Study on the Mechanical Performance of H-Shaped Steel-Concrete Laminated Plate Composite Beams under Negative Bending Moment

Abstract

To make the construction of assembled steel-reinforced truss concrete laminated plate composite structure faster, safer, and more efficient, this paper proposes an H-shaped steel-reinforced truss concrete laminated plate composite structure with new angle connectors embedded in the precast bottom panel. Through experimental studies on the H-shaped steel-concrete laminated plate composite beams with precast bottom panels protruding from the bent-up bars, precast bottom panels with embedded new angle connectors and laminated whole cast slab, the similarities and differences of load-deflection, deflection distribution, interface slip, crack distribution and cross-section strain distribution of three groups of composite beams under negative bending moment were analyzed and compared. Using ABAQUS finite element software, we established a finite element model and found the numerical simulation results were in good agreement with the experimental results. Based on this, five groups of finite element models were established for parametric analysis to investigate the effect of concrete strength on the flexural load capacity and flexural stiffness of the steel-laminated plate composite beams with embedded angle connectors. The results of the study show that the combined performance of the H-shaped steel-concrete laminated plate composite beams with the new angle connection embedded in the precast bottom panel was better and the flexural stiffness was greater. The slippage of the H-shaped steel-concrete laminated plate composite beams with embedded new angle connectors in the precast bottom panel was less than the slippage of the precast bottom slab bent-up bars protruding and the laminated cast plate, with the maximum slippage being only 1/2 of the precast bottom panel bent-up bars protruding. In the composite structure of H-shaped steel-concrete composite slabs under negative bending moment, shear angle connectors can replace the bent-up bars protruding from the laminated bottom panel to achieve without extending the reinforcement of the laminated bottom panel.

1. Introduction

In recent years, with the vigorous promotion of the steel structure residential system and the level of building industrialization, the assembled steel-concrete composite structure building is widely used and favored in residential buildings due to its structural advantages, and its significance for low carbon transformation. Steel-concrete composite beams are widely used in steel buildings because of their excellent characteristics of light self-weight and high load-bearing capacity [1,2].

In the traditional steel-reinforced truss concrete laminated plate system, the precast bottom panel is constructed with a bent “beard bar” at the end of the steel beam, see Figure 1. However, during construction the bent “beard bar” is often a problem due to collisions, resulting in slow progress. Secondly, the precast bottom panel does not form a solid connection with the steel beam and there are safety issues. Shear connectors have many advantages such as convenience, speed, and efficiency, and can be used in steel-concrete systems to replace the bent “bearded bars” under certain conditions to achieve a prefabricated laminated plate without extending the reinforcement [3,4,5,6]. Connectors are essential to ensure that steel and concrete work together, and common connectors include stud connectors and PBL connectors [7]. Stud connectors require special welding equipment and often require bending tests to ensure quality construction [8], while PBL connectors require openings in the steel plate and generally require a reinforcement mesh to be placed in the concrete to ensure the performance of the connectors. The construction process of angle steel connectors is relatively simple and only requires the use of conventional fillet welds to weld the angle steel connectors to the connecting flange plate, and the mechanical performance of the angle steel connectors can be guaranteed through conventional construction and weld quality testing [9]. In addition, by connecting the angle steel to the flange plate, the stiffness of the flange plate during pouring can be improved and the bulging of the flange plate reduced. In engineering applications, the arrangement of the angle steel connectors usually must meet certain requirements as well. According to the design formula for angle connectors in the Japanese Meiji structural guidelines [10], the spacing between angle connectors should not be too small, preferably greater than 10 times the height of the angle connectors. To reduce the out-of-plane bulging of the flange connected to the angle steel at the pouring stage and to improve the buckling resistance of the connected flange, the spacing of the angle connectors should not be too large.

The concrete slab of the combined beam shows good synergistic effects with the steel beam under the action of positive bending moments. At present, the mechanical performance of cast-in-place and prefabricated assembled composite beams under positive bending moments have been relatively well studied in academia [11,12,13]. In frame structures, the parts of continuous beams located at the support positions often need to bear large negative moments, and it is necessary to study the mechanical performance of steel-concrete composite beams under the action of negative moments. The concrete slab bears tensile stresses under the action of negative moments in the combined beam, and the development of cracks has a large adverse effect on the mechanical performance of the combined beam due to the low cracking strength of the concrete. Liu Hanbing et al. [14,15] investigated the cracking resistance of cast-in-place stud composite beams under negative bending moments. The results showed that the external prestressing could effectively improve the comprehensive stress performances of the composite beam and have a significant effect on the slip. Liu Hanbing et al. [16] and Fan Jiansheng et al. [17,18] considered the adverse effects of sliding between concrete slab and steel beam on the stiffness of combined beams. The deflection calculation method was improved based on the original equivalent cross-section to calculate the stiffness, which has a high accuracy for the deflection calculation of cast-in-place stud composite beams. In the literature [19,20,21,22,23,24,25,26], a new technique of uplift-restricted and slip-permitted is proposed. It was shown that improvements to shear connectors can greatly improve the cracking of concrete without changing the stiffness and ultimate bearing capacity of the specimen.

At present, the mechanical performance of steel-concrete laminated plate composite beams under negative bending moments is unclear. This paper analyses the differences in failure pattern, load-deflection, deflection distribution, interface slip, fracture distribution, and section stress distribution of three different structural forms of steel-concrete laminated plate composite beams under negative bending moments, to verify the reasonableness of the stresses in the steel-laminated plate composite beams with the precast bottom panel with embedded angle connectors. According to the test using ABAQUS finite element software to establish a fine finite element model and compare with the experimental results, the numerical simulation results are in good agreement with the experimental results. Based on this, six groups of finite element models were established for parametric analysis. To investigate the effect of concrete strength on the flexural load capacity and flexural stiffness of the steel-laminated slab composite beam with embedded angle connectors. The study of the mechanical performance of the assembled steel truss laminated plate with steel beam connection studied in this paper can provide a reference basis for application and design in engineering, expanding the scope of use of assembled steel-concrete composite structures.

2. Experimental Overview

2.1. Experimental Design

According to the codes [27,28,29], three full-scale composite beam specimens ZJ, SCL1, and SCL2 were designed. The ZJB was a laminated full-cast H-shaped steel-concrete laminated plate composite beam, hereinafter referred to as the full-cast beam. The SCL1 was an H-shaped steel-concrete laminated plate composite beam in the form of the precast bottom plane with bent-up bars, hereinafter referred to as the with reinforcement beam. The SCL2 was an H-shaped steel-concrete laminated plate composite beam in the form of a precast bottom panel with embedded new angle connectors, the specific dimensions of the combined beam are shown in Figure 2.

