain length but never reaches the other the hinge according to Figure 1(b). end. Failure mode 3 occurs due to the withdrawal of the In both studies, the distance between the nails in the nails in the sheathing-to-framing joint. This failure mode sheathing-to-timber joints was 50 mm. For each specimen, is directly linked to the distance between the nails in the the moisture content and density of the bottom rail were sheathing-to-framing joint. In Caprolu et al. (2014), two measured after the test, according to ISO 3130 (1975) and experimental studies were presented, where this distance ISO 3131 (1975), respectively. was set as 25 and 50 mm, respectively. In this study, the distance was chosen as 50 mm since it is a more realistic distance to use in practice. This failure mode does not give rise to any cracks in the bottom rail. 3. Results In Figures 3 and 4, the number of observations of the 3.1. Failure modes three different failure modes is graphically shown. It is Three primary failure modes were observed during the noted that failure mode 1, the splitting failure along the tests: bottom side of the rail, is predominant. It should be men- tioned that in sets 3 and 4 there were a high number of (1) Splitting along the bottom side of the rail accord- bottom rails with pre-cracks that caused premature split- ing to Figure 2(a). ting of the bottom side of the rail (mode 1). This is noted (2) Splitting along the edge side of the rail in line in Figure 2(b), where a vertical crack due to the pre-crack with the sheathing-to-framing joints according to of the bottom rail is visible despite the rail failed in mode Figure 2(b). The splitting occurred independently 2. However, after the small drop of the load that occurred on one or both edges. due to that splitting, the applied load could be increased (3) Yielding and withdrawal of the nails in the sheath- and the final failure was in the mode shown in Figure 4 ing-to-framing joints, according to Figure 2(c). (cf. also Section 5). The IES Journal Part A: Civil & Structural Engineering 5
Figure 2. (a) Splitting failure along the bottom side of the rail; (b) splitting failure along the edge side of the rail; (c) yielding and with- drawal of the nails in the sheathing-to-framing joints. The left column of pictures refers to bottom rail with pith downwards (PD D N) and the right column with pith upwards (PU D U). The picture of specimens 441 U and 446 U indicates a mixed failure mode. However, since the first noted failure modes for these specimens were number 2 and 3, respectively, it was assumed that these modes also were the decisive one. 6 G. Caprolu et al.
material characteristics, it should first be mentioned that the timber members have been conditioned at the sawmill down to about 18% and then planed. After that the mem- bers were stored in the laboratory reducing the moisture content to about 12%, causing distortions like twisting and cupping of the bottom rails. At this stage, also resid- ual stresses and cracks appear. It is also noted that in the case of having the PU, knots of a certain size are more likely to be found on the bottom surface of the rail than when the pith is oriented downwards. Concerning the fastening of the bottom rail, it should be observed that due to cupping tensile stresses, pre-cracks may appear in con- Figure 3. Recorded failure modes for the different sets belong- nection with the tightening of the anchor bolts (cf. ing to study A (PD D pith downwards, PU D pith upwards). Figure 5). Note: Distance from washer edge to loaded edge of the bottom In the case of pith oriented upwards, such cracks will rail (mm); size of washer (mm). appear on the bottom side of the rail. However, in the case of pith oriented downwards, compression stresses will appear on the bottom side of the rail and restrain the It is also noted that failure modes 2 and 3 only appear development of cracks. It is also important to note that the for small values of the distance s. drilling of a hole for the anchor bolt can have a significant influence on the development of cracks. In connection 3.2. Load time curves and crack development with the tightening of the anchor bolt cracks may easily The displacements of the specimens were not recorded, appear at the boundary of the hole. This fact might deter- but since the displacement was applied with a constant mine whether the crack, during the bottom rail failure, rate, it is possible to obtain fictitious load displacement will start propagating from the hole to the end of the rail curves by plotting load time curves. Typical load time or vice versa. curves, from study B, are shown in Figure 6. In Figure 6(a), typical curves for specimens failing in As a background to the evaluation of the different splitting along the bottom side of the rail are shown. Three curves, it is appropriate to discuss the material characteris- examples are illustrated, two with pith oriented down- tics of the specimens and the conditions with regard to wards (with the label N) and one with pith oriented fastening of the bottom rail to the test rig. Concerning the upwards (with the label U). Two kinds of crack
Figure 4. Recorded failure modes for the different sets belonging to study B (PD D pith downwards, PU D pith upwards). Note: Distance from washer edge to loaded edge of the bottom rail (mm); size of washer (mm). Set 1-BC(A) had boundary conditions as in study A. The IES Journal Part A: Civil & Structural Engineering 7
Figure 5. Effect of shrinkage due to drying for specimens with pith oriented (a) downwards and (b) upwards.
propagation are observed, one crack propagating all the washer, and also the need for higher load to propagate through the length of the bottom rail or more than one an existing crack. crack propagating partly overlapping each other. In the Figure 6(b) shows the influence of splitting along the first case, the crack usually starts from one end of the rail edge side of the rail, mode 2, for some specimens tested and propagates to the other end. When more than one failing in a similar way. A different behaviour of these crack appears, separate cracks usually start from each end curves is noted in relation to those obtained for failure of the rail and propagate to the centre of the rail. It is also mode 1. In this case, the failure load is taken as the maxi- noted that in the rail with pith oriented upwards, there are mum failure load, point 1, recorded for the specimen knots of such sizes that the crack path often is affected. tested. Even if there is some drop in load before the maxi- From Figure 6(a), it is observed that the failure loads for mum load, the maximum failure load was chosen as fail- the bottom rails with pith oriented downwards are signifi- ure load because no visible cracks were seen during the cantly higher than the failure load for the rail with pith ori- previous drops. The horizontal crack appeared at one end ented upwards. of the bottom rail and propagated along the bottom rail Three main drops in the load are sometimes visible as for a certain length, but not up to the other end. Finally, in shown in Figure 6(a). In detail, it is very difficult to be Figure 6(c), typical curves for specimens exposed to fail- sure how the crack propagation really takes place since ure mode 3 yielding and withdrawal of the nails in the the bottom surface of the rail is not visible at the time of sheathing-to-framing joints are shown. In this case, as for the testing. The first drop, point 1, likely appears when the the specimens exposed to failure mode 2, the maximum first crack propagates from one end of the rail up to the failure load, point 1, was taken as failure load. After fail- closest anchor bolt. Alternatively, the crack propagates ure a ductile behaviour of the curves is noted. Even for from the bolt hole up to the end of the rail. The second these curves some drop in load is noted before the maxi- drop, point 2, corresponds either to a continuation of the mum load. However, as for the curves in Figure 6(b), no crack propagation in the middle part of the rail or to a new visible damages were seen in the rail during these drops. crack propagating in the other end of the rail. The third The yielding and withdrawal of the nails in the sheathing- drop, point 3, corresponds to final failure, either when the to-framing joints started from one end of the rail and grad- same crack has propagated all through the length of the ually increased along the rail never reaching the other end. rail or when two cracks have propagated from each end to In Figure 6(c), the picture of specimen 445 N indicates the central part of the rail. The reason why the load both mode 1 and mode 3 failures. However, since the first increases after a crack is, for example, due to the tighten- noted failure mode for this specimen was number 3, it ing of the bolts, friction with respect to the substrate and was assumed that this mode also was the decisive one. 8 G. Caprolu et al.
Figure 6. Examples of measured load time curves. (a) Failure mode 1 (crack from the bottom side of the rail). Point 1 is probably caused by a crack propagating from one end of the bottom rail up to the closest anchor bolt or from the bolt hole up to the end of the rail; point 2 is probably caused by a crack propagating between the two anchor bolts or to a new crack propagating in the other end of the rail. Finally, point 3 corresponds to final failure, either when the same crack has propagated all through the length of the rail or when two cracks have propagated from each end to the central part of the rail. (b) Failure mode 2 (crack from the edge side of the rail). Point 1 is caused by the horizontal crack propagating along the longitudinal direction of the bottom rail. (c) Failure mode 3 (yielding and with- drawal of fasteners). Point 1 depicts the withdrawal of fasteners. The picture for specimen 445 N shows both failure modes 1 and 3. However, this specimen is considered to be failed in mode 3 since this was the first failure mode occurring.
It is interesting to see how the cracks are formed on The one in Figure 7(d) occurred only twice and the crack the end cross section of the bottom rail with regard to pith probably propagates in this way because it finds a weaker orientation and washer size. The crack shapes found here crack plane. The crack shape in Figure 7(e) is affected by are quite similar to those noted in Caprolu et al. (2014) for the pith position. In all other specimens, the pith was on single-sided sheathing. the border of the rail and more or less at the middle of the For bottom rails with the pith oriented upwards, five cross-sectional width. Usually, the crack propagates typical types of crack formations are shown in Figure 7 towards the pith. The same happens in this case, but due for failure mode 1. For this failure mode, the crack is initi- to the pith position the crack propagates in an oblique ated at the bottom side of the bottom rail and always starts direction towards the pith and then it changes direction. It to propagate vertically across (more or less perpendicular is of interest to note the location of the crack initiation, to) the annual rings and then continues (1) in the same or the distance bcrack1, somewhere between the middle of the somewhat deviating direction heading towards the pith width and the edge of the washer as presented in Table 3. location (Figure 7(a) and (b)), or (2) by changing direction For failure mode 2, two crack formations are shown in to propagate along a certain annular ring (Figure 7(c)). In Figure 7. In both of them, the crack is initiated at the side Figure 7(d) and 7(e), two unusual crack shapes are shown. of the bottom rail along the line of the nails in the The IES Journal Part A: Civil & Structural Engineering 9
Figure 7. Crack development for bottom rail with pith oriented upwards (PU). (a) Mode 1 crack developed in a straight line, starting and propagating vertically in the middle of the bottom rail; (b) mode 1 crack developed in an oblique line, starting at a location close to the edge of the washer and propagating towards the pith; (c) mode 1 crack developed in a straight line for a certain length and then fol- lowing the annual ring shape; (d) mode 1 crack developed in an unusual direction, probably due to a weaker crack plane; (e) mode 1 crack developed towards the pith (due to pith in an unusual position) and then in another direction; (f) mode 2 crack development, start- ing horizontally and then propagating vertically across the annual rings; (g) mode 2 crack development, starting horizontally and then propagating vertically parallel the annual rings.
sheathing-to-framing joints and develops in the horizontal deviating direction towards the middle of the bottom rail direction for about 20 mm and then changes to a more ver- width (Figure 8(b)) or (3) to follow the annual ring shape tical direction (1) across the annual rings (Figure 7(f)) and and then to change direction propagating along a more (2) parallel to the annual rings (Figure 7(g)). The location vertical direction (Figure 8(c)). In Figure 8(d), a further where the crack changes direction, the distance bcrack2,is crack formation for mode 1 is shown. This crack does not presented in Table 3. have a defined direction but propagates in a “zig-zag” Specimens with pith oriented downwards (PD) direction. showed failure modes 1, 2 and 3. In Figure 8, typical The distance bcrack1 is given in Table 4. For mode 2, examples of crack formations are shown: four for mode 1 the crack is initiated at the side of the bottom rail along (Figure 8(a) (d)) and one for mode 2 (Figure 8(e)). For the line of the nails in the sheathing-to-framing joints and mode 1, the crack is initiated at the bottom side of the bot- develops in the horizontal direction for about 20 mm and tom rail and always starts to propagate vertically and then then changes to a more vertical direction, often parallel to to continue (1) in the same direction (Figure 8(a)), (2) in a the annual rings as shown in Figure 8(e). The location 10
Table 3. Measured crack data for specimens with the pith oriented upwards (PU). Specimens are related to both study A and study B. For failure mode 1, the distance between vertical crack and an edge of the bottom rail (bcrack1 ) is given. For failure mode 2, the length of the horizontal crack before it changes direction (bcrack2 ) is given. When two distances for one end are given for failure mode 2, it means that there are two horizontal cracks, one in each edge. End 1 and End 2 indicate the two bottom rail ends, but no distinction is made here between them. All distances and crack lengths are given in mm, whilst the failure load is given in kN.
Study A
Set 1 Set 2 Set 3 Set 4 Failure Failure Failure Failure mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2
1/23.2 62 60 1/37.5 55 34 1/26.8 56 55 1/27.2 38 56 1/27.6 53 60 Caprolu G.
Study B
Set 1-BC(A)a Set 1 Set 2 Set 3 Set 4 Failure Failure Failure Failure Failure al. et mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2
1/17.7 52 65 1/16.9 58 67 1/17.3 62 57 1/32.5 56 63 2/32.4 20-20b 1/17.2 59 63 1/18.6 57 70 1/23.0 64 55 1/31.2 55 86 2/38.0 23-15b 1/13.1 70 58 1/15.6 44 64 1/18.3 53 69 1/34.1 29 59 3(2)c/50.0 10 1/20.6 53 85 1/17.3 40 70 1/20.9 67 60 1/33.6 54 75 2/37.8 22-16b 1/14.6 52 63 1/20.5 50 67 1/20.8 75 104 1/34.7 57 75 2/39.5 10 1/21.3 57 63 1/16.8 47 63 1/18.4 56 62 1/34.3 58 80 3(2)c/39.0 23-23b 1/13.0 48 78 1/19.5 44 62 1/16.1 57 80 2/34.1 17 2/43.8 21 1/18.6 64 78 1/15.6 34 56 1/21.0 58 60 2/37.4 14 2/35.3 16 aSet with boundary conditions as in study A. bHorizontal crack on both edges of the bottom rail. cFor this specimen it was difficult to establish if the failure mode was 2 or 3. The IES Journal Part A: Civil & Structural Engineering 11
Figure 8. Crack development for bottom rail with pith oriented downwards (PD). (a) Mode 1 crack developed in a straight line, starting and propagating vertically in the bottom rail; (b) mode 1 crack developed in an oblique line, starting at a location close to the edge of the washer and propagating towards the middle of the bottom rail width; (c) mode 1 crack developed following the annual ring shape and then changing in a more vertical direction; (d) mode 1 crack developed in an unusual direction; (e) mode 2 crack development, starting horizontally and then propagating vertically. 12
Table 4. Measured crack data for specimens with the pith oriented downwards (PD). Specimens are related to both study A and study B. For failure mode 1, the distance between ver- tical crack and an edge of the bottom rail (bcrack1 ) is given. For failure mode 2, the length of the horizontal crack before it changes direction (bcrack2 ) is given. When two distances for one end are given for failure mode 2, it means that there are two horizontal cracks, one in each edge. End 1 and End 2 indicate the two bottom rail ends, but no distinction is made here between them. All distances and crack lengths are given in mm, whilst the failure load is given in kN.
Study A
Set 1 Set 2 Set 3 Set 4 Failure Failure Failure Failure mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2
1/23.4 44 26 1/28.3 62 82 1/43.0 75 95 1/41.9 57 62 1/22.5 51 40 1/32.8 80 51 1/45.4 74 76 1/41.1 62 62 1/23.0 63 66 1/26.7 65 110 1/40.3 88 64 1/41.0 47 55 1/22.4 71 65 1/31.3 45 40 1/35.7 50 64 1/41.7 71 62 1/20.2 69 64 1/27.7 57 66 1/35.7 53 78 1/42.5 78 69 1/20.4 69 84 1/27.9 68 69 3/35.9 1/40.4 60 62 Caprolu G. 1/22.8 58 55 1/29.2 61 60 1/33.9 56 79 1/31.9 56 62 1/23.3 70 65 1/30.1 69 66 1/35.6 61 50 1/19.8 62 57 1/38.0 57 66 1/23.3 71 53 2/43.4 17 18 al. et
Study B
Set 1-BC(A)a Set 1 Set 2 Set 3 Set 4 Failure Failure Failure Failure Failure mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2 mode/load End 1 End 2
1/22.5 50 72 1/15.0 53 40 1/27.6 68 55 2/31.5 24 13 25 2/47.4 20 1/21.0 90 52 1/24.0 84 40 1/29.6 98 54 1/38.5 89 50 2/46.1 20 1/23.1 60 54 1/17.3 59 44 1/29.5 62 45 1/34.3 54 44 3/41.9 1/23.2 65 57 1/23.7 65 48 1/26.1 82 55 1/37.9 19 14 2/48.0 10 1/25.8 63 60 1/20.9 65 36 1/26.1 47 55 1/44.0 65 39 3/46.3 1/21.9 65 40 1/23.2 62 40 1/26.3 66 32 1/35.5 80 64 1/45.4 50 24 1/21.0 54 54 1/18.3 66 45 1/27.5 59 50 2/44.5 15 16 3/44.3 1/22.5 91 72 1/21.3 90 67 1/31.3 85 55 1/46.6 91 69 2/47.2 15 aSet with boundary conditions as in study A. The IES Journal Part A: Civil & Structural Engineering 13 where the crack changes direction, the distance bcrack2,is carrying capacities of the specimens from study B are presented in Table 4. somewhat lower than the corresponding ones found in Since there are ongoing theoretical studies based on a study A (see Table 8). Regarding the ratios between the fracture mechanic theory approach (see, for instance, two studies for specimens with PU, the different number Caprolu et al. [2012b] and Serrano, Vessby, and Olsson of specimens tested in the two studies should be remem- [2012]), it is interesting to give a few details of the crack bered. Regarding the ratios between the two studies for characteristics. In Tables 3 and 4, the distance between specimens with PD, the higher load-carrying capacity for the vertical crack and the edge of the bottom rail, for fail- study A is confirmed, with the exception of set 4 and, in ure mode 1, and the length of the horizontal crack before minor extent, sets 1-BC(A) and 3. The results in set 4 it changes direction, for failure mode 2, are given. The could be regarded as exceptional or less accurate due to data are presented with respect to pith orientation for the different number of specimens that failed in the same study A and study B. mode. One reason for the difference in load-carrying capacity could be the different boundary conditions. The more rigid boundary conditions in study A will render 3.3. Failure loads higher failure loads, because the straining of the bottom The failure load, for the two brittle failure modes 1 and 2, rail is more equally distributed along its whole length. is defined as the load at which there is a first distinct From Figures 9 11, the relationship between failures decrease in the load-carrying capacity due to a propagat- loads and distance s from washer edge to the edge of the ing crack in the bottom rail. For failure mode 3, the failure bottom rail is shown for studies A and B, respectively. load is defined as the maximum load. The results of the Since too few specimens were tested with pith upwards different tests are summarised in Tables 5 and 6. In a pre- for study A, the results are not presented. For each graph, vious study by Caprolu et al. (2014), the pith orientation two different curves are visible: a linear trend line and a turned out to be an important parameter at the evaluation polynomial regression type of second order. Regarding of the test results. The failure load is presented with specimens with pith oriented downwards (Figures 9 and respect to this parameter in Table 5 (pith upwards) and 10), good correlation is obtained between the distance s Table 6 (pith downwards). Mean failure load and mean and the failure load for both studies. This is spotlighted by density are presented with respect to failure mode. The a coefficient of determination R2 ranging from 0.81 to dry density, defined as the ratio between the mass of the 0.89 for the linear trend lines and by a coefficient of deter- specimen after drying and the volume of the specimen mination R2 ranging from 0.85 to 0.89 for a polynomial before drying at v moisture content, indicated as r0,v,is regression type of second order, meaning that there is a shown in Tables 5 and 6 as a mean value per set and fail- strong influence of the parameter s on the final failure ure mode. The mean moisture content per set, defined as load. The same good correlation is noted in Figure 11 by a the ratio between the difference of the mass of the coefficient of determination R2 of 0.84 for the linear trend specimen before and after drying and the mass of the lines and by a coefficient of determination R2 D 0.85 for a specimen after drying, indicated as v, is also shown in polynomial regression type of second order. It is evident Tables 5 and 6. from Figures 9 11 that the failure load increases when From Tables 5 and 6, it is seen that the density of the the distance s decreases. bottom rail in study A is about 5% lower than the one In Table 9, the R2 and the standard error of the esti- used in study B. This difference may have a slight influ- mate (SEE) values for each linear trend line shown in ence on the recorded failure loads. The moisture content Figures 9 11 are summarised. The SEE value is a mea- is comparable in the two studies, except for two speci- sure of the accuracy of the predictions. Smaller values are mens with the pith oriented upwards (PU) belonging to better because it indicates that the observations are closer set 2 of study A. Comparing the results in Tables 5 and 6 to the fitted line, i.e. the SEE value for study A in Table 9 shows a higher load-carrying capacity for the specimens tells us that the average magnitude of the data points with pith oriented downwards, as compared to the ones away from the fitted line is 5.09 kN. with the pith oriented upwards. In Table 7, where the ratios between the load-carrying capacity for specimens with PD and PU are presented for studies A and B, this 4. Analysis difference is quantified. In viewing the ratios, the different In this section, the failure load of the bottom rail for number of specimens tested within the same set should be modes 1 and 3 is evaluated. In order to keep the analysis kept in mind. Especially, it should be noted that the ratio simple, some influencing parameters such as the friction given for study A is very uncertain due to the very small under the rail, the friction between the rail and the washer, number of tests with pith upwards in that study. the effect of the pretension force and the discretely placed Also, by comparing the two studies A and B in washers are not taken into account. The inclusion of fric- Tables 5 and 6, respectively, it is found that the load- tion would result in a higher calculated load-carrying 14
Table 5. Results from testing of specimens with the pith orientation upwards (PU). Failure modes: (1) splitting along the bottom side of the rail; (2) splitting along the edge side of the rail; (3) yielding and withdrawal of the nails in the sheathing-to-framing joints. r0, v is the dry density with respect to volume at v, where v is the moisture content.
Failure load Number of tests r v 0, v All failure modes Failure mode 1 Failure mode 2 Failure mode 3 (1) (2) (3) All (1) (2) (3) All
Number Mean Std. dev. COV Mean Std. dev. COV Mean Std. dev. COV Mean Std. dev. COV Mean Mean Mean Mean Mean Set of tests (kN) (kN) (%) (kN) (kN) (%) (kN) (kN) (%) (kN) (kN) (%) Mean Mean Mean [kg/m3] [kg/m3] [kg/m3] [kg/m3] [%]
Study A 1 2 2 25.0 2.55 10.2 25.0 2.55 10.2 2 405 405 9.05 3 3 30.8 5.83 19.0 30.8 5.83 19.0 3 378 378 13.0 Caprolu G. 4
All Mean value 392 392 11.0
Study B al. et
1-BC(A)a 8 17.0 3.20 18.8 17.0 3.20 18.8 8 436 436 13.3 1 8 17.6 1.78 10.1 17.6 1.78 10.1 8 412 412 13.6 2 8 19.5 2.31 11.8 19.5 2.31 11.8 8 424 424 12.7 3 8 34.0 1.79 5.26 33.4 1.32 3.95 35.8 2.33 6.51 62 427b 436 402 13.1b 4c 8 39.5 5.37 13.6 37.8 (39.5) 3.86 (5.37) 10.2 (13.6) 44.5 7.78 17.5 6(8) 2(0) 410 407 (410) 420 (-) 12.0
All Mean value 422 427 12.8 aSet with boundary conditions as in study A. bResults calculated using seven specimens. cFor two specimens of this set, it was difficult to establish if the failure mode was mode 2 or 3. The results without parenthesis refer to the case of six failure mode 2 and two failure mode 3, while the results in parenthesis refer to the case of eight failure mode 2. Table 6. Results from testing of specimens with the pith orientation downwards (PD). Failure modes: (1) splitting along the bottom side of the rail; (2) splitting along the edge side of the rail; (3) yielding and withdrawal of the sheathing-to-framing joints. r0, v is the dry density with respect to volume at v, where v is the moisture content. h E ora atA ii tutrlEngineering Structural & Civil A: Part Journal IES The
Failure load Number of tests r v 0, v All failure modes Failure mode 1 Failure mode 2 Failure mode 3 (1) (2) (3) All (1) (2) (3) All
Set Number Mean Std. dev. COV Mean Std. dev. COV Mean Std. dev. COV Mean Std. dev. COV Mean Mean Mean Mean Mean of tests (kN) (kN) (%) (kN) (kN) (%) (kN) (kN) (%) (kN) (kN) (%) Mean Mean Mean [kg/m3] [kg/m3] [kg/m3] [kg/m3] [%]
Study A 1 10 22.1 1.41 6.37 22.1 1.41 6.37 10 395 395 13.1 2 8 29.2 2.05 7.00 29.2 2.05 6.37 8 398 398 11.8 3 7 38.6 4.38 11.4 39.0 4.62 11.8 35.9 6 1 384 392 334 12.2 4 10 39.7 3.58 9.01 39.3 3.55 9.02 43.4 91 371 374 343 13.3
All Mean value 387 390 343 334 12.6
Study B
1-BC(A)a 8 22.6 1.53 6.77 22.6 1.53 6.77 8 0 0 414 414 13.0 1 8 20.5 3.29 16.0 20.5 3.29 16.0 8 0 0 404 404 13.4 2 8 28.0 1.94 6.94 28.0 1.94 6.94 8 0 0 404 404 13.1 3 8 39.1 5.41 13.8 39.5 4.84 12.3 38.0 9.19 24.2 6 2 0 441 425 491 13.2 4 8 45.8 1.98 4.32 45.4 47.1 0.78 1.65 44.2 2.20 4.98 1 4 3 399 396 404 392 12.2
All Mean value 412 407 448 392 13.0 aSet with boundary conditions as in study A. 15 16 G. Caprolu et al.
Table 7. Ratio between load-carrying capacity of specimens with different pith orientation of the bottom rail within study A and study B, respectively.
Study A Ratio PD/PU per failure mode Study B Ratio PD/PU per failure mode Washer Bolt Distance s Set size [mm] position [mm] All (1) (2) (3) All (1) (2) (3)
1-BC(A) 40 £ 40 £ 15 b/2 40 1.33 1.33 140£ 40 £ 15 b/2 40 1.16 1.16 260£ 60 £ 15 b/2 30 1.17a 1.17a 1.44 1.44 380£ 70 £ 15 b/2 20 1.25a 1.27a 1.15 1.18 1.06 4b 100 £ 70 £ 15 b/2 10 1.16 1.25 (1.19) (0.99)
Total mean 1.21 1.22 1.25 1.28 1.16 (1.13) (0.99)
Note: . PD D pith downwards, PU D pith upwards. aOnly few test results are behind these values. bFor two specimens of this set, it was difficult to establish if the failure mode was mode 2 or 3. The results without parenthesis refer to the case of six fail- ure mode 2 and two failure mode 3, while the results in parenthesis refer to the case of eight failure mode 2.
Table 8. Ratio between load-carrying capacity of specimens from study A compared to study B for different pith orientations.
