Experimental and Numerical Investigations on Load Capacity of SRC Beams with Various Sections

Abstract

Steel-reinforced concrete (SRC) structures combine steel skeletons with concrete components, improving load-bearing capacity and streamlining construction. In this study, four full-size lattice SRC members were tested under pure bending to validate fundamental assumptions and were further analyzed numerically. The experimental specimens demonstrated a 15.3% increase in ultimate load-carrying capacity and an average 58.7% increase in the ductility index compared with conventional members. Notably, the improvement in ductility was substantially greater than the enhancement in load-bearing capacity. In parallel, a load-bearing capacity formula for lattice SRC members was proposed, yielding an error margin of 0.136 when compared with existing formulae for section steel members. The flexural strength predictions of formulae derived from simplified elastic–plastic theory and numerical analysis agreed with the test results.

1. Introduction

Steel-reinforced concrete (SRC) systems were originally developed to mitigate the overproduction of steel and to address housing shortages [1]. In the building industry, prefabrication has enhanced efficiency [2], precision [3], and safety [4] of construction. However, conventional SRC members are often associated with higher costs and potential quality concerns [2]. To overcome these limitations, researchers have introduced innovative prefabrication systems in recent years [5,6,7].

Extensive studies have focused on enhancing individual building SRC components with various sections [8,9,10,11,12,13,14,15,16,17]. Studies have shown that the compressive strength of precast steel-stud concrete members is usually higher than that of plain concrete members [8]. Lou et al. [9] investigated the bending behavior of four space lattice deep beams with various sections in four-point bending tests, finding significant improvements in stiffness and load-bearing capacity. Similarly, Guo et al. [10] examined the load-bearing capacity of twelve built-in steel member ends with different shear span ratios in three-point tests, noting substantial enhancements in node performance. It indicates that the lattice SRC structures have an effective seismic performance compared with RC beams subsequently. Shear tests have further elucidated the role of steel reinforcement in enhancing the shear strength of SRC members, particularly in high-shear regions [11]. Dynamic testing, including static cyclic tests and shaking table experiments, has been conducted to evaluate the seismic performance of SRC structures [12]. Xu et al. [17] investigated the SRC nodes through numerical modeling, incorporating diverse mesh sizes within each component. The findings of the study suggest a strong correlation between the numerical models and the experimental results. Xu et al. [18] conducted an analysis of the element types of SRC special-shaped interior joints, determining that the embedded region performs well in the collaborative interaction between different materials. However, the extant literature on SRC members is predominantly focused on H-beam combined members [15,16,17,18], with limited research addressing hollow web lattice-type members [19,20,21,22,23]. The bearing capacity of angle SRC members has been proposed [13,14], and it is suggested that this capacity can be extended to the calculation of the bearing capacity of lattice SRC members.

Therefore, pure bending tests of lattice SRC beams were performed and analyzed. This beam features a thin steel plate integrated with the web at the ends, forming a steel-like connection node, which is depicted in Figure 1. The design allows the beam ends to connect securely to the steel columns, supporting substantial construction loads. This connection method is more straightforward and reliable than traditional prefabricated nodes, enabling construction methods akin to those used for structural steel members, but with significantly less steel. The external concrete layer protects the load-bearing steel and maintains the connection through splices and baseboards.

This study presents a comprehensive experimental investigation of full-scale lattice SRC beams. Four-point bending tests were performed to evaluate failure modes, load–deflection behavior, and the validity of design assumptions. Complementary numerical analyses were then carried out, comparing experimental results with theoretical predictions to examine the influence of construction methods and member parameters on beam performance. Based on both experimental and numerical findings, a simplified design method for lattice SRC beams is proposed.

2. Experimental Setup

Five experimental tests were conducted to evaluate the performance of novel prefabricated beams reinforced with Q355 steel, alongside conventional concrete beams reinforced with HRB400 steel as control specimens. The concrete cover thickness was consistent across all specimens, except for GL3, where the lateral cover thickness was increased to 50 mm. Each experimental component featured distinct structural details, as outlined in

Table 1. Construction details of the specimens.

