Strengthening of large diameter singel dowel joints

SP Technical Research Institute of Sweden

R

Roberto C

Crocetti,

, Mats A

Axelson

Buildin

and Tizi

iano Sar

rtori

Strengthening of large diameter single

dowel joints

Abstract

A preliminary study for implementation of a novel truss node is presented. For this purpose, the load-slip behaviour of double-shear loaded single large dowel joints was investigated. Out of a total of 26 laboratory shear tests, 5 were performed on non-reinforced specimens. The remaining 21 tests were performed on specimens non-reinforced by means of self-tapping screws. All laboratory tests were conducted under monotonic quasi-static loading. The distance between the dowel and the loaded edge of the timber element was considerably smaller than the minimum distance suggested by building codes. The influence of both i) the placement and ii) the diameter of the reinforcing screws on the load-slip behaviour of the joint was studied.

The study shows that the scatter in test results is considerably reduced when reinforcing screws are used. The study also shows that the reinforcing screws prevent the joint to fail due to premature splitting. Thus, due to the presence of the reinforcing screws, no reduction of load-carrying capacity of the dowel caused by the short distance between dowel and loaded edge of the timber element needs to be applied. Further, the reinforced specimens exhibited a very ductile load-slip behaviour and - after the first drop in the load-slip curve occurred - the joints still showed a significant reserve of load-carrying capacity.

Key words: Shear connection, timber-concrete structure, dry connection

SP Sveriges Tekniska Forskningsinstitut

SP Technical Research Institute of Sweden SP Report 2010:14

ISBN 978-91-86319-52-6 ISSN 0284-5172

Contents

Abstract 3

Contents 4

Preface

5

Sammanfattning / Summary

6

1

Introduction 7

2

State of the art

9

3

Laboratory tests

10

3.1  Specimens and test set-up 10 

3.2   Test results 11 

4

Discussion 15

5

Conclusions 19

Appendix 1

21

Preface

The investigations described in this report are a preliminary study of a larger research project that focus on the implementation of a novel truss node. The work was carried out at SP, Technical Research Institute of Sweden, division Building Technology and Mechanics, between September 2009 and February 2010. The timber material was kindly supplied by Svenskt Limträ AB. Most of the screws used in the experiments were kindly supplied by the company E.u.r.o.Tec GmbH, and a few screws from the company SFS intec AB. The authors wish to express their gratitude to all the above mentioned companies. Without their help this project would not have been possible.

Sammanfattning / Summary

Träfackverk kan i dagsläget inte konkurrera med stålfackverk för spännvidder över 25 m. Begränsningen finns i knutförbanden som inte kan göras tillräckligt kostnadseffektiva för stora spännvidder.

För att öka konkurrensförmågan behöver i första hand knutförband utvecklas där träets hållfasthet vinkelrätt fibrerna kan ökas. Olika varianter med armerade knutförband har provats i Europa, men flera frågor återstår att lösa för att dessa ska kunna omsättas i bra tekniska lösningar och produktionsvänliga tillverknings- och montagemetoder.

Traditionella dymlingsförband är relativt komplicerade och dyra. Dessutom, vid olämpligt val av dymlingsdiameter i förhållandet till virkestjocklek, kan dessa förband uppvisa ett sprött brottförlopp. Genom att kombinera dymling och armering vinkelrätt fibrerna har man experimentellt visat att både en högre bärförmåga och ett segare brottförlopp kan uppnås. Långa självborrande helgängade skruvar med relativt små diametrar är kommersiellt tillgängliga, vilket ger nya förutsättningar för skruvarmerade knutpunkter för grova dimensioner. Erfarenheter av sådana knutar saknas fortfarande, både teoretiskt och praktiskt.