Ratio study A/study B (PU) per failure mode Ratio study A/study B (PD) per failure mode Washer Bolt Distance s Set size [mm] position [mm] All (1) (2) (3) All (1) (2) (3)
1-BC(A) 40 £ 40 £ 15 b/2 40 0.98 0.98 140£ 40 £ 15 b/2 40 1.08 1.08 260£ 60 £ 15 b/2 30 1.28 1.28 1.04a 1.04a 380£ 70 £ 15 b/2 20 0.91 0.92 0.99 0.99a 4 100 £ 70 £ 15 b/2 10 0.87b 0.87b 0.92b
Total meanc 1.10 1.10 1.02 1.02
Note: PD D pith downwards, PU D pith upwards. The values in the table are based on the values in Tables 5 and 6. aThese values are more accurate than the others, because the number of specimens that failed in the same mode is equal for studies A and B. bThese two values (set 4) could be regarded as exceptional or less accurate due to the different number of specimens that failed in the same mode. cThe total mean for the ratio study A/study B (PD) is calculated excluding set 4, due to the different number of specimens that failed in the same mode.
Figure 10. Failure load versus distance s from washer edge to Figure 9. Failure load versus distance s from washer edge to edge of the bottom rail. All test results are from study B (pith ori- edge of the bottom rail. All test results are from study A (pith ented downwards).Note: 1)These results are not included in the oriented downwards). The vertical line shows a border between trend lines since these tests had different boundary conditions than failure modes. the others. The vertical line shows a border between failure modes. The IES Journal Part A: Civil & Structural Engineering 17
Figure 11. Failure load versus distance s from washer edge to edge of the bottom rail. All test results are from study B (pith ori- ented upwards). The vertical line shows a border between failure modes. Note: 1)These results are not included in the trend lines since these tests had different boundary conditions than the others. capacity. The effect of the pretension force depends on the magnitude of the pretension force, the cupping shape and its orientation. Here a two-dimensional (2D) model is adopted meaning that the anchoring of the bottom rail is assumed to be continuous along its whole length. The influence of the third dimension is thus not evaluated in this paper; the results can only indicate whether the 2-D model is acceptable or not.
4.1. Analytical failure load The basic analytical expressions for the failure load of the bottom rail in failure mode 1 are the same as those pre- sented in Caprolu et al. (2014) for a wall with single-sided Figure 12. The model used for calculating the load-carrying capacity for mode 1 failure. s is the distance between the edge of sheathing. The bottom rail was modelled as a cantilever the washer and the edge of the bottom rail; a is the added dis- beam clamped at the section of the highest tensile stress tance to s to give the effective cantilever length le. (the location of the initiation of the crack) as shown in Figure 12. The failure load with respect to the shear force the grain of the timber; L is the length of the bottom rail; can be excluded as shown in Caprolu et al. (2014). The h is the depth of the bottom rail and l is the cantilever failure load due to bending is given by P ¼ 2ðLh2= e span relative to failure mode 1 according to Figure 12. 6l Þf ; , where f is the tensile strength perpendicular to e t 90 t,90 Note that the Euler Bernoulli beam theory is not, in gen- Table 9. R2 and SEE values for the trend lines of the relation- eral, applicable to cantilevers with such short span to ship between failure load and distance s shown in Figures 9 11. depth ratio. Note also that the tensile strength and not the bending strength is used. For f , a mean value of 2.5 2 2 t,90 R and SEE values R values for polynomial MPa was used according to Serrano et al. (2011). for linear trend regression type of lines per study second order per study The results of the analysis for failure mode 1 are shown in Figures 13 15 for studies A and B and for dif- Study R2 SEE (kN) R2 ferent pith orientation (for study A, the results of bottom rail with pith upwards are not shown since the data are too Study A (PD) 0.81 5.09 0.85 few). Note that in these figures only test results for failure Study B (PD) 0.89 3.76 0.89 mode 1 are included. Four different values of l were used Study B (PU) 0.84 4.65 0.85 e as in Caprolu et al. (2014), ranging from le D 15 C s to le Note: PD D pith downwards, PU D pith upwards. D 30 C s (unit in mm), indicating that the “free” distance 18 G. Caprolu et al.
Figure 13. Results of the analysis for failure mode 1. Results Figure 15. Results of the analysis for failure mode 1. Results are from study A (pith oriented downwards). are from study B (pith oriented upwards). Note: 1)These values are from tests with boundary conditions as in study A.
this might be attributed to the fact that specimens with pith oriented upwards have a lower load-carrying capacity than those with pith oriented downwards, as shown in Table 7.) As discussed in Caprolu et al. (2014), the failure load of the bottom rail in failure mode 3 corresponds to the sit- uation where plastic hinges in the nails are formed in both thepffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi timberp andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sheathing, and is given by P ¼ 2b=ð1 C bÞ 2Myfh;sd C Prope, where b D fh,w/fh,s is the ratio between the embedment strength of the members, fh, s and fh,w are the embedment strength of the hardboard sheathing and of the wood, respectively, d is the fastener 3 diameter, My is the fastener yield moment (My D fyd /6) and Prope is the load associated with the rope effect (with- drawal of the fastener). Figure 14. Results of the analysis for failure mode 1. Results The rope effect is taken into account by considering are from study B (pith oriented downwards). Note: 1)These values are from tests with boundary conditions as the angle of the nail between the two plastic hinges and is in study A. expressed as Prope ¼ sina Fax ¼ sina faxdtpen, where Fax is the axial withdrawal capacity of the fastener, fax is the s, which takes into account both the bolt position and the axial withdrawal capacity per unit circumference area, washer size, needs to be increased with 15 30 mm in tpen is the point-side penetration length or the length of the order to represent the position of the clamped end, i.e. rep- threaded part of the point-side member, and a is the angle resent an “effective” cantilever span. The variation will between the two plastic hinges. How to determine the indicate the empirical value for the “additional” length location of the two plastic hinges is shown in Caprolu that might be appropriate. et al. (2014) (a method based on the work of Bejtka and The shapes of the curves in Figures 13 and 14 agree Blass [2002]). reasonably well with the test results. The results fall more The evaluation of failure mode 3 is given in Appendix 1. or less all inside the four curves. Even if the variation of The calculated failure loads become Panal,mean,PD D 33.9 kN the results is quite wide, it seems that a reasonable value for study A with PD; Panal,mean,PD D 32.2 kN for study B of le, giving good results, should be between 20 C s and with PD and Panal,mean,PU D 32.0 kN for study B with PU. 25 C s.InFigure 15, it is evident that the trend of the The results are shown in Figures 16 18 together with the results with respect to the distance s corresponds to the test results. The mean value of the test results of study A analytical curves, but that the results of sets 1-BC(A), with PD (Figure 16)isPtest,mean,PD D 35.9 kN. The corre- 1 and 2 are lower than the predicted ones. (One reason for sponding values for study B with PD (Figure 17)isPtest, The IES Journal Part A: Civil & Structural Engineering 19
Figure 16. Results of the analysis for failure mode 3. Results Figure 18. Results of the analysis for failure mode 3. Results are from study A (pith oriented downwards). are from study B (pith oriented upwards).
As already found in Caprolu et al. (2014), the failure modes are strongly dependent on the distance s from the washer edge to the loaded edge of the bottom rail. For val- ues of distance s > 20 mm, the failure mode 1 is the only failure mode (splitting along the bottom side of the rail). When values of distance s 20 mm are used, failure modes 2 (splitting along the edge side of the rail) and 3 (yielding and withdrawal of the nails) also occur, espe- cially much more frequent in study B. In this study, pre-cracks were observed in many of the bottom rails in sets 3 and 4. When the anchor bolt was tightened, a pre-crack appeared on the bottom side of the rail due to the cupping shape of the rail caused by drying. The rails were enveloped in a plastic cover and kept in the laboratory for three months. The pre-cracks were found only in specimens of sets 3 and 4, which were exposed to Figure 17. Results of the analysis for failure mode 3. Results moisture reduction for a longer time than the other speci- are from study B (pith oriented downwards). mens. The cracks appeared only when big washer was used. When the specimens were loaded, the extension of the pre-crack at the bottom increased until a first drop D mean,PD 44.2 kN and for study B with PU (Figure 18)is in the load was observed (failure mode 1). However, after D Ptest,mean,PU 44.5 kN. this bottom crack failure, the load increased a lot, some- A statistical analysis, as in Caprolu et al. (2014), was times more than twice, of this initial failure load, and carried out in order to evaluate the possible influence of failed finally in mode 2 or 3. The failure loads in mode 1 the distance s and pith orientation on the failure load. The due to the propagation of pre-cracks have, therefore, not analysis was done only for study B, since in study A most been reported in this study. Instead, a few comments are of the piths were oriented downward. The results confirm given below. that both distance s and pith orientation have an influence In Figures 19 and 20, a comparison is shown between on the failure load. the failure mode 1 occurring in a specimen without a pre- crack and that in a specimen with a pre-crack. In Figure 19 (a), no pre-cracks are visible. At the time of failure, big 5. Discussion cracks have developed (Figure 19(b)). In Figure 19(c), the In Figures 3 and 4, the number of observations of the three crack is shown that has developed from one side to the different failure modes is graphically shown for studies A other at the time of failure. and B, respectively. The predominant failure mode is The specimen shown in Figure 20 had a visible pre- splitting along the bottom side of the rail, failure mode 1. crack on the side 1, as shown by the circled area in 20 G. Caprolu et al.
Figure 19. Failure mode 1 occurred in a specimen without defects: (a) ends of the bottom rail before test (no pre-crack on both sides); (b) ends of the bottom rail after testing (cracks on both sides after failure mode 1 occurred) and (c) development of the splitting on the underneath surface of the bottom rail.
Figure 20(a). When the test started, the crack started to comments can be made for specimens of set 3 with pith develop immediately from side 1 towards the closest oriented upwards. anchor bolt. This failure coincides with the first drop in A further comparison between the specimens in the load for specimen 441 PU as shown in Figure 23. Figures 19 and 20 is made in Figure 21,wheretheir Also, in Figure 23, a second small drop in the load may be load time curves are plotted. The comparison is made seen after an increase of the load. This failure is due to a regardingthesizeofthedropintheloadwhenthefirst second vertical crack at the other end that also developed crack appears. For specimen 428 PU, the drop is quite from the end towards the closest anchor bolt. However, the big while it is small for specimen 441 PU (with a visi- final failure is rather in mode 2 as shown in Figure 20(b). ble pre-crack). In other curves, as those shown in It is also noted that the vertical bottom crack is quite small Figure 5(b) and 5(c), drops of the same size appeared compared with the one shown in Figure 19(b). As is evi- before the final crack, even if no visible cracks were dent from Figure 23, the influence of the vertical premature seen in the specimens. In both types of cases, the drops crack (mode 1) on the load-carrying capacity with respect were considered negligible (cf. the discussion for to the horizontal crack (mode 2) is negligible. The same Figures 22 and 23). The IES Journal Part A: Civil & Structural Engineering 21
Figure 20. Failure occurred in a specimen with defects: (a) ends of the bottom rail before test (pre-crack on side 1); (b) ends of the bottom rail after testing (cracks on both sides after failure); and (c) development of the splitting on the underneath surface of the bottom rail.
In Caprolu et al. (2014), it was found that specimens with pith oriented downwards have a higher load-carrying capacity than the specimens with the pith oriented upwards. This is confirmed by the results given in Table 7. In Figures 22 and 23, typical load vs. time curves are shown for some specimens of set 3 and some specimens of set 4, respectively, with both pith oriented upwards and mode 1 as the failure mode. It is noted that the load for the first crack is much lower than that for the final failure. The first drop in the load is due to the pre-crack develop- ment from the end of the bottom rail, where the pre-crack was to the closest anchor bolt. Usually, after the first crack, there is a second drop in the load, probably due to a Figure 21. Comparison of the load time curves for specimens corresponding second vertical crack at the other end. The 428 PU and 441 PU. final failure load is usually almost twice the failure load 22 G. Caprolu et al.
column (c) are given the failure loads obtained in the cor- responding study with single-sided sheathing (Caprolu et al. 2014), but multiplied by two to account for the two- sided sheathing in this study (cf. Girhammar and K€allsner 2009). It is evident that the results for the failure loads for sets 3 and 4 obtained in this study (Table 10, column (b)) and those obtained in the parallel study multiplied by two (Table 10, column (c); see Caprolu et al., 2014) are in very good agreement.
Figure 22. Typical load vs. time curves for rails with pith ori- 6. Conclusions ented upwards of set 3. Specimen ID 432 U, 434 U and 437 U Tests on the splitting failure capacity and failure mode of according to Caprolu (2012). the bottom rail in partially anchored shear walls have been conducted. The rail was sheathed on both sides and it was subjected to an uplift force applied on the two sheets. The results in this study on double-sided sheathed walls are similar and confirm the results obtained in a pre- vious parallel study on single-sided ones Caprolu et al. (2014). The test results show that the distance s between the edge of the washer and the edge of the bottom rail has a significant impact on the load-carrying capacity of the bottom rail and the failure mode. There is also, to some degree, an influence of the pith orientation of the bottom rail. Decreasing the distance s increases the failure load and the pith is preferred to be oriented downwards. Three primary failure modes are discussed, two brittle Figure 23. Typical load vs. time curves for rails with pith oriented modes that need to be avoided and one ductile mode, upwards of set 4. Specimen ID 441 U, 444 U and 447 U according to Caprolu (2012). which are the desired failure modes in order to apply the plastic design method developed by K€allsner and Girham- due to the propagation of the pre-crack, indicating that the mar (2005): (1) splitting of the bottom side of the rail. pre-crack has negligible influence on the final load-carry- This brittle failure occurs when a large value of the dis- ing capacity. In Table 10, the mean failure loads for study tance s is used; (2) splitting along the edge side of the bot- B are given with respect to failure due to pre-cracks and tom rail. This brittle failure occurs when the distance s is final failure in columns (a) and (b), respectively. Also, in decreased; and (3) yielding and withdrawal of the sheath- ing-to-framing joints. This ductile failure mode occurs especially when the distance s is small. Table 10. Comparison of the load-carrying capacities using (a) Pre-cracks in the bottom rail can occur at the time of test results considering failure due to pre-cracks and (b) test tightening of the bottom rail to the foundation due to the results using the final (maximum) failure load for specimens in cupping shape of the rail caused by drying. Cracks occur sets 3 and 4. In column (c), twice the failure loads are obtained on the bottom side of the rail when the pith is oriented from the parallel study for single-sided sheathing (Caprolu et al. 2014), for specimens with the pith oriented upwards (PU). upwards independent of the size of the washer. However, cracks on the upper side of the rail can also occur when Failure load the pith is oriented downwards if the washer is big. It is Sets Number of tests (a) (b) (c) shown in this study that pre-cracks on the bottom side of the rail do not adversely affect the final failure capacity of Mean (kN) Mean (kN) Mean (kN) the bottom rail. The failure loads obtained in this study for double- 1 8 17.5a 17.5a 19.0 a a sided sheathing are also shown to be in good agreement 2 8 19.3 19.3 21.1 with twice the failure loads obtained in the parallel study 3 8 23.7 34.7 34.1 by Caprolu et al. (2014) valid for single-sided sheathing. 4 8 20.0 39.4 38.7 In conclusion, the distance s can be chosen small aSets 1 and 2, where the first and final failure coincides, are included for enough to avoid brittle failures and, hence, allow the plas- completeness. tic design method to be used without using any hold- The IES Journal Part A: Civil & Structural Engineering 23 downs. The pith of the bottom rail should preferably be Part 1-1: General Common Rules and Rules for Building). oriented downwards and/or the surfaces should be planed (prEN 1995-1-1:2003), Brussels. carefully after drying to avoid the formation of a cupped Girhammar, U. A., and H. Juto. 2009. Testing of Cross-wise Bending and Splitting of Wooden Bottom Rails in Partially shape of the rail. Anchored Shear Walls. [in Swedish]. (Technical Report). For information, it can be mentioned that in order to Lulea: Lulea University of Technology. (Originally pre- theoretically determine the splitting capacity with respect sented as an internal report, Umea University, 2009). to the critical distance s, a study based on fracture Girhammar, U. A., and B. K€allsner. (2009) “Design Aspects on mechanics for the two brittle failure modes is being con- Anchoring the Bottom Rail in Partially Anchored Wood- Framed Shear Walls.” Paper presented at the annual ducted. In this context, further experimental studies will CIBW18 Timber Structures Meeting, Dubendorf,€ August. be conducted in order to evaluate the parameters used in (Paper 42-15-1). the fracture mechanics models. Girhammar, U. A., B. K€allsner, and P. A. Daerga. 2010. “Recommendations for Design of Anchoring Devices for Bottom Rails in Partially Anchored Timber Frame Shear Walls.” Paper presented at the 10th World Conference on Acknowledgements Timber Engineering, Riva del Garda, June 20 24. The authors would like to thank the assistant professor Helena ISO 3130, International Organization for Standardization. 1975. Lidelow€ for her valuable comments and support. Wood Determination of Moisture Content for Physical and Mechanical Tests, Geneva. ISO 3131, International Organization for Standardization. 1975. Wood Determination of Density for Physical and Mechan- Funding ical Tests, Geneva. The authors would like to express their sincere appreciation for K€allsner, B., and U. A. Girhammar. 2005. “Plastic Design of the financial support from the County Administrative Board in Partially Anchored Wood-Framed Wall Diaphragms with Norrbotten [grant number 303-2602-13 (174311)]; the Regional and Without Openings.” Paper presented at the annual Council of V€asterbotten [grant number REGAC-2013-000133 CIBW18 Timber Structures Meeting, Karlsruhe, August. (00179026)]; the European Union’s Structural Funds-The (Paper 38-15-7). Regional Fund [grant number 2013-000828 (174106)]. Serrano, E., J. Vessby, and A. Olsson. 2012. “Modeling of Frac- ture in the Sill Plate in Partially Anchored Shear Walls.” Journal of Structural Engineering 138: 1285 1288. Serrano, E., J. Vessby, A. Olsson, U. A. Girhammar, and B. References K€allsner. 2011. “Design of Bottom Rail in Partially Bejtka, I., and H. J. Blass. 2002. “Joints with Inclined Screws.” Anchored Shear Walls Using Fracture Mechanics.” Paper Paper presented at the Annual CIB-W18 Timber Structures presented at the annual CIBW18 Timber Structures Meeting, Meeting, Kyoto, September. (Paper 35-7-4). Alghero, Sardinia, August September. (Paper 44-15-4). Caprolu, G. 2012. Experimental Testing of Anchoring Devices for Bottom Rails in Partially Anchored Timber Frame Shear Walls with Two-Sided Sheathing. (Technical Report, Appendix 1. Evaluation of failure mode 3 ISBN 978-91-7439-387-3). Lulea: Lulea University of Technology. In the evaluation of the failure load for mode 3, the following D 2 D Caprolu, G., U. A. Girhammar, B. K€allsner, and H. Johnsson. mean values have been used: fh,s 83.6 N/mm , fh,w 27.6 2 D D 2 D 2012a. “Tests on the Splitting Failure Capacity of the Bot- N/mm , d 2.1 mm, fy 900 N/mm , tpen 30.5 mm, D tom Rail Due to Uplift in Partially Anchored Timber Shear My 1389 N mm. Walls.” Paper presented at the 12th World Conference on The mean value for the vertical distance (u) between the two D Timber Engineering, Auckland, July 16 19. plastic hinges at maximum load in study A was umean D Caprolu, G., U. A. Girhammar, B. K€allsner, and J. Vessby. 14.2 mm based on one test result with PD; in study B, umean D 2012b. “Analytical and Experimental Evaluation of the 11.1 mm (CoV 4.77%) based on the three test results with PD; D D Capacity of the Bottom Rail in Partially Anchored Timber and in study B, umean 10.9 mm (CoV 9.78%) based on the Shear Walls.” Paper presented at the 12th World Conference two test results with PU. Note that in study A, the boundary con- on Timber Engineering, Auckland, July 16 19. ditions were partially fixed according to Figure 1(a), and in study Caprolu, G., U. A. Girhammar, B. K€allsner, and H. Lidelow.€ B, they were hinged according to Figure 1(b). 2014. “Splitting Capacity of Bottom Rail in Partially With these values, the following results are obtained: The Anchored Timber Frame Shear Walls with Single-Sided distances xw and xs between the bottom rail edge and the plastic Sheathing.” The IES Journal Part A: Civil & Structural hinge in the wood and in the sheathing, respectively, are given by xw D 8.49 mm and xs D 2.80 mm; the angles between the two Engineering 7: 83 105. plastic hinges by aA,PD D 51.5 , aB,PD D 44.5 and aB,PU D EN 338, European Committee for Standardization. 2009. Struc- tural timber Strength classes, Brussels. 44.0 , where the subscripts A and B refer to the studies A and B, EN 594, European Committee for Standardization. 2008. Timber respectively, and PD and PU to the pith orientation (downwards D Structures Test Methods Racking Strength and Stiffness and upwards, respectively); and the rope effect by Prope,A,PD D D of Timber Frame Wall Panels, Brussels. 0.78Fax, Prope,B,PD 0.70Fax, and Prope,B,PU 0.69Fax. For a D r 2 EN 622-2, European Committee for Standardization. 2004. withdrawal capacity equal to fax,mean 9( mean/420) MPa (see r D 3 Fibreboards Specifications Part 2: Requirements for Caprolu et al. 2014), where the mean density is mean 420 kg/m , D Hardboard, Brussels. the failure loads become Panal,mean,PD 33.9 kN for study A with D D Eurocode 5, European Committee for Standardization. 2004. PD; Panal,mean,PD 32.2 kN for study B with PD and Panal,mean,PU Design of Timber Structures. (prEN 1995-1-1:2003 32.0 kN for study B with PU.
Paper III
1
Analytical Models for Splitting Capacity Bottom Rails in Partially Anchored Timber Frame Shear Walls Based on Fracture Mechanics Giuseppe Caprolu*1, Ulf Arne Girhammar1 and Bo Källsner2 1Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden 2Department of Building Technology, Faculty of Technology, Linnaeus University, Växjö, Sweden
Abstract. Plastic design methods can be used for determining the load-carrying capacity of partially anchored shear walls. For such walls, the leading stud is not fully anchored against uplift and tying down forces are developed in the sheathing-to-framing joints. Since the forces in the anchor bolts and the sheathing-to-framing joints do not act in the same vertical plane, the bottom rail will be subjected to cross-wise bending, leading to possible splitting failure of the rail. In order to use these plastic design methods, a ductile behaviour of the sheathing-to-framing joints must be ensured, i.e. splitting needs to be avoided. In two earlier experimental programs, the splitting failure capacity of the bottom rail have been studied, one for specimens with single-sided and one for double-sided sheathing, where different distances between the washer edge and the loaded edge of the bottom rail were evaluated. The pith orientation of the bottom rail was another investigated parameter. Two brittle failure modes occurred during testing: (1) a crack opening from the bottom surface of the bottom rail and (2) a crack opening from the side surface of the bottom rail along the line of the fasteners of the sheathing-to- framing joints. In this article a fracture mechanics approach for the two failure modes is used to evaluate the experimental results. The comparison shows a good agreement between the experimental and analytical results. The failure mode is largely dependent on the distance between the edge of the washer and the loaded edge of the bottom rail. The fracture mechanics models seem to capture the essential behaviour of the splitting modes and to include the decisive parameters.
Keywords: bottom rail; splitting of bottom rail; timber shear walls; partially anchored
1. Introduction
1.1. Background In Eurocode 5 (2008), two parallel methods for the design of shear walls are given: (1) method A, which has a theoretical background and is used to design fully anchored shear walls and (2) method B (together with the test protocol according to EN 594, 2008), which is a soft conversion of the procedure developed in the United Kingdom for racking strength and given in BS 5268 (1996), (Porteous and Kermani, 2007). The boundary conditions for method B correspond to partially anchored conditions for the shear wall. Method B does not take into account the problem of the possible splitting of the bottom rail due to the absence of hold downs.
* Corresponding author, PhD student, email: [email protected] 2
A European research programme sponsored by Wood Focus OY identified a need for a unified approach in Europe for the design of the racking resistance of timber framed shear walls, Griffiths et al. (2005). A new plastic design method for timber frame shear walls at ultimate limit state has been developed in Sweden by Källsner and Girhammar (see e.g. 2005). The method can be used also for partially anchored shear walls. The model covers only static loads and can be used only if plastic behaviour of the sheathing-to-framing joints is ensured. The use of the plastic design method would lead to more economic structures with greater flexibility with respect to the anchoring of the shear walls against vertical uplift. As pointed out by Prion and Lam (2003), in partially anchored timber frame shear walls there are no hold downs taking the vertical uplifting loads, hence the corresponding tying-down forces need to be replaced by dead and service loads from upper storeys and the roof, by the shear connections between the shear and transversal walls or by the sheathing-to-framing joints along the bottom rail close to the leading stud. The anchor bolts will further transmit those forces into the floor or foundation. With respect to the sheathing-to-framing joints, the bottom rail is then subjected to tensile loads perpendicular to grain, which can often cause splitting failure in addition to the splitting failure that can occur along the line of fasteners in the bottom rail. The difference in structural behaviour between using some kind of hold-downs (or vertical stabilising loads) and using the sheathing-to-framing joints as tying down forces is shown in Figure 1. In Figure 1a, the shear wall is connected to the substrate by hold-down devices, resulting in a concentrated force. If they are adequately designed, the shear wall is considered as fully anchored and essentially no uplift of the leading stud takes place. When hold-down devices are not provided, the uplift is resisted by the sheathing-to-framing joints along the bottom rail, resulting in distributed anchoring forces along the bottom rail, as shown in Figure 1b. The shear wall is considered as partially anchored and some uplift of the studs occurs. In Figure 1c and 1d, single-sided and double-sided sheathing designs are shown.
Figure 1 Structural behaviour of timber frame shear walls subjected to horizontal loading: (a) a fully anchored shear wall – concentrated anchorage of the leading stud, e.g. by using a hold-down; (b) a partially anchored shear wall – distributed anchoring forces in the sheathing-to-framing joints along the bottom rail and through the anchoring bolts down to the substrate; (c) a cross-section in case of a single-sided sheathing; and (d) a cross- section in case of double-sided sheathing. 3
Experimental programmes on the splitting capacity of the bottom rail due to uplift in partially anchored shear walls with both single- and double-sided sheathing have earlier been carried out and a comprehensive evaluation of these studies has been presented by Caprolu et al. (2014a; 2014b). The failure load P (Figure 1c and 1d) was evaluated for the two failure modes: (1) a crack opening from the bottom surface of the bottom rail and (2) a crack opening from the side surface of the bottom rail along the line of the fasteners of the sheathing-to-framing joints. The analytical evaluation was based on a simple strength-of-material approach, the bottom rail was modelled as a cantilever beam fixed at the location of the crack. In this paper, a more realistic theoretical evaluation of the experimental results is made and fracture mechanics models are presented and validated. Closed form solutions for the splitting capacity for failure modes 1 and 2 are derived. A preliminary discussion and comparison between experimental and analytical results have been presented in Caprolu et al. (2012).
