# Flexural Capacity of Steel-Concrete Composite Beams under Hogging Moment

Authors: Jing Liu; Fa-xing Ding; Xue-mei Liu; Zhi-wu Yu; Zhe Tan; Jun-wen Huang
Journal: Advances in Civil Engineering
 (2019)

---

## Abstract

This study investigates the flexural strength of simply supported steel-concrete composite beams under hogging moment. A total of 24 composite beams are included in the experiments, and ABAQUS software is used to establish finite element (FE) models that can simulate the mechanical properties of composite beams. In a parametric study, the influences of several major parameters, such as shear connection degree, stud arrangement and diameter, longitudinal and transverse reinforcement ratios, loading manner, and beam length, on flexural strength were investigated. Thereafter, three standards, namely, GB 50017, Eurocode 4, and BS 5950, were used to estimate the flexural strength of the composite beams. These codes were also compared with experimental and numerical results. Results indicate that GB 50017 may provide better estimations than the other two codes.


---

## Body

## 1. Introduction

Steel-concrete composite beams have been widely used in building construction. In engineering, situations occur in which composite beams undergo hogging bending. Examples of such situations include the following: (a) hogging bending regions near interior supports for continuous composite beams and (b) a beam is typically subjected to a hogging moment in areas near the column for a multistory frame structure.Flexural capacity, which has become a major parameter due to its large cross section, has been widely applied in practice. Some studies have suggested that shear connection degree exerts a certain influence on flexural capacity, which can be theoretically divided into partial and full shear connections. The former reduces the stud number and benefits the colligation of reinforcing bars, whereas the latter guarantees bearing strength.Therefore, various methods recommended by different codes have been proposed to estimate the flexural strength of composite beams. GB 50017 [1] presents a formula for calculating the flexural strength of the partial shear connection of composite beams in accordance with simplified plastic theory, which considers partial and full shear connections. BS 5950 [2] states that beams under hogging moment should be adequately anchored, and longitudinal reinforcement should be assumed to be stressed to its design strength 0.87fy, where it is in tension. The American Institute of Steel Construction (AISC)-Load Resistance Factor Design (LRFD) [3] and Eurocode 4 [4] rule that tension reinforcement should be adequately anchored and should be curtailed to suit the stud spacing in the negative moment regions of continuous beams. Experimental research and theoretical research on composite beams under hogging bending moment have been conducted in recent years. Some researchers have decided to study simply supported beams in the interest of simplicity.Nie and Cai [5] considered the slips at the steel girder and concrete slab interface and then developed a model for predicting the mechanical behavior of composite beams under hogging moment. The finite element (FE) software, ANSYS, was also used. Amadio et al. [6] dealt with the evaluation of the effective width of composite beams; the effective width increased with the load for all the test specimens. Loh et al. [7] studied the behavior of eight composite beams under hogging moment through an extensive experiment. Parameters, including reinforcement percentage and shear connection degree, were varied. Pecce et al. [8] conducted four experimental tests on simply supported composite beams under negative moment, in which the type, width, and connection degree were varied. Lin et al. [9, 10] studied the mechanical behavior of composite beams under negative bending moment through research test on fatigue and ultimate static loading. Vasdravellis et al. [11] presented a numerical and experimental study on steel-concrete composite beams subjected to the combined effects of negative or positive bending and axial compression.FE modeling is a major analysis method for predicting the response of steel-concrete composite structures.Zhu et al. [12] presented a numerical study on the property of studs and its application to steel-concrete composite beams. Chang et al. [13, 14] investigated the property of rock and composite structures through ABAQUS. Mirza and Uy [15] researched the mechanical behavior of composite beam-column flush end-plate connections subjected to high-consequence, low-probability loading via ABAQUS. Vasdravellis et al. [11] developed a nonlinear FE model to predict the nonlinear response of tested composite beams. The model relies on ABAQUS software. Li et al. [16] presented an FE modeling to investigate the behavior of concrete-filled steel tubular column-column connections. Zhao et al. [17] investigated the bearing capacity of a corroded reinforced concrete beam using ABAQUS.The aforementioned literature indicates that steel-concrete composite beams generally perform well under flexural loadings. Some parameters, including shear connection degree, stud diameter, transverse and longitudinal reinforcement ratios, and loading condition, which influence the flexural strength of composite beams, have not been thoroughly investigated through experimental studies. Also, other factors, such as beam span, studs in double row layout, and loading manner and position, have not been discussed. Moreover, the standards of various countries have not been compared under a considerably wide range of factors that cover experimental and FE results.Hence, the current study aims to make a thorough investigation on the flexural strength of steel-concrete composite beams and evaluating different methods for calculating flexural strength proposed in various standards. On the basis of the experimental, theoretical, and numerical research of our team [18–20], this study has four objectives: (1) to investigate the flexural capacity of 24 simply supported steel-concrete composite beams under hogging moment through an experimental study; (2) to simulate the flexural performance of the composite beams by establishing FE models using the ABAQUS program; (3) to investigate the effects of different factors on the flexural behavior of steel-concrete composite beams through parametric analysis; and (4) to evaluate different methods, including those of GB 50017, Eurocode 4, and BS 5950, with respect to the experimental and numerical results.


