Experimental and numerical study on the lateral torsional buckling of full-scale steel-timber composite beams

Abstract

The lateral torsional buckling (LTB) of steel-timber composite (STC) beam with partial interaction was investigated in this paper. The composite beam is constructed by connecting the timber to both flanges of the H-shaped steel with bolts or screws. Twelve push-out specimens were designed to evaluate the shear performance of bolt or screw connectors. It was shown that the slip stiffness and the shear bearing capacity of the connectors increased with the thickness of timber increasing. Then, eight full-scale composite beams with lengths of 6000 mm were studied through bending tests and compared to a bare steel beam. The experimental behaviors of the specimens were identified, including the failure mode, load-deflection relationship and load-strain response. The LTB phenomenon and composite action were discussed by analyzing the strain distribution, stiffness and strength. The results demonstrated that the STC beams fastened with bolts or screws displayed partial composite action. Although the stiffness of the composite beam showed little augmentation, the maximum strength of the composite beam substantially increased by suppressing the LTB phenomenon. A finite element analysis was conducted to reveal the failure mechanism of the specimens with different geometric and physical parameters, including the number of timber layers, the interface shear stiffness and the initial imperfection. It was found that increasing the number of timber layers in the upper flange suppressed the lateral torsional buckling, and the interface shear stiffness was the key factor to control the stiffness and failure modes of STC beams.

Keywords

steel-timber composite beam push-out test composite action interface slip finite element analysis

Introduction

Timber structure is a sustainable and prefabricated structure with mechanical advantages such as light weight and good seismic behavior (Izzi et al., 2018; Van de Lindt et al., 2011a, 2011b), and with ecological advantages such as low carbon dioxide emission and low energy consumption (Green and Karsh, 2012; Gustavsson and Sathre, 2006; Gustavsson et al., 2010). Nonetheless, the low elastic modulus and large mechanical diversity of the timber material inhibit its application to large-span structures. As one of the most commonly used building materials, steel often works with concrete to utilize the tensile strength of steel and the compressive strength of concrete (De Angelis et al., 2019; Liu et al., 2017; Vasdravellis et al., 2015). Similarly, a steel-timber composite (STC) structure is also reasonably designed to utilize the advantages of both materials (Felipe, 2016; Hassanieh et al., 2016a). Steel can dramatically increase the span and space utilization (Smith et al., 2012), while timber provides a fire-retardant coating (Erchinger et al., 2010; Koshihara et al., 2005; Saburou et al., 2002) and delays buckling (Ghanbari Ghazijahani et al., 2015; Koshihara et al., 2005). Additionally, such a combination still maintains the attributes of a natural appearance and rustic feeling. Therefore, STC structures have experienced rapid development in recent years.

Different types of STC structures have been proposed and studied. Hassanieh et al. (2016b, 2017a, 2017b, 2017c, 2018) proposed composite floors consisting of prefabricated Cross-laminated timber (CLT) panels and steel beams connected with different types of shear connectors. Loss et al. (2016a, 2016b, 2018a, 2018b; Loss and Davison, 2017; Loss and Frangi, 2017) studied different arrangements of screws and adhesives at the interface between the steel and CLT panels. Hu et al. (2020) proposed a STC column made of H-shaped steel and glulam. Li et al. (2020) investigated another type of STC column made of L-shaped steel and glulam. In the STC structures, different types of steel have been used to reinforce or strengthen timber beams, such as self-tapping screws (Dietsch and Brandner, 2015), steel plates (Ghanbari Ghazijahani et al., 2017), steel equal-leg angle (Ghanbari Ghazijahani et al., 2020) and steel bars (Soriano et al., 2016). In short, the STC structures showed better mechanical performance than the bare timber structures.

A wood I-joist is a common timber structural member aiming to increase the spans of beams and floors. Nonetheless, the requirements for the strength and deflection of long-span elements usually lead to a large cross-sectional size due to the low elastic modulus of timber. To solve this problem, the wood I-joist could be strengthened using steel bars and composite materials (Ghanbari Ghazijahani et al., 2020; Chen et al., 2021). Additionally, steel could be also used to replace the web and partial flanges to enhance the stiffness and load-carrying capability. Three forms of STC beams have been proposed and studied. The first form involved attaching the timber onto the upper flange of the steel I-beam with adhesive. The results of the bending tests showed that the composite beams with strong adhesive connections had good ductility and a high load-carrying capacity, but the early cracking of the adhesive would reduce the mechanical performance of the beams (Lou et al., 2017). The other form involved attaching the timber onto both flanges of the steel I-beam with adhesive. These results showed consistent conclusions. The adhesive connection was still the governing factor, and a weak connection would lead to partial composite action. Considering the potential decay of the adhesive materials, a third form using mechanical shear connectors like bolts or screws was developed and applied in practical engineering (Chen et al., 2016; Chiniforush et al., 2019; Hassanieh et al., 2016a, 2017b, 2018; Nouri et al., 2019a, 2019b; Tsai and Le, 2018).

