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Experimental and numerical investigations on load-carrying capacity of dowel-type bolted bamboo joints
Engineering Structures xxx (xxxx) xxxx
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Experimental and numerical investigations on load-carrying capacity of dowel-type bolted bamboo joints Feiliang Wanga,b,c, Jian Yanga,b,c,d,
⁎
a
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China c Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, PR China d School of Civil Engineering, University of Birmingham, Birmingham B15 2TT, UK b
A R T I C LE I N FO
A B S T R A C T
Keywords: Bamboo Prefabricated structures Dowelled joints Infilling grout Laboratory test Numerical simulations Design model
Bamboo has been widely used for structural and non-structural purpose, for example as scaffolding and cladding for many centuries in South East Asian countries such as China and India, due to its high strength-to-weight ratio, low price and recyclability. In today’s trend of sustainable development, there is a renewed interest in the use of bamboo for modern prefabricated structures. In this paper, dowel-type bamboo joints are introduced for prefabricated bamboo structures. An experimental study has been undertaken to investigate the structural behaviour and the failure mechanisms of the dowelled joints with varying configurations. Test results reveal that the ductile failure mode of the bamboo occurred when large end spacing was applied, and the infilling grout can significantly increase the load-carrying capacity of the dowelled joint. Three-dimensional finite element models were established and validated using available experimental data. Extensive parametric studies were carried out based on the simulation approach to investigate the effects of key influencing variables involved, i.e. hole clearance, friction coefficient, bolt strength, bamboo thickness, grout strength and end spacing. Moreover, analytical models for designing the dowelled joints are proposed and compared with the current codified approach.
1. Introduction Bamboo grows rapidly and matures to structural strength within five years, so it can be harvested more quickly than conventional materials such as timber. It is an important construction material particularly in rural and remote areas where access to steel or reinforced concrete production and heavy machinery is limited [1]. For instance, Kao Jue (Bambusa pervariabilis) or Moso bamboo (Phyllostachys pubescens) have been widely adopted in South East Asia as scaffoldings and working platforms [2–4]; Guadua angustifolia, which is a native species of bamboo, has been frequently used in the construction of rural houses and temporary structures in the South and Central America [5]. As a natural composite material, bamboo is longitudinal reinforced by strong fibres [6] and has excellent mechanical properties against compression and bending. The compressive strength for Moso bamboo can up to 70 MPa [7] and the thickness of the bamboo was found to be in direct proportion to its outer diameter, and the bamboo with greater thickness exhibits higher load capacity [8]. Nowadays, construction applications of bamboo, such as in low-rise
⁎
dwellings [1,9], short-span bridges [10], long-span roofs [11] and laminated structural components [12–16], are experiencing a rapidlygrowing market recently as increasing demands for sustainable building materials and prefabricated structures. The safety and serviceability of such bamboo structures are often governed by the capacity of the connections between bamboo culms. Many types of structural joints have been proposed to connect bamboo culms as described in various documents [17,18]. Traditional joints were made by cutting curved surfaces into the culms, to form a fish-mouth joint (see Fig. 1), which was intended to increase the contact area between the culms. Later on, bamboo joints evolved to incorporate pins, bolts, hooks [19], and fibre reinforced plastic (FRP) that is used to wrap the bamboo connection [1]. In order to fulfil the requirements for off-site construction, efforts have to be made to design a bamboo joint that allows modern industrialized production and which needs a minimum operation on site. To this end, a novel dowelled bamboo joint has been presented in the paper and its structural performance has been examined. The joint, which constructed with slotted-in T-shape steel connectors, can adapt
Corresponding author at: Mulan Building A727, Shanghai Jiao Tong University, Dongchuan Road 800, 201100 Shanghai, China. E-mail address: [email protected] (J. Yang).
https://doi.org/10.1016/j.engstruct.2019.109952 Received 14 June 2019; Received in revised form 7 November 2019; Accepted 15 November 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Feiliang Wang and Jian Yang, Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.109952
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The current code of practice provides the design approaches for dowelled wood joints [23,24]. Such codified methods were based on the European Yield Model proposed by Johansen [25]. However, the Johansen model only considers ductile failure modes, which is deemed as the dominant mode for timber structures. Brittle failure modes, such as splitting and shear-out of the wood in multiple-bolted wood joints [26,27], or failure of the bamboo which the slotted-in bamboo-to-steel dowelled joint often experiences, were omitted. Moreover, compared with extensive numerical and experimental studies on dowelled joints in timber structures, only limited physical test data or design models are available for slotted-in dowelled joints in bamboo structures. To this end, a series of laboratory tests have been devised and carried out in the study to investigate the behaviour of bamboo-to-steel dowelled joints with and without infilling grout. Numerical models were established and validated against the experimental results. Extensive parametric studies were conducted based on the established modelling technique to reveal the effect of key design parameters on the joint. Finally, an analytical approach is proposed to predict the load-resistance capacity of the dowelled joint in bamboo structures. The aim of this paper is to provide an aid for engineers in the design and construction of bambooto-steel dowelled type connections in prefabricated bamboo structures.
Fish-mouth joints
Fig. 1. An example of fish-mouth joints.
to culms with varying diameters and can be easily produced in the factory with a standard dimension, and only bolts and steel ties are needed in-situ for assembly, as shown in Fig. 2. Test results from various sources imply that with timber, for single or multiple fastener connections loaded either longitudinally, transversely or at an angle to the grain, failure of the wood can be the dominant failure mode. It was found that wood connections using small diameter tight-fit steel tube fasteners can produce a ductile response while at the same time attaining high strength properties [20]. Based on experimental works, a mechanical model was proposed to predict the load-bearing capacity of dowel-type fastener connections perpendicular to the grain in timber structures and the classification of these connections in terms of ductility was provided [21]. In addition, an analytical procedure was proposed to predict the splitting resistance of riveted connections under perpendicular-to-grain loading. The closedform analytical method, which takes into account the partial or full width splitting failure modes of wood, was confirmed by the existing tests and has more precise predictions on the effect of different connection configuration parameters, such as connection width and length, fastener penetration depth, loaded and unloaded edge distances, end distance, and member thickness. [22].
(a) Bamboo preparation
(d) End-column connection
2. Experimental methods A series of laboratory tests on bamboo-to-steel dowel-type joints was conducted in the structural laboratory of Shanghai Jiao Tong University. In the test, the adopted bamboo type was Moso bamboo, which is an abundant resource in southern China and has good mechanical performance and quick growth speed. The prepared bamboo specimens were harvested at the age of 3 years and have an average density of 0.7 g/cm3. As the previous study showed that the mechanical properties of bamboo samples would undergo degradation when associated with water, and the bamboo material has a better mechanical performance when the moisture content is less than 15% [28,29]. Therefore, all bamboo specimens used in the test were dried in oven at up to 100 °C in advance and were supplied by Hape International (Ningbo) Ltd. The test was conducted in accordance with the EN26891
(b) Steel connectors
(e) Sub-assemblage
(c) Slotted-in joint
(f) Assembly on site
Fig. 2. Construction process of bamboo structures with the proposed dowelled joints. 2
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200 T-1 T-2 T-3 C-1 C-2 C-3 C-4
180 160
(a) Tension test setup
Stress (MPa)
140
(b) Culm compression test
120 100 80 60 40 20 0 0
10
20
30
Strain (%)
40
50
Fig. 4. Stress-strain curves of tested specimens.
(c) Tested coupons under tension
with the double bolts (DJD; see Fig. 7(b)) and the dowelled joint with the double bolts and infilling grout (DJDI; see Fig. 7(c)). The configurations of the T-shape steel connectors and bolt plates are illustrated in Fig. 7(d–f). It should be noted that the connector with the slotting (see Fig. 7(d)) was used for the specimens with single bolt and the connector with bolt holes (see Fig. 7(e)) was used for the specimens with double bolts. The bolt diameters range from 8 mm to 12 mm in this study. The bamboo diameter at the connections varied from 90 mm to 110 mm and the end spacing from 40 to 100mm . A static load was applied under static using MTS-SANS test machine with a maximum loading capacity of 100 kN. The load was applied through the displacement-controlled mode and the test was terminated when the load was reduced by 15% of the ultimate load or when significant damage to the connection was observed, whichever occurred first. The characteristics of the test specimens from three groups are plotted in Fig. 8. The grout used for DJDI-1 and DJDI-2 was provided from the supplier and has a nominal yield stress of 50 MPa and a maximum expansion rate of 0.04%. It is a high-strength grout material made from cementations materials, fine aggregate, and admixture. Before infilling this grout by injection pipe (see Fig. 8(c)), both ends of the bamboo members had to be sealed by means of silicone glue for leakage prevention.
(d) Tested coupons under compression
Fig. 3. Coupon test setup.
standard [30].