Målet är att utveckla ett skruvarmerat dymlingsförband för träfackverk med spännvidder över 25 m. Knutförbandet ska kunna dimensioneras med konventionella beräkningsmetoder. Tillverkningen ska vara rationell och montaget ska kunna utföras på byggarbetsplatsen på kort tid med enkla verktyg. Montering på arbetsplatsen möjliggör även enklare och billigare transporter.

Denna rapport avser den första delen av ett större projekt som är uppdelat i två etapper; en experimentell förstudie med syfte att verifiera knutpunktens principiella beteende på nedskalade förbandsdimensioner (denna rapport), och ett fullskaleförsök på knutförband i verklig storlek där bärförmåga och brottbeteende fastställs och jämförs med teoretiska beräkningar.

Denna förstudie har utförts på nedskalade dymlingsförband för att utvärdera armeringsskruvarnas bidrag till knutförbandets bärförmåga och brottbeteende, samt i vilken utsträckning armeringsskruvarna förmår öka förbandets styvhet vid statisk last. Som referensförband har oarmerade knutförband använts.

1

Introduction

1.1

Background

Collapse of timber structures are often related to malfunctioning of the joints, e.g. as confirmed by some recent failures of large timber structures were breaking down of dowel joints occurred. Ideally, joints should be designed for strength capacity approaching the capacity of the jointed members. The principal function of a timber joint is to adequately transfer axial forces, bending moments and shear forces between different structural members with acceptable slip and rotations. Moreover, timber joint should also posses other important prerequisites such as i) satisfactory ductility, especially if used in earthquake risk zones and ii) easy to product and assemble, due its considerable influence on the overall cost of a timber structure.

In large-scale structures, heavy-duty joints are normally adopted. Such joints are generally the most crucial parts of the structure and they often determine the dimensions of the other elements. Within the zone of the joint, the wood is usually subjected to a very complex stress state. This aspect, together with the great variability of wood – following from its natural origin – can lead to a rather cumbersome prediction of the structural behaviour of a dowel-type joint.

Dowel-type joints often fail by splitting parallel to the grain or by plug shear failure, if loaded in tension parallel to the grain. Both these modes of failure may be classified as premature as they are in disagreement with the Johansen´s yielding theory (Johansen, 1949), in which full embedment or bearing strength of the timber is assumed.

The study presented in this report is an effort to the implementation of a novel type of joint, where a single large-diameter dowel is used in combination with reinforcing screws. If appropriate reinforcing screws are used, the strength of the joint can be increased and the scatter in results dramatically reduced. Moreover, the failure mode of reinforced joints is extremely ductile, also when distance between the dowel and the loaded edge of the timber is considerably smaller than the minimum distance suggested by building codes. These aspects make the use of reinforced joints very suitable for structural engineering purposes.

1.2

Objective

The main objective of this study was to investigate the feasibility of a new joint to improve and ensure competitiveness of long span timber structures, such as truss structures. For this purpose, the load-slip behaviour of single large-dowel joints reinforced by reinforcing screws placed in different positions was investigated.

2

State of the art

Design rules for dowel-type joints are generally based on Johansen´s yielding theory (Johansen, 1949), in which perfect plasticity of both the dowels and the timber is assumed. In Eurocode 5 (2004) this is taken account of by considering different failure modes. However, Johanssen’s theory is generally not valid, when failure of the joint occurs before the full embedment of the timber reached.

In recent years, a number of researchers have investigated the possibility of reinforcing dowel joints by different techniques. Leijten (1988) used thin steel plates (1–2 mm thickness) bonded onto the interface surfaces with epoxy resin, in tests on both single-dowel tension joints and multisingle-dowel moment transmitting joints. Glass fibre reinforced plastic (GFRP) of various types has been tried by Chen and Haller (1994) to reinforce truss joints and by Larsen (1996) and Claisse and Davis (1998), among others, to reinforce single-dowel joints. Another material that has been investigated for its reinforcing potential is Densified Veneer Wood, DVW (Leijten et al. 1994).