The steel beams of the three groups of specimens were of the same size and material; the dimensions of the beams were hot rolled medium flange H-beam, HM 316 mm × 200 mm × 6 mm × 8 mm, i.e., the height of the beam was 316mm, the width of the flange was 200 mm, the thickness of the web was 6 mm, and the thickness of the flange was 8 mm. The design strength of the steel beam was Q235 and the total length of the beam was 3960 mm. The beam was welded with single-row studs shear connectors, the type of the studs was M16-100, i.e., 16 mm in diameter and 100 m in height (the height of 100 mm included the thickness of the nut of 10 mm and the diameter of the nut was 32 mm), the spacing of the studs was 250 mm.

The concrete flange slab of the combined beam was dimensioned and reinforced according to Codes [27,28,29], and the total length of the concrete slab was the same as that of the steel beam, 3960 mm. The dimensions of the single precast bottom panel were 1320 mm × 450 mm × 60 mm, the longitudinal and transverse reinforcement was C8@100. The design strength of the precast bottom panel and the cast-in-place layer of concrete was C30, and the protective layer thickness was taken as 20 mm for the reinforcement trusses and 15 mm for the reinforcement mesh. The number of precast bottom panels for both SCL1 and SCL2 was 6. The top and bottom chords of the precast bottom panels were 10 mm and 8 mm HRB400 grade reinforcement, respectively, and the webs were 6mm HPB300 grade reinforcement. Each precast bottom panel of SCL2 contained two embedded angle steel connectors, which were fixed in position during the fabrication of the precast bottom panel in the PC factory, with a spacing of 500 mm and symmetrical distribution concerning the slab. The angles were ∠50 mm × 32 mm × 4 mm and the length was 60 mm, and the bending bars on the angles were 6 mm HRB400 grade bars. The physical and dimensional precast bottom panel extending the reinforcement and angle connectors are shown in Figure 3. The height of the cast-in-place layer was 70 mm and the width and height of the concrete laminated plate formed by the precast and cast-in-place layers were 1020 mm and 130 mm (60 mm the height of the precast layer + 70 mm the height of the cast-in-place layer). The cast-in-place layer reinforcement network was also double-reinforced in both directions with a reinforcement specification of C8@100. The ZJB was a comparison group poured in SJ1 and SJ2 cast-in-place layers, the reinforcement network was a double layer of two-way reinforcement, and the reinforcement specification was C8@100. The specific dimensions of the three groups of specimens are shown in Figure 4 and the reinforcement is shown in

Table 1. Table of specimen parameters.

Numbers	Length × Width × Thickness/mm	Differences in Connection Methods	Transverse and Longitudinal Reinforcement Mesh	Upper Chord Rebar	Web Reinforcement	Lower Chord Rebar
SCL1	3960 × 1020 × 130 (60 + 70)	Bend up bars to anchor into the cast-in-place layer	C8@100	C10	A6	C8
SCL2		Welding of embedded angles to steel beams
ZJB	3960 × 1020 × 130	Complete pouring	C8@100	-	-	-

.

The process of processing the combined H-shaped steel-concrete laminated plate composite beams is shown in Figure 4, Figure 5 and Figure 6. The SC1 and SC2 were processed in two steps, with the beams and concrete bottom panels first prefabricated at the Anhui Fuhuang Construction Technology PC prefabrication yard, then transported to the Anhui Provincial Structure and Underground Space Key Experiment for assembly and pouring of the cast-in-place layer. The comparison test piece ZJB was cast and formed in one single whole.

The steel truss laminated bottom panel was fabricated in Anhui Fuhuang Construction Technology PC prefabrication yard, and the PC prefabrication yard fabrication process is shown in Figure 6. The prefabricated bottom panel was made according to the requirements of the Technical Code for the Application of Reinforced Truss Concrete Stacked Slabs TCECS 715-2020 [28], and the new angle-embedded parts of SCL2 were positioned and clamped with the steel formwork after tying the reinforcing steel mesh. The bent hook part of the new embedded angle connectors will be higher than the precast bottom panel, and the bent hook part of the bent hook reinforcement on the angles can play the role of connecting the angle connectors with the precast bottom panel better, to transfer the shear force between the steel beam and the laminated slab. In addition, the bending hooks above the precast base panel will strengthen the bond between the precast layer and the cast-in-place layer and act to take up part of the shear forces on the laminated surface of the precast and cast-in-place layers. The new angle connector was welded to the flange of the steel beam in the form of a right-angle weld; the welding diagram of the angle joint is shown in Figure 5.

The form of the joints in the precast bottom panel has been studied by scholars, and because of the advantages of easy installation and good overall stressing, the close-fitting integral joints are used between adjacent precast bottom panels. The longitudinal direction of the precast bottom panel was arranged following the Technical Code for the Application of Reinforced Truss Concrete Laminated Slabs TCECS 715-2020 [28] using a dense overall joint with lap bars perpendicular to the joint. The length of the lap bars shall not be less than 1.6l_a, the basic anchorage length according to the code [30] $l_{\mathrm{a}}=\alpha f_{\mathrm{y}}d/f_{\mathrm{t}}$ = 0.14 × 400 × 8/1.43 = 313 mm, 1.6l_a = 500.8 mm, perpendicular to the direction of the lapped reinforcement shall be arranged transverse distribution reinforcement. The final lap bars length was set at 1240 mm, the lap bars spacing was 130 mm and four lap reinforcement bars were set for the closely spaced integral splice between each precast base slab. The spacing between the transverse distribution reinforcement was set at 250 mm, with a total of five transverse distribution reinforcement bars and a transverse distribution reinforcement length of 420 mm. Four close-spaced integral joints were placed in each of the two groups of specimens, each with four additional reinforcement nets consisting of lap bars and transverse distribution reinforcement bars, the additional reinforcement nets were of HRB400 grade reinforcement of 8 mm diameter. The relative positions of the additional reinforcement mesh and the components are shown in Figure 7.

2.2. Material Performance Experiments

Standard specimens of 150 mm size were reserved when pouring both precast and cast-in-place layers of concrete. After curing for 28 days under the same conditions as the specimens, standard compressive strength tests were carried out. Following the requirements of the code [31], the same batch of reinforcement and steel beam parent material was intercepted for material properties testing at the time of specimen fabrication. The measured mechanical properties of the materials are shown in

Table 2. Material properties of concrete.

Types	Prefabricated Layer/MPa	Cast-in-Place Layer/MPa
fcu	35.6	33.2
fc	27.1	25.2
Ec	3.14 × 104	3.08 × 104

and

Table 3. Material properties of reinforcement and steel.

Types	fy/MPa	fu/MPa
HRB400 (10 mm)	456	620
HRB400 (8 mm)	480	660
HPB300 (6 mm)	452	560
Q235 (Steel beam flange)	270	390
Q235 (Steel beam flange)	278	400

.

2.3. Loading Device and Loading Scheme

The experimental loading device is shown in Figure 8. A hydraulic jack with a range of 50 kN was used to provide a vertical concentrated load in the span of the simply supported beam. To equate the stress state of the concrete slab on the composite beam in tension and the lower flange of the steel beam in compression under negative bending moments, the top and bottom of the composite beam are inverted and simply supported, and the load is applied to the lower flange of the steel beam in the middle of the span of the composite beam through a steel plate of 2 mm thickness and 200 mm edge length. The test ensures that the vertical load is in the same vertical plane as the center of gravity of the combined beam.