The typical composite beams consist of steel I-beam and timber with mechanical shear connectors are summarized in Figure 1. The method of placing the timber onto the upper flange is much comprehensive to utilize the tensile strength of steel as shown in Figure 1(a) (Hassanieh et al., 2017b). Nonetheless, the composite beams shown in Figure 1(b) (Corradi et al., 2007) also satisfied the requirements to reinforce wood buildings without dismantling the existing part. A typical STC beam named Techno Beam shown in Figure 1(c) (Panasonic,1995) was composed of H-shaped steel and two timber flanges, which had been used in Japanese building systems since 1995. Another composite beam made use of the timber to mainly strengthen the shear performance of the steel web (Tsai and Le, 2018), as shown in Figure 1(d). Moreover, the encased steel-timber beams (Felipe, 2016) shown in Figures 1(e) and (f) were also investigated to fully exploit the advantages of timber and steel. Though the third form of STC beam has been applied, little research focused on the instability phenomenon especially for large-span beams.

Figure 1.

Typical composite beams. (a) Timber onto the upper flange (Hassanieh et al., 2017b), (b) timber beneath the lower flange (Corradi et al., 2007), (c) timber placed at both flanges (Panasonic, 1995), (d) timber placed at the web (Tsai and Le, 2018), (e) timber strengthening lower flange and web, and (f) timber strengthening both flanges and web (Felipe., 2016).

The instability of I-beam without lateral support could be classified as local (web or flange local buckling) and global (Lateral torsional buckling (LTB)) failure modes. The LTB occurs to the slender beam that loses its stability in the main bending plane, presenting lateral displacements with additional twisting (Rossi et al., 2020). The LTB of timber beam (Burow HBM and Janowiak, 2006; Hu et al., 2018; Xiao et., 2017) and steel I-beam (Ozbasaran et al., 2015; Sorf and Jandera, 2020; Rossi et al., 2020) have been widely investigated. H-shaped steel beams in timber structures are often connected with floors and cladding through mechanical shear connectors. When such connectors are not tough enough, the H-shaped steel beam is prone to show LTB failure. Though Chinese design standards (GB 50005, 2017; GB 50017, 2017) have given design guidance for laterally supported beams, few provisions are developed to assess the load-carrying capacity of STC beams with LTB. For the STC beam, it is comprehensible that the timber flanges are helpful to provide partial lateral restraint to the H-shaped steel beam. In addition, the timber coating makes it easier to connect the composite beams with other wooden components such as floors and columns.

The previous research suggested that STC beams showed better mechanical properties. In this paper, a STC beam consisting of H-shaped steel and SPF timber with different mechanical shear connections was proposed. The push-out tests were conducted to evaluate the shear performance of the connectors. Four-point bending tests were conducted to study the influences of the timber thickness, connection method, and connector spacing on the LTB of the composite beam. Moreover, numerical analysis was conducted using ANSYS software to simulate the failure process and combined with parametric studies to further optimize the cross-sectional combination of the composite.

Push-out tests

The shear connectors in STC beams mainly withstand the horizontal shear force between the steel and timber. The composite action primarily relies on the stiffness of the shear connectors. Therefore, push-out tests were conducted to obtain the shear stiffness of bolt and screw connectors. The experimental shear stiffness of connectors could be used in theoretical analysis and numerical simulation of the STC beams.

Specimens details

Six types of STC joints were tested to evaluate the shear performance by push-out tests as shown in Figure 2. Two specimens were repeated for each type. The timber and H-shaped steel were connected by two kinds of steel connectors, which were hex head bolts (M6, Class 8.8) and self-taping screws (M4). The diameter of holes drilled on the flange was 1 mm larger than the bolt diameter.

Figure 2.

Schematic views of the push-out specimens. (a) Front view and (b) cross-sectional view.

Material properties

The beam was made of first grade Spruce imported from Canada, which satisfied the design requirements of Chinese standard (GB/T 50708, 2012). The Spruce is one species of the spruce-pine-fir (SPF), with the advantages of high strength-to-weight ratio and dimensional stability. Additionally, it has competitive price benefiting from the sustainable management of forests. The mean moisture content of the timber was 12%. Middle flange hot-rolled H-shaped steel with a strength class of Q235 B was selected. The bending yield strength of connectors and the embedment strength of the Spruce were examined (ASTM F1575, 2017). The mechanical properties of the materials are shown in Table 1 and Table 2.