2. Experimental background
2.1. General The details of the experimental programmes have earlier been presented in Caprolu et al. (2014a; 2014b). Those papers were based on the original studies, Girhammar and Juto (2009) and Caprolu (2011; 2012), here called study A and study B, respectively.
2.2. Test specimen and material properties The specimens were built by hand using rails of length 900 mm with a cross section of 45×120 mm, fastened to a hardboard sheet of 900×500 mm by nails 50×2.1 mm. The bottom rail was anchored to a supporting steel foundation by two anchor bolts (with washers) spaced 600 mm. The details of the test specimens were as follow: x Bottom rail: Spruce (Picea Abies), C24 according to EN 338 (2009), 45×120 mm. x Sheathing: Hardboard, 8 mm (wet process fibre board, HB.HLA2, EN 622-2 (2004), Masonite AB). x Sheathing-to-timber joints: Annular ringed shank nails, 50×2.1 mm (Duofast, Nordisk Kartro AB). The joints were nailed manually and the holes were pre-drilled, only in the sheet, 1.7 mm. x Anchor bolt: Ø 12 (M12). The holes in the bottom rail were pre-drilled, 13 mm. All washers were assumed rigid with a thickness of about 15 mm (the other dimensions are given in Table 1).
2.3. Testing programs The two experimental studies differed with respect to the boundary conditions of the test set-ups (in study A, the connection between the loading point (hydraulic piston) and the uplifting device along the length of the bottom rail (900 mm) was partly restrained with respect to rotation (the connection itself was rigid but the vertical bar above the connection was fairly flexible with respect to bending), while the connection in study B was hinged). The main investigated parameter was the distance between the edge of the washer and the loaded edge of the bottom rail, distance s, as shown in Figure 2 (where also the width b and depth h of the bottom rail are shown). The distance was changed by the variation of the size of washer and the location of the anchor bolt for specimens with single-sided sheathing, and by the variation of the washer size, for specimens with double-sided sheathing (for this case, the anchor bolt was located in the middle). Another parameter investigated was the pith orientation of the bottom rail (PU = pith upwards and PD = pith downwards). 4
Figure 2 Cross-section view of the specimen tested: (a) single-sided sheathing; and (b) double-sided sheathing.
The testing programs of study A and study B are specified in Table 1, divided into series and sets. For single-sided sheathing, the total number of specimens tested was 89 and 142, respectively, and for double-sided sheathing 40 and 80, respectively.
Table 1 Specification of specimen tested in the study A and study B. Notation: SS = single-sided specimens, DS = double-sided specimens, b = width of rail, s = distance from washer edge to loaded edge of the bottom rail (cf. Figure 2).
Study A Study B Anchor bolt position Size of washer Distance s Set Number of tests Number of tests
Series SS DS SS DS [mm] [mm] [mm] 1-BC(A)a) ---16 40×40×15 40 1 10 10 16 16 40×40×15 40 b/2 1 2 10 10 16 16 60×60×15 30 60 mm from sheathing 3 10 10 16 16 80×70×15 20 4 10 10 16 16 100×70×15 10 110 14 40×40×15 25 3b/8 2 2 10- 16- 60×60×15 15 45 mm from sheathing 3 10 16 80×70×15 5 110 16 b/4 40×40×15 10 3 - - 2 9 1630 mm from sheathing 60×60×15 0 a) Set with boundary conditions as study A.
2.4. Test results
2.4.1. Failure modes The following three primary failure modes are shown in Figure 3: (1) Splitting along the bottom side of the rail according to Figure 3a. (2) Splitting along the edge side of the rail according to Figure 3b. (3) Yielding and withdrawal of the nails in the sheathing-to-framing joints according to Figure 3c. The first two failure modes are brittle while the third is ductile. Failure mode 1 is due to crosswise bending of the bottom rail introducing horizontal tension perpendicular to the grain. The crack is usually located at the middle of the bottom rail width, but when the distance s is decreased it appears 5 closer to the loaded edge of the bottom rail. Failure mode 2 is due to vertical shear forces in the nails of the sheathing-to-framing joints introducing vertical tensile forces perpendicular to the grain of the bottom rail. The crack appears along the line of the nails and it propagates in the horizontal width direction for a certain length, about 20 mm, before it changes its direction and propagates in a more vertical direction. Finally, the failure mode 3 is due to bending and withdrawal of the nails in the sheathing-to-framing joints.
a) Mode 1
b) Mode 2
c) Mode 3 Figure 3 (a) Splitting failure along the bottom side of the rail; (b) splitting failure along the edge side of the rail; (c) yielding and withdrawal of the nails in the sheathing-to-framing joints. The left hand pictures refer to bottom rails with single-sided sheathing and the right hand to double-sided sheathing.
The dominant failure was mode 1 in both studies. The failure mode depended on the distance s: for distance s > 20 mm, failure mode 1 was the only failure mode, while for distance s PPIDLOXUH mode 2 and 3 also appeared.
2.4.2. Failure loads For mode 1 and 2, the failure load is defined as the load when a crack caused a first distinct drop of the load value. For mode 3, the failure load is defined as the maximum load. The mean values of the failure loads for the different failure modes observed in the two studies are presented with respect to the pith orientation in Table 2 (pith upwards) and Table 3 (pith downwards). For single-sided sheathing, it was found that the failure loads were about 10 % higher when the pith was oriented downwards than oriented upwards. The corresponding value for double-sided sheathing was between 13 and 28%. One of the main reasons for those differences is the cupping shape of the bottom rail created due to drying (a downward cupping shape (concave surface of rail oriented downwards) was created when the pith was oriented upwards; then, when the bottom rail was anchored and tightened a pre-crack developed at the bottom surface of the rail; this happened in study B, double-sided tests, set 3 and 4). 6 2 (0) 1 6 (8) Set with boundary conditions as (1) (2) (3) b) sis refer to the case of six 2 mode of six case refer the to sis 0-2-0- 7-0-0- Number of tests per failure mode failure per of tests Number e rail; (2) splitting along the edge side 44.5 6 2 1 [kN] Mean of study A. 37.8 [kN] refers to double-sided tests. double-sided to refers Mean (39.5) [kN] Mean - - [kN] Mean Mean failure loadper failure mode 8 39.5 - 8 17.0 17.0 - - - 8 - 0 - 0 of tests Number Study B Study Study A Study
b) Set c) [kN] Mean parenthesis refer to the case of eight mode 2 failures. [kN] Mean [kN] Mean - 1-BC(A) [kN] Mean Mean failure loadper failure mode Single-sided testsSingle-sided testsSingle-sided tests Double-sided SS DS SS DS tests Double-sided SS DS SS DS SS DS SS DS All failure modes failure All (1) (2) (3) modes failure All (1) (2) (3)
of tests Number Set For two specimens of this set it difficultwas to establish if the failure mode was 2number orThe 3. results parenthewithout 123 24 2 22 2 12.63 11.3 2 17.02 2 12.6 24.1 11.3 1 - 12.9 21.2 - 24.3 28.9 21.0 -2 23.8 - - 27.13 - - 30.6 84 1 27.1 21.2 8 3 2 - 4 8 - -2 - 10.63 27.1 3 2 17.1 8 - -2 8 19.4 10.5 16.8 8 - 30.8 25.0 - 16.9 19.4 - 22.6 - 18.1 - 18.7 30.8 25.0 20.1 16.6 21.3 - 23.2 17.5 - - 3 2 4 22.2 ------8 8 21.4 1 2 20.8 2 3 2 - - 1 0 1 34.0 19.5 0 0 0 - 0 0 - 1 33.4 19.5 0 0 0 35.8 - 1 0 - - 0 - - - - - 1 2 0 7 8 - - - 6 8 0 0 1 0 0 - - 2 - 0 1 0 0 0 - 0 5 3 - - 3 0 5 - - - 0 6 0 - - - 2 - 1 21 1 21.51 19.9 - 8 21.5 - - 1 9.49 19.9 7 -1 9.49 8 - 12.2 - 12.2 18.6 - 1 17.9 - 18.6 8 18.9 17.6 17.6 - - 0 8 - 8 1 0 - 0 0 0 - 0 1 - 6 - 1 - c)
Results testingfrom specimensof pith the orientedwith upwards (PU). Failure modes: (1) splitting along the bottom side th of Series a) 2 3 1 2 3 1 Series 1 of study A for both single- both for A 1 of study Series 3 2 and as series of 25 for mm of 50 instead mm distance a nail had tests double-sided and failures and two and failures 3 failures,mode the results within while of the rail; (3) and the of yielding the of nails thewithdrawal sheathing-to-framing in joints. to single-side SS refers tests and DS Table 2 a) in study A. 7 (1) (2) (3) the rail;the (2) splitting along the edge 4-4-1- 8-0-0- 7-0-0- Number of tests per failure mode failure per of tests Number [kN] Mean of study A, except for one specimen in series in specimen one for except A, study of [kN] Mean and DS refers to double-sided tests. double-sided to refers DS and [kN] Mean - - [kN] Mean Mean failure loadper failure mode 8 22.6 22.6 - - - 8 - 0 - 0 of tests Number Study B Study Study A Study Probably this specimen had some defect since if we compare with the same series in compare the if defectseries we same some since with specimen Probablyhad this 2 Table )
c
d) Set b) -7-1-0- [kN] Mean d) [kN] Mean This by specimen, a of 25 had distancenail as of 50 mistake, ofinstead themm the other specimens mm This same is series. [kN] Mean b) - 1-BC(A) [kN] Set with boundary conditions as in study A. A. study in as conditions boundary with Set Mean c) Mean failure loadper failure mode Single-sided testsSingle-sided testsSingle-sided tests Double-sided SS DS SS DS tests Double-sided SS DS SS DS SS DS SS DS All failure modes failure All (1) (2) (3) modes failure All (1) (2) (3)
of tests Number Set 282.2.2.41 973.4.-691110 39.343.4- 10 39.7 461230 - - 880000 35.9860001 -1 22 3 13.5- 29.2- 8 83 8 17.4- 39.0- 8 74 22.128.620.74 8 13.5 29.2 39.538.0- 82 17.4 38.6 45.447.144.2211453 8 12.03 22.8 39.1 8 45.8 2 8 12.0 8 - - - 20.7 880000 29.1 2 -2 13.5- 28.0- 8 8 20.3 29.23 17.916.719.03 8 30.34 23.6 23.520.721.44 1 8 28.0 13.5 28.0 - 28.62 18.2 -3 29.5 21.8 10 8 -2 8 22.1 8 17.9 23.7 22.1 19.3 23.8 - 23.5 7.70 25.6 - 21.3 - 8 25.4 10 22.1 0 0 0 0 7 4 - - 1 3 4 - - - 0 5 0 - - - 0 - 1 - 4 0 - - 3 4 - - 4 - 1 81 9 - - 16.0 880000 11 10.2- 20.5- 8 8 16.0 21.6 - 10.3 20.5 21.71 - 23.1 15.1 71 8 14.0 14.0 18.1 - 15.9 - 19.5 19.4 3 - 3 - 2 -
Results from testing specimensof pith the orientedwith downwards (PD). Failure (1)modes: splitting along the side bottom of Series a) 2 3 1 2 3 1 Series A of study A for both single- and double-sided tests had a nail distance of 50 mm instead of 25 mm as for series 2 and 3 2 and series as for single- 25 mm both of for A instead study of 50 mm A of Series distance a nail had tests double-sided and the reason reason a ductile the for failure. the failure load failure the is too low. Table 3 a) side of the rail; (3)side and the of yielding of the nails thewithdrawal in sheathing-to-framing joints. to single-sidedSS refers tests 3 where the distance was 50 mm by mistake. by mistake. 50 mm was distance the 3 where 8
From Figure 4 to 7 the relationship between failure load and distance s from washer edge to the loaded edge of the bottom rail is shown for studies A and B, respectively. The results are grouped with respect to the position of the anchor bolts along the bottom rail width (b) and are separated with respect to the pith orientation. All test results are shown independently of the failure mode. Results for specimens with both single- (SS) and double-sided (DS) sheathing are shown. It should be noted that Figure 5 is based on very few data and, therefore, a statistical treatment of the data is not reliable and for some data not even meaningful. This figure is shown only for completeness, but its statistical values will not be considered. In each figure, linear trend lines are shown for single-sided and double- sided sheathing, respectively. For all cases, good correlation is obtained between the failure load and the distance s (coefficient of determination R2 = 0.69 – 0.77 for single-sided sheathing, and R2 = 0.82 - 0.84 for double-sided sheathing). The standard error of estimate (SEE) for each trend line is also shown in Figures 4-7.
Centre b/2 - SS 50 3b/8 - SS b/4 - SS 45 Centre b/2 - DS 40 Trend R2 = 0.77 - SEE = 5.83 kN Trend R2 = 0.82 - SEE = 5.09 kN 35
30
25
20 Failure load [kN] load Failure 15
10 Failure mode 1, 2 and 3 Only failure mode 1 5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 4 Failure load versus distance s from washer edge to loaded edge of bottom rail. All test results from study A (pith oriented downwards). The vertical line shows a border between failure modes. SS refers to single- sided tests and DS refers to double-sided tests. 9
Centre b/2 - SS 50 3b/8 - SS b/4 - SS 45 Centre b/2 - DS 40 Trend R2 = 0.72 - SEE = 6.69 kN Trend R2 = 0.35 - SEE = 5.09 kN 35
30
25
20 Failure load [kN] load Failure 15
10 Failure mode 1 and 2 Only failure mode 1 5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 5 Failure load versus distance s from washer edge to loaded edge of bottom rail. All test results from study A (pith oriented upwards). The vertical line shows a border between failure modes. SS refers to single- sided tests and DS refers to double-sided tests.
Centre b/2 - SS 50 3b/8 - SS b/4 - SS 45 Centre b/2 - DS* Centre b/2 - DS 40 Trend R2 = 0.71 - SEE = 6.62 kN 35 Trend R2 = 0.89 - SEE = 3.76 kN
30
25
20 Failure load [kN] load Failure 15
10
5 Failure mode 1, 2 and 3 Only failure mode 1 0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 6 Failure load versus distance s from washer edge to loaded edge of bottom rail. All test results from study B (pith oriented downwards). The vertical line shows a border between failure modes. SS refers to single- sided tests and DS refers to double-sided tests. *Set with boundary conditions as in study A. Results of this set are not included in the linear trend line. 10
Centre b/2 - SS 50 3b/8 - SS b/4 - SS 45 Centre b/2 - DS* 40 Centre b/2 - DS Trend R2 = 0.69 - SEE = 6.81 kN 35 Trend R2 = 0.84 - SEE = 4.65 kN
30
25
20 Failure load [kN] load Failure 15
10
5 Failure mode 1, 2 and 3 Only failure mode 1 0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 7 Failure load versus distance s from washer edge to loaded edge of bottom rail. All test results from study B (pith oriented upwards). The vertical line shows a border between failure modes. SS refers to single- sided tests and DS refers to double-sided tests. *Set with boundary conditions as in study A. Results of this set are not included in the linear trend line.
3. Theory
3.1. Fracture mechanics Fracture mechanics models are used to describe the influence of cracks and defects on material behaviour. The fracture mechanics theory is divided into two branches, depending on the material assumptions: (1) linear elastic fracture mechanics (LEFM) if the material under consideration is supposed to exhibit a linear or close to linear elastic behaviour up to the point on the load-deformation curve where fracture occurs and if it is assumed that all the available strain energy is consumed for propagating the crack; and (2) nonlinear fracture mechanics (NLFM) if the microstructural mechanisms that are capable of dissipating strain energy, such as deformations around the crack tip in metals, fibre bridging in wood, etc. are considered, Smith et al. (2003). In this analysis the strain energy release rate, part of the LEFM branch, will be used in order to derive formulas able to predict the failure load of a bottom rail failing in mode 1 and 2 (see section 2.4.1).
3.2. LEFM – Strain energy release rate Griffith (1921) made a study in order to provide a quantitative criterion for crack growth. If an elastic body is deformed by an external load, there is an elastic strain energy stored in the body in addition to a change in the potential energy of the load system. The Griffith criterion for crack growth is given by
ddW FU (1) ddAA
where dA is the incremental change in the crack area, F is the external work of load, U is the strain energy and W is the surface energy associated with crack formation. The left-hand side of Eq. (1) is 11 commonly referred to as the strain energy release rate Ȟ, while the right-hand side of Eq. (1) is commonly referred to as the crack resistance R.
Ȟ is often interpreted as the energy available to grow a crack of unit area, while R is interpreted as the energy required for the propagation of a crack of unit area. Usually there is a critical strain release energy c which is required to make a crack grow. In this case, the condition for crack growth is then
* c .
The material parameter c is usually determined experimentally. Ȟ can be calculated for an elastic body subjected to a load or displacement. If compliance C is defined as the reciprocal of the slope of the load-displacement curve, then Ȟ becomes:
1dC * P2 (2) 2dba
where b is the thickness of the specimen, P is the value of the force which causes the crack growth and a is the crack length. The failure load is then obtained as:
2 P c (3) dCA dA
where A is the area of the crack under consideration.
3.3. Splitting capacity of bottom rail for failure mode 1 and 2 The senior authors of this paper initiated a study for deriving the ultimate load for failure mode 1 (splitting at the bottom of the rail) and 2 (splitting at the side of the rail) by using a fracture mechanics approach. The result of the first part of the work was presented in Serrano et al. (2012) concerning failure mode 1. The work was then extended by one of the senior authors (Professor Bo Källsner) to include also failure mode 2, and the result was first presented at the CIB-W18 meeting in 2011 (see Serrano et al., 2011). Both fracture mechanics models, for failure mode 1 and 2, were presented in the WCTE 2012 conference (see Caprolu et al., 2012).
3.3.1. Splitting along the bottom side of the rail – Failure mode 1 The model for failure mode 1, splitting along the bottom side of the rail, is shown in Figure 8 (Serrano et al., 2012). A part of the bottom rail is considered as a fully clamped cantilever beam, where be represents the cantilever length (this is effective length consisting of the distance s and an additional length c discussed below). The length of the bottom rail is denoted by l, and the crack is assumed to propagate in the width direction simultaneously over the entire length of the bottom rail (the crack propagation is considered as a 2-dimensional problem). Considering both the flexural and the shear deformations, the compliance of the cantilever beam is obtained as:
3 4 §·bbeseE Ca ¨¸ (4) Elha©¹ Glha
where E is the modulus of elasticity, G is the (rolling) shear modulus and ȕs is the shear correction factor. Notice that E and G are the appropriate values for the perpendicular to grain direction. Using Eq. (3) with A = al and the compliance as given by Eq. (4), the failure load is obtained as: 12
2Gb ce Plha 2 (5) G §·be 12 ¨¸ Es Eha©¹
For small crack lengths a, Eq. (5) is simplified to
2Gb ce Plh 2 (6) G §·be 12 ¨¸ Es Eh©¹
Figure 8 Geometry of the bottom rail used for splitting along the bottom side of the rail.
The effective cantilever length is given by be = s + c (Figure 8), where c is an additional length taking into account the fact that fully clamped conditions cannot be assumed at the very edge of the washer (distance s), but practically at an additional distance beyond the edge due to local deformations, c. This additional length will be evaluated empirically (see below). It is obvious that the failure load for mode 1 increases as the distance s decreases.
3.3.2. Splitting along the edge side of the rail – Failure mode 2 For failure mode 2, splitting along the edge side of the rail, we present here the new model (cf. earlier conference presentations Serrano et al., 2011 and Caprolu et al., 2012). The fully clamped cantilever beam, as shown in Figure 9, is considered. In this case the cantilever length is represented by a. As for failure mode 1, taking into account both flexural and shear deformations, the compliance of the cantilever beam becomes:
3 4 §·aaE Ca ¨¸s (7) El©¹ hee Gl h
Using Eq. (3) with A = al and the compliance as given by Eq. (7), the failure load is obtained as:
2Gh ce (8) Pl 2 Ga§· 12 ¨¸ Es Eh©¹e
For small crack lengths a, the bending deformations can be ignored, leading to: 13
Pl 2 G ce hE s (9)
Again, for E and G, the appropriate values for the perpendicular to grain direction should be used. In general, these values are not necessarily the same as those used for failure mode 1. However, according to the derivations above the E- and G-modulus are the same for mode 1 and 2.
Figure 9 Geometry of the bottom rail used for splitting along the edge side of the rail.
It is noted that the failure load for mode 2 is independent of the distance s. This would suggest that the upper surface is free from any washer and that the model is applicable only if the distance s is larger than the cantilever length a (s > a). However, it is obvious on the other hand that mode 2 compared to mode 1 occurs only for smaller s-values (see below), which is confirmed by the experimental results. This means that the side crack opens even when there is a washer within the distance a. This may due to the fact that large portions of the bottom rail have no washer on the upper side and that the cracks develop in those areas and then later (or immediately) reach the area where the washers are located. There is a 3-dimensional effect. It is also noted that the anchor bolts and washers are discretely located along the bottom rail in the experiments and, therefore, the third dimension of the problem will have an effect on the initiation of cracks.
3.3.3. Initial crack length An input value for the initial crack length is needed in order to use the equations derived in the two previous sections. A proper crack length, a, for the two failure modes, using the initial crack method, is given in Serrano and Gustafsson (2006) as:
E c a 2 (10) S ft
where ft is the tension strength. Note that for E and ft, the appropriate values for the perpendicular to grain direction should be used.
3.3.4. Limit between failure mode 1 and 2
The limit (be,0) between failure mode 1 and mode 2 can be determined in the following way. The following condition:
lh() a1 22GGh1 c,1 2 c,2 e PlP1 t 2 (11) bGa2 be,0 G1 e,02 2 2 12 ( ) Es 12 ( ) Es Eha11 Eh2e 14
where, for generality, subscripts for respective failure mode are added and where the initial crack length is expressed as,
Ei c,i ai 2 ; i 1, 2 (12) S ft,i
can be written as
2 3 Es D1 bbe,0d e,0 2 0 (13) DDD323
where
Ga222 DE111c,1 ()212()ha G s (14) Eh2e
D22c,2e 2Gh (15)
12G1 D3 2 (16) Eh11() a
The solution is given by
22 22 DD23EE DD 23 3311ss 11 be,0 d22()() 22 ()() (17) 223223DD23 DD 23 D 3 DD 23 DD 23 D 3
For bscbee,0 d , failure mode 2 is applicable and for higher be values failure mode 1 applies. For isotropic conditions and without an initial crack length (a = 0), this limit is reduced to
442 442 EEEEh Eh23 Eh EEE Eh Eh 23 Eh 33sss sss be,0 d()() ()() (18) 24Ghee 24 Gh 36 G 24 Gh ee 24 Gh 36 G
In Figure 10 and 11 the limit between failure mode 1 and 2 using Eq. (17) and (18) are shown, respectively. Two different timber strength classes have been used in the plots: C24 and C50, this was done in order to evaluate the influence of the strength class on the limit between failure modes and also to see the influence on the failure mode. The values used in the equations are according to Table
4, where the subscript “iso” and “ortho” refer to isotropic and orthotropic, respectively. Eiso is the modulus of elasticity used when isotropy is considered for the analysis, ET is the modulus of elasticity in tangential direction, used for failure mode 1 and 2 when orthotropy is considered for the analysis,
Giso and Gortho are the rolling shear for isotropic and orthotropic analysis, respectively, ft,90 is the tensile strength perpendicular to grain, c is the fracture energy of the wood, b is the bottom rail width, h is the bottom rail depth, l is the length of the bottom rail and he is the position along the bottom rail depth where the horizontal crack appears. In an orthotropic material, the effective modulus of elasticity and shear modulus varies with the grain direction. As mentioned above, the parameters corresponding to a tangential annual ring orientation are used for the calculations in this paper. 15
For Eq. (17) orthotropic values have been used while for Eq. (18) isotropic values. The values for timber strength class C24 are according to Caprolu et al. (2012) and Serrano et al. (2012). The values for timber strength class C50 have been calculated in this way: the same ratio between Eiso and EL for
C24, with EL according to EN 338 (2009), was used to calculate Eiso for C50, with EL for C50 as given in the standard. To calculate ET the ratio EEELRT: :| 20 :1.6 :1, given in Bodig and Jayne (1993), was used, with EL according to EN 338 (2009). Regarding Giso and Gortho for C50, the first is taken according to EN 338 (2009), while the second is calculated using the same procedure as for ET for strength class C50, described above.
Table 4 Material properties for timber strength class C24 and C50 and data used in the evaluation. The subscripts iso and ortho refer to isotropic and orthotropic, respectively. ET is used for failure mode 1 and 2 for the orthotropic case.
Timber strength class C24 C50 Unit Material properties
Eiso 400 580 MPa
ET 500 800 MPa
Giso 70 100 MPa
Gortho 50 70 MPa
ft,90 2.50 MPa 2 Gc 300 J/m b 120 mm h 45 mm l 900 mm
he 22.5 mm
For Figure 10 a be,0 of 35.9 and 32.4 mm was found for strength classes C24 and C50, respectively. c 20 mm was chosen, then the limit between failure modes was found at s 15.9 mm for C24 and s 12.4 mm for C50.
25 C 50
20 C 24
15 Failure mode 2
10
Failure load [kN] load Failure Failure mode 1
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 10 Limit between failure mode 1 and 2 for timber strength classes C24 and C50. Orthotropic values used, according to Table 4. Plots according to Eq. (17). 16
It is noted that the curve for failure mode 1 is almost the same for strength class C24 and C50, at least until the limit for class C24. However it is noted that a higher failure load is obtained if the strength class used is higher and the limit between failure modes, in terms of distance s, decreases. In
Figure 11 the limit between failure modes was found to be really similar,be,0 38.9 and 39.1 mm for C24 and C50, respectively. Using the same c as for the previous case, the limit was given at s 18.9 and s 19.1mm, for C24 and C50, respectively.
35
30 C 50
25 C 24
20
Failure mode 2 15
Failure load [kN] load Failure Failure mode 1 10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 11 Limit between failure mode 1 and 2 for timber strength classes C24 and C50. Isotropic values used, according to Table 4. Plots according to Eq. (18).
In this case the parallelism between the two strength classes is more marked. Analysing the formulas used it is noted that the only varied parameters were E, G and be,0. Since the ratio between E and G was of the same magnitude for C24 and C50 for both isotropic and orthotropic case, it seems that the distance be,0 has the strongest influence in the formula. In the case of Figure 10 the be,0 values were different while for Figure 11 the be,0 was found to be really close for both C24 and C50, and this is the reason of the more marked parallelism.