2.1. Test setup Coupon tests were initially conducted to assess the material properties of the Moso bamboo. Two groups of tests were performed: the parallel-to-grain tensile test (see Fig. 3(a)) and the parallel-to-grain culm compression test (see Fig. 3(b)). The chosen specimens were labelled with ‘T’ and ‘C’ respectively. The coupons in the tension test were cut from the culms aligned in the parallel-to-grain direction (See Fig. 3(c)). Coupon tests were carried out by using a Zwick Roell-Z100 materials testing system (MTS) and the loading rate was 2 mm/min. Table 1 summarizes the characteristics of the coupons and the recorded test data. It shows that the average parallel-to-grain tensile and compressive strengths for the Moso bamboo are 147.7 MPa and 48.2 MPa, respectively, with a modulus of elasticity of 910 MPa. The obtained stress-strain curves are plotted in Fig. 4. As depicted in the figure, a fair consistency can be found in the results. In the elastic stage, the specimens under tension and under compression exhibit a similar stress-strain relationship. The specimens show brittle failure mode under tension and ductile failure mode under compression. In order to reveal the capacity and failure mechanism of the dowelled joints (Fig. 5), specimen connections with and without infilling grout under a tensile load were further tested. In the test, eleven dowelled connected specimens were prepared and tested using to the test set-up shown in Fig. 6. The descriptions of the specimens, including geometric dimensions and bolt configurations, are summarized in Table 2. In the table, three groups of connections are included: the dowelled joint with the single bolt (DJ; see Fig. 7(a)), the dowelled joint
2.2. Experimental results The failure modes for tested specimens are plotted in Fig. 9, and the corresponding ultimate loads are tabulated in Table 2. As shown in Fig. 9, five different failure modes were observed in the test and the failure behaviours for all specimens can be divided into two categories: (1) ductile failure (bolt bending failure and/or bamboo bolt-hole bearing); (2) brittle failure (bamboo splitting failure or bamboo shearout failure). The failure modes for the DJ type of connections include (1) bolt bending (Fig. 9(a)); (2) bolt bending and bamboo bearing (Fig. 9(b) and Fig. 9(c)); (3) bamboo splitting (Fig. 9(d) and Fig. 9(g)); and (4) bamboo shear-out (Fig. 9(e) and Fig. 9(f)). The failure modes for the DJD and DJDI type of connections are (1) bamboo splitting
Table 1 Summarized geometric dimensions and material properties for the coupon. Specimen
Width (mm)
Thickness (mm)
Ultimate strength (MPa)
E (GPa)
Specimen
External diameter (mm)
Bamboo thickness (mm)
Ultimate strength(MPa)
T-1 T-2 T-3
12.6 9.88 11.4
8.36 8.36 8.36
136.2 157.4 149.5
0.876 1.020 0.848
C-1 C-2 C-3 C-4
110 110 110 110
9.3 9.3 9.3 9.3
45.1 53.0 45.6 49.2
147.7
0.91
Mean
Mean
Note: T-represents tension test; C-represents compression test. 3
48.2
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Beam element Dowelled joint
Dowelled joint Column
Brace
Column element
Beam
(a) Brace joint
Beam
(b) beam-to-column joint
Fig. 5. Plot of representative dowelled joints.
(Fig. 9(h)) and (2) grout cracking (Fig. 9(i)). In Table 2, the ductility is defined as the joint displacement at the ultimate load divided by the displacement at the apparent yield load. The apparent yield load is evaluated based on the 5% offset method. In this method, a straight line to the initial linear portion of the curve is shifted in the positive x-direction by 5% of the bolt diameter, and the apparent yield load is defined as the intersection of this line and the load-displacement curve [31], as illustrated in Fig. 10. It is worth noting that the test on specimen DJD-1 was not completed due to the recording program auto-terminated during the test. According to the load-deflection response of DJ, DJD and DJDI specimens plotted in Fig. 10, the behaviour of each specimen shows two stages before the failure occurs: (1) Elastic stage: all specimens behave elastically at the initial stages of loading, and the bolt shows flexural behaviour due to the applied bending moment at this stage. The maximum load can up to approximately 75% of the ultimate load at this stage; (2) Elastic-to-plastic stage: the deformation develops quickly with a limited increase in applied load. Meanwhile, yielding occurs on the mid-section of the bolt and then followed by the failure of the bamboo. A post-failure stage with large-deformation behaviour can be noticed for the DJDI specimens after the ultimate load is attained and the failure behaviour is the cracking of the grout. The load-resistance capacities of the joints tested are dramatically influenced by the bolt diameter and infilling grout, as implies in Fig. 11. The ultimate load-resistance increases with increasing bolt diameter, and the joint with M10 bolt (7.50 kN) has an ultimate load which is 40% higher than that with M8 bolt (5.34 kN), and 40% lower than that with M12 bolt (12.64 kN). When comparing between the DJD and DJDI
Fig. 6. Test setup.
Table 2 Specimen design details and test results. Specimen
Bamboo length (mm)
Bamboo diameter (mm)
Thickness (mm)
End spacing (mm)
Top and bottom Bolt diameter (mm) × number
Failure load (kN)
Failure mode
Ductility
DJ-1 DJ-2
269 269
90 90
7.3 7.3
100 100
M8 × 1, M8 × 1 M10 × 1, M10 × 1
5.34 7.5
4.4 2.6
DJ-3
279
100
7.9
100
M12 × 1, M12 × 1
11.3
DJ-4 DJ-5# DJ-6# DJ-7# DJD-1# DJD-2# DJDI-1# DJDI-2#
191 301 226 268 302 301 299 298
100 110 110 110 109 110 112 107
8.1 11.42 11 11.3 10.2 10.2 10.9 10.7
50 40 40 50 100 100 100 100
M10 M12 M12 M12 M10 M10 M10 M10
7.5 13.64 12.4 13.2 N/A* 19.66 35.89 35.62
Bolt bending Bolt bending and bamboo bearing Bolt bending and bamboo bearing Bamboo splitting Bamboo shear-out Bamboo shear-out Bamboo splitting Bamboo splitting Bamboo splitting Grout cracking Grout cracking
Note: # – represents the joint with bolt plates. 4
× × × × × × × ×
1, 1, 1, 1, 2, 2, 2, 2,
M12 M12 M12 M12 M10 M10 M10 M10
× × × × × × × ×
1 1 1 1 2 2 2 2
3.8 2.1 2.4 2.0 2.0 N/A 3.3 2.2 1.0
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Fig. 7. Test rigs (unit mm).
bolt and the hole, (2) the interface between the nut and the external surface of the culm and (3) the interface between the grout and the internal surface of the culm, were considered in the model. The interaction property for each contact pair was modelled adopting the penalty method with a friction coefficient of 0.4. The most satisfactory mesh size and friction factor were decided based on extensive sensitive studies. In the model, the bamboo was considered as an isotropic elastic material with the properties based on the coupon test and it was assumed that the section area of each bamboo component is the same along the culm length. The applied stress-strain curves for the grout and bolt are shown in Fig. 13.
joints, it indicates that the infill grout can slow down the yielding of the bolt, and hence its use will greatly enhance the average connection capacity by 82%, from 19.52 kN to 35.45 kN. 3. Numerical analysis The numerical approach has recently attracted extensive engineering attentions in the investigation of the bolted timber joints subjected to a load either perpendicular or parallel to the grain. The finite element (FE) modelling offers an opportunity to consider realistic issues in the lab, such as contact behaviour, material nonlinearly and the deformation of fasteners, meanwhile saving the trial-out cost [32–39]. In this study, a series of three-dimensional numerical models were established to obtain a better understanding of the behaviour of bamboo-to-steel dowelled joints. The commercial finite-element program ABAQUS 6.13.1 [40] was selected for developing the numerical models.
3.2. Model validation and result discussions To validate the numerical modelling approach, the load-displacement curves given by the FE models are compared with those from laboratory tests, as shown in Fig. 14. The yield load for each joint is also attached in the figures. A general set of conclusions can be drawn according to the resistances and failure modes recorded in the FEM. The ductile failure modes occurred when large end spacing (100 mm) was applied (DJ-1 to 3). Take DJ-3 for example (Fig. 14(c)), at the initial stage, the joint yields due to the bending of the bolt, and this is followed by extensive plastic deformation of the bolt-hole, and the maximum plastic deformation is up to 60 mm. The failure mode of DJ-1 to 3 is desirable for engineering application; as the plastic deformation of the bamboo and bolt can be fully developed under this failure phenomenon. Specimens DJ-4 to 7 with short culm length or short end spacing (40 mm) tended to undergo a brittle failure mode. For these specimens, the yielding starts on the mid-span of the bolt and no obvious damage can be seen on the outer surface of the bamboo at the initial stage. The crack or fracture then appears along the bolt-hole, and the failure occurs instantaneously without any pre-warning as the curve shows a sudden
3.1. Modelling process The geometry of a finite element model is shown in Fig. 12(a) where the 8-node solid element C3D8R was used for the steel bolt, grout (for DJDI only) and the bamboo culm. In order to increase the computing efficiency, only 1/2 of the connection was modelled for the DJ specimen and 1/4 was modelled for the DJD and DJDI specimens. A symmetrical condition was enforced to inhibit horizontal displacement along the centreline, a displacement controlled point load was applied in the mid-span section of the top-bolt, and the translation movement of the bottom bolt was restrained to represent the pinned support provided by the bottom T-shaped connector (see Fig. 12(a)). The overall model was meshed with a general mesh size of 20 mm, and a refined mesh size 10 mm was applied for the bolt-hole region, as shown in Fig. 12(b). Three contact pairs, namely (1) the interface between the
(a) DJ
(b) DJD Fig. 8. Photographs of the test specimens. 5
(c) DJDI
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(a) DJ-1
(b) DJ-2
(e) DJ-5
(c) DJ-3
(f) DJ-6
(d) DJ-4
(g) DJ-7
(h) DJD-2
(i) DJDI-1 and DJDI-2 Fig. 9. Failure modes.