The use of self-tapping screws as a reinforcement to prevent splitting of timber in dowel type joints has been investigated by Bejtka et al. (2002). A calculation model based on Johansen´s yield theory valid for joints reinforced with self-tapping full threaded screws was developed. The authors found that although small cracks in the wood, directly under the dowels were visible during the experiments, a complete splitting of the specimens – as normally observed in non-reinforced specimens – did not occur. The authors also found that - by means of this reinforcing method - both an increase of the load-carrying capacity up to 80% and a ductile load-carrying behaviour could be achieved. Moreover, compared to non-reinforced connections with a brittle load-carrying behaviour, the method showed an increase of the load-carrying capacity of up to 120%.

3

Laboratory tests

3.1

Specimens and test set-up

The experiments described herein were monotonic quasi-static tensile tests of double-shear single large-dowel wood joint. The load direction was parallel-to-grain for all experiments. The type of joint used in this investigation is shown in Fig. 2. The timber used for all joints was machine graded Norway spruce with characteristic tensile strength parallel to the grain, ft,0,k ≥ 22 MPa and with cross section 45 mm x 140 mm. The density

ρ of the specimens was obtained at current moisture content MC= 12-13% and it varied in the range 417 ≤ ρ ≤ 546kg/m3_{. The steel dowel was 32 mm in diameter and the}

diameter of the drill was 33 mm. The end distance was set to 3.5 times the diameter of the dowel, i.e. 112 mm, which is one half of the minimum end distance as given in EC5, see Fig. 1. After manufacturing, the specimens were loaded until failure. The transmission of the tensile load from the testing machine to the dowel, occurred by means of steel plates provided with 33 mm hole. In order to force failure to occur in the instrumented part of the specimen (i.e. the upper part of the specimen, see Fig. 2), the other end of the specimen was reinforced with screw-glued boards. Tests were performed under displacement control, with rate of loading 0.5 mm/min. During tests, the load was recorded and the relative displacement of the dowel was measured by two independent LVDTs, attached on opposite sides of the specimen.

Figure 2 Test setup.

In the reinforced specimens, fully threaded self-tapping screws were inserted perpendicularly to the axis of the dowel, at different positions , see Fig. 3. Three different screw diameters were used for the reinforcement of the specimens, namely d = 6.3 mm, d

= 10 mm and d = 13 mm (d is the nominal diameter of the screw). The yield strength of

the reinforcing screws was fyk ≥ 900 MPa. In order to avoid possible splitting failure of the

wood close to the end grain during the insertion of the reinforcing screws, small secondary reinforcing screws with dimension 4.0 mm x 40 mm were inserted in advance.

Figure 3 Placement of the reinforcing screws for the specimen. In the figure specimen A(1_d6.3)+B(1_d6.3)+C(1_d6.3_r) is shown.

In Fig. 4, the explanation of the numbers and letters used to denominate the different specimens is given.

Figure 4 Explanation of the number and letters used to denominate the different specimens.

3.2

Test results

A total of 26 specimens were tested, divided into nine groups . Each group had a different configuration of the reinforcing screws. Eight groups included specimens with reinforcing screws and one group had specimens with no reinforcing screws. At least three nominally identical specimens were tested for each group. The only exceptions were the following groups, in which the number of tested specimens was less than three:

• A(1_d6.3)+C(1_d6,3_r) two specimens • A(1_d6.3)+B(1_d6,3)+C(1_d6,3_r) one specimen • A(2_d6.3)+B(2_d6,3)+C(2_d6,3_r) one specimen

Table 1 summarizes the results of the experimental programme. The numbers shown in the table are mean values of test results for each group. The failure load Pmaxwas defined

as the load corresponding to the first evident change in slope of the load-slip curve. The value δmax is the slip of the joint at P = Pmax . The value Pult indicates the maximum load

reached during testing of the specimen. The value Pδ=5 gives an indication of the ductility

of the joint, as it shows the remaining load-carrying capacity of the joint at a slip δ = 5mm, which is considered as an upper limit deformation for a real joint. See Fig. 5.