3.3.5. Limit fastener spacing for ensuring ductile behaviour of the sheathing-to-timber joints In Caprolu et al. (2014a), a formula based on Johansen (1949) plus the rope effect was proposed:
2E PMfdF 2 K (19) 31 E y h,s ax
3 where the fastener yield moment is Mfdyy 6 , fy is the tensile strength, d is the diameter of the fastener, E ffh,s h,w , fh,s is the embedment strength of the sheathing, fh,w is embedment strength of the wood, Ffdtax ax pen is the axial withdrawal force capacity, fax the axial withdrawal strength, tpen the point side penetration length or the length in the threaded part in the point side member, and K is a factor depending on the angle between the two plastic hinges in the fastener in the 17 bottom rail and sheathing, respectively, when the joint reaches its failure load (for the details the reader is referred to Caprolu et al., 2014a). In this paper, the value K 1/4 will be assumed, as in Eurocode 5 (2008). If n is taken as the number of nails along the bottom rail length l and the spacing between the nails is e, then including the corner nails nlee ()/ , which approximately can be written as nle / . The limit for ductile behaviour of the sheathing-to-framing joints is found by multiplying nle / times Eq. (19) and equating that to the expression for failure mode 1 as given in the left hand side of Eq.
(11). The limit spacing e versus the effective cantilever length be can then be expressed as:
2 ªº be G1 §·be 2E eMfdF 12¨¸EKsyax«» 2 h,s (20) Eha 1 ha 11c12 G 11©¹¬¼E
For PP21d , failure mode 2 is applicable, with a constant value for e. In Figure 12 and 13 the limit for ductile behaviour of the sheathing-to-timber joints in terms of distance e and distance s is shown plotting Eq. (20). The limit between the curve for failure mode 1 and the line for failure mode 2 is as in the previous section 3.3.4. Two different timber strength classes have been used in the plots: C24 and C50. The values used in the equation are according to Table 4. The values needed for Eq. (19) are taken from Caprolu et al. (2014a). In Figure 12 the Eqs. (5) and (8) with orthotropic values are used. Choosing the right values for distance e and distance s the ductile behaviour could be reached. In Caprolu et al. (2014a) was found that decreasing the distance s the failure load increases. Failure mode 3 was found to appear only for small values of the distance s. The graphs in Figures 12 and 13 verify these findings. If higher timber strength class is used the “area” for the combinations of e and s, where ductile failure occurs is increased, especially if isotropic properties are considered.
60
55
50
Failure mode 3 45 [mm] e 40
35 Distance Failure mode 1 C 24 30
25 C 50 Failure mode 2 20 0 5 10 15 20 25 30 35 40 Distance s [mm] Figure 12 Limit for ductile behaviour of the sheathing-to-timber joints for timber strength classes C24 and C50. Plot according to Eqs. (5), (8) and (20), with orthotropic values of wood according to Table 4.
In Figure 13 the Eqs. (6) and (9) with isotropic values are used. The same but more marked behaviour in terms of strength classes, as in Figure 12, is noted. 18
50
45
40
Failure mode 3 35 [mm] e 30
C 24 25 Distance
20 Failure mode 1 C 50 15 Failure mode 2
10 0 5 10 15 20 25 30 35 40 Distance s [mm] Figure 13 Limit for ductile behaviour of the sheathing-to-timber joints for timber strength classes C24 and C50. Plot according to Eqs. (6), (9) and (20), with isotropic values of wood according to Table 4.
4. Evaluation of theory and tests In Caprolu et al. (2014a; 2014b) an analysis of the failure load of the bottom rail for mode 1 and 3 based on a strength-of-material approach was presented. Failure mode 2 was not taken into account since the analysis did not work properly. In this section an analysis of the failure load of the bottom rail for failure mode 1 and 2, based on a fracture mechanics approach, is presented. For failure mode 1 the bottom rail is modelled as in Figure 8 and Eqs. (5) and (6) are used, while for failure mode 2 the bottom rail is modelled as in Figure 9 and Eqs. (8) and (9) are used. Where needed, Eq. (10) is used for calculating the initial crack length a. The formulas are tested with both isotropic and orthotropic material parameters, according to Table 4, but only for the strength class C24.
As pointed out in Serrano et al. (2011), the value of c is strongly dependent on which failure mode is involved during crack propagation, and this mode of fracture will in general vary during loading.
For simplicity, here only mode I (opening mode) is taken into account so that cc,I .This simplification is practical and in general a safe approach, since c,I c,II . Further, since wood is an orthotropic material, the three directions (longitudinal, radial and tangential) give six possible orientations of the crack. The possible orientations are called: RL, TL, LT, RT, LR and TR. In this notation the first letter indicates the direction normal to the crack plane while the second letter indicates the direction of the crack growth. Since there are three loading modes for crack orientation, there are a total of 18 crack situations, with different values of the crack resistance. According to this crack notation, failure mode 1 has orientation TR and failure mode 2 RT. A further approximation made for simplicity is that the value of c,I is set as independent of the crack direction. 19
4.1. Failure mode 1
4.1.1. Evaluation of the effective cantilever length
As has already been shown bcse . In Caprolu et. al (2014a; 2014b), four different values for c (= 15; 20; 25 and 30 mm) were used to find the best fit with the test results. In this article the root- mean-square error (RMSE) has been calculated to find the “optimal” c for the experimental results. To the distance s was added the additional length c, ranging from 0 to 60 mm. The value giving the “optimal” c was then taken as the value of c giving the smallest RMSE. This was done for Eqs. (5) and (6) with both orthotropic and isotropic properties according to Table 4. The procedure was repeated for both single- and double-sided sheathing specimens. In Table 5 the “optimal” c and the corresponding value of the RMSE are listed.
Table 5 Results of the evaluation of the effective cantilever length c.
Study A -PD Study A -PU Study B -PD Study B -PU Single-sided specimens c [mm] 21.5 20.6 24.6 27.9 Eq. (5) - Ortho RMSE [kN] 2.35 2.98 2.68 3.09 c [mm] 24.2 23.4 26.9 30.0 Eq. (5) - Iso RMSE [kN] 2.41 2.79 2.73 3.05 c [mm] 32.4 32.3 37.9 41.8 Eq. (6) - Ortho RMSE [kN] 2.43 3.71 2.68 3.32 c [mm] 32.8 32.3 37.0 40.6 Eq. (6) - Iso RMSE [kN] 2.34 3.32 2.66 3.20 Double-sided specimens c [mm] 23.4 26.5 19.8 29.5 Eq. (5) - Ortho RMSE [kN] 4.73 4.08 4.03 4.04 c [mm] 25.9 28.3 21.9 30.8 Eq. (5) - Iso RMSE [kN] 5.07 4.09 3.92 3.88 c [mm] 36.1 41.5 33.8 47.0 Eq. (6) - Ortho RMSE [kN] 4.09 4.09 4.74 4.67 c [mm] 35.5 39.7 32.5 44.0 Eq. (6) - Iso RMSE [kN] 4.32 4.07 4.37 4.40
The results show RMSE-values of the same magnitude between the different equations and assumptions used. For specimens with single-sided sheathing the RMSE-values range from 2.34 to 3.71. Lower values were found for specimens with pith downwards, however, the variation with respect to specimens with pith upwards is negligible. The variation between the different equations is also negligible. Regarding specimens with double-sided sheathing, the RMSE-values are higher compared those for single- sided sheathing, and range from 3.88 to 5.07. Even in this case the variation between the equations and pith orientations is negligible. As an illustration, in Figure 14 the test results vs. Eq. (5) with orthotropic properties is shown for single-sided specimens from study B with pith oriented upwards. The related graph for RMSE vs. distance c is shown in Figure 15. 20
30 35
30 25
25 20
20 15 15 RMSE [kN]
Failure load [kN] load Failure 10 10
5 5
0 0 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 Distance s [mm] Effective cantilever length c [mm] Figure 14 Failure load versus distance s from washer Figure 15 RMSE versus the effective cantilever length edge to loaded edge of the bottom rail. Test results c for Eq. (5) and test results from study B (pith from study B (pith oriented upwards). Curve according oriented upwards). “Optimal” c found as c 27.9 to Eq. (5) with orthotropic values according to Table 4 mm. and c according to Table 5.
4.1.2. Comparison between analytical and experimental results The results of the analysis for failure mode 1 are shown in Figures 16-19 for specimens with both single- and double-sided sheathing for study A and B and for different pith orientations. In these figures only the mean values of the results of specimens failed in mode 1 are included. The failure loads versus distance s for all specimens, independently on the failure modes, are shown in Figures 4- 7. In the figures curves according to Eqs. (5) and (6) are given using both isotropic and orthotropic material parameters according to Table 4. For specimens with double-sided sheathing, the failure loads given in Eqs. (5) and (6) have been multiplied by a factor of 2. These four curves are the curves on the upper part of the figures. The value of be used was calculated using the value of c evaluated in the previous section and listed in Table 5. For simplicity, instead of referring to the equation number, the curves are identified by the material properties chosen and by the inclusion of the initial crack length a, Eq. (5), or without it a 0 , Eq. (6). 21
50 Single-Sided 45 Double-Sided Ortho, a 40 Ortho, a = 0 Iso, a 35 Iso, a = 0 30
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 16 Results of the analysis for failure mode 1 for specimens with single- and double-sided sheathing. Only mean values for specimens failed in mode 1 are shown, while the failure loads for all specimens, independently on the failure mode, are shown in Figures 4-7. Curves according to Eqs. (5) and (6) using both isotropic and orthotropic values. Results from study A (pith oriented downwards). The c values used in the equations are according to Table 5. 22
50 Single-Sided 45 Double-Sided Ortho, a 40 Ortho, a = 0 Iso, a 35 Iso, a = 0 30
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 17 Results of the analysis for failure mode 1 for specimens with single- and double-sided sheathing. Only mean values for specimens failed in mode 1 are shown, while the failure loads for all specimens, independently on the failure mode, are shown in Figures 4-7. Curves according to Eqs. (5) and (6) using both isotropic and orthotropic values. Results from study A (pith oriented upwards). The c values used in the equations are according to Table 5. 23
50 Single-Sided 45 Double-Sided Double-Sided* 40 Ortho, a Ortho, a = 0 35 Iso, a 30 Iso, a = 0
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 18 Results of the analysis for failure mode 1 for specimens with single- and double-sided sheathing. Only mean values for specimens failed in mode 1 are shown, while the failure loads for all specimens, independently on the failure mode, are shown in Figures 4-7. Curves according to Eqs. (5) and (6) using both isotropic and orthotropic values. Results from study B (pith oriented downwards). The c values used in the equations are according to Table 5. *Results of set 1-BC(A) of study B, with boundary conditions according to study A. 24
50 Single-Sided 45 Double-Sided Double-Sided* 40 Ortho, a Ortho, a = 0 35 Iso, a 30 Iso, a = 0
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 19 Results of the analysis for failure mode 1 for specimens with single- and double-sided sheathing. Only mean values for specimens failed in mode 1 are shown, while the failure loads for all specimens, independently on the failure mode, are shown in Figures 4-7. Curves according to Eqs. (5) and (6) using both isotropic and orthotropic values. Results from study B (pith oriented upwards). The c values used in the equations are according to Table 5. *Results of set 1-BC(A) of study B, with boundary conditions according to study A.
In general it seems like both Eqs. (5) and (6) are good predictors of the final failure load. However it is noted that they have a different behaviour since Eq. (6) gives higher failure loads for large values of distance s than Eq. (5). On the other hand Eq. (5) gives higher failure load for small values of distance s, showing behaviour according to test results. However it should be noted that for small values of distance s the experimental failure loads are probably influenced by the low failure loads of mode 2 (censored data).
4.2. Failure mode 2 The results of the analysis for failure mode 2 are shown in Figures 20-23 for specimens with single- and double-sided sheathing, for study A and B and for different pith orientations. In these figures only results of specimens failed in mode 2 are included and the mean value for each set tested is shown. The failure loads are calculated according to Eqs. (8) and (9) using both isotropic and orthotropic values and they are shown by the 8 straight lines, four for single-sided and four for double- sided sheathing, in Figures 20-23. For specimens with double-sided sheathing, the failure loads given in Eqs. (8) and (9) have been multiplied by a factor of 2, therefore the four lines below the failure load value of 30 kN refer to single-sided sheathing, while the four lines above the failure load value of 40 kN refer to double-sided sheathing. In Figure 21 no results are shown for specimens with double-sided sheathing since in this case no specimens failed with failure mode 2. The linear trend lines of the test results for specimens with single-sided sheathing with their coefficients of determination R2 and 25 standard error of the estimate (SEE) values are also shown in Figures 20-23. In Figure 22, the failure load for the set with a distance s of 15 mm is not taken into account for calculating the linear trend line for specimens with single-sided sheathing since it is believed to be an unrealistic value. In Figure 23, for specimens with double-sided sheathing and distance s of 10 mm two mean failure loads are shown. It is due to the fact that for two specimens of this set it was difficult to establish if the failure mode was 2 or 3. Therefore one value refers to the case of six mode 2 failures and one value to the case of eight mode 2 failures. It is observed in Figures 20-23 that the trend lines for the test results are not horizontal as may be expected from the analytical model. There may be several reasons for that. As indicated earlier, the model is based on the assumption that there is no washer above the crack preventing the crack opening, i.e. for large s-values the model should give better predictions of failure load. For small s- values the washer restricts the vertical displacement and, therefore, a higher failure is obtained. Also, the interaction between the failure modes 1 and 2 influences the test results. For large s-values mode 1 failure dominates and the loads are low implying that the loads for mode 2 failure also will become low. For small s-values mode 2 failure dominates and the load levels for mode 2 failure will not be much affected. These so called censured test data should be evaluated statistically in order to obtain more reliable load levels with respect to the two failure modes.
60
55
50
45
40
35
30 Single-Sided 25 Failure load [kN] load Failure Double-Sided 20 Ortho, a Ortho, a = 0 15 Iso, a Iso, a = 0 10 R2 = 0.57 - SEE = 4.31 5 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 20 Results of the analysis for failure mode 2 for specimens with single- and double-sided sheathing. Values according to Eqs. (8) and (9) using both isotropic and orthotropic values. Results from study A (pith oriented downwards). 26
30
25
20
15
Failure load [kN] load Failure Single-Sided Ortho, a Ortho, a = 0 10 Iso, a Iso, a = 0 R2 = 0.55 - SEE = 6.29 5 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 21 Results of the analysis for failure mode 2 for specimens with single-sided sheathing. Values according to Eqs. (8) and (9) using both isotropic and orthotropic values. Results from study A (pith oriented upwards).
60
55
50
45
40
35
30 Single-Sided 25 Failure load [kN] load Failure Double-Sided 20 Ortho, a Ortho, a = 0 15 Iso, a Iso, a = 0 10 R2 = 0.87 - SEE = 3.04 5 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 22 Results of the analysis for failure mode 2 for specimens with single- and double-sided sheathing. Values according to Eqs. (8) and (9) using both isotropic and orthotropic values. Results from study B (pith oriented downwards). The value with a distance s of 15 mm is not taken into account for calculating the linear trend line since it is believed to be unrealistic. 27
60
55
50
45
40
35
30 Single-Sided Double-Sideda) 25 Failure load [kN] load Failure Double-Sidedb) 20 Ortho, a Ortho, a = 0 15 Iso, a Iso, a = 0 10 R2 = 0.77 - SEE = 3.19 5 0 5 10 15 20 25 30 35 40 Distance s [mm]
Figure 23 Results of the analysis for failure mode 2 for specimens with single- and double-sided sheathing. Values according to Eqs. (8) and (9) using both isotropic and orthotropic values. Results from study B (pith oriented upwards). For two specimens with double-sided sheathing and distance s of 10 mm it was difficult to establish if the failure mode was 2 or 3, therefore case a) refers to the case of six failure mode 2 and the case b) to the case of eight failure mode 2.
Both Eqs. (8) and (9) seem to predict the failure load with a reasonable agreement with the test results. For double-sided sheathing Eq. (8) with orthotropic values seems to give the best fitting. Unlike failure mode 1, the initial crack length a seems to be less decisive, since even Eq. (9) with orthotropic values gives a good prediction, while the use of orthotropic values seems to be decisive for a better agreement. Regarding specimens with single-sided sheathing it is harder to state which equation gives the best fitting, due to the wide scatter of the results.
5. Discussion The test results, with respect to failure mode and load carrying capacity, have already been discussed in detail in Caprolu et al. (2014a; 2014b), therefore only a short summary of the main findings is presented here. The failure modes are strongly dependent on the distance s from the washer edge to the loaded edge of the bottom rail. For s PPRQO\IDLOXUHPRGHRFFXUV The results show that splitting failure in the bottom rail can be avoided by using a proper distance s, i.e. an appropriate bolt position and washer size. As seen in Tables 2 and 3, the load-carrying capacities of specimens with the pith oriented downwards are higher than those with the pith oriented upwards. The reason for this effect with respect to the pith orientation is probably caused by the initial cupping due to the anisotropic shrinkage from drying (cf. Caprolu et al. 2014a; 2014b), but may also be an effect of the anisotropic material properties in the radial-tangential plane of the timber. Figures 4-7 show that both the distance s and the pith orientation are factors influencing the failure load. As noted by Serrano et al. (2011), the analyses here performed are in 2D. It is likely that using a two dimensional model, the predicted load-carrying capacity will be overestimated, since such a model does not take into account the variation in stress distribution in the longitudinal direction of the 28 rail. Stress concentrations prior to fracture probably occur close to the anchor bolts. A three dimensional analysis could be used to evaluate the significance of this, and to suggest some factor that would compensate for it in the two dimensional mode l. Further, in order to keep the analysis simple, factors such as the friction between the washer and the rail, the friction between the substrate and the rail, pretension of the anchor bolt and how the load P is introduced to the rail are not taken into account. Despite all these simplifications, the results of the analysis of failure mode 1, shown in Figures 16- 19, agree quite well with the test results. For large s-values, Eq. (6), where the initial crack length a was not taken into account, tends to predict a failure load too high compared to the test results, for both experimental studies. Even for study A, with a higher failure load for the tests with respect to study B, the predicted failure load is too high. The formula has been tested with both isotropic and orthotropic values, but in both cases the predicted failure load is too high. A good agreement has been found using Eq. (5). The introduction of the initial crack length a, seems to improve the prediction of the failure load. As for Eq. (6), Eq. (5) has been tested with both isotropic and orthotropic values. The predicted failure load agrees well with the experimental results in both cases, meaning that it may be sufficient to only consider isotropic values in order to get acceptable good prediction on the final failure load. Regarding the analysis of failure mode 2, shown in Figures 20-22, a good agreement between predicted failure load and test results is found even in this case. The good agreement is given by both Eqs. (8) and (9) and, unlike of Eqs. (5) and (6), the decisive parameter for the good prediction of the failure load seem to be given by the orthotropic values. It should be considered that when the equation with the initial crack length is used, for failure mode 2, the values used for its calculation, listed in Table 4, give an a equal to 6.11 mm and 7.64 mm for isotropic and orthotropic cases, respectively. In general the simple fracture mechanics models discussed here contain the essential parameters governing the behaviour with respect to splitting of bottom rails in partially anchored shear walls. The values of the different parameters can then be adjusted to the experimental results and used for design.
6. Conclusions Two experimental programs on the splitting capacity of bottom rails in partially anchored timber frame shear walls have been conducted. The bottom rail was sheathed on one and or both sides and the load was applied on the sheathing as a vertical uplifting force. The test results show that the distance s between the edge of the washer and the loaded edge of the bottom rail has a significant impact on the failure mode and load carrying capacity of the bottom rail. The capacity is also to some degree dependent on the pith orientation of the bottom rail. The results show that using small values of distance s help to reach a ductile failure mode of the sheathing-to- framing joints and to increase the load carrying capacity of the bottom rail. An improved capacity is obtained by orienting the pith downwards. The two analytical models for determining the load-carrying capacity give results that are in good agreement with the test results. The analytical model derived for failure mode 1 gives a behaviour which is in good agreement with the test results, with a failure load that increases when the distance s is decreased. The influence of the isotropic and orthotropic material properties and the use of the initial crack length a in the equation has some minor influence on the curve shape. The analytical model for failure mode 2 gives also a good agreement with the test data resulting in a constant capacity independent on the distance s. For this model the influence of the isotropic and orthotropic properties and the use of the initial crack length a in the equation has somewhat more influence on the capacity than the model for failure mode 1. A limit between the two failure modes has been calculated, in terms of distance s, which shows that decreasing the distance s the failure mode would change from mode 1 to mode 2. Finally a method for obtaining a ductile behaviour of the sheathing-to-framing 29 joints is demonstrated by choosing proper values on the distance between the fasteners and the distance s.
7. Future work Tests should be done to evaluate values of fracture energy in the crack direction in the TR- and RT- plane and of ft,90 in tangential and radial direction. For simplification the same values was used here for both failure mode. A 3D analysis should be done to evaluate the significance of other parameter not taken into account in this 2D study, as variation in stress distribution in the longitudinal direction of the rail.
8. Acknowledgements The authors would like to express their sincere appreciation for the financial support from the County Administrative Board in Norrbotten, the Regional Council of Västerbotten and the European Union’s Structural Funds – The Regional Fund.
9. References Bodig J. and Benjamin A. J. (1993) Orthotropic Elasticity. In J. Bodig and A. J. Benjamin. Van Nostrand Reinhold (ed) New york, USA, pp 87-126. BS 5268 (1996) The Structural Use of Timber. British Standards Institution. Caprolu G. (2011) Experimental testing of anchoring devices for bottom rails in partially anchored timber frame shear walls. Technical Report, ISBN 978-91-7439-302-6, Luleå University of Technology, Sweden. Caprolu G. (2012) Experimental testing of anchoring devices for bottom rail in partially anchored timber frame shear walls with two-sided sheathing. Technical Report, ISBN 978-91-7439-387-3, Luleå University of Technology, Sweden. Caprolu G., Girhammar U. A., Källsner B. and Vessby J. (2012) Analytical and experimental evaluation of the capacity of the bottom rail in partially anchored timber shear walls. In: 12th World Conference on Timber Engineering, Auckland, New Zealand. Caprolu G., Girhammar U. A., Källsner B. and Lidelöw H. (2014a) Splitting capacity of bottom rail in partially anchored timber frame shear walls with single-sided sheathing. The IES Journal Part A: Civil & Structural Engineering, 7:83-105. Caprolu G., Girhammar U. A. and Källsner B. (2014b) Splitting capacity of bottom rails in partially anchored timber frame shear walls with double-sided sheathing. The IES Journal Part A: Civil & Structural Engineering, DOI:10.1080/19373260.2014.952607. Eurocode 5 (2008) Design of Timber Structures. prEN 1995-1-1:2003 Part 1-1: General – Common Rules and Rules for Building. EN 338 (2009) Structural timber – Strength classes. European Committee for Standardization, Brussels, Belgium. EN 594 (2008) Timber Structures – Test methods – Racking strength and stiffness of timber frame wall panels. European Committee for Standardization, Brussels, Belgium. EN 622-2 (2004) Fibreboards – Specifications – Part 2: Requirements for hardboard. European Committee for Standardization, Brussels, Belgium. Girhammar U. A. and Källsner B. (2009) Design aspects on anchoring the bottom rail in partially anchored wood-framed shear walls. In: Proceedings CIB-W18 Timber Structures Meeting, Dübendorf, Switzerland, Paper 42-15-1. Girhammar U. A., Källsner B. and Daerga P. A. (2010) Recommendations for design of anchoring devices for bottom rails in partially anchored timber frame shear walls. In: 10th World Conference on Timber Engineering, Riva del Garda, Italy. 30
Girhammar, U. A. and Juto H. (2009) Testing of cross-wise bending and splitting of wooden bottom rails in partially anchored shear walls (in Swedish). Luleå University of Technology, Technical Report, Luleå, Sweden 2013 (originally presented as an internal report, Umeå University, 2009). Griffth A. A. (1921) The phenomena of rupture and flow in solids. Philosophical Transaction of the Royal Society of London, 221:163-197. Griffiths B., Enjily V., Blass H. and Källsner B. (2005) A unified method for the racking resistance of timber framed walls for inclusion in Eurocode 5. In: Proceedings CIB-W18 Timber Structures Meeting, Karlsruhe, Germany, Paper 38-15-9. ISO 3130 (1975) Wood – Determination of moisture content for physical and mechanical tests. International Organization for Standardization, Geneva, Switzerland. ISO 3131 (1975) Wood – Determination of density for physical and mechanical tests. International Organization for Standardization, Geneva, Switzerland. Johansen, K. W. (1949). Theory of Timber Connections. Paper presented at the International Association of Bridge and Structural Engineering, Bern. Källsner B. and Girhammar U. A. (2005) Plastic design of partially anchored wood-framed wall diaphragms with and without openings. In: Proceedings CIB-W18 Timber Structures Meeting, Karlsruhe, Germany, Paper 38-15-7. Porteous J. and Kermani A. (2007) Design of Stability Bracing, Floor and Disphragms. In J. Porteous and A. Kermani (ed) Structural Timber Design to Eurocode 5. Wiley-Blackwell (ed) Malden, USA, pp 338-371. Prion H. G. L. and Lam F. (2003) Shear walls Diaphragms. In S. Thelandersson and H. J. Larsen (ed) Timber Engineering. John Wiley & Sons Ltd (ed) Chichester, England, pp 383-408. Serrano E. and Gustafsson P. J. (2006) Fracture mechanics in timber engineering – Strength analyses of components and joints. Material and Structures, 40:87-96. Serrano E., Vessby J., Olsson A., Girhammar U. A. and Källsner B. (2011) Design of bottom rail in partially anchored shear walls using fracture mechanics. In: Proceedings CIB-W18 Timber Structures Meeting, Alghero, Sardinia, Italy, Paper 44-15-4. Serrano E., Vessby J. and Olsson A. (2012) Modeling of fracture in the sill plate in partially anchored shear walls. Journal of Structural Engineering, 138:1285-1288. Smith I., Landis E. and Gong M. (2003) Principle of Fracture Mechanics. In Smith I., Landis E. and Gong M. (ed) Fracture and Fatigue in Wood. John Wiley & Sons Ltd (ed), Chichester, England, pp 67-97. Vessby J., Serrano E., Olsson A., Girhammar U. A. and Källsner B. (2012) Simulation of bottom rail fracture in partially anchored shear walls using XFEM. In: Proceedings CIB-W18 Timber Structures Meeting, Växjö, Sweden, Notes.
