# Flexural Response of Steel-Concrete Composite Truss Beams

Authors: Lisheng Luo; Xiaofeng Zhang
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

This paper presents an experimental and analytical study on the flexural response of a steel-concrete composite truss beam. This integrated unit consists of a triangular steel truss, a concrete slab on it, and stud connectors. Three simply supported composite trusses with different configurations of shear connection (η) were evaluated via three-point bending tests. The effects of the shear connectors’ configuration on the flexural response (i.e., load-deflection, load-slippage, and load-strain curves) of the composite trusses were examined. The commercial finite-element (FE) software ANSYS was employed to conduct numerical simulations. An FE model was developed for the composite truss and was validated using experimental results. A parametric study was performed to investigate the effect of the shear connectors’ configuration on the flexural response of the composite trusses. If η < 1, the bending capacity increased with η. In contrast, if η ≥ 1, the effect of η on the bending capacity was negligible. Finally, a design method based on the degree of the shear connection was proposed to predict the ultimate capacity of the composite truss, and the predictions agreed well with the experimental results.


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## Body

## 1. Introduction

Steel-concrete composite structural members are formed by bonding a steel component to a concrete component, so that the two components function as an integrated unit [1]. Composite structures can efficiently utilise the properties of the constituting materials to achieve material saving and cost efficiency. Composite members have been extensively applied in civil engineering, e.g., composite floors [2], composite columns [3, 4], and composite beams [5]. Among these members, the composite beam, which consists of a steel beam on which a reinforced concrete slab is cast with shear connectors, is the most widely used, because the properties of both materials are fully utilised (i.e., steel is strong in tension and concrete is strong in compression). To ensure composite action, shear connectors are commonly employed at the steel-concrete interface for resisting slippage and separation between the concrete slab and steel beam [1].There are many types of mechanical shear connectors with various shapes, sizes, and methods of attachment, such as studs, bolts, channels, and angles. The stud connector is probably the most commonly used connector for steel-concrete composite beams [1]. To investigate the strength and load-slip behaviour of the stud shear connection, push tests have been widely conducted [6–8]. The failure modes of the stud connection mainly include failure at the shank of the stud, fracture in the welding zone, and concrete crushing [9]. The shear capacity of the stud generally depends on the diameter of the stud, strength of the steel used for the stud, and material properties of the concrete (i.e., strength and elastic modulus). Many calculation formulas have been proposed by researchers for estimating the strength and load-slip relationship of stud connections [9, 10]. Current standards use similar formulas to estimate the shear capacity of stud connectors (Fu0). Taking the standard GB 50017 [11] as an example and ignoring partial factors, we have(1)Fu0=min0.43AsEcfc,0.7Asfu,where As is the cross-sectional area of the stud, Ec is the elastic modulus of concrete, fc is the strength of concrete, and fu is the ultimate strength of stud connectors. The US and Europe standards adopt different coefficients to replace 0.43 and 0.7 in equation (1), 0.5 and 0.75, respectively, in AISC [12], and 0.37 and 0.8, respectively, in EN1994.1.1 [13].Studies on steel-concrete composite plane truss beams (also called “open-web composite steel joists”) began in the 1960s, and these beams have been successfully applied in engineering projects, such as Reed Arena in the US and 1000 De La Gauchetiere Buildings in Canada [14]. Composite trusses are capable of achieving a large span with low cost, providing routes for ventilation and electrical lines and reducing the overall floor-to-floor height [14]. Robinson and Fahmy [15] experimentally investigated a composite joist with a partial shear connection. The joist failed via the buckling of the top chord in compression prior to full yielding of the bottom chord, and a design method was proposed for the composite joist with a partial shear connection. Two full-scale composite trusses were tested under bending by Brattland and Kennedy [16], which failed via shear-connector failure, followed by the overloading of the top chords. Muhammad [17] tested two composite trusses and adopted puddle welding or small screws as shear connectors. The composite truss with the puddle-welding connector exhibited better composite action, with a significantly higher flexural capacity and failed via the overall buckling of the top chords, while shear-bond failure was observed for the other specimen. Lopez [18] performed an in situ study on a composite truss floor system, and the buckling of diagonals near the support, which experienced strong axial forces, was identified as the major failure mode. A parametric study on a composite truss was conducted by Bouchair et al. [19], revealing that the top chord does not significantly affect the bending capacity of composite trusses. According to previous studies, the failure modes of composite trusses vary greatly, e.g., shear connectors’ failure, buckling of the top chords, buckling of the diagonals, and fracture of the bottom chords. The complexity of the failure modes makes it difficult to develop an accurate method for predicting the structural behaviour of composite truss beams. A simple model was adopted by “Standard specifications for composite steel joists” [20] to estimate the moment capacity of the composite truss by ignoring the contribution of the top chords to the bending resistance [14].In recent years, the steel-concrete composite space truss, which is made of tubular steel members, has attracted the attention of architects and researchers owing to its aesthetical qualities and higher out-of-plane stability compared with the plane truss. As reported by Reis and Oliveira Pedro [21], the composite space truss with a triangular section was first proposed by Jean Muller and applied in Roize Bridge. Thus far, a few studies have been performed on this type of composite truss. Braz [22] tested a specimen with a midspan of 6 m and a cantilever span of 1.5 m. An unexpected local failure near the support occurred during the test, which was caused by the large compressive forces in the diagonals. A moment-curvature model was proposed in [22], which exhibited reasonable accuracy. Machacek and Cudejko [23, 24] performed an experimental and numerical study on composite steel and concrete trusses to investigate the shear-force distributions along the beams.Reviewing the literature reveals a lack of studies on the steel-concrete composite space truss, which may hinder the application of this type of structural member. The influence of the degree of the shear connection on the structural performance of the composite truss has not been clarified. Furthermore, design methods are required to estimate the bending capacity of the composite truss. To fill this knowledge gap, this paper presents an experimental and analytical study on the flexural responses of steel-concrete composite truss beams (SCCTBs). Three simply supported composite trusses with different configurations of shear connection studs were evaluated via three-point bending tests. The effects of the shear connectors’ configuration on the flexural response of the composite truss were examined. A finite-element (FE) model was developed and validated by the experimental results. A parametric study was conducted to investigate the effects of the degree of the shear connection on the flexural response of the composite trusses. Finally, a design method was proposed for predicting the ultimate capacity, and it exhibited good agreement with the experimental and FE results.