Label	Beam Section b × h × l (mm)	Steel	Thickness of Steel tw (mm)	Steel Wire Mesh	Width of Cover cl (mm)	Strips/Hoop (mm)
GL1	200 × 400 × 4000	Q355	6		30	−20 × 5@100/200
GL2	200 × 400 × 4000	Q355	6	√	30	−20 × 5@200/400
GL3	200 × 400 × 4000	Q355	8		50	−20 × 5@100/200
GL4	200 × 400 × 4000	Q355	6	√	30	−20 × 5@100/200
LH	200 × 400 × 4000	HRB 400	8		30	Ф8@100/200

. The variation in structural details aimed to assess their impact on beam performance. The results from specimens GL1 to GL4 were utilized to validate the applicability of current codes and the accuracy of the proposed models.

The SRC beams were fabricated using Q355 steel and concrete designed to achieve a compressive strength of 30 MPa. According to [24], concrete cubes measuring 150 mm per side were cast, and, under standard curing conditions, achieved a 28-day strength of 32.5 MPa, meeting code requirements. The reinforcing steel exhibited a tensile strength of 399 MPa, in compliance with specified standards [25], as detailed in

Table 2. Material properties of the specimens.

Material	Thickness (mm)	fy (MPa)	fu (MPa)	fc (MPa)
Steel (Q235)	6	335	417	-
Steel (Q355)	10	399	522	-
Concrete (C30)	-	-	-	32.5

.

2.1. Specimen Preparation

A total of five beam specimens were designed for this study: GL1 through GL4, representing new assembled truss concrete beams, and LH, serving as an ordinary concrete beam for comparison. All specimens shared the following parameters: structural measures (spigot, wire mesh, and longitudinal reinforcement, etc.) and form of steel distribution (type of stressed steel: including steel plate type and size). The calculated span (l = 3800 mm), section size (b = 200 mm, h = 400 mm), and concrete cover (c = 30 mm) of the specimens remain unchanged; only the lateral protective layer and structural measures are changed. The design strength of the concrete is C30; the design variations among the specimens are depicted in Figure 2.

GL1 served as the baseline specimen, without additional structural modifications; GL2 incorporated double-spaced strips to investigate their effect on beam performance; GL3 featured an increased lateral concrete cover thickness of 50 mm to assess its impact; and GL4 combined both strips and increased lateral cover to evaluate their combined effects. The reinforcing details, including wire mesh, longitudinal reinforcement, and steel distribution, varied among the specimens to study their influence on beam behavior.

The structural steel plates are fabricated using steel plates of standard thickness that are commonly available on the construction site, ensuring a more favorable material procurement for construction purposes. The steel framework is first fixed and welded using large-spaced strips on both sides. Then, the spacing of the strips at the midspan is adjusted according to experimental requirements for complete welding. Concrete pouring is carried out in a precast component factory, using the same pouring method as for ordinary precast components. Subsequent to the rectification of the wooden formwork, a layer of mineral oil or alternative release agent that does not react with concrete is applied to the inner surface of the test mold. The concrete mixture is prepared with the sensor wire outlet facing upward, and it is thoroughly mixed at least three times with a shovel until uniform. The on-site flat plate vibration casting of concrete is a process in which the mixture is loaded into the test mold in a single step. During the loading process, it is essential to utilize a trowel to ensure the concrete mixture exceeds the mold opening. This can be achieved by vibrating the mixture along the walls of the test mold. The excess concrete must be removed from the top of the test mold. As the concrete approaches its initial setting phase, the use of a trowel becomes essential for achieving a level surface. The specimen should be transferred to a room maintained at 20 ± 0.5 °C for standard curing. Subsequent to a 28-day period, the specimen should be meticulously extracted from the mold and positioned in a suitable location. The specimen preparation is complete. The load-bearing steel plates of the four components should be measured three times at both ends and the midpoint. The average value of these measurements should then be calculated. The error is displayed in the following table, and the cross-sectional error is indicated in

Table 3. Dimensional tolerance of specimens.

