Construction of All-Wood Trusses with Plywood Nodes and Wooden Pegs: a Strategy Towards Resource-Efﬁcient Timber Construction

applied sciences

Article Construction of All-Wood Trusses with Plywood Nodes and Wooden Pegs: A Strategy towards Resource-Efﬁcient Timber Construction

Benjamin Kromoser * , Matthias Braun and Maximilian Ortner

Research Group for Resource-Efﬁcient Structural Engineering, Institute of Structural Engineering, University of Natural Resources and Life Sciences Vienna (BOKU Vienna), Peter-Jordan-Straße 82, 1190 Vienna, Austria; [email protected] (M.B.); [email protected] (M.O.) * Correspondence: [email protected]

Abstract: Timber truss systems are very efficient load-bearing structures. They allow for great free- dom in design and are characterised by high material use in combination with a low environmental impact. Unfortunately, the extensive effort in design and production have made the manufacturing and application of these structures, in this day and age, a rarity. In addition, the currently mainly used steel gusset plates adversely affect the costs and environmental impact of the trusses. The authors’ goals are to optimise the design of timber trusses and to solely use wood for all building components. The two research areas, (1) optimisation of the truss geometry and (2) optimisation of the joints by using solely wood–wood connections, are addressed in this paper. The numerical optimisation strategy is based on a parametric design of the truss and the use of a genetic solver for the optimisation regarding minimal material consumption. Furthermore, first results of the tensile and compression behaviour of the chosen wood–wood connections are presented. The basic idea for Citation: Kromoser, B.; Braun, M.; the joints is to use a plywood plate as a connector, which is inserted into the truss members and fixed Ortner, M. Construction of All-Wood with wooden pegs. The housing of the new robot laboratory located at BOKU Vienna is considered a Trusses with Plywood Nodes and special case study for the research and serves as an accompanying example for the application of the Wooden Pegs: A Strategy towards research within the present paper. Resource-Efficient Timber Construction. Appl. Sci. 2021, 11, 2568. https://doi.org/10.3390/ Keywords: wood construction; engineered wood product; genetic optimisation algorithm; structural app11062568 optimisation; timber construction; timber truss; wood–wood connection

Academic Editor: Jürgen Reichardt

Received: 4 February 2021 1. Introduction Accepted: 10 March 2021 Wood is a natural inhomogeneous anisotropic material with discontinuities due to Published: 13 March 2021 defects as, for example, pitch pockets, branches and fibre twist. When used for building construction, the original material undergoes multistage sorting and processing [1–3]. Publisher’s Note: MDPI stays neutral These processes, and if applied gluing, allow for a compensation of the defects, resulting with regard to jurisdictional claims in in smoother and consequently better material properties [4,5]. In addition, subsequent published maps and institutional affil- geometry changes due to an adjustment of the equilibrium moisture can be reduced [6]. iations. The drawback regarding these products is that the production process is accompanied by many subtractive machining operations. The yield rate sinks to 25–35% within the processing of the tree trunk into the finished building component. Consequently, good mechanical properties and advantageous behaviour regarding geometric deformations are Copyright: © 2021 by the authors. the opposite of a low yield of the raw material. Licensee MDPI, Basel, Switzerland. Compared to other construction materials, timber has advantageous properties re- This article is an open access article garding the CO2 footprint as it is able to store part of the CO2 that was absorbed within distributed under the terms and the growing phase of the trees. Nevertheless, the energy for transport and processing is conditions of the Creative Commons still mainly produced by burning fossil fuels. Apart from that, wood is a growing natural Attribution (CC BY) license (https:// material with superior properties but a limited resource. Thus, the growth rate combined creativecommons.org/licenses/by/ with sustainable forestry limits maximum harvesting. In Austria, for example, according 4.0/).

Appl. Sci. 2021, 11, 2568. https://doi.org/10.3390/app11062568 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 2568 2 of 17

to the Austrian Research Centre for Forests, 46.2% of the total country area is covered with wood with still a rising trend. Nevertheless, the increasing use of wood currently necessitates an import percentage of 40%. Many literature sources refer to the possibility of buildings to be a serious sink of CO2, called the building sink effect (BSE) [7,8]. However, within an objective view, the share of the stored CO2 compared to the human-caused CO2 is currently significantly below 1% [9]. Thus, an increased use of wood has a positive but limited influence on the CO2 balance but, in any case, only if it goes along with sustainable forestry. Unfortunately, contrary examples do not confirm this basic need. In [10], for example, an abrupt increase in the harvested forest area over Europe after 2015 is described. To sum up this discussion, if timber is used as a construction material, minimisation of the quantity of material is a basic requirement. Based on these facts, it can be clearly shown that structural optimisation of building components is of the highest importance for efficient use of wood. Unfortunately, this basic principle is being ignored by the wood construction industry in industrialised countries. These countries currently clearly focus on saving costs rather than natural resources, since material costs are low in comparison to the high costs for personnel. Elements produced using industrialised manufacturing processes are cheaper and are therefore preferred by construction companies over resource-saving but more complicated structures. A specific example is the extensive use of cross-laminated timber as mass-produced construction material for the use as plate girders. Wooden trusses, for example, are rarely implemented nowadays and have been replaced by plate girders due to economic reasons, even though the material yield rate is comparatively lower [11]. The aim of the authors is to industrialise the design and production process of wood structures in order to allow for more efficient usage of valuable wood, while still being economically feasible. The authors have split the research development into three subpro- cesses: (1) optimisation of the geometry of supporting structures, (2) optimisation of joints and (3) optimisation of the production technology and the interface between computer- aided design (CAD) and computer-aided manufacturing (CAM). (1) and (2) are addressed in this paper. A detailed presentation of structural optimisation, load-bearing mechanisms of joints, as well as the full-scale load-bearing behaviour of the introduced structures will be published separately. Regarding material use, the authors focus within the presented strategy on solely using wood for all construction parts, including connections. This has three major, quantifiable, benefits: (1) reduction of costs since steel parts have a major impact on the total costs of timber trusses, (2) improvement of the ecologic impact as steel production and processing consumes considerably more energy (currently mostly produced by using fossil fuels) and (3) improvement of fire resistance as steel parts heat up and have therefore a negative impact on the load-bearing behaviour [12,13]. BOKU Vienna recently set up a new robot laboratory intended for investigations of different numerical controlled subtractive and additive manufacturing processes. The housing of the robot laboratory was part of the current research strategies and serves as a case study.

2. Parametric Design and Optimisation The fundamental idea for the new robot laboratory was the robot arm, which was set up ﬁrst to build its own housing. The shape of the housing was designed according to the working area of the robot, as shown in Section A-A of Figure1. The main supporting structure was executed as a curved truss solely made from wood without using any steel components. To design the construction, the plug-in Grasshopper [14] of the CAD software Rhinoceros [15] was used. Based on available known optimisation strategies, the built-up parametric model was used for the optimisation of the truss. The following parameters were deﬁned as variables: number of subdivisions, distance between subdivisions, alignment of diagonal members and cross section of the members of the truss. The main goal of Appl. Sci. 2021, 11, 2568 3 of 17

optimisation was to minimise the mass (and in general the environmental impact), while still obtaining the desired load-bearing behaviour.