Paper IV
1
Fracture Mechanics Models for Brittle Failure of Bottom Rails due to Uplift in Timber Frame Shear Walls Joergen L. Jensena, Giuseppe Caprolu*1 and Ulf Arne Girhammar1 1Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden
Abstract. In partially anchored timber frame shear walls hold down devices are not provided, hence the uplift forces are transferred by the fasteners of the sheathing-to-framing joints into the bottom rail and via anchor bolts from the bottom rail into the foundation. Since the force in the anchor bolts and the sheathing-to-framing joints do not act in the same vertical plane, the bottom rail is subjected to tensile stresses perpendicular to the grain and splitting of the bottom rail may occur. This paper presents simple analytical models based on fracture mechanics for the analysis of such bottom rails. An existing model is reviewed and several alternative models are derived and compared qualitatively and with experimental data. It is concluded that several of the fracture mechanics models lead to failure load predictions which seem in sufficiently good agreement with the experimental results to justify their application in practical design.
Keywords: bottom rail; splitting of bottom rail; timber shear walls; partially anchored
1. Introduction The problem of splitting of the bottom rail in partially anchored shear walls due to uplift has previously been studied by Girhammar and Källsner (2014) with an empirical approach and with a fracture mechanics treatment in Serrano et al. (2011), where a comparison between a finite element analysis and analytical solutions was made. The analytical models presented in Serrano et al. (2011) were preliminary presented at the WCTE 2012 conference (Caprolu et al. 2012) and more in detail in Caprolu et al. (2014c), where a comparison was made between the analytical models and experimental results. In the present paper, the models presented in Serrano et al. (2011) and Caprolu et al. (2014c) are reviewed and alternative models are derived. Model predictions are compared with experimental data previously presented in Caprolu et al. (2014a; 2014b).
2. Experimental background An experimental background based on Caprolu et al. (2014a; 2014b) is reviewed here. The aim of this section is to give the essential information needed to understand and evaluate the capabilities of the fracture mechanics models presented.
2.1. Test specimen and material properties The specimen was made up of a bottom rail joined to sheathing by nails. The material properties were as follow: x Bottom rail: spruce (PiceaAbies), C24 according to EN 338 (2009). a Email: [email protected] * Corresponding author, PhD Student, email: [email protected] 2
x Sheathing: hardboard, 8 mm (wet process fibre board, HB.HLA2, EN 622-2 (2004), Masonite AB). x Sheathing-to-timber joints: annular ringed shank nails, 50×2.1 mm (Duofast, Nordisk Kartro AB). The holes in the sheathing were pre-drilled, 1.7 mm. x Anchor bolt: Ø 12 (M12). The holes in the bottom rail were pre-drilled 13 mm.
2.2. Test programme and setup Two studies on the splitting failure capacity of bottom rail were carried out, here called study A and study B. Both of them studied bottom rails with single- and double-sided sheathing. The differences between the two studies were for single-sided sheathing: (1) the boundary conditions. Details can be found in Caprolu et al. (2014a; 2014b).In study A, the load was applied in a distributed way while in study B a hinge was created allowing the specimen to rotate; (2) the nail spacing in the sheathing-to-framing joints. In study A, the nail spacing was 50 mm for series 1 and 25 mm for series 2 and 3, while in study B it was 50 mm for all specimens; (3) the torque used to tighten the bolts. 40 Nm was applied in study A and 50 Nm in study B; (4) the displacement rate. 2 mm/min was used in study A and, by mistake, 10 mm/min in study B. For double-sided sheathing the only difference between the two studies was the boundary conditions. The main aim of the experimental programme was to study the influence of the distance between the edge of the washer and the loaded edge of the bottom rail, here denoted s, on the failure load and mode of the bottom rail. The distance was varied changing the washer size and the anchor bolt position according to Table 1 for specimens with single- sided sheathing, and only the washer size for specimens with double-sided sheathing, where the anchor bolt was kept at the centre of the bottom rail for all tests. The specimens were fixed to a supporting structure and loaded with an uplifting load. Figure 1a and 1b show the test set-up of the experiments for single- and double-sided sheathing, respectively.
a) b)
Figure 1 Cross-section view of the specimen tested: (a) single-sided sheathing; and (b) double-sided sheathing.
In Table 1, the test program of study A and B is specified. 3
Table 1 Specification of specimen tested in study A and study B. Notation: SS = single-sided specimens, DS = double-sided specimens, b = width of rail, s = distance from washer edge to loaded edge of the bottom rail (cf. Figure 1).
Study A Study B Anchor bolt position Size of washer Distance s Set Number of tests Number of tests
Series SS DS SS DS [mm] [mm] [mm] 1-BC(A)a) ---16 40×40×15 40 1 10 10 16 16 40×40×15 40 b/2 1 2 10 10 16 16 60×60×15 30 60 mm from sheathing 3 10 10 16 16 80×70×15 20 4 10 10 16 16 100×70×15 10 110 14 40×40×15 25 3b/8 2 2 10- 16- 60×60×15 15 45 mm from sheathing 3 10 16 80×70×15 5 110 16 b/4 40×40×15 10 3 - - 2 9 1630 mm from sheathing 60×60×15 0 a) Set with boundary conditions as study A.
2.3. Test programme and setup
2.3.1. Failure modes Three primary failure modes as shown in Figure 2 were found during the experimental programmes: Mode 1: Splitting along the bottom side of the rail according to Figure 2a. Mode 2: Splitting along the edge side of the rail according to Figure 2b. Mode 3: Yielding and withdrawal of the nails in the sheathing-to-framing joints according to Figure 2c.
a) Mode 1
b) Mode 2
c) Mode 3 Figure 2 (a) Splitting failure along the bottom side of the rail; (b) splitting failure along the edge side of the rail; and (c) yielding and withdrawal of the nails in the sheathing-to-framing joints. 4
The failure mode was found to be mainly dependent on the distance s in both studies. For distance s PPIDLOXUHPRGHZDVWKHRQO\IDLOXUHPRGHZKLOHIRUGLVWDQFHs PPIDLOXUHPRGHDQG 3 also appeared (for specimens with pith upwards and single-sided sheathing, the limit for exclusion of failure modes 2 and 3 was s PP).
2.3.2. Failure loads and crack development In Tables 2 and 3 the failure load recorded during the experimental studies are listed. Table 2 refers to specimens with pith oriented upwards and Table 3 to specimens with pith oriented downwards. The mean failure load for each set is shown. Further, the mean failure load for each failure mode, according to Figure 2, is listed. In each table specimens with both single- and double-sided sheathing are included.
Table 2 Results from testing of specimens with the pith oriented upwards (PU).
Mean failure load [kN] Mean failure load [kN] Set Failure mode Set Failure mode Series All failure modes (1) (2) (3) All failure modes (1) (2) (3) Study A Single-sided tests Double-sided tests 1a) 1 12.6 12.6 - - 1 - - - - 2 11.3 11.3 - - 2 25.0 25.0 - - 3 17.0 12.9 21.0 - 3 30.8 30.8 - - 4 24.1 24.3 23.8 - 4 - - - - 2 1 21.5 - 21.5 - 2 21.2 - 21.2 - 3 28.9 30.6 27.1 - - 3 1 19.9 - 19.9 - 2 27.1 - 27.1 - Study B Single-sided tests Double-sided tests -1-BC(A)b) 17.0 17.0 - - 1 1 9.49 9.49 - - 1 17.6 17.6 - - 2 10.6 10.6 - - 2 19.5 19.5 - - 3 17.1 16.8 - 18.7 3 34.0 33.4 35.8 - 37.8 4 19.4 19.4 18.1 20.1 4c) 39.5 - 44.5 (39.5) 2 1 12.2 12.2 - - 2 16.9 16.6 17.5 - 3 22.6 23.2 22.2 - - 3 1 18.6 17.9 18.6 18.9 2 21.3 - 21.4 20.8 Failure modes are defined in Figure 2.a) Series 1 of study A had a nails distance of 50 mm instead of 25 mm as the other two series of study A. b) Set with boundary conditions as in study A. c) For two specimens of this set it was difficult to establish if the failure mode was mode 2 or 3. The results without parenthesis refer to the case of six failure mode 2 and two failure of mode 3, while the results in parenthesis refer to the case of eight failure mode 2. 5
Table 3 Results from testing of specimens with the pith oriented downwards (PD).
Mean failure load [kN] Mean failure load [kN] Set Set
Series Failure mode Failure mode All failure modes (1) (2) (3) All failure modes (1) (2) (3) Study A Single-sided tests Double-sided tests 1a) 1 12.0 12.0 - - 1 22.1 22.1 - - 2 13.5 13.5 - - 2 29.2 29.2 - - 3 17.4 17.4 - - 3 38.6 39.0 - 35.9 4 22.8 22.1 28.6 20.7 4 39.7 39.3 43.4 - 2 1 16.0 16.0 - - 2 20.7 20.3 23.6 - 3 29.1 30.3 28.0 - - 3 1 21.6 21.7 23.1 15.1b) 2 29.2 28.6 29.5 - Study B Single-sided tests Double-sided tests -1-BC(A)c) 22.6 22.6 - - 1 1 10.3 10.2 - - 1 20.5 20.5 - - 2 13.5 13.5 - - 2 28.0 28.0 - - 3 18.2 17.9 16.7 19.0 3 39.1 39.5 38.0 - 4 21.8 23.5 20.7 21.4 4 45.8 45.4 47.1 44.2 2 1 14.0 14.0 - - 2 17.9 19.3 7.70d) - 3 23.7 23.5 25.6 21.3 - 3 1 18.1 15.9 19.5 19.4 2 23.8 - 25.4 22.1 Failure modes are defined in Figure 2.a) Series 1 of study A had a nail spacing of 50 mm while the other two series of study A had a nail spacing of 25 mm(except for one specimen in series 3 where the spacing by mistake was 50 mm). b) This specimen had by mistake a nail spacing of 50 mm instead of 25 mm, which is the reason for the ductile failure. c) Set with boundary conditions as in study A. d) Exceptionally low failure load, cause unknown.
Since the tests were a collection of data for a future fracture mechanics approach, the crack characteristics, i.e. path and length, were studied. It was found that the crack formation depends on the bolt position, the pith orientation and the annual ring pattern. For specimens with single-sided sheathing and pith upwards (PU), three types of cracks were found for mode 1 and one for failure mode 2, as shown in Figure 3. In the same figure, the cracks for double- sided sheathing is also shown, for which two additional types of cracks for failure mode 1 and one additional type for failure mode 2 have been found, with respect to specimens with single-sided sheathing. For failure mode 1, the crack always initiates at the bottom side of the bottom rail, usually in line with the bolt position along the width of the bottom rail, and then it develops in most specimens vertically in a straight line across the annual rings toward the pith (Figure 3a) or the crack initiates off the centre and propagates in a straight line towards the pith (Figure 3b). In some cases the crack develops vertically for a certain length and then changes direction following the annual rings (Figure 3c). For specimens with double-sided sheathing in Figure 3d and 3e, two additional crack paths are shown: the one in Figure 3d occurred only twice and the crack probably propagates in this way because it finds a weaker crack plane, while the crack shape in Figure 3e is affected by the pith position. In all other specimens the pith was on the border of the rail and more or less at the middle of the cross section width. Usually the crack propagates towards the pith. 6
The crack for failure mode 2 is always initiated at the nails in the sheathing-to-framing joint and it propagates horizontally for a certain length and then deviates in a more vertical direction across the annual ring (Figure 3f) or, for double-sided sheathing, following the annual rings (Figure 3g).
a)
b)
c)
d) e)
f)
g) Figure 3 Crack development for bottom rail with pith oriented upwards (PU). (a) Mode 1 crack developing in a straight line, starting and propagating vertically at the centre of the bottom rail; (b) mode 1 crack developing in an oblique line initiating at the bottom surface of the bottom rail at a vertical position close to the edge of the washer and propagating towards the pith; (c) mode 1 crack developing in a straight line for a certain length and then following the annual rings; (d) mode 1 crack developing in an unusual direction, probably due to a weaker crack plane; (e) mode 1 crack developing toward the pith (pith in an unusual position); (f) mode 2 crack starting horizontally and then propagating vertically; and (g) mode 2 crack horizontally and then propagating vertically following the annual rings.
In Figure 4 examples of cracks for specimens with pith downwards are shown for specimens with both single and double-sided sheathing. The crack characteristics are similar to those of specimens with pith upwards. The crack starts at the bottom side of the rail and develops vertically in a straight line (Figure 4a) or in an oblique line toward the loaded edge of the bottom rail (Figure 4b), the latter 7 only for single-sided specimens. In some cases the crack starts along the annual rings and then it changes in vertical direction across the annual rings (Figure 4c) or “jump” to another annual ring and then following again its orientation (Figure 4d), the latter only in double-sided specimens. In Figure 4e an unusual “zig-zag” crack path is shown for a double-sided specimen. For failure mode 2, the crack appears at the line of the nails and propagates horizontally a certain length before it follows the annual rings (Figure 4f).
a)
b)
c)
d) e)
f) Figure 4 Crack development for bottom rail with pith oriented downwards (PD). (a) Mode 1 crack developing in a straight line starting and propagating vertically at the centre of the bottom rail; (b) mode 1 crack developing in an oblique line starting at a location close to the pith and propagating towards the loaded edge of the bottom rail; (c) mode 1 crack first following the annual rings and then propagates in a straight line towards the line of the anchor bolts; (d) mode 1 crack initiating off the centre on the bottom surface of the bottom rail and follows an annual ring for a certain length and then jumps to another annual ring and propagates towards the centre of the upper surface of the bottom rail;(e) mode 1 crack propagating in an unusual “zig-zag” line across the annual rings; and (f) mode 2 crack development, starting horizontally and then propagating vertically following the annual rings.
For most of the specimens the distance between the position of crack initiation and the edge of the bottom rail, denoted bcrack1 in Figures 3 and 4, was measured on the end of the bottom rail for failure mode 1. For failure mode 2 the length of the horizontal part of the crack before it changes direction, denoted bcrack2 in Figures 3 and 4, was measured. In Caprolu et al. (2014a; 2014b) the measured bcrack1 and bcrack2 values are listed. In Table 4 and 5 the measured values for bcrack2 are presented for specimens with pith upwards and downwards, respectively. 8 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End End [kN] [kN] Failure load Failure load 2 2 End End End [mm] [mm] crack2 crack2 1 1 ingle- sheathing. and double-sided b b End End End [kN] [kN] Failure load Failure load 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End End - Uncertain whether failure was mode 2 or 3. mode was failure whether Uncertain [kN] [kN] b) Failure load Failure load 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End End Study B Study A Single-sided Single-sided Double-sided [kN] [kN] 2 for specimens with the pith oriented downwards (PU) for s for (PU) downwards oriented pith the with specimens 2 for Failure load Failure load 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End End [kN] [kN] Horizontal crack on both edges of the bottom rail. rail. the bottom of edges both on crack Horizontal a) Failure load Failure load a) a) - - 2 2 23- 20- 23 20 End End End [mm] [mm] a) a) crack2 crack2 1 1 22- 23- b b 16 15 End End End 50.0 -39.0 10 - [kN] [kN] b) b) Failure load Failure load Series 1Series 1 Series 2 Series 2 Series 3 Series 3 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End End Set 3 Set 4Set 3 Set 1 Set 4 Set 2 Set 1 Set 3 Set 2 Set 1 Set 3 Set 2 Set 1 Set 2 Measured failure loads and horizontal crack lengths crack horizontal and loads failure Measured mode failure for is the length of the horizontal crack before it changes direction. direction. it changes before crack the the length of horizontal is ------21.916-20.61614------15.4-1725.5-22------19.722------22.2-12------37.8 ---39.5-10 ------43.821- ----35.3-16 - - - 17.1 - 18 26.3 26 13 16.5 12 - - - - 21.0 15 13 23.8 12 - 21.2 22 2734.137.4 21.8 17 14 - 20 16 - 32.4 27.1 38.0 - 5 - 19.9 11 - 27.1 20 - [kN] [kN] crack2 Failure load Failure load Table 4 ends. rail bottom two the 2 indicate End 1 and End b 9 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End [kN] [kN] Failure load Failure load 2 2 End End End ingle- sheathing. and double-sided [mm] [mm] crack2 crack2 1 1 b b End End End [kN] [kN] Failure load Failure load - 2 2 End End End [mm] [mm] crack2 crack2 1 1 b b End End End [kN] [kN] Failure load Failure load 2 2 Study B Study A End End End Single-sided Single-sided Double-sided Double-sided [mm] [mm] 2 for specimens with the pith oriented downwards (PD) for s for (PD) downwards oriented pith the with specimens 2 for crack2 crack2 1 1 b b End End End [kN] [kN] Failure load Failure load 2 2 End End End Horizontal crack on both edges of the bottom rail. the bottom of edges both on crack Horizontal [mm] [mm] a) crack2 crack2 1 1 b b End End End [kN] [kN] Failure load Failure load -46.120- 2 2 Series 1Series 1 Series 2 Series 2 Series 3 Series 3 25 47.4 - 20 End End End [mm] [mm] a) a) crack2 crack2 b b 13 16 24 – 24 15 – 15 End 1 End End 1 Set 3 Set 4Set 3 Set 2 Set 4 Set 3 Set 2 Set 1 Set 3 Set 2 Set 1 Set 2 Measured failure loads and horizontal crack lengths crack horizontal and loads failure Measured mode failure for is the length of the horizontal crack before it changes direction. it changes before crack the the length of horizontal is -4.11 ------27.113----29.510------27.817----29.417------25.631------43.41718 ------28.822------27.518------21.5-37------23.6 ----48.010- 20---47.2-15 20.7 - 21 31.4 - 22 7.70 - - 20.5 21 11 24.5 - - 33.4 39 18 ------44.5 [kN] [kN] 2/31.5 Failure load Failure load crack2 Table 5 ends. rail bottom two the 2 indicate End 1 and End b 10
3. Theory A linear elastic body with a pre-existing crack with area A is considered. The body is subjected to a single- force, P, and the value Pu, which causes the pre-existing crack to propagate, is sought. The so- called compliance method of fracture mechanics, which follows from simple energy considerations, leads to (Gustafsson (2003)):
2G P f (1) u dCA d A where Pu is the failure load, Gf is the fracture energy, A is the crack area, and C is the compliance, i.e. the deflection at the loading point for a unit force. Bottom rails in partially anchored shears wall are subjected to uplift forces from the sheathing, which may result in splitting of the bottom rail. Experiments show (Figure 2) that cracks may form either at the bottom side of the rail and propagate vertically (mode 1) or at the side of the rail and propagate horizontally (mode 2). Both types of cracks are treated in Serrano et al. (2011), Caprolu et al. (2012), and Caprolu et al. (2014c) and a fracture mechanics solution based on Eq. (1) is derived. In the present paper, the existing fracture mechanics model is reviewed and alternative models also based on Eq. (1) are derived and compared with each other and with the experimental data presented in Section 2.
3.1. Horizontal cracking (mode 2)
3.1.1. Model 1 Figure 5 shows the geometry, boundary conditions and loading conditions assumed in Serrano et al. (2011) for a crack propagating horizontally in a bottom rail.
Figure 5 Geometry, boundary conditions and loading conditions used in Serrano et al. (2011) for a horizontal crack.
The out-of-plane width of the bottom rail is denoted b, and the crack is assumed to propagate simultaneously over the entire width, b. The problem considered in Serrano et al. (2011) is reduced to determination and differentiation of the compliance of a simple cantilever beam with depth he, width b, and length a, where a is the crack length. The compliance of such a cantilever beam, if taking flexural as well as shear deformations into account, is given by Eq. (2), 11
3 4 § a · Es a C a ¨ ¸ (2) Eb © he ¹ Gb he
where E is the modulus of elasticity, G is the shear modulus, he is shown in Figure 5 and ȕs is the shear correction factor (usually 6/5 for a rectangular cross section). E and G are the appropriate values for the perpendicular-to-grain direction. It may here be noted that timber has different properties in the tangential and radial directions. This fact may be taken properly into account when using numerical methods like the Finite Element Method, but is difficult to handle in simple analytical models. It is further for practical applications usually not possible to know with certainty how the timber is cut and oriented in the structure. It is thus often in analytical models for simplicity assumed that the timber has the same properties in the radial and tangential directions. This assumption will also be applied here. Using Eq. (1) with A = ba and the compliance as given by Eq. (2), the following expression for the failure load is obtained:
2GGf he Pu b 2 (3) G § a · ¨ ¸ 12 ¨ ¸ Es E © he ¹
It is noted that the solution does not depend on the total depth, h, of the bottom rail. Assuming small crack length (a ĺ or assuming that bending deformations can be ignored as compared with the shear deformations, (i.e. G/E ĺ OHDGVWR
Pu b 2GG f he / E s (4)
Eqs. (3) and (4) are the same solutions as derived in Serrano et al. (2011).
3.1.2. Model 2 In Gustafsson (1988), splitting failure of an end-notched beam as shown in Figure 6 is considered.
4. Figure 6 Geometry of end-notched beam as considered in Gustafsson (1988).
While the model presented in Serrano et al. (2011) assumes that only shear and bending deformations of the cantilever beam shown in Figure 5 give contributions to the compliance, the model derived in Gustafsson (1988) also takes into account contributions from the part of the beam with depth h and from additional rotation of the cantilever due to the fact that the stiffness of the beam with depth h cannot be fully activated in the immediate vicinity of the corner of the notch. The solution given in Gustafsson (1988) reads: 12
GGf h Pu bDh (5) G § 1 · 3 D 1D E 6 ¨ D 2 ¸ 5 E ©D ¹
where Į and ȕ are defined in Figure 6. It should be noted that Eq. (5) is based on Eq. (1) and the compliance is determined using simple beam theory and assuming the shear correction factor ȕs = 6/5. Using Eq. (5) on a bottom rail as considered in Figure 5, (ȕK is then the crack length, a) the following failure load is obtained:
GGf
h he Pu bh , D (6) 3 1D a G § 1 · h 6 ¨ 1¸ 5 D h E ©D 3 ¹
It is noted that Eq. (6) takes into account the effect of the total depth, h, of the rail. In the special case of a small crack (a ĺ RU LI DVVXPLQJ WKDW WKH EHQGLQJ GHIRUPDWLRQV DUH negligible as compared with the shear deformations (G/E ĺ (T UHGXFHVWR
h P bC e , C 5 GG (7) u 1 h 1 3 f 1 e h
Eq. (7) leads to Eq. (4) for he/hĺ
3.1.3. Model 3 In Jensen (2005), a beam loaded perpendicular to the grain by a bolt located close to the edge and close to the end of the beam was considered. Figure 7 defines the geometry.
Figure 7 Geometry of beam considered in Jensen (2005).
Based on the theory for a Timoshenko-beam on a Winkler-foundation, a so-called quasi-non-linear fracture mechanics solution was derived. The general expression for the failure load does not become simple, but for a small crack length (a ĺ WKH UHODWLYHO\ VLPSOH VROXWLRQ JLYHQ DV (T ZDV obtained: 13
1 bf tle ° °2 2] 1 P0 Pu P0 min® ° 2] 1 (8) ¯° ] 1
5 C1 G 1 P0 2bC1 he , C1 3 GGf , ] 10 f t E he
where ft is the perpendicular-to-grain tensile strength.
The horizontal crack in a bottom rail may be considered a special case of Eq. (8), namely for le ĺ 0, which leads to:
1 P P u 0 2 2] 1 (9) 5 C1 G 1 P0 2bC1 he , C1 3 GGf , ] 10 ft E he
It is noted that Eq. (9) for ft ĺOHDGVWR(T LIȕs = 6/5. In van der Put and Leijten (2000), a linear elastic fracture mechanics model was derived for a simply supported beam loaded perpendicular to grain by a single- load at mid-span. The solution given in Eq. (10) was obtained, where again h is the beam depth and he is the loaded edge distance.
h P 2bC e , C 5 GG (10) u 1 h 1 3 f 1 e h
It is noted that Eq. (10) gives exactly twice the failure load as obtained from Eq. (7).
It is also noted that Eq. (10) for small edge distances (he/h ĺ) leads to Pu = P0, where P0 is given in Eq. (9). P0 may therefore be regarded as a special case of Eq. (10). A semi-empirical generalized version of Eq. (9) may be proposed:
h P JbC e u 1 h 1 e h (11)
5 1 C1 G 1 C1 3 GGf , J , ] 10 2] 1 ft E he
Eq. (11) then leads to Eq. (7) for G/E ĺ or ft ĺ Eqs. (3), (4), and (9) do not include the total depth of the bottom rail. This means that cracking is predicted also for situations, where the loaded edge distance is very close to the total depth of the bottom rail. Intuitively, the propensity to splitting should disappear in such situations since the part with depth (h - he) has little stiffness as compared with the part with depth he and thus offers little resistance against following the deflection of the part with depth he. Eqs. (6), (7) and (11) take the effect of the total depth of the bottom rail into account and predict infinitely high failure loads for he/h ĺ LH. horizontal splitting is not an issue if the nails are placed sufficiently close to the bottom surface of the bottom rail. 14
3.2. Vertical cracking (mode 1)
3.2.1. Model 1 For a crack propagating vertically from the bottom surface of a bottom rail, Serrano et al. (2011) consider a fully clamped beam as shown in Figure 8.
Figure 8 Geometry, boundary conditions and loading conditions used in Serrano et al. (2011) for a vertical crack.
The problem is in Serrano et al. (2011) again, as in the case of a horizontal crack, reduced to determination and differentiation of the compliance of a simple cantilever beam. Here a cantilever beam with depth (h – a), width b, and length le. The crack length is a, i.e. the crack area again becomes A = ba. The compliance of such a cantilever beam, if taking flexural as well as shear deformations into account, is given by Eq. (12).
