Flexural Behavior and Deformation Analysis of Top-Chord-Free Vierendeel-Truss Composite Slab with Square-Tube Bottom Chords

Abstract

This study examines a top-chord-free open-web steel-truss composite floor in which the concrete slab functionally replaces the traditional top chord and works jointly with vertical square-tube web members and a square-tube bottom chord. Two scaled specimens—with and without concrete infill in the end shear-bending blocks—were fabricated and tested under static loading. The load–deflection response delineates three stages: elastic, elastic–plastic, and failure. Tests show that infilling the shear-bending blocks does not enhance global mechanical performance. In the elastic range, the mid-span open-web section satisfies the plane-section assumption with a linear strain profile, whereas the solid-web section exhibits a bilinear distribution. A validated ANSYS finite-element model reproduces the measured responses and supports a parametric study showing that span-to-depth ratio, opening-to-span ratio, slab (flange) thickness, and width-to-span ratio significantly affect ultimate capacity and deflection. Design recommendations are proposed: span-to-depth ratios of 11–14 and opening-to-span ratios of 0.04–0.07. An equivalent-stiffness-based simplified linear-elastic deflection formula with a reduction factor is derived, which accurately tracks deflection evolution and enables serviceability-driven selection of web spacing and overall structural depth.

1. Introduction

Composite floor systems are widely used structural forms in building and bridge engineering, consisting primarily of steel–concrete combinations. According to their structural configuration, composite floors can be classified into various types, such as composite beams, cellular (or castellated) beams, and steel truss–concrete composite floor systems, each exhibiting distinct mechanical characteristics and ranges of application. With evolving engineering demands, extensive research has been conducted in both academia and industry to enhance the load-carrying capacity, stiffness, and spatial efficiency of these systems. A brief overview of several typical composite floor types and their research progress is given below.

Steel–concrete composite floor systems are commonly employed as primary load-resisting systems for floors and bridge decks. By exploiting the high strength and toughness of steel members in combination with the favorable compressive behavior of concrete slabs, they achieve complementary material advantages and efficient utilization of sectional performance [1,2,3,4]. At the same time, it has been demonstrated that interface slip and the fatigue performance of shear studs can significantly affect both load-bearing capacity and ductility [5,6].

For composite I-beams with flat webs, studies have shown that improved design strategies—such as the use of ultra-high-performance concrete (UHPC) in critical regions—can markedly enhance the load-carrying capacity in negative bending regions, reduce cracking, and increase the overall ultimate flexural strength [7]. In addition, the shear behavior of headed studs plays a key role in composite beam performance; both the number of studs and the concrete strength have been found to exert a pronounced influence on the load-bearing capacity [8].

However, as the requirements of mechanical and electrical systems for story height and clear headroom have increased, composite beams relying solely on solid webs have gradually revealed limitations in terms of vertical space utilization. To improve story clearance and material efficiency, both academia and industry have proposed a cellular beam–concrete composite beam strategy: regular openings are created in the steel web to form panels, providing dedicated pathways for service ducts while maintaining the overall beam depth and stiffness. Related studies have demonstrated that the opening geometry, spacing between openings, and residual web width significantly influence the flexural stiffness, shear capacity, and local buckling behavior of such members. Furthermore, an approximate analytical approach has been proposed in which the concrete slab is idealized as an equivalent top chord in structural calculations [9,10,11,12,13,14,15].

In the research on perforated composite beams, it has been found that increasing the area of stiffeners can markedly enhance the ultimate load-carrying capacity of beams with web openings, with bidirectional stiffening in particular enabling the ultimate capacity to approach that of solid-web beams. For cellular composite beams incorporating hollow slabs, studies indicate that while the hollow-slab scheme can improve the overall structural efficiency, the shear capacity of the floor system imposes a certain constraint on the ultimate load-carrying capacity [16,17].

For steel truss–concrete composite beams—where vertical or inclined web members and the lower chord form a truss, and the upper concrete slab participates in load resistance—the system attains higher porosity and greater flexibility for service integration and layout [18]. Representative engineering applications of the above two types of structural systems are shown in Figure 1. Experimental and numerical investigations have demonstrated that such members exhibit distinct crack development patterns and strain distributions in the pure-bending region at midspan and in the combined bending–shear regions. Their failure modes include flexure-dominated, shear-dominated, and flexure–shear interactive failures, with size effects also playing a non-negligible role [19,20,21,22]. In addition, variations in the degree of shear connection, web member arrangement, and material strength have significant effects on ductility, peak load-carrying capacity, and service-stage deflections [23,24].