## 2. Experimental Study

### 2.1. Materials and Specimens

Ding et al. [19] conducted 22 simply supported steel-concrete composite beam experimental investigations on hysteretic behavior. In the current work, 24 steel-concrete composite beams, including SCB19-SCB20 (loading mode was monotonic), were included in the test study.Figure1 shows the cross section details of the girders. Figures 2 and 3 present the composite beam test loading device. Table 1 lists the geometric properties and characteristics of the composite beams. l is the specimen length, hc is the concrete slab depth, wc is the concrete slab width, hs is the steel beam height, ws is the steel beam width, and d is the stud diameter. ρst and ρsl are the transverse and longitudinal reinforcement ratios of the concrete slab, respectively. η is the degree of shear connection in the hogging moment region (based on GB 50017).Figure 1
Cross section details of the girders: (a) SCB1∼2, (b) SCB3∼8, (c) SCB9∼13, and (d) SCB14∼24.Figure 2
Test setup on the spot: (a) SCB1∼2, (b) SCB3∼8, (c) SCB9∼13, and (d) SCB14∼24.
(a)
(b)
(c)
(d)Figure 3
Experimental setup for all specimens: (a) SCB1∼8, (b) SCB9∼13, and (c) SCB14∼24.Table 1
Geometric properties and characteristics of composite beams.
Source of the specimens
No.
Loading mode
l (mm)
w
c (mm)
h
c (mm)
w
s (mm)
h
s (mm)
d (mm)
η
ρ
st (%)
ρ
sl (%)
M (kN)
This paper
SCB1
Dynamic cyclic
3000
650
75
258
140
13
1.44
0.62
3.47
120
SCB2
Dynamic cyclic
3000
650
75
258
140
13
0.55
0.62
3.47
121
SCB3
Dynamic cyclic
3000
650
75
258
140
13
1.44
0.62
3.47
158
SCB4
Dynamic cyclic
3000
650
75
258
140
13
1
0.62
3.47
146
SCB5
Dynamic cyclic
3000
650
75
258
140
13
0.55
0.62
3.47
132
SCB6
Dynamic cyclic
3000
650
75
258
140
13
2.64
0.62
1.89
131
SCB7
Dynamic cyclic
3000
650
75
258
140
13
1.83
0.62
1.89
123
SCB8
Dynamic cyclic
3000
650
75
258
140
13
1.01
0.62
1.89
120
SCB9
Dynamic cyclic
4000
1000
100
408
258
13
3.14
0.38
1.58
390
SCB10
Dynamic cyclic
4000
1000
100
408
258
16
3.25
0.38
1.58
399
SCB11
Dynamic cyclic
4000
1000
100
408
258
19
3.22
0.38
1.58
395
SCB12
Dynamic cyclic
4000
1000
100
408
258
16
2.26
0.38
1.58
392
SCB13
Dynamic cyclic
4000
1000
100
408
258
16
4.24
0.38
1.58
405
SCB14
Dynamic cyclic
3800
800
120
100
200
16
1.83
0.32
2.51
207
SCB15
Dynamic cyclic
3800
800
120
100
200
16
1.59
0.32
2.51
198
SCB16
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.32
2.51
193
SCB17
Dynamic cyclic
3800
800
120
100
200
16
1.06
0.32
2.51
189
SCB18
Dynamic cyclic
3800
800
120
100
200
16
0.83
0.32
2.51
187
SCB19
Monotonic
3800
800
120
100
200
16
1.74
0.32
1.88
172
SCB20
Monotonic
3800
800
120
100
200
16
2.22
0.32
1.47
165
SCB21
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.20
2.51
200
SCB22
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.43
2.51
211
SCB23
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.59
2.51
206
SCB24
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.78
2.51
224
Nie [21]
NSCB5
Monotonic
3840
800
125
100
200
16
4.62
0.60
0.88
132
NSCB6
Monotonic
3840
800
125
100
200
16
3.05
0.60
1.33
144
NSCB7
Monotonic
3840
800
125
100
200
16
2.60
0.60
1.55
175
NSCB8
Monotonic
3840
800
125
100
200
16
2.02
0.60
2.01
183
Lin et al. [9]
LCB1
Monotonic
4000
800
250
400
641
22
1.79
1.06
1.98
3981
LCB5
Monotonic
4000
800
250
400
641
22
1.79
1.06
1.98
4003
LCB7
Monotonic
4000
800
250
400
641
22
1.51
1.06
1.98
3801
Vasdravellis et al. [11]
VCB1
Monotonic
4000
600
120
133.9
206.8
19
2.68
0.24
0.63
186For convenient calculation and analysis, parameters related to the specimens in the literature (Lin et al. [9], Nie [21], and Vasdravellis et al. [11]) are also provided in Table 1. The maximum load per stud was investigated via a push-out test [11].Table2 presents the properties of steel and concrete. fcu is the cubic compressive strength of concrete, fs,b is the yield strength of steel, fs,s is the yield strength of stud, fs,r is the yield strength of longitudinal reinforcement, and fu is the ultimate strength of stud. Various concrete grades are included in the study with concrete strength varying from 35.5 MPa to 49.7 MPa. The tensile strengths of steel are ranging from 250 to 324 MPa as per design.Table 2
Properties of steel and concrete.
No.
f
s,s (MPa)
f
u (MPa)
f
s,b (MPa)
f
s,r (MPa)
f
cu (MPa)
SCB1
330
440
324
453
35.5
SCB2
330
440
324
453
35.5
SCB3
330
440
324
453
35.5
SCB4
330
440
324
453
35.5
SCB5
330
440
324
453
35.5
SCB6
330
440
324
453
35.5
SCB7
330
440
324
453
35.5
SCB8
330
440
324
453
35.5
SCB9
330
440
320
440
43.7
SCB10
350
460
320
440
43.7
SCB11
350
455
320
440
43.7
SCB12
350
460
320
440
43.7
SCB13
350
460
320
440
43.7
SCB14
350
480
250
380
44.3
SCB15
350
480
250
380
44.3
SCB16
350
480
250
380
43.4
SCB17
350
480
250
380
48.5
SCB18
350
480
250
380
42.2
SCB19
350
480
250
380
38.2
SCB20
350
480
250
380
46.2
SCB21
350
480
320
380
41.9
SCB22
350
480
320
380
42.1
SCB23
350
480
320
380
49.7
SCB24
350
480
320
380
40.8
NSCB5
417
535
394
389
36
NSCB6
417
535
394
389
38.2
NSCB7
417
535
394
389
27.4
NSCB8
—
—
370
510
21
CB1
417
535
394
389
36
CB5
417
535
394
389
38.2
CB7
417
535
394
389
27.4
CB1
—
—
370
510
21


### 2.2. Testing System and Method

A total of 24 test specimens were designed and experimented using two approaches. The first approach adopted the monotonic loading mode and included two specimens labeled SCB19 and SCB20. The second approach applied the dynamic cyclic loading mode and included the remaining 22 specimens. The failure process and phenomenon of such beams can be found in the study of Ding et al. [18]. The experimental load-deflection curves of composite beams under dynamic cyclic loading are also described in that article.


### 2.3. Experimental Results and Discussion

Shear connection degree is a principal factor for the calculation of composite beams’ flexural strength under various codes; therefore, its definition is presented here with the expression for the subsequent discussion:(1)η=nnf,where nf is the number of connectors for full shear connection, nf=Vs/Vu. n is the actual number of studs between the adjacent support and the intermediate point. Vs is the entire horizontal shear at the interface between the concrete slab and the steel girder, Vs=Astfst, where Ast is the longitudinal reinforcement area and fst is the yield strength of the longitudinal reinforce area. Vu is the nominal strength of a single stud shear connector. The definitions of Vs and Vu may vary with the standards, including GB 50017, BS 5950, AISC-LRFD, and Eurocode 4.To understand the factors that influence the flexural capacity of composite beams, this section focuses on discussing such factors.


#### 2.3.1. Shear Connection Degree

Figure4 shows the relationship between flexural strength and shear connection degree. The contrast of SCB3–SCB5, SCB11–SCB13, and SCB14–SCB18 illustrates that a higher shear connection degree leads to greater flexural strength. When η is high, the steel-concrete composite beams exhibit good interaction behavior, which can minimize the deflection of composite beams under loading and guarantee bearing capacity.Figure 4
Relationship betweenM and η.


#### 2.3.2. Ratio of Transverse Reinforcement

Figure5 shows the relationship between transverse reinforcement ratio and flexural strength. The contrast of SCB21–SCB24 shows that the transverse reinforcement ratios of 0.20%–0.78% exert a certain influence on bearing strength. The capacity in the negative moment of SCB24 is 12.0% higher than that of SCB21. This result contributes to the higher transverse reinforcement ratio and exerts the confined effect, which ensures that the concrete slab, stud, and steel girder work better to improve the flexural capacity of composite beams.Figure 5
Relationship betweenM and ρst.


#### 2.3.3. Ratio of Longitudinal Reinforcement

Figure6 illustrates the relationship between M and ρsl. The contrast of SCB3–SCB8 shows that the longitudinal reinforcement ratios of 1.89% or 3.47% exert an appreciable impact on limit bearing capacity. Flexural capacity increases with the longitudinal reinforcement ratio. This result contributes to the higher longitudinal reinforcement ratio that can participate in force, which improves the ultimate flexural strength of the composite beams in the negative moment region.Figure 6
Relationship betweenM and ρsl.


#### 2.3.4. Diameter of Studs

Figure7 illustrates the relationship between M and d. The diameters of the studs of SCB21–SCB23 are 13, 16, and 19 mm, respectively. These specimens have the same shear connection degree (approximately 2.5). The flexural capacity of SCB10 is 2.3% higher than that of SCB9, and the bearing capacity of SCB11 is 1.4% higher than that of SCB9, thereby indicating that bearing capacity is unaffected by stud diameter.Figure 7
Relationship betweenM and d.