interface between grout and bamboo gradually separates. With an increasing applied load, failure occurs when the grout on the contact region becomes crushed. At that moment, the load-displacement curves of the DJDI joints show that the joints experience a sudden load decrease after reaching the maximum load, but they can still resist the applied load before completely failing due to the friction between the interface of grout and bamboo. Overall, numerically achieved load-to-displacement response is
decline of the load-resistance. Therefore, a better ductility can be achieved when the flexural capacity of the bolt (DJ-1) or the bearing elongation (DJ-2 and DJ-3) can be fully developed (as shown in Table 2). For connections with infilling grout (DJDIs), the deformations of the joints are quite limited in the initial linear stage, and the bending of the bolt and bearing deformation of the bamboo bolt-hole is relatively small. Then, the first crack appears on the bolt-to-grout surface and the
6
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Load (kN)
30 25
similar to that from experimental observation, as shown in Fig. 14. The numerically obtained the load-slip curves for the specimens are found to be steeper than the experimental curves, especially for those failed at brittle splitting, because the fracture criterion of the bamboo material was ignored in the model. Fig. 15 indicates that the ultimate load from the numerical study is in close correlation with experimental data and with the average error of 1.5%. Fig. 16 shows the embedment strength of the bamboo member (ultimate stress to crush the wood) against displacement responses for the specimens with ductile failure behaviour. It can be concluded that the average embedment strength of Moso bamboo is 47.2 MPa, which is very close to the compression strength of the bamboo. Contour plots generated from the numerical results illustrate the stress development on the joint at the ultimate loads. In Fig. 17, the DJ-2 specimens are found to have formed one plastic hinge on the mid-span section of the bolt (DJ1-3 all show the same pattern); DJ-5 has formed three plastic hinges, the first on the bolt mid-span section, and the rest on the bolt-bamboo interface (DJ-4 to 7 all show the same pattern); the DJDI specimens are also found to have one plastic hinge, with the yielding of the bolt and the cracking of the grout. For the DJDI joints, the second plastic hinge is not formed due to the shear slip on the interface between grout and bamboo.
DJ-1 DJD-2 DJDI-1 Yield load-DJ Yield load-DJD Yield load-DJDI
35
3.2, 27.5
20 15 10
11.5, 11.5
4.5, 4.0
5 0 0
5
10
15
20
25
30
35
40
Displacement (mm)
Fig. 10. Typical load-displacement curves for DJ, DJD and DJDI joints. 40 30 25 20
3.3. Parametric studies
15
The numerical approach was undertaken to optimize the design of the bamboo-to-steel dowelled joints. The following variables of the DJ1 model were modified in the analysis, (1) hole clearance, (2) friction coefficient between the bamboo and bolt, (3) bolt strength, (4) bamboo thickness, (5) grout strength and (6) end spacing, and only one variable was changed at a time during the analysis. As shown in Fig. 18(a), the ultimate load is slightly influenced by the bolt-hole clearance between the bolt and the hole. The increase from 0 mm to 1 mm leads to a reduction of 1.8% in the ultimate load, and the increase from 1 mm to 2 mm lead to a reduction of 1.5%. It can be concluded that a decrease in the clearance will lead to a growth in the initial stiffness of the joint. Fig. 18(b) shows that the friction coefficient almost has no effect on the capacity of the dowelled joint as the horizontal movement of the bolt was not a critical factor under such load scenario. The effect of bolt strength is evident from the load vs. deflection curves in Fig. 18(c). The grade of bolts used are G4.8 ( f y = 320 MPa), G8.8 ( f y = 640 MPa) and G10.9 ( f y = 900 MPa). As the strength of the bolt increases, the ultimate load of the dowelled joint increases. It shows that the ultimate bearing capacity of the joint with the G8.8 bolt is higher by 82% than that of the joint with the G4.8 bolt, and the joint bearing capacity with the G10.9 bolt is higher by 29% than that of the G8.8 bolt. The bolt strength seems to play an important role because failure initiates at the bolt prior to the bamboo when bolt diameter is relatively small. As expected, the bamboo thickness could improve the ultimate capacity of the dowelled joint, as demonstrated by the numerical results given in Fig. 18(d). When the thickness changes
10 5 0
M8
M10
M12
DJD
DJDI
Fig. 11. Comparison of ultimate loads between specimens with varying configurations.
(a) Geometric model (DJ)
(b) Meshed model (DJDI)
Fig. 12. Geometric model and mesh pattern.
Tension
Compression 60
Stress (MPa)
50 40 Compression
30
Tension
20 10 0 0
0.005
0.01
Strain
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
0.015
850
Stress (MPa)
Ultimate load (kN)
35
800 750 700 650 600
0
0.04
0.08
Strain
(a) Grout
(b) Bolt
Fig. 13. Stress-strain curves for bolt and grout in the FE model. 7
0.12
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Fig. 14. Comparison of load-displacement curves between test and FEM.
failure occurs. A similar trend of the load vs. deflection response can be observed in Fig. 18(e) between models with different grout yield strengths. This shows that the increase in the joint ultimate resistance is 15.0%, as the yield strength of the grout increases from 30 MPa to 50 MPa. The effect of end spacing on the ultimate joint load is insignificant (see Fig. 18(f)). However, the failure performance of the
from 5 mm to 7 mm, and from 7 mm to 9 mm, this leads to a 5% and 6% growth, respectively, in the ultimate load. It indicates that the effect of bamboo thickness on the load-carrying capacity is less significant when compares with bolt strength for DJ-1 specimen, which is because of that the bolt diameter in the specimen is relatively small and hence the bearing strength of the bamboo was not fully developed when the 8
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40 35
Bolt yielding
Ultimate laod (kN)
30 25 20 15 10 5 0 Test FEM
DJ-1 5.34 5.45
DJ-2 7.5 8.06
DJ-3 7.5 9.64
DJ-4 11.3 7.74
DJ-5 13.64 13.1
DJ-6 12.4 13.1
DJ-7 13.2 13
DJD-2 DJDI-1 DJDI-2 19.52 35.4 35.5 20 36.5 36.5
(a) DJ-2
Fig. 15. Comparison between test results and FEM outcomes.
Plastic hinge
(b) DJ-5 Fig. 16. Typical bearing stress – displacement curves.
Plastic hinge dowelled joint could be influenced significantly by reducing the end spacing of the bolt. It can be concluded from Table 2 that the dowelled joint with end spacing less than 50 mm will lead to brittle failure.
4. Analytical approaches Based on the yield theory proposed by Johansen [25] and the theoretical model of the wood dowelled joint presented by Sawata and Yasumura [41], analytical design models of bamboo-to-steel slotted-in dowelled joints are presented in this section. The failure mode of the dowelled joints could be: (a) yielding of the bamboo, (b) yielding of the bolt with one plastic hinge and (c) yielding of the bolt with two plastic hinges, as shown in Fig. 19. The failure mechanisms of the dowelled joints with infilling grout are: (a′) yielding of the grout, (b′) yielding of the bolt with one plastic hinge and (c′) yielding of the bolt with two plastic hinges, as shown in Fig. 20. Equilibrium equations for dowelled joints with a slotted-in steel plate are listed as follows: Without infilling grout: (Case-a in Fig. 19)
Fy 2
= fe dt
(c) DJDI-1 Fig. 17. Stress contour for DJ and DJDI connections. Fy
⎧ 2 = fe dy ⎪ y My = fe dy 2 + R − My ⎨ ⎪F = 16fe dMy + 4fe2 d 2R2 − 2fe dR ⎩ y
(
)
(3)
With infilling grout: (Case-a′ in Fig. 20)
Fy
(1)
2
(Case-b in Fig. 19)
= fc dR
(4)
(Case-b′ in Fig. 20) Fy
⎧ 2 = fe d (y − x ) ⎪ t=y+x ⎨ y ⎪ My = fe dy 2 + R − fe dx (t − ⎩
(
Fy =
)
Fy
x 2
+ R)
⎧ 2 = fc d (R − y ) ⎪ (R − y )2 M = fc d 2 ⎨ y ⎪ F = 8f dM y c ⎩ y
(2)
4fe d (4My + fe dt 2) + 4fe2 d 2 (t + 2R)2 − 2fe d (t + 2R)
(Case-c′ in Fig. 20)
(Case-c in Fig. 19) 9
(5)
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Fig. 18. comparison of load-displacement curves.
where Fy is the load-carrying capacity of the joint (kN); fe is the embedment strength in the bamboo member; fc is the compression strength of the grout; t is the thickness of the bamboo; d is the bolt diameter; R is the internal diameter of the bamboo; My is the bolt yield moment.