The simplified design model for steel–concrete composite floor systems and trusses given by the Steel Joist Institute (SJI) [25] explicitly neglects the contribution of the top chord to the global flexural resistance. Likewise, the Canadian Institute of Steel Construction (CISC) [26] stipulates that, for composite open-web floor systems and trusses, the contribution of the top chord may be omitted in strength evaluations, with only the necessary local and stability checks being required. From the viewpoint of structural mechanics, previous studies have indicated that the top chord is typically located close to the neutral axis and therefore has little effect on enhancing the global flexural stiffness and load-carrying capacity, although it does influence the internal force distribution within the shear connection [27]. On this basis, engineering design commonly adopts a “concrete slab in compression–bottom chord in tension” force couple as an approximate bending-resistance model for composite trusses, neglecting the global bending contribution of the top chord. Building on this premise, the present study introduces the Top-Chord-Free Vierendeel-truss Composite Slab (TVCS) (Figure 2), an open-web steel truss composite floor system without a top chord, in which the concrete slab functionally replaces the conventional top chord and, together with the vertical web and bottom chord, participates in load resistance, thereby simplifying the structural configuration and improving space utilization.

Xu et al. [28] first proposed the TVCS configuration, conducted three-point static loading tests on two specimens, and compared the results with those from a finite-element model, thereby systematically evaluating deformation, crack development, ultimate load-carrying capacity, and failure modes. On this basis, they established theoretical methods for internal force computation, linear-elastic deflection prediction, and ultimate flexural capacity. A parametric analysis was further carried out to quantify the effects of concrete and steel strengths, vertical web width, and web spacing ratio. Building on this prior work, Xu et al. [29] subsequently performed a combined experimental and numerical study using an engineering case, identifying three response stages—elastic, elastic–plastic, and failure—and providing the sectional stress distribution in the elastic stage. The test results showed dense cracking in the pure bending region and good system ductility. Through a more comprehensive parametric analysis, they proposed a modified flexural capacity formula incorporating a vertical web spacing ratio adjustment factor, which exhibited good agreement with the numerical results. These studies laid the foundation for the mechanistic understanding and design calculation of TVCS and constitute the point of departure for the present research.

On this basis, the present paper focuses on a Top-Chord-Free Vierendeel-Truss Composite Slab with Square-Tube Bottom Chord (ST-TVCS), in which the bottom chord and vertical web are formed by square steel tubes. Two scaled specimens are designed, with and without concrete infill in the end shear–bending blocks, and subjected to static loading tests together with ANSYS-based numerical verification to capture the complete response process from the elastic stage, through the elastic–plastic stage, to final failure. Furthermore, a parametric analysis is conducted, and a simplified linear-elastic deflection formula based on equivalent stiffness is proposed, which can be used to guide the design selection of web spacing and overall structural depth.

2. Test Overview

2.1. Specimens Design

The geometric dimensions of the specimen were similar to those in Refs. [28,29], except that the I-shaped sections originally used for the bottom chord and vertical web members were replaced by square steel tube sections with a side length of 50 mm and a wall thickness of 4 mm. Two specimens were fabricated for testing, denoted as SJ-1 and SJ-2.

The main dimensions of the specimens are shown in Figure 3. The overall span is 2360 mm, and the depths of the concrete slab, bottom chord, and vertical web members are 50 mm, 50 mm, and 80 mm, respectively. Each specimen contains a total of twelve vertical web members. In specimen SJ-2, eight of the vertical web members were filled with concrete, as illustrated in Figure 3b. A steel top plate with a thickness of 4 mm and a plan dimension of 110 mm × 110 mm was welded to the top of each vertical web member, through which a shear connector with a diameter of 6 mm and a length of 30 mm was used to connect to the concrete slab. The top concrete slab was reinforced with a single layer of orthogonal distributed rebars placed at the mid-depth of the slab. The reinforcement layout was Ø6 @100 mm in one direction and Ø6@50 mm in the orthogonal direction, and the rebar grade was HRB300. The rebars were continuous along the span, and no additional edge reinforcement or local densification was provided. In the present study, this slab reinforcement was mainly intended for constructability and crack control (e.g., shrinkage/temperature effects), while the global flexural mechanism and design-oriented evaluation focus on the slab–bottom-chord force couple validated by the tests and FE analyses.