## 2.1. Materials and Specimens

Ding et al. [19] conducted 22 simply supported steel-concrete composite beam experimental investigations on hysteretic behavior. In the current work, 24 steel-concrete composite beams, including SCB19-SCB20 (loading mode was monotonic), were included in the test study.Figure1 shows the cross section details of the girders. Figures 2 and 3 present the composite beam test loading device. Table 1 lists the geometric properties and characteristics of the composite beams. l is the specimen length, hc is the concrete slab depth, wc is the concrete slab width, hs is the steel beam height, ws is the steel beam width, and d is the stud diameter. ρst and ρsl are the transverse and longitudinal reinforcement ratios of the concrete slab, respectively. η is the degree of shear connection in the hogging moment region (based on GB 50017).Figure 1
Cross section details of the girders: (a) SCB1∼2, (b) SCB3∼8, (c) SCB9∼13, and (d) SCB14∼24.Figure 2
Test setup on the spot: (a) SCB1∼2, (b) SCB3∼8, (c) SCB9∼13, and (d) SCB14∼24.
(a)
(b)
(c)
(d)Figure 3
Experimental setup for all specimens: (a) SCB1∼8, (b) SCB9∼13, and (c) SCB14∼24.Table 1
Geometric properties and characteristics of composite beams.
Source of the specimens
No.
Loading mode
l (mm)
w
c (mm)
h
c (mm)
w
s (mm)
h
s (mm)
d (mm)
η
ρ
st (%)
ρ
sl (%)
M (kN)
This paper
SCB1
Dynamic cyclic
3000
650
75
258
140
13
1.44
0.62
3.47
120
SCB2
Dynamic cyclic
3000
650
75
258
140
13
0.55
0.62
3.47
121
SCB3
Dynamic cyclic
3000
650
75
258
140
13
1.44
0.62
3.47
158
SCB4
Dynamic cyclic
3000
650
75
258
140
13
1
0.62
3.47
146
SCB5
Dynamic cyclic
3000
650
75
258
140
13
0.55
0.62
3.47
132
SCB6
Dynamic cyclic
3000
650
75
258
140
13
2.64
0.62
1.89
131
SCB7
Dynamic cyclic
3000
650
75
258
140
13
1.83
0.62
1.89
123
SCB8
Dynamic cyclic
3000
650
75
258
140
13
1.01
0.62
1.89
120
SCB9
Dynamic cyclic
4000
1000
100
408
258
13
3.14
0.38
1.58
390
SCB10
Dynamic cyclic
4000
1000
100
408
258
16
3.25
0.38
1.58
399
SCB11
Dynamic cyclic
4000
1000
100
408
258
19
3.22
0.38
1.58
395
SCB12
Dynamic cyclic
4000
1000
100
408
258
16
2.26
0.38
1.58
392
SCB13
Dynamic cyclic
4000
1000
100
408
258
16
4.24
0.38
1.58
405
SCB14
Dynamic cyclic
3800
800
120
100
200
16
1.83
0.32
2.51
207
SCB15
Dynamic cyclic
3800
800
120
100
200
16
1.59
0.32
2.51
198
SCB16
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.32
2.51
193
SCB17
Dynamic cyclic
3800
800
120
100
200
16
1.06
0.32
2.51
189
SCB18
Dynamic cyclic
3800
800
120
100
200
16
0.83
0.32
2.51
187
SCB19
Monotonic
3800
800
120
100
200
16
1.74
0.32
1.88
172
SCB20
Monotonic
3800
800
120
100
200
16
2.22
0.32
1.47
165
SCB21
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.20
2.51
200
SCB22
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.43
2.51
211
SCB23
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.59
2.51
206
SCB24
Dynamic cyclic
3800
800
120
100
200
16
1.3
0.78
2.51
224
Nie [21]
NSCB5
Monotonic
3840
800
125
100
200
16
4.62
0.60
0.88
132
NSCB6
Monotonic
3840
800
125
100
200
16
3.05
0.60
1.33
144
NSCB7
Monotonic
3840
800
125
100
200
16
2.60
0.60
1.55
175
NSCB8
Monotonic
3840
800
125
100
200
16
2.02
0.60
2.01
183
Lin et al. [9]
LCB1
Monotonic
4000
800
250
400
641
22
1.79
1.06
1.98
3981
LCB5
Monotonic
4000
800
250
400
641
22
1.79
1.06
1.98
4003
LCB7
Monotonic
4000
800
250
400
641
22
1.51
1.06
1.98
3801
Vasdravellis et al. [11]
VCB1
Monotonic
4000
600
120
133.9
206.8
19
2.68
0.24
0.63
186For convenient calculation and analysis, parameters related to the specimens in the literature (Lin et al. [9], Nie [21], and Vasdravellis et al. [11]) are also provided in Table 1. The maximum load per stud was investigated via a push-out test [11].Table2 presents the properties of steel and concrete. fcu is the cubic compressive strength of concrete, fs,b is the yield strength of steel, fs,s is the yield strength of stud, fs,r is the yield strength of longitudinal reinforcement, and fu is the ultimate strength of stud. Various concrete grades are included in the study with concrete strength varying from 35.5 MPa to 49.7 MPa. The tensile strengths of steel are ranging from 250 to 324 MPa as per design.Table 2
Properties of steel and concrete.
No.
f
s,s (MPa)
f
u (MPa)
f
s,b (MPa)
f
s,r (MPa)
f
cu (MPa)
SCB1
330
440
324
453
35.5
SCB2
330
440
324
453
35.5
SCB3
330
440
324
453
35.5
SCB4
330
440
324
453
35.5
SCB5
330
440
324
453
35.5
SCB6
330
440
324
453
35.5
SCB7
330
440
324
453
35.5
SCB8
330
440
324
453
35.5
SCB9
330
440
320
440
43.7
SCB10
350
460
320
440
43.7
SCB11
350
455
320
440
43.7
SCB12
350
460
320
440
43.7
SCB13
350
460
320
440
43.7
SCB14
350
480
250
380
44.3
SCB15
350
480
250
380
44.3
SCB16
350
480
250
380
43.4
SCB17
350
480
250
380
48.5
SCB18
350
480
250
380
42.2
SCB19
350
480
250
380
38.2
SCB20
350
480
250
380
46.2
SCB21
350
480
320
380
41.9
SCB22
350
480
320
380
42.1
SCB23
350
480
320
380
49.7
SCB24
350
480
320
380
40.8
NSCB5
417
535
394
389
36
NSCB6
417
535
394
389
38.2
NSCB7
417
535
394
389
27.4
NSCB8
—
—
370
510
21
CB1
417
535
394
389
36
CB5
417
535
394
389
38.2
CB7
417
535
394
389
27.4
CB1
—
—
370
510
21


## 2.2. Testing System and Method

A total of 24 test specimens were designed and experimented using two approaches. The first approach adopted the monotonic loading mode and included two specimens labeled SCB19 and SCB20. The second approach applied the dynamic cyclic loading mode and included the remaining 22 specimens. The failure process and phenomenon of such beams can be found in the study of Ding et al. [18]. The experimental load-deflection curves of composite beams under dynamic cyclic loading are also described in that article.


## 2.3. Experimental Results and Discussion

Shear connection degree is a principal factor for the calculation of composite beams’ flexural strength under various codes; therefore, its definition is presented here with the expression for the subsequent discussion:(1)η=nnf,where nf is the number of connectors for full shear connection, nf=Vs/Vu. n is the actual number of studs between the adjacent support and the intermediate point. Vs is the entire horizontal shear at the interface between the concrete slab and the steel girder, Vs=Astfst, where Ast is the longitudinal reinforcement area and fst is the yield strength of the longitudinal reinforce area. Vu is the nominal strength of a single stud shear connector. The definitions of Vs and Vu may vary with the standards, including GB 50017, BS 5950, AISC-LRFD, and Eurocode 4.To understand the factors that influence the flexural capacity of composite beams, this section focuses on discussing such factors.


### 2.3.1. Shear Connection Degree

Figure4 shows the relationship between flexural strength and shear connection degree. The contrast of SCB3–SCB5, SCB11–SCB13, and SCB14–SCB18 illustrates that a higher shear connection degree leads to greater flexural strength. When η is high, the steel-concrete composite beams exhibit good interaction behavior, which can minimize the deflection of composite beams under loading and guarantee bearing capacity.Figure 4
Relationship betweenM and η.


### 2.3.2. Ratio of Transverse Reinforcement

Figure5 shows the relationship between transverse reinforcement ratio and flexural strength. The contrast of SCB21–SCB24 shows that the transverse reinforcement ratios of 0.20%–0.78% exert a certain influence on bearing strength. The capacity in the negative moment of SCB24 is 12.0% higher than that of SCB21. This result contributes to the higher transverse reinforcement ratio and exerts the confined effect, which ensures that the concrete slab, stud, and steel girder work better to improve the flexural capacity of composite beams.Figure 5
Relationship betweenM and ρst.


### 2.3.3. Ratio of Longitudinal Reinforcement

Figure6 illustrates the relationship between M and ρsl. The contrast of SCB3–SCB8 shows that the longitudinal reinforcement ratios of 1.89% or 3.47% exert an appreciable impact on limit bearing capacity. Flexural capacity increases with the longitudinal reinforcement ratio. This result contributes to the higher longitudinal reinforcement ratio that can participate in force, which improves the ultimate flexural strength of the composite beams in the negative moment region.Figure 6
Relationship betweenM and ρsl.


### 2.3.4. Diameter of Studs

Figure7 illustrates the relationship between M and d. The diameters of the studs of SCB21–SCB23 are 13, 16, and 19 mm, respectively. These specimens have the same shear connection degree (approximately 2.5). The flexural capacity of SCB10 is 2.3% higher than that of SCB9, and the bearing capacity of SCB11 is 1.4% higher than that of SCB9, thereby indicating that bearing capacity is unaffected by stud diameter.Figure 7
Relationship betweenM and d.