2.1. Grasshopper Evolutionary Algorithm Galapagos Grasshopper’s evolutionary solver Galapagos was used to determine the most efficient truss by varying the previously mentioned geometric parameters. A similar application with focus on the optimisation of a truss frame subjected to wind is described in [16]. The use of the basic tool set for the optimisation of trusses is also explained in [17]. The optimisation strategy of the solver is based on the principle of genetic evolution and consists of five steps to optimise a so-called fitness value [18]. The fitness value represents the numerical parameter that can be optimised by the solver. The goal is to either minimise or maximise the fitness value. In this project, a simple, single-objective optimisation was applied, with only one numerical value being optimised in the calculation process at a time. Here, the five optimisation steps of the evolutionary solver are briefly explained. (1) An initial population (different trusses) is randomly assembled by the algorithm from the single slider variables. (2) The fitness values of the resulting trusses are evaluated and qualitatively ranked according to their performance. (3) In the next step, trusses are chosen by the algorithm according to a determined selection procedure for further analysis. (4) The variables of the selected trusses are then recombined similar to genetic reproduction in order to obtain better solutions for the structure. (5) Steps (3) and (4) are repeated until one of the three abort criteria (calculation time exceeded, no improvement, best result achieved) is reached.

2.2. Optimisation Strategy and Dimensioning According to EC 5 The aim of the optimisation was to achieve the lowest-possible wood consumption, while maintaining the same static load-bearing capacity and complying with the requirements regarding serviceability (deformation). The internal forces of the structure were calculated using the plug-in Karamba3D [19]. The static calculations were conducted according to Eurocode 5 (EN1995-1-1:2019-06-01) and the current Austrian application document within a separately integrated self-programmed tool-box. In addition to the calculation of the deformation of the truss, buckling and cross-section analysis were carried out. The calculation focused on the individual truss members based on a 2D model that prohibits any global buckling of the structure (the nodes were modelled in 2D and therefore fixed out of plane). The truss nodes were assumed to be ideally rotatable as a conservative assumption. The later chosen knot design represents a semi-rigid joint.. The influence on the global load-bearing behaviour and therefore on the optimisation was assumed to be low as preparatory tests showed that the joint design, especially the tensile behaviour, is decisive for the maximum load-bearing capacity of the truss. A ductile failure occurs in the connection, as the small-scale experiments presented below show. Large deformations are visible before failure. An additional torsion has only a minor influence on the ultimate load-bearing behaviour of the connection. This proves that the chosen calculation approach is adequate for this approach. The final truss design was also cross-checked with the conventional finite-element-modelling software Rstab (Dlubal). A full-scale test also showed very good accordance between the calculation and the actual behaviour. If stability is decisive for the maximum load-bearing behaviour, more investigations are required. Appl. Sci. 2021, 11, 2568 4 of 17 Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 18

FigureFigure 1. Top 1. Top view view and and cross cross section section of the of therobot robot labo laboratoryratory with with the thecurved curved optimised optimised timber timber truss trussstructure. structure

2.3.2.3. Reference Reference Model Model In theIn thebeginning, beginning, a first a first version version of the of thetruss, truss, as shown as shown in Figure in Figure 2, was2, was conceptualised conceptualised basedbased on the on authors’ the authors’ engineering engineering know-how. know-how. The predefined The predefined floor area, floor the area, existing the existingroof of theroof hall of theas well hall as the well working as the working area of the area robot of the served robot as served boundary as boundary conditions. conditions. The mentionedThe mentioned first truss first design truss was design used was as useda reference as a reference model for model all the for results all the of results the opti- of the misation.optimisation. It consisted It consisted of 12 segments, of 12 segments, alternating alternating diagonal diagonal struts and struts regular and regular spacing spacing betweenbetween the subdivisions. the subdivisions. Appl. Sci. 2021, 11, 2568 5 of 17 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18

FigureFigure 2. Reference 2. Reference model, model, 12 segments, 12 segments, alternating alternating diagonals. diagonals.

2.4.2.4. Boundary Boundary Conditions Conditions TheThe geometry geometry of the of thetruss truss was was determined determined by bythe theavailable available area area in the inthe existing existing hall hall wherewhere the therobot robot laboratory laboratory is located. is located. It spans It spans from from the themiddle middle of the of thehall, hall, where where it is it fixed is fixed directlydirectly to the to thefloor, floor, to a to support a support attached attached to the to thewall wall at a at height a height of 4.92 of 4.92 m, m,resulting resulting in a in a horizontalhorizontal truss truss span span of 8.20 of 8.20 m. m. TheThe geometry geometry of the of theupper upper and and lower lower chords chords is affected is affected by several by several boundary boundary condi- condi- tions.tions. The The accessibility accessibility to the to therobot robot laboratory laboratory through through a 3.20-m-high a 3.20-m-high sliding sliding door door made made it it necessarynecessary for forthe the upper upper chord chord to tobe be vertical vertical up up to to that that height. height. The The upper upper part part of of the the truss, on on the otherother hand,hand, had had to to follow follow the the shape shape of of the the existing existing glulam glulam beam beam of the of roofthe roof construction con- of the hall. Based on these limitations, the authors decided to focus on the optimisation of struction of the hall. Based on these limitations, the authors decided to focus on the opti- the inner structure as well as the cross section of the truss itself. Consequently, the global misation of the inner structure as well as the cross section of the truss itself. Consequently, geometry was not part of the optimisation, and the geometries of the upper and lower the global geometry was not part of the optimisation, and the geometries of the upper and chords were set as fixed curves. lower chords were set as fixed curves. The applied loads for the supporting structure consisted of the dead weight plus the The applied loads for the supporting structure consisted of the dead weight plus the load of the board panelling with 1 kN/m, which was applied to the truss at the nodes as load of the board panelling with 1 kN/m, which was applied to the truss at the nodes as concentrated forces. The truss is situated inside a machine hall; therefore, weather effects concentrated forces. The truss is situated inside a machine hall; therefore, weather effects like snow and wind are neglected. An additional load of 3 kN was applied between 2.00 like snow and wind are neglected. An additional load of 3 kN was applied between 2.00 and 3.20 m from the existing machine hall wall (the wall to which the right nodes of the and 3.20 m from the existing machine hall wall (the wall to which the right nodes of the trusses are attached). This load is also introduced into the truss via a node and is intended trusses are attached). This load is also introduced into the truss via a node and is intended to allow the attachment of cables of possible future experimental set-ups. to allow the attachment of cables of possible future experimental set-ups. 2.5. Optimisation Results 2.5. Optimisation Results The results are summarised in Table1. Depending on which fitness value is de- finedThe andresults which are summarised parameters are in Table released 1. Depending for optimisation, on which different fitness truss value configurations is defined andare which generated. parameters are released for optimisation, different truss configurations are generated.The early optimisation processes were calculated with deformation as the fitness value. ForThe these early calculations, optimisation the valueprocesses was setwere to becalculated as low as with possible. deformation The results as werethe fitness very stiff value.trusses, For these with deformationscalculations, the smaller value than was 5 set mm, to abe value as low of lessas possible. than one-sixth The results of the were limit of very32 stiff mm trusses, according with to deformations Eurocode 5 (EN1995-1-1:2019-06-01). smaller than 5 mm, a value The resulting of less than material one-sixth savings of of the1.4% limit wereof 32 notmm considered according asto relevantEurocode improvements. 5 (EN1995-1-1:2019-06-01). Ultimately the The deformation resulting wasmate- only rialimproved savings of from 1.4% 7 were to 5 mm.not considered as relevant improvements. Ultimately the deformation wasThe only next improved attempt was from optimising 7 to 5 mm. the structure using the maximum absolute normal forceThe (bothnext attempt compression was optimising and tensile the forces) structure as theusing fitness the maximum value of theabsolute algorithm. normal The forcecompression (both compression forces were andconsiderably tensile forces) reduced as the fitness (−22%), value while of the algorithm. tensile forces The decreased com- pressiononly slightly forces were (−6%). considerably The detailed reduced values (− can22%), be foundwhile the in Table tensile1. Theforces goal decreased of achieving only an slightlyoptimal (−6%). structure The detailed through values the minimisation can be found of in the Table occurring 1. The normal goal of forcesachieving in all an struts opti- and malchord structure members through of the the truss minimisation resulted in of a the mass occurring reduction normal of 6.7%. forces in all struts and chord members of the truss resulted in a mass reduction of 6.7%. Appl.Appl. Sci. Sci.2021 2021, 11, 11, 2568, x FOR PEER REVIEW 66 of of 17 18