The combination beam is preloaded with 20 kN before formal loading and then unloaded. The formal loading regime is divided into force control and displacement control, with 15 kN as the first level of loading until the load reaches 150 kN and 30 kN after 150 kN until the force cannot be significantly increased then it is switched to continuous loading with displacement. Continuous loading of the specimen after excessive deformation until the component reaches the test stopping condition.

2.4. Measurement Program

Measurements include deflection, slip, cracks, and angle stress-strain. Deflection, slip, and corner angle are measured using displacement gauges; cracks are measured using a crack observer for width.

The W-1 to W-6 are combination beam deflection determination displacement gauges, R-1 to R-4 are combination beam combination interface free end slips, and S-1 to S-3 are combination beam combination interface relative slip determination displacement gauges. The specific arrangement is shown in Figure 9, Figure 10 and Figure 11.

3. Experimental Phenomena and Failure Patterns

Three simply supported H-shaped steel-concrete laminated plate composite beams were tested with single-point loading in the span. When the load reached 60–75 kN, all produced the first crack in the span, which also eventually developed into the main fracture. As the load continued to increase, cracks were produced along the entire length of the combined beam. The cracks that first run through the concrete slab were produced in the middle of the span, which gradually withdrew from the work, with the load being carried entirely by the steel beam and reinforcement. As the load continued to increase, the flange of the steel beam under the loading point showed local buckling, but the load-bearing capacity of the combined beam could continue to increase. Three combined beam specimens were eventually damaged due to the reinforcement in the concrete slab being pulled out, showing typical bending damage characteristics, and the final damage diagram is shown in Figure 12.

For specimen SCL1, when loaded to 60~75 kN, a slight crack appeared at the side of the cast-in-place layer at one of the joints, which was due to the presence of the joints reducing the moment of inertia of the joints section. When it was loaded to 90 kN, the first transverse crack appeared at the side and bottom of the span. As the load increased the cracks developed smoothly. When it was loaded to 150 kN, two symmetrical penetration cracks appeared at the bottom of the joints, and the cracks around the span showed a symmetrical distribution. When loaded to 180 kN, a longitudinal splitting crack along the length of the beam appeared near the bearing, and the longitudinal splitting crack gradually developed towards the center of the span resulting in a diagonal crack. As the concrete near the support was subjected to greater pressure from the steel beam and shear cracks were produced, several cracks extending from the cast-in-place layer to the precast layer appeared on the side of the support section, indicating that the precast layer was well-bonded to the cast-in-place layer concrete and no shear damage occurs along the laminated surface. As the load increased, the cracks developed smoothly in the mid-span section, more cracks extended and penetrated. Sporadic scattered inclined cracks appeared at the top surface of the support, the width of existing cracks increased significantly, and the deflection of the combined beam developed faster. When loaded to 270 kN, the rate of new crack generation dropped significantly, and the steel beam appeared slightly compressed buckling at the compressed flange. The sound of slight cracking and spalling of the concrete was heard. When loaded at 290 kN, the steel beam exhibited compression buckling which was easily visible to the naked eye. After reaching the ultimate bearing capacity of 296.0 kN, the load dropped, and eventually, the steel beam buckled too much, the concrete slab fractured, and the test was stopped.

For specimen SCL2, when it was loaded to 60~75 kN, the first transverse crack through the bottom surface of the span appeared, and a slight crack was produced on the side of the cast-in-place layer at both joints. When it was loaded to 90 kN, a second crack through the span was produced near the bottom surface of the span. As the load increased, the crack developed smoothly. When it was loaded to 135 kN, in addition to the slight production and development of cracks, the bottom surface of the joints appeared with two symmetrical transverse cracks, one of which penetrates. When loaded to 180 kN, there were multiple crack extensions and penetrations, and between the joint and the support section, transverse cracks appeared, indicating good force transfer at the joint. When loaded to 210 kN, similar to SCL1, a longitudinal splitting crack along the length of the beam appeared near the support, the longitudinal splitting crack gradually developed towards the span to derive a diagonal crack, and the diagonal crack gradually developed into a transverse crack on both sides of the slab, and a shear crack was produced due to the high pressure of the concrete near the support transmitted by the steel beam. When loaded to 270 kN, the cracks developed smoothly, the width of the initial crack increased significantly, the deflection of the specimen changed significantly, the concrete slab gradually withdrew from the work and the cracks on the side of the slab extended from the cast-in-place layer to the precast layer, indicating that the bond between the precast layer and the cast-in-place layer concrete was good and no shear damage occurred along the laminated surface. When loaded to 275 kN, a slight buckling of the flange occurred near the loading point of the steel beam. As the load continued to rise, a slight cracking and spalling of the concrete were heard and the displacement increased significantly. When the ultimate bearing capacity reached 296.3 kN, the load increased, and finally the local buckling of the steel beam was too large, and the crack width at the bottom of the slab was large, so the test stops.

At a loading of 60–75 kN on ZJB, the first crack appeared at the interface between the span on the south side of the slab and the bottom of the slab. At a loading of 120 kN, cracks continued to develop in all parts of the load. As the load increased, the cracks continued to develop and continued to increase in width. At a loading of 180 kN, new cracks appear in the span on the south side of the slab. When the loading was 210 kN, cracks appeared on the upper surface of the plate, and the cracks appearing on the surface of the plate were symmetrical. The first crack appeared developed to a width of 1 mm, new cracks appeared on the side and bottom of the plate, and new cracks appeared at the location of the supports. As the loading process continued, the first crack produced by the loading gradually became the main crack of the damage. When the loading was 282 kN, the plate’s low middle displacement reached 16.3 mm, and the steel beam at the concentrated loading position began to buckle. When the plate’s low middle displacement increased to 17.6 mm, the bearing capacity of the plate suddenly dropped sharply and the specimen yielded. The bottom surface and both sides of the plate formed through-cracks, the cracks below the middle line of the plate formed into a symmetrical distribution, and the concentrated loading position of the steel beam caused serious buckling, and the whole plate bent; loading then stopped. The characteristic damage phenomena of the specimens are shown in Figure 13