Fy
⎧ 2 = fc dR + fe dx ⎪ R2 x M = fc d 2 + fe dy 2 + R − My ⎨ y ⎪ F = 4fe d (4My − fc dR2 + fe dR2) + 2dR (fc − fe ) ⎩ y
(
)
(6)
Plastic hinge
Plastic hinge
(a) Yielding of the bamboo and (b), (c) Yielding of the bolt with one plastic hinge and two plastic hinges Fig. 19. Load-resistance mechanism of the dowelled joint. 10
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Plastic hinge
Plastic hinge
(a’) Yielding of the grout and (b’), (c’) Yielding of the bolt with one plastic hinge and two plastic hinges Fig. 20. Load-resistance mechanism of the dowelled joint with infilling grout.
yielding of the bolt and will introduce an increase of up to 82% in the ultimate load-resistance. (2) Bearing capacities of the dowelled joints are evidently influenced by the thickness of the bamboo, bolt strength, and grout strength. Increasing the bolt strength is considered the most effective way to induce higher bearing capacity. The variation of end spacing does not significantly affect the joint capacity but can lead to brittle failure at the end. (3) The analytical predicted bearing capacities for the joints are in good agreement with the experimental results and the relative error is less than 5%. In contrast, the codified method is not recommended for describing the bamboo-steel slotted-in dowelled joint, and the corresponding relative ratio is greater than 35%.
The design of the bolt yielding moment in accordance with EC5 [23] is as follows:
My = 0.3fu, k d 2.6
(7)
where My is the characteristic value for the yield moment, in N∙mm; fu, k is the characteristic tensile strength, in N/mm2; and d is the bolt diameter, in mm. A comparison between experimental correlations, analytical results and EC5 obtained values is shown in Table 3. The results listed in Table 3 show that the analytical predicted ultimate load-resistance values according to Eqs. (1)–(7) are in good agreement with the experimental results; their relative ratio is 0.98, with a standard deviation of 0.09. It can be concluded from Table 3 that the failure mode model proposed in EC5 is not recommended for describing the bamboo-steel slotted-in dowelled joint, as it results in a corresponding ratio of 1.38, with a standard deviation of 0.5. This is due to that the failure modes included in EC5 were governed by the load-carrying capacity of the fasteners and the thickness of the timber, while the formation mode of plastic hinges is different and the brittle failure mode is omitted when compares with bamboo joints.
Comparison between FEM and laboratory test shows the numerical approach has limitation for modelling brittle fracturing problems. The authors are going to conduct a series of tests on the Moso bamboo in order to establish the fracture criterion of the material, and thus can improve the proposed model in the future. Declaration of Competing Interest
5. Conclusion
The authors declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
The slotted-in dowelled type joint for bamboo-to-steel connections, which can be used in the construction of prefabricated bamboo structures, is presented in this study. Both experimental and numerical approaches are applied to reveal the failure mechanism and load resistance of dowelled joints with and without infilling grout. The main conclusions can be drawn as follows:
Acknowledgement The authors are grateful for the financial support of the National Major Science and Technology Projects of China (2016YFC0701400) and China Postdoctoral Science Foundation (17Z102060052).
(1) The application of infilling grout is demonstrated to be an effective solution for enhancing joint capacity. The method can postpone the Table 3 Comparison of results from different approaches. Specimen
My (Nm)
Test results (kN)
EC5 results (kN)
Failure mode (EC3)
Analytical (kN)
Failure mode (analytical)
EC5/test
Analytical/test
DJ-1 DJ-2 DJ-3 DJ-4 DJ-5 DJ-6 DJ-7 DJD-2 DJDI-1 DJDI-2
53.49 95.55 95.55 153.49 153.49 153.49 153.49 153.49 95.55 95.55
5.34 7.50 7.50 11.30 13.64 12.40 13.20 19.52 35.40 35.50
7.04 10.84 10.66 15.22 21.45 21.45 21.45 42.89 19.64 19.64
g g g g h h h h k k
5.20 6.89 7.65 8.95 12.50 12.41 12.48 21.12 37.99 37.99
c a a a c c c c b′ b′
1.32 1.45 1.42 1.35 1.57 1.73 1.62 2.20 0.55 0.55
0.99 0.92 1.02 0.79 0.92 1.00 0.95 1.08 1.07 1.07
1.38 0.50
0.98 0.09
Mean S.D.
11
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Appendix A. Supplementary material
2007;19:965–71. [21] Schoenmakers JCM, Jorissen AJM. Failure mechanisms of dowel-type fastener connections perpendicular to grain. Eng Struct 2011;33:3054–63. [22] Zarnani P, Quenneville P. Splitting strength of small dowel-type timber connections: rivet joint loaded perpendicular to grain. J Struct Eng 2014;140:1–13. [23] BSEN. 1995-1-1 Design of timber structures: part 1-1: General rules and rules for buildings. Brussels: European Committee for Standardization; 2004. [24] ANSI. National design specification (NDS) for wood construction. Washington, DC: American Forest & Paper Association, Inc.; 2005. [25] Johansen KW. Theory of timber connections. Int Assoc Bridge Struct Eng 1949;1949:249–62. [26] Daudeville L, Yasumura M. Failure analysis of timber bolted joints by fracture mechanics. Mater Struct 1996;29:418–25. [27] Yasumura M, Daudeville L. Fracture of multiply-bolted joints under lateral force perpendicular to wood grain. J Wood Sci 2000;46:187–92. [28] Xu QF, Harries K, Li XM, Liu Q, Gottron J. Mechanical properties of structural bamboo following immersion in water. Eng Struct 2014;81:230–9. [29] Wakchaure M, Kute S. Effect of moisture content on physical and mechanical properties of bamboo. Asian J Civ Eng 2012;13:753–63. [30] EN26891. Timber structures. Test methods. Determination of embedding strength and foundation values for dowel type fasteners: European Committee for Standardization; 1993. [31] ASTM. Standard test methods for bolted connections in wood and wood-based products. ASTM D-5652. West Conshohocken, PA, US: American Society for Testing and Materials; 1995. [32] Kharouf N, McClure G, Smith I. Fracture modelling of bolted connections in wood and composites. J Mater Civ Eng 1999;345–52. [33] Kharouf N, McClure G, Smith I. Elasto-plastic modeling of wood bolted connections. Comput Struct 2003;81:747–54. [34] Moses DM, Prion HGL. A three-dimensional model for bolted connections in wood. Can J Civ Eng 2003;30:555–67. [35] Chen CJ, Lee TL, Jeng DS. Finite element modeling for the mechanical behavior of dowel-type timber joints. Comput Struct 2003;81:2731–8. [36] Santos CL, De Jesus AMP, Morais JJL, Lousada JLPC. Quasi-static mechanical behaviour of a double-shear single dowel wood connection. Constr Build Mater 2009;23:171–82. [37] Hong JP, Barrett D. Three dimensional finite element modelling of nailed connections in wood. J Struct Eng 2010;136:715–22. [38] Xu BH, Bouchair A, Taazout M, Vega EJ. Numerical and experimental analyses of multiple-dowel steel-to-timber joints in tension perpendicular to grain. Eng Struct 2009;31:2357–67. [39] Xu BH, Taazout M, Bouchair A, Racher P. Numerical 3D finite element modelling and experimental tests for dowel-type timber joints. Constr Build Mater 2009;23:3043–52. [40] Abaqus-6.13. Analysis User's Manual: SIMULIA; 2013. [41] Sawata K, Yasumura M. Estimation of yield and ultimate strengths of bolted timber joints by nonlinear analysis and yield theory. J Wood Sci 2003;49:383–91.