## 2. Experimental Program

### 2.1. Test Specimens

Three SCCTBs, which consisted of a steel truss, a concrete slab on it, and shear connectors resisting the slippage between them, were tested. The main parameter was the degree of the shear connection (i.e., the quantity of shear connectors). The dimensions of the SCCTB specimens are plotted in Figure1, and a photograph of the SCCTBs is shown in Figure 2.Figure 1
Dimensions of the SCCTB specimens.
(a)
(b)Figure 2
Photograph of the SCCTB specimens.A square pyramid structure was selected for the steel truss to achieve sufficient lateral stiffness. The height, width, and length of the steel truss were 500, 500, and 4000 mm, respectively. The steel truss was made of circular tubes with fillet welds connecting them together. The dimensions of the top chord, bottom chord, diagonals, and upper braces were Φ42 × 3 mm2, Φ70 × 5 mm2, Φ32 × 4 mm2, and Φ42 × 3 mm2, respectively (Figure 1).The concrete slab was 80 mm deep and 1500 mm wide, with reinforcement meshes placed on both the top and bottom sides in the concrete slab. The nominal diameter and spacing of the longitudinal reinforcements were 6 and 100 mm, respectively, and those of the transverse reinforcements were 6 and 150 mm, respectively.Stud connectors were employed to connect the steel truss and the concrete slab (Figure1). These stud connectors had a diameter of 13 mm and an ultimate strength of 425 MPa. The critical amount of shear connectors was defined as the quantity of shear connectors that made the shear resistance of the shear connectors equal to the yield capacity of both the top and bottom chords. According to Code for design of steel structures [11], the critical amount of shear connectors for the composite truss is 34. To investigate the effect of the quantity of shear connectors on the flexural response of the composite truss, three quantities of shear connectors were selected: 30, 34, and 42 (corresponding to specimens B1, B2, and B3, respectively). A shear interaction factor k is defined as the ratio of critical amount of shear connectors to actual amount of stud connectors. As a result, the shear interaction factors for specimen B1, B2, and B3 are 0.88, 1.0, and 1.24, respectively.


### 2.2. Materials

The steel truss was manufactured using Q345B steel with a nominal yield strength of 345 MPa. Three tensile coupons, which were cut from steel tubes, and three reinforcement coupons were tested to obtain the material properties of the steel tubes in the truss and the rebars in the concrete slab. The tensile-coupon tests were conducted in accordance with GB/T228-2010 [25]. The test results, including the yield strength fy, ultimate strength fu, and elongation, are presented in Table 1 (average values).Table 1
Material properties.
Material
f
y (MPa)
f
u (MPa)
Elongation
f
cu,0 (MPa)
f
c (MPa)
E
c (MPa)
Steel
437.0
542.4
0.287
—
—
—
Reinforcement bar
405.7
550.8
0.318
—
—
—
Concrete
—
—
—
35.0
23.4
31324The concrete slab was made of ordinary Portland cement concrete with a strength grade of C30. When mixing concrete, the ratio of raw materials is 1 : 1.6 : 3 : 0.5 (by weight) for cement : sand : coarse aggregate : water. Three concrete cubes with dimensions of 150 mm × 150 mm × 150 mm were prepared and axially compressed in accordance with GB/T50081 [26] to obtain the mechanical properties. The measured material properties of the concrete slab are presented in Table 1 (average values). Here, the cubic strength fcu0 was converted into the cylindrical strength fc, and Ec represents the elastic modulus.


### 2.3. Test Setup and Instrumentation

The composite truss was simply supported on steel bases, in which roller support was achieved by placing steel rods between the beam and the bases, as shown in Figure3(a). A concentrated load was applied at the middle of the concrete slab through a 1000 kN hydraulic Jack connected to a self-balancing reaction frame.Figure 3
Arrangement of the measurement points for the SCCTB specimens. (a) Simply support. (b) Dial gauges. (c) LVDTs. (d) Strain gauges. (e) Photos of SCCTB specimens.
(a)
(b)
(c)
(d)
(e)Dial gauges were placed along the composite truss with a spacing of 1/8-span to monitor the slippage between the concrete slab and the steel truss, as shown in Figure3(b). The dial gauges were fixed on the bottom surface of the concrete slab using a custom-manufactured holder, which was mounted in the concrete slab. The spindles of the dial gauges were in contact with a timber plate, which was glued to the top chord of the steel truss. Therefore, the relative movement between the concrete slab and the steel truss could be measured.The LVDTs were located at 1/8-span positions along the length of the SCCTB specimen to measure the deflection, as shown in Figure3(c). The vertical LVDTs were placed on the bottom surface of the concrete slab and the top chord of the steel truss. In addition, two vertical LVDTs were placed at the supports to measure their settlements.Longitudinal strain gauges were affixed to the top side of the concrete slab and the top chords at 1/8-span positions along the beam. Longitudinal strain gauges were also attached to the middle part of each chord and diagonal, as shown in Figure3(d).All the data, including the loads, deflections, and strains, were simultaneously acquired by a dataTaker and recorded on a personal computer, as shown in Figure3(e).


### 2.4. Test Procedures

A concentrated force was acted at midspan by the hydraulic jack. To avoid the local concrete crushing, a loading beam was designed to disperse concentrated force, as shown in Figure3(e). A preload, which was approximately 10%-20% of the estimated ultimate load obtained via FE analysis, was first applied to ensure that the specimen and equipment were working properly. After everything was examined, the test was started. When the specimen was in the elastic phase, the load was applied with a rate of 20 kN/min until the deflection of the specimen increased rapidly, which indicated a nonlinear response. For each loading level, the load was kept constant for approximately 3 min to record the stable data. After the nonlinear region was reached, the loading form was changed to displacement control with a rate of 5 mm/min.


## 2.1. Test Specimens

Three SCCTBs, which consisted of a steel truss, a concrete slab on it, and shear connectors resisting the slippage between them, were tested. The main parameter was the degree of the shear connection (i.e., the quantity of shear connectors). The dimensions of the SCCTB specimens are plotted in Figure1, and a photograph of the SCCTBs is shown in Figure 2.Figure 1
Dimensions of the SCCTB specimens.
(a)
(b)Figure 2
Photograph of the SCCTB specimens.A square pyramid structure was selected for the steel truss to achieve sufficient lateral stiffness. The height, width, and length of the steel truss were 500, 500, and 4000 mm, respectively. The steel truss was made of circular tubes with fillet welds connecting them together. The dimensions of the top chord, bottom chord, diagonals, and upper braces were Φ42 × 3 mm2, Φ70 × 5 mm2, Φ32 × 4 mm2, and Φ42 × 3 mm2, respectively (Figure 1).The concrete slab was 80 mm deep and 1500 mm wide, with reinforcement meshes placed on both the top and bottom sides in the concrete slab. The nominal diameter and spacing of the longitudinal reinforcements were 6 and 100 mm, respectively, and those of the transverse reinforcements were 6 and 150 mm, respectively.Stud connectors were employed to connect the steel truss and the concrete slab (Figure1). These stud connectors had a diameter of 13 mm and an ultimate strength of 425 MPa. The critical amount of shear connectors was defined as the quantity of shear connectors that made the shear resistance of the shear connectors equal to the yield capacity of both the top and bottom chords. According to Code for design of steel structures [11], the critical amount of shear connectors for the composite truss is 34. To investigate the effect of the quantity of shear connectors on the flexural response of the composite truss, three quantities of shear connectors were selected: 30, 34, and 42 (corresponding to specimens B1, B2, and B3, respectively). A shear interaction factor k is defined as the ratio of critical amount of shear connectors to actual amount of stud connectors. As a result, the shear interaction factors for specimen B1, B2, and B3 are 0.88, 1.0, and 1.24, respectively.


