Mechanics of Traditional Connections with Metal Devices in Timber Roof Structures

Mechanics of traditional connections with metal devices in timber roof structures

L. Candelpergher & M. Piazza

Department of Mechanical and Structural Engineering, Trento UniversiQ Italy

Abstract

The preservation of ancient buildings (also if not monumental structures) has evolved, during recent years, from a mainly cultural issue into an economic opportunity and instrument of correct administration of the real estate. In this field the presence of wooden structures is significant. Structural timber, however, is affected by several problems related to the material itself. the structural elements and the connections. The arising of these difficulties often leads, in restoration design, to drastic solutions, such as the complete substitution of elements or whole sub-structures or, even worse? the use of elements made of other materials. Results, then, have been shown to be questionable not only from the aesthetic point of view but also from the strictly structural one. Justifications for similar interventions are very often related to the difficulty, complexity and burden of acquiring the understanding and knowledge about the existing structures. Within this framework, it appears necessary to struggle in deepening the methods to investigate mechanical and structural characteristics of existing structures, along with the techniques for effective restorations. This article reports the most recent results from the research held in Trento about connections typical of traditional timber roof structures (trusses) and especially about carpentry joints retrofitted with metal devices. The purpose of the specific research is to gain an understanding of the mechanisms and factors that influence the behavior of these connections and to set up synthetic models in order to characterize and verify the overall joint structural behavior.

Traditional connections

Most of the joints concerned, as the ones shohn in figure 1, provide connection between elements that are mainly subjected to axial loads. In practice, they are usually modeled as perfect hinges or, where a rotational stiffness is required for

4 16 Structaral Studies, Repairs and ,Maintenance ofHistorica1 Buildings

equilibrium, a full moment transmission is assumed (Ehlbeck, Kromer, 1995). Actually, traditional joints, based on frictional behavior, are capable of internal constraints that could be hardly described with the classical hinged or fixed schemes. Such connections, indeed, show a limited but nevertheless non negligible rotational stiffness, so that they could be correctly classified as semi-

rigid joints. Along with the monolateral nature of carpentry joints, relying on friction only, comes the need to employ metal reinforcements. This must be done in order to partially restore the continuity of the connection in case of exceptional loading events: unloading of compressed elements, whch warrant

contact between surfaces and development of friction, may lead to disconnection of elements and, in extreme conditions, to structural collapse. The types of metal reinforcements commonly used in practice, however, do not transmit directly all forces across the joint, as modem devices do: they are thought to exclusively maintain the functionality of the connection under unusual conditions.

Figure l: Typical traditional timber roof truss, with details of carpentry connections based on the birdsmouth joint.

The research presented here was essentially directed to parametric characterization of the mechanical behavior of reinforced connections. Results shown here refer to the most common type of connection in traditional timber trusses: the birdsmouth joint. The research path has gone through three subsequent phases: experimental tests on physical models in real size, numerical modeling and parametric analysis and eventually reinterpretation of results by means of simplified physical models.

Experimental analysis

The phase of direct experimental investigation was first started with tests on models of plain connections, built according to the two most frequently used geometries, i.e. nodes with skew angles (angle between the axis element lines) of

30" and 60". Afterwards, in two subsequent series, tests where carried out under monotonic and cyclic loading conditions on the same models reinforced by means of three different metal devices: bolt passing through rafter and chord, strip tightly binding the elements and couple of lateral stirrups (see figure 2).

Structrrral Studies, Repairs and Mazrttenance of Historical Buildings 4 17

Figure 2: Types of reinforcement under investigation: passing-through bolt (a), strip bmding the elements (b), couple of lateral stirrups (c).

Tests on assembled connections were preceded by an accurate determination of the mechanical properties of the elements used for all h11 scale models. The wood used was obtained fiom the demolition of a building from XVII century, and was classified as coniferous timber of class from C18 to C22, according to the European Standard EN338. Loading conditions and measuring instrumentation are shown in figure 3. The assembled connections were placed on a steel test-stand that could be arranged, depending on the skew angle of the tested joint, so that the compressed rafter would always be initially vertical. By means of two independent hydraulic jacks an axial compression load (W, maintained constant during the whole test, and a transversal load (F),acting at the upper end of the rafter, were applied. The latter load generated a bending moment in the joint and could be monotonic or cyclic. Throughout all loading steps several measurements were taken, namely applied loads and corresponding displacements and deformations at significant locations. Direct results fiom such measurements were therefore expressed in terms of diagrams force F versus displacement s (channel "00" in figure 3). both monitored at the upper end of the rafter. The employment of strain gauges in the nodal region allowed to evaluate localized phenomena with particular regard to the strains perpendicular to fiber direction.