TheThe optimisationoptimisation was was most most successful successful when when the the ﬁtness fitness value value was was set set as as the the total total mass mass ofof thethe construction,construction, which which is is directlydirectly proportional proportional to to the the wood wood consumption. consumption. This This resulted resulted inin a a signiﬁcant significant reduction reduction of of 14.9% 14.9% compared compared to to the the reference reference model. model.

TableTable 1. 1.Results Results with with different different ﬁtness fitness values values (optimisation (optimisation with with constant constant cross cross section). section). Fitness Value Reference Model Deformation Normal Force Mass Fitness Value Reference Model Deformation Normal Force Mass Subdivisions 12 13 8 6 Subdivisions(n) 12 13 8 6 Buckling(n) Buckling 0.460.46 0.810.81 0.700.70 0.900.90 (-) (-) Cross section Cross section 0.390.39 0.300.30 0.300.30 0.370.37 (-)(-) Deformation Deformation 77 55 88 77 (mm)(mm) WeightWeight 147.5 145.4 137.6 125.5 147.5 145.4 137.6 125.5 (kg)(kg) ResourceResource reduction reduction (%) (%) - - −−1.41.4 −6.7−6.7 −−14.914.9

OnlyOnly chosen chosen variables variables were were released released within within the the optimisation optimisation for for the the truss truss configuration configura- oftion the of housing. the housing. The distance The distance between between the divisions the divisions was defined was defined evenly evenly in order in toorder meet to aestheticmeet aesthetic requirements. requirements. Figure 3Fi showsgure 3 a shows truss with a truss uneven with distribution uneven distribution of the subdivisions. of the sub- Indivisions. addition, In the addition, cross section the cross of the section chords of andthe chords struts wasand setstruts to 80 was× 80set mm to 802 in × 80 regard mm2 to in theregard envisaged to the envisaged node configuration. node configuration.

FigureFigure 3. 3.Optimisation Optimisation resultresult with with uneven uneven distribution distribution of of subdivisions subdivisions (reference (reference model model in in grey). grey).

ForFor thethe finalfinal implementationimplementation ofof thethe housing,housing,shown shownin inFigures Figures1 1and and4, Figure a truss 4, with a truss 7 segments,with 7 segments, regular spacingregular betweenspacing between the subdivisions the subdivisions and free diagonaland free memberdiagonal arrange-member mentarrangement was defined, was requiringdefined, requiring 129.4 kg of129.4 timber, kg 18.1of timber, kg less 18.1 than kg the less reference than the model. reference model.If the entire truss structure is calculated on a pure theoretical basis, without the consideration of node configurations, the environmental impact can be reduced even further. By allowing the algorithm to change the cross-sectional dimensions of the chords and struts, a reduction of 60% in material consumption is possible. For this case, the truss would need more subdivisions, use smaller cross sections and have a total weight of 59.3 kg for the 8.20 m span. Figure5 shows a comparison of a solution with cross section of 80 × 80 mm2 and 7 subdivisions and the result of the rather theoretical optimisation allowing for optimisation of the cross section, leading to 11 subdivisions and cross sections of 60 × 60 mm2 and 40 × 40 mm2 (inner struts). Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 18

Appl. Sci. 2021, 11, 2568 7 of 17 Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 18

Figure 4. Final optimisation result and chosen configuration for the robot laboratory (reference model in grey).

If the entire truss structure is calculated on a pure theoretical basis, without the consideration of node configurations, the environmental impact can be reduced even further. By allowing the algorithm to change the cross-sectional dimensions of the chords and struts, a reduction of 60% in material consumption is possible. For this case, the truss would need more subdivisions, use smaller cross sections and have a total weight of 59.3 kg for the 8.20 m span. Figure 5 shows a comparison of a solution with cross section of 80 × 80 mm2 and 7 subdivisions and the result of the rather theoretical optimisation allowing forFigureFigure optimisation 4.4.Final Final optimisation optimisationof the cross result resultsection, and and chosenleading chosen conﬁguration configto 11 urationsubdivisions for for the the robot robotand laboratory cross laboratory sections (reference (reference of 60 model × 2 2 60in modelmm grey). and in grey). 40 × 40 mm (inner struts).

If the entire truss structure is calculated on a pure theoretical basis, without the consideration of node configurations, the environmental impact can be reduced even further. By allowing the algorithm to change the cross-sectional dimensions of the chords and struts, a reduction of 60% in material consumption is possible. For this case, the truss would need more subdivisions, use smaller cross sections and have a total weight of 59.3 kg for the 8.20 m span. Figure 5 shows a comparison of a solution with cross section of 80 × 80 mm2 and 7 subdivisions and the result of the rather theoretical optimisation allowing for optimisation of the cross section, leading to 11 subdivisions and cross sections of 60 × 60 mm2 and 40 × 40 mm2 (inner struts).