Table 1.

The mechanical properties of the timber and steel

Materials	Elastic modulus (MPa)			Shear modulus (MPa)			Poisson’s ratio
Materials	E _L	E _R	E _T	G _LR	G _LT	G _RT	μ _LR	μ _RT	μ _TL
Spruce (Bergman (2010))	8900	1139	525	1104	1068	89	0.422	0.530	0.058
H-shaped steel	1.99 × 10⁵			7.65 × 10⁴			0.3

Table 2.

The mechanical properties of connectors

Connector type	d (mm)	L (mm)	Grade	f_yb (MPa)	f_em (MPa)
Bolt	6	100	8.8	468.21 (1.80%)	37.10 (4.3%)
Bolt	6	60	8.8	407.06 (4.10%)	36.09 (9.9%)
Screw	4	45	NA	410.88 (2.00%)	29.41 (10.3%)

Note: f_yb represents the bending yield strength of the connector (MPa); f_em represents the embedment strength of the Spruce (MPa). The value in parentheses represents the coefficient of variation (%).

Setup and instrumentation

For each specimen, four linear variable differential transformers (LVDTs) were used to measure the slip value. The LVDT was fixed on the timber, and its threaded core touched a wood block which was fixed on the steel. The specimens were loaded according to the loading protocol (ASTM D1761-88, 2008). The experimental setup and instrumentation are shown in Figure 3.

Figure 3.

Experimental setup and instrumentation. (a) Overall view and (b) schematic view.

Experimental results

Failure modes

The specimens showed the typical failure modes of timber splitting, timber crushing and plastic hinge failure of bolts or screws, as shown in Figure 4. Initially, no visible damage was observed, but the slip was obvious with load increasing. When the load reached the yield load, the sound of gradual crushing of timber was heard. The timber showed local damage including indentation of bolts and splitting cracks parallel to grain. It was worth noting that one plastic hinge of bolts occurred for specimens with 38 mm timber thickness, while two plastic hinges were observed for specimens with 76 mm timber thickness. The failure modes were similar for specimens connected with screws. No obvious deformation and damage were observed for the H-shaped steel.

Figure 4.

Typical failure modes. (a) Timber, (b) bolts and (c) screws.

Load-slip relationship

The load-slip curves are shown in Figure 5. Since the friction existed at the interface due to the post-tensioning of shear connectors, the specimens behaved as a nearly full composite in the early stage (Yang et al., 2020). When the load reached around 8 kN, the bolts began to slip resulted from the diameter of the hole being slightly larger than that of the bolt. When shear force became greater than the friction, the curve exhibited a linear development. When approaching the yield load, the excessive slip was observed due to the local damage of the timber. The continuous reducing stiffness caused the curve to reach the maximum point. The specimens with screw and bolt connectors experienced similar load-slip relationships, but the maximum load was lower for the specimens with screw connectors.

Figure 5.

Load-slip curves of the STC joints. (a) B-200-1, (b) B-300-1, (c) B-200-2, (d) B-300-2, (e) S-200-1, and (f) S-300-1.

Table 3 shows the results obtained from the push-out tests. The initial slip stiffness could be evaluated by the tangent of the elastic stage. It was found that the initial slip stiffness and maximum load improved when increasing the timber thickness. The experimentally initial slip stiffness could be used to define the spring stiffness at the interface in the finite element model.

Table 3.

Experimental results from the load-slip curves

Specimen	Initial slip stiffness (kN/mm)		Maximum load (kN)
Specimen	Test	Average	Test	Average
B-200-1-a	6.68	6.73	54.25	52.10
B-200-1-b	6.78	6.73	49.94	52.10
B-300-1-a	11.34	9.14	60.28	58.00
B-300-1-b	6.94	9.14	55.72	58.00
B-200-2-a	11.64	8.87	72.72	67.72
B-200-2-b	6.09	8.87	62.72	67.72
B-300-2-a	10.51	10.17	69.56	75.31
B-300-2-b	9.82	10.17	81.05	75.31
S-200-1-a	2.90	2.92	22.8	22.52
S-200-1-b	2.94	2.92	22.24	22.52
S-300-1-a	5.25	5.39	21.91	21.65
S-300-1-b	5.52	5.39	21.39	21.65

Bending tests of full-scale STC beams

Design of the specimens

Base on the above research of the shear performance of the connectors, the bending behaviors of full-scale STC beams were investigated in this section. The bending tests were conducted using the same materials as the push-out tests. Resorcinol adhesive was used for the production of two-layer glulam.