Label	GL1	GL2	GL3	GL4
Upper steel plate	6.10 (1.67%)	5.97 (0.50%)	7.98 (0.25%)	5.92 (1.33%)
Below steel plate	5.83 (2.83%)	5.97 (0.50%)	7.97 (0.38%)	5.94 (1.00%)
Length of the specimen	4008.8 (0.2%)	4008.4 (0.2%)	4010.1 (0.3%)	3991.8 (0.2%)
Height of sections	400.1 (0.03%)	403.6 (9.0%)	401.4 (0.4%)	399.7 (0.08%)
Width of sections	201.1 (0.6%)	201.4 (0.7%)	202.7 (1.35%)	199.8 (0.1%)

.

2.2. Instrumentation and Measurement

As shown in Figure 3a, in order to obtain steel strains of different cross-sectional heights, eight electrical resistance strain gauges were symmetrically placed on the upper and lower surfaces of the steel plates at critical cross-sections to capture strain variations. All strain gauges arrangements are shown in Figure 3b.

To verify whether SRC beams satisfy plane section assumptions or not, eight electrical resistance strain gauges were installed in the surface at 100 mm from the middle line symmetrically, which indicate concrete cracking primarily, as shown in Figure 3c. In addition, the other side is set up with eight linear variable displacement transducers (LVDT) symmetrically to record displacement data, facilitating the analysis of beam deflection post-cracking, as show in Figure 3d. Two additional LVDTs were mounted on the upper surface near the supports to monitor support deformation, and three on the beam’s underside to measure vertical displacement at mid-span.

2.3. Testing Procedure

All specimens underwent four-point bending tests in a controlled laboratory setting, which was defined in [17], following the configuration depicted in Figure 4. A vertical loading actuator (VLA) with a capacity of 500 kN was utilized to precisely control the loading level.

In order to ensure that the device was normal, before the formal loading of the experiment, the first two levels of loading were carried out first, while observing the loading status as well as acquisition of data. The experiments were divided into three parts according to [26]. In the cracking period, the loading step was at a rate of 7 kN within two minutes until reaching 28 kN. Then, the loading step was reduced to 3 kN within two minutes to observe the development of cracks sufficiently. Once cracks exceed 0.05 mm, the load rate was increased to 20 kN in two minutes until approaching failure. Afterwards, the loading step was switched to displacement-controlled loading at 0.7 mm per minute until the specimen reached failure criteria. Throughout the testing, data on displacement, strain, crack width, and crack patterns were meticulously recorded after each loading increment to facilitate comprehensive analysis.

3. Experimental Test

Table 4. Test results.

Label	Pcr (kN)	Pyu (kN)	Dyu (mm)	Pu (kN)	Du (mm)	k1 (×103 kN/m)	Du/Dy
GL1	40	180	23.83	187.54	78.59	37.42	3.3
GL2	29.5	185.5	23.01	196.62	88.49	41.31	3.8
GL3	37	177	33.10	192.62	88.45	38.68	2.7
GL4	46	186	17.38	223.45	84.28	38.08	4.8
LH	58	158	16.62	164.98	37.75	27.66	2.3

presents the results of the experimental tests, detailing the key performance indicators of the beams under investigation, where P_cr denotes the load when the maximum crack width reaches 0.05 mm. P_yu and D_yu denote the load and deflection at the yielding of the member. P_u and D_u denote the load and mid-span deflection, respectively, at which the member reaches the termination condition of the test. k₁ denotes the initial stiffness of the member, which is expressed as the slope of the initial linear portion of the load–deflection curve prior to the occurrence of cracking. The index of ductility of components is denoted by D_u/D_y.

3.1. Crack Pattern and Failure Modes

The damage patterns of all test specimens are depicted in Figure 5. Given that the component is only affected by bending moments in the area between the two supports of the distribution beam, its cracking characteristics primarily develop vertically along the height of the beam. This section is henceforth referred to as the pure bending section. Given its position between the support of the distribution beam and the bearing on its side, the component is subject to bending moments and shear forces. The fissures initially manifest vertically and subsequently extend diagonally. This area is henceforth referred to as the diagonal shear section. Initial cracks typically appeared near the supports in the pure bending region, starting as microcracks (less than 0.02 mm) at approximately one-quarter of the web height, as shown in Figure 6a. As the load increased, these microcracks expanded, and new cracks developed along the span’s pure bending section. Vertical tensile cracks emerged in the bending–shear regions, progressing into diagonal shear cracks. Upon yielding, the cracks in the pure bending section widened rapidly, eventually leading to concrete damage in the top compression zone, as illustrated in Figure 6b [20,23]. Throughout the tests, damage was primarily attributed to excessive deflection, highlighting the beams’ notable ductility [22].