## 2.3.1. Shear Connection Degree

Figure4 shows the relationship between flexural strength and shear connection degree. The contrast of SCB3–SCB5, SCB11–SCB13, and SCB14–SCB18 illustrates that a higher shear connection degree leads to greater flexural strength. When η is high, the steel-concrete composite beams exhibit good interaction behavior, which can minimize the deflection of composite beams under loading and guarantee bearing capacity.Figure 4
Relationship betweenM and η.


## 2.3.2. Ratio of Transverse Reinforcement

Figure5 shows the relationship between transverse reinforcement ratio and flexural strength. The contrast of SCB21–SCB24 shows that the transverse reinforcement ratios of 0.20%–0.78% exert a certain influence on bearing strength. The capacity in the negative moment of SCB24 is 12.0% higher than that of SCB21. This result contributes to the higher transverse reinforcement ratio and exerts the confined effect, which ensures that the concrete slab, stud, and steel girder work better to improve the flexural capacity of composite beams.Figure 5
Relationship betweenM and ρst.


## 2.3.3. Ratio of Longitudinal Reinforcement

Figure6 illustrates the relationship between M and ρsl. The contrast of SCB3–SCB8 shows that the longitudinal reinforcement ratios of 1.89% or 3.47% exert an appreciable impact on limit bearing capacity. Flexural capacity increases with the longitudinal reinforcement ratio. This result contributes to the higher longitudinal reinforcement ratio that can participate in force, which improves the ultimate flexural strength of the composite beams in the negative moment region.Figure 6
Relationship betweenM and ρsl.


## 2.3.4. Diameter of Studs

Figure7 illustrates the relationship between M and d. The diameters of the studs of SCB21–SCB23 are 13, 16, and 19 mm, respectively. These specimens have the same shear connection degree (approximately 2.5). The flexural capacity of SCB10 is 2.3% higher than that of SCB9, and the bearing capacity of SCB11 is 1.4% higher than that of SCB9, thereby indicating that bearing capacity is unaffected by stud diameter.Figure 7
Relationship betweenM and d.


## 3. Methods for Estimating Flexural Capacity

### 3.1. GB 50017

In the Chinese national standard GB 50017, the flexural capacityM of composite beams under hogging moment is expressed as follows:(1)
Whenη≥1,(2)M=Ms+Astfsty3+y42,(3)Ms=S1+S2fy,where S1 = the area moment above the steel beam’s neutral axis, S2 = the area moment below the steel beam’s neutral axis, y3 = the distance between the longitudinal reinforcement’s neutral axis to the composite beam neutral’s axis, y4 = the distance between the steel beam axis to the composite beam neutral axis, Ms = the flexural load capacity of the steel beams, and Ast = the longitudinal reinforce area in the effective width of the concrete slab.Vu denotes the nominal strength of a single stud. It is defined as follows:(4)Vu=0.43kAsdfcEc0.5<0.7kAsdfu,where Asd = the cross-sectional area of the stud, Ec = Young’s modulus of concrete, fc = the compressive strength of concrete, Vs=Asfs, As = the cross-sectional area of steel, and Ac = is the cross-sectional area of concrete. For the negative moment, the shear bearing capacity of the studs should be multiplied by a folding coefficient k, where k = 0.9.(2)
Whenη≤1, the bending capacity is still in accordance with formula (2). Astfst should be regarded as a smaller value of Astfst and nrNv. nr indicates the number of studs in the shear span.


### 3.2. BS 5950

For hogging moment, the longitudinal reinforcement is supposed to be stressed to its design strength of0.87fy, where it is in tension, and the beam should be adequately anchored.


### 3.3. Eurocode 4

Eurocode 4 and AISC–LRFD state that, in the negative moment regions, tension reinforcement should be curtailed to suit shear connector spacing and should be adequately anchored.


## 3.1. GB 50017

In the Chinese national standard GB 50017, the flexural capacityM of composite beams under hogging moment is expressed as follows:(1)
Whenη≥1,(2)M=Ms+Astfsty3+y42,(3)Ms=S1+S2fy,where S1 = the area moment above the steel beam’s neutral axis, S2 = the area moment below the steel beam’s neutral axis, y3 = the distance between the longitudinal reinforcement’s neutral axis to the composite beam neutral’s axis, y4 = the distance between the steel beam axis to the composite beam neutral axis, Ms = the flexural load capacity of the steel beams, and Ast = the longitudinal reinforce area in the effective width of the concrete slab.Vu denotes the nominal strength of a single stud. It is defined as follows:(4)Vu=0.43kAsdfcEc0.5<0.7kAsdfu,where Asd = the cross-sectional area of the stud, Ec = Young’s modulus of concrete, fc = the compressive strength of concrete, Vs=Asfs, As = the cross-sectional area of steel, and Ac = is the cross-sectional area of concrete. For the negative moment, the shear bearing capacity of the studs should be multiplied by a folding coefficient k, where k = 0.9.(2)
Whenη≤1, the bending capacity is still in accordance with formula (2). Astfst should be regarded as a smaller value of Astfst and nrNv. nr indicates the number of studs in the shear span.


## 3.2. BS 5950

For hogging moment, the longitudinal reinforcement is supposed to be stressed to its design strength of0.87fy, where it is in tension, and the beam should be adequately anchored.


## 3.3. Eurocode 4

Eurocode 4 and AISC–LRFD state that, in the negative moment regions, tension reinforcement should be curtailed to suit shear connector spacing and should be adequately anchored.


## 4. FE Analysis

### 4.1. FE Modeling

#### 4.1.1. Material Constitutive Models

The material constitutive models of concrete and steel suggested by Ding et al. [18] are used for the model. The detailed parameters are provided in the study of Ding et al. [18].The stiffness of the spring element is defined by load-slip curves and is used to simulate the shear stud. The formula proposed by Ding et al. [20] through a bidirectional push-off test can be used for concrete in tension.The equation can be written as(5)y=A4x+B4−1x21+A4−2x+B4x2,x≤1,x0.15x−12+x,x>1,where y=p/pu, x=s/s0, and B4=1.6A4−12. s0 is the value of slip corresponding to the peak load, and s0=100/d. The ascending parameter A4 is defined as the ratio of bond stiffness to peak secant stiffness, and A4=10d−80/0.7d−5. pu is the shear capacity per stud. For a slip up to 5 mm, V reaches 99% of the ultimate load Vu. When the longitudinal, lateral, and vertical stiffness adopt expression (5) in this paper, good results can be obtained.


#### 4.1.2. Model Skills

FE models are established using the ABAQUS program [22], which is extensively adopted in analyzing rock and composite structures (Chang et al. [13, 14]). Steel beams are modeled by using four-node reduced integral format shell elements (S4R). Concrete is modeled by using eight-node brick elements (C3D8R). Reinforcement bars in the specimens are modeled by the truss element T3D2 because this truss element is effective and accurate in simulating reinforcement in steel-concrete composite beams according to Ding et al. [18].Figure8 shows the simplified FE models for steel-concrete composite beams. Spring and beam elements (B31) are used to model the studs, which can be seen in Figures 8(a) and 8(b), respectively. The model uses a structured meshing technique. The surface-to-surface and Coulomb friction model is defined as the type of contact between the steel girder and the concrete slab.Figure 8
Simplified FE models for steel-concrete composite beams. (a) Spring elements for studs and (b) beam elements for studs.
(a)
(b)