4. Experimental Results

4.1. Load-Midspan Displacement Curves

Figure 14 shows that the curves of the three slabs follow roughly the same trend and go through four stages: elastic stage, crack development stage, yielding stage, and damage stage. At the beginning of the loading phase, the combined beam is in the elastic stage, and the displacement increases linearly as the load increases, with the steel beam and the concrete laminated plate acting together to resist the load. The cracking load of SC1 and SC2 was the same, roughly around 75 kN, and the line stiffness at this stage was 39 kN/m. The ZJB was smaller than the two, with a cracking load of around 60 kN and a line stiffness of 30 kN/m. When the specimen cracked, with the increase of force, the curve changed from linear to non-linear and gradually became slower, the line stiffness gradually became less and the flexural load capacity of all three groups of specimens decreased. The reason for this phenomenon is that as the force increases, the concrete laminated plate and the steel beam gradually slip, the synergistic effects decreases, and the crack grows rapidly. The yield load of SCL1 was 240.9 kN, the yield load of SCL2 was 255.2 kN, and the yield load of the whole cast slab was 248.2 Kn. The yield displacement of SCL1 was 10.2 mm, and the yield displacement of SCL1 was 13.8 mm. This shows that the angle shear connectors can resist a certain amount of slip between the concrete laminated slab and the steel beam, strengthen the integrity of the steel beam-concrete laminated plate, increase its synergistic capacity, and improve the overall stiffness. The later stage of loading is the damage stage, due to the increase in load, the local buckling of the steel beam flange near the loading pad occurs. With the increase in displacement, the load-bearing capacity decreases sharply, and the final damage of the three slabs takes approximately the same form, with a penetration crack forming at the center of the concrete slab bottom of the combined beam. The ultimate loads of the three slabs are approximately the same and it can be seen that the shear connectors have a small effect on the ultimate loads, a conclusion that is consistent with the literature [32].

The main results of the tests on the three groups of specimens are shown in

Table 4. Summary of main test results.

Numbers	Pcr/kN	δcr/mm	Py/kN	δy/mm	Pu/kN	δu/mm
SCL1	75	1.96	240.9	10.9	296.5	24.1
SCL2	75	1.97	255.12	9.9	296.1	16.3
ZJB	60	1.95	248.2	10.3	285.3	18.2

, where P_cr and δ_cr represent the cracking load of the test beam and its corresponding mid-span deflection value, respectively. Variables p_u and δ_u represent the ultimate load of the test beam and its corresponding mid-span deflection value, respectively. There is currently no uniform method for determining the yield point of a generalized force-displacement relationship without a significant yielding platform, and the calculation of the yield point in this paper was determined according to the commonly used Guo Zhenhai geometry method [33].

Figure 15 shows that the deflection distribution along the height direction is approximately the same for all three groups of specimens. The deflection of SCL1, SCL2, and ZJB changed significantly when loaded at around 90 kN and around 120 kN. The value 0.5 P_u was used as an indicator to calculate the flexural stiffness, and when loaded at 0.5P_u, the deflection of SCL1, SCL2, and ZJB were 6.24 mm, 5.11 mm, and 6.18 mm, respectively. The deflection of SCL2 was 18.1% and 17.3% lower than that of SCL1 and ZJB, respectively. Therefore, the presence of shear connectors inhibits the development of cracks in the composite beam and increases flexural stiffness.

4.2. Load-Slip Distribution

The tie bar of the shear connector extends into the interior of the laminated plate and is poured together with the whole slab, and the lower part is welded with the steel beam. It can transfer the shear force generated at the interface between the concrete laminated slab and the steel beam, which is the key to the synergy of the whole steel-concrete composite slab beam. Considering the symmetry of the loading and placement of the specimen, half of the span was selected to measure the relative slip of the steel-mixed interface between the mid-span, 1/4 L, the section above the support and the end of the beam. As the slip showed irregularities due to a more severe crack opening in the late loading period, only the relative slip before the member yielded was selected for analysis in this paper.

Figure 16 shows the slip at the beam ends of the three sets of combined beams were approximately the same as the slip at the supports except for the later stages of loading. With the increase of the load, the slip of the relative position also increased, and the slip of the mid-span section was basically zero. For SCL1, when the load was 90 kN, the amount of slip changed abruptly, and the abrupt change was at the joints of the two precast bottom panels. This phenomenon was the same as SCL2, but the loading force for SCL2 was 180 kN. The location of the abrupt change in the slip of ZJB was similar to that of SCL2, which shows that the integrity of SCL2 was the same as that of the cast-in-place slab, which was better than that of SCL1 and can transfer the interface shear force better. The maximum slip of SCL1 was generated at 1/4 L, which is consistent with the rule derived from the experiments in the literature [19]. The maximum slip of SCL2 and ZJB was generated at the end of the combined beam, which is consistent with the theoretical calculation in [34]. The main reason for this phenomenon was that SCL2 has the best shear connection degree, SCL1 was the worst, and ZJB was in the middle. For SCL1 with the loading, the local reaction force generated by the bearing on the plate was large, which was greater than the shear force generated by the slip, greatly limiting its slip. For SCL2 and ZJB, the local pressure generated by the support was small, and the combined force generated by the combined effect of the concrete laminated plate and steel beam exceeded the local pressure of the support, which reduced the inhibition of the slip of the support. As a whole, under the same relative position and the same level of loading, SCL2 produced the smallest amount of slip, ZJB the second largest, and SCL1 the largest. With a load of 0.8 P_u, for example, the slip of SCL1 was 0.356 mm, that of SCL2 was 0.184 mm and that of ZJB was 0.196 mm. The slip of SCL2 was less than half that of SCL1 and was 95% of that of the ZJB. As the slip at the interface decreases with increasing shear connection degree, the angle of the shear connection not only has tie bars extending into the upper laminated slab but is also welded to the steel beam, which can effectively transfer part of the shear force generated by the laminated slab and the steel beam section, thus inhibiting the slip of the section.

4.3. Crack Distribution and Features

Comparing the test phenomena, it was obvious that the crack generation of SCL2 was delayed compared to SCL1 and ZJB. The reason for this phenomenon is that the shear connection degree of SCL2 was greater than that of SCL1 and ZJB, therefore the slip of SCL1 and ZJB will be greater than that of SCL2, it can be understood that the longitudinal deformation of SCL1 and ZJB concrete slab was greater than that of SCL2. It was found that the deflection of SCL2 was smaller than that of SCL1 and ZJB under the same level of load, so the bending curvature was also smaller and less likely to produce cracks.

The main cracks in all three sets of composite beams occurred in the mid-span section and the distribution of the cracks shows that the alignment and distribution of the three sets of composite beams were similar. This indicates that the concrete bonding performance between the precast and cast-in-place layers was good and no shear damage along the laminated surface occurred. Between the joint and the support section, transverse cracks appeared, indicating good force transfer at the joint. As the load increased, longitudinal splitting fractures appeared in the shear span zone near the support, and shear cracks occurred in the concrete near the support due to the high pressure transmitted from the steel beam. The SCL2 had fewer shear oblique cracks than SCL1 and ZJB. The reason for this phenomenon is that the connection effect between the concrete slab with angle shear connectors and steel beams was better under the same level of loading and the shear lag effect was more pronounced. Therefore, fewer oblique cracks appeared in the supporting section than in the outgoing reinforcement. According to the literature [35], the precast bottom panel out reinforcement helps to stop longitudinal splitting cracks, which demonstrates the effect of the angle connectors in inhibiting longitudinal splitting cracks in the steel-laminated plate combination beams. This again verifies that the transverse reinforcement has the effect of inhibiting longitudinal splitting cracks. Please see Figure 17 for the exact distribution of cracks.