FigureFigure 5. Different 5. Different kinds kinds of optimisation of optimisation results: results: truss trusswith 7 with subdivisions 7 subdivisions and cross and section cross section of the of trussthe members truss members of 80 × of80 80mm×2 80and mm final2 and design ﬁnal for design the housing for the of housing the robot of thelaboratory robot laboratory (left); theo- (left); reticaltheoretical result of result the optimisation of the optimisation by also byconsider also consideringing the cross the section cross as section a parameter, as a parameter, leading to leading a trussto awith truss 11 with subdivisions 11 subdivisions and a cross and section a cross of section 60 × 60 of mm 60 2× of60 the mm outer2 of members the outer as members well 40 × as 40 well 2 mm40 ×for40 the mm internal2 for the members internal (right). members (right).

3. 3.Joining Joining of ofthe the Truss Truss Members Members TheThe load-bearing load-bearing behaviour behaviour of oftimber timber trusse trussess is isaffected affected by by the the material material properties, properties, thethe geometry geometry and and the the joint joint performance performance in in part particular.icular. Therefore, aa specialspecial focus focus is is set set on on the theinvestigation investigation of of the the load-bearing load-bearing behaviour behaviour of joints.of joints. The The main main defined defined requirement requirement of the of researchFigurethe research 5. isDifferent to transferis to kinds transfer loads of optimisation loads without withou using results:t using any truss steel any with elements. steel 7 subdivisions elements. Derived and Derived fromcross section the from research ofthe the researchpresentedtruss members presented in [20 of], 80 in a × node[20], 80 mm elementa node2 and finalelement with design smooth wi forth thesmooth appearance, housing appearance, of whichthe robot can which laboratory easily can be easily(left); produced theo- be producedforretical the result joining for the of the ofjoining trussoptimisation membersof truss by members also at different consider at differenting angles, the cross isangles, used. section is The used.as authorsa parameter, The authors chose leading plywood chose to a plywoodpanels,truss with panels, which 11 subdivisions are which notched are an notched intod a cross truss into section members truss of members 60 and × 60 fixed mm and2with of fixedthe wooden outer with members wooden pegs. This as pegs. well allows 40This × for40 2 allowsthemm transfer forfor the internal oftransfer compression members of compression and(right). tensile and forces tensile in forces the joint. in the joint. Most of the research with timber dowels focuses on historical constructions, as de- scribed3. Joining in [21of –the24]. Truss The use Members of timber pegs is additionally investigated in [25,26]. Different test methodsThe load-bearing for wooden behaviour peg connections of timber are trusse investigateds is affected in [27 by], the and material a new yield properties, model forthe wooden geometry dowel and the connections joint performance is proposed in part in [28icular.]. However, Therefore, detailed a special investigations focus is set for on multi-rowthe investigation dowel connectionsof the load-bearing focusing behavi on differentour of woodjoints. species The main are notdefined available. requirement of theTherefore, research the is to authors transfer performed loads withou compressiont using asany well steel as tensileelements. tests Derived on the all-woodfrom the connectionsresearch presented in order in to [20], find a the node optimal element design withand smooth wood appearance, species and which to investigate can easily the be occurringproduced load-bearingfor the joining mechanisms. of truss members at different angles, is used. The authors chose plywood panels, which are notched into truss members and fixed with wooden pegs. This allows for the transfer of compression and tensile forces in the joint. Appl. Sci. 2021, 11, 2568 8 of 17

3.1. Design of the Wood–Wood Connections For the above-mentioned curved optimised truss, spruce (C24) with a cross section of 80 × 80 mm2 was chosen for all truss members, making this the ﬁrst boundary condition for the joint design. Due to manufacturing tolerances, however, the cross sections of all provided specimens turned out to be 78 × 78 mm2. The node elements (plates) were made from plywood panels and were inserted into the truss members and ﬁxed with wooden pegs. According to [29], the spacing of the pegs in the direction of force was chosen with three times the peg diameter (3d). As the cutting depth for notching the truss member for the plywood panel was limited, due to the manufacturing process, to 115 mm, the diameter of the pegs was set to 14 mm. The combination of all geometric boundary conditions resulted in a total of four pegs per connection.

3.2. Experimental Investigations of Different Wooden Pegs under Tension In the first experimental test series, the influence of the wood species of the pegs on the mechanical behaviour of the connection was investigated. Thus, the authors manufactured (using the robot for cutting and milling) and tested a total of nine configurations of the tensile connection (with three specimens each). The test set-up is shown in Figure6. A uniaxial hydraulic testing machine by Walter+Bai was used with a maximum load of 63kN. The loading speed was chosen at 0.5 mm/min in the beginning for thermo ash and ash and was increased to 1 mm/min for all other configurations. The force was measured Appl. Sci. 2021, 11, x FOR PEER REVIEWwith a load cell integrated in the testing machine, and the displacement was measured9 of 18

with two displacement transducers mounted at the spruce member and the plywood plate (see Figure6).

FigureFigure 6. 6. IllustrationIllustration of of the the test test set-up set-up for for the the tensile tensile connections connections (mm). (mm).

AccordingAccording to to [29], [29], the thicknessthickness ofof thethe plywood plywood panel panel should should approximately approximately equal equal the thepegs’ pegs’ diameter diameter in orderin order to to ensure ensure adequate adequate load-bearing load-bearing behaviour behaviour and and ductile ductile failure failure of ofthe the connection. connection. For For the the ﬁrst first tests, tests, a bircha birch plywood plywood panel panel was was chosen chosen with with a thicknessa thickness of of 15 mm (BI15). The following wood species were examined for the pegs: thermo ash (TA), ash (A), oak (O), larch (L), beech (B), spruce (S), beech LVL with the glue joint parallel to the load direction (B_LVL_0) and beech LVL with the joint normal to the load direction (B_LVL_90). The tested configurations are summarised in Table 2, and the test results are summarised in Figure 7. The result curves represent regressive lines summarising the three specimens of every configuration. To limit the deformation in the final structure, the stiffness in the joint should be as high as possible. The results of the experimental investigation show that the combination of beech pegs and 15 mm birch plywood (B-BI15) provided the highest stiffness if configuration B-BI18 was ignored, as it was part of the second test series. Appl. Sci. 2021, 11, 2568 9 of 17

15 mm (BI15). The following wood species were examined for the pegs: thermo ash (TA), ash (A), oak (O), larch (L), beech (B), spruce (S), beech LVL with the glue joint parallel to the load direction (B_LVL_0) and beech LVL with the joint normal to the load direction (B_LVL_90). The tested configurations are summarised in Table2, and the test results are summarised in Figure7. The result curves represent regressive lines summarising the three specimens of every configuration. To limit the deformation in the final structure, the stiffness in the joint should be as high as possible. The results of the experimental investigation show that the combination of beech pegs and 15 mm birch plywood (B-BI15) provided the highest stiffness if configuration B-BI18 was ignored, as it was part of the second test series.