As shown in Figure 5, The first cracking loads for all test specimens ranged from 29 to 46 kN, representing approximately 15% to 21.3% of the ultimate load capacity. Doubling the splice bar spacing resulted in a 35% reduction in cracking load, likely due to the decreased bond surface area between concrete and steel, leading to higher interface stresses and earlier cracking. Conversely, incorporating ribs increased the cracking load by about 15%. Other construction modifications had a minimal impact on the cracking load.

As shown in Figure 5, the crack development and damage patterns were largely consistent across specimens, with rapid crack propagation in the pure bending sections as failure approached. Ribbed designs generally improved damage resistance, possibly due to the increased steel stiffness. Enhancing the bond between steel and concrete, by such methods as reducing splice spacing, improved beam properties. Due to the length of the test specimens, the data acquisition equipment was incapable of collecting all the data simultaneously. The corresponding high-definition images can be found in Appendix A.

3.2. Load–Displacement Curve

Figure 7 illustrates the mid-span load–displacement curves for each specimen. Before yielding, the deformation behavior of the test beams closely matched that of the control beam, indicating a similar initial stiffness. Post-yielding, the beams remained within the strengthened section, benefiting from the steel’s excellent deformation capacity [20]. Compared to the control beam (LH), the test beams exhibited a 13.4% to 28.5% increase in load-carrying capacity and demonstrated enhanced ductility.

3.3. Strain Development

3.3.1. Steel Strain Behavior

The strain curves of the steel plates at splice sections within the pure bending region are presented in Figure 8a, where ucs and lcs indicate the upper and lower surface strain of compressive steel, respectively; uts and lts indicate the upper and lower surface strain of tensile steel, respectively. Notably, tensile regions experienced significant strain changes near the cracking load, indicative of bilinear load–deflection behavior [23]. In contrast, strains in the spandrel regions remained relatively stable, likely due to the concrete’s energy release post-cracking, which subjected the steel plates to increased tensile stresses, accelerating strain development. This observation is consistent with the hypothesis that, following the onset of concrete cracking, the tensile stresses in the steel are predominantly influenced by the residual concrete stiffness, which declines as the cracking process progresses. Compression zone strains showed linear growth until failure, with abrupt changes corresponding to concrete damage. Construction variations had minimal impact on steel strain behavior, primarily because steel plates deformed more slowly than reinforcing steel, as shown in Figure 8b.

3.3.2. Concrete Strain Behavior

Figure 9a displays the average concrete strain across the span’s pure bending section, with insets showing strains measured in the tension zone. Concrete strains increased notably around a 25 kN load, signifying initial cracking, even before visible cracks exceeded 0.02 mm. Post-cracking, the load–deflection curve exhibited bilinear characteristics, with rapid strain escalation in the tension zone upon yielding, while compression zone strains remained relatively unaffected, increasing linearly until failure, aligned with the predictions of elastic theory, as shown in Figure 9b.

Figure 10a compares the average strains of concrete and steel at corresponding section heights under varying loads, illustrating coordinated deformation. The coordinated strain behavior observed at these sections is consistent with the theoretical assumption of compatible deformation, in which the steel and concrete should deform together under the load. The section cut along the largest crack in the pure bending region, shown in Figure 10b, reveals a tight bond between concrete and steel, confirming the assumption of compatible deformation between the two materials aligned with the predictions of the classical beam theory [13,20,22].

These findings provide valuable insights into the structural behavior of the novel beam design, highlighting the effects of construction modifications on performance and the interplay between material strains under loading.