Nine full-scale specimens with lengths of 6000 mm were designed to study the bending performance. The specimens were divided into two categories. The first one contained a bare steel beam and was designated as the steel beam. The second one contained eight STC beams with the designations shown in Table 4. The schematic types of the specimens are shown in Figure 6. To investigate the LTB of the STC beam, the buckling bearing capacity and strength bearing capacity of the STC beam were calculated in the design of specimens. It was assumed that the full composite action between steel and timber was reached. The timber area was converted to steel area by the equivalent area method. The calculation result showed that for the designed STC beam with one timber layer, the buckling bear capacity is less than the strength bearing capacity. This ensures that some STC beams will exhibit LTB finally.

Table 4.

The details of specimens

Specimens	Timber layer		Height (mm)	Shear connector	Spacing (mm)
Specimens	Top	Bottom	Height (mm)	Shear connector	Spacing (mm)
Steel beam	NA	NA	194	NA	NA
T1B1-B-200	1	1	270	Bolts	200
T1B1-B-300	1	1	270	Bolts	300
T1B2-B-200	1	2	308	Bolts	200
T1B2-B-300	1	2	308	Bolts	300
T2B1-B-200	2	1	308	Bolts	200
T2B1-B-300	2	1	308	Bolts	300
T1B1-S-200	1	1	270	Screws	300
T1B1-S-300	1	1	270	Screws	300

Figure 6.

Schematic views of the specimens. (a) Assembled view and (b) cross-sectional views.

Setup and instrumentation

Four-point loading conditions for simply supported beams were applied to study the bending strength. The typical test setups are shown in Figure 7. One LVDT was installed to measure the mid-span deformation of the specimens. Four strain gauges were installed on the web of the H-shaped steel beam, and two strain gauges were installed on the timber. The specimens were loaded according to (GB/T 50329, 2012) with a loading rate of 7 mm/min. The tests were stopped when the load dropped to 80% of the maximum load.

Figure 7.

Schematic of specimens. (a) Experimental setup and instrumentation, (b) side view, and (c) layout of strain gauges.

Experimental results

Experimental observation and failure modes

The steel beam showed the typical failure mode of lateral torsional buckling, as shown in Figure 8(a). The deflection was obvious with increasing load. When the load reached the yield point, the lateral displacement and twisting started to develop due to the unrestrained compression flange. Local damage under the loading roller was also observed, as shown in Figure 8(b). Finally, when approaching the maximum load, the LTB resulted in a decline in the load-carrying capacity, and accordingly, the test was terminated.

Figure 8.

Failure modes and experimental observations. (a) Failure modes and (b) local damages.

The STC beams exhibited different failure processes. When reaching the yield load, a weak timber fiber breaking sound was occasionally heard from inside the beam. However, no visible cracks were seen from the appearance of the timber. Thereafter, slight lateral deformation and twisting were observed. When reaching the maximum load, the fiber breaking sound grew louder and more frequent. The timber of the lower flange in the pure bending region began to crack and fracture. Transverse cracks perpendicular to the grain direction were first observed, followed by splitting cracks parallel to the grain direction, as shown in Figure 8(b). The cracks were mostly developed around the bolt holes and the knots. The load of specimens T1B1 slowly decreased after reaching the maximum load, and the failure mode was still LTB. However, the load of specimens T1B2 and T2B1 experienced a sharp drop when approaching the maximum load due to the tensile fracture of the timber. The final failure mode showed slight LTB.

Load-displacement relationships

The load-displacement curve was obtained from the linear variable displacement transducer placed at the bottom of the midspan. A total of nine load-displacement curves were obtained, as shown in Figure 9(a).

Figure 9.

Load-displacement relationships at the midspan. (a) Experimental curves and (b) typical relationships and yield points.

In comparison to the steel beam, the STC beams had a larger load-carrying capacity and more ductile deformation. However, the initial stiffness of the composite beams showed a slight improvement due to the partial composite action. Most of the steel-timber specimens with one layer of timber exhibited similar load-displacement relationships to that of the steel beam. The curves were linear at the beginning. When approaching the yield load, the stiffness gradually softened with the steel of the upper flange yielding. Additionally, the stiffness continued to gradually soften until reaching a maximum point. After this point, the curves began to decrease, and the specimen entered the residual load-carrying capacity phase. It was evident that the rate of load decline of the STC beams was much slower than that of the steel beam, resulting from the enhanced buckling resistance provided by the timber. When the timber was increased to two layers, especially in the upper flange, the buckling resistance exhibited remarkable improvement. The curves were composed of two stages, including the initial linear portion and subsequent hardening portion. Additionally, these curves had a sharp drop off due to the sudden fracture of the timber at the lower flange.