Table 2. Test conﬁgurations of the tensile tests (14 mm peg diameter).

Wood Species of Wood Species of Thickness of Conﬁguration Failure Pegs Plywood Plywood (mm) TA-BI15 Thermo ash Birch 15 3× ductile 2× ductile A-BI15 Ash Birch 15 1× brittle L-BI15 Larch Birch 15 3× ductile O-BI15 Oak Birch 15 3× ductile B-BI15 Beech Birch 15 3× brittle S-BI15 Spruce Birch 15 3× ductile B_LVL_0-BI15 Beech LVL Birch 15 3× brittle B_LVL_90-I15 Beech LVL Birch 15 3× brittle Appl. Sci. 2021, 11, x FOR PEER REVIEW B-B 18 Beech Beech 18 3× ductile10 of 18

DM, diameter.

FigureFigure 7. 7. ComparisonComparison of of the the influence inﬂuence of of the the wood wood spec speciesies of of pegs pegs on on the the load-bearing load-bearing capacity and andstiffness stiffness of theof the tensile tensile joint joint of of test test series series I (xx-BI15)I (xx-BI15) and and the the ultimately ultimately chosen chosen combinationcombination from from series II (B-B18). Results are shown as regressive lines of the mean values of three specimens series II (B-B18). Results are shown as regressive lines of the mean values of three specimens each. each. Coefficient of determination R2 > 0.992 (xx-BII5) and R2 = 0.949 (B-B18). Coefﬁcient of determination R2 > 0.992 (xx-BII5) and R2 = 0.949 (B-B18).

However,However, failure failure of of this this configuration conﬁguration (B-B (B-BI15)I15) for for all allthree three specimens specimens as well as well as for as allfor three all three specimens specimens in the in configuration the conﬁguration B_LVL_0-BI15 B_LVL_0-BI15 and B_LVL_90-BI15 and B_LVL_90-BI15 and one and spec- one imenspecimen in A-BI15 in A-BI15 occurred occurred in the inplywood the plywood panel next panel to next the pegs to the in pegs a brittle in a manner brittle manner after a shortafter period a short of period softening of softening (a specimen (a specimen after failure after is failureshown isFigure shown 8). Figure As brittle8). As failure brittle is unwanted,failure is unwanted, a further series a further of tests series was of carried tests was out. carried The specimen out. The with specimen the best with results the best is listedresults in is the listed last inline the of last Table line 2. of The Table 152 .mm The birch 15 mm plywood birch plywood was replaced was replaced by 18 mm by 18 beech mm plywoodbeech plywood to ensure to ensurethat the that failure the failurewould wouldnot occur not occurin the inplywood the plywood panel. panel. Beech Beechpegs were chosen due to their good availability and the stiffest load-bearing behaviour of the previously tested specimens. Not only was it possible to achieve ductile failure in the combination of 14 mm beech pegs and 18 mm beech plywood (B-BI18), but it was also possible to achieve high stiffness and increase the load-bearing capacity from 25.01 kN in the first series up to 29.56 kN (see Figure 7). Figure 9 shows the single curves for all three test specimens of the configurations B-BI15_1-3, L-BI15_1-3 and B-B18_1-3 to show the low scattering of the different experiments as well as the similar behaviour at a low load level for the configurations B-BI15 and B-B18.

Table 2. Test configurations of the tensile tests (14 mm peg diameter).

Wood Species of Wood Species of Thickness of Ply- Configuration Failure Pegs Plywood wood (mm) TA-BI15 Thermo ash Birch 15 3x ductile 2x ductile A-BI15 Ash Birch 15 1x brittle L-BI15 Larch Birch 15 3x ductile O-BI15 Oak Birch 15 3x ductile B-BI15 Beech Birch 15 3x brittle S-BI15 Spruce Birch 15 3x ductile B_LVL_0- Beech LVL Birch 15 3x brittle BI15 B_LVL_90- Beech LVL Birch 15 3x brittle I15 B-B 18 Beech Beech 18 3x ductile Appl. Sci. 2021, 11, 2568 10 of 17

pegs were chosen due to their good availability and the stiffest load-bearing behaviour of the previously tested specimens. Not only was it possible to achieve ductile failure in the combination of 14 mm beech pegs and 18 mm beech plywood (B-BI18), but it was also Appl. Sci. 2021, 11, x FOR PEER REVIEWpossible to achieve high stiffness and increase the load-bearing capacity from 25.01 kN11 of in 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 18 the first series up to 29.56 kN (see Figure7). Figure9 shows the single curves for all three test specimens of the configurations B-BI15_1-3, L-BI15_1-3 and B-B18_1-3 to show the low scattering ofDM, the differentdiameter. experiments as well as the similar behaviour at a low load level for the configurationsDM, diameter. B-BI15 and B-B18.

Figure 8. Test specimen from configuration B-BI15 after failure; truss member with beech dowels FigureFigure 8.8. TestTest specimenspecimen from conﬁgurationconfiguration B-BI15 afte afterr failure; failure; truss truss member member with with beech beech dowels dowels (left) and birch plywood plate (right). (left)(left) andand birch birch plywood plywood plate plate (right). (right).