Figures 4 shows some relevant F-s experimental diagrams: observing and comparing all the curves obtained in such way allowed a first comprehension: mainly qualitative, of the Influence on the joint behavior played by the reinforcements: first of all should be noticed the strongly non-linear rotational response of the plain connection: after an initially elastic phase, a sudden loss of stiffness follows at the time when the limit conditions of resistance based on friction only are reached along the contact surfaces. The roughly discontinuous response, more evident for the lower skew angle, is consequent upon phenomena of surface interloclung, plastic squashing, instantaneous losses of equilibrium localized in the contact areas.

Adding a metal reinforcement allows to reach much higher strength than that of the plain connection and to observe large excursions in the post-elastic field, with values of rotational stiffness and ductility still very significant. Connections reinforced with bolt and binding strip appear to be, from this point of view,

4 18 Structural Studies, Repairs and Maintenance of Historical Buildings

Figure 3: Loading conditions and measuring instrumentation (plain birdsmouth joint, skew angle a=60°).

X / -Plain 0 Bolt % St~rru~s Strw

Figure 4: Birdsmouth joint, skew angle a=30°, axial compression o,=O,SOMPa: Force - Displacement of rafter's upper end diagram for various types of reinforcement.

retrofitting techniques of low impact but high effectiveness: they indeed do not alter the elastic response typical of the plain joints (stiffness remains almost identical), but play a substantial role when the bearing capacity due to simple friction comes to its limit, and this especially in the case of cyclic loading

conditions. On the other hand the solution with lateral stirrups looks far less interesting, due to the radical modification, already at very low load levels,

induced by the reinforcement on the nodal response of the plain connection and, furthermore, due to the completely unsatisfactory performances shown under cyclic conditions (Parisi, Piazza, 2000).

Numerical modeling

The experimental measurements became the fundamental reference for the subsequent phase of the research: finite element numerical modeling of connections reinforced with bolt and binding strip (figure 5). Bi-dimensional models were set up, accurate enough so that they could simulate the experimental test conditions (finite element code Abaqus 5.8). Some aspects, typical of modeling continuous structural problems involving wood and complex geometries, are worth reporting here.

~igure5: Example of f~teelement model simulation of the experimental test conditions. Birdsmouth joint (a=60°) with passing-through bolt (left side) and detail of the finite element mesh (right side).

The performed simulations took first of all into account the anisotropic nature of wood as a continuous material (Kollmann, Cote, 1984). The constitutive law was reproduced according to an orthortopic elasticity approximation, thus prescribing different elastic moduli in direction parallel and perpendicular to the grain (Bodig, Jayne, 1982). Furthermore, the material response to compression perpendicular to fibers beyond the elastic limit was considered by means of a yielding model according to Hill's potential and an appropriate hardening rule, fitted on the plastic behavior perpendicular to the grain (Edlund, 1995). Another constitutive law, as complete as the one decribed for wood, was then defined to model the steel behavior of the reinforcements. The elastic-plastic characterization of steel was obtained using the traditional Von Mises yielding model and a bi-linear hardening rule.

420 Structural Studies, Repairs and 'Vaintenawe ofHistorica1 Buildings

Boundary conditions were also a major issue of complexity. The interaction based on friction between the various surfaces forced to contact (timber-to- timber and steel-to-timber) was reproduced through the "jhite sliding" formulation (Oden, Pires, 1983) which allows for arbitrary detachments and surface penetrations perpendicular to the contact interface. Friction, along with tangential constraints or relative displacements between contact surfaces, was implemented with reference to Coulomb's friction model after an appropriate choice of friction coefficients. (McKenzie, Karpovic, 1968). Due attention was finally paid to determine the optimal discretization of the structure. All models have been created using quadrilateral and triangular second order isoparametric elements with a 'plane stress" formulation. Through a sensitivity analysis the best size and shape of the elements has been chosen in order to obtain the most effective mesh arrangement at the lowest computational costs, especially in the complex nodal regions (see figure 5).

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

S [mm1 Figure 6: Comparison between experimental and numerical curves. Birdsmouth joint (a=60°, a,=l,SMPa, positive load) reinforced with passing- through bolt.