4. Numerical Analysis

4.1. Model Verification

To facilitate the sensitivity analysis of various member parameters, an Abaqus-based script was developed, as Appendix B shows, allowing for systematic variation in key parameters. SRC beams were modeled using C3D8R solid elements. The concrete was assigned four sections, with load application points and bearing points appropriately paired. The two steel flanges formed a cage with paired strips, which were embedded within the concrete. Given the established correlation between mesh quality and analysis accuracy, the mesh parameters employed in this experiment were sourced from the sensitivity analysis of mesh parameters in finite element experiments related to SRC [17]. The mesh sizes were approximately 25 mm for the steel and 50 mm for the concrete. As demonstrated in Figure 10, the concrete and steel exhibit robust bonding, with no discernible separation. Consequently, the interaction between concrete and steel used the embedded method in Abaqus 2022. The concrete damage plastic model (CDP) of concrete in this study is based on the material property test results and [20], as shown in Figure 11a. It can be decided by Equations (1) and (2) as follows:

$$\sigma =\left\{\begin{array}{cccccc}{f}_{c,r}\cdot {\displaystyle \frac{\epsilon /{\epsilon }_{c,r}}{n-1+{\left(\epsilon /{\epsilon }_{c,r}\right)}^n}}& & & & & (\epsilon \le {\epsilon }_{c,r})\\ \\ \\ f_{c,r}\cdot {\displaystyle \frac{\epsilon /{\epsilon }_{c,r}}{{\alpha }_c{\left(\epsilon /{\epsilon }_{c,r}-1\right)}^2+\epsilon /{\epsilon }_{c,r}}}& & & & & (\epsilon >{\epsilon }_{c,r})\end{array}\right.$$

(1)

$$\sigma =\left\{\begin{array}{cccccc}{f}_{t,r}\left[1.2\epsilon /{\epsilon }_{t,r}-0.2{\left(\epsilon /{\epsilon }_{t,r}\right)}^6\right]& & & & & (\epsilon \le {\epsilon }_{t,r})\\ \\ \\ f_{t,r}\cdot {\displaystyle \frac{\epsilon /{\epsilon }_{t,r}}{{\alpha }_t{\left(\epsilon /{\epsilon }_{t,r}-1\right)}^{1.7}+\epsilon /{\epsilon }_{t,r}}}& & & & & (\epsilon >{\epsilon }_{t,r})\end{array}\right.$$

(2)

where σ denotes the stress of the concrete, ε denotes the strain of the concrete, f_c,r and f_t,r indicate the axial compressive and tensile strength of the concrete, α_c = 3.38 and α_t = 1.52 indicate the parameters for the compressive and tensile descending curve, respectively, ε_c,r = 1684.8 × 10⁻⁶ and ε_t,r = 127.44 × 10⁻⁶ indicate ultimate compressive and tensile strain of the concrete, respectively, and n = 2.85 in this study.

The constitutive model of steel is adopted using an ideal elasto-plastic model, as shown in Figure 11b, where f_y denotes the yield strength and ε_y denotes the yield strain.

The comparison between the experimental and numerical load–displacement curves, shown in Figure 12, indicates good agreement, validating the numerical model. The yield loads of each finite element model were obtained using the farthest point sampling method. The yield loads of the numerical models of the four components were 188.8 kN, 186.88 kN, 207.17 kN, and 175.77 kN, respectively, with a relative average error of 6.45%. The numerical analysis revealed partial plastic strain in the tension zone of the steel plate in the pure bending section due to excessive deformation, as shown in Figure 13a,b. Figure 13c,d illustrate the occurrence of microcracks in the web and the concrete damage in the compression zone at failure, respectively. These observations closely match the experimental results, confirming that the finite element model accurately reflects the performance characteristics of the lattice SRC members.

The above results demonstrate that the finite element model effectively captures the mechanical behavior of lattice SRC members. As a result, five key parameters—concrete strength, steel strength, steel plate thickness, side protection layer thickness, and spandrel spacing—were analyzed through further modeling. These parameters are summarized in

Table 5. Parameter of FEM.