### 4.2. Flexural Capacity from FE Analysis (FEA)

Figure9 shows the comparison between the calculated and tested load-deformation curves of a composite beam. Figure 10 illustrates the comparison between the calculated and tested load-end slips of a composite beam. Figure 11 demonstrates the comparison between the calculated and tested longitudinal reinforcement and bottom flange strains of a composite beam.Figure 9
Comparison between the calculated and tested load-deformation curves of a composite beam. (a) SCB19 (present study), (b) NSCB5 (Nie and Cai [5]), and (c) VCB1 (Vasdravellis et al. [11]).
(a)
(b)
(c)Figure 10
Comparison between the calculated and tested load-end slips of a composite beam.Figure 11
Comparison between the calculated and tested longitudinal reinforcement and bottom flange strains of a composite beam.Good agreement between FEA and the measured results is found in the elastic stage. Thereafter, the curve from the calculated and test results appeared with a certain deviation in the elastic-plastic and failure stages.Table3 presents the comparison between the simulated and test results. A total of 32 groups of test data regarding steel-concrete composite beams are included for analysis and model validation. M is the measured values of flexural capacity, M11 is the flexural strength obtained via the spring element modeling method, and M12 is the flexural strength obtained via the beam element modeling method. M2, M3, and M4 are the flexural capacities under GB 50017, BS 5950, and Eurocode 4, respectively. The test results are compared using different methods, including FEA and three standards.Table 3
Comparison among the three standards and simulated and test results.
No.
Source of the specimens
Total number of specimens
Characteristic value
Spring element
Beam element
GB 50017
BS 5950
Eurocode 4
M/M11
M/M12
M/M2
M/M3
M/M4
1
This paper
24
Average
1.037
0.981
1.031
1.161
1.049
Coefficient of variation
0.063
0.093
0.058
0.151
0.065
2
Nie [21]
4
Average
0.993
0.932
1.098
1.195
1.060
Coefficient of variation
0.091
0.034
0.061
0.067
0.064
3
Lin et al. [9]
3
Average
1.000
0.962
1.169
1.306
1.073
Coefficient of variation
0.104
0.088
0.031
0.032
0.033
4
Vasdravellis et al. [11]
1
Average
1.099
0.863
1.208
1.348
1.083
Coefficient of variation
—
—
—
—
—
5
All above
32
Average
1.026
0.963
1.058
1.185
1.036
Coefficient of variation
0.073
0.085
0.073
0.140
0.088The averageM/M11 ratio is 1.026 with a coefficient of variation at 0.073 for the spring element, and the average M/M12 ratio is 0.963 with a coefficient of variation at 0.085 for the beam element. Such findings indicate that the FE simulation results are extremely close to the test results.


### 4.3. Parametric Study

Parameter analysis is conducted in this section. In addition, a comparison study is also performed between the FEA results and the standard results. The spring element is used for FEA in the subsequent study, given the following reasons. First, the spring element method exhibits faster computational speed. Second, the spring element can accurately simulate the stud stiffness value in each direction, which is important for the simulation because stud stiffness reflects stud mechanical properties.


#### 4.3.1. Influence of Shear Connection Degree

Figure12 shows the geometric properties of a composite beam that is loaded at midspan. Steel-concrete composite beam depth-span ratio, steel girder section size, and concrete slab size are according to the specifications in GB 50017. The span is 12 m, the stud diameter is 19 mm, and its yield strength and limit strength are 350 MPa and 455 MPa, respectively. The studs are arranged in a single row layout. The steel-concrete composite beam models have six types of material combination groups: (1) C30 and C40 concrete paired with Q235 steel, (2) C40 and C50 concrete paired with Q345 steel, and (3) C50 and C60 concrete paired with Q420 steel. In total, 43 cases are available for study.Figure 12
Geometric properties of a steel-concrete composite beam.Figure13 shows the M-ç relationship, which is also obtained from three methods. GB 50017, BS 5950, and Eurocode 4 are compared with the FEA results. The results show that shear connection degree exerts a marked impact on the flexural strength of composite beams. M is increased with the ç value. However, this phenomenon is not evident when ç is more than 1.Figure 13
M-ç relationships: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)


#### 4.3.2. Influences of Other Factors

(1) Studs in Double Row Layout. In this research, stud diameter, loading position and manner, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. Two groups of composite beams are tested. The first group uses C30 concrete and Q235 steel, whereas the second group uses C50 concrete and Q420 steel. Figure 14 illustrates the influence of a double row layout for studs on M-ç relationship. The double row stud arrangement exerts minimal impact on the flexural strength of composite beams. The M-ç relationships of the composite beam with C30 concrete and Q235 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 14.Figure 14
Influence of the double row stud layout onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(2) Stud Diameter. In this research, the number of shear studs per row across the flange, loading position and manner, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. One group of composite beams that use C40 concrete and Q345 steel is tested. The stud diameters are 13, 16, and 22 mm, respectively. Figure 15 illustrates the influence of stud diameter on M-ç relationship. Stud diameter exerts minimal impact on the flexural strength of composite beams. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 15.Figure 15
Influence of the stud diameter onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(3) Loading Position and Manner. In this research, the number of shear studs per row across the flange, stud diameter, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. Two groups of composite beams are studied. One group uses C30 concrete and Q235 steel, and the other group uses C50 concrete and Q420 steel. The loading positions are 1/4, 1/3, and 5/12 of the beam span. Figure 16 shows the influences of loading position and manner on M-ç relationship. Loading position and manner exert minimal impacts on the flexural strength of composite beams. The relationships between M and ç under the three types of methods are selected from the C30 and Q235 sample. The M-ç relationships of the composite beam with C30 concrete and Q235 steel obtained from GB 50017, Eurocode 4, and BS 5950 are also shown in Figure 16 and compared with the FEA results.Figure 16
Influences of the loading position and manner onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(4) Longitudinal Reinforcement Ratio. In this research, the number of shear studs per row across the flange, stud diameter, loading position and manner, beam span, and section size are the same as those shown in Section 4.1. One group of composite beams (with C30 concrete and Q235 steel) is studied. The longitudinal reinforcement ratios are 0.38%, 1.28%, and 5.15%. Figure 17 illustrates the influence of the longitudinal reinforcement ratio on M-ç relationship. The longitudinal reinforcement ratio exerts a certain impact on the flexural strength of composite beams; that is, M is increased with the longitudinal reinforcement ratio at ç. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 17.Figure 17
Influence of the longitudinal reinforcement ratio onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(5) Span. In this research, the number of shear studs per row across the flange, stud diameter, loading position and manner, and longitudinal reinforcement ratio are the same as those shown in Section 4.1. Two groups of composite beams are studied. One group uses C40 concrete and Q235 steel, whereas the other group uses Q345 steel and C40 concrete. The span ranges from 4 m to 20 m. Figures 18(a)–18(d) show the influence of beam length on M-ç relationship. M is increased with the ç value at different beam spans. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are presented in Figure 18.Figure 18
Influence of the beam length onM-ç relationship: comparison between the results of (A) GB 50017 and FEA, (B) BS 5950 and FEA, and (C) Eurocode 4 and FEA. (a) l = 4 m. (b) l = 8 m. (c) l = 16 m. (d) l = 20 m.
(a)
(b)
(c)
(d)The parameters of a composite beam considered in the parametric study include steel strength from Q235 to Q420, concrete strength from C30 to C60, stud row layout (single or double), stud yield strength, limit strength from 350 MPa to 455 MPa, beam span from 4 m to 20 m, stud diameter from 16 mm to 25 mm, shear span ratio from 1/4 to 1/2, and load manner (point loading or uniformly distributed loading). Table4 provides the parameters of a steel-concrete composite beam.Table 4
Parameters of a steel-concrete composite beam.
l (m)
h
c (m)
b
c (m)
h
s (m)
w
s (m)
d (mm)
f
s,s (MPa)
f
u (MPa)
f
cu (MPa)
f
rl (MPa)
f
s,b (MPa)
ρ
sl (%)
4
0.08
0.8
0.2
0.1
16
350
455
C40
350
235, 345
1.88
8
0.12
1.5
0.4
0.25
19
350
455
C40
350
235, 345
2.23
12
0.15
2.2
0.5
0.4
19
350
455
C30, C40, C50, C60
350
235, 345, 420
2.56
16
0.16
2.4
0.75
0.45
22
350
455
C40
350
235, 345
2.72
20
0.20
2.6
0.9
0.5
22
350
455
C40
350
235, 345
2.54