The constant reference to experimental tests allowed the calibration first and the validation of numerical results afterwards. In the example shown in figures 6 the significant reliability of numerical simulations in comparison to the corresponding experimental conditions can be observed, except for the hasty discontinuities noticed during physical testing, whose dynamic nature could not be reproduced with models based on a quasi-static formulation. Results obtained, however, demonstrate the applicability of a numerical approach to the study of retrofitted connections, despite the unavoidable approxmatlons introduced with finite element modeling.

Synthetic characterization

The refined models just discussed have, clearly, limited practical applicability, slnce they require adequate modeling capabilities and a significant computational effort. The concluding phase of the investigation methodology, consisted

therefore in re-elaboration of numerical solutions obtained from the fmite element models, also studying conditions not directly investigated during the experimental campaign.

Bending moment M 4

Elastic proportlonallty ltmit MiI ./

M-$ numerical diagram

- Rotatm at elast~c Rotation 4 proportlonal~iyilmlt $p*l

Figure 7: Definition of the characteristic parameters for rotational joint behavior based on a moment-rotation numerical diagram.

With the fmal goal of analyzing the behavior of an entire timber sub-structure as a whole, the quasi-static response of connections can be essentially reduced to the evaluation of an axial stiffness (slip moduls) and of a non-linear law in terms of relative rotation between elements as a function of the bending moment transmitted to the node. The latter is synthesized in a moment-rotation diagram.

Numerical solutions, were re-elaborated in order to derive such diagrams and to simplify them according to a bi-linear approximation (see figure 7). This was done for both types of reinforcement and for several loading levels of either sign. The information obtained through these elaborations, together with the knowledge grasped experimentally and numerically, gave the chance to eventually set up simple physical models that could help in reinterpreting the load bearing mechanisms, as shown in the following. These models are based on the hypothesis of a simplified joint behavior. They allow the direct estimation of all parameters necessary to characterize the so-called ''frst -load curves", i.e. the quasi-static response. The effectiveness of such models, however, is directly related to the correctness of the assumptions made on the connection behavior. As a result, they lead to a very essential insight, highlighting the most relevant

422 Structural Studies, Repairs and Maintenance ofHistorica1 Buildings aspects and parameters: the elastic and post-elastic rotational stiffness remains basically constant, regardless of the axial compression, while the threshold corresponding to the transition from elastic to post-elastic response clearly depends upon axial compression in a nearly linear way. As an example, the synthetic model for direct estimation of the elastic rotational stiffness of bolted birdsmouth joints is now described. Figure 8 shows the load bearing mechanism assumed at the positive elastic limit (where positive means bending moment forcing the skew angle to decrease).

Axial load b h "C -,

Lever arm of eccentric axal load

-- Center of rotatlon

\ Elast~cbendlng moment resistance of the bolt l \ M,, ,D,, Lever arm of the fr~ct!on \\\_ forces resultantI Figure8: Synthetic model of the resisting mechanism at elastic proportionality limit for positive bending load.

It is assumed that the achievement of the limit conditions corresponds to the incipient development of a rigid rotation of the rafter about the left end of the carving in the chord. With respect to this point, rotational equilibrium is imposed. Such equilibrium is sought considering the ideal lower portion of the rafter, from the front side of the beveled surfaces to the first full size rafter section, where the rotation center is also placed. The force that, due to friction, is developed along the larger surface of the carving contributes, in this simplified scheme, to the transmission of the axial load only. The contribution of friction to the rotational resistance is, in practice, fully ascribed to the front smaller surface of the carving: in ths region a stress gradient can be observed. Numerical models provide full support to this interpretation and have been referenced in order to assess the values of coefficient C,, which accounts for the rate of the total axial load passing through the concerned surface. The eccentricity of the load in the rafter is accounted when evaluating the contribution to the rotational resistance given by the axial force, through coefficient C2 shown again in figure 8. Values for this latter coefficient, as the former, have been determined on the basis of the observations made with numerical models for the most characteristic skew angles (Candelpergher, Piazza, 2000).