## 2.2. Materials

The steel truss was manufactured using Q345B steel with a nominal yield strength of 345 MPa. Three tensile coupons, which were cut from steel tubes, and three reinforcement coupons were tested to obtain the material properties of the steel tubes in the truss and the rebars in the concrete slab. The tensile-coupon tests were conducted in accordance with GB/T228-2010 [25]. The test results, including the yield strength fy, ultimate strength fu, and elongation, are presented in Table 1 (average values).Table 1
Material properties.
Material
f
y (MPa)
f
u (MPa)
Elongation
f
cu,0 (MPa)
f
c (MPa)
E
c (MPa)
Steel
437.0
542.4
0.287
—
—
—
Reinforcement bar
405.7
550.8
0.318
—
—
—
Concrete
—
—
—
35.0
23.4
31324The concrete slab was made of ordinary Portland cement concrete with a strength grade of C30. When mixing concrete, the ratio of raw materials is 1 : 1.6 : 3 : 0.5 (by weight) for cement : sand : coarse aggregate : water. Three concrete cubes with dimensions of 150 mm × 150 mm × 150 mm were prepared and axially compressed in accordance with GB/T50081 [26] to obtain the mechanical properties. The measured material properties of the concrete slab are presented in Table 1 (average values). Here, the cubic strength fcu0 was converted into the cylindrical strength fc, and Ec represents the elastic modulus.


## 2.3. Test Setup and Instrumentation

The composite truss was simply supported on steel bases, in which roller support was achieved by placing steel rods between the beam and the bases, as shown in Figure3(a). A concentrated load was applied at the middle of the concrete slab through a 1000 kN hydraulic Jack connected to a self-balancing reaction frame.Figure 3
Arrangement of the measurement points for the SCCTB specimens. (a) Simply support. (b) Dial gauges. (c) LVDTs. (d) Strain gauges. (e) Photos of SCCTB specimens.
(a)
(b)
(c)
(d)
(e)Dial gauges were placed along the composite truss with a spacing of 1/8-span to monitor the slippage between the concrete slab and the steel truss, as shown in Figure3(b). The dial gauges were fixed on the bottom surface of the concrete slab using a custom-manufactured holder, which was mounted in the concrete slab. The spindles of the dial gauges were in contact with a timber plate, which was glued to the top chord of the steel truss. Therefore, the relative movement between the concrete slab and the steel truss could be measured.The LVDTs were located at 1/8-span positions along the length of the SCCTB specimen to measure the deflection, as shown in Figure3(c). The vertical LVDTs were placed on the bottom surface of the concrete slab and the top chord of the steel truss. In addition, two vertical LVDTs were placed at the supports to measure their settlements.Longitudinal strain gauges were affixed to the top side of the concrete slab and the top chords at 1/8-span positions along the beam. Longitudinal strain gauges were also attached to the middle part of each chord and diagonal, as shown in Figure3(d).All the data, including the loads, deflections, and strains, were simultaneously acquired by a dataTaker and recorded on a personal computer, as shown in Figure3(e).


## 2.4. Test Procedures

A concentrated force was acted at midspan by the hydraulic jack. To avoid the local concrete crushing, a loading beam was designed to disperse concentrated force, as shown in Figure3(e). A preload, which was approximately 10%-20% of the estimated ultimate load obtained via FE analysis, was first applied to ensure that the specimen and equipment were working properly. After everything was examined, the test was started. When the specimen was in the elastic phase, the load was applied with a rate of 20 kN/min until the deflection of the specimen increased rapidly, which indicated a nonlinear response. For each loading level, the load was kept constant for approximately 3 min to record the stable data. After the nonlinear region was reached, the loading form was changed to displacement control with a rate of 5 mm/min.


## 3. Test Phenomena and Failure Modes

### 3.1. Test Phenomena

The test phenomena of the SCCTB specimens comprised three phases. (1) At the beginning of the loading process, the deformation of the SCCTB specimens was inconspicuous, signifying the elastic phase. (2) As the load increased, the behaviour of the SCCTB specimens entered the nonlinear region, leading to rapid deformation. (3) When the load increased to approximately 85% of the ultimate load, cracks appeared at the bottom surface of the concrete slab. Meanwhile, the cracks developed with the increase of the load, until the SCCTB specimens collapsed.The cracks initially appeared in the middle area of the concrete slab. The amount of cracks increased with the load. Finally, the cracks expanded and ran through the concrete slab, as shown in Figure4. The cracks on the bottom side of the concrete slab indicate that the neutral axis was located in the slab; thus, tensile stress was induced on the bottom surface of the slab. The failure of the composite truss was caused by the yielding of the bottom chords and the concrete crushing of concrete slab. After specimen failure, extensive cracks were observed on the bottom side of the concrete slab.Figure 4
Failure mode of the composite truss.


### 3.2. Load-Deflection Curves

The load-deflection curves of the specimens are shown in Figure5, where the deflection is the deflection at the midspan subtracted by the support settlement. The applied load increased linearly until reaching approximately 200 kN, indicating that the specimen was in the elastic phase. The stiffness (slope of the load-deflection curve) was almost identical for the specimens, i.e., approximately 10 kN/mm. Then, the nonlinear response was observed. The curves deviated from each other owing to the different connector arrangements. Finally, the concrete slab at the middle of the beam specimen crushed, signifying the failure mode of SCCTBs. Meanwhile, the ultimate bearing capacity of the designed beam specimens was mainly controlled by the collapse of the concrete slab. On the one hand, a concentrated force was applied at the middle of the beam specimen so that a large local compressive stress was generated at the loading point. On the other hand, the bending moment also created a compressive stress at the loading point of the concrete slab. Hence, multidirectional compressive stress field existed in this region, leading to an easy concrete crushing of these designed SCCTBs. As shown in Figure 5 and Table 2, the stiffness of specimen B1 decreased most rapidly, with the lowest ultimate load of 385.6 kN, while specimen B3 had the highest capacity of 408.7 kN. The stud connectors’ distribution affected the mechanical behaviours of the composite truss. The stiffness and ultimate load of the composite truss increased with the shear connection factor (k).Figure 5
Load-deflection curves.Table 2
Ultimate load (kN).
Specimen
Test
FE
RE (%)
B1
385.6
401.4
4.97
B2
405.9
415.4
2.34
B3
408.7
419.7
2.68
Mean
—
—
3.33


### 3.3. Load-Slippage Curves

The load-slippage curves of the tested specimens are shown in Figure6, in which the slippage is the relative movement between the concrete slab and the top chord at the midspan. Initially, the load increased linearly with the increase of the slippage, as the composite truss was in the elastic phase. After reaching approximately 300 kN, the curves showed nonlinearity, similar to the load-deflection curves. The connector quantity significantly affected the slippage of the composite truss. Specimen B1 exhibited the lowest stiffness and largest slippage, because the shear interaction factor (k) was <1, indicating a partial shear connection. With the increase of the connector quantity, the slippage decreased, as shown in Figure 6. When the shear interaction factor increased from 1.0 (B2) to 1.24 (B3), the load-slippage curve did not change significantly. It is concluded that after a full shear connection was reached (i.e., k ≥ 1), the influence of the connector quantity was not evident.Figure 6
Load-slippage curves.