Label	Concrete	Steel	Thickness of Steel (mm)	Thickness of Cover (mm)	Distance of Hoop (mm)
PSRCB-0	C30	Q355	6	30	20
PSRCB-C1/C2	C40, C50	Q355	6	30	20
PSRCB-S1/S2	C30	Q275, Q390	6	30	20
PSRCB-TS1/TS2	C30	Q335	8, 10	30	20
PSRCB-TC1/TC2	C30	Q335	6	40, 50	20
PSRCB-D1	C30	Q335	6	30	40

, where SRCB-0 denotes the reference member, C40 and C50 are used for C1/C2, respectively; Q275 and Q390 are used for S1/S2, respectively; 8 mm and 10 mm steel plate thicknesses are used for TS1/TS2, respectively; 40 mm and 50 mm concrete cover thicknesses are used for TC1/TC2, respectively; and D1 is used with double splicing spacing.

4.2. Parameter Analysis

To assess the impact of concrete strength on SRC members, two finite element models were created to compare foundation members. The resulting load–displacement curves are presented in Figure 14a. Additionally, the generalized stiffness–load curve, shown in Figure 14b, demonstrates the stiffness variation in three stages: in the first stage, the stiffness of the members does not change much, and the stiffness decreases after exceeding the cracking load; in the second stage, the stiffness decreases in an inverse proportional function until the members yield; in the third stage, the stiffness decreases in a linear manner, which is due to the larger plastic deformation, and increases with the deformation until reaching the termination condition of the test. The results indicate a minimal increase in stiffness with higher concrete strength, primarily observed in the first stage.

Three models were created to investigate the effect of steel strength on SRC members. As shown in Figure 14c, the yield strength is more pronounced in the test beams, though its impact on stiffness is mostly evident during the plastic phase. The load–displacement curves for these models follow the same three-phase behavior, as seen in Figure 14d.

To explore the effect of member geometry, five additional finite element models were developed. The results, shown in Figure 14e,f, reveal that steel plate thickness has a significant impact on both strength and stiffness. Increasing the steel plate thickness by 30% leads to an 18% increase in the ultimate load, though the stiffness decreases as the load increases and the initial stiffness is smaller. The concrete cover thickness influences the initial stiffness, but its effect becomes more pronounced during the plastic phase, as shown in Figure 14g,h. Splice spacing notably affects both initial stiffness and ultimate strength, with larger spacing resulting in decreased strength and stiffness as the plastic phase progresses, as illustrated in Figure 14i,j.

To quantify the effects of each parameter, a comparison plot of parameter influence on ultimate strength is shown in Figure 15a. The ratio of each parameter to the base member (denoted as c/c₀) is plotted against the ratio of ultimate strength. The steeper the slope, the more sensitive the ultimate strength is to that parameter. The results demonstrate that steel strength has the most significant impact, followed by protective layer thickness, while concrete strength has the least influence on strength. The analysis revealed a substantial marginal effect on steel plate thickness, which indicates that augmenting the thickness of the steel plate by 25% does not result in a 25% enhancement in load-bearing capacity. Consequently, the utilization of SRC components does not necessitate an augmentation in the amount of steel employed to enhance load-bearing capacity.

Figure 15b illustrates the relationship between displacement ductility coefficients and the ultimate loads of the finite element model. The data points for varying thicknesses of the concrete cover and concrete strength approximately align along the dash line in the figure, indicating consistent trends across these parameters. In contrast, specimens with higher steel strengths exhibit larger displacement ductility coefficients, suggesting that increased steel strength enhances the member’s bearing capacity to undergo larger deformations before failure. As cracks evolve and extend, the embedded steel reinforcement provides additional confinement, thereby increasing the ultimate load-carrying capacity of the member. This phenomenon is reflected in the observed increase in displacement ductility coefficients, highlighting the steel skeleton’s contribution to both strength and ductility.

4.3. Basic Assumption

According to the experimental results, the test members satisfy the flat section assumption under bending moments. Moreover, as shown in Figure 10a, cut along the cracked section of the member, the internal materials of the member remain tightly bonded to ensure their joint action.

Therefore, based on the relevant equations for plain concrete beams, the following assumptions will be used:

(1) The critical section remains plane after deformation.

(2) Relative slip between materials is not considered.

(3) The action of tension concrete is not considered.

(4) There is a uniform strain distribution in the section.