3 4 § l · E l C a ¨ e ¸ s e (12) Eb © h a ¹ Gb h a
where E is the modulus of elasticity, G is the shear modulus, ȕs is the shear correction factor, and the geometry is given in Figure 8. It should be noted that the compliance as given by Eq. (12) is a conservative estimate since the part of the cantilever beam below the crack tip is not considered but in fact gives a contribution to the stiffness. Using Eq. (1) with A = ba and the compliance as given by Eq. (12), the following expression for the failure load is obtained:
2GGf /le Pu b h a 2 (13) G § le · 12 ¨ ¸ Es E © h a ¹
Assuming a small crack length (a ĺ OHDGVWR 15
2GGf /le Pu bh 2 (14) G § le · 12 ¨ ¸ Es E © h ¹
Assuming that bending deformations can be ignored (G/E ĺ ; Eq. (13) leads to:
2GGf Pu b h a (15) le Es
Assuming both small crack length and that bending deformations can be ignored leads to:
2GGf Pu bh (16) leEs
3.2.2. Model 2 The cantilever beam as shown in Figure 8 is considered again. However, it is here assumed that the cantilever is not completely rigidly clamped at the end, but a finite rotation occurs. The deflection of the loading point, į, is then given by:
GG bvr G G (17)
where įb is the contribution from bending of the cantilever, įv is the contribution from shear of the cantilever, and įr is the contribution from a rotation at the clamped end of the cantilever. The rotation at the clamped end of the cantilever may be thought of as a simple linear elastic rotational spring with compliance cr, and the deflection due to the rotation is then given by:
2 Grer Pl c (18)
where cr in general is a function of the crack length, a. The compliance due to bending and shear is again given by Eq. (12), and the total compliance thus becomes:
3 4 §·lleseE 2 Ca ¨¸ lcer (19) Ebha©¹ Gbha
Differentiation of C(a) with respect to a and use of Eq. (1) leads to:
2/GlGfe Pbhau 2 (20) G §·le 2 d car 12 ¨¸bGles h a E Eha©¹ d a
If the following choice is made for the spring compliance:
11Es cr 12 (21) bGE ha 2
a particularly simple expression is obtained for the failure load, namely: 16
2/GlG Pbha fe (22) u G l 12 e E Eh a s
The similarity/difference between Eq. (22) and Eq. (13) is noted. For a small crack length, Eq. (22) gives:
2/GlG Pbh fe (23) u G l 12 e E Eh s
Assuming negligible bending deformations, Eq. (22) leads to:
2GGf Pu b h a (24) le Es
And both small crack length and insignificant bending deformations:
2GGf Pu bh (25) leEs
Eq. (24) is the same as Eq. (15), and Eq. (25) is the same as Eq. (16).
3.2.3. Model 3 In the derivation of the end-notched beam model by Gustafsson (1988), the cantilever has been assumed fixed to a rotational spring in exactly the same way as in model 2. However, in Gustafsson
(1988) the compliance, cr, of the rotational spring was chosen as:
3 12 11DD c (26) r bh2 10 GE D 4
where Į = 1-a/h. The compliance of the spring was also in Gustafsson (1988) chosen so as to result in a simple expression for the failure load. However, since the crack propagation considered in Gustafsson (1988) makes the length of the cantilever increase, while the crack considered here propagates so that the length of the cantilever is constant but its depth decreases, the influence of crack propagation becomes different in the two cases, and thus different expressions (Eq. (21) and Eq. (26)) for the spring compliance optimize the simplicity. The spring compliance as given by Eq. (26) has been proven to give good results for end-notched beams. If Eq. (26) is used in Eq. (20), the following expression is obtained for the failure load:
2/GlG Pbh D fe (27) u 2 3 GG§·llee18 4 3DD 12 ¨¸Es Eh©¹DD5 E 11DD 3 h
For a small crack length, Į ĺDQGWKXV 17
2/GlGfe Pbhu 2 (28) GG§·llee6 12¨¸ 6 Es Eh©¹ 5 Eh
If the deformations from bending are assumed to be negligible as compared with the shear deformations, Eq. (27) gives:
2GGf Pbhu D (29) Esel
And for small crack length and negligible bending deformations:
2GGf Pbhu (30) Esel
Eq. (29) is the same as Eqs. (15) and (24), and Eq. (30) is the same as Eqs. (16) and (25).
3.3. Additional failure modes and modifications Figure 2c shows a failure mode (mode 3) where the nails and/or the wood yield and the nails are pulled out of the bottom rail. This failure mode is treated in Caprolu et al. (2014c) and is outside the scope of the present paper, which focuses on failure of the bottom rail. The models presented in sections 3.1 and 3.2 consider horizontal and vertical crack propagation, respectively. However, in addition to crack propagation, bending and shear failures of the considered cantilever beams may also occur and cause failure of the bottom rail. Here simplified models will be used. For horizontal crack propagation (mode 2), the following equations should also be considered for bending and shear, respectively:
bh2 Pf e (31) ut6a
2 Pbhfuev 3 (32)
where ft is the perpendicular to grain tensile strength, and fv the rolling shear strength. For vertical crack propagation (mode 1), the following equations for bending and shear should be considered in addition to the fracture mechanics models:
bh a2 Pfut (33) 6le
2 Pbhafuv 3 (34)
The failure load of the bottom rail subjected to uplift is the minimum value of the failure loads given by Eqs. (31)-(34) and two selected models (one for horizontal cracking and one for vertical cracking) from section 3.1 and 3.2. The fracture mechanics models considered in Sections 3.1 and 3.2 are all based on Eq. (1) and consider an existing crack of length a. All the derived models predict that the load needed to propagate the crack decreases with increasing crack length, and the maximum load which the bottom rail can 18 sustain is thus obtained from the models by assuming zero crack length. However, it may be relevant to assume a certain minimum or critical value, ac, of the crack length as suggested in Serrano et al. (2011):
E90G f ac 2 (35) ʌ f t
where E90 is the modulus of elasticity in the perpendicular to grain direction. Different values of the material properties may be used in Eq. (35) for the tangential and radial directions if such distinction is made. In Caprolu et al. (2014c), Eq. (35) was considered together with the models presented in Section 3.1.1 for a horizontally propagating crack (mode 2) and in Section 3.2.1 for a vertically propagating crack (mode 1). The length, le, of the cantilever beam considered in Section 3.2 was introduced as le = s + c as shown in Figure 8, where s is the distance from the loaded edge of the bottom rail to the edge of the washer and c is an additional length in recognition of the fact that the bottom rail may not be fully clamped at the edge of the washer. From Eqs. (3) and (13), theoretical expressions, le0, were given for the value of le which determines the limit between vertical crack propagation (mode 1) and horizontal crack propagation (mode 2) for general orthotropic conditions and inclusion of Eq. (35). For the special case of isotropic conditions (assuming the same material properties in the radial and tangential directions) and assuming zero initial crack length led to
2 3 2 3 E Eh4 § E Eh4 · § E Eh2 · E Eh4 § E Eh4 · § E Eh2 · 3 s ¨ s ¸ ¨ s ¸ 3 s ¨ s ¸ ¨ s ¸ le0 ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ (36) 24Ghe © 24Ghe ¹ © 24G ¹ 24Ghe © 24Ghe ¹ © 24G ¹
A horizontally propagating crack (mode 2) leads to failure of the bottom rail if le < le0 and a vertically propagating crack (mode 1) leads to failure if le > le0. Further, in Caprolu et al. (2014c) c was estimated from experimental data by fitting using Eq. (13).
4. Discussion While the crack path is predetermined for problems such as end-notched beams or splitting of beams loaded perpendicular to grain by bolted connections where the crack propagates along the grain, this is not the case in a bottom rail as considered here. The models presented in Sections 3.1 and 3.2 assume that the crack propagates either horizontally or vertically, but it is in fact very likely that the direction of the crack propagation changes as the crack grows. For instance, at any stage of the propagation of a horizontal crack as considered in section 3.1, the crack may start propagating vertically (as considered in section 3.2) if this requires less energy. For simplicity, consider the simplest models for horizontal and vertical crack propagation, i.e. the models given in Sections 3.1.1 and 3.2.1 and first presented in Serrano et al. (2011). Assume that a horizontal crack has been initiated and grown to the length, a, as shown in Figure 5. At what length will the crack start growing vertically (if at all at any crack length)? The solution is given by taking
Eq. (3) as is, and setting it equal to Eq. (14), in which le = a and h = he. These equations lead to the solution that the crack will start propagating in the vertical direction when a = he. Figure 9 illustrates the problem. According to Eq. (3), the horizontal crack will propagate at decreasing load levels until a
= he, then the crack will start propagating vertically. In Figure 9 is the failure load per mm of the length of the bottom rail given as a function of the horizontal crack length, a, using h = 45 mm, he =
22.5 mm, E = 400 MPa, G = 70 MPa, Gf = 0.30 N/mm and ȕs = 6/5. The material properties are those used in Serrano et al. (2011). Using Eqs. (3) and (14), the point where the horizontal crack starts 19
propagating vertically is a = he, and is independent of the geometry and material properties of the bottom rail. The same exercise may be done using other models for the horizontal and vertical crack propagation, but an explicit expression can in general not be given for the point, where the horizontal crack starts propagating vertically.
50
40
30
20 Horizontal crack, Eq. (3) 10 Failure load [N/mm] Vertical crack, Eq. (14) with le=a and h=he 0 0 5 10 15 20 25 30
Horizontal crack length, a, [mm] Figure 9 Example of propagation of initial horizontal crack in bottom rail and possible change to vertical propagation.
In Serrano et al. (2011), the perpendicular-to-grain tensile strength is assumed to be ft = 2.5 MPa. If further assuming the (rolling) shear strength fv = 3 MPa, inclusion of Eqs. (31) – (32) leads to Figure 10 for the initially horizontally propagating crack also considered in Figure 9.
50
Horizontal 40 crack, Eq. (3)
Vertical crack, 30 Eq. (14) with le=a and h=he Eq. (31) 20
10 Eq. (32) Failure load [N/mm]
0 0 5 10 15 20 25 30
Horizontal crack length, a, [mm] Figure 10 Example of propagation of horizontal crack including possible bending and shear failure modes and change of crack propagation direction.
According to Figure 10, the horizontal crack will propagate to a length of 8.5 mm, and then bending failure will occur in the cantilever as given by Eq. (31). 20
If the perpendicular-to-grain tensile strength is assumed to be ft = 4.5 MPa (instead of 2.5 MPa), then Eq. (31) leads to a curve very close to the curve corresponding to the vertical crack in Figure 10 and intersects with the horizontal crack curve at a = 22.5 mm. The perpendicular-to-grain tensile strength of wood is always a debatable property partly due to the fact that different testing standards may lead to significantly different values, partly due to the fact that the strength is volume dependent. In the experimental programs, the length of the horizontal part of the crack before it changes direction has been measured for some of the specimens and is given in Tables 4 and 5.The crack lengths were measured on the ends of the bottom rail as illustrated in Figure 11 for specimens with single- and double-sided sheathing.
a) b)
c) d)
Figure 11 Examples of length of horizontally propagating cracks measured on the test specimens.
All test specimens had bottom rails with h = 45 mm and he = 22.5 mm. Accordingly, Eqs. (3) and (14) predict that the crack will change to propagating in the vertical direction after having propagated 22.5 mm horizontally. Though the measured figures given in Tables 4 and 5 are roughly in agreement with this prediction, the experimental results are too scarce and the variation too large to make any firm conclusions about agreement between theory and experiments. Further, as illustrated in Figure 10, the change of direction of the crack may not only be due to vertical crack propagation, but also due to bending failure of the cantilever beam considered in the models. The perpendicular-to-grain tensile strength of wood is associated with significant variation, and as illustrated in Figure 10 this may lead to significant variation in the length of the horizontal crack. It is further uncertain how much the washers influence the measured horizontal cracks. The influence of the washers is not considered in any of the models presented in Section 3.1 for horizontally propagating cracks. Finally, it should be noted that the fracture models presented are all idealized models, which e.g. assume that the load is applied as a point load at the edge of the bottom rail. In reality, the load on the bottom rail is transferred by the nails over a certain length in the horizontal direction. This may have some significant effects, which are not considered in the models. It should, however, be noted that Eq. (14) for the vertical crack propagation and Eq. (31) for the bending failure of the cantilever predict infinitely high failure loads for an initially horizontal crack a
= 0 (le = 0), and Eqs. (3) and (32) will thus determine the failure load of the bottom rail for a horizontally propagating crack. For most practical applications, the shear failure will not be relevant either. 21
A crack, which starts propagating vertically at the bottom side of the rail, will usually not change direction and start propagating horizontally if the timber is considered homogeneous and isotropic (i.e. no distinction is made between radial and tangential directions). For real orthotropic and inhomogeneous materials, the crack may, however, follow different paths as exemplified by Figures 3c and 4e. Figure 10 indicates that shear failure will usually not occur for horizontal cracks and is even more unlikely for vertical cracks. The failure of the rail in case of a vertically propagating crack is therefore realistically the minimum of vertical crack propagation and bending of the cantilever, i.e. for instance Min {Eq. (13); Eq. (33)}. Figure 12 shows a vertical crack propagation using the material properties that apply to Figure 9 and three different values of ft (= 2 MPa, 3 MPa, or 4 MPa). Here the total depth of the bottom rail is assumed to be 45 mm and the vertical crack is assumed to initiate 45 mm from the loaded edge.
40 Vertical crack, Eq. (13) Eq. (33), ft = 2 MPa
30 Eq. (33), ft = 3 MPa
Eq. (33), ft = 4 MPa 20 Horizontal crack, Eq. (3)
10 Failure load [N/mm]
0 0 5 10 15 20 25 30
Vertical crack length, a, [mm] Figure 12 Example of propagation of vertical crack including possible bending failure and the possibility for the crack to change to propagation in the horizontal direction.
For the vertical crack, the bending capacity as given by Eq. (33) takes on a finite value for zero crack length and may thus overrule the fracture mechanics solution for crack propagation depending on the value of the perpendicular-to-grain tensile strength. For the example considered in Figure 12, bending failure will occur if ft = 3MPa or less, vertical crack propagation will occur if ft = 4 MPa or above. In Figure 12 is also included Eq. (3) in the following form
2GGf he Pu b 2 (37) G § l · ¨ e ¸ 12 ¨ ¸ Es E © he ¹
where le is the distance from the loaded edge of the rail to the crack tip and he = h– a, a being the distance of the crack tip above the bottom side of the rail. Eq. (37) thus gives the load at which the crack will propagate horizontally at any stage of a vertically propagating crack. The use of Eqs. (3) and (13) for an initially assumed vertical crack at the bottom surface of the bottom rail leads to the fact that that the crack will continue its vertical propagation if it initiates a distance le > h from the loaded edge. Assuming le < h leads to horizontal crack propagation until le = h, 22 and then the crack will propagate vertically. Horizontal crack propagation along the bottom side of the rail is physically not meaningful, but may be interpreted in the way that Eqs. (3) and (13) exclude vertical crack initiation closer to the loaded edge than the depth of the rail. This prediction seems to be roughly in agreement with the experimental observations (Figures 3 and 4). However, the alternative models for horizontal crack propagation as presented in Sections 3.1.2 and 3.1.3 predict infinitely high failure loads for he = h, i.e. a horizontal crack will not propagate near the bottom surface of the bottom rail. In Figure 13 are Eqs. (14), (23), and (28) corresponding to Models 1, 2, and 3, respectively, for vertical crack propagation (mode 1) compared with the experimental data. Figure 13a refers to specimens with single-sided sheathing, while Figure 13b to specimens with double-sided. All three equations are based on the assumption that failure occurs for a ĺ7KHIROORZLQJPDWHULDOSURSHUWLHV were used: h = 45 mm, E = 400 MPa, G = 70 MPa, Gf = 0.30 N/mm and ȕs = 6/5. The effective length, le = s + c, has been used with c = 20 mm which is roughly the value determined from the experimental data by minimization of the error using Eqs. (13) and (35) as described in Caprolu et al. (2014c) for all specimens considered. The total load applied on the 900 mm long bottom rail is plotted as a function of the distance s. For double-sided sheathing the theoretical expressions have been multiplied by two.
50 100 Study A - PD Study A - PD 45 Study A - PU 90 Study A - PU Study B - PD Study B - PD 40 80 Study B - PU Study B - PU Eq. (14) Eq. (14) 35 70 Eq. (23) Eq. (23) 30 Eq. (28) 60 Eq. (28)
25 50
20 40
Failure load [kN] 15 Failure load [kN] 30
10 20
5 10
0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] a) b) Figure 13 Comparison between theory and experiments for vertical cracking of a bottom rail assuming zero initial crack length. (a) Specimens with single-sided sheathing; and (b) specimens with double-sided sheathing. PD = pith downwards, PU = pith upwards.
Eqs. (23) and (28) lead to better agreement with the experimental data than does Eq. (14). Eqs. (23) and (28) differ from Eq. (14) by taking into account an additional rotation of the cantilever at the clamped end. It may be argued that the additional contribution, c, to the length of the cantilever accounts for the same effect as the additional rotation and should not be included when using Eqs. (23) and (28). However, since the washer only has a very limited extension in the length direction of the bottom rail, it is not reasonable to expect that any 2D model should result in perfect agreement with tests without some kind of empirical adjustment. Use of le = s + c, c = 20 mm seems to render very good results together with Eqs. (23) and (28) though the value of c has been optimized for use with Eq. (13). Figure 14 compares Eqs. (13) and (22) with the experimental results. Figure 14a refers to specimens with single-sided sheathing, while Figure 14b to specimens with double-sided. Here the initial crack length as given by Eq. (35) has been used. The same material properties as used in Figure
13 apply, and further ft = 2.5 MPa has been assumed. Again le = s +c, c = 20 mm has been assumed. 23
40 80 Study A - PD Study A - PD 35 Study A - PU 70 Study A - PU Study B - PD Study B - PD Study B - PU Study B - PU 30 60 Eq. (13) Eq. (13) Eq. (22) Eq. (22) 25 50
20 40
15 30 Failure load [kN] Failure load [kN]
10 20
5 10
0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] a) b) Figure 14 Comparison between theory and experiments for vertical cracking of a bottom rail assuming a finite initial crack length. (a) Specimens with single-sided sheathing; and (b) specimens with double-sided sheathing. PD = pith downwards, PU = pith upwards.
While Eq. (13) in general seems to slightly overestimate the failure load for c = 20 mm, Eq. (22) in general slightly underestimates the failure load. Eq. (13) with the use of Eq. (35), Eqs. (23) and (28) lead to approximately equally good agreement with the experimental data. In Figure 15 are Eqs. (4), (7), and (11) corresponding to Models 1, 2, and 3, respectively, for horizontal crack propagation (mode 2) compared with the experimental data. Figure 15a refers to specimens with single-sided sheathing, while Figure 15b to specimens with double-sided. All three equations are based on the assumption that failure occurs for a ĺ7KHVDPHPDWHULDOSURSHUWLHVDV apply to Figure 14 here and h = 45 mm, he = 22.5 mm are used here.
40 80 Study A - PD Study A - PD 35 Study A - PU 70 Study B - PD Study B - PD Study B - PU Study B - PU Eq. (4) 30 60 Eq. (4) Eq. (7) Eq. (7) Eq. (11) 25 Eq. (11) 50
20 40
15 30 Failure load [kN] Failure load [kN]
10 20
5 10
0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Distance s [mm] Distance s [mm] a) b) Figure 15 Comparison between theory and experiments for horizontal cracking of a bottom rail. (a) Specimens with single-sided sheathing; and (b) specimens with double-sided sheathing. PD = pith downwards, PU = pith upwards.
Eq. (11) gives a slightly better prediction of the failure load than does Eq. (4). Eq. (3) used together with Eq. (35) gives very precisely the same failure load as Eq. (11). Here it may for practical reasons be recommended to use the simpler Eq. (4). It is, however, again emphasized that Eq. (11) takes into 24 account the total depth of the bottom rail while Eqs. (3) and (4) do not. If the theory is applied to bottom rails with larger depths and the sheathing is nailed to the bottom rail close to the bottom of the bottom rail, it may be significant to take into account this effect.
5. Conclusions New alternative analytical models based on fracture mechanics were presented and compared with an existing model for determination of the failure load of bottom rails subjected to uplift in partially anchored timber frame shear walls. All the models presented are based on the compliance method of fracture mechanics, and the compliance is determined using simple beam theory. Beam theory is formally not applicable to situations where the beam length is short as compared with the beam depth as is often the case in the applications to fracture problems. However, the compliance according to the simple beam theory has previously shown remarkably good results when used in fracture mechanics analysis of e.g. end-notched beams and bolted connections loading beams perpendicular to the grain. In addition to the formal problems associated with the use of beam theory for very short beams, the bottom rail analysis also includes the difficulty that it is a 3D-problem. This is due to the fact that the bottom rail is anchored to the foundation by means of anchor bolts with washers placed along the length of the bottom rail with spacing relatively large as compared with the cross section dimensions of the bottom rail. The analytical models are 2D-models, and the boundary conditions assumed in the 2D-models cannot be valid for all positions along the bottom rail. However, in spite of the seemingly over-simplified analysis, several of the models presented in this paper were found capable of giving failure load predictions in surprisingly good agreement with the experimental data. The only minor empirical adjustment made in the models is assuming that the length of the beam considered in the models for analysis of a vertically propagating crack is the distance from the loaded edge of the bottom rail to the nearest edge of the washer plus an empirically estimated length of 20 mm. For vertically propagating cracks, the existing model was found to produce excellent predictions if assuming a certain initial crack length as estimated theoretically. A new alternative model was found to produce equally good predictions if assuming that the failure load is obtained for zero crack length. For horizontally propagating cracks, the experimental data show considerably larger variation and the goodness of the models is harder to estimate. However, a new model based on a semi-empirically modified quasi-nonlinear fracture mechanics approach was found to produce equally good predictions as the existing model. The new model has previously been applied with considerable success to analysis of splitting in beams loaded perpendicular to the grain by bolted connections and has the advantage of taking into account the total depth of the bottom rail. This effect may become significant if bottom rails with larger depths are to be analysed. In addition to failure load prediction, the capability of the simple analytical models to predict the crack propagation including change of direction of the crack was explored. The predictions seem roughly in agreement with the available experimental data. However, lack of sufficient experimental data and the large variation in the available data does not allow for any firm conclusions to be drawn.
6. Acknowledgements The authors would like to thanks the County Administrative Board in Norrbotten; the Regional Council of Västerbotten; and the European Union’s Structural Funds – The Regional Fund for their financial support.
7. References Caprolu G., Girhammar U. A., Källsner B. and Vessby J. (2012) Analytical and experimental evaluation of the capacity of the bottom rail in partially anchored timber frame shear walls. Paper presented at 12th World Conference on Timber Engineering, Auckland, July 16-19. 25
Caprolu G., Girhammar U. A., Källsner B. and Lidelöw H. (2014a) Splitting capacity of bottom rail in partially anchored timber frame shear walls with single-sided sheathing. The IES Journal Part A: Civil & Structural Engineering, 7:83-105. Caprolu G., Girhammar U. A. and Källsner B. (2014b) Splitting capacity of bottom rails in partially anchored timber frame shear walls with double-sided sheathing. The IES Journal Part A: Civil & Structural Engineering, DOI:10.1080/19373260.2014.952607. Caprolu G., Girhammar U. A. and Källsner B. (2014c) Analytical models for splitting capacity of bottom rails in partially anchored timber frame shear walls based on fracture mechanics. Engineering Structures, (submitted). EN 338 (2009) Structural timber – Strength classes. European Committee for Standardization, Brussels, Belgium. EN 622-2 (2004) Fibreboards – Specifications – Part 2: Requirements for hardboard. European Committee for Standardization, Brussels, Belgium. Girhammar U. A. and Källsner B. (2014) Design against brittle failure of bottom rails in partially anchored wood frame shear walls. Construction and Building Material, (submitted). Serrano E., Vessby J., Olsson A., Girhammar U. A. and Källsner B (2011) Design of bottom rails in partially anchored shear walls using fracture mechanics. In: Proceeding CIB-W18 Timber Structures Meeting, Alghero, Sardinia, Italy, Paper 44-15-4. Gustafsson P. J. (2003) Fracture perpendicular to grain – structural applications. In: Thelandersson S. And Larsen H. J. (ed.) Timber Engineering. John Wiley & Sons Ltd (ed), Chichester, England. Gustafsson P. J. (1988) A study of strength of notched beams. In: Proceeding CIB-W18 Timber Structures Meeting, Vancouver, Canada, Paper 21-10-1. Jensen J. L. (2005) Quasi-non-linear fracture mechanics analysis of splitting failure in moment- resisting dowel joints. J Wood Sci, 51:583-588. van der Put T. A. C. M., Leijten A. J. M. (2000) Evaluation of perpendicular to grain failure of beams caused by concentrated loads of joints. In: Proceeding CIB-W18 Timber Structures Meeting, Delft, The Netherlands, Paper 33-7-7.
Paper V
1
Comparison of Models and Tests on Bottom Rails in Timber Frame Shear Wall Experiencing Uplift Giuseppe Caprolu*1, Ulf Arne Girhammar1 and Bo Källsner2 1Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden 2Department of Building Technology, Faculty of Technology, Linnaeus University, Växjö, Sweden
Abstract. The authors present two different studies: one experimental and one where analytical models developed to calculate the splitting failure capacity of bottom rails in partially anchored timber frame shear walls are evaluated and validated. The experimental study was divided into three parts with specimens matched to each other: (1) first the splitting capacity and failure mode of bottom rails subjected to uplift were studied; (2) then material properties as tensile strength perpendicular to the grain; and (3) fracture energy were determined by testing specimens cut from the specimens belonging to (1). The experimental results were compared with already presented models based on a linear fracture mechanics approach, using as input values results from (2) and (3). Almost all tested models show good agreement with the test results. The models showing the best agreement have been selected and proposed to be used as basis for calculation of the splitting failure capacity of bottom rails in partially anchored timber frame shear walls.
Keywords: bottom rail; splitting of bottom rail; timber shear walls; partially anchored; fracture energy; tensile strength perpendicular to the grain
1. Introduction Källsner and Girhammar (2005) developed a plastic model for the design of timber frame shear walls and proposed it as the unified design method needed in Eurocode 5 (2008), as pointed out by Griffiths et al. (2005). The model covers only static loads and can be used for both fully and partially anchored shear walls. However, in order to use the method, the bottom rail must not experience brittle failure and a plastic behaviour of the sheathing-to-framing joints has to be ensured. In Caprolu et al. (2014a; 2014b) two experimental programs on the splitting capacity of bottom rails with single- and double-sided sheathing, respectively, were presented, and it has been shown that two brittle failure modes may take place in the bottom rail: (1) a crack opening from the bottom surface of the bottom rail; and (2) a crack opening from the edge surface of the bottom rail along the line of the sheathing-to-framing joints. In Caprolu et al. (2014c) two models based on a linear fracture mechanics approach, one for each failure mode were presented and evaluated. In Jensen et al. (2014) other analytical models, still based on a linear fracture mechanics approach, have been developed and evaluated. Some of those models were based on the assumptions in Caprolu et al. (2014c) while others were derived using the end- notched beam model by Gustafsson (1988), the beam model loaded perpendicular to the grain by a bolt located close to the edge model by Jensen (2005) and a linear elastic fracture mechanics model for
* Corresponding author, PhD student, email: [email protected] 2 a simply supported beam loaded perpendicular to the grain by a single load at mid-span derived by van der Put (2000).