### 3.4. Load-Strain Curves

The load-strain curves for the bottom chord and for the concrete slab at the midspan are presented in Figures7 and 8, respectively. In Figure 7, the load-strain curves are linear and almost identical. When the truss approached failure, the strain in the bottom chord did not increase dramatically, confirming that the failure of the composite truss was not caused by bottom-chord yielding. In contrast, the load-compressive strain curves for the concrete slab (Figure 8) were highly nonlinear, and the strain reached approximately 0.003 at the failure load. As the strain gauges were located at the midheight (i.e., half of the slab thickness), the compressive strain on the top surface of the concrete slab at the failure load was expected to be significantly higher than 0.003, causing the crush failure of the concrete slab. The influence of the connector quantity on the stress-strain curve was not evident, likely because the neutral axis was in the concrete slab.Figure 7
Curves of load-tensile strain in the bottom chord.Figure 8
Curves of load-compressive strain in the concrete slab.


## 3.1. Test Phenomena

The test phenomena of the SCCTB specimens comprised three phases. (1) At the beginning of the loading process, the deformation of the SCCTB specimens was inconspicuous, signifying the elastic phase. (2) As the load increased, the behaviour of the SCCTB specimens entered the nonlinear region, leading to rapid deformation. (3) When the load increased to approximately 85% of the ultimate load, cracks appeared at the bottom surface of the concrete slab. Meanwhile, the cracks developed with the increase of the load, until the SCCTB specimens collapsed.The cracks initially appeared in the middle area of the concrete slab. The amount of cracks increased with the load. Finally, the cracks expanded and ran through the concrete slab, as shown in Figure4. The cracks on the bottom side of the concrete slab indicate that the neutral axis was located in the slab; thus, tensile stress was induced on the bottom surface of the slab. The failure of the composite truss was caused by the yielding of the bottom chords and the concrete crushing of concrete slab. After specimen failure, extensive cracks were observed on the bottom side of the concrete slab.Figure 4
Failure mode of the composite truss.


## 3.2. Load-Deflection Curves

The load-deflection curves of the specimens are shown in Figure5, where the deflection is the deflection at the midspan subtracted by the support settlement. The applied load increased linearly until reaching approximately 200 kN, indicating that the specimen was in the elastic phase. The stiffness (slope of the load-deflection curve) was almost identical for the specimens, i.e., approximately 10 kN/mm. Then, the nonlinear response was observed. The curves deviated from each other owing to the different connector arrangements. Finally, the concrete slab at the middle of the beam specimen crushed, signifying the failure mode of SCCTBs. Meanwhile, the ultimate bearing capacity of the designed beam specimens was mainly controlled by the collapse of the concrete slab. On the one hand, a concentrated force was applied at the middle of the beam specimen so that a large local compressive stress was generated at the loading point. On the other hand, the bending moment also created a compressive stress at the loading point of the concrete slab. Hence, multidirectional compressive stress field existed in this region, leading to an easy concrete crushing of these designed SCCTBs. As shown in Figure 5 and Table 2, the stiffness of specimen B1 decreased most rapidly, with the lowest ultimate load of 385.6 kN, while specimen B3 had the highest capacity of 408.7 kN. The stud connectors’ distribution affected the mechanical behaviours of the composite truss. The stiffness and ultimate load of the composite truss increased with the shear connection factor (k).Figure 5
Load-deflection curves.Table 2
Ultimate load (kN).
Specimen
Test
FE
RE (%)
B1
385.6
401.4
4.97
B2
405.9
415.4
2.34
B3
408.7
419.7
2.68
Mean
—
—
3.33


## 3.3. Load-Slippage Curves

The load-slippage curves of the tested specimens are shown in Figure6, in which the slippage is the relative movement between the concrete slab and the top chord at the midspan. Initially, the load increased linearly with the increase of the slippage, as the composite truss was in the elastic phase. After reaching approximately 300 kN, the curves showed nonlinearity, similar to the load-deflection curves. The connector quantity significantly affected the slippage of the composite truss. Specimen B1 exhibited the lowest stiffness and largest slippage, because the shear interaction factor (k) was <1, indicating a partial shear connection. With the increase of the connector quantity, the slippage decreased, as shown in Figure 6. When the shear interaction factor increased from 1.0 (B2) to 1.24 (B3), the load-slippage curve did not change significantly. It is concluded that after a full shear connection was reached (i.e., k ≥ 1), the influence of the connector quantity was not evident.Figure 6
Load-slippage curves.


## 3.4. Load-Strain Curves

The load-strain curves for the bottom chord and for the concrete slab at the midspan are presented in Figures7 and 8, respectively. In Figure 7, the load-strain curves are linear and almost identical. When the truss approached failure, the strain in the bottom chord did not increase dramatically, confirming that the failure of the composite truss was not caused by bottom-chord yielding. In contrast, the load-compressive strain curves for the concrete slab (Figure 8) were highly nonlinear, and the strain reached approximately 0.003 at the failure load. As the strain gauges were located at the midheight (i.e., half of the slab thickness), the compressive strain on the top surface of the concrete slab at the failure load was expected to be significantly higher than 0.003, causing the crush failure of the concrete slab. The influence of the connector quantity on the stress-strain curve was not evident, likely because the neutral axis was in the concrete slab.Figure 7
Curves of load-tensile strain in the bottom chord.Figure 8
Curves of load-compressive strain in the concrete slab.