4.4. Stress-Strain of Reinforcement

Figure 18a,b shows that the cross-sectional strains in the height direction of the SCL1 midspan section had a non-linear distribution and the section did not conform to the plane section hypothesis. The reason for this is the relative slip at the combined interface between the steel beam and the reinforced truss concrete laminated plate, which caused the section strains to jump at the combined interface and the respective neutral axes within the steel beam and the reinforced truss concrete laminated plate.

Figure 18c,d shows that the cross-sectional strains in the height direction of the SCL2 midspan section had a linear distribution in the first stage of loading, except for the non-linear variation of individual concrete strains due to the shear hysteresis effect, and the cross-section conforms to the plane section hypothesis. The steel truss concrete laminated plate works well with the steel beam, and by default, no relative slip was generated at the interface between the steel beam and the steel truss concrete laminated plate. At the later stage of loading, the section strains in the height direction showed approximately linear distribution, and very little relative slip was generated at the interface between the steel beam and the steel truss concrete laminated plate, but the section conforms to the plane section hypothesis.

Figure 18e,f shows that the stress-strain distribution trend of ZJB was roughly the same as that of SCL2, which was linear, and the cross-section conforms to the plane section hypothesis. As the stress-strain at the relative positions of ZJB was greater than that of SCL1 and SCL2 under the same load, it indicates that the transfer performance of the laminated plate was superior to that of the whole cast plate under the same conditions.

The strain distribution diagram of the mid-span section before 75 kN shows that the neutral axis of the steel beam in the three groups of specimens tends to rise during the elastic phase due to concrete cracking. The strain distribution diagram for the entire mid-span section shows a slight downward trend in the neutral axis during the late plastic phase due to the yielding of the upper flange of the steel beam, with the section developing more fully in plastic form as it approaches the ultimate bearing capacity.

4.5. Angle Stress-Strain

The load-angle strain curve for SCL2 during the test loading is shown in Figure 19. Three angles along one side of the girder length of the combined beam are taken in the figure, one for the precast laminated bottom panel in the middle of the span and two for the precast laminated bottom panel at the support side. The angle connectors show a gradual increase in the compressive strain as the load increases, but the rate of growth varies, with the linear growth rate of compressive strain in the elastic phase being less than after the member has yielded. The farther away from the mid-span, the greater the compressive strain, with the maximum compressive strain reaching around 1411. The different locations of the compressive strains also reflect the greater effect of the shear connections near the bearing on the shear performance of the member.

5. Numerical Simulation

The forces and deformations in steel-concrete laminated plate composite beams are non-linear. Finite elements not only provide a qualitative observation of features that cannot be observed in the tests but also provide a view of the specific forces within the component, which can validate and complement the experimental study of the flexural performance of H-shaped steel-concrete laminated plate composite beams under negative bending moments. In this section, the bending performance tests of H-shaped steel-concrete laminated plate composite beams under negative bending moments were modeled and analyzed using the large general-purpose software ABAQUS. To verify the reliability and correctness of the constructed model, the mid-span load-displacement curves and concrete cracking damage characteristics were extracted in post-processing for comparison with the experimental results. This provided a basis for the subsequent parametric analysis of the H-shaped steel-steel truss laminated plate composite beams (the effect of concrete strength on the flexural loading capacity and flexural stiffness of the H-shaped steel-steel laminated plate composite beams with embedded angle connectors).

5.1. Finite Element Modeling

5.1.1. Material Constitutive Model

(1)

Concrete

The ABAQUS software offers three models for the constitutive relationship of concrete materials. One of these models is the concrete dispersion cracking model, which is suitable for simulating relatively low surrounding pressure situations and is mainly used in the performance of concrete in tension subjected to relatively monotonic loads. The concrete brittle cracking model is suitable for brittle materials, such as ceramics and plain concrete, and is mainly used in the performance of tensile cracking. The concrete plastic damage model is suitable for simulating low envelope pressure situations and is mainly used in structural analysis to strengthen concrete subjected to monotonic, cyclic, and dynamic loads [36]. In this paper, the Concrete damage plasticity (CDP) model was chosen.

The CDP model assumes that uniaxial tension and compression of concrete are characterized by damaged plasticity [37], as shown in Figure 20. In the case of uniaxial compression, the stress-strain is in the linear-elastic range in the initial phase, and microscopic cracks begin to develop and form within the concrete, with the stress-strain relationship exhibiting plasticity when the initial yield stress ${\sigma }_{\mathrm{c}}{}_0$ is reached. Internal microscopic cracks develop, and numerous microscopic cracks penetrate, eventually reaching the ultimate stress ${\sigma }_{\mathrm{cu}}$. The strain increases, cracks develop dramatically, and the strain then softens. In the case of uniaxial tension, the stress-strain falls in the linear elastic range in the initial phase, reaching the failure stress ${\sigma }_{\mathrm{t}0}$ implies microscopic cracking within the concrete, after which the strain increases rapidly and the concrete constitutive follows a softening stress-strain response to represent it.

At present, many scholars have done in-depth research on the equation of the compressive stress-strain curve [38,39,40,41]. China’s concrete structure design code [25] compressive stress-strain equation was obtained based on many tests after verification, with a deep theoretical foundation and extensive verification. The relationships in the code are determined by Equations (1)–(5):

$$\sigma =\left(1-d_{\mathrm{c}}\right)E_{\mathrm{c}}\epsilon$$

(1)

$$d_{\mathrm{c}}=\left\{\begin{array}{c}1-\frac{{\rho }_{\mathrm{c}}n}{n-1+x^{\mathrm{n}}}\hspace{1em}x⩽1\\ 1-\frac{{\rho }_c}{{\alpha }_{\mathrm{c}}{(x-1)}^2+x}\hspace{1em}x>1\end{array}\right.$$

(2)

$${\rho }_{\mathrm{c}}=f_{\mathrm{c},\mathrm{r}}/E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}$$

(3)

$$n=E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}/(E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}-f_{\mathrm{c},\mathrm{r}})$$

(4)

$$x=\epsilon /{\epsilon }_{\mathrm{c},\mathrm{r}}$$

(5)

where α_c is the parameter value of the falling phase of the concrete uniaxial compressive stress-strain curve, calculated according to Equation (6); f_cr is the representative value of the concrete uniaxial compressive strength, taken as f_ck; ε_cr is the peak compressive strain corresponding to the concrete uniaxial compressive strength f_cr, calculated according to Equation (7); d_c is the concrete uniaxial compressive damage evolution parameter. Stress-strain and damage parameter-strain relationships for compression and tension are cited from the literature [41,42].

$${\alpha }_{\mathrm{c}}=0.157f_{\mathrm{c},\mathrm{r}}^{0.785}-0.905$$

(6)

$${\epsilon }_{\mathrm{c},\mathrm{r}}=\left(700+172\sqrt{f_{\mathrm{c}}{}_{,\mathrm{r}}}\right)\times {10}^{-6}$$