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2019.109952. References [1] Awaludin A, Andriani V. Bolted bamboo joints reinforced with fibers. Proc Eng 2014;95:15–21. [2] Yu WK, Chung KF, Chan SL. Axial buckling of bamboo columns in bamboo scaffolds. Eng Struct 2005;27:61–73. [3] Yu WK, Chung KF, Tong YC. Full scale tests of bamboo scaffolds for design development against instability. Adv Build Technol 2002;1:661–8. [4] Yu WK, Chung KF, Chan SL. Column buckling of structural bamboo. Eng Struct 2003;25:755–68. [5] Villegas L, Morán R, García JJ. A new joint to assemble light structures of bamboo slats. Constr Build Mater 2015;98:61–8. [6] Amada S, Sun U. Fracture properties of bamboo. Compos B Eng 2001;32:451–9. [7] Chung KF, Yu WK. Mechanical properties of structural bamboo for bamboo scaffordings. Eng Struct 2002;24:429–42. [8] Lo TY, Cui HZ, Leung HC. The effect of fiber density on strength capacity of bamboo. Mater Lett 2004;58:2595–8. [9] Kaminsky S. Engineered bamboo houses for low-income communities. Eng Struct 2013;91:14–23. [10] Xiao Y, Zhou Q, Shan B. Design and construction of modern bamboo bridges. J Bridge Eng 2010;15:533–41. [11] Trujillo DJA, Ramage M, Chang WS. Lightly modified bamboo for structural applications. Construct Mater 2013;166:238–47. [12] Li HT, Zhang QS, Huang DS, Deeks AJ. Compressive performance of laminated bamboo. Compos B Eng 2013;54:319–28. [13] Sharma B, Gatóo A, Ramage MH. Effect of processing methods on the mechanical properties of engineered bamboo. Constr Build Mater 2015;83:95–101. [14] Sharma B, Gatóo A, Bock M, Ramage M. Engineered bamboo for structural applications. Constr Build Mater 2015;81:66–73. [15] Sinha A, Way D, Mlasko S. Structural performance of glued laminated bamboo beams. J Struct Eng 2014;140:04013021. [16] Mahdavi M, Clouston PL, Arwade SR. A low-technology approach toward fabrication of Laminated Bamboo Lumber. Constr Build Mater 2012;29:257–62. [17] Janssen J. Bamboo in building structures. Holland: Eindhoven University of Technology; 1981. [18] Gernot M. Building with Bamboo. Basel: Birkhauser Verlag AG; 2012. [19] Jayanetti D, Follet P. Bamboo in construction: an introduction. International Network for Bamboo and Rattan; 1998. [20] Murty B, Smith I, Asiz A. Wood and engineered wood product connections using small steel tube fasteners: applicability of European yield model. J Mater Civ Eng
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Experimental and numerical investigations on load-carrying capacity of dowel-type bolted bamboo joints Feiliang Wanga,b,c, Jian Yanga,b,c,d,
⁎
a
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China c Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, PR China d School of Civil Engineering, University of Birmingham, Birmingham B15 2TT, UK b
A R T I C LE I N FO
A B S T R A C T
Keywords: Bamboo Prefabricated structures Dowelled joints Infilling grout Laboratory test Numerical simulations Design model
Bamboo has been widely used for structural and non-structural purpose, for example as scaffolding and cladding for many centuries in South East Asian countries such as China and India, due to its high strength-to-weight ratio, low price and recyclability. In today’s trend of sustainable development, there is a renewed interest in the use of bamboo for modern prefabricated structures. In this paper, dowel-type bamboo joints are introduced for prefabricated bamboo structures. An experimental study has been undertaken to investigate the structural behaviour and the failure mechanisms of the dowelled joints with varying configurations. Test results reveal that the ductile failure mode of the bamboo occurred when large end spacing was applied, and the infilling grout can significantly increase the load-carrying capacity of the dowelled joint. Three-dimensional finite element models were established and validated using available experimental data. Extensive parametric studies were carried out based on the simulation approach to investigate the effects of key influencing variables involved, i.e. hole clearance, friction coefficient, bolt strength, bamboo thickness, grout strength and end spacing. Moreover, analytical models for designing the dowelled joints are proposed and compared with the current codified approach.
1. Introduction Bamboo grows rapidly and matures to structural strength within five years, so it can be harvested more quickly than conventional materials such as timber. It is an important construction material particularly in rural and remote areas where access to steel or reinforced concrete production and heavy machinery is limited [1]. For instance, Kao Jue (Bambusa pervariabilis) or Moso bamboo (Phyllostachys pubescens) have been widely adopted in South East Asia as scaffoldings and working platforms [2–4]; Guadua angustifolia, which is a native species of bamboo, has been frequently used in the construction of rural houses and temporary structures in the South and Central America [5]. As a natural composite material, bamboo is longitudinal reinforced by strong fibres [6] and has excellent mechanical properties against compression and bending. The compressive strength for Moso bamboo can up to 70 MPa [7] and the thickness of the bamboo was found to be in direct proportion to its outer diameter, and the bamboo with greater thickness exhibits higher load capacity [8]. Nowadays, construction applications of bamboo, such as in low-rise
⁎
dwellings [1,9], short-span bridges [10], long-span roofs [11] and laminated structural components [12–16], are experiencing a rapidlygrowing market recently as increasing demands for sustainable building materials and prefabricated structures. The safety and serviceability of such bamboo structures are often governed by the capacity of the connections between bamboo culms. Many types of structural joints have been proposed to connect bamboo culms as described in various documents [17,18]. Traditional joints were made by cutting curved surfaces into the culms, to form a fish-mouth joint (see Fig. 1), which was intended to increase the contact area between the culms. Later on, bamboo joints evolved to incorporate pins, bolts, hooks [19], and fibre reinforced plastic (FRP) that is used to wrap the bamboo connection [1]. In order to fulfil the requirements for off-site construction, efforts have to be made to design a bamboo joint that allows modern industrialized production and which needs a minimum operation on site. To this end, a novel dowelled bamboo joint has been presented in the paper and its structural performance has been examined. The joint, which constructed with slotted-in T-shape steel connectors, can adapt
Corresponding author at: Mulan Building A727, Shanghai Jiao Tong University, Dongchuan Road 800, 201100 Shanghai, China. E-mail address: [email protected] (J. Yang).
https://doi.org/10.1016/j.engstruct.2019.109952 Received 14 June 2019; Received in revised form 7 November 2019; Accepted 15 November 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Feiliang Wang and Jian Yang, Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.109952
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The current code of practice provides the design approaches for dowelled wood joints [23,24]. Such codified methods were based on the European Yield Model proposed by Johansen [25]. However, the Johansen model only considers ductile failure modes, which is deemed as the dominant mode for timber structures. Brittle failure modes, such as splitting and shear-out of the wood in multiple-bolted wood joints [26,27], or failure of the bamboo which the slotted-in bamboo-to-steel dowelled joint often experiences, were omitted. Moreover, compared with extensive numerical and experimental studies on dowelled joints in timber structures, only limited physical test data or design models are available for slotted-in dowelled joints in bamboo structures. To this end, a series of laboratory tests have been devised and carried out in the study to investigate the behaviour of bamboo-to-steel dowelled joints with and without infilling grout. Numerical models were established and validated against the experimental results. Extensive parametric studies were conducted based on the established modelling technique to reveal the effect of key design parameters on the joint. Finally, an analytical approach is proposed to predict the load-resistance capacity of the dowelled joint in bamboo structures. The aim of this paper is to provide an aid for engineers in the design and construction of bambooto-steel dowelled type connections in prefabricated bamboo structures.
Fish-mouth joints
Fig. 1. An example of fish-mouth joints.
to culms with varying diameters and can be easily produced in the factory with a standard dimension, and only bolts and steel ties are needed in-situ for assembly, as shown in Fig. 2. Test results from various sources imply that with timber, for single or multiple fastener connections loaded either longitudinally, transversely or at an angle to the grain, failure of the wood can be the dominant failure mode. It was found that wood connections using small diameter tight-fit steel tube fasteners can produce a ductile response while at the same time attaining high strength properties [20]. Based on experimental works, a mechanical model was proposed to predict the load-bearing capacity of dowel-type fastener connections perpendicular to the grain in timber structures and the classification of these connections in terms of ductility was provided [21]. In addition, an analytical procedure was proposed to predict the splitting resistance of riveted connections under perpendicular-to-grain loading. The closedform analytical method, which takes into account the partial or full width splitting failure modes of wood, was confirmed by the existing tests and has more precise predictions on the effect of different connection configuration parameters, such as connection width and length, fastener penetration depth, loaded and unloaded edge distances, end distance, and member thickness. [22].
(a) Bamboo preparation
(d) End-column connection
2. Experimental methods A series of laboratory tests on bamboo-to-steel dowel-type joints was conducted in the structural laboratory of Shanghai Jiao Tong University. In the test, the adopted bamboo type was Moso bamboo, which is an abundant resource in southern China and has good mechanical performance and quick growth speed. The prepared bamboo specimens were harvested at the age of 3 years and have an average density of 0.7 g/cm3. As the previous study showed that the mechanical properties of bamboo samples would undergo degradation when associated with water, and the bamboo material has a better mechanical performance when the moisture content is less than 15% [28,29]. Therefore, all bamboo specimens used in the test were dried in oven at up to 100 °C in advance and were supplied by Hape International (Ningbo) Ltd. The test was conducted in accordance with the EN26891
(b) Steel connectors
(e) Sub-assemblage
(c) Slotted-in joint
(f) Assembly on site
Fig. 2. Construction process of bamboo structures with the proposed dowelled joints. 2
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200 T-1 T-2 T-3 C-1 C-2 C-3 C-4
180 160
(a) Tension test setup
Stress (MPa)
140
(b) Culm compression test
120 100 80 60 40 20 0 0
10
20
30
Strain (%)
40
50
Fig. 4. Stress-strain curves of tested specimens.