Figure 9. Single curves of all three test specimens of the configurations B-BI15_1-3, L-BI15_1-3 and Figure 9. Single curves of all three test specimens of the configurations B-BI15_1-3, L-BI15_1-3 and FigureB-B18_1-3 9. Single to show curves the oflow all scattering three test of specimens the different of the experiments. conﬁgurations B-BI15_1-3, L-BI15_1-3 and B-B18_1-3B-B18_1-3 toto showshow thethe lowlow scatteringscattering ofof thethe differentdifferent experiments. experiments. 3.3. Experimental Investigations on Buckling of Beech Plywood 3.3.3.3. ExperimentalExperimental InvestigationsInvestigations onon BucklingBuckling ofof BeechBeech PlywoodPlywood The design of the curved truss resulted in some cases in acute angles between the TheThe designdesign ofof thethe curvedcurved trusstruss resultedresulted inin somesome casescases inin acuteacute anglesangles betweenbetween thethe truss members. Hence, a free length of the plywood panel of up to 650 mm appears in the trusstruss members.members. Hence,Hence, aa freefree lengthlength ofof thethe plywoodplywood panelpanel ofof upup toto 650650 mmmm appearsappears inin thethe truss. Since the joints of the truss structure not only have to transmit tensile stresses but truss.truss. SinceSince thethe jointsjoints ofof thethe trusstruss structurestructure notnot onlyonly havehave toto transmittransmit tensiletensile stressesstressesbut but also compressive stresses, the risk of out-of-plane buckling of the slender plywood panel alsoalso compressivecompressive stresses,stresses, thethe riskrisk ofof out-of-planeout-of-plane bucklingbuckling ofof thetheslender slender plywoodplywood panelpanel had to be ruled out. To investigate the influence of different free lengths of the plywood hadhad toto bebe ruled ruled out. out. To To investigate investigate the the inﬂuence influence of of different different free free lengths lengths of theof the plywood plywood in in comparison to the load direction regarding buckling failure, a series of compression comparisonin comparison tothe to loadthe load direction direction regarding regarding buckling buckling failure, failure, a series a series of compression of compression tests tests was performed. The test set-up is shown in Figure 10. The loading speed was chosen wastests performed. was performed. Thetest The set-up test set-up is shown is show in Figuren in Figure 10. The10. The loading loading speed speed was was chosen chosen at at 1 mm/min for all specimens. Again, the hydraulic uniaxial testing machine by Wal- 1at mm/min 1 mm/min for allfor specimens.all specimens. Again, Again, the hydraulicthe hydraulic uniaxial uniaxial testing testing machine machine by Walter+Bai by Wal- ter+Bai with a maximum load of 63kN was used. The force as well as the axial displace- withter+Bai a maximum with a maximum load of 63kN load wasof 63kN used. was The used. force The as well force as as the well axial as displacement the axial displace- were ment were measured with the integrated load cell. An optical displacement transducer measuredment were with measured the integrated with the load integrated cell. An load optical cell. displacement An optical displacement transducer was transducer used for was used for documentation of the deviation of the plate out of plane (see Figure 10). documentationwas used for documentation of the deviation of ofthe the deviation plate out of of the plane plate (see out Figure of plane 10 ).(see Figure 10). Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 18 Appl. Sci. 2021, 11, 2568 11 of 17

FigureFigure 10. 10.IllustrationIllustration of the of test the set-up test set-up for compression for compression tests to tests investigate to investigate local buckling local buckling failure fail- (mm).ure (mm). As the truss nodes are stressed in different directions, three orientations of the main As the truss nodes are stressed in different directions, three orientations of the main load-bearing direction of the plywood panel were tested. The joints consisted of 18 mm load-bearing direction of the plywood panel were tested. The joints consisted of 18 mm beech plywood panels inserted into the truss members and fixed with four wooden pegs beech plywood panels inserted into the truss members and fixed with four wooden pegs (beech) with a 14 mm diameter. The joint configuration was chosen according to the B-B18 (beech) with a 14 mm diameter. The joint configuration was chosen according to the B- configuration of the tensile tests, presented in Section 3.2. The aim was to transfer the B18 configuration of the tensile tests, presented in Section 3.2. The aim was to transfer the compression loads not only through the peg/plywood joint but also through the contact compression loads not only through the peg/plywood joint but also through the contact surface between the beech plywood panel and the spruce truss member. The free length in surface between the beech plywood panel and the spruce truss member. The free length this test series was set to 250 mm and increased in 100 mm steps up to 650 mm. Each step of in this test series was set to 250 mm and increased in 100 mm steps up to 650 mm. Each the free length was tested at an angle of 0◦, 45◦ and 90◦ of the plywood’s main load-bearing step of the free length was tested at an angle of 0°, 45° and 90° of the plywood’s main load- direction to the direction of force. The investigated configurations are summarised in bearing direction to the direction of force. The investigated configurations are summa- Table3 . Three specimens per configuration were tested again. The test results are shown in risedFigure in Table 11. The 3. Three diagrams specimens (a)–(e) per show configurat the comparisonion were of tested the influence again. The of thetest orientation results are of shownthe top in layerFigure of 11. the The plywood diagrams according (a)–(e) to sh theow loadthe comparison direction for of the the different influence free of lengths. the orientationThe diagrams of the (f)–(h)top layer show of the the plywood influence according of the free to length the load for direction different orientationsfor the different of the freetop lengths. layer ofThe the diagrams plywood. (f)–(h) show the influence of the free length for different orientations of the top layer of the plywood. Appl. Sci. 2021, 11, 2568 12 of 17 Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 18

Figure 11. Force–displacementFigure 11. Force–displacement curves for the compression curves for tests. the compression (a)–(e) Comparison tests. (a –ofe )the Comparison influence of of the the orientation inﬂuence of the top layer of theof theplywood orientation according of the to topthe layerload direction of the plywood for different according free lengths. to the load (f)–( directionh) Influence for of different the free free length for different orientationslengths. of (f –theh) Inﬂuencetop layer of of the the plywood. free length All for curves different represent orientations mean values of the of top three layer specimens of the plywood. each. Leg- end (1) free length in mm (25, 35, 45, 55, 65 mm); (2) angle between load-bearing direction and force direction (0°, 45°, 90°). All curves represent mean values of three specimens each. Legend (1) free length in mm (25, 35, 45, 55, 65 mm); (2) angle between load-bearing direction and force direction (0◦, 45◦, 90◦). Appl. Sci. 2021, 11, 2568 13 of 17

As expected, the results of the test series prove that the load-bearing capacity decreases with an increase in free length. A test specimen under load showing the buckling mode is depicted in Figure 12. However, in each configuration of the free length, the specimens with an angle of 45◦ between the main load-bearing direction and the direction of force showed the lowest load-bearing capacity. Each specimen with an angle of 0◦ between the orientation of the main layers of the plywood and the direction of force, labelled xx-0, provided the highest load-bearing capacity for a defined plate length. These findings show that the governing stress direction in the truss node has to coincide with the load-bearing direction of the plywood in order to fully use its potential. Furthermore, it was observed that the bending shape was similar to Euler case 4, leading to the assumption that the designed joints act like rigid ends (within the tested boundary conditions). Furthermore, it can be derived that the turning points of the bending shape are also relevant for the global investigation of the buckling behaviour. Within the calculation, they were expected Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 18 to occur at the intersection of the truss member axis in the plywood plate. In reality, they occur at the intersection between the truss member and the plywood plate (Figure 11).

Figure 12. Test specimen underFigure compression. 12. Test specimen under compression.