(7)

The following equations are derived from the ABAQUS User Manual relationship (8)–(10) with Figure 20:

$${\epsilon }_{\mathrm{c}}^{\mathrm{in}}={\epsilon }_{\mathrm{c}}-{\epsilon }_{0\mathrm{c}}^{\mathrm{el}}$$

(8)

$${\epsilon }_{0\mathrm{c}}^{\mathrm{el}}={\sigma }_{\mathrm{c}}/E_0$$

(9)

$${\epsilon }_{\mathrm{c}}^{\mathrm{pl}}={\epsilon }_{\mathrm{c}}^{\mathrm{in}}-\frac{d}{(1-d)}\frac{{\sigma }_{\mathrm{c}}}{E_0}$$

(10)

where ε_c is the actual strain; ${\epsilon }_{\mathrm{c}}^{\mathrm{in}}$ is the compressed inelastic strain; ${\epsilon }_{0\mathrm{c}}^{\mathrm{el}}$ is the elastic strain at initial stiffness; ${\epsilon }_{\mathrm{c}}^{\mathrm{pl}}$ is the compressed plastic strain.

Utilizing the above equation, the inelastic strain without damage is subtracted from the inelastic strain reduced by damage to obtain the plastic strain under compression. Based on the energy equivalence principle proposed by Sidoroff [43] and others who suggested that the elastic residual energy with and without material damage is formally equal, the damage factor is calculated as in Equation (11) and brought into the above equation to obtain the compressive plastic damage model for concrete used in the model.

$$d=1-\sqrt{\frac{\sigma }{\left(E_0\epsilon \right)}}$$

(11)

where d is the concrete damage factor; $\sigma$ is the true stress in concrete; ε is the true strain in concrete; and E₀ is the initial modulus of elasticity. The true stress/strain needs to be converted from the nominal stress/strain calculated in the previous equation and imported as true stress/strain in the CAE interface.

There are relatively few studies of stress-strain relationships for concrete subjected to uniaxial monotonic tension, similar to uniaxial compression, and this paper is based on the use of the stress-strain curve relationship for concrete in uniaxial tension from code [25] as determined by Equations (12)–(15):

$$\sigma =\left(1-d_{\mathrm{t}}\right)E_{\mathrm{c}}\epsilon$$

(12)

$$d_{\mathrm{t}}=\left\{\begin{array}{cc}1-{\rho }_{\mathrm{t}}\left[1.2-0.2x^5\right]& x⩽1\\ 1-\frac{{\rho }_{\mathrm{t}}}{{\alpha }_{\mathrm{t}}{(x-1)}^{1.7}+x}& x>1\end{array}\right.$$

(13)

$$x=\epsilon /{\epsilon }_{\mathrm{t},\mathrm{r}}$$

(14)

$${\rho }_{\mathrm{t}}=f_{\mathrm{t},\mathrm{r}}/E_{\mathrm{c}}{\epsilon }_{\mathrm{t},\mathrm{r}}$$

(15)

where the meaning of the symbols in the formula is similar to that of uniaxial compression and will not be repeated. Where ${\alpha }_{\mathrm{t}}$ is chosen according to the formula (16); ${\epsilon }_{\mathrm{t},\mathrm{r}}$ is chosen according to the formula (17):

$${\epsilon }_{\mathrm{t},\mathrm{r}}=f_{\mathrm{t},\mathrm{r}}^{0.54}\times 65\times {10}^{-6}$$

(16)

$${\alpha }_{\mathrm{t}}=0.312f_{\mathrm{t},\mathrm{r}}^2$$

(17)

The following equations are derived from the ABAQUS User Manual relationship (18)–(20) with Figure 20.

$${\epsilon }_{\mathrm{t}}^{\mathrm{ck}}={\epsilon }_{\mathrm{t}}-{\epsilon }_{0\mathrm{t}}^{\mathrm{el}}$$

(18)

$${\epsilon }_{0\mathrm{t}}^{\mathrm{el}}={\sigma }_{\mathrm{t}}/E_0$$

(19)

$${\epsilon }_{\mathrm{t}}^{\mathrm{pl}}={\epsilon }_{\mathrm{t}}^{\mathrm{ck}}-\frac{d}{(1-d)}\frac{{\sigma }_{\mathrm{t}}}{E_0}$$

(20)

The meaning of the symbols in the equation is similar to that of uniaxial compression and will not be repeated.

Through the above equation, the inelastic strain without damage is subtracted from the inelastic strain reduced by damage to obtain the tensile plastic strain, where the concrete damage factor is the same as before and brought into the above equation to obtain the concrete tensile plastic damage model used in the model.

The concrete has a strength class of C30, a density of 2.4 × 10⁻⁹ t/mm³, a modulus of elasticity of 30,000 MPa and a Poisson’s ratio of 0.2. Stress-strain and damage parameter-strain relationships for compression and tension are cited in reference [42]. The following

Table 5. CDP model shaping parameter settings.

$\mathbf{Expansion} \mathbf{Angle}\mathit{\phi }{(}^{\circ })$	$\mathbf{Eccentricity} \mathit{\epsilon }$	${\mathit{f}}_{\mathbf{b}0}/{\mathit{f}}_{\mathbf{c}0}$	${\mathit{K}}_{\mathit{C}}$	$\mathbf{Viscosity} \mathbf{Parameter} \mathit{\mu }$
30	0.1	1.16	0.666667	0.005

shows the values set for the CDP model plasticity parameters:

(2)

Steel Constitutive Model

The I-beam was made of Q235 steel with Young’s modulus of 210 GPa, a transverse deformation factor of 0.3, and a yield strength of 245 MPa. The studs were made of Q235 steel with Young’s modulus of 210 GPa, a transverse deformation factor of 0.3, a yield strength of 235 MPa, and an ultimate strength of 457 MPa. To implement strain and stress relationships in ABAQUS, engineering stress and strain were converted to true stress and strain [42]. More researchers [44,45] have defined the constitutive model of the stud as a stress-strain bilinear hypothesis model, so this paper used the bilinear hypothesis model l for stud connectors, angle shear connectors, steel beams and reinforcement. The hypothesis model refers to the constitutive relation in the code [25], as follows:

$${\sigma }_{\mathrm{p}}=\left\{\begin{array}{ll}{E}_{\mathrm{s}}{\epsilon }_{\mathrm{s}}\hfill & {\epsilon }_{\mathrm{s}}⩽{\epsilon }_{\mathrm{y}}\hfill \\ f_{\mathrm{y},\mathrm{r}}+k\left({\epsilon }_{\mathrm{s}}-{\epsilon }_{\mathrm{y}}\right)\hfill & {\epsilon }_{\mathrm{y}}<{\epsilon }_{\mathrm{s}}⩽{\epsilon }_{\mathrm{u}}\hfill \\ 0\hfill & {\epsilon }_{\mathrm{s}}>{\epsilon }_{\mathrm{u}}\hfill \end{array}\right.$$

(21)

As shown in Figure 21, the code requires a bilinear hypothesis model, i.e., after the steel has reached the plastic phase, a different slope from that of the elastic phase was used within the hardening phase where the steel reaches yield and ultimate strength. Variable k is called the hardening section modulus of steel and its value was taken as 0.01–0.03 E_s, with E_s being the elastic modulus of the elastic phase.