(c) Tested coupons under tension
with the double bolts (DJD; see Fig. 7(b)) and the dowelled joint with the double bolts and infilling grout (DJDI; see Fig. 7(c)). The configurations of the T-shape steel connectors and bolt plates are illustrated in Fig. 7(d–f). It should be noted that the connector with the slotting (see Fig. 7(d)) was used for the specimens with single bolt and the connector with bolt holes (see Fig. 7(e)) was used for the specimens with double bolts. The bolt diameters range from 8 mm to 12 mm in this study. The bamboo diameter at the connections varied from 90 mm to 110 mm and the end spacing from 40 to 100mm . A static load was applied under static using MTS-SANS test machine with a maximum loading capacity of 100 kN. The load was applied through the displacement-controlled mode and the test was terminated when the load was reduced by 15% of the ultimate load or when significant damage to the connection was observed, whichever occurred first. The characteristics of the test specimens from three groups are plotted in Fig. 8. The grout used for DJDI-1 and DJDI-2 was provided from the supplier and has a nominal yield stress of 50 MPa and a maximum expansion rate of 0.04%. It is a high-strength grout material made from cementations materials, fine aggregate, and admixture. Before infilling this grout by injection pipe (see Fig. 8(c)), both ends of the bamboo members had to be sealed by means of silicone glue for leakage prevention.
(d) Tested coupons under compression
Fig. 3. Coupon test setup.
standard [30].
2.1. Test setup Coupon tests were initially conducted to assess the material properties of the Moso bamboo. Two groups of tests were performed: the parallel-to-grain tensile test (see Fig. 3(a)) and the parallel-to-grain culm compression test (see Fig. 3(b)). The chosen specimens were labelled with ‘T’ and ‘C’ respectively. The coupons in the tension test were cut from the culms aligned in the parallel-to-grain direction (See Fig. 3(c)). Coupon tests were carried out by using a Zwick Roell-Z100 materials testing system (MTS) and the loading rate was 2 mm/min. Table 1 summarizes the characteristics of the coupons and the recorded test data. It shows that the average parallel-to-grain tensile and compressive strengths for the Moso bamboo are 147.7 MPa and 48.2 MPa, respectively, with a modulus of elasticity of 910 MPa. The obtained stress-strain curves are plotted in Fig. 4. As depicted in the figure, a fair consistency can be found in the results. In the elastic stage, the specimens under tension and under compression exhibit a similar stress-strain relationship. The specimens show brittle failure mode under tension and ductile failure mode under compression. In order to reveal the capacity and failure mechanism of the dowelled joints (Fig. 5), specimen connections with and without infilling grout under a tensile load were further tested. In the test, eleven dowelled connected specimens were prepared and tested using to the test set-up shown in Fig. 6. The descriptions of the specimens, including geometric dimensions and bolt configurations, are summarized in Table 2. In the table, three groups of connections are included: the dowelled joint with the single bolt (DJ; see Fig. 7(a)), the dowelled joint
2.2. Experimental results The failure modes for tested specimens are plotted in Fig. 9, and the corresponding ultimate loads are tabulated in Table 2. As shown in Fig. 9, five different failure modes were observed in the test and the failure behaviours for all specimens can be divided into two categories: (1) ductile failure (bolt bending failure and/or bamboo bolt-hole bearing); (2) brittle failure (bamboo splitting failure or bamboo shearout failure). The failure modes for the DJ type of connections include (1) bolt bending (Fig. 9(a)); (2) bolt bending and bamboo bearing (Fig. 9(b) and Fig. 9(c)); (3) bamboo splitting (Fig. 9(d) and Fig. 9(g)); and (4) bamboo shear-out (Fig. 9(e) and Fig. 9(f)). The failure modes for the DJD and DJDI type of connections are (1) bamboo splitting
Table 1 Summarized geometric dimensions and material properties for the coupon. Specimen
Width (mm)
Thickness (mm)
Ultimate strength (MPa)
E (GPa)
Specimen
External diameter (mm)
Bamboo thickness (mm)
Ultimate strength(MPa)
T-1 T-2 T-3
12.6 9.88 11.4
8.36 8.36 8.36
136.2 157.4 149.5
0.876 1.020 0.848
C-1 C-2 C-3 C-4
110 110 110 110
9.3 9.3 9.3 9.3
45.1 53.0 45.6 49.2
147.7
0.91
Mean
Mean
Note: T-represents tension test; C-represents compression test. 3
48.2
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Beam element Dowelled joint
Dowelled joint Column
Brace
Column element
Beam
(a) Brace joint
Beam
(b) beam-to-column joint
Fig. 5. Plot of representative dowelled joints.
(Fig. 9(h)) and (2) grout cracking (Fig. 9(i)). In Table 2, the ductility is defined as the joint displacement at the ultimate load divided by the displacement at the apparent yield load. The apparent yield load is evaluated based on the 5% offset method. In this method, a straight line to the initial linear portion of the curve is shifted in the positive x-direction by 5% of the bolt diameter, and the apparent yield load is defined as the intersection of this line and the load-displacement curve [31], as illustrated in Fig. 10. It is worth noting that the test on specimen DJD-1 was not completed due to the recording program auto-terminated during the test. According to the load-deflection response of DJ, DJD and DJDI specimens plotted in Fig. 10, the behaviour of each specimen shows two stages before the failure occurs: (1) Elastic stage: all specimens behave elastically at the initial stages of loading, and the bolt shows flexural behaviour due to the applied bending moment at this stage. The maximum load can up to approximately 75% of the ultimate load at this stage; (2) Elastic-to-plastic stage: the deformation develops quickly with a limited increase in applied load. Meanwhile, yielding occurs on the mid-section of the bolt and then followed by the failure of the bamboo. A post-failure stage with large-deformation behaviour can be noticed for the DJDI specimens after the ultimate load is attained and the failure behaviour is the cracking of the grout. The load-resistance capacities of the joints tested are dramatically influenced by the bolt diameter and infilling grout, as implies in Fig. 11. The ultimate load-resistance increases with increasing bolt diameter, and the joint with M10 bolt (7.50 kN) has an ultimate load which is 40% higher than that with M8 bolt (5.34 kN), and 40% lower than that with M12 bolt (12.64 kN). When comparing between the DJD and DJDI
Fig. 6. Test setup.
Table 2 Specimen design details and test results. Specimen
Bamboo length (mm)
Bamboo diameter (mm)
Thickness (mm)
End spacing (mm)
Top and bottom Bolt diameter (mm) × number
Failure load (kN)
Failure mode
Ductility
DJ-1 DJ-2
269 269
90 90
7.3 7.3
100 100
M8 × 1, M8 × 1 M10 × 1, M10 × 1
5.34 7.5
4.4 2.6
DJ-3
279
100
7.9
100
M12 × 1, M12 × 1
11.3
DJ-4 DJ-5# DJ-6# DJ-7# DJD-1# DJD-2# DJDI-1# DJDI-2#
191 301 226 268 302 301 299 298
100 110 110 110 109 110 112 107
8.1 11.42 11 11.3 10.2 10.2 10.9 10.7
50 40 40 50 100 100 100 100
M10 M12 M12 M12 M10 M10 M10 M10
7.5 13.64 12.4 13.2 N/A* 19.66 35.89 35.62
Bolt bending Bolt bending and bamboo bearing Bolt bending and bamboo bearing Bamboo splitting Bamboo shear-out Bamboo shear-out Bamboo splitting Bamboo splitting Bamboo splitting Grout cracking Grout cracking
Note: # – represents the joint with bolt plates. 4
× × × × × × × ×
1, 1, 1, 1, 2, 2, 2, 2,
M12 M12 M12 M12 M10 M10 M10 M10
× × × × × × × ×
1 1 1 1 2 2 2 2
3.8 2.1 2.4 2.0 2.0 N/A 3.3 2.2 1.0
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Fig. 7. Test rigs (unit mm).
bolt and the hole, (2) the interface between the nut and the external surface of the culm and (3) the interface between the grout and the internal surface of the culm, were considered in the model. The interaction property for each contact pair was modelled adopting the penalty method with a friction coefficient of 0.4. The most satisfactory mesh size and friction factor were decided based on extensive sensitive studies. In the model, the bamboo was considered as an isotropic elastic material with the properties based on the coupon test and it was assumed that the section area of each bamboo component is the same along the culm length. The applied stress-strain curves for the grout and bolt are shown in Fig. 13.
joints, it indicates that the infill grout can slow down the yielding of the bolt, and hence its use will greatly enhance the average connection capacity by 82%, from 19.52 kN to 35.45 kN. 3. Numerical analysis The numerical approach has recently attracted extensive engineering attentions in the investigation of the bolted timber joints subjected to a load either perpendicular or parallel to the grain. The finite element (FE) modelling offers an opportunity to consider realistic issues in the lab, such as contact behaviour, material nonlinearly and the deformation of fasteners, meanwhile saving the trial-out cost [32–39]. In this study, a series of three-dimensional numerical models were established to obtain a better understanding of the behaviour of bamboo-to-steel dowelled joints. The commercial finite-element program ABAQUS 6.13.1 [40] was selected for developing the numerical models.