Figure 5 Typical load-slip (P-δ )curve for a reinforced joint, with explanation of symbols used in Table 1.

The choice of the zone of the (P-δ )curve to be used for calculating the stiffness k of the

joint, was made according to the following criteria:

i) loads within the range for serviceability limit state, i.e. P ≤ 0.5Pmax

ii) zone of the P-δ curve that shows a nearly linear behaviour

Based on these considerations, the stiffness k was calculated as:

P P

P

P

k

0

.

2

5

.

0

δ

δ

−

⋅

−

⋅

=

Table 1 Summary of test results. N is the number of tested specimens,Pmax is the first

maximum load, δmax is the slip at P = Pmax, CoV is the coefficient of

variance of Pmax, Pult is the absolute maximum load, Pδ=5 is the load

corresponding to a slip δ = 5 mm, k is the stiffness of the joint, ρ is the density. The MC varied in the range 12-13%, for all specimens. The numbers in the table indicate the mean values of test results for each group.

Specimen group N Pmax [kN]

(δmax) [mm] CoV Pult Pδ=5 k ρ [kN] [kN] [N/mm] [kg/m3_] Non-reinforced 5 20.9 (1.0) 0.7 20.9 0.0 26164 459 A(1_d6.3) 3 41.2 (1.6) 0.03 43.5 25.3 39960 485 A(1_d13_r)+C(2_d6.3_r) 3 37.5 (1.4) 0.17 44.7 32.2 41413 484 A(1_d10_r)+C(2_d6.3_r) 3 37.9 (2.0) 0.11 48.7 41.5 37595 461 C(2_d6.3_r) 3 39.6 (1.4) 0.17 40.6 33.4 41286 458 A(2_d6.3_r)+C(2_d6.3_r) 3 40.2 (1.7) 0.06 52.7 37.4 36586 482 A(1_d6.3)+C(1_d6.3_r)** 2 40.9 (1.5) 0.06 41.1 28.2 43838 488 A(1_d6.3)+B(1_d6.3)+C(1_d6.3_r)* 1 38.8 (1.4) - 38.8 25.2 41571 478 A(2_d6.3)+B(2_d6.3)+C(2_d6.3_r)* 1 36.6 (1,3) - 49.1 42.8 45750 485 * : only one specimen was tested in this group

**: only two specimens were tested in this group

Most of the tests were interrupted after very large deformations had occurred. All specimens – with exception for the non-reinforced ones – were loaded at least until a deformation of d=10 mm was reached. Some specimens were also loaded up d=20 mm. All reinforced specimens, showed a reserve of strength of more than 50% Pmax at the

moment when the loading was interrupted.

For the non-reinforced specimens the failure occurred suddenly, directly after the maximum load was reached. The typical failure mode was a formation of a crack at the end grain and for some of the specimens eventually a plug shear failure. Normally, the width of the plug was smaller than the diameter of the dowel. At failure, a splitting crack could be observed on the diametrically opposite side of the loaded hole edge (see Fig. 6). No evident sign of deformations due to embedding stress were observed.

Figure 6 Typical failure mode for non-reinforced specimens. In this Figure, specimen D12 is shown Pmax = 17.5 kN , δmax = 0.41 mm.

The common failure mode of all reinforced specimens was a formation of a splitting crack visible at the end grain and successively – normally after considerable further deformation – a plug-shear failure eventually occurred. After failure, in almost all specimens reinforced with larger reinforcing screws (d = 10 mm and d = 13 mm), a splitting crack could be observed through the thickness of the wood, parallel to the axis of the reinforcing screw. Clear large deformations due to embedding stress occurred in all reinforced specimens.

Figure 7 Typical failure mode for reinforced specimens. In this Figure, specimen D2 is shown Pmax = 36,6kN, δmax = 1,3mm. In the picture on the left, the

specimens was split into two pieces in order to study the deformation of the reinforcing screws. The upper screws close to the end grain (Level C) were removed in the specimen on the right.