#### 4.3.3. Summary and Discussion

Table3 shows the comparison between the test results and those of the three standards (GB 50017, BS 5950, and Eurocode 4). The average M/M2 ratio is 1.058 with a coefficient of variation at 0.073 for GB 50017. The average M/M3 ratio is 1.185 with a coefficient of variation at 0.140 for BS 5950. The average M/M4 ratio is 1.095 with a coefficient of variation at 0.086 for Eurocode 4.Table5 shows the comparison between the test results and those of the three standards. MFE is the measured values of flexural capacity using ABAQUS. The shear connection degree is generally larger than 0.5 in practice; therefore, a shear connection degree that is smaller than 0.5 is not considered in the validation. The average MFE/M2 ratio is 1.043 with a coefficient of variation at 0.084. The average MFE/M3 ratio is 1.044 with a coefficient of variation at 0.117. The average MFE/M4 ratio is 0.945 with a coefficient of variation at 0.106.Table 5
Comparison between the results of the three standards and the FE results.
No.
Type
Total number of specimens
Characteristic value
GB 50017
BS 5950
Eurocode 4
M
FE/M2
M
FE/M3
M
FE/M4
1
Material
50
Average
1.048
1.048
0.949
Coefficient of variation
0.087
0.097
0.087
2
Row of stud
16
Average
0.996
1.011
0.920
Coefficient of variation
0.080
0.092
0.085
3
Diameter of stud
24
Average
1.039
1.061
0.962
Coefficient of variation
0.049
0.079
0.075
4
Load pattern
21
Average
1.000
0.927
0.848
Coefficient of variation
0.104
0.093
0.089
5
Span
32
Average
1.041
1.065
0.955
Coefficient of variation
0.074
0.111
0.104
6
Longitudinal ratio
27
Average
1.097
1.097
0.992
Coefficient of variation
0.069
0.152
0.134
7
Total
170
Average
1.043
1.044
0.945
Coefficient of variation
0.084
0.117
0.106Therefore, the calculation method of GB 50017 achieves higher accuracy than the other two standards.


## 4.1. FE Modeling

### 4.1.1. Material Constitutive Models

The material constitutive models of concrete and steel suggested by Ding et al. [18] are used for the model. The detailed parameters are provided in the study of Ding et al. [18].The stiffness of the spring element is defined by load-slip curves and is used to simulate the shear stud. The formula proposed by Ding et al. [20] through a bidirectional push-off test can be used for concrete in tension.The equation can be written as(5)y=A4x+B4−1x21+A4−2x+B4x2,x≤1,x0.15x−12+x,x>1,where y=p/pu, x=s/s0, and B4=1.6A4−12. s0 is the value of slip corresponding to the peak load, and s0=100/d. The ascending parameter A4 is defined as the ratio of bond stiffness to peak secant stiffness, and A4=10d−80/0.7d−5. pu is the shear capacity per stud. For a slip up to 5 mm, V reaches 99% of the ultimate load Vu. When the longitudinal, lateral, and vertical stiffness adopt expression (5) in this paper, good results can be obtained.


### 4.1.2. Model Skills

FE models are established using the ABAQUS program [22], which is extensively adopted in analyzing rock and composite structures (Chang et al. [13, 14]). Steel beams are modeled by using four-node reduced integral format shell elements (S4R). Concrete is modeled by using eight-node brick elements (C3D8R). Reinforcement bars in the specimens are modeled by the truss element T3D2 because this truss element is effective and accurate in simulating reinforcement in steel-concrete composite beams according to Ding et al. [18].Figure8 shows the simplified FE models for steel-concrete composite beams. Spring and beam elements (B31) are used to model the studs, which can be seen in Figures 8(a) and 8(b), respectively. The model uses a structured meshing technique. The surface-to-surface and Coulomb friction model is defined as the type of contact between the steel girder and the concrete slab.Figure 8
Simplified FE models for steel-concrete composite beams. (a) Spring elements for studs and (b) beam elements for studs.
(a)
(b)


## 4.1.1. Material Constitutive Models

The material constitutive models of concrete and steel suggested by Ding et al. [18] are used for the model. The detailed parameters are provided in the study of Ding et al. [18].The stiffness of the spring element is defined by load-slip curves and is used to simulate the shear stud. The formula proposed by Ding et al. [20] through a bidirectional push-off test can be used for concrete in tension.The equation can be written as(5)y=A4x+B4−1x21+A4−2x+B4x2,x≤1,x0.15x−12+x,x>1,where y=p/pu, x=s/s0, and B4=1.6A4−12. s0 is the value of slip corresponding to the peak load, and s0=100/d. The ascending parameter A4 is defined as the ratio of bond stiffness to peak secant stiffness, and A4=10d−80/0.7d−5. pu is the shear capacity per stud. For a slip up to 5 mm, V reaches 99% of the ultimate load Vu. When the longitudinal, lateral, and vertical stiffness adopt expression (5) in this paper, good results can be obtained.


## 4.1.2. Model Skills

FE models are established using the ABAQUS program [22], which is extensively adopted in analyzing rock and composite structures (Chang et al. [13, 14]). Steel beams are modeled by using four-node reduced integral format shell elements (S4R). Concrete is modeled by using eight-node brick elements (C3D8R). Reinforcement bars in the specimens are modeled by the truss element T3D2 because this truss element is effective and accurate in simulating reinforcement in steel-concrete composite beams according to Ding et al. [18].Figure8 shows the simplified FE models for steel-concrete composite beams. Spring and beam elements (B31) are used to model the studs, which can be seen in Figures 8(a) and 8(b), respectively. The model uses a structured meshing technique. The surface-to-surface and Coulomb friction model is defined as the type of contact between the steel girder and the concrete slab.Figure 8
Simplified FE models for steel-concrete composite beams. (a) Spring elements for studs and (b) beam elements for studs.
(a)
(b)


## 4.2. Flexural Capacity from FE Analysis (FEA)

Figure9 shows the comparison between the calculated and tested load-deformation curves of a composite beam. Figure 10 illustrates the comparison between the calculated and tested load-end slips of a composite beam. Figure 11 demonstrates the comparison between the calculated and tested longitudinal reinforcement and bottom flange strains of a composite beam.Figure 9
Comparison between the calculated and tested load-deformation curves of a composite beam. (a) SCB19 (present study), (b) NSCB5 (Nie and Cai [5]), and (c) VCB1 (Vasdravellis et al. [11]).
(a)
(b)
(c)Figure 10
Comparison between the calculated and tested load-end slips of a composite beam.Figure 11
Comparison between the calculated and tested longitudinal reinforcement and bottom flange strains of a composite beam.Good agreement between FEA and the measured results is found in the elastic stage. Thereafter, the curve from the calculated and test results appeared with a certain deviation in the elastic-plastic and failure stages.Table3 presents the comparison between the simulated and test results. A total of 32 groups of test data regarding steel-concrete composite beams are included for analysis and model validation. M is the measured values of flexural capacity, M11 is the flexural strength obtained via the spring element modeling method, and M12 is the flexural strength obtained via the beam element modeling method. M2, M3, and M4 are the flexural capacities under GB 50017, BS 5950, and Eurocode 4, respectively. The test results are compared using different methods, including FEA and three standards.Table 3
Comparison among the three standards and simulated and test results.
No.
Source of the specimens
Total number of specimens
Characteristic value
Spring element
Beam element
GB 50017
BS 5950
Eurocode 4
M/M11
M/M12
M/M2
M/M3
M/M4
1
This paper
24
Average
1.037
0.981
1.031
1.161
1.049
Coefficient of variation
0.063
0.093
0.058
0.151
0.065
2
Nie [21]
4
Average
0.993
0.932
1.098
1.195
1.060
Coefficient of variation
0.091
0.034
0.061
0.067
0.064
3
Lin et al. [9]
3
Average
1.000
0.962
1.169
1.306
1.073
Coefficient of variation
0.104
0.088
0.031
0.032
0.033
4
Vasdravellis et al. [11]
1
Average
1.099
0.863
1.208
1.348
1.083
Coefficient of variation
—
—
—
—
—
5
All above
32
Average
1.026
0.963
1.058
1.185
1.036
Coefficient of variation
0.073
0.085
0.073
0.140
0.088The averageM/M11 ratio is 1.026 with a coefficient of variation at 0.073 for the spring element, and the average M/M12 ratio is 0.963 with a coefficient of variation at 0.085 for the beam element. Such findings indicate that the FE simulation results are extremely close to the test results.


## 4.3. Parametric Study

Parameter analysis is conducted in this section. In addition, a comparison study is also performed between the FEA results and the standard results. The spring element is used for FEA in the subsequent study, given the following reasons. First, the spring element method exhibits faster computational speed. Second, the spring element can accurately simulate the stud stiffness value in each direction, which is important for the simulation because stud stiffness reflects stud mechanical properties.