5.1.2. Meshing and Unit Type Selection

The model consisted of five parts: steel beam, concrete, stud shear connectors, angle-embedded parts, and reinforcement. The overall meshing of the combined beam and the meshing of some areas are shown in Figure 22. As the model has more layers in the bending direction, six layers of elements were used through the thickness of the web while four layers of elements were used through the thicknesses of flanges and stiffeners. Ten layers of elements were employed through the thickness of the concrete plate to be able to accurately represent the bending of this member. According to previous analyses [42,46,47,48], at least three concrete layers should be utilized for thickness. The C3D8R units were used for the steel beam, concrete, stud shear connectors and angle-embedded members to save computational costs and improve convergence. The model was meshed using a structural mesh [39], with a refined mesh for the stud shear connectors and the angle steel pre-embedded parts, and a refined mesh for the concrete parts in contact with them. The steel reinforcement was all in three-dimensional two-nodal linear truss units (T3D2).

Considering both calculation accuracy and efficiency, the mesh was locally refined at the location where there existed high-stress concentration. After conducting several mesh sensitivity analyses, the mesh size at the single stud shear connectors was set as around 10 mm, the size of mesh at the steel beams was set as 15 mm, while the size of sizes of angle embedded parts was set as 50 mm. As a result, the total number of meshes in the model was 16,048. Furthermore, referring to the literature [40], the mesh division method is roughly the same as this paper, therefore the division method of this paper was verified [40].

5.1.3. Setting of Interactions

The contact and constraint relationships between the individual components affect the results and convergence of the entire finite element model, so the interactions between the components must be defined more accurately in practice.

The steel reinforcement was embedded into the concrete substrate with perfect bonding [49,50]. The bond between the concrete and the steel beam has a weak contribution in the process of slip, so the model ignored the bond between the steel beam and the concrete interface and only considered the face-to-face contact between the concrete and the steel beam, i.e., the normal direction is “Hard Contact”. The tangential friction was modeled using a ‘penalty’ function and the tangential friction coefficient was determined to be 0.4 through the final model comparison and reference. No slippage or misalignment was found between the reinforcing truss laminated bottom slab and the cast-in-place layer during the test, and the two were simulated by binding. The reinforcement mesh and the reinforcement trusses in the reinforcement truss laminated base slab and the cast-in-place layer were simulated using a simplified model ignoring the slip effect between the two, and the reinforcement mesh and the reinforcement trusses were simulated using Embedded throughout the model. The ABAQUS software automatically couples the reinforcement mesh and the reinforcement trusses to the concrete. The rigid spacers above the steel beam and the steel beam were tightly fitted together during the loading process, so the binding order was used. The stud shear connectors, which are welded to the steel beam at the factory, were simulated using binding. The stud shear connectors may not be able to deform synergistically when subjected to high forces due to the large difference in the modulus of elasticity between the studs and the concrete, so the part of the studs in contact with the concrete above the root was defined surface to surface contact, i.e., the surface of the stud shear connectors was normal to the surrounding concrete using the “Hard“ function. The tangential friction was modeled as a “penalty” function, with the same tangential friction coefficient of 0.4 at the interface between the concrete and the steel beam. The corner welds exist between the angle shear connectors and the steel beams, so triangular column-shaped welds were set up to bind the angle shear connectors to the steel beams, and similar to the stud connectors, face-to-face contact was used between the angle connectors and the concrete, and the same volume of shapes as the angle connectors and stud connectors were dug out in the laminated bottom slab and cast-in-place layer using the stretch command, and the components were assembled precisely according to their specific positions in the assembly. A diagram of the interaction between some areas of the finite element model is shown in Figure 23.

Face-to-face contact was set up in such a way that the faces were allowed to separate after contact, and a certain tolerance was set between the faces to make the model converge easily. To avoid mesh penetration during the analysis, the slave faces were chosen to be less stiff and the mesh of the slave faces was denser than that of the main faces.

Figure 23. Interaction schematic of the finite element model.

Figure 23. Interaction schematic of the finite element model.

5.1.4. Loads and Boundary Conditions

A rigid mat with a modulus of elasticity much greater than the modulus of elasticity of the steel beam was assembled above the geometric center of the beam, and the upper surface of the rigid mat was coupled to a reference point RP1 established above the geometric center of the rigid mat. A vertical downward displacement load was then applied to RP1, the magnitude of which can be obtained by extracting the inverse of the reference point in post-processing. In addition, a gravity load was applied to the whole model with a gravitational acceleration of 9.8 m/s².

A line perpendicular to the span direction was cut in the lower center of the pad at each end of the combined beam, and a boundary condition was applied to the cut-out center line to constrain the lateral and gravitational direction of the combined beam to release only the translational movement along the span direction of the beam, with the load and boundary condition schematically shown in Figure 24.

5.1.5. Analysis Step Setting

The model is analyzed using a static analysis step, which is added to the initial analysis step that comes with the system. Based on the above non-linear problem solution and equilibrium iterations and convergence judgment, the initial analysis step should be as small as possible, the minimum analysis step should be as small as possible, the incremental step length should be selected from the system’s own “automatic incremental step method”, and the conversion of severe discontinuity iteration switch should be turned on to ensure convergence. The CDP model has been chosen for this construction and the post-processing needs to look at the damaged plasticity of the concrete, so it is necessary to turn on the pressure injury and tension injuries switch in the output of the field variables.

5.2. Finite Element Results and Model Validation

A finite element model for the experiments was established using the above method. To verify the reliability and correctness of the constructed model, the mid-span load-displacement curves and concrete cracking damage characteristics were extracted in post-processing for comparison with the experimental results, giving a basis for subsequent research and parametric analysis of the steel-steel truss laminated plate composite beams.

5.2.1. Mid-Span Load-Deflection Curves

As shown in Figure 25. Based on refined modeling, the trend of the test curve variation and the level of inflection points of the three groups of members matched well with the results of the finite element simulation, and the stages of the finite element model were comparable to the test. The maximum error of the three loads at the same displacement does not exceed 5%, which verifies the validity and reliability of the model.

Simulation can be seen, SCL2 in the yield phase of the maximum force, the smallest displacement. It can be seen that the new angle shear connectors have better flexural stiffness under negative bending moments and better flexural performance than SCL1 and ZJB, which is consistent with the experimental results and in line with the design concept of the new angle shear connectors.

Figure 25. Comparison of test and finite element mid-span load-deflection curves.

Figure 25. Comparison of test and finite element mid-span load-deflection curves.