3.4. Final Design of the TrussTable Joints 3. Test conﬁgurations of the compression tests (all pegs were made of beech, with a diameter For the final design ofof 14the mm). curved truss, the members consisted of spruce with a cross section of 80 × 80 mm2 (78 × 78 mm2). One joint design was chosen for all joints to simplify Free Length of Plywood Angle of Plywood’s Load-Bearing the manufacturing process. Thus,Conﬁguration four beech pegs with a 14 mm diameter and 18 mm (mm) Direction (◦) beech plywood panels were used for the joints. A recently performed full-scale test showed that global buckling of the25–0 nodes subjected to compression 25 due to the lower ma- 0 25–45 25 45 terial thickness of the plywood plate significantly reduces the expected load-bearing ca- 25–90 25 90 pacity. Thus, the authors decided35–0 to fill up the plywood of the 35 compression joints to the 0 full cross section of 78 × 78 mm2. This35–45 measure finally allowed 35 for full use of the joints that 45 was then proven within another full-scale35–90 test with the filled-up 35 joints. The ultimate load- 90 bearing capacity was limited due 45–0to the tensile load-bearing 45behaviour of the joints. The 0 tensile tests described above as well45–45 as the full-scale test showed 45 a very good correlation, 45 45–90 45 90 confirming the chosen research strategy. The chosen modelling strategy using Rhinoceros with the plug-ins Grasshopper and Karamba 3D in combination with a self-programmed EC 5 calculation for the conceptual design of timber truss structures was based on hinged joints. The realised joints are semi- rigid, bringing up the question whether the modelling strategy is adequate to represent a secure dimensioning of the structure. The member cross section is low compared to the member length, in combination with a very ductile failure behaviour of the connection under tension. In addition, the tensile behaviour is decisive, as mentioned above. There- fore, the chosen approach can clearly be presumed as appropriate to predict the ultimate load-bearing behaviour in an adequate manner. The chosen tensile node is shown in Figure 13, the final chosen compression node in Figure 14 and a picture of the realised laboratory in Figure 15. The erection of the laboratory was assembled by a joint work effort of all work group members: Matthias Braun, Mathias Hammerl, Maximilian Ortner, Marc Pantscharowitsch, Sara Reichenbach, Na- dine Stoiber and Benjamin Kromoser. Appl. Sci. 2021, 11, 2568 14 of 17

Table 3. Cont.

Free Length of Plywood Angle of Plywood’s Load-Bearing Conﬁguration (mm) Direction (◦) 55–0 55 0 55–45 55 45 55–90 55 90 65–0 65 0 65–45 65 45 65–90 65 90 DM, diameter.

3.4. Final Design of the Truss Joints For the final design of the curved truss, the members consisted of spruce with a cross section of 80 × 80 mm2 (78 × 78 mm2). One joint design was chosen for all joints to simplify the manufacturing process. Thus, four beech pegs with a 14 mm diameter and 18 mm beech plywood panels were used for the joints. A recently performed full-scale test showed that global buckling of the nodes subjected to compression due to the lower material thickness of the plywood plate significantly reduces the expected load-bearing capacity. Thus, the authors decided to fill up the plywood of the compression joints to the full cross section of 78 × 78 mm2. This measure finally allowed for full use of the joints that was then proven within another full-scale test with the filled-up joints. The ultimate load-bearing capacity was limited due to the tensile load-bearing behaviour of the joints. The tensile tests described above as well as the full-scale test showed a very good correlation, confirming the chosen research strategy. The chosen modelling strategy using Rhinoceros with the plug-ins Grasshopper and Karamba 3D in combination with a self-programmed EC 5 calculation for the conceptual design of timber truss structures was based on hinged joints. The realised joints are semi- rigid, bringing up the question whether the modelling strategy is adequate to represent a secure dimensioning of the structure. The member cross section is low compared to the member length, in combination with a very ductile failure behaviour of the connection under tension. In addition, the tensile behaviour is decisive, as mentioned above. Therefore, the chosen approach can clearly be presumed as appropriate to predict the ultimate load- bearing behaviour in an adequate manner. The chosen tensile node is shown in Figure 13, the final chosen compression node in Figure 14 and a picture of the realised laboratory in Figure 15. The erection of the laboratory was assembled by a joint work effort of all work group members: Matthias Braun, Mathias Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 18 Hammerl, Maximilian Ortner, Marc Pantscharowitsch, Sara Reichenbach, Nadine Stoiber and Benjamin Kromoser.

FigureFigure 13.13.Tensile Tensile node. node.

Figure 14. Compression node with filled cross section.

Figure 15. Realised structure.

4. Conclusions Industrialising the complete process chain shows great potential for the wood construction sector, allowing for an increase in resource efficiency and the ability to compete with other construction materials regarding economic efficiency. Within this context, the Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 18

Appl. Sci. 2021, 11, 2568 15 of 17

Figure 13. Tensile node. Figure 13. Tensile node.

Figure 14. Compression node with filled cross section. FigureFigure 14. 14.Compression Compression node node with with ﬁlled filled cross cross section. section.

Figure 15. Realised structure. FigureFigure 15. 15.Realised Realised structure. structure. 4. Conclusions 4.4. ConclusionsConclusions Industrialising the complete process chain shows great potential for the wood con- IndustrialisingIndustrialising thethe completecomplete processprocess chainchain showsshows greatgreat potentialpotential forfor thethe woodwood con-construction sector, allowing for an increase in resource efficiency and the ability to compete structionstruction sector, sector, allowing allowing for for an an increase increase in in resource resource efficiency efficiency and and the the ability ability to to compete compete with other construction materials regarding economic efficiency. Within this context, the withwith other other construction construction materials materials regarding regarding economic economic efficiency. efficiency. Within Within this this context, context, the the present paper focuses on the practical optimisation of the truss geometry and the connections of trusses by solely using wood as the construction material for all building elements. The housing of the BOKU Vienna robot laboratory was chosen as the first pilot project, implementing the research approach in a very practical manner. The optimisation of the geometry was based on the use of a parametric model, and a genetic solving algorithm allowed for a reduction of the required construction material by 14.9% in comparison to the first design based on engineering knowledge. For this case, the cross section of the truss members was predefined to 80 × 80 mm2. A theoretical optimisation of the cross section showed further a reduction potential of 60%. A pure wood–wood connection was chosen using plywood as the connection panel and wooden pegs as shear connectors to minimise the environmental impact of the load- bearing structure. New findings regarding this connection type could be found within a series of tensile investigations. The main investigation parameters were the influence of Appl. Sci. 2021, 11, 2568 16 of 17

the wood species of the pegs on the mechanical behaviour of the connection. The results showed that using beech pegs provides the stiffest connection and the highest load-bearing capacity. Furthermore, the investigations showed that special attention is needed to be paid to the interaction between the peg diameter and the thickness of the plywood panel in order to ensure ductile failure of the connection. To estimate local buckling failure in the plywood panel, compression tests were conducted, obtaining information about the inﬂuence of the free length. The results showed the importance of the main load-bearing direction of the plywood panel. In addition, it could be observed that if only the plywood plate is used without additional ﬁlling, the turning point of the bending shape moves from the ideal intersection point of the truss members to the intersection between truss member and plywood plate, leading to more turning points in one node.

5. Outlook The clear focus of the present paper was to introduce the basic strategy and a ﬁrst practical application for the construction of all-wood trusses with plywood knots and wooden pegs. The authors currently focus on a detailed investigation of the failure mechanisms of the joints under tension and compression, which are intended to be presented in more detailed separate publications.