### 4.3.1. Influence of Shear Connection Degree

Figure12 shows the geometric properties of a composite beam that is loaded at midspan. Steel-concrete composite beam depth-span ratio, steel girder section size, and concrete slab size are according to the specifications in GB 50017. The span is 12 m, the stud diameter is 19 mm, and its yield strength and limit strength are 350 MPa and 455 MPa, respectively. The studs are arranged in a single row layout. The steel-concrete composite beam models have six types of material combination groups: (1) C30 and C40 concrete paired with Q235 steel, (2) C40 and C50 concrete paired with Q345 steel, and (3) C50 and C60 concrete paired with Q420 steel. In total, 43 cases are available for study.Figure 12
Geometric properties of a steel-concrete composite beam.Figure13 shows the M-ç relationship, which is also obtained from three methods. GB 50017, BS 5950, and Eurocode 4 are compared with the FEA results. The results show that shear connection degree exerts a marked impact on the flexural strength of composite beams. M is increased with the ç value. However, this phenomenon is not evident when ç is more than 1.Figure 13
M-ç relationships: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)


### 4.3.2. Influences of Other Factors

(1) Studs in Double Row Layout. In this research, stud diameter, loading position and manner, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. Two groups of composite beams are tested. The first group uses C30 concrete and Q235 steel, whereas the second group uses C50 concrete and Q420 steel. Figure 14 illustrates the influence of a double row layout for studs on M-ç relationship. The double row stud arrangement exerts minimal impact on the flexural strength of composite beams. The M-ç relationships of the composite beam with C30 concrete and Q235 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 14.Figure 14
Influence of the double row stud layout onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(2) Stud Diameter. In this research, the number of shear studs per row across the flange, loading position and manner, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. One group of composite beams that use C40 concrete and Q345 steel is tested. The stud diameters are 13, 16, and 22 mm, respectively. Figure 15 illustrates the influence of stud diameter on M-ç relationship. Stud diameter exerts minimal impact on the flexural strength of composite beams. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 15.Figure 15
Influence of the stud diameter onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(3) Loading Position and Manner. In this research, the number of shear studs per row across the flange, stud diameter, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. Two groups of composite beams are studied. One group uses C30 concrete and Q235 steel, and the other group uses C50 concrete and Q420 steel. The loading positions are 1/4, 1/3, and 5/12 of the beam span. Figure 16 shows the influences of loading position and manner on M-ç relationship. Loading position and manner exert minimal impacts on the flexural strength of composite beams. The relationships between M and ç under the three types of methods are selected from the C30 and Q235 sample. The M-ç relationships of the composite beam with C30 concrete and Q235 steel obtained from GB 50017, Eurocode 4, and BS 5950 are also shown in Figure 16 and compared with the FEA results.Figure 16
Influences of the loading position and manner onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(4) Longitudinal Reinforcement Ratio. In this research, the number of shear studs per row across the flange, stud diameter, loading position and manner, beam span, and section size are the same as those shown in Section 4.1. One group of composite beams (with C30 concrete and Q235 steel) is studied. The longitudinal reinforcement ratios are 0.38%, 1.28%, and 5.15%. Figure 17 illustrates the influence of the longitudinal reinforcement ratio on M-ç relationship. The longitudinal reinforcement ratio exerts a certain impact on the flexural strength of composite beams; that is, M is increased with the longitudinal reinforcement ratio at ç. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 17.Figure 17
Influence of the longitudinal reinforcement ratio onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(5) Span. In this research, the number of shear studs per row across the flange, stud diameter, loading position and manner, and longitudinal reinforcement ratio are the same as those shown in Section 4.1. Two groups of composite beams are studied. One group uses C40 concrete and Q235 steel, whereas the other group uses Q345 steel and C40 concrete. The span ranges from 4 m to 20 m. Figures 18(a)–18(d) show the influence of beam length on M-ç relationship. M is increased with the ç value at different beam spans. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are presented in Figure 18.Figure 18
Influence of the beam length onM-ç relationship: comparison between the results of (A) GB 50017 and FEA, (B) BS 5950 and FEA, and (C) Eurocode 4 and FEA. (a) l = 4 m. (b) l = 8 m. (c) l = 16 m. (d) l = 20 m.
(a)
(b)
(c)
(d)The parameters of a composite beam considered in the parametric study include steel strength from Q235 to Q420, concrete strength from C30 to C60, stud row layout (single or double), stud yield strength, limit strength from 350 MPa to 455 MPa, beam span from 4 m to 20 m, stud diameter from 16 mm to 25 mm, shear span ratio from 1/4 to 1/2, and load manner (point loading or uniformly distributed loading). Table4 provides the parameters of a steel-concrete composite beam.Table 4
Parameters of a steel-concrete composite beam.
l (m)
h
c (m)
b
c (m)
h
s (m)
w
s (m)
d (mm)
f
s,s (MPa)
f
u (MPa)
f
cu (MPa)
f
rl (MPa)
f
s,b (MPa)
ρ
sl (%)
4
0.08
0.8
0.2
0.1
16
350
455
C40
350
235, 345
1.88
8
0.12
1.5
0.4
0.25
19
350
455
C40
350
235, 345
2.23
12
0.15
2.2
0.5
0.4
19
350
455
C30, C40, C50, C60
350
235, 345, 420
2.56
16
0.16
2.4
0.75
0.45
22
350
455
C40
350
235, 345
2.72
20
0.20
2.6
0.9
0.5
22
350
455
C40
350
235, 345
2.54


### 4.3.3. Summary and Discussion

Table3 shows the comparison between the test results and those of the three standards (GB 50017, BS 5950, and Eurocode 4). The average M/M2 ratio is 1.058 with a coefficient of variation at 0.073 for GB 50017. The average M/M3 ratio is 1.185 with a coefficient of variation at 0.140 for BS 5950. The average M/M4 ratio is 1.095 with a coefficient of variation at 0.086 for Eurocode 4.Table5 shows the comparison between the test results and those of the three standards. MFE is the measured values of flexural capacity using ABAQUS. The shear connection degree is generally larger than 0.5 in practice; therefore, a shear connection degree that is smaller than 0.5 is not considered in the validation. The average MFE/M2 ratio is 1.043 with a coefficient of variation at 0.084. The average MFE/M3 ratio is 1.044 with a coefficient of variation at 0.117. The average MFE/M4 ratio is 0.945 with a coefficient of variation at 0.106.Table 5
Comparison between the results of the three standards and the FE results.
No.
Type
Total number of specimens
Characteristic value
GB 50017
BS 5950
Eurocode 4
M
FE/M2
M
FE/M3
M
FE/M4
1
Material
50
Average
1.048
1.048
0.949
Coefficient of variation
0.087
0.097
0.087
2
Row of stud
16
Average
0.996
1.011
0.920
Coefficient of variation
0.080
0.092
0.085
3
Diameter of stud
24
Average
1.039
1.061
0.962
Coefficient of variation
0.049
0.079
0.075
4
Load pattern
21
Average
1.000
0.927
0.848
Coefficient of variation
0.104
0.093
0.089
5
Span
32
Average
1.041
1.065
0.955
Coefficient of variation
0.074
0.111
0.104
6
Longitudinal ratio
27
Average
1.097
1.097
0.992
Coefficient of variation
0.069
0.152
0.134
7
Total
170
Average
1.043
1.044
0.945
Coefficient of variation
0.084
0.117
0.106Therefore, the calculation method of GB 50017 achieves higher accuracy than the other two standards.