Overall, all the curves can be categorized into two typical groups with respect to the two failure modes, as shown in Figure 9(b). One group was for the specimens that failed from LTB. The other was for the specimens that failed from the fracture of the timber. To determine the yield point, the farthest-point method was applied due to the relationships of the specimens without an obvious yield plateau (Feng et al., 2015, 2017). The initial stiffness of the panels could be evaluated by the tangent of the linear stage. The displacement ductility coefficient μ = u_ultimate/u_y was also introduced to evaluate the ductility performance. The detailed experimental results are summarized in Table 5.

Table 5.

Experimental results from the load-displacement curves

Specimen	Initial stiffness (kN/mm)	Yield point		Maximum point		u_ultmate (mm)	μ
Specimen	Initial stiffness (kN/mm)	u_y (mm)	P_y (kN)	u_max (mm)	P_max (kN)	u_ultmate (mm)	μ
Steel beam	1.68	40.14	61.86	76.02	71.99	108.55	2.70
T1B1-B-200	1.70	46.63	72.13	102.98	90.08	156.95	3.37
T1B1-B-300	1.74	46.04	70.73	100.74	83.08	158.50	3.44
T1B2-B-200	1.81	42.81	68.55	81.81	82.96	142.11	3.32
T1B2-B-300	1.79	47.11	74.69	129.68	94.21	129.68	2.75
T2B1-B-200	1.73	45.54	75.12	141.71	104.61	137.24	3.01
T2B1-B-300	1.71	47.76	78.69	168.13	103.63	168.13	3.52
T1B1-S-200	1.73	43.15	70.07	68.97	80.35	129.18	2.99
T1B1-S-300	1.69	43.47	70.02	110.71	78.27	124.27	2.86

Load-strain response

The load-strain relationships of the typical specimens are shown in Figure 10, where the strain values come directly from the mid-span strain gauges. The curves for the specimens with a bolt spacing of 300 mm are not shown due to their similar characteristics with those of the specimens with a spacing of 200 mm.

Figure 10.

Load-strain curves of the typical specimens. (a) Steel beam, (b) T1B1-B-200, (c) T1B2-B-200, (d) T2B1-B-200, and (e) T1B1-S-200.

The STC beams exhibited larger plastic deformation than the steel beam when analyzing the increment of the steel strain after yielding, as shown in Figure 10. The maximum plastic strain increment was approximately 5000 με for specimen T2B1-B-200, which was much larger than 3000 με for the steel beam. Moreover, it was confirmed that the STC beams had a larger yield load than that of the steel beam. For the steel beam, yielding started when the load reached approximately 55 kN. However, the yield load improved to 65 kN for the composite beams.

It was evident that the lower flange of the steel first yielded when comparing the values of strain for S4 with that of S1 for all the specimens. However, both flanges of specimen T2B1-B-200 yielded at almost the same time. Additionally, the trend of the strain S4 curves after yielding for the composite beams was similar to the hardening stage, but the steel beam displayed a typical plastic plateau. For strain S2, it was evident that most of the specimens showed a “return” phenomenon after yielding, except for specimen T2B1-B-200, indicating that LTB could be prevented by restraining the upper flange with more timber.

Strain distribution and slip strain

To analyze the interface slip, the typical strain distribution in the mid-span section under different load levels is shown in Figure 11. Since the plane section assumption was not valid, the timber strain and the adjacent steel strain were connected with a dashed line. For the composite beams, it was assumed that the curvature was consistent for each layer (Nie and Cai, 2003). Thus, the slip strain could be derived by extending the strain distribution according to the average curvature determined by the steel strain. The typical strain distribution when the load was 40 kN was selected and analyzed.

Figure 11.

Strain distribution and slip strain of typical specimens.

It was demonstrated that the location of the neutral axis did not change until the lower steel flange yielded. Then, the neutral axis shifted upward. By comparing the location of the neutral axis when the load was 60 kN, it was shown that the location shifted upward for the steel beam but not for the composite beam. The neutral axis of the composite beam maintained its position even when the load increased to 70 kN, as shown in Figures 11(d) and (e).

Through analyzing the slip strain of the composite beams, it could be deduced that the interface slip was relatively large resulting from the substantially large slip strain values in the upper and lower interfaces. Nevertheless, the bending stiffness of the composite beams displayed an improvement when comparing the curvatures, which suggested that the most efficient method was to increase the timber on the upper flange.