## 4. FE Simulation

### 4.1. FE Modelling

A three-dimensional (3D) nonlinear FE model was developed using the commercial FE software ANSYS. The geometric dimensions of the FE model were identical to those of the tested specimens, as shown in Figure1.The concrete slab was modelled with the eight-node solid element SOLID65 having three degrees of freedom at each node (i.e., translations in thex, y, and z axes). SOLID65 is capable of cracking under tension and crushing under compression. The rebars in the concrete slab were modelled by the 3D spar element LINK8, which is a uniaxial tension-compression element with three degrees of freedom at each node. The members in the steel truss were modelled by the 3D linear beam element BEAM188, which is suitable for analysing slender to moderately thick beam structures. BEAM188 has six degrees of freedom at each node (i.e., three translations and three rotations). The connectors were also modelled by BEAM188, and the slippage and vertical deformation between the concrete slab and top chord were modelled by the nonlinear spring element COMBIN39. COMBIN39 is a unidirectional element with a generalised force-deflection capacity and three degrees of freedom (translation) at each node. An overview of the 3D FE model is shown in Figure 9. The element types for each component are shown in Figure 10, along with the mesh.Figure 9
FE model.Figure 10
FE mesh.According to [27], it is assumed that the concrete has ideal plasticity after reaching the ultimate strength. Figure 11 illustrates the simplified stress-strain relationship (f-ε) for concrete, which was converted into piecewise linear curves for easy inputting to ANSYS. During compression, the stress increased linearly until reaching 0.3fc and the strain at 0.3fc was calculated using equation (2), where Ec is the elastic modulus of concrete. In the nonlinear region, the stress-strain curve was obtained using equation (3) [28], where ε0 is the strain at the maximum concrete strength fc, as calculated via equation (4). Perfectly plastic behaviour was assumed when the concrete reached the maximum concrete strength. The performance of concrete under tension is approximately linear up to the tensile strength of the concrete. After this point, the tensile strength decreases to zero [29]. The tensile strength of the concrete was not recorded during the experiment; thus, it was considered as 10% of the compressive strength [30].(2)Ec=fε,(3)f=Ecε1+ε/ε02,(4)ε0=2fcEc.Figure 11
Stress-strain relationship for concrete.An elastic-linear hardening model was used to define the uniaxial stress-strain relationship for the steel materials, including the truss members, rebars in the concrete slab, and shear connectors (Figure12). The stress-strain relationship for steel was assumed to be identical under tension and compression. The key parameters in Figure 12, such as fy, fu, and εu, were obtained via the tensile coupon test (Section 2.2).Figure 12
Stress-strain relationship for steel.In order to simulate the slip effect between the concrete slab and the upper chord and transfer the force of the stud connector to the concrete slab effectively, the shear connector is simulated in the following way: (1) beam 188 is used to simulate the part of the stud connector in the concrete slab and (2) COMBIN39 element is used to simulate the part of the stud connector between the concrete slab and the upper chord. For the spring (COMBIN39) element, the relative movement between the top chord of truss and the concrete flange is taken into account, as illustrated in Figure13. The analytical relationship that was considered for the headed shear connectors was presented by Ollgaard et al. [10]. This relationship is given by the following equation:(5)Fi=Fu01−e−0.7Δi0.4,where Fi is the horizontal shear force in the shear connector, Fu0 is the ultimate capacity of the shear connector, and Δi is the slippage between the concrete flange and the top chord of the truss.Figure 13
Shear force-slippage curve for the shear connectors.The normal stiffness was calculated as follows:(6)Kn=EAL,where Kn is the normal stiffness, E is the elastic modulus of the shear connector, and A is the cross-sectional area of the shear connector.


### 4.2. Model Verification

A comparison of the load-deflection curves obtained from the experiments and the FE analysis is shown in Figure14. Generally, the FE curves agreed well with the experimental curves. The ultimate-capacity relative error (RE) between the FE analysis and the experimental test was <5% (Table 2). The ultimate deflection obtained via the FE analysis was larger than the corresponding experimental value. This overestimation of the deflection was probably caused by the assumption in the concrete constitutive model that the concrete remained constant after reaching ε0 (Figure 11). Figure 15 shows a comparison of the load-slippage curves from the experimental test and FE analysis, where the slippage is the relative movement between the concrete slab and the top chord at the midspan. The FE curves agree well with the experimental curves for specimens B2 and B3. The discrepancy for specimen B1 may be caused by errors introduced during the experiment. Figure 16 shows a comparison of the load-strain curves obtained from the experiments and FE analysis, which exhibit good agreement. The relative error of the load-strain curves between the test and FE analysis was <5%. Overall, the FE results agree well with the experimental results, confirming the accuracy and reliability of the FE model. As described in Section 4.3, this FE model was used to conduct a parametric study to investigate the influence of the shear connectors on the flexural response of the composite truss.Figure 14
Comparison of the load-deflection curves from the test and FE analysis.
(a)
(b)
(c)Figure 15
Comparison of the load-slippage curves from the test and FE analysis.
(a)
(b)
(c)Figure 16
Comparison of the load-strain curves from the test and FE analysis. (a) Bottom chord at midspan. (b) Concrete slab at midspan.
(a)
(b)


### 4.3. Effect of Shear Connectors

As discussed in Section4.2, the FE results agreed well with the experimental results, confirming the accuracy and reliability of the FE model. A parametric study was conducted to derive formulas for predicting the bending capacity of the composite truss.To characterize the collaborative performance between flange plate and steel truss of composite truss beam, the degree of the shear connectionη is defined. A larger degree of the shear connection η signified a better collaborative performance. Therefore, the degree of the shear connection η is an important index to study the mechanical properties of SCCTBs. The degree of the shear connection η is calculated using the following equation:(7)η=nsFu0fAs1+As2,where ns is the quantity of shear connectors within the shear span, Fu0 is the ultimate capacity of the shear connector determined by GB50017 (i.e., equation (1)), f is the ultimate strength of the steel, As1 is the cross-sectional area of the top chord in the steel truss, and As2 is the cross-sectional area of the bottom chord in the steel truss. As1 is the cross-sectional area of the top chord in steel truss and As2 is the cross-sectional area of the bottom chord in steel truss.In the parametric study, the degree of the shear connection was changed by varying the spacing of the shear connectors. The relationship between the ultimate capacity of the composite truss and the degree of the shear connection is shown in Figure17. When η was ≤1, the ultimate capacity of the composite truss increased with the degree of the shear connection. When η was >1, the ultimate capacity of the composite truss did not change with the variation of η.Figure 17
Effect of the degree of the shear connection on the ultimate load.The von Mises stress contour of the steel truss at failure (i.e., the ultimate capacity) is shown in Figure18, and the strain contour of the concrete slab at failure is shown in Figure 19. As shown in Figure 18, most of the top and bottom chords at the midspan were in the plastic region. Figure 19 indicates that the top surface of the concrete slab at the midspan reached its ultimate strength.Figure 18
von Mises stress in the steel truss.Figure 19
Strain in the concrete slab.