When evaluating these models, the values of fracture energy, Gf, and tensile strength perpendicular to the grain, ft,90, were taken from literature. The failure modes found during the bottom rail tests needed a Gf value in the TR and RT planes and a ft,90 value in the tangential and radial directions, for failure mode 1 and 2, respectively. Due to the orthotropic characteristics of the timber, it was hard to find these values for the needed orientation and for the same timber species. Further, Gustafsson
(2003) summarized the results of few studies about ft,90: Boström (1992), Holmberg (1998) and Siimes
(1967). He pointed out that ft,90 strongly depends on the annual ring orientations, the strain rates applied during the tests, the density, the moisture, the temperature and the volume of the specimen. The aim of the present study is as follows: x to experimentally determine the splitting capacity and failure modes of bottom rails subjected to uplift;
x to experimentally determine the fracture energy Gf in the TR and RT planes and the tensile
strength perpendicular to the grain ft,90 in the tangential and radial directions from the same specimen tested in the bottom rail experimental program; x to evaluate the models presented in Caprolu et al. (2014c) and Jensen et al. (2014) using the material properties determined above and compare the results with the experimental results obtained in the tests of bottom rails subjected to uplift.
2. Material and methods
2.1. Matching test program A comprehensive number of tests of bottom rails subjected to vertical uplift have been reported in Caprolu et al. (2014a; 2014b). In order to obtain a deeper understanding of the timber material properties used in the testing of the bottom rails, an additional experimental program was decided to be run. The reason was to obtain more reliable information on material parameters that may be used in connection with the fracture mechanics analyses. In this new test series with matched specimens three types of tests were run: x Bottom rails subjected to uplift; x Tensile strength perpendicular to the grain in the radial and tangential directions; x Fracture energy in the RT and TR planes. First the bottom rail was tested and then the two other specimens for the material testing were cut from the bottom rail specimen, in order to have all parameters needed to evaluate the formulas given in Caprolu et al. (2014c) and Jensen et al. (2014) using the individual material properties of each bottom rail. In Caprolu et al. (2014c) and Jensen et al. (2014) the analyses were carried out with bottom rail test results from experimental programs run by the first author, but with values of ft,90 and
Gf found in literature, which might have resulted in imprecise results. The original boards from which the specimens were cut had a cross section of 120×45 mm and a length of about 5 m. Each board was cut into four parts; then two parts were used to build bottom rail specimens with expected failure mode 1 and the other two to build bottom rail specimens with expected failure mode 2, according to Figure 1. Figure 2 was used to foresee which kind of failure mode would occur in the bottom rail. It refers to study A of Caprolu et al. (2014a). In that study, the distance between the nails in the timber-to-sheathing joints was 25 mm. This distance was chosen; despite it is not a realistic distance, in order to avoid failure due to yielding and withdrawal of the nails. For the bottom rail experimental program, as given in Table 1, the same characteristics were used as in study A in Caprolu et al. (2014a). The plan was to test 15 specimens for Gf tests for side crack and 33 for bottom crack, and 15 specimens for ft,90 in radial direction and 33 in tangential 3 direction. According to Figure 2 we can expect that the bottom crack failure mode will occur for rails like the ones in Series 1, Set 1, 2 and 3 and that the side crack failure mode will occur for rails like the ones in Series 2, Set 3 and Series 3, Set 1 and 2.
Figure 1 Scheme of how to cut and select the boards for the specimens (PU = pith upwards, PD = pith downwards). *Specimens with expected mode 1 failure according to Figure 2. These boards were then selected and specimens for tests for Gf in TR direction and ft,90 in tangential direction were cut. ** Specimens with expected mode 2 failure according to Figure 2. These boards were then selected and specimens for test for Gf in RT direction and ft,90 in radial direction were cut. For bottom rails with expected mode 2 failure, it was decided to test the fracture energy in both the RT and TR planes and the tensile strength perpendicular to grain in both the radial and tangential directions. This was done to see if there were any relationships between the material properties and the failure modes of the bottom rail.
9 8 7 6 5 4 3 2 Mode 3 1 Mode 2 0 Mode 1 Set 3 (5)* PD 3 (5)* Set PU 3 (5)* Set PD 2 (0)* Set PU 2 (0)* Set Set 1 (40)* PD 1 (40)* Set PU 1 (40)* Set PD 2 (30)* Set PU 2 (30)* Set PD 3 (20)* Set PU 3 (20)* Set PD 4 (10)* Set PU 4 (10)* Set PD 1 (25)* Set PU 1 (25)* Set PD 2 (15)* Set PU 2 (15)* Set PD 1 (10)* Set PU 1 (10)* Set 40** 60** 80** 100** 40** 60** 80** 40** 60** Serie 1 (b/2)*** Serie 2 (3b/8)*** Serie 3 (b/4)*** Figure 2 Recorded failure modes for the different test series and sets belonging to study A of Caprolu et al. (2014a) (PD = pith downwards, PU = pith upwards). *Distance from washer edge to loaded edge of the bottom rail [mm]; **size of washer [mm]; and ***bolt position.
2.2. Bottom Rail
2.2.1. Material properties The specimens were built by hand using rails of length 900 mm with a cross section of 45×120 mm, joined to a hardboard sheet of 900×500 mm by nails 50×2.1 mm. The details of the test specimens were as follow: x Bottom rail: spruce (Picea Abies), C24 according to EN 338 (2009), 45×120 mm. 4
x Sheathing: hardboard, 8 mm (wet process fibre board, HB.HLA2, EN 622-2 (2004), Masonite AB). x Sheathing-to-timber joints: Annular ringed shank nails, 50×2.1 mm (Duofast, Nordisk Kartro AB). The joints were nailed manually and the holes were pre-drilled, only in the sheet, 1.7 mm. The centre distance between nails was 25 mm. x Anchor bolt: Ø 12 (M12). The holes in the bottom rails were pre-drilled, 13 mm.
2.2.2. Test program A total of 54 specimens, according to Figure 3, were tested. The specimens were divided into three different series, where each series was divided into different sets. The series were subdivided with regard the washer size and the position of the anchor bolt with respect to the width “b” of the bottom rail (Figure 3b). Knowing the anchor bolt position and the washer size, the distance s between the washer edge and the edge of the bottom rail at the loaded side as shown in Figure 3b, is defined. The depth of the bottom rail is defined as h. Six specimens were tested in each set, three with the pith oriented downwards (PD) and three with the pith oriented upwards (PU). The test program is specified in Table 1.
Table 1 Test program for bottom rail tests. PD = pith downwards, PU = pith upwards, b = width of rail (notations as in Figure 3).
Series Set Number of tests Anchor bolt position Size of washer Distance sa) PD PU [mm] [mm] 13 3 40×40×15 40 2 3 3b/2 60×60×15 30 1 3 3 360 mm from sheathing 80×70×15 20 4 3 3 100×70×15 10 13 3 40×40×15 25 3b/8 2 2 3 3 60×60×15 15 45 mm from sheathing 3 3 3 80×70×15 5 13 3 b/4 40×40×15 10 3 2 3 330 mm from sheathing 60×60×15 0 a) Distance from washer edge to loaded edge of the bottom rail.
2.2.3. Test set-up The test set-up is shown in Figure 3, for further details the reader should refer to Caprolu et al. (2014a). The bottom rail was fastened to a supporting welded steel structure by two anchor bolts. The distance between the bolts was 600 mm and the distance between bolt and the end of the bottom rail was 150 mm. A rigid square-or rectangular-shaped washer was inserted between the bottom rail and the bolt head throughout all tests. The thickness of the washer (15 mm) was chosen so that there would not arise any visible permanent deformations in the washers. A hydraulic piston (static load capacity 100 kN) was attached to a steel bar, that was connected to the upper part of the hardboard sheathing using C-shaped steel profiles and four bolts Ø16. A hinge was used allowing the specimen to rotate, according to Figure 3a. The distance between the nails in the sheathing-to-timber joint was 25 mm. The reason to have such a small nail distance was to have strong sheathing-to-framing joints in order to avoid yielding and withdrawal of the nails and have splitting failure in the bottom rails. A torque moment of 50 Nm was used to tighten the bolts. A tensile load was applied to the upper part of the panel with a displacement rate of 2 mm/min. 5
Figure 3 Test set-up and boundary conditions of sheathed bottom rails subjected to single-sided vertical uplift. (a) Boundary conditions: a hinge is used allowing the specimen to rotate; and (b) cross-section of the specimen. The distance s is the distance between the washer edge and the loaded edge of the bottom rail. Units in mm.
For each specimen the moisture content and density of the bottom rail were measured after the test, according to ISO 3130 (1975) and ISO 3131 (1975), respectively.
2.3. Tensile strength perpendicular to the grain
2.3.1. Material properties In this section for specimen is meant the part needed to be tested, while for full specimen is meant the specimen glued to the two timber pieces needed for the tests. The full specimens were built by hand using two different dimensions dependent on the direction tested. The specimen was glued to two pieces of timber one month before testing and kept in a climate controlled chamber with relative humidity RH 65%. The density of the specimens was measured before gluing; however for few of them, by mistake, it was not measured. Once that the full specimens were built, the surfaces were accurately prepared to ensure that they were plane. This was made with an electronic planer. The details of the test specimens were as follow: x Specimen: the timber was the same as for the bottom rail tests. The dimensions of the specimen were as follow: 45×70×45 mm and 45×70×120 mm for radial and tangential direction, respectively. Glue (two different glues were used for the specimens): 1. Wood Glue PU Light 421 1-component moisture-curing polyurethane adhesive, water resistant according to EN 204 (2001) and EN 205 (2003) class D4; 2. CASCO Adhesive, Adhesive 1711 + Hardener 2520 (Phenol Resorcinol). x Reinforcement: Fiberglass. 2.3.2. Material properties According to EN 408 (2010), the dimensions of a structural timber specimen for determination of the tensile strength perpendicular to grain should be as given in Figure 4a with an area of 45×70 mm 6 for the glued interface and with a depth e of 180 mm. However, due to the small dimensions of the bottom rails studied it was not possible to follow these requirements. The dimensions of the specimens used in the experimental program are specified in Table 2. In Figures 4b and 4c it is shown how the specimens were cut from the bottom rails and in what direction they were tested.
Figure 4 Dimensions of test specimens for determination of tensile strength perpendicular to grain. (a) Specimen according to EN 408 (2010); (b) specimen for determination of the tensile strength perpendicular to the vertical crack (tangential direction), corresponding to mode 1 failure; and (c) specimen for determination of the tensile strength perpendicular to the horizontal crack (radial direction), corresponding to mode 2 failure. Only the part to the right, surrounded by dashed lines, belongs to the specimen.
It is important to note that the difference in specimen size gives a difference in specimen volume. As highlighted by Gustafsson (2003) the perpendicular to grain tensile strength is strongly size dependent and this should be taken into account when analysing the results. A total of 48 specimens, according to Figure 5, were tested: 15 in the radial direction and 33 in the tangential direction. For both the directions, a few trial tests were made. When the trial tests failed in the right way, they were included in the test program. The dimensions of the test specimens differ with respect to the direction tested. For the radial direction the specimen had dimensions according to Figure 5a and 5b while for the tangential direction the specimen had dimensions according to Figure 5d and 5e. The width “u”, the thickness “v” and the depth “e” are also defined in Figure 5b and 5e. The test program and specimen sizes are specified in Table 2; where in the last row the dimensions of the specimens according to the EN 408 (2010) are given.
Table 2 Test program of ft,90 tests (notation as in Figure 5).
Series Direction Specimen size [mm] Number of tests uve 1Radial70454518a) 2 Tangential 70 45 120 34b) Specimen size as in EN 408 (2010) 70 45 180 - a) 15 tests were planned but the three trial tests have been added. b) 33 tests were planned but one of the three trial tests has been added. 7
2.3.3. Test set-up The test set-up is shown in Figure 5. Each specimen was glued to two pieces of timber, with dimensions according to Table 2 and Figure 5a and 5d, dependent on the direction tested. The full specimen was then connected to steel bars which in turn were connected to the testing machine by dowels, as shown in Figure 5g. The machine used was a universal testing Machine UTM “Alwetron” TCT 50. The tests were performed under displacement control and a tensile load was applied by a hydraulic piston with a rate of 10 mm/min until a load of 20 N was reached and then with a rate of 0.5 mm/min until failure. The displacement rate was chosen according to EN 408 (2010), where it is suggested that it shall be adjusted so that the maximum load is reached within (300 ± 120) seconds. A few trial tests were performed in order to find the right displacement rate. During the trial tests the failure was found to occur in the glued interface instead of the specimen. Two measures were then taken. For the specimens tested in tangential direction, the volume of the specimen was reduced by two half circles having a diameter of 18 mm. They were positioned at the middle of the specimen depth along the edges, as shown in Figure 5a and 5d. The reason for this was to have a part of the specimen with a smaller cross section and to have the failure there. For the specimens tested in radial direction the tensile strength perpendicular-to-grain was found to be higher than that found for the tangential direction, therefore the addition of the two half circles was not enough in order to get the failure within the specimen. For that reason the glue lines were strengthened by addition of fiberglass (this was made also for a few specimens in tangential direction), as shown in Figure 5c and 5f. (It should be mentioned that due to the reduction of the area the failure plane is directed to that area and then the usually used Weibull theory to account for the volume effect is not directly applicable under these circumstances. Also, the reduced area creates some stress concentrations that can have some influence). 8 adial direction; (b) the of test dimensions ection; the and (g) connection between the ieces of timber test infor tangential the direction; ecimen tested in radial direction; (d) specimen glued to two p two to glued (d) specimen direction; radial in tested ecimen Test the tensile for set-up strength perpendicular to tests. pieces (a) Specimen grain glued of to the two r timber test in for (e) dimensions of the test specimen in tangential direction; (f) reinforcement specimenfiberglass for tested in tangential dir piston. to the hydraulic connected bars steel the and specimen specimen in radial direction; (c) fiberglass reinforcement sp for reinforcement (c) fiberglass radial direction; in specimen Figure 5 9
2.4. Fracture energy
2.4.1. Material properties The preparation of the specimens was the same as for the specimens for the tensile strength perpendicular to the grain tests in section 2.3.1. The details of the test specimens were as follow: x Specimen: the timber was the same as for the bottom rail tests. Test the dimensions of the specimen were as follow: 45×45×45 mm for both TR and RT orientation, with a notch length of 0.6×45 mm and a width of 2 mm. In order to obtain a stable curve after the peak load had been passed, the notch length was increased by 3 mm with a razor blade. Glue (two different glues were used for the specimens): 1. Wood Glue PU Light 421 1-component moisture-curing polyurethane adhesive, water resistant according to EN 204 (2001) and EN 205 (2003) class D4; 2. CASCO Adhesive, Adhesive 1711 + Hardener 2520 (Phenol Resorcinol). 2.4.2. Test program A total of 48 specimens, according to Figure 6 and the NT BUILD 422 (1993), were tested: 15 for the RT orientation and 33 for the TR orientation. For both the directions, a few trial tests were made. The dimensions of the test specimens were chosen according to Figure 6a and 6b. The width “c”, the thickness “d” and the depth “c” are also defined in Figure 6a and 6b. The dimensions of the notch are defined in Figure 6b. The two different orientations tested are shown in Figure 6c and 6d, while in Figure 6e and 6d details of the test set-up are shown. The test program is specified in Table 3.
Table 3 Test program of Gf tests (notation as in Figure 6).
Series Crack Specimen size [mm] Number of tests orientation cd 1RT454515 2TR454533
2.4.3. Test set-up The test set-up is shown in Figure 6. The specimen was glued to two pieces of timber, according to Figure 6a. The dimensions were chosen according to Figure 6a and 6b. The tests were made according to NT BUILD 422 (1993). The full test specimen was simply supported at both ends by two steel cylinders, as shown in Figure 6f, and loaded at midpoint through a cone connected to the load cell, according to Figure 6e. A 1 mm thick rubber layers were placed between the wood test specimen and the supports. The same was done between the wood test specimen and the cone connected to the load cell. The machine used was the same as for the tensile strength perpendicular to the grain tests; a universal testing Machine UTM “Alwetron” TCT 50. The tests were performed under displacement control and a compression load with a rate of 1.30 mm/min until failure was applied by a hydraulic piston. The displacement rate was chosen according to NT BUILD 422 (1993), where it is suggested that it shall be adjusted so that collapse is obtained in about 3±1 minutes. A few trial tests were performed in order to find the right displacement rate. During the trial tests the load vs. deflection curve was found to be unstable. As a solution, the length of the notch was increased by 3 mm using a razor blade, according to Figure 6e. 10 annual ring orientation for specimens of the of test set-up; (f) and details the of test set-up. Test set-up (a) the tests. for energy (c) piecesSpecimen of the specimen; to two offracture test (b) dimensions timber; glued tested in thetested in ring (d)RT annual orientation orientations; specimens for crack tested in the TR crack orientations; (e) details Figure 6 The dashed lines in (c) and (d) show the part of the rail from where the specimen was cut. the specimen was where the rail from part of the show (d) in (c) and lines The dashed 11
3. Results
3.1. Bottom rail Two primary failure modes were found during the tests: 1) Splitting along the bottom side of the rail according to Figure 7a. 2) Splitting along the edge side of the rail according to Figure 7b. This is a difference with what was found during the other experimental programs related to bottom rail tests, Caprolu et al. (2014a; 2014b), where a third failure mode, yielding and withdrawal of the nails in the sheathing-to-framing joints, was found. This failure mode did not happen in this experimental program probably due to the small distance 25 mm between the nails.
bcrack1 bcrack1
a) Mode 1
bcrack2 bcrack2
b) Mode 2 Figure 7 (a) Splitting failure along the bottom side of the rail; and (b) splitting failure along the edge side of the rail. The left column of pictures refers to bottom rails with the pith oriented downwards (PD = N) and the right column with the pith oriented upwards (PU = U).
In Figure 8, the number of observations of the two different failure modes is graphically shown for the series of the study. It is noted that the predominant failure mode is failure mode 1, splitting failure along the bottom side of the rail. It is also possible to note an influence between the distance s and the failure mode. For small values of distance s, failure mode 2 occurs. 12
3
2
1
Mode 2 0 Mode 1 Set 3 Set - PU (5)* 3 Set - PD (5)* 2 Set - PU (0)* 2 Set - PD (0)* Set 1 Set - PU (40)* 1 Set - PD (40)* 2 Set - PU (30)* 2 Set - PD (30)* 3 Set - PU (20)* 3 Set - PD (20)* 4 Set - PU (10)* 4 Set - PD (10)* 1 Set - PU (25)* 1 Set - PD (25)* 2 Set - PU (15)* 2 Set - PD (15)* 1 Set - PU (10)* 1 Set - PD (10)* 40** 60** 80** 100** 40** 60** 80** 40** 60** Series 1 (b/2)*** Series 2 (3b/8)*** Series 3 (b/4)*** Figure 8 Recorded failure modes for the different test series and sets belonging to the experimental study (PU = pith upwards, PD = pith downwards). *Distance from washer edge to the loaded edge of the bottom rail [mm]; **size of washer [mm]; and ***bolt position.
The failure load for the two brittle failure modes is defined as the load at which there is a first distinct decrease in the load carrying capacity due to a propagating crack in the bottom rail. The results of the different tests are summarized in Table 4. The failure loads of the study are presented with respect to the pith orientation. Mean failure load and mean density are presented with respect to failure mode. The dry density, defined as the ratio between the mass of the specimen after drying and the volume of the specimen before drying at moisture content Ȧ, indicated as ȡȦ, is shown in Table 4 as mean value per set and failure mode. The mean moisture content per set, indicated as Ȧ, is also show.
For failure mode 1 the location of the crack initiation, the distance bcrack1, somewhere between the middle of the width and the loaded edge of the bottom rail, according to Figure 7a, was recorded. For failure mode 2 the length of the horizontal crack before it changes in a more vertical direction, bcrack2, according to Figure 7b, was also recorded. These values, together with failure mode and load, are given in Table 5 for each specimen. 13 Ȧ [%] value Mean Mean ] 3
Ȧ ȡ mode mode [kg/m ttom ttom side the of rail; and (2) Mean value per failure per failure value Mean Mean valueMean 388 390 347 14.9 valueMean 389 389 391 14.8 (1) (2) All (1) (2) Number of tests per failure mode per failure [%] COV [kN] Stddev Stddev [kN] Mean Mean = moisture content. = moisture [%] Pith Up Ȧ COV Pith Down (PD) and upwards (PU). (1) Failure modes: splitting along the bo [kN] Stddev Stddev [kN] Mean Mean Mean failure load per failure loadmode failure per failure Mean [%] COV [kN] = dry density = dry respect towith at volume Stddev Stddev Ȧ ȡ All failure modes failure All (1) (2) [kN] Mean Mean
of tests of Number Number Set 234 32 33 3 12.12 17.1 3 4.09 21.6 3 1.40 33.7 1.51 15.8 3 8.192 27.4 12.1 7.00 2.073 17.1 2.834 26.7 4.09 21.6 13.1 1.40 3 10.3 6.10 33.72 1.51 3 15.8 8.193 3 27.4 22.8 7.00 12.1 2.07 -2 15.5 2.83 - 3 28.9 3.39 13.1 18.0 - 3 5.39 10.3 - 28.0 - 4.25 11.7 - - 3 31.5 24.5 - - 12.1 19.7 1.43 - 15.5 - 2.83 23.1 3.39 - - 18.0 9.08 5.39 - - 10.3 2.30 28.0 22.5 3 4.25 11.7 31.5 3 - 25.2 8.58 19.7 3 1.43 ------9.08 - - 3 - - 3 - - 410 - - 409 - - - - 410 342 - - 2 409 23.2 - - 342 372 - - - 390 - 1 3 372 - - 16.3 3 - 23.1 390 15.1 3 382 - 14.5 - 2.30 - - - 3 399 8.58 14.1 - 418 14.3 347 2 378 - 0 418 368 14.3 378 1 368 398 - 3 - 398 403 - 16.5 390 14.7 409 - 14.9 - 393 14.8 14.4 390 13.7 1 31 10.81 3 2.74 25.3 12.3 31 10.8 2.66 22.9 2.74 21.5 3 2.17 25.31 12.3 9.49 8.62 2.66 -1 3 22.9 1.14 21.5 2.17 - 10.5 11.4 - 3 9.49 8.62 2.91 - 17.5 1.14 - - 23.6 2.12 10.5 3 11.4 - - 9.24 2.91 - - 16.4 23.6 3 - - 421 - - - 3 421 - - - 367 - - 19.7 3 367 16.0 - 403 - - - 403 3 14.5 - 416 - - 416 14.7 2 365 - 1 365 15.4 365 - 353 14.2 390 14.8
Results from bottom rail tests the pithwith oriented downwards Series 1 2 3 1 2 3 All All Table 4 splitting along the edge side of rail. the 14
2 2
End End End Set 2 Set 2 Set
1 1
End End End
mode/load mode/load
Failure Failure Failure 1/24.0 28 28
-
2 2
End End End e 1 Set 1 Set - c) b) 1 1 31 30 End End End
vertical crack and loaded edge loaded edge and crack vertical
mode/load mode/load a)
Failure Failure Failure Failure 1- 2/22.6
2 2
End End End Set 3 Set 3 Set 1 1 End End End ad is given in kN.
) is given. End 1 and End 2 indicate the two bottom bottom two the 2 indicate End 1 and End given. ) is mode/load mode/load
Failure Failure Failure crack2 b
2 2
End End End Set 2 Set 2 Set
1 1
End End End
mode/load mode/load
Failure Failure Failure
2 2
End End End Set 1 Set Set 1 Set are given. 1 1 crack2 End End End
b
Pith Up
mode/load Pith Down mode/load
Failure Failure Failure Failure and crack1 rds (PD)rds 1 the (PU). failure mode For upwards and between distance b
2 2
End End End Set 4 Set 4 Set
1 1
End End End
mode/load mode/load
Failure Failure Failure
2 2
End End End Set 3 Set 3 Set
1 1
End End End
mode/load mode/load
Failure Failure Failure Series 1Series 1 Series 2 Series 2 Series 3 Series 3
2 2
End End End Set 2 Set 2 Set 1 1 End End End
) is given. For failure mode 2 the length of the horizontal crack before it changes direction ( mode/load mode/load
Failure Failure Failure crack1 b
2 2
End End End Set 1 Set 1 Set
1 1 Measured crack data for specimens with the pith oriented downwa pith oriented the data specimens with crack Measured for
if failure mode 1 is considered as failure mode. mode. failure as considered 1 is mode failure if if failure mode 2 is considered as failure mode. failure mode. as considered 2 is mode failure if End End End
mode/load mode/load
crack1 crack2
Failure Failure Failure Failure b For this specimenFor this difficult towas distinguish the failure both mode then b rail ends, but no distinction no but rail ends, is them. between here made and aredistances All lengths in crack given the whilst mm, failure lo Table 5 1/10.91/13.5 53 551/8.04 58 53 58 1/12.1 1/16.2 52 57 53 1/8.03 56 53 60 1/15.7 1/18.5 63 55 54 1/17.0 67 51 64 1/22.1 1/22.81/9.89 59 551/7.69 60 62 1/19.9 701/8.28 74a) 52 63 58 1/9.43 60b) 51 1/13.0 1/9.66 62 42 58c) 1/15.9 40 58 1/14.6 50 1/10.6 65 45 63 65 1/14.4 69 56 1/14.8 1/17.1 52 45 30 1/9.43 60 58 1/18.2 48 1/19.8 70 42 60 58 1/27.8 64 44 1/24.4 1/17.2 44 45 50 1/22.5 50 81 1/30.0 50 1/14.1 62 29 57 52 40 1/20.9 58 1/14.7 57 1/25.2 36 15 1/9.44 50 26 1/9.99 45 - 42 51 31 47 1/11.9 2/22.5 1/33.7 41 1/13.0 41 12 40 1/10.2 60 52 - 47 - 34 1/22.6 44 1/27.8 45 2/23.2 37 48 22 - 1/15.5 - 38 2/19.7 1/17.3 21 23 30 2/24.7 - 29 21 2/20.5 2/24.2 - 24 35 - - of the bottom the of rail ( 15
3.2. Tensile strength perpendicular to the grain All curves were found to show a similar stiffness and a brittle failure load, typical for timber loaded by a tensile load perpendicular to the grain. The results are presented in Table 6 with respect to the direction tested. Mean failure load, defined as the maximum load reached during the test, mean tensile strength perpendicular to grain and mean density are presented.
Table 6 Results from testing of specimens in tensile strength perpendicular to grain. R = radial direction, T = tangential direction.