Bending stiffness

The bending stiffness was an important value that accounted for the composite action. A total of four kinds of bending stiffnesses were calculated and compared, as shown in Table 5, including the stiffness (EI)_full with full composite action, the stiffness (EI)_non with non-composite action, the stiffness (EI)_disp calculated from the load-displace relationship and the stiffness (EI)_partial derived from the additional curvature. The stiffness (EI)_full and (EI)_non can be calculated based on the transformed section (Nie and Cai, 2003; Nie et al., 2008). The analysis model for the STC beams for calculating the stiffness (EI)_partial is shown in Figure 12. In this model, the slip strain contains additional compressive or tensile strain of the timber due to the lower elastic modulus of wood, which was much different from that of the other composite systems such as steel-concrete (Liu et al., 2017; Souici et al., 2013) and steel-FRP (Benachour et al., 2008; Satasivam et al., 2017; Teng et al., 2012; Youssef, 2006).

Δ ϕ = \frac{Δ ε_{t} - Δ ε_{wt}}{h_{1} + h_{2 t}} = \frac{Δ ε_{b} - Δ ε_{wb}}{h_{2 b} + h_{3}} = \frac{Δ ε_{t} + Δ ε_{b} - Δ ε_{wt} - Δ ε_{wb}}{h_{1} + h_{2 t} + h_{2 b} + h_{3}} = \frac{Δ ε_{total}}{h_{total}}

(1)

where

Δ ε_{total}

is the total slip strain only caused by the rotation of each layer, not concluding the compressive or tensile strain of the timber. h_total is the height of the whole section.

Figure 12.

Analysis model for the STC beams. The additional curvature due to slip can be calculated as.

To simplify the calculation, the additional curvature due to slip can also be calculated by comparing the actual curvature and the full-composite curvature. The stiffness reduction factor can be calculated as

ξ = \frac{ϕ_{partial} - ϕ_{full}}{ϕ_{full}} = \frac{Δ ϕ}{ϕ_{full}}

(2)

Then, the partial-composite stiffness is

{(E I)}_{partial} = \frac{{(E I)}_{full}}{1 + ξ}

(3)

The analysis results for different bending stiffness are listed in Table 6, and a comparison between the specified bending stiffness and the non-composite stiffness is shown in Figure 13(a).

Table 6.

Analysis results for the bending stiffness (p = 40 kN)

Specimen	$ϕ_{full}$	$ϕ_{partial}$	$Δ ϕ$	$ξ$	EI (×10⁶ N·m²)
Specimen	$ϕ_{full}$	$ϕ_{partial}$	$Δ ϕ$	$ξ$	(EI)_full	(EI)_partial	(EI)_disp	(EI)_non
T1B1-B-200	0.00654	0.00727	0.00073	0.11144	6.42	5.78	5.14	5.16
T1B1-B-300	0.00654	0.00734	0.00080	0.12265	6.42	5.72	5.18	5.16
T1B2-B-200	0.00561	0.00728	0.00167	0.29814	7.48	5.77	5.33	5.20
T1B2-B-300	0.00561	0.00752	0.00191	0.34061	7.48	5.58	5.29	5.20
T2B1-B-200	0.00561	0.00669	0.00108	0.19177	7.48	6.28	5.21	5.20
T2B1-B-300	0.00561	0.00696	0.00135	0.23987	7.48	6.04	5.54	5.20
T1B1-S-200	0.00654	0.00728	0.00074	0.11341	6.42	5.77	5.46	5.16
T1B1-S-300	0.00654	0.00800	0.00146	0.22294	6.42	5.25	5.29	5.16

Figure 13.

Comparison results. (a) The bending stiffness and (b) yield load and maximum load.

(EI)_disp was much lower than (EI)_partial for two reasons. One reason was that the shear deformation was not excluded from the overall deformation, and the other was that the strain measurement was more accurate than the displacement measurement for one displacement transducer. Therefore, the stiffness (EI)_partial was selected to represent the actual bending stiffness. It was demonstrated that the more layers of timber that were on the upper flange, the larger the composite action was.

Additionally, the specimens with bolt shear connectors exhibited a higher bending stiffness than the specimens with self-tapping screw connectors with the same cross-section. Considering the relatively low bending stiffness of specimen T1B1-S-300, it could be speculated that the bolt connector should employ a more reliable installation method than that of the self-tapping screw connector.

Comparing the stiffness of the specimens with different spacings, it was evident that a closer spacing would achieve a higher stiffness for the specimens with the bolt or screw shear connectors. However, careful consideration should be given to the potential damage of the steel flange and timber layer when determining the minimum spacing.

Strength

The comparison of the strength between the STC beams and the steel beam is shown in Figure 13(b). The yield load and maximum load are selected from Table 6.