5.2.2. DAMAGET Damage Clouds

The tensile damage DAMAGET cloud in ABAQUS can reflect the cracking and failure characteristics of the concrete to some extent. A tensile damage value of 0 indicates that no damage has occurred, above 0.5 microscopic cracks begin to appear in the concrete, and above 0.9 the concrete is considered to be completely cracked and nearly failed. The finite element DAMAGET cloud diagrams for the concrete slab bottom, slab side, and slab end are shown in Figure 26. They show that the range of cracks at the bottom of the slab was more consistent with the experiments, shear cracks also appeared at the bottom ends of the slab, shear cracks at the slab end, and multiple cracks extending from the cast-in-place layer to the precast layer also appeared at the slab end. The main characteristics of the test cracks were more consistent with the distribution of the tensile damage cloud, which further validates the reliability and correctness of the model.

The damage to SCL2 under negative bending moments was mainly concentrated in the span and at the concrete laminated slab joints, with a larger damaged area than SCL1 and ZJB, but with a smaller damaged maximum stress value than the two. The new angle shear connectors can transfer and resist the upper loads to a certain extent, thus reducing the stress concentration phenomenon in SCL2. At the same time, it can be obtained that when using the new angle steel shear connectors, certain measures can be taken at the span and in the middle of the span to prevent the failure of the whole member due to the failure of the concrete slab in the middle of the span and at the span.

Figure 26. Concrete tensile damage cloud.

Figure 26. Concrete tensile damage cloud.

5.3. Computational Model Design

Based on the above model, 5 sets of finite element models were designed for the concrete strength for non-linear analysis; the specimen numbers and comparison of design parameters are shown in

Table 6. Finite element model design parameters.

Specimen Number	fcu,k	l/mm	q
FEM1	C20	40	12
FEM2	C30	40	12
FEM3	C40	40	12
FEM4	C50	40	12
FEM5	C60	40	12

.

The load-span displacement curves corresponding to different concrete strength grades are shown in Figure 27. The concrete strength grades for FEM1, FEM2, FEM3, FEM4 and FEM5 were C20, C30, C40, C50, and C60, respectively. Figure 27 shows that the curves are relatively close together in the elastic phase and close to the load carrying capacity, with the load carrying capacity of each specimen differing by only 1.3% when the concrete strength grade was increased from C20 to C60. This shows that the change in concrete strength grade has little effect on the load-bearing capacity of the steel-laminated plate composite beam under negative bending moments. The method of increasing the load-bearing capacity by increasing the concrete strength class is not feasible from an economic point of view.

The curves of the effect of different concrete strengths on the initial and posterior stiffnesses are shown in Figure 28. The initial flexural stiffness is the flexural stiffness in the online elastic phase, and the posterior flexural stiffness is the flexural stiffness corresponding to the yield point determined by the geometric method. The graph shows that the initial and posterior stiffnesses continue to increase as the concrete strength level increases, but the growth rate of the initial and posterior stiffnesses continues to slow down. When the concrete strength increased from C20 to C40, the initial and late stiffness increased by 3.495 × 10¹² N·mm²and 1.972 × 10¹² N·mm², an increase of 7.78% and 8.21%. As the concrete strength increased from C40 to C60, the initial and posterior stiffnesses increased by 1.288 × 10¹² N·mm² and 0.934 × 10¹² N·mm², an increase of 2.66% and 3.59%. From the above analysis, it can be concluded that the increase in concrete strength can improve the initial and posterior stiffness, but the trend of improvement continues to weaken with the increase in concrete strength.

Figure 27. Load-medium span displacement comparison curve.

Figure 27. Load-medium span displacement comparison curve.

Figure 28. Curve of the effect of different concrete strengths on stiffness.

Figure 28. Curve of the effect of different concrete strengths on stiffness.

5.4. Summary of This Section

This section first establishes the finite element model using ABAQUS based on experiments and compares the simulation results with the experimental results. The model results match the experimental results and verifies the accuracy of the finite element model. On this basis,five groups of finite element models were established for parametric analysis to investigate the influence law of flexural load-bearing capacity and flexural stiffness of the steel-laminated plate composite beam with prefabricated bottom slab embedded angle steel connectors of concrete strength. In this paper, although the finite element analysis of the concrete strength on the flexural load-bearing capacity and flexural stiffness of the component has been carried out, the influence law of the concrete strength on the laminated plate of the precast bottom panel with embedded angle steel connectors needs further experimental research. The influence of the parameters was not only on the concrete strength but also on the lap length and the spacing of the angles, which must be investigated in finite elements and experiments.

6. Conclusions

In this paper, the experimental study of three groups of H-beam-concrete laminated plates of different structural forms under the action of the negative bending moment was first carried out. Based on the experiments, an experimental model was established using the finite element software ABAQUS and compared with the experimental results, and the model results were in good agreement with the experimental results. Based on the above study five groups of finite element models were established for parametric analysis to investigate the effect of concrete strength on the flexural load-carrying capacity and flexural stiffness of steel-laminated plate composite beams with a prefabricated bottom panel with embedded angle steel connectors. The conclusions of this study are as follows:

(1)

All three composite beam specimens were eventually damaged by the pulling of the reinforcement in the concrete slab, showing typical bending damage characteristics and similar ultimate bearing capacity.

(2)

No shear failure occurred at the composite surface of the laminated beam, and the overall stressing performance of the composite beam was good. The distribution of cracks in the three groups of composite beams was similar, and the angle steel connectors had the effect of inhibiting longitudinal splitting cracks in the H-shaped steel-concrete laminated plate composite beams.

(3)

Precast bottom slab embedded new angle steel connectors of H-shaped steel-concrete laminated plate composite beams were a combination with better performance and greater flexural stiffness.

(4)

The slippage of the H-shaped steel-concrete laminated plate composite beam with embedded new angle connections in the precast bottom panel was less than the slippage of the precast bottom slab bent-up bars protruding and the laminated cast slab, with the maximum slippage being only 1/2 of the precast bottom slab bent-up bars protruding.

(5)

In the composite structure of H-shaped steel-concrete composite slabs under negative bending moment, shear angle connectors can replace the bent-up bars protruding from the laminated bottom panel to achieve without extending the reinforcement of the laminated bottom panel.

(6)

The numerical simulations revealed that the concrete strength had almost no effect on the flexural load capacity of the members. The increase in initial and posterior stiffness was 7.78% and 8.21% when the concrete strength was increased from C20 to C40, and 2.66% and 3.59% when it was increased from C40 to C60.

7. Future Needs and Recommendations

In this study, the effect of the mechanical performance of an H-shaped steel-concrete laminated plate composite beams under negative bending moment was discussed based on both experimental study and FE modeling. Then the influence of concrete strength was analyzed based on the FE modeling. More experiments may be conducted in the future for proving the FE results concerning the effect of concrete strength. In addition, the effect of lap-splice length and the gap between the shear connectors may be taken into consideration in further research. Through the literature [51,52,53], we found a parameter that we did not study, i.e., the fracture of the reinforcement as a, which could also be a direction for research in the next step.