3.2. Model validation and result discussions To validate the numerical modelling approach, the load-displacement curves given by the FE models are compared with those from laboratory tests, as shown in Fig. 14. The yield load for each joint is also attached in the figures. A general set of conclusions can be drawn according to the resistances and failure modes recorded in the FEM. The ductile failure modes occurred when large end spacing (100 mm) was applied (DJ-1 to 3). Take DJ-3 for example (Fig. 14(c)), at the initial stage, the joint yields due to the bending of the bolt, and this is followed by extensive plastic deformation of the bolt-hole, and the maximum plastic deformation is up to 60 mm. The failure mode of DJ-1 to 3 is desirable for engineering application; as the plastic deformation of the bamboo and bolt can be fully developed under this failure phenomenon. Specimens DJ-4 to 7 with short culm length or short end spacing (40 mm) tended to undergo a brittle failure mode. For these specimens, the yielding starts on the mid-span of the bolt and no obvious damage can be seen on the outer surface of the bamboo at the initial stage. The crack or fracture then appears along the bolt-hole, and the failure occurs instantaneously without any pre-warning as the curve shows a sudden
3.1. Modelling process The geometry of a finite element model is shown in Fig. 12(a) where the 8-node solid element C3D8R was used for the steel bolt, grout (for DJDI only) and the bamboo culm. In order to increase the computing efficiency, only 1/2 of the connection was modelled for the DJ specimen and 1/4 was modelled for the DJD and DJDI specimens. A symmetrical condition was enforced to inhibit horizontal displacement along the centreline, a displacement controlled point load was applied in the mid-span section of the top-bolt, and the translation movement of the bottom bolt was restrained to represent the pinned support provided by the bottom T-shaped connector (see Fig. 12(a)). The overall model was meshed with a general mesh size of 20 mm, and a refined mesh size 10 mm was applied for the bolt-hole region, as shown in Fig. 12(b). Three contact pairs, namely (1) the interface between the
(a) DJ
(b) DJD Fig. 8. Photographs of the test specimens. 5
(c) DJDI
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(a) DJ-1
(b) DJ-2
(e) DJ-5
(c) DJ-3
(f) DJ-6
(d) DJ-4
(g) DJ-7
(h) DJD-2
(i) DJDI-1 and DJDI-2 Fig. 9. Failure modes.
interface between grout and bamboo gradually separates. With an increasing applied load, failure occurs when the grout on the contact region becomes crushed. At that moment, the load-displacement curves of the DJDI joints show that the joints experience a sudden load decrease after reaching the maximum load, but they can still resist the applied load before completely failing due to the friction between the interface of grout and bamboo. Overall, numerically achieved load-to-displacement response is
decline of the load-resistance. Therefore, a better ductility can be achieved when the flexural capacity of the bolt (DJ-1) or the bearing elongation (DJ-2 and DJ-3) can be fully developed (as shown in Table 2). For connections with infilling grout (DJDIs), the deformations of the joints are quite limited in the initial linear stage, and the bending of the bolt and bearing deformation of the bamboo bolt-hole is relatively small. Then, the first crack appears on the bolt-to-grout surface and the
6
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Load (kN)
30 25
similar to that from experimental observation, as shown in Fig. 14. The numerically obtained the load-slip curves for the specimens are found to be steeper than the experimental curves, especially for those failed at brittle splitting, because the fracture criterion of the bamboo material was ignored in the model. Fig. 15 indicates that the ultimate load from the numerical study is in close correlation with experimental data and with the average error of 1.5%. Fig. 16 shows the embedment strength of the bamboo member (ultimate stress to crush the wood) against displacement responses for the specimens with ductile failure behaviour. It can be concluded that the average embedment strength of Moso bamboo is 47.2 MPa, which is very close to the compression strength of the bamboo. Contour plots generated from the numerical results illustrate the stress development on the joint at the ultimate loads. In Fig. 17, the DJ-2 specimens are found to have formed one plastic hinge on the mid-span section of the bolt (DJ1-3 all show the same pattern); DJ-5 has formed three plastic hinges, the first on the bolt mid-span section, and the rest on the bolt-bamboo interface (DJ-4 to 7 all show the same pattern); the DJDI specimens are also found to have one plastic hinge, with the yielding of the bolt and the cracking of the grout. For the DJDI joints, the second plastic hinge is not formed due to the shear slip on the interface between grout and bamboo.
DJ-1 DJD-2 DJDI-1 Yield load-DJ Yield load-DJD Yield load-DJDI
35
3.2, 27.5
20 15 10
11.5, 11.5
4.5, 4.0
5 0 0
5
10
15
20
25
30
35
40
Displacement (mm)
Fig. 10. Typical load-displacement curves for DJ, DJD and DJDI joints. 40 30 25 20
3.3. Parametric studies
15
The numerical approach was undertaken to optimize the design of the bamboo-to-steel dowelled joints. The following variables of the DJ1 model were modified in the analysis, (1) hole clearance, (2) friction coefficient between the bamboo and bolt, (3) bolt strength, (4) bamboo thickness, (5) grout strength and (6) end spacing, and only one variable was changed at a time during the analysis. As shown in Fig. 18(a), the ultimate load is slightly influenced by the bolt-hole clearance between the bolt and the hole. The increase from 0 mm to 1 mm leads to a reduction of 1.8% in the ultimate load, and the increase from 1 mm to 2 mm lead to a reduction of 1.5%. It can be concluded that a decrease in the clearance will lead to a growth in the initial stiffness of the joint. Fig. 18(b) shows that the friction coefficient almost has no effect on the capacity of the dowelled joint as the horizontal movement of the bolt was not a critical factor under such load scenario. The effect of bolt strength is evident from the load vs. deflection curves in Fig. 18(c). The grade of bolts used are G4.8 ( f y = 320 MPa), G8.8 ( f y = 640 MPa) and G10.9 ( f y = 900 MPa). As the strength of the bolt increases, the ultimate load of the dowelled joint increases. It shows that the ultimate bearing capacity of the joint with the G8.8 bolt is higher by 82% than that of the joint with the G4.8 bolt, and the joint bearing capacity with the G10.9 bolt is higher by 29% than that of the G8.8 bolt. The bolt strength seems to play an important role because failure initiates at the bolt prior to the bamboo when bolt diameter is relatively small. As expected, the bamboo thickness could improve the ultimate capacity of the dowelled joint, as demonstrated by the numerical results given in Fig. 18(d). When the thickness changes
10 5 0
M8
M10
M12
DJD
DJDI
Fig. 11. Comparison of ultimate loads between specimens with varying configurations.
(a) Geometric model (DJ)
(b) Meshed model (DJDI)
Fig. 12. Geometric model and mesh pattern.
Tension
Compression 60
Stress (MPa)
50 40 Compression
30
Tension
20 10 0 0
0.005
0.01
Strain
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
0.015
850
Stress (MPa)
Ultimate load (kN)
35
800 750 700 650 600
0
0.04
0.08
Strain
(a) Grout
(b) Bolt
Fig. 13. Stress-strain curves for bolt and grout in the FE model. 7
0.12
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Fig. 14. Comparison of load-displacement curves between test and FEM.
failure occurs. A similar trend of the load vs. deflection response can be observed in Fig. 18(e) between models with different grout yield strengths. This shows that the increase in the joint ultimate resistance is 15.0%, as the yield strength of the grout increases from 30 MPa to 50 MPa. The effect of end spacing on the ultimate joint load is insignificant (see Fig. 18(f)). However, the failure performance of the
from 5 mm to 7 mm, and from 7 mm to 9 mm, this leads to a 5% and 6% growth, respectively, in the ultimate load. It indicates that the effect of bamboo thickness on the load-carrying capacity is less significant when compares with bolt strength for DJ-1 specimen, which is because of that the bolt diameter in the specimen is relatively small and hence the bearing strength of the bamboo was not fully developed when the 8
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40 35
Bolt yielding
Ultimate laod (kN)
30 25 20 15 10 5 0 Test FEM
DJ-1 5.34 5.45
DJ-2 7.5 8.06
DJ-3 7.5 9.64
DJ-4 11.3 7.74
DJ-5 13.64 13.1
DJ-6 12.4 13.1
DJ-7 13.2 13
DJD-2 DJDI-1 DJDI-2 19.52 35.4 35.5 20 36.5 36.5
(a) DJ-2
Fig. 15. Comparison between test results and FEM outcomes.
Plastic hinge
(b) DJ-5 Fig. 16. Typical bearing stress – displacement curves.
Plastic hinge dowelled joint could be influenced significantly by reducing the end spacing of the bolt. It can be concluded from Table 2 that the dowelled joint with end spacing less than 50 mm will lead to brittle failure.