## 4.1. FE Modelling

A three-dimensional (3D) nonlinear FE model was developed using the commercial FE software ANSYS. The geometric dimensions of the FE model were identical to those of the tested specimens, as shown in Figure1.The concrete slab was modelled with the eight-node solid element SOLID65 having three degrees of freedom at each node (i.e., translations in thex, y, and z axes). SOLID65 is capable of cracking under tension and crushing under compression. The rebars in the concrete slab were modelled by the 3D spar element LINK8, which is a uniaxial tension-compression element with three degrees of freedom at each node. The members in the steel truss were modelled by the 3D linear beam element BEAM188, which is suitable for analysing slender to moderately thick beam structures. BEAM188 has six degrees of freedom at each node (i.e., three translations and three rotations). The connectors were also modelled by BEAM188, and the slippage and vertical deformation between the concrete slab and top chord were modelled by the nonlinear spring element COMBIN39. COMBIN39 is a unidirectional element with a generalised force-deflection capacity and three degrees of freedom (translation) at each node. An overview of the 3D FE model is shown in Figure 9. The element types for each component are shown in Figure 10, along with the mesh.Figure 9
FE model.Figure 10
FE mesh.According to [27], it is assumed that the concrete has ideal plasticity after reaching the ultimate strength. Figure 11 illustrates the simplified stress-strain relationship (f-ε) for concrete, which was converted into piecewise linear curves for easy inputting to ANSYS. During compression, the stress increased linearly until reaching 0.3fc and the strain at 0.3fc was calculated using equation (2), where Ec is the elastic modulus of concrete. In the nonlinear region, the stress-strain curve was obtained using equation (3) [28], where ε0 is the strain at the maximum concrete strength fc, as calculated via equation (4). Perfectly plastic behaviour was assumed when the concrete reached the maximum concrete strength. The performance of concrete under tension is approximately linear up to the tensile strength of the concrete. After this point, the tensile strength decreases to zero [29]. The tensile strength of the concrete was not recorded during the experiment; thus, it was considered as 10% of the compressive strength [30].(2)Ec=fε,(3)f=Ecε1+ε/ε02,(4)ε0=2fcEc.Figure 11
Stress-strain relationship for concrete.An elastic-linear hardening model was used to define the uniaxial stress-strain relationship for the steel materials, including the truss members, rebars in the concrete slab, and shear connectors (Figure12). The stress-strain relationship for steel was assumed to be identical under tension and compression. The key parameters in Figure 12, such as fy, fu, and εu, were obtained via the tensile coupon test (Section 2.2).Figure 12
Stress-strain relationship for steel.In order to simulate the slip effect between the concrete slab and the upper chord and transfer the force of the stud connector to the concrete slab effectively, the shear connector is simulated in the following way: (1) beam 188 is used to simulate the part of the stud connector in the concrete slab and (2) COMBIN39 element is used to simulate the part of the stud connector between the concrete slab and the upper chord. For the spring (COMBIN39) element, the relative movement between the top chord of truss and the concrete flange is taken into account, as illustrated in Figure13. The analytical relationship that was considered for the headed shear connectors was presented by Ollgaard et al. [10]. This relationship is given by the following equation:(5)Fi=Fu01−e−0.7Δi0.4,where Fi is the horizontal shear force in the shear connector, Fu0 is the ultimate capacity of the shear connector, and Δi is the slippage between the concrete flange and the top chord of the truss.Figure 13
Shear force-slippage curve for the shear connectors.The normal stiffness was calculated as follows:(6)Kn=EAL,where Kn is the normal stiffness, E is the elastic modulus of the shear connector, and A is the cross-sectional area of the shear connector.


## 4.2. Model Verification

A comparison of the load-deflection curves obtained from the experiments and the FE analysis is shown in Figure14. Generally, the FE curves agreed well with the experimental curves. The ultimate-capacity relative error (RE) between the FE analysis and the experimental test was <5% (Table 2). The ultimate deflection obtained via the FE analysis was larger than the corresponding experimental value. This overestimation of the deflection was probably caused by the assumption in the concrete constitutive model that the concrete remained constant after reaching ε0 (Figure 11). Figure 15 shows a comparison of the load-slippage curves from the experimental test and FE analysis, where the slippage is the relative movement between the concrete slab and the top chord at the midspan. The FE curves agree well with the experimental curves for specimens B2 and B3. The discrepancy for specimen B1 may be caused by errors introduced during the experiment. Figure 16 shows a comparison of the load-strain curves obtained from the experiments and FE analysis, which exhibit good agreement. The relative error of the load-strain curves between the test and FE analysis was <5%. Overall, the FE results agree well with the experimental results, confirming the accuracy and reliability of the FE model. As described in Section 4.3, this FE model was used to conduct a parametric study to investigate the influence of the shear connectors on the flexural response of the composite truss.Figure 14
Comparison of the load-deflection curves from the test and FE analysis.
(a)
(b)
(c)Figure 15
Comparison of the load-slippage curves from the test and FE analysis.
(a)
(b)
(c)Figure 16
Comparison of the load-strain curves from the test and FE analysis. (a) Bottom chord at midspan. (b) Concrete slab at midspan.
(a)
(b)


## 4.3. Effect of Shear Connectors

As discussed in Section4.2, the FE results agreed well with the experimental results, confirming the accuracy and reliability of the FE model. A parametric study was conducted to derive formulas for predicting the bending capacity of the composite truss.To characterize the collaborative performance between flange plate and steel truss of composite truss beam, the degree of the shear connectionη is defined. A larger degree of the shear connection η signified a better collaborative performance. Therefore, the degree of the shear connection η is an important index to study the mechanical properties of SCCTBs. The degree of the shear connection η is calculated using the following equation:(7)η=nsFu0fAs1+As2,where ns is the quantity of shear connectors within the shear span, Fu0 is the ultimate capacity of the shear connector determined by GB50017 (i.e., equation (1)), f is the ultimate strength of the steel, As1 is the cross-sectional area of the top chord in the steel truss, and As2 is the cross-sectional area of the bottom chord in the steel truss. As1 is the cross-sectional area of the top chord in steel truss and As2 is the cross-sectional area of the bottom chord in steel truss.In the parametric study, the degree of the shear connection was changed by varying the spacing of the shear connectors. The relationship between the ultimate capacity of the composite truss and the degree of the shear connection is shown in Figure17. When η was ≤1, the ultimate capacity of the composite truss increased with the degree of the shear connection. When η was >1, the ultimate capacity of the composite truss did not change with the variation of η.Figure 17
Effect of the degree of the shear connection on the ultimate load.The von Mises stress contour of the steel truss at failure (i.e., the ultimate capacity) is shown in Figure18, and the strain contour of the concrete slab at failure is shown in Figure 19. As shown in Figure 18, most of the top and bottom chords at the midspan were in the plastic region. Figure 19 indicates that the top surface of the concrete slab at the midspan reached its ultimate strength.Figure 18
von Mises stress in the steel truss.Figure 19
Strain in the concrete slab.