## 4.3.1. Influence of Shear Connection Degree

Figure12 shows the geometric properties of a composite beam that is loaded at midspan. Steel-concrete composite beam depth-span ratio, steel girder section size, and concrete slab size are according to the specifications in GB 50017. The span is 12 m, the stud diameter is 19 mm, and its yield strength and limit strength are 350 MPa and 455 MPa, respectively. The studs are arranged in a single row layout. The steel-concrete composite beam models have six types of material combination groups: (1) C30 and C40 concrete paired with Q235 steel, (2) C40 and C50 concrete paired with Q345 steel, and (3) C50 and C60 concrete paired with Q420 steel. In total, 43 cases are available for study.Figure 12
Geometric properties of a steel-concrete composite beam.Figure13 shows the M-ç relationship, which is also obtained from three methods. GB 50017, BS 5950, and Eurocode 4 are compared with the FEA results. The results show that shear connection degree exerts a marked impact on the flexural strength of composite beams. M is increased with the ç value. However, this phenomenon is not evident when ç is more than 1.Figure 13
M-ç relationships: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)


## 4.3.2. Influences of Other Factors

(1) Studs in Double Row Layout. In this research, stud diameter, loading position and manner, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. Two groups of composite beams are tested. The first group uses C30 concrete and Q235 steel, whereas the second group uses C50 concrete and Q420 steel. Figure 14 illustrates the influence of a double row layout for studs on M-ç relationship. The double row stud arrangement exerts minimal impact on the flexural strength of composite beams. The M-ç relationships of the composite beam with C30 concrete and Q235 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 14.Figure 14
Influence of the double row stud layout onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(2) Stud Diameter. In this research, the number of shear studs per row across the flange, loading position and manner, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. One group of composite beams that use C40 concrete and Q345 steel is tested. The stud diameters are 13, 16, and 22 mm, respectively. Figure 15 illustrates the influence of stud diameter on M-ç relationship. Stud diameter exerts minimal impact on the flexural strength of composite beams. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 15.Figure 15
Influence of the stud diameter onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(3) Loading Position and Manner. In this research, the number of shear studs per row across the flange, stud diameter, longitudinal reinforcement ratio, beam span, and section size are the same as those shown in Section 4.1. Two groups of composite beams are studied. One group uses C30 concrete and Q235 steel, and the other group uses C50 concrete and Q420 steel. The loading positions are 1/4, 1/3, and 5/12 of the beam span. Figure 16 shows the influences of loading position and manner on M-ç relationship. Loading position and manner exert minimal impacts on the flexural strength of composite beams. The relationships between M and ç under the three types of methods are selected from the C30 and Q235 sample. The M-ç relationships of the composite beam with C30 concrete and Q235 steel obtained from GB 50017, Eurocode 4, and BS 5950 are also shown in Figure 16 and compared with the FEA results.Figure 16
Influences of the loading position and manner onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(4) Longitudinal Reinforcement Ratio. In this research, the number of shear studs per row across the flange, stud diameter, loading position and manner, beam span, and section size are the same as those shown in Section 4.1. One group of composite beams (with C30 concrete and Q235 steel) is studied. The longitudinal reinforcement ratios are 0.38%, 1.28%, and 5.15%. Figure 17 illustrates the influence of the longitudinal reinforcement ratio on M-ç relationship. The longitudinal reinforcement ratio exerts a certain impact on the flexural strength of composite beams; that is, M is increased with the longitudinal reinforcement ratio at ç. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are shown in Figure 17.Figure 17
Influence of the longitudinal reinforcement ratio onM-ç relationship: comparison between the results of (a) GB 50017 and FEA, (b) BS 5950 and FEA, and (c) Eurocode 4 and FEA.
(a)
(b)
(c)(5) Span. In this research, the number of shear studs per row across the flange, stud diameter, loading position and manner, and longitudinal reinforcement ratio are the same as those shown in Section 4.1. Two groups of composite beams are studied. One group uses C40 concrete and Q235 steel, whereas the other group uses Q345 steel and C40 concrete. The span ranges from 4 m to 20 m. Figures 18(a)–18(d) show the influence of beam length on M-ç relationship. M is increased with the ç value at different beam spans. The M-ç relationships of the composite beam with C40 concrete and Q345 steel obtained from GB 50017, Eurocode 4, and BS 5950, which are also compared with the FEA results, are presented in Figure 18.Figure 18
Influence of the beam length onM-ç relationship: comparison between the results of (A) GB 50017 and FEA, (B) BS 5950 and FEA, and (C) Eurocode 4 and FEA. (a) l = 4 m. (b) l = 8 m. (c) l = 16 m. (d) l = 20 m.
(a)
(b)
(c)
(d)The parameters of a composite beam considered in the parametric study include steel strength from Q235 to Q420, concrete strength from C30 to C60, stud row layout (single or double), stud yield strength, limit strength from 350 MPa to 455 MPa, beam span from 4 m to 20 m, stud diameter from 16 mm to 25 mm, shear span ratio from 1/4 to 1/2, and load manner (point loading or uniformly distributed loading). Table4 provides the parameters of a steel-concrete composite beam.Table 4
Parameters of a steel-concrete composite beam.
l (m)
h
c (m)
b
c (m)
h
s (m)
w
s (m)
d (mm)
f
s,s (MPa)
f
u (MPa)
f
cu (MPa)
f
rl (MPa)
f
s,b (MPa)
ρ
sl (%)
4
0.08
0.8
0.2
0.1
16
350
455
C40
350
235, 345
1.88
8
0.12
1.5
0.4
0.25
19
350
455
C40
350
235, 345
2.23
12
0.15
2.2
0.5
0.4
19
350
455
C30, C40, C50, C60
350
235, 345, 420
2.56
16
0.16
2.4
0.75
0.45
22
350
455
C40
350
235, 345
2.72
20
0.20
2.6
0.9
0.5
22
350
455
C40
350
235, 345
2.54


## 4.3.3. Summary and Discussion

Table3 shows the comparison between the test results and those of the three standards (GB 50017, BS 5950, and Eurocode 4). The average M/M2 ratio is 1.058 with a coefficient of variation at 0.073 for GB 50017. The average M/M3 ratio is 1.185 with a coefficient of variation at 0.140 for BS 5950. The average M/M4 ratio is 1.095 with a coefficient of variation at 0.086 for Eurocode 4.Table5 shows the comparison between the test results and those of the three standards. MFE is the measured values of flexural capacity using ABAQUS. The shear connection degree is generally larger than 0.5 in practice; therefore, a shear connection degree that is smaller than 0.5 is not considered in the validation. The average MFE/M2 ratio is 1.043 with a coefficient of variation at 0.084. The average MFE/M3 ratio is 1.044 with a coefficient of variation at 0.117. The average MFE/M4 ratio is 0.945 with a coefficient of variation at 0.106.Table 5
Comparison between the results of the three standards and the FE results.
No.
Type
Total number of specimens
Characteristic value
GB 50017
BS 5950
Eurocode 4
M
FE/M2
M
FE/M3
M
FE/M4
1
Material
50
Average
1.048
1.048
0.949
Coefficient of variation
0.087
0.097
0.087
2
Row of stud
16
Average
0.996
1.011
0.920
Coefficient of variation
0.080
0.092
0.085
3
Diameter of stud
24
Average
1.039
1.061
0.962
Coefficient of variation
0.049
0.079
0.075
4
Load pattern
21
Average
1.000
0.927
0.848
Coefficient of variation
0.104
0.093
0.089
5
Span
32
Average
1.041
1.065
0.955
Coefficient of variation
0.074
0.111
0.104
6
Longitudinal ratio
27
Average
1.097
1.097
0.992
Coefficient of variation
0.069
0.152
0.134
7
Total
170
Average
1.043
1.044
0.945
Coefficient of variation
0.084
0.117
0.106Therefore, the calculation method of GB 50017 achieves higher accuracy than the other two standards.


## 5. Conclusions

This study explores and discusses the flexural strength of steel-concrete composite beams subjected to hogging moment through experimental and numerical studies, and then the results are compared with current widely used standard methods. The following conclusions can be obtained:(1)
The test results suggest that the higher the connection degree, the greater the flexural strength. The flexural strength increases with the transverse and longitudinal reinforcement ratios. The stud diameter and loading condition slightly affect flexural capacity.(2)
The stud can be simulated well using the beam and spring elements, and the calculated results achieve good agreement with the experimental results. In addition, compared with the beam element method, the spring element method exhibits faster computational speed and higher accuracy.(3)
On the basis of FEA with the spring element, the flexural capacity connection degree and longitudinal reinforcement ratio are identified as primary control factors. The larger the degree of shear connection, the greater the flexural strength. In addition, the growth of flexural capacity is insignificant when the shear connection degree reaches 1. Other factors, including loading location and manner, beam span, stud diameter, and studs in double row layout, exert minimal impact on flexural capacity.(4)
Through experimental research and parametric analysis, the three calculation methods for flexural strength of composite beams are compared. The results show that China’s specification may provide better estimations than the other two standard methods.



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*Source: 3453274-2019-03-04.xml*