(5) The compressive steel yields when the member breaks down.

4.4. Prediction and Validation

A method for calculating the moment capacity of the new SRCB is obtained based on the simplified plasticity theory. Ref. [9] shows that symmetrical reinforcement improves the ductility as well as the ultimate load-carrying capacity of this type of members. Based on the flat section assumption, the neutral axis position of symmetrically reinforced members is determined according to Equation (1) in order to determine the load-carrying capacity of the SRCB under the bending moment. The design parameters of the critical cross-section of the SRC beam are shown in Figure 16a. According to the plane section assumption, strain distribution in the section is shown in Figure 16b, and compressive stress σ_c is approximately satisfied as Equation (3) when the stress is small:

σ_c = E_c · ε_c

(3)

The height of the concrete in the compression zone, x_n, is satisfied without considering the action of concrete in the slip and tension zones:

x_n = ξ_n · h₀

(4)

$${\xi }_n=\sqrt{{\left({\alpha }_E\rho \right)}^2+2{\alpha }_E\rho }-{\alpha }_E\rho$$

(5)

where ξ_n indicates the factor of the relative compressive zone, α_E indicates the ratios of E_s and E_s, and ρ indicates the ratio of steel reinforcement.

The actual stress distribution in the section is shown in Figure 16c, which is satisfied by the concrete form center y₀ in the pressure zone:

y₀= x_n · y_cu/ε_cu

(6)

where y_cu indicates the equivalent center of the compressive stress zone according to the CDP model of concrete, as shown in Figure 11a, and ε_cu indicates the ultimate compressive strain of the concrete.

Adopting the principle of equivalent force and moment generated by the concrete in the pressure zone within the cross-section, the equivalent compressive stress distribution is shown in Figure 16d, and the cross-section equilibrium relationship has the following equations:

$$\left\{\begin{array}{c}{\alpha }_1{f}_{c}bx=k_1{f}_{c}b{x}_n\\ \\ x=2\left(x_n-y_0\right), x=2\left(1-k_2\right)x_n\end{array}\right.$$

(7)

where k₁ and k₂ denote the coefficients of equivalent cross-section height for concrete, which are only related to the strain–stress curve of the concrete.

According to the equivalent stress zone, the equations used to calculate the moment capacity by balancing the forces and moments in the section are shown in Equations (8) and (9). Ref. [27] points out that x = 0.2h₀ can be considered when 0.2h₀ > 2a_s^′. Therefore, the equations for this type of symmetrically reinforced reinforcement can be shown in Equation (10).

αf_cbx + f_y′A_s′ = f_yA_s

(8)

M_u ≤ f_yA_s(h₀ − a_s′) − α₁f_cbx(x/2 − a_s′)

(9)

M_u ≤ f_yA_s(h₀ − a_s′) − 0.2α₁f_cbh₀(0.1h₀ − a_s′)

(10)

where α indicates the equivalence factor of compressive concrete stress, f_c is the equivalent stress of compressive concrete, f_y and f_y′ indicate the tensile stress and compressive stress of the encased steel plate, respectively, A_s and A_s′ indicate section areas of the tensile steel plate and compressive steel plate, respectively, x is the equivalent section height of the compressive concrete, a_s and a_s′ are the thicknesses of the bottom and top concrete cover, respectively, b is the width of the SRC beams, h₀ is the effective height of the SRC beams, which means the height, except for the thickness of cover, to the center of the tensile steel, and M_u indicates the ultimate bearing capacity of the SRC beams.

4.5. Design Recommendations

In order to ensure the feasibility of the realistic prefabricated construction of SRC beams and the economic efficiency and reliability for future use, a number of design recommendations for steel plates, construction measures, and building measures for SRC beams have been proposed.

(1) Steel plate

Experimental data indicate that the ultimate load-bearing capacity of SRC beams is significantly influenced by the steel’s strength. It is advisable to utilize steel plates with a minimum yield strength of 355 MPa, such as Q355 steel, to achieve an optimal load capacity while minimizing material usage. Additionally, employing plates with a thickness of at least 6 mm is recommended. Thicker plates, such as those with a thickness of 8 mm, have demonstrated superior cross-sectional properties and stiffness, enhancing overall beam performance.