## 5. Prediction of Ultimate Capacity

### 5.1. Assumptions

According to the FE analysis, the following assumptions were made in deriving the formulas for calculating the ultimate capacity of the composite truss.(1)
The tensile strength in the concrete slab is ignored(2)
Only the top and bottom chords in the steel truss are considered in the calculation of the ultimate capacity, and the contribution of the diagonals in the steel truss to resisting the bending moment is ignored(3)
The top and bottom chords are in the plastic region, and the concrete slab is designed as a column under the combined axial load and bending moment (i.e., eccentric compression)(4)
Capacity-prediction formulas are derived separately for two cases:η < 1 and η ≥ 1.


### 5.2. Prediction Method Based on Full Shear Connection (η ≥ 1)

IfAs1+As2f≤fcbeh+fsy′At+fsyAb, the plastic neutral axis is located in the concrete slab (Figure 20), and the bending capacity of the composite truss can be determined as follows:(8)Mu=As1fz1+As2fz2+Mc,where Mu is the bending capacity of the composite truss, z1 is the distance between the centre lines of the top chord and concrete slab, z2 is the distance between the centre lines of the bottom chord and concrete slab, and f is the ultimate strength of the steel.Figure 20
Sketches of the composite truss with the plastic neutral axis in the concrete slab.The bending capacity of the concrete slab (Mc) can be calculated using three different stress distributions (Figure 21). If the axial force (N) calculated using equation (9) is less than the critical compression capacity (Nu) calculated using equation (10), the concrete slab is under eccentric compression with large eccentricity (i.e., tension failure with tensile reinforcements yielding, as shown in Figure 21(a)). The depth of the equivalent compressive stress block (hc) can be determined using equation (11), and Mc can be determined using equation (12):(9)N=minAs1+As2f,nsFu0,(10)Nu=fcbeh0ξb+fsy′At−fsyAb,(11)hc=N−fsy′At+fsyAbfcbe,(12)Mc=fcbehch−hc2+fsy′Ath2−as′+fsyAbh2−as,where N is the axial force in the concrete slab, Nu is the critical compressive capacity for distinguishing large or small eccentricity (i.e., tension or compression failure of the column), h is depth of cross section of concrete slab, fc is the strength of the concrete, At is the cross-sectional area of the reinforcement on the compression side (top side), Ab is the cross-sectional area of the reinforcement on the tension side (bottom side), fsy′ is the compressive yield strength of the reinforcement, fsy is the tensile yield strength of the reinforcement, be is the effective width of the concrete slab, as′ is the distance between the centroid of the reinforcements on the compressive side and the extreme compressive fibre of the cross section, and ξb is the limit of the neutral-axis depth factor, as shown in Table 3.Figure 21
Diagrams for the calculation ofMc.
(a)
(b)
(c)Table 3
Limit of the neutral-axis depth factor.
Grade of reinforcement
300 MPa
335 MPa
400 MPa
500 MPa
ξ
b
0.576
0.550
0.518
0.482IfN > Nu, the concrete slab is under eccentric compression with small eccentricity (i.e., compression failure with tensile reinforcements unyielding). In this case, hc is determined using equations (13) and (14). If hc < (1.6 − ξb)h0, the stress distribution in the concrete slab is as shown in Figure 21(b), and Mc can be calculated using equation (15). If hc < (1.6 − ξb)h0, the stress distribution is as shown in Figure 21(c); hc can be recalculated using equation (14) by assuming that σsy=fsy′ and Mc is then determined using equation (16):(13)σsy=hc/h0−0.8ξb−0.8fsy,(14)hc=N+σsyAb−fsy′Atfcbe,(15)Mc=fcbehch−hc2+fsy′Ath2−as′+σsyAbh2−as,(16)Mc=fsy′Ath2−as′+fsy′Abh2−as.IfAs1+As2f>fcbeh+fsy′At+fsyAb, the plastic neutral axis is located in the steel truss (Figure 22). In this case, the bending capacity of the composite truss can be determined using equation (18):(17)As3=As1+As22−0.5behfcf,(18)Mu=2As3−As1fz3+fcbeh0z4,where As3, determined by equation (17), is the compressive area of top chord of steel truss in SCCTBs, z3 is the distance between the centre lines of the top and bottom chords, z4 is the distance between the centre lines of the bottom chord and concrete slab, and h is the thickness of the concrete slab.Figure 22
Sketches of the composite truss with the plastic neutral axis in the steel truss.


### 5.3. Prediction Method Based on Partial Shear Connection (η < 1)

If the degree of the shear connection is <1, the plastic neutral axis is located within the steel truss (Figure23), and the bending capacity is determined using the following equations:(19)N=nsFu0,(20)As4=As1+As22−nsFu02f,(21)Mu=2As4−As1fz5+Nz6+Mc,where As4, determined by equation (20), is the compressive area of top chord of steel truss in SCCTBs, z5 is the distance between the centre lines of the top and bottom chords, and z6 is the distance between the centre lines of the bottom chord and the compression region of the concrete slab. The calculation of Mc is the same as that introduced in Section 5.2 for the case where the neutral axis is located within the concrete slab.Figure 23
Sketches of the composite-truss partial connection stiffness.


### 5.4. Predicted Results

The bending capacities obtained using the proposed formulas and the experiments are compared in Table4. Appendix provides a detailed example of calculating the ultimate capacity of the specimen B1. The predicted capacity agrees well with the experimental results (difference of <10%), indicating the reasonability and accuracy of the proposed method.Table 4
Comparison of the ultimate loads of the SCCTB specimens.
No.
Test (mm)
Formulas (mm)
Deviation (%)
B1
382.4
357.2
6.58
B2
405.9
368.2
9.29
B3
408.7
378.6
7.37
Mean
—
—
7.75A comparison between the predicted results and FE results is presented in Figure24, where η is varied from 0.3 to 1.5, covering both full and partial shear connections. As shown in the figure, the predicted values are slightly lower than the FE results, but the difference is <15%, and the change trends are similar. Thus, the proposed formulas properly consider the effect of the degree of the shear connection on the ultimate capacity of the composite truss.Figure 24
Comparison between the predicted results and FE results.The results predicted using proposed formulas are generally lower than the experimental and FE results. This slight underestimation is acceptable in engineering practice and falls within a safe margin.


## 5.1. Assumptions

According to the FE analysis, the following assumptions were made in deriving the formulas for calculating the ultimate capacity of the composite truss.(1)
The tensile strength in the concrete slab is ignored(2)
Only the top and bottom chords in the steel truss are considered in the calculation of the ultimate capacity, and the contribution of the diagonals in the steel truss to resisting the bending moment is ignored(3)
The top and bottom chords are in the plastic region, and the concrete slab is designed as a column under the combined axial load and bending moment (i.e., eccentric compression)(4)
Capacity-prediction formulas are derived separately for two cases:η < 1 and η ≥ 1.