Structural Studies, Repairs and ,Woirntenance of Historical Buildings 423

Further contribution to the bending resistance of the joint eventually depends upon the presence of the metal reinforcement. In particular, the steel bolt is subjected to bending: as a f~stapproximation, its contribution to the joint resistance has been evaluated as the corresponding elastic limit bending moment of the bolt taken alone, thus at first yield in the outer fibers. Only in the post-elastic phase and after significant joint rotations, the axial traction in the bolt becomes relevant. At that stage the bolt prevents the complete disconnection by pressing the wood fibers beneath large washers. The synthetic model set up for the post-elastic conditions takes this aspect into due account, linking the maximum joint capacity to the wood strength in compression perpendicular to the grain.

According to the mechanism assumed in figure 8, it is then possible to derive the following expression: 7 7

The binomial formulation of eqn (1) helps a clear understanding of the three contributions just mentioned: the constant term, available even at complete axial unload of the rafter, is obviously the one due to the elastic resistance of the reinforcement. The linear dependence from axial load is moreover evident: its contribution to resistance is indeed formulated as the product of the rafter force N times an appropriate lever arm. Such lever arm, in particular, allows for: piction in the front carving (through coefficient C,), and is therefore function of the friction coefficient K the carving depth and the skew angle;

moment due eccentric axial load in the rafter (through coefficient C?). Estimating the rotational stiffness is then possible, once determined an appropriate value of limit moment through eqn (l), provided a corresponding value of the relative rotation between chord and rafter can be assessed. The estimation of the stiffness can be obtained using a reference axial load in the rafter corresponding to a stress value of 1,O MPa. For this particular load level, indeed, an accurate evaluation both experimental and numerical has been done of the relative slip 6 along the front surface of the carving. Under the assumption of this displacement, deducing the joint rotation corresponding to the limit of linear proportionality is then possible through:

The elastic rotational stiffness is eventually evaluated as follows, where the moment to be used is derived from eqn (1) for the reference axial load:

With the same approach of this example, based upon limit equilibrium considerations, other models have been set up for the evaluation of the negative and post-elastic rotational stiffness and of the axial one. They altogether allow the full static characterization of birdsmouth joints reinforced both with bolts and

424 Structural Studies, Repairs and Maintenance of Hlstot-ical Buildings

binding strips, information that could be easily included in the analysis of entire

trusses modeled with semi-rigid non-linear joints and linear elastic structural members.

Conclusions and further developments

The derived models are proposed as tools, which are handful and immediately employable for practical design and analysis At the same time, they lead to a

significant improvement of the quality of global structural analyses of traditional timber trusses, since they allow the transition from classical schemes (with hmged or fixed joints) to more sophsticated ones with semi-rigid joints. The phase in which the numerical models have been set up, calibrated and

validated has, so far, been a relevant part of the work done within the study of retrofitted connections. The realization of a parametric analysis of a certain amplitude is now planned. It will help to consolidate and possibly improve the simplified formulas proposed and furthermore investigate other connection geometries, completing the already studied cases.

The additional experimental campaign, already scheduled, will be directed to the analysis of some ancient trusses that have been recovered and fully reassembled and retrofitted in laboratory. Ths will provide the possibility to verify the reliability and accuracy of the analyses performed on a global scale

with semi-rigid joints characterized according to the simplified formulas partially presented here.

References

[l] EHLBECK J., KROMER M,, "Carpentry joints", Lecture C12 da "Timber

Engineering STEP l", Centrum Hout, Almere, 1995. [2] EN338, "Structural Timber classes", CENlTC124, Brussels, Belgium, 1995. [3] PARIS1 M.A., PIAZZA M., "Mechanics of plain and retrofitted traditional timber structures", J. Struct.Engnrg., ASCE, 126 (12), pp. 1395-1403, 2000. [4] KOLLMANN F.P., COTE' W.A., "Principles of wood science and

technology", Springer Verlag, Berlin, 1984. [5] BODIG J., JAYNE B.A., "Mechanics of Wood and Wood Composites", Van Nostrand, New York, 1982. [6] EDLUND B., "Tension and compression", Lecture B2 da "Timber Engineering STEP l ", Centrum Hout, Almere, 1995.

[7] ODEN,J.T., PIRES, E.B. "Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity", Journal of Apllied Mechanics, 50, pp. 67-73, 1983. [S] MCKENZIE W.M., KARPOVIC H., "The fvictional behavior of wood", Wood Science and Technology, 2, 1968.

[9] CANDELPERGHER L., PlAZZA M,, "Meccanica delle connessioni tradizionali con elementi metallici nelle capriate in legno", L'Edilizia, n.9110, settembrelottobre 2000, pp. 42-5 1.