(2) Structural Measures

While sensitivity analyses suggest that the ultimate load capacity is relatively unaffected by construction measures, as shown in Figure 15a, the observed damage patterns underscore the importance of thoughtful structural detailing. To ensure uniform damage progression and improved performance, it is recommended that splice spacing should not exceed 200 mm or 10 times the plate thickness, whichever is smaller. Furthermore, tests have shown satisfactory interfacial bonding without the need for additional construction measures on the contact surfaces.

(3) Construction measures

The formation of microcracks in the beam web indicates significant stress variations at the steel–concrete interface, as evidenced by Figure 13. Given the reduced structural integrity during early stages, it is advisable to avoid applying concentrated construction loads or additional measures at the tensile steel–concrete interface. This approach will help maintain the serviceability and longevity of the SRC beam members.

A comparison of the load-carrying capacity of the test beams and the finite element beams calculated by the formulae is shown in

Table 6. Comparison of calculation and test results.

Label	Ultimate Capacity Fu (kN)	Calculation Capacity Fc (kN)	Ding et al. [22]	Kim et al. [23]
SRCB-0	189.54	172.41 (0.91)	150.38 (0.79)	158.48 (0.83)
SRCB-C1	205.26	174.05 (0.85)	150.38 (0.73)	158.48 (0.77)
SRCB-C2	206.25	175.69 (0.85)	150.38 (0.72)	158.48 (0.76)
SRCB-S1	166.94	145.99 (0.87)	134.67 (0.80)	141.93 (0.85)
SRCB-S2	227.03	193.17 (0.85)	179.56 (0.79)	189.24 (0.83)
SRCB-TS1	229.28	192.45 (0.84)	199.31 (0.86)	210.71 (0.91)
SRCB-TS2	269.01	236.40 (0.88)	247.63 (0.92)	262.64 (0.97)
SRCB-TC1	163.33	129.63 (0.79)	123.37 (0.75)	133.72 (0.81)
SRCB-TC2	147.91	120.65 (0.82)	109.86 (0.74)	122.47 (0.82)
SRCB-D1	175.32	172.41 (0.98)	150.38 (0.85)	158.48 (0.90)

, achieving an average relative error for the formulae of about 0.12. Meanwhile, the C and S groups show that the formulae are more accurate in reflecting the changes in the material property parameters. For geometrical parameters, as shown in groups TS and TC, the formulae do not show their effects well, and thus underestimate the load-carrying capacity of the members. For changes in structural measures, the formulae can effectively predict the corresponding load-carrying capacity, as shown in group D. Since the formulae do not take into account the strength of the reinforcement stage, the formulae will not reflect the effect of the structural measures in the plastic stage well for some structural measures that affect the ultimate load-carrying capacity, which is usually considered as strength redundancy to ensure the safety of the members.

5. Conclusions

In this paper, the mechanical properties of lattice SRC beams under pure bending loads are investigated through experimental and parametric analyses. Four members with different construction measures are taken to investigate their effects, and five potential factors affecting the mechanical properties are analyzed by Abaqus. Finally, a simplified SRC formula is proposed to calculate the load-carrying performance of the new beams with reference to the relevant formulae and the results of parametric analysis, and the main conclusions are shown below:

1. The finite element and experimental results are in good agreement, and the damage of SRC members is in line with the damage characteristics of general members.

2. SRC beams are sensitive to the spacing of the splices; doubling the spacing of the splices decreases the bearing capacity by more than 5%, and the stiffness decreases significantly.

3. The SRC beam pure bearing strength is limited by the influence of structural measures, with a variation in capacity between different measures amounting to less than 5%. A comparative analysis reveals that, in contrast to conventional members, there is an average augmentation in ductility of 125.1% and an average escalation in bearing capacity of 15.3%. Notably, the increase in ductility surpasses that of bearing capacity by eightfold.

4. The formulae presented in this article are in good agreement with the test results, which can help in the design of SRC members. The experimental findings corroborate that the bearing capacity formula for solid web SRC members can be extrapolated to hollow lattice members.