It was evident that the STC beams could improve the yield load and maximum load, with increases of 11%–27% and 9%–45%, respectively. In terms of the timber arrangements, specimens T2B1 had the largest yield load and the maximum load increased by an average of 24% and 45%, respectively. Specimens T1B1 showed the smallest improvement by 14% and 15%, with specimens T1B2 in between. Overall, the timber placed above the upper flange of the H-shaped steel beam was more instrumental in improving the strength due to the change in the failure mode from overall buckling to timber fracture, especially for the maximum load.

Comparing the strength of the specimens with different shear connectors, it was evident that the specimens with bolt shear connectors exhibited higher yield loads and maximum loads than the specimens with self-tapping screw connectors. Moreover, an interesting result was found that the increment of the maximum load was lower than that of the yield load for the specimens with screw connectors, but the specimens with bolt connectors showed a higher improvement for the maximum load. Therefore, the load-carrying capacity would require more attention when using self-tapping screw connectors.

For the connector spacing, it was demonstrated that the specimens with a connector spacing of 200 mm usually achieved a higher maximum load, but a consistent conclusion for the yield load could not be drawn. The yield load decreased when reducing the connector spacing for specimens T2B1 and T1B2, while it reversely increased for specimens T1B1. Additionally, the maximum load for specimen T2B1 showed little difference in terms of the connector spacing, resulting from the maximum load being reached due to the fracture of the timber.

Finite element analysis

Modeling

To assess the failure modes and to study the key design parameters, a finite element analysis (FEA) was conducted using ANSYS. In the finite element model (FEM), the 8-node hexahedral solid element (SOLID185) was used to simulate the steel and timber, and the 2-node linear spring element (COMBIN39) was used to simulate the shear connectors. The spring elements spread over all the interfaces to equivalently simulate the effect of shear connection by connecting two adjacent nodes, rather than individually modeled each connector due to the unknown friction coefficient. The equivalent shear stiffness was the only factor concerned for the linear spring elements. To reduce the computational cost, one half of the structure was modeled, as shown in Figure 14. In addition, a mesh convergence test was conducted through element refinement, and the element size was then determined. In this model, the element size was 5 mm × 20 mm. The elements of the steel and timber at the interface had coincident nodes to create the spring elements. The actual loading and support block were also built to avoid the local stress concentration. The load was directly applied to the nodes of the loading block. All the loads were applied in the manner of displacement control.

Figure 14.

Boundary conditions and analysis results of the FEM. (a) Typical specimen T1B1, (b) steel beam, (c) T1B1-B-200 and (d) failure modes for all specimens.

To consider the geometrical imperfections, the first buckling mode obtained from the eigenvalue buckling prediction was introduced as the initial geometrical imperfection distribution, and its magnitude was usually 1/500 of the structural span.

The elastic-plastic behavior of the steel was considered. A multilinear stress-strain relationship was used and validated by the steel beam considering the initial material defects. The shear stiffness of the spring element was calculated as

k_{s p r i n g} = \frac{k_{p u s h}}{n_{p u s h}} \cdot \frac{n_{e f}}{n_{s p r i n g}}

(4)

where k_push represents the shear stiffness obtained from the push-out tests. n_push stands for the number of connectors of each specimen in push-out tests and takes as 8. n_spring represents the spring element number in the finite element model. In this paper, n_spring is 18662. n_ef is the number of effective connectors, of each STC beam considering the group effect of connectors and was calculated according to the (EN 1995-1-1, 2004).

Simulation verification

The experimental results are simulated by the FEM. In particular, the failure modes and the load-displacement relationships are compared and discussed, as shown in Figures 14 and 15. The numerical results and important parameters of the FEA are listed in Table 6.

Figure 15.

Load-displacement relationship comparison between the experimental and numerical results. (a) Connector spacing of 200 mm and (b) connector spacing of 300 mm.

The modeling method had good agreement with the experimental results. Figures 14(b) and (c) show that the FEA could accurately simulate the LTB failure mode with the introduction of an initial geometrical imperfection. However, the ratio ranged from 1/50 to 1/1000 of the span to agree well with the experimental results, as listed in Table 6. The shear stiffness of the spring element also had a small range from 5.017 to 6.609, but a large range from 0.5 to 5 for the specimens with screw shear connectors.

The load-displacement relationships also agreed well with the experimental results, as shown in Figure 15. However, the sharp drop off of the load-carrying capacity due to the fracture of the timber could not be simulated because the failure criterion for the composite material in ANSYS was used to represent the damage without changing the constitutive relationship. By comparing the maximum loads, the error between the experimental and numerical results was less than 9.5%, as shown in Table 7.