In reinforced specimens, large deformation of the screws were achieved. The screws placed closed to the dowel (i.e. at level A), were subjected to the largest deformation normally showing the formation of three plastic hinges. The screws placed at level B were subjected to smaller deformations than those placed in level A, normally showing the formation of one or in some cases three plastic hinges. Screws placed at level C, were subjected to the smallest deformation, showing no formation of plastic hinges, or in some case the formation of just one plastic hinge.

Plug-shear

4

Discussion

When a dowel joint is unidirectional, laterally loaded, tensile loading causes the stress lines to run around the dowel hole resulting in tensile stresses perpendicular to the grain (see Fig. 8), which promotes premature splitting of the timber.

Figure 8 Principal stress trajectories for a elastic plate with a hole loaded with a concentrated load. Left: hole far away from the end grain. Right: hole close to the end grain.

The shortest the distance between the dowel and the end-grain, the largest is the tensile stress perpendicular to the grain. In order to gain a better understanding of this phenomenon, a “strut-and-tie” model of the joint can be created, Fig. 9. The blue continues lines represent the “struts”, which are in compression. The red dotted lines represent the “ties”, which are in tension. According to Saint-Venant’s principle, outside the perturbed region the stress flow in the plate is not influenced by the presence of a discontinuity (in this case a hole). Such a region has an extension similar to the width of the plate. Therefore, outside this region the “flow pattern” consists of parallel lines. In Fig. 9, the external tension load was divided into ten smaller loads. In both cases of Fig. 9, away from the hole, the flow pattern consists of ten parallel trajectories, each with the same load intensity. Due to the different position of the hole, the flow patterns are different in the area above the hole (i.e. the area directly loaded by the dowel). In the case of a hole placed close to the end grain (Fig. 8, right), the lines are gathering in a small area.

Figure 9 “Strut-and-tie model” for a plate with a hole loaded with a concentrated load. Left: hole far away from the loaded edge. Right: hole close to the loaded edge.

The following aspects should be considered:

- the number of lines approaching the compression struts are the same regardless if the hole (dowel) is placed close to or far away from the end grain,

- when the hole (dowel) is placed close to the end grain (Fig. 9, right), the length of the compression strut is shorter than in the case when the hole is placed far away from the end grain (Fig. 9, left).

It is evident therefore, that the concentration of lines (read: forces) is higher in the case of hole placed close to the end grain. Moreover, also in this case, the relatively large inclination of the tension ties on the external parts of the two compression struts, makes the tensile forces in the area between the two compression struts to increase. Therefore, relatively large tension perpendicular to the grain is expected when dowels are placed close to the end grain.

This model is just a qualitative tool. However, it could be calibrated with FE and laboratory tests to make it a quantitative tool that could be used e.g. for design of the reinforcing screws.

It is evident, therefore, that large tensile stresses perpendicular to the grain occur, which considerably reduce the load carrying capacity in non-reinforced joints. Moreover, as it is common when tension perpendicular to the grain is involved, brittle failures and normally large scatter in test results are expected.

In the tested specimens the distance between the axis of the dowel and the end grain was only 3.5d, i.e. 112 mm. This corresponds to one half of the distance recommended be e.g. the Eurocode 5.

The first observation concerning the non-reinforced specimens is the large scatter in laboratory test results. As shown in Table 1, the coefficient of variation (CoV) is 70%, which is considerably larger than the CoV observed in reinforced specimens. Moreover, failure of non-reinforced specimens always occurred in a very brittle manner, after the peak load was reached with a corresponding slip of approximately 1 mm. In some specimens, failure occurred due to pure splitting, whereas in some other by splitting and then plug-shear.