## 5.2. Prediction Method Based on Full Shear Connection (η ≥ 1)

IfAs1+As2f≤fcbeh+fsy′At+fsyAb, the plastic neutral axis is located in the concrete slab (Figure 20), and the bending capacity of the composite truss can be determined as follows:(8)Mu=As1fz1+As2fz2+Mc,where Mu is the bending capacity of the composite truss, z1 is the distance between the centre lines of the top chord and concrete slab, z2 is the distance between the centre lines of the bottom chord and concrete slab, and f is the ultimate strength of the steel.Figure 20
Sketches of the composite truss with the plastic neutral axis in the concrete slab.The bending capacity of the concrete slab (Mc) can be calculated using three different stress distributions (Figure 21). If the axial force (N) calculated using equation (9) is less than the critical compression capacity (Nu) calculated using equation (10), the concrete slab is under eccentric compression with large eccentricity (i.e., tension failure with tensile reinforcements yielding, as shown in Figure 21(a)). The depth of the equivalent compressive stress block (hc) can be determined using equation (11), and Mc can be determined using equation (12):(9)N=minAs1+As2f,nsFu0,(10)Nu=fcbeh0ξb+fsy′At−fsyAb,(11)hc=N−fsy′At+fsyAbfcbe,(12)Mc=fcbehch−hc2+fsy′Ath2−as′+fsyAbh2−as,where N is the axial force in the concrete slab, Nu is the critical compressive capacity for distinguishing large or small eccentricity (i.e., tension or compression failure of the column), h is depth of cross section of concrete slab, fc is the strength of the concrete, At is the cross-sectional area of the reinforcement on the compression side (top side), Ab is the cross-sectional area of the reinforcement on the tension side (bottom side), fsy′ is the compressive yield strength of the reinforcement, fsy is the tensile yield strength of the reinforcement, be is the effective width of the concrete slab, as′ is the distance between the centroid of the reinforcements on the compressive side and the extreme compressive fibre of the cross section, and ξb is the limit of the neutral-axis depth factor, as shown in Table 3.Figure 21
Diagrams for the calculation ofMc.
(a)
(b)
(c)Table 3
Limit of the neutral-axis depth factor.
Grade of reinforcement
300 MPa
335 MPa
400 MPa
500 MPa
ξ
b
0.576
0.550
0.518
0.482IfN > Nu, the concrete slab is under eccentric compression with small eccentricity (i.e., compression failure with tensile reinforcements unyielding). In this case, hc is determined using equations (13) and (14). If hc < (1.6 − ξb)h0, the stress distribution in the concrete slab is as shown in Figure 21(b), and Mc can be calculated using equation (15). If hc < (1.6 − ξb)h0, the stress distribution is as shown in Figure 21(c); hc can be recalculated using equation (14) by assuming that σsy=fsy′ and Mc is then determined using equation (16):(13)σsy=hc/h0−0.8ξb−0.8fsy,(14)hc=N+σsyAb−fsy′Atfcbe,(15)Mc=fcbehch−hc2+fsy′Ath2−as′+σsyAbh2−as,(16)Mc=fsy′Ath2−as′+fsy′Abh2−as.IfAs1+As2f>fcbeh+fsy′At+fsyAb, the plastic neutral axis is located in the steel truss (Figure 22). In this case, the bending capacity of the composite truss can be determined using equation (18):(17)As3=As1+As22−0.5behfcf,(18)Mu=2As3−As1fz3+fcbeh0z4,where As3, determined by equation (17), is the compressive area of top chord of steel truss in SCCTBs, z3 is the distance between the centre lines of the top and bottom chords, z4 is the distance between the centre lines of the bottom chord and concrete slab, and h is the thickness of the concrete slab.Figure 22
Sketches of the composite truss with the plastic neutral axis in the steel truss.


## 5.3. Prediction Method Based on Partial Shear Connection (η < 1)

If the degree of the shear connection is <1, the plastic neutral axis is located within the steel truss (Figure23), and the bending capacity is determined using the following equations:(19)N=nsFu0,(20)As4=As1+As22−nsFu02f,(21)Mu=2As4−As1fz5+Nz6+Mc,where As4, determined by equation (20), is the compressive area of top chord of steel truss in SCCTBs, z5 is the distance between the centre lines of the top and bottom chords, and z6 is the distance between the centre lines of the bottom chord and the compression region of the concrete slab. The calculation of Mc is the same as that introduced in Section 5.2 for the case where the neutral axis is located within the concrete slab.Figure 23
Sketches of the composite-truss partial connection stiffness.


## 5.4. Predicted Results

The bending capacities obtained using the proposed formulas and the experiments are compared in Table4. Appendix provides a detailed example of calculating the ultimate capacity of the specimen B1. The predicted capacity agrees well with the experimental results (difference of <10%), indicating the reasonability and accuracy of the proposed method.Table 4
Comparison of the ultimate loads of the SCCTB specimens.
No.
Test (mm)
Formulas (mm)
Deviation (%)
B1
382.4
357.2
6.58
B2
405.9
368.2
9.29
B3
408.7
378.6
7.37
Mean
—
—
7.75A comparison between the predicted results and FE results is presented in Figure24, where η is varied from 0.3 to 1.5, covering both full and partial shear connections. As shown in the figure, the predicted values are slightly lower than the FE results, but the difference is <15%, and the change trends are similar. Thus, the proposed formulas properly consider the effect of the degree of the shear connection on the ultimate capacity of the composite truss.Figure 24
Comparison between the predicted results and FE results.The results predicted using proposed formulas are generally lower than the experimental and FE results. This slight underestimation is acceptable in engineering practice and falls within a safe margin.


## 6. Conclusions

This paper presents an experimental and theoretical analysis of steel-concrete composite trusses under bending. According to the results, the following conclusions are drawn.The composite truss beams failed via the yielding of the bottom chords, which exhibited ductile behaviour.The quantity of the shear connectors affected the flexural response of the composite truss. A specimen with a partial shear connection (B1) exhibited a lower capacity and stiffness than specimens with a full shear connection (B2 and B3). When the quantity of shear connectors exceeded the critical amount, the influence of the shear-connector quantity became less significant.An FE model with proper consideration of the constitutive models of concrete and steel could accurately predict the structural behaviour (i.e., load-deflection, load-slippage, and load-strain curves) of the steel-concrete composite truss, as verified by experimental results. This FE model was employed for a parametric study. The results indicated that if the degree of the shear connection (η) is <1, the bending capacity increases with η. However, if η ≥ 1, the effect of η on the bending capacity is negligible.According to the degree of the shear connection, a design method was proposed to predict the ultimate bending capacity of the composite truss. The prediction results agreed well with the experimental results.



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*Source: 1502707-2019-06-12.xml*