Failure load Tensile strength perpendicular to the Mean
grain ft,90 density
Mean Min. and Stddev COV Mean Min. and Stddev COV [kg/m3] Series
Direction Max Max
Number tests of [kN] [kN] [kN] [%] [MPa] [MPa] [MPa] [%] 3.26 1.54 1 R 18 4.73 ÷ 0.83 17.4 2.28 ÷ 0.40 17.4 467a) 6.45 3.10 1.98 0.98 2 T 34 3.63 ÷ 0.88 24.1 1.79 ÷ 0.39 22.1 463b) 6.11 2.84 a) Result calculated with 9 specimens. b) Result calculated with 31 specimens.
3.3. Fracture energy The load-deflection curve for each specimen has been recorded. They have been determined by measuring continuously corresponding values of load, F, and deflection or cross head movement, u. For the test to be valid it is required that the load deflection response is stable, where by stable curve is meant a continuous curve. For specimens tested in the RT plane 6 curves were stable, 4 almost stable and 5 unstable. For specimens tested in the TR plane 2 curves were stable, 6 almost stable and 25 unstable. In Figure 9 one example of each type of curve is shown. The reason for this high number of unstable curves in the TR plane, which was already known before testing, is discussed below. 16
100
80
60
40 a) [N] Load
20
0 02468 Displacement [mm]
100
80
60
40 b) [N] Load
20
0 0246810 Displacement [mm]
200
160
120
80 c) [N] Load
40
0 024681012 Displacement [mm]
Figure 9 Examples of load-deflection curves. (a) Stable curve; (b) almost stable curve; and (c) non stable curve.
For specimens with TR orientation most of the curves were unstable. This is believed to be due to the annual ring orientation, as shown in Figure 10. In Figure 10a the crack for specimens with RT orientation is shown. In this case most of the curves were found to be stable or almost stable. The stability is probably due to the annual ring orientation since the crack is able to develop following an annual ring. In Figure 10b the crack has TR orientation. In this case most of the curves were found to be unstable. The difference in the crack path is noted with respect to the RT orientation, since in this case the crack develops perpendicular to the annual ring “jumping” from one annual ring to another. It is believed that the drops of load in the post peak behaviour of the load displacement curves are due to this. 17
a)
b)
Figure 10 Examples of crack growth during the fracture energy tests. (a) RT orientation of the crack; and (b) TR orientation of the crack.
The results of the tests are summarized in Table 7. The results are presented with respect to the direction tested. Mean failure load, mean fracture energy and mean density are presented.
Table 7 Results from fracture energy testing in RT and TR direction.
Failure load Fracture energy Gf Mean density
Mean Min. and Max Stddev COV Mean Min. and Stddev COV Series
Direction Max 3 Number tests of [N] [N] [N] [%] [N/m] [N/m] [N/m] [%] [kg/m ] 60.0 190 1 RT 15 98.0 ÷ 27.4 27.9 322 ÷ 86.7 26.9 455a) 169 476 69.0 196 2 TR 33 123 ÷ 29.7 24.2 303b) ÷ 66.5 21.9 474b) 192 432 a) Result calculated with 14 specimens. b) Result calculated with 31 specimens.
3.4. Compilation of matched experimental results Since the three types of tests are performed with specimens having matched material properties, it is interesting to show results of the three types of experiments with specimens cut from the same board. Tables 8 and 9 show the results of this correlation. The tables are divided with regard to the pith orientation of the bottom rail, PD for Table 8, and PU for Table 9. Not all bottom rail specimens are presented but only those for which the fracture energy and the tensile strength were tested. The first number of the bottom rail ID refers to the series tested, the second number to the set and the third is just the progressive number of the specimen. N refers to PD and U to PU. When planning the experiments it was decided that for bottom rail specimens of series 1 the fracture energy and the tensile strength would be tested only in the TR and T directions, respectively, since we were sure that the failure mode would become failure mode 1. For bottom rail specimens of series 2 and 3, on the contrary, there were the same possibilities to get failure mode 1 and 2, therefore, it was decided to test the fracture energy and the tensile strength for both cases. This was done also in order to see the possible influence of these properties on the failure mode, since specimens of the same set could fail in different ways. For each Gf–value the type of curve characteristics is also listed in the last column. 18
Table 8 Compilation of the matched experimental results. Bottom rail specimens with PD. Gf = fracture energy, ft,90 = tensile strength perpendicular to the grain. TR crack orientation for failure mode 1 in bottom rail specimens and RT crack orientation for failure mode 2. T in the tangential direction, tested in case of failure mode 1 for bottom rail specimens and R is the radial direction, tested in case of failure mode 2. S, A and U: stable, almost stable and unstable Gf curve, respectively. When two results are given in the column for the type of the Gf curve, the first refers to specimens with orientation TR and the second to specimens with orientation RT.
Bottom rail Bottom rail Gf (TR) Gf (RT) ft,90 (T) ft,90 (R) Failure Type of
failure load mode Gf curve Specimen ID [kN] [N/m] [N/m] [MPa] [MPa] 111 N 10.9 231 - 1.44 - 1 U 112 N 13.5 237 - 1.82 - 1 U 113 N 8.04 356 - 1.93 - 1 A 121 N 12.1 251 - 1.89 - 1 U 122 N 16.2 432 - 2.14 - 1 S 123 N 8.03 285 - 1.49 - 1 U 131 N 15.7 279 - 1.70 - 1 A 132 N 18.5 225 - 1.36 - 1 U 133 N 17.0 364 - 1.69 - 1 U 231 N 27.8 - 352 1.75 2.15 1 - 232 N 24.4 366 441 1.37 2.53 1 A/U 233 N 30.0 316 371 2.34 2.06 1 U/A 311 N 20.9 266 381 1.71 3.10 1 U/U 312 N 25.2 245 225 1.24 1.88 1 U/S 313 N 22.6 233 310 1.40 1.75 1 U/U 321 N 22.5 356 436 1.44 2.33 2 A/U 322 N 33.7 375 476 2.84 2.11 1 U/S 323 N 24.0 271 280 1.89 2.50 1 U/A 19
Table 9 Compilation of the matched experimental results. Bottom rail specimens with PU. Gf = fracture energy, ft,90 = tensile strength perpendicular to the grain. TR crack orientation for failure mode 1 in bottom rail specimens and RT crack orientation for failure mode 2. T in the tangential direction, tested in case of failure mode 1 for bottom rail specimens and R is the radial direction, tested in case of failure mode 2. S, A and U: stable, almost stable and unstable Gf curve, respectively. When two results are given in the column for the type of the Gf curve, the first refers to specimens with orientation TR and the second to specimens with orientation RT.
Bottom rail Bottom rail Gf (TR) Gf (RT) ft,90 (T) ft,90 (R) Failure Type of
failure load mode Gf curve Specimen ID [kN] [N/m] [N/m] [MPa] [MPa] 111 U 9.89 - - - - 1 - 112 U 7.69 - - 2.08 - 1 - 113 U 8.28 231 - 1.44 - 1 - 121 U 9.66 300 - 2.58 - 1 U 122 U 15.9 423 - 1.76 - 1 U 123 U 10.6 1032a) -1.90-1 S 131 U 17.1 345 - 1.99 - 1 A 132 U 9.43 196 - 0.98 - 1 U 133 U 19.8 373 - 1.98 - 1 U 231 U 22.6 233 - 2.05 2.75 1 U 232 U 27.8 328 - 2.40 1.54 1 U 233 U 23.2 212 352 2.11 2.15 2 U/U 311 U 15.5 306 299 1.65 2.24 1 U/A 312 U 19.7 388 190 1.51 2.59 2 U/S 313 U 17.3 249 260 1.52 2.13 1 U/S 321 U 24.7 316 331 1.34 1.99 2 U/S 322 U 20.5 246 231 1.65 2.44 2 U/S 323 U 24.2 390 243 1.80 2.10 2 U/A a) This result is considered not trustable due to the difference with the other results.
4. Results In Caprolu et al. (2014c) and Jensen et al. (2014), models based on a fracture mechanics approach have been presented and derived in order to calculate the load carrying capacity of bottom rails in partially anchored shear walls. The formulas derived depend on the failure mode. In those papers the analysis have been carried out using values of fracture energy and tensile strength perpendicular to the grain found in literature. However, due to the orthotropic characteristics of the wood material, it was hard to find proper values for the orientations wanted. With the values listed in Tables 8 and 9, the same formulas used in Caprolu et al. (2014c) and Jensen et al. (2014) are here used and their precision evaluated. When referring to mean values in this paper, the values listed in Table 10 below are used, where the ft,90 and Gf values are the mean values calculated from the tests presented in this paper and E and G according to Caprolu et al. (2014c). Other values listed in Table 10 are the width b, and depth h of the bottom rail, the depth he of the “cantilever beam” considered when deriving the formulas and the shear correction factor ȕs. 20
Table 10 Material properties and data used in the evaluation.
Material properties Values Unit E 500 MPa G 50 MPa a) ft,90,T 1.80 MPa b) ft,90,R 2.30 MPa a) Gf,TR 300 N/m b) Gf,RT 320 N/m b 900 mm h 45 mm
he 22.5 mm
ȕs 1.20 a) Values calculated in the tests and used in equations for failure mode 1. b) Values calculated in the tests and used in equations for failure mode 2.
4.1. Compilation of matched experimental results The formulas used are listed below. For their derivation the reader should refer to Caprolu et al. (2014c) and Jensen et al. (2014). All of them have been derived using the compliance method, a branch of the linear elastic fracture mechanics theory (LEFM). Eq. (1) was derived considering a part the bottom rail as a cantilever beam fully clamped at the crack position. The compliance has been calculated considering both flexural and shear deformations.
2/GbGfe Plha 2 (1) G §·be 12 ¨¸ Es Eha©¹
Simplified versions of Eq. (1) can be obtained assuming a small crack length (a ĺ (T assuming that bending deformations can be ignored (G/E ĺ (T DQGDVVXPLQJERWKVPDOOFUDFN length and that bending deformations can be ignored, Eq. (4).
2/GbGfe Plh 2 (2) G §·be 12 ¨¸ Es Eh©¹
2GG Plha f (3) besE
2GG Plh f (4) besE
Eq. (5) was derived using the same geometry as Eq. (1). However, in this case is assumed that the cantilever is not completely rigidly clamped at end, but some finite rotation occurs. In Jensen et al. (2014) the compliance was calculated and then Eq. (5) was derived. 21
2/GbG Plha fe (5) G b 12 e E Eh a s
Again, if a small crack length is considered, a simplified version of Eq. (5), given by Eq. (6) can be obtained.
2/GbG Plh fe (6) G b 12 e E Eh s
Assuming negligible bending deformations or both small crack length and negligible bending deformations would lead to Eqs. (3) and 4. Eq. (7) has been derived using the end-notched beam model of Gustafsson (1988). However, since that model has different crack propagation with respect to that of failure mode 1 of bottom rails, a different compliance has been used.
2/GbG Plh D fe (7) 2 3 GG§·bbee18 4 3DD 12 ¨¸Es Eh©¹DD5 E 11DD 3 h
In Eq. (8), a simplified version, considering small crack length, of Eq. (7) is given.
2/GbGfe Plh 2 (8) GG§·bbee6 12¨¸ 6 Es Eh©¹ 5 Eh
The formulas above have been used, together with the values listed in Table 10, to calculate the
n “root mean square error” (RMSE) values, RMSE 1 n ¦ '2 , where n is the number of 1 specimens testeGDQGǻLVGHILQHGDVWKHYDOXHRIWKHGLIIHUHQFHEHWZHHQIDLOXUHORDGIURPWHVWVDQG failure load calculated according to the formulas above. The RMSE-values are calculated in two ways:
(1) by using the individual values for Gf and ft,90 for each specimen listed in Table 8 and 9, i.e.
n 2 RMSE 1 n ¦ 'ind , and (2) by using the mean values for values for Gf and ft,90 as listed in Table 1
n 2 10, i.e. RMSE 1 n ¦ 'mean . These calculated RMSE-values are listed in Table 11, where the 1 values are divided with respect to the pith orientation.
In the formulas above, be is considered as the “cantilever span” of the “cantilever beam” considered for deriving the formulas. be = s + c, where s is the distance between the edge of the washer and the loaded edge of the bottom rail and c is an additional length. In this case c = 20 mm has been used. 22
Table 11 Comparison between mean values of individual RMSE-values and RMSE-values using mean values of
Gf and ft,90 for failure mode 1.
Eq. (1) Eq. (2) Eq. (3) Eq. (4) Eq. (5) Eq. (6) Eq. (7) Eq. (8) [kN] [kN] [kN] [kN] [kN] [kN] [kN] [kN] RMSE- values for PD 7.87 8.54 6.68 15.4 10.2 3.33 10.0 3.39 individual test PU 4.49 9.19 6.54 16.4 7.01 3.13 6.70 3.19 values RMSE- PD 4.48 8.94 5.88 16.0 8.48 3.02 8.15 3.21 values for mean test PU 3.44 11.3 8.48 18.7 5.74 4.88 5.49 4.89 values
From Table 11 it is noted that the difference in magnitude between RMSE-values for individual test values and RMSE-values for mean test values is negligible, since the values are in the same order of magnitude. It is evident that the best agreement is given by the Eqs. (6) and (8), for the case of RMSE-values for individual test values, and by Eqs. (1), (6), and (8) for the case of RMSE-values for mean test values. In Figure 11 the failure load versus distance s has been plotted, with the failure load curves calculated with Eqs. (1) – (8). In the figure only specimens failed in mode 1 are included, and a polynomial regression line of second order for the test results is included. Figures 11a and 11b refer to specimen with pith oriented downwards and upwards, respectively, while in Figures 11c all specimens failed in mode 1 are shown independently of the pith orientation. The curves are plotted using the mean values listed in Table 10.
Eq. (1) 50 Eq. (2) Eq. (3) 45 Eq. (4) Eq. (5) 40 Eq. (6) 35 Eq. (7) Eq. (8) 30 R2 = 0.82
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] a) 23
Eq. (1) 50 Eq. (2) Eq. (3) 45 Eq. (4) Eq. (5) 40 Eq. (6) 35 Eq. (7) Eq. (8) 30 R2 = 0.57
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] b) Eq. (1) 50 Eq. (2) Eq. (3) 45 Eq. (4) Eq. (5) 40 Eq. (6) Eq. (7) 35 Eq. (8) 30 R2 = 0.72
25
20 Failure load [kN] load Failure 15
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] c) Figure 11 Failure load versus distance s for specimen failed in mode 1. Curves according to Eqs. (1) – (8). (a) Specimens with pith downwards; (b) specimens with pith upwards; and (c) all specimens independently on the pith orientation.
Eqs. (2) and (4) give values too high with respect to the test results, while Eqs. (5) and (7) too low. The Eqs. (1), (3), (6) and (8) were found to give the best agreement. However, if graphical comparison 24 between them is made, is noted that Eq. (3) gives values too high for distance s > 10 mm and Eq. (1) follow the general behaviour of the results but predicting low values. The best agreement is shown by Eq. (6) and (8). Good agreement is also shown, with respect to the test results, between the failure load and the distance s, spotlighted by 0.57ddR2 0.82 .
4.2. Analysis for failure mode 2 For failure mode 2, a total of six equations, given in Caprolu et al. (2014c) and Jensen et al. (2014) have been tested. The equations are listed below. As Eq. (1), Eq. (9) was derived considering a part the bottom rail as a cantilever beam fully clamped at the crack position and the compliance has been calculated in the same way considering both flexural and shear deformations.
2GhGfe Pl 2 (9) Ga§· 12 ¨¸ Es Eh©¹e
Assuming small crack length (a ĺ RU DVVXPLQJ WKDW EHQGLQJ GHIRUPDWLRQFDQ EH LJQRUHG DV compared with the shear deformations, (i. e. G/E ĺ OHDGVWRDVLPSOLILHGYHUVLRQRI(T
Pl 2/ GhGfeE s (10)
Eq. (11) has been derived using again the model of splitting failure of an end-notched beam derived by Gustafsson (1988). The difference with the previous model is given by a different compliance, calculated taking into account contributions from the part of the beam with depth h and from additional rotation of the cantilever due to the fact that the stiffness of the beam with depth h cannot be fully activated in the immediate vicinity of the corner of the notch. The solution given in Gustafsson (1988), if used on a bottom rail, leads to Eq. (11).
GGf Plh h (11) 31D aG§· 1 61¨¸3 5 DDhE©¹
A simplified version may be obtained in the special case of a small crack or if assuming that the bending deformations are negligible as compared with the shear deformations, giving Eq. (12):
h PlC e 1 h 1 e h (12) 5 CG G 1f3
Eq. (13) is based on the model derived by Jensen (2005) when a beam loaded perpendicular to the grain by a bolt located close to the edge and close to the end is considered. The horizontal crack in a bottom rail may be considered as a special case of that solution, namely forbe o 0 . 25
1 PP 0 22] 1 (13) C G 1 ] 1 10 fEhte
In van der Put and Leijten (2000), a linear elastic fracture mechanics model was derived for a simply supported beam loaded perpendicular to grain by a single load at mid-span. For that model, if small edge distance hhe o 0 is considered, the failure load PP 0 , with P0 from Eq. (13). P0 may therefore be considered as a special case of the van der Put and Leijten (2000) model. A semi- empirical generalized version of Eq. (9) may be proposed, as in Eq. (14).
h PlC J e 1 h 1 e h (14) 1 J 21]
In Table 12 the RMSE-values for individual test values and the RMSE-values for mean test values, as previously defined, are listed. The table shows values only for specimens with pith upwards, since for pith downwards only one specimen failed in mode 2 and a statistical evaluation would not be meaningful.
Table 12 Comparison between mean values of individual RMSE-values and RMSE-values using mean values of Gf and ft,90 for failure mode 2.
Eq. (9) Eq. (10) Eq. (11) Eq. (12) Eq. (13) Eq. (14) [kN] [kN] [kN] [kN] [kN] [kN] RMSE- values for individual PU 4.30 2.85 9.56 6.36 8.06 2.46 test values RMSE- values for PU 2.94 2.03 8.66 9.04 6.92 2.00 mean test values
The best agreement is given by the Eqs. (9), (10) and (14). In Figure 12 the failure load versus distance s has been plotted, with the failure load calculated according to Eqs. (9) – (14). Only specimens failed in mode 2 are included, and the linear regression line for the test results is included, where possible. Figures 12a and 12b refer to specimen with pith oriented downwards and upwards, respectively, while in Figures 12c all specimens, independent of the pith orientation, are included. The failure load has been calculated using the mean values listed in Table 10. 26
40 Eq. (9) 35 Eq. (10) Eq. (11) Eq. (12) 30 Eq. (13) Eq. (14) 25
20
15 Failure load [kN] load Failure
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] a)
40 Eq. (9) 35 Eq. (10) Eq. (11) Eq. (12) 30 Eq. (13) Eq. (14) 25 R2 = 0.36
20
15 Failure load [kN] load Failure
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] b) 27
40 Eq. (9) 35 Eq. (10) Eq. (11) Eq. (12) 30 Eq. (13) Eq. (14) 25 R2 = 0.33
20
15 Failure load [kN] load Failure
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] c) Figure 12 Failure load versus distance s for specimen failed in mode 2. Failure load calculated according to Eqs. (9) – (14). (a) Specimens with pith oriented downwards; (b) specimens with pith oriented upwards; and (c) all specimens independent on the pith orientation.
Eq. (12) gives values too high with respect to the test results, while Eqs. (11) and (13) give too low values. This agrees with the results listed in Table 12. The Eqs. (9), (10) and (14), which were found to give the best agreement, are pretty close to test results. Eq. (9) gives lower values compared to Eqs. (10) and (14), which give more or less the same value (they have similar RMSE-values).
4.3. Combined design curves for mode 1 and mode 2 In the previous two sections Eq. (6) and Eq. (14) have be found to give the best RMSE-value with respect to the test results. A limit between the two formulas has been determined, according which failure mode 2 is applicable for s < 10 mm and mode 1 for s t10mm. The limit is shown in Figure 13, together with the test results. Figure 13a and 13b show test results for specimens with pith downwards and upwards, respectively, while Figure 13c include all test results independently on the pith orientations. Further the RMSE-value calculated for Eq. (6) versus test results of failure mode 1 for specimens with s t10mm and for Eq. (14) versus test results of failure mode 2 for specimens with s < 10 mm, is shown. 28
40 Failure mode 1 35 Failure mode 2 Eq. (6) - RMSE = 2.73 Eq. (14) - RMSE = 0.22 30
25
20
15 Failure load [kN] load Failure
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] a)
40 Failure mode 1 35 Failure mode 2 Eq. (6) - RMSE = 4.88 Eq. (14) - RMSE = 1.79 30
25
20
15 Failure load [kN] load Failure
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] b) 29
40 Failure mode 1 35 Failure mode 2 Eq. (6) - RMSE = 4.88 Eq. (14) - RMSE = 1.79 30
25
20
15 Failure load [kN] load Failure
10
5
0 0 5 10 15 20 25 30 35 40 Distance s [mm] c) Figure 13 Limit between failure mode 1 and 2 for Eq. (6) and (14). (a) Specimens with pith oriented downwards; (b) specimens with pith oriented upwards; and (c) all specimens independent on the pith orientation.
5. Discussion The results from the bottom rail experimental program are in line with the previous experimental programmes presented in Caprolu et al. (2014a; 2014b). For the details the reader should refer to those papers, here only a summary of the main findings is given. Two brittle failure modes were found during the experimental program: (1) a crack opening from the bottom surface of the bottom rail; and (2) a crack opening from the edge surface of the bottom rail along the line of the sheathing-to-framing joints. In comparison with Caprolu et al. (2014a; 2014b) one less failure mode has been found, yielding and withdrawal of the nails in the sheathing-to-framing joint. This ductile behaviour has not been found probably due to the small distance used between the nails: 25 mm. The failure mode is dependent on the distance s between the washer edge and the loaded edge of the bottom rail; in fact for s t10 failure mode 1 is the only failure mode, while for s d10 mm failure mode 2 appears. The failure load was also found to be dependent on the distance s, and increases when s is decreased. Further, as the previous experimental programmes, the failure load of bottom rails with the pith oriented downwards is higher than for specimens with the pith oriented upwards. Since the density and moisture content of all the specimens are similar, it is believed that this is an effect of the initial cupping of the bottom rail due to the anisotropic shrinkage from drying or a consequence of the anisotropic material properties in the radial-tangential plane of the timber. The tensile strength perpendicular to the grain was found to be higher in radial direction than that in tangential. Results of Siimes (1967) discussed in Gustafsson (2003), show that ft,90 increases with increasing density and decreases with the increasing moisture content and temperature. However, the influence of these parameters do not explain the difference found between values for radial and tangential direction, since the mean density has been found to be similar for the specimens tested in the two directions and the moisture and temperature were kept constant for all tests. 30
One reason for the difference between radial and tangential direction could be the different volumes between the two specimens, which is commonly explained by the weakest link of theory of Weibull. However, for such small specimens and small difference in volume, and, as mentioned earlier, with the presence of the waist in the specimens, it is not believed that the volume has any major influence.
Hence it can be concluded that the difference between ft,90 in tangential and radial direction is just due to the orthotropic characteristic of wood. Boström (1992) has presented results of ft,90 strength of Scots pine at various load directions and his results also show that the strength value for radial direction is higher than for tangential direction in agreement with the results presented in this paper. It is noted that the tensile strength values are lower for both radial and tangential directions, than the values used earlier in Caprolu et al. (2014c) and Jensen et al. (2014). It is believed that the tensile strength together with the fracture energy, are the governing parameters for the failure capacity of the bottom rail. From this point of view, the results of the tensile strength tests are important. The reliability of the fracture energy test results could be questioned, since most of the curves were found to be unstable or almost stable and just a few were stable. However the results have been compared with fracture energy values of previous experiments as Larsen and Gustafsson (1990) and those shown in Smith et al. (2003) of Reiterer et al. (2000), where similar values were found, meaning that even if the curves are not stable the Gf values calculated from them are not far from the values found in literature. Further, similar values have already been used in Caprolu et al. (2014c) and Jensen et al. (2014). When the values have been used in the analysis in the previous section, not all formulas gave results in agreement with the test results. Regarding failure mode 1, the RMSE-values in Table 11 shows a rather good agreement for almost all formulas, with the exception of Eq. (4). This was expected, since that equation is a simplified version of Eq. (1), which was one of those giving the best agreement, where the initial crack length and the bending deformations were ignored. Eq. (6) was found to give the best agreement. The results here confirm the good agreement with bottom rail test results as already found in Caprolu et al. (2014c) and Jensen et al. (2014). Regarding failure mode 2, the results for pith downwards can be omitted, since only one specimen failed in mode 2 and hence it is not statistically reliable. The RMSE-values in Table 12 shows that the best agreement is given by Eq. (14), which is a simplified version of Eq. (13) Also in this case the results confirm the good agreement with bottom rail test results, as already found in Caprolu et al. (2014c) and Jensen et al. (2014).
6. Conclusions Tests on the splitting capacity of the bottom rail, fracture energy in RT and TR planes and tensile strength perpendicular to the grain in radial and tangential direction have been conducted. The result of the bottom rail tests confirm the behaviour presented in previous studies presented in Caprolu et al. (2014a; 2014b). Results of tensile strength tests show a tensile strength higher in radial direction than that in tangential. This confirms results from a previous stud found in literature. It is noted that the resulting values are lower than the values used in Caprolu et al. (2014c) and Jensen et al. (2014). Since it is believed that the tensile strength together with the fracture energy, are the governing parameters with respect to the failure capacity, the results of this study are considered very important. The results of the fracture energy tests instead are questionable due the high number of unstable curves. However, since the mean values from the tests have been found to be in good agreement with literature values, they have been considered trustable. Most formulas investigated in this paper, gave good agreement with the tests results. The formulas giving the best agreement, one per failure mode, have been chosen and it is believed that they can be used for calculating the splitting failure capacity of the bottom rail. If the splitting failure capacity can 31 be calculated and, hence, these brittle failure modes can be avoided and the plastic behaviour of the sheathing-to-framing joints can be ensured, the plastic design method can then be applied.
7. Future work This paper is the last one of five papers where the splitting failure capacity of bottom rails in partially anchored shear walls was studied, both experimentally and analytically. In this paper the equations believed to be the best for calculating this capacity have been compared. Since these models do not consider some influencing factors as the friction under the bottom rail, the cupping of the bottom rail, the effect of the pretension force and the discretely placed washers a future work based on an XFEM analysis, which has been already started, could be continued in order to study in more detail the influence of these and of the third dimension, which is not taken into account in the models here evaluated.
8. Acknowledgements The authors would like to express their sincere appreciation for the financial support from the County Administrative Board in Norrbotten, the Regional Council of Västerbotten and the European Union’s Structural Funds – The Regional Fund.
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