The reinforced specimens showed a shear strength (Pmax) approximately twice the

ultimate strength of the non-reinforced specimens. However, this consideration refers to mean values. If a characteristic value of the shear strength was to be calculated, the discrepancy between reinforced and non-reinforced joint would be considerably bigger, due to the different CoVs. The shear strength of the reinforced specimens is about the same as the strength of a non reinforced joint, if end distance requirement recommended by building codes had been fulfilled. For example, if the distance between the axis of the dowel and the end-grain was taken as 7d = 224 mm, the load-carrying capacity of the connection according to EC5 – assuming a density value ρ = 470 kg/m3 _{– would have}

been:

(

)

[

]

which is a value close to the values obtained during testing of the reinforced specimens, see Table 1.

The placement of the reinforcing screws does not seem to have a significant influence on the overall behaviour of the joint. The reason of that is probably the fact that the reinforcing screw adds a considerable stiffness in the direction perpendicular to the grain. Thus, regardless if the placement is at level A or level B or level C, the reinforcing screw “collects” the tension stresses generated by the loading of the dowel, and transmits it to the “tension ties” converging to the compression struts. In other words, depending on where the reinforcing screw is placed , an ad-hoc “strut-and-tie” system is naturally generated.

However, it seems that the diameter of the screw may have a certain influence on the load-carrying capacity of the joint. In fact, the Pmax for reinforced specimens with large

screw diameter, i.e. d=10 mm and d=13 mm, was somewhat lower than the Pmax for

specimens reinforced with smaller screws. The reason of such a lower strength is perhaps the fact that a big screw occupies a large part of the thickness of the timber (e.g. t=45 mm, d=13 mm) and thus it has a wedge effect. Therefore, when the load is transferred from the dowel to the reinforcing screw, the specimen tends to split through the thickness. This phenomenon was also observed during the test of specimens with large reinforcing screws.

Most of the specimens failed due to plug-shear. At, failure, i.e. at a load level Pmax ≈ 40

kN, the nominal shear stress at the interface between the wooden plug and the rest of the specimen was approximately 4.5 MPa, which is close to the shear strength of spruce. This means that the reinforcing screws only prevent premature failure of the joint by “neutralising” the tension stresses perpendicular to the grain generated during loading. On the other hand, the screws do not prevent plug-shear.

A considerable reserve of load-carrying capacity could be observed after plug-shear failure occurred. The reason of such a reserve of capacity is most probably the fact that the reinforcing screws - after large bending deformations – act as “ropes”, i.e. they take

load by tension action, see Fig. 10. Moreover, a certain load can also be transmitted by the friction that is generated by the horizontal component of the tensile force in the reinforcing screw.

Figure 10 “Rope effect” of the deformed reinforcing screws. The wooden plug is prevented to be pushed out by tension action in the screws and by friction at the interface between the plug and the surrounding wood.

The reinforcing screws contributes also to increase the stiffness of the joint. Increase in stiffness of 40-60% due to the presence of reinforcing screws were observed during testing. The reason of such an increase can be explained by the fact that the screw is acting as a beam on elastic foundation, thus augmenting the stiffness for upwards vertical translations of the dowel. Since the “beam on elastic foundation” is patch-loaded – and not uniformly distributed loaded – its contribution to the stiffness of the joint is limited.

Figure 11 Increase of stiffness due to the presence of the reinforcing screw. Left:

5

Conclusions

A total of 26 monotonic quasi-static tensile tests of double-shear single large-dowel wood joint on both non-reinforced specimens and specimens reinforced by means of self-tapping screws. On the basis of the results obtained during this investigation, the following main conclusions can be drawn:

- the scatter in test results is considerably reduced when reinforcing screws are used.

- when reinforcing screws are used, the end distance of the connector (e.g. a dowel) can be considerably reduced without negatively compromising the strength and the stiffness of the joint.

- for connectors placed close to the end grain, the use of reinforcing screws considerably increases both strength and stiffness.