Author Contributions: Conceptualisation: B.K. and M.B.; writing—original draft: B.K., M.B. and M.O.; writing—review and editing: B.K.; visualisation: B.K., M.B. and M.O.; experiments and investigation: M.B. and M.O., supervision: B.K. All authors have read and agreed to the published version of the manuscript. Funding: Open access funding provided by BOKU Vienna Open Access Publishing Fund. Data Availability Statement: The data supporting the findings of this study are available on request from the authors. Acknowledgments: The authors gratefully acknowledge the company Rubner Holzbau GmbH for good cooperation and support. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Bodig, J.; Jayne, B.A. Mechanics of Wood and Wood Composites; Van Nostrand Reinhold: New York, NY, USA, 1982; ISBN 9780442008222. 2. Möller, E. Tendenzen Im Holzbau. Bautechnik 2013, 90, 42–46. [CrossRef] 3. Shmulsky, R.; Jones, P.D. Forest Products and Wood Science: An Introduction; John Wiley & Sons: New York, NY, USA, 2011; ISBN 9780813820743. 4. Neuhaus, H. Ingenieurholzbau: Grundlagen—Bemessung—Nachweise—Beispiele, 4th ed.; Springer Vieweg: Berlin/Heidelberg, Germany, 2017; ISBN 978-3-658-14177-6. 5. Muszynski, L.; Hansen, E.; Fernando, S.; Schwarzmann, G.; Rainer, J. Insights into the Global Cross-Laminated Timber Industry. Bioprod. Bus. 2017, 22, 77–92. 6. Holz als Konstruktionswerkstoff. In Ingenieurholzbau; John Wiley & Sons, Ltd.: New York, NY, USA, 2019; pp. 1–15. ISBN 9783433609255. 7. Churkina, G.; Organschi, A.; Reyer, C.P.O.; Ruff, A.; Vinke, K.; Liu, Z.; Reck, B.K.; Graedel, T.E.; Schellnhuber, H.J. Buildings as a Global Carbon Sink. Nat. Sustain. 2020, 3, 269–276. [CrossRef] 8. Amiri, A.; Ottelin, J.; Sorvari, J.; Junnila, S. Cities as Carbon Sinks—Classiﬁcation of Wooden Buildings. Environ. Res. Lett. 2020, 15, 094076. [CrossRef] 9. Heräjärvi, H. Wooden Buildings as Carbon Storages—Mitigation or Oration? Wood Mater. Sci. Eng. 2019, 14, 291–297. [CrossRef] 10. Ceccherini, G.; Duveiller, G.; Grassi, G.; Lemoine, G.; Avitabile, V.; Pilli, R.; Cescatti, A. Abrupt Increase in Harvested Forest Area over Europe after 2015. Nature 2020, 583, 72–77. [CrossRef][PubMed] 11. Kromoser, B.; Braun, M. Towards Efﬁciency in Constructive Timber Engineering—Design and Optimization of Timber Trusses. In Proceedings of the IABSE Congress, New York, NY, USA, 6 September 2019. 12. Maraveas, C.; Miamis, K.; Matthaiou, C.E. Performance of Timber Connections Exposed to Fire: A Review. Fire Technol. 2015, 51, 1401–1432. [CrossRef] Appl. Sci. 2021, 11, 2568 17 of 17

13. Peng, L.; Hadjisophocleous, G.; Mehaffey, J.; Mohammad, M. Fire Resistance Performance of Unprotected Wood–Wood–Wood and Wood–Steel–Wood Connections: A Literature Review and New Data Correlations. Fire Saf. J. 2010, 45, 392–399. [CrossRef] 14. McNeel Europe Kangaroo—Grasshopper. Available online: https://www.grasshopper3d.com/group/kangaroo (accessed on 28 January 2020). 15. McNeel Europe Rhino 6 Für Windows. Available online: https://www.rhino3d.com/de/ (accessed on 28 January 2020). 16. Gerbo, E.J.; Saliklis, E.P. Optimizing a Trussed Frame Subjected to Wind Using Rhino, Grasshopper, Karamba and Galapagos. Proc. IASS Annu. Symp. 2014, 2014, 1–7. 17. Danhaive, R.A.; Mueller, C.T. Combining Parametric Modeling and Interactive Optimization for High-Performance and Creative Structural Design. Proc. IASS Annu. Symp. 2015, 2015, 1–11. 18. Nissen, V. Einführung in Evolutionäre Algorithmen: Optimierung Nach Dem Vorbild Der Evolution; Springer: Berlin/Heidelberg, Germany, 2013. 19. Bollinger und Grohmann ZT GmbH Karamba3D—Parametric Engineering 2020. Available online: https://www.karamba3d.com/ (accessed on 1 March 2021). 20. Kromoser, B.; Pachner, T. Optiknot 3D—Free Formed Frameworks out of Wood with Customized Knots Produced by FDM Additive Manufacturing: Experimental Investigations, Design Approach and Construction of a Prototype. Polymers 2020, 12, 965. [CrossRef][PubMed] 21. Frontini, F.; Siem, J.; Renmaelmo, R. Load-Carrying Capacity and Stiffness of Softwood Wooden Dowel Connections. Int. J. Archit. Herit. 2018.[CrossRef] 22. Ceraldi, C.; Lippiello, M.; D’ambra, C.; Prota, A. The Inﬂuence of Dowel-Bearing Strength in Designing Timber Pegged Timber Joints. Int. J. Archit. Herit. 2018, 12, 362–375. [CrossRef] 23. Ceraldi, C.; D’Ambra, C.; Lippiello, M.; Prota, A. Restoring of Timber Structures: Connections with Timber Pegs. Eur. J. Wood Prod. 2017, 75, 957–971. [CrossRef] 24. Jorissen, A.; Dorlijn, J.; Leijten, A.; Snijder, B. Strength and Stability of Traditional Timber Frames. In Proceedings of the World Conference on Tmber Engineering, Vienna, Austria, 22–25 August 2016; Volume 8. 25. Shanks, J.D.; Chang, W.-S.; Komatsu, K. Experimental Study on Mechanical Performance of All-Softwood Pegged Mortice and Tenon Connections. Biosyst. Eng. 2008, 100, 562–570. [CrossRef] 26. Schmidt, R.J. Considerations for Mortise and Tenon Joint Design. Struct. Mag. 2006, 4. 27. Youn, G.J.; Kon, J.H. Evaluate Test Methods on Bearing Property of Wood Peg Connection. In Proceedings of the World Conference on Tmber Engineering, Vienna, Austria, 22–25 August 2016; pp. 5479–5487. 28. Miller, J.F.; Schmidt, R.J.; Bulleit, W.M. New Yield Model for Wood Dowel Connections. J. Struct. Eng. 2010, 136, 1255–1261. [CrossRef] 29. Chang, W.-S.; Thomson, A.; Harris, R.; Walker, P.; Shanks, J. Development of All-Wood Connections with Plywood Flitch Plate and Oak Pegs. Adv. Struct. Eng. 2011, 14, 123–131. [CrossRef]