4. Analytical approaches Based on the yield theory proposed by Johansen [25] and the theoretical model of the wood dowelled joint presented by Sawata and Yasumura [41], analytical design models of bamboo-to-steel slotted-in dowelled joints are presented in this section. The failure mode of the dowelled joints could be: (a) yielding of the bamboo, (b) yielding of the bolt with one plastic hinge and (c) yielding of the bolt with two plastic hinges, as shown in Fig. 19. The failure mechanisms of the dowelled joints with infilling grout are: (a′) yielding of the grout, (b′) yielding of the bolt with one plastic hinge and (c′) yielding of the bolt with two plastic hinges, as shown in Fig. 20. Equilibrium equations for dowelled joints with a slotted-in steel plate are listed as follows: Without infilling grout: (Case-a in Fig. 19)
Fy 2
= fe dt
(c) DJDI-1 Fig. 17. Stress contour for DJ and DJDI connections. Fy
⎧ 2 = fe dy ⎪ y My = fe dy 2 + R − My ⎨ ⎪F = 16fe dMy + 4fe2 d 2R2 − 2fe dR ⎩ y
(
)
(3)
With infilling grout: (Case-a′ in Fig. 20)
Fy
(1)
2
(Case-b in Fig. 19)
= fc dR
(4)
(Case-b′ in Fig. 20) Fy
⎧ 2 = fe d (y − x ) ⎪ t=y+x ⎨ y ⎪ My = fe dy 2 + R − fe dx (t − ⎩
(
Fy =
)
Fy
x 2
+ R)
⎧ 2 = fc d (R − y ) ⎪ (R − y )2 M = fc d 2 ⎨ y ⎪ F = 8f dM y c ⎩ y
(2)
4fe d (4My + fe dt 2) + 4fe2 d 2 (t + 2R)2 − 2fe d (t + 2R)
(Case-c′ in Fig. 20)
(Case-c in Fig. 19) 9
(5)
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Fig. 18. comparison of load-displacement curves.
where Fy is the load-carrying capacity of the joint (kN); fe is the embedment strength in the bamboo member; fc is the compression strength of the grout; t is the thickness of the bamboo; d is the bolt diameter; R is the internal diameter of the bamboo; My is the bolt yield moment.
Fy
⎧ 2 = fc dR + fe dx ⎪ R2 x M = fc d 2 + fe dy 2 + R − My ⎨ y ⎪ F = 4fe d (4My − fc dR2 + fe dR2) + 2dR (fc − fe ) ⎩ y
(
)
(6)
Plastic hinge
Plastic hinge
(a) Yielding of the bamboo and (b), (c) Yielding of the bolt with one plastic hinge and two plastic hinges Fig. 19. Load-resistance mechanism of the dowelled joint. 10
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Plastic hinge
Plastic hinge
(a’) Yielding of the grout and (b’), (c’) Yielding of the bolt with one plastic hinge and two plastic hinges Fig. 20. Load-resistance mechanism of the dowelled joint with infilling grout.
yielding of the bolt and will introduce an increase of up to 82% in the ultimate load-resistance. (2) Bearing capacities of the dowelled joints are evidently influenced by the thickness of the bamboo, bolt strength, and grout strength. Increasing the bolt strength is considered the most effective way to induce higher bearing capacity. The variation of end spacing does not significantly affect the joint capacity but can lead to brittle failure at the end. (3) The analytical predicted bearing capacities for the joints are in good agreement with the experimental results and the relative error is less than 5%. In contrast, the codified method is not recommended for describing the bamboo-steel slotted-in dowelled joint, and the corresponding relative ratio is greater than 35%.
The design of the bolt yielding moment in accordance with EC5 [23] is as follows:
My = 0.3fu, k d 2.6
(7)
where My is the characteristic value for the yield moment, in N∙mm; fu, k is the characteristic tensile strength, in N/mm2; and d is the bolt diameter, in mm. A comparison between experimental correlations, analytical results and EC5 obtained values is shown in Table 3. The results listed in Table 3 show that the analytical predicted ultimate load-resistance values according to Eqs. (1)–(7) are in good agreement with the experimental results; their relative ratio is 0.98, with a standard deviation of 0.09. It can be concluded from Table 3 that the failure mode model proposed in EC5 is not recommended for describing the bamboo-steel slotted-in dowelled joint, as it results in a corresponding ratio of 1.38, with a standard deviation of 0.5. This is due to that the failure modes included in EC5 were governed by the load-carrying capacity of the fasteners and the thickness of the timber, while the formation mode of plastic hinges is different and the brittle failure mode is omitted when compares with bamboo joints.
Comparison between FEM and laboratory test shows the numerical approach has limitation for modelling brittle fracturing problems. The authors are going to conduct a series of tests on the Moso bamboo in order to establish the fracture criterion of the material, and thus can improve the proposed model in the future. Declaration of Competing Interest
5. Conclusion
The authors declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
The slotted-in dowelled type joint for bamboo-to-steel connections, which can be used in the construction of prefabricated bamboo structures, is presented in this study. Both experimental and numerical approaches are applied to reveal the failure mechanism and load resistance of dowelled joints with and without infilling grout. The main conclusions can be drawn as follows:
Acknowledgement The authors are grateful for the financial support of the National Major Science and Technology Projects of China (2016YFC0701400) and China Postdoctoral Science Foundation (17Z102060052).
(1) The application of infilling grout is demonstrated to be an effective solution for enhancing joint capacity. The method can postpone the Table 3 Comparison of results from different approaches. Specimen
My (Nm)
Test results (kN)
EC5 results (kN)
Failure mode (EC3)
Analytical (kN)
Failure mode (analytical)
EC5/test
Analytical/test
DJ-1 DJ-2 DJ-3 DJ-4 DJ-5 DJ-6 DJ-7 DJD-2 DJDI-1 DJDI-2
53.49 95.55 95.55 153.49 153.49 153.49 153.49 153.49 95.55 95.55
5.34 7.50 7.50 11.30 13.64 12.40 13.20 19.52 35.40 35.50
7.04 10.84 10.66 15.22 21.45 21.45 21.45 42.89 19.64 19.64
g g g g h h h h k k
5.20 6.89 7.65 8.95 12.50 12.41 12.48 21.12 37.99 37.99
c a a a c c c c b′ b′
1.32 1.45 1.42 1.35 1.57 1.73 1.62 2.20 0.55 0.55
0.99 0.92 1.02 0.79 0.92 1.00 0.95 1.08 1.07 1.07
1.38 0.50
0.98 0.09
Mean S.D.
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Appendix A. Supplementary material
2007;19:965–71. [21] Schoenmakers JCM, Jorissen AJM. Failure mechanisms of dowel-type fastener connections perpendicular to grain. Eng Struct 2011;33:3054–63. [22] Zarnani P, Quenneville P. Splitting strength of small dowel-type timber connections: rivet joint loaded perpendicular to grain. J Struct Eng 2014;140:1–13. [23] BSEN. 1995-1-1 Design of timber structures: part 1-1: General rules and rules for buildings. Brussels: European Committee for Standardization; 2004. [24] ANSI. National design specification (NDS) for wood construction. Washington, DC: American Forest & Paper Association, Inc.; 2005. [25] Johansen KW. Theory of timber connections. Int Assoc Bridge Struct Eng 1949;1949:249–62. [26] Daudeville L, Yasumura M. Failure analysis of timber bolted joints by fracture mechanics. Mater Struct 1996;29:418–25. [27] Yasumura M, Daudeville L. Fracture of multiply-bolted joints under lateral force perpendicular to wood grain. J Wood Sci 2000;46:187–92. [28] Xu QF, Harries K, Li XM, Liu Q, Gottron J. Mechanical properties of structural bamboo following immersion in water. Eng Struct 2014;81:230–9. [29] Wakchaure M, Kute S. Effect of moisture content on physical and mechanical properties of bamboo. Asian J Civ Eng 2012;13:753–63. [30] EN26891. Timber structures. Test methods. Determination of embedding strength and foundation values for dowel type fasteners: European Committee for Standardization; 1993. [31] ASTM. Standard test methods for bolted connections in wood and wood-based products. ASTM D-5652. West Conshohocken, PA, US: American Society for Testing and Materials; 1995. [32] Kharouf N, McClure G, Smith I. Fracture modelling of bolted connections in wood and composites. J Mater Civ Eng 1999;345–52. [33] Kharouf N, McClure G, Smith I. Elasto-plastic modeling of wood bolted connections. Comput Struct 2003;81:747–54. [34] Moses DM, Prion HGL. A three-dimensional model for bolted connections in wood. Can J Civ Eng 2003;30:555–67. [35] Chen CJ, Lee TL, Jeng DS. Finite element modeling for the mechanical behavior of dowel-type timber joints. Comput Struct 2003;81:2731–8. [36] Santos CL, De Jesus AMP, Morais JJL, Lousada JLPC. Quasi-static mechanical behaviour of a double-shear single dowel wood connection. Constr Build Mater 2009;23:171–82. [37] Hong JP, Barrett D. Three dimensional finite element modelling of nailed connections in wood. J Struct Eng 2010;136:715–22. [38] Xu BH, Bouchair A, Taazout M, Vega EJ. Numerical and experimental analyses of multiple-dowel steel-to-timber joints in tension perpendicular to grain. Eng Struct 2009;31:2357–67. [39] Xu BH, Taazout M, Bouchair A, Racher P. Numerical 3D finite element modelling and experimental tests for dowel-type timber joints. Constr Build Mater 2009;23:3043–52. [40] Abaqus-6.13. Analysis User's Manual: SIMULIA; 2013. [41] Sawata K, Yasumura M. Estimation of yield and ultimate strengths of bolted timber joints by nonlinear analysis and yield theory. J Wood Sci 2003;49:383–91.
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