- the strength and stiffness of the tested joints is not significantly influenced by the size and the position of the reinforcing screws.

- the ductility of the joint is significantly increased when reinforcing screws are used.

References

Johansen, K. W. (1949). ‘‘Theory of timber connections.’’ Int. Assn. of Bridge and Struct. Engrg. J., 9, 249–262.

Sjödin, J. (2006) “Steel-to-Timber dowel Joints – Influence of Moisture Induced Stresses”. PhD Dissertation.School of Technology and Design Växjö University Växjö, Sweden.

Bejtka I., Blaß H.J. (2005) ”Self-tapping screws as reinforcements in connections with dowel-type fasteners” CIB W18 – Timber Structures. Meeting 38, Karlsruhe, Germany. Blass, H. J. (2003) “Joints with dowel-type fasteners”. Timber Engineering.

Thelandersson S., Larsen, H.J., Eds, Wiley & Sons, ISBN 0-470-84469-8.

Pedersen M. U. (2002) “Dowel Type Timber Connections Strength modelling”. PhD dissertation, Rapport BYG·DTU R-039. Department of Civil Engineering DTU-building 118, 2800 Kgs. Lyngby.

Rodd PD. Timber joints made with new and improved circular dowel connectors. In: Proc. Int. Timber Engineering Conference, Seattle, Washington State University 1988;1:26–37.

Leijten ADJM. The concept of the pre-stressed DVW reinforced joint with expanded tubes. In: Proceedings of the International Wood Engineering Conference, New Orleans, Louisiana State University 1996;2:295–9.

Werner H. Reinforced joints with dowels and expanded tubes loaded in tension. In: Proceedings of the International Wood Engineering Conference, New Orleans, Louisiana State University 1996;2:307–11.

Quenneville, J. H. P., Mohammad, M. (2000) “On the failure modes and strength of steel-to-timber bolted connections loaded parallel-to-grain”. Can. J. Eng., 27, 761-773.

Larsen, H. J. (1996). ‘‘Glass fibre reinforcement of dowel-type joints.’’ Proc., Int. Wood Engrg. Conf., Louisiana State University, New Orleans, 1, 293–302

Guan Z., Rodd P. (2001) “DVW—Local reinforcement for timber joints”. Journal of structural Engineering. August.

Cristovao L. S., De Jesus A.M.P., Morais J.J.L., Lousada J. L.P.C. (2009)

”

Appendix 1 Test results and pictures

Without screws

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D1 10.9 0.8 13080 10.9 0 442 12 D4_2 8.4 1.2 8129 8.4 0 488 12.6 D8 23.3 0.7 31846 23.3 0 452 12.7 D11_3 44.2 1.7 42764 44.2 0 466 12.6 D12 17.5 0.4 35000 17.5 0 449 12.2 Mean 20.9 1.0 26164 20.9 Std. Dev 14.3 0.5 14852 14.3 CoV 0.7 0.5 0.6 Figure A1 Specimens D4_2, D11_3.

A(1_d_6.3)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D7_2 42.0 1.3 42007 42.0 21.9 488 13 D10 42.1 1.7 38273 42.9 20.5 466 12.6 D11_2 39.6 1.7 39600 45.6 33.4 501 12.7 Mean 41.2 1.6 39960 43.5 25.3 Std. Dev 1.4 0.2 1893 1.9 7.1 CoV 0.03 0.1 0.05 0.04 0.28 Figure A2 Specimens D7_2, D10, D11_2.

A(1_d13_r)+C(2_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D5 33.2 1.7 34345 45.0 28.5 435 13 D13 44.8 1.5 46345 44.8 37.6 470 12.3 D15 34.5 1.2 43550 44.4 30.5 546 11.7 Mean 37.5 1.4 41413 44.7 32.2 Std. Dev 6.4 0.3 6279 0.3 4.8 CoV 0.17 0.2 0.15 0.01 0.15 Figure A3 Specimens D5, D13, D15.