Table 7.

The parameters used in the finite element model for all the specimens

Specimen	spring stiffness k_spring (N/mm)	Geometrical imperfection	P_{max (EXP)} (kN)	P_{max (FEA)} (kN)	Error
Steel beam	NA	l₁/1000	71.99	71.14	−1.18%
T1B1-B-200	5.017	l₁/600	90.08	89.49	−0.65%
T1B1-B-300	5.143	l₁/150	83.08	82.88	−0.24%
T1B2-B-200	5.017	l₁/150	82.96	81.74	−1.47%
T1B2-B-300	5.143	l₁/1000	94.21	96.45	2.38%
T2B1-B-200	6.609	l₁/200	104.61	94.77	−9.41%
T2B1-B-300	5.719	l₁/350	103.63	111.89	7.97%
T1B1-S-200	5	l₁/50	80.35	79.68	−0.83%
T1B1-S-300	0.5	l₁/500	78.27	80.88	3.33%

Parametric study

Based on the proposed modeling method, a parametric study using the FEM was conducted to address the influence of timber layer, shear stiffness of spring element and initial geometrical imperfection on the failure mode and load-carrying capacity of the STC beams. The specimens were designated using the same rule as those in the experimental tests.

First, the timber layer was changed from one layer to two layers with different combinations. The FEA results are shown in Figure 16(a). The STC beams exhibited a substantial improvement in the load-carrying capacity compared to that of the steel beam. The maximum load of T2B1 model was around 67% larger than that of the steel beam. However, the stiffness and yield load of the STC beam showed a slight enhancement. Additionally, with the layer of timber increasing, especially for timber on the upper flange, the failure modes changed from LTB to timber fracture.

Figure 16.

Parametric study on the behavior of STC beams. (a) Timber layers, (b) shear stiffness of the connectors, and (c) initial geometrical imperfections.

Secondly, the stiffness of the spring element was changed from 0.1 to 50, a full composite beam was also analyzed, as shown in Figure 16(b). The stiffness of the specimens exhibited an unsubstantial increasing increment as interface slip occurred. The stiffness of the STC beam changed from 0.71 kN/mm to 1.67 kN/mm. The larger stiffness of the spring element also enhanced the load-carrying capacity considerable, as a result of better composite action. It was clear that the composite beam with a relatively low shear stiffness could prevent LTB. However, buckling failure was prone to occur when full composite action was achieved.

Finally, the initial geometrical imperfection was changed from 1/25 to 1/1000 of the span, as shown in Figure 16(c). It was found that the geometrical imperfection influenced the load-carrying capacity more than the stiffness. As the imperfection decreased, the LTB get alleviated, the load-carrying capacity greatly improved, and the displacement of the maximum load decreased, but the stiffness of the composite beam displayed a very small increasing increment.

Conclusions

In this work, a STC beam consisting of H-shaped steel and SPF timber with different mechanical shear connections was proposed. Push-out tests were carried out to assess the shear behavior of bolted connectors. Four-point bending tests were conducted to investigate the influences of the design properties on the LTB. The following conclusions can be drawn from this work:

(1) Two failure modes of shear connectors in the push-out tests were observed, including one plastic hinge and two plastic hinges. As the timber thickness increased, the failure mode changed from one plastic hinge to two plastic hinges, and the slip stiffness and maximum load were increased. The specimens with bolt connectors showed larger load-carrying capacity than that of the specimens with screw connectors.

(2) The STC beams with mechanical shear connectors demonstrated LTB and timber fracture. Moreover, as the number of layers of timber increased on the upper flange, the failure mode changed from buckling to timber fracture. The maximum strength of the composite beam was substantially improved by suppressing the buckling, while the stiffness showed slight increment due to the partial composite action.

(3) The STC beams with bolts or self-tapping screws shear connectors showed partial composite action. The slip strain was observed from the strain distribution, and a model considering the interface slip was suggested for predicting the partial composite stiffness of the STC beams. The bolts were recommended for their larger shear connection stiffness and higher mechanical stability than those of the self-tapping screws.

(4) A finite element model constructed using ANSYS is proposed and validated with the experimental results. The proposed model is found to have excellent accuracy in predicting the load-carrying capacity and the failure modes of STC beams. The increasing shear stiffness in the parametric study changes the failure mode from lateral buckling to timber fracture.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported by he Fundamental Research Funds for the Central Universities of China (BLX201706), the National Key R&D Program of China (2017YFC 0703503), the Special Fund for Beijing Common Construction Project (2015GJ-01), and support from the National Natural Science Foundation of China (31770602 and 51908038).

ORCID iD

Xinmiao Meng

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