A(1_d10_r)+C(2_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D1F10 33.7 1.3 38885 49.5 41.7 442 12 D8 F10 37.9 1.7 37900 43.0 40.1 452 12.7 D14 F10 42.0 2.9 36000 53.7 42.8 490 12.6 Mean 37.9 2.0 37595 48.7 41.5 Std. Dev 4.2 0.8 1466 5.4 1.4 CoV 0.11 0.4 0.04 0.11 0.03 Figure A4 Specimens D1 F10, D8 F10, D14 F10.

C(2_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D5_2 38.72 1.5 51170 38.7 34.1 435 13.0 D6_2 39.31 1.2 39340 42.1 40.6 460 13.2 D10_2 31.82 1.6 28076 33.3 31.6 466 12.6 D13_2 48.4 1.4 46559 48.11 27.1 470 12.3 Mean 39.6 1.4 41286 40.6 33.4 Std. Dev 6.8 0.2 10063 6.2 5.6 CoV 0.17 0.1 0.2 0.15 0.17 Figure A5 Specimens D10_2, D6_2.

A(2_d6.3_r)+C(2_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D2_2 42.7 2.8 19409 55.3 49.2 485 12.8 D3_2 39.3 1.5 39300 56.9 36.4 478 13.2 D14 41.5 1.2 47885 54.2 29.9 419 12.6 D15_2 37.1 1.3 39750 44.3 33.9 546 11.7 Mean 40.2 1.7 36586.0 52.7 37.4 Std. Dev 2.5 0.7 12111.9 5.7 8.3 CoV 0.06 0.4 0.33 0.11 0.22 Figure A6 Specimens D3_2, D2_2.

A(1_d6.3)+C(1_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] % D7 42.6 1.4 44119 42.6 22.5 475 13.0 D11 39.2 1.6 43556 39.6 33.9 501 12.7 Mean 40.9 1.5 43837.5 41.1 28.2 Std. Dev 2.40 0.1 398.1 2.1 8.1 CoV 0.06 0.1 0.01 0.05 0.29 Figure A7 Specimens D7, D11. A(1_d6.3)+B(1_d6.3)+C(1_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] %

D3 38.8 1.4 41571 38.8 25.2 478 13.2

A(2_d6.3)+B(2_d6.3)+C(2_d6.3_r)

Pmax d K Pult P(d=5 mm) Density Moisture

[kN] [mm] [N/mm] [kN] [kN] [kg/m3] %

D2 36.6 1.3 45750 49.1 42.8 485 12.8

Appendix 2

Example of calculated member forces in a Warren-type truss.

Type of Value Coefficient Value ULS Spacing Load

[kN/m2_{] [kN/m}2_{] [m] [kN/m}2_] Snow 2 1.5 3 6 18 Self weight 0.5 1.35 0.675 6 4.05 Tot 22.05 kN/m GEOMETRY Span 30 40 50 60 Max height 2.15 2.85 3.5 4.3 Inclination 3 3 3 Inclination 45 45 45 45

LOAD IN THE TRUSS MEMBERS   Hinged joints Span [m] Member 30 40 50 60 1-2 -326 -436 -548 -659 kN 2-3 425 571 720 866 kN 3-4 -401 -535 -673 809 kN 4-5 270 360 452 543 kN 5-6 -256 -341 -427 513 kN 6-7 131 173 217 261 kN 7-8 -131 -173 -217 -261 kN 8-9 -10 -15 -20 -24 kN 9-10 10 15 20 24 kN 1-3 0 0 0 0 kN 3-5 603 809 1017 1224 kN 5-7 984 1318 1656 1991 kN 7-9 1175 1572 1974 2372 kN 9-11 1161 1550 1945 2336 kN 2-4 322 430 541 655 kN 4-6 807 1079 1356 1663 kN 6-8 1081 1446 1821 2188 kN 8-10 1172 1561 1966 2361 kN

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