2.2. Material Properties

In view of the dense reinforcement typically present in thin slab structures, the use of ordinary cast-in-place concrete would be prone to aggregate segregation. Therefore, in this study, a grout with a design strength grade of C40 was adopted in lieu of conventional concrete. The steel truss portion of each specimen was fabricated entirely from square steel tubes with identical cross-sectional dimensions, using Q235B structural steel. The results of the corresponding material property tests are summarized in

Table 1. Material test results of the slab concrete.

$\mathbf{Cubic} \mathbf{Compressive} \mathbf{Strength} {\mathit{f}}_{\mathit{c}\mathbf{u}}^0$ (MPa)	$\mathbf{Axial} \mathbf{Compressive} \mathbf{Strength} {\mathit{f}}_{\mathit{c}}^0$ (MPa)	$\mathbf{Axial} \mathbf{Tensile} \mathbf{Strength} {\mathit{f}}_{\mathit{t}}^0$ (MPa)	$\mathbf{Elasticity} \mathbf{Modulus} {\mathit{E}}_{\mathit{c}}^0$ (N/mm2)
39.57	30.07	2.99	3.25 × 104

and

Table 2. Material test results of steel.

$\mathbf{Yield} \mathbf{Point} {\mathit{f}}_{\mathbf{y}}$ (MPa)	$\mathbf{Tensile} \mathbf{Strength} {\mathit{f}}_{\mathbf{u}}$ (MPa)	Yield Ratio	Elongation δ (%)
324.3	374.6	0.86	33.34

.

2.3. Test Setup

The loading setup used in this test consisted, from top to bottom, of a reaction frame, a hydraulic jack, a distribution beam, bearing blocks, and support piers. A hand-operated hydraulic jack with a capacity of 50 kN was employed, and the load was transferred via the distribution beam to bearing blocks located at the left and right one-third points of the span, thereby realizing a four-point bending test, as shown in Figure 4. On the left side, a solid steel bar with a triangular cross-section was placed to simulate a fixed hinged support, while on the right pier a circular steel bar was placed to simulate a sliding hinged support.

The loading scheme adopted monotonic static loading. Throughout the test, the applied load was increased in increments of 5 kN per level. When the jack load could no longer be increased in a stable manner, the control mode was switched to displacement control, and loading continued until failure of the specimen. Based on the test observations, the entire loading process was divided into 19 load levels.

The arrangement of measurement points for specimens SJ-1 and SJ-2 is shown in Figure 5. For specimen SJ-1, a total of 26 uniaxial strain gauges were installed on the steel truss (denoted S1–S26), 16 uniaxial strain gauges on the concrete slab (denoted H1–H16), 2 strain rosettes (denoted by the Arabic numerals 1 and 2), and 9 displacement transducers (denoted WY1–WY9). For specimen SJ-2, 33 uniaxial strain gauges were installed on the steel truss, 6 uniaxial strain gauges on the concrete slab, 3 strain rosettes, and 9 displacement transducers.

3. Discussion of Test Results

3.1. Experimental Observations and Crack Pattern

Figure 6 illustrates the evolution of the specimen response at different loading stages.

At the initial loading stage, the specimen remained in the elastic stage, exhibiting relatively high global stiffness. As the load increased from 5.2 kN to 40.2 kN, the overall integrity of the member was good, deformations were small, and no cracking was observed in the concrete slab. When the load reached 44.8 kN, fine cracks first appeared at the bottom surface of the slab at the junctions between the concrete slab and the steel top plates above several vertical webs near the loading points. With further loading to 54.4 kN, fine cracks developed on the top surface of the slab in the vicinity of the supports, and new cracks also formed at the locations of the steel top plates over the vertical webs; small cracks appeared at the bottom of the slab beneath the two loading points and extended toward the slab edges. By the time the load reached 59.6 kN, previously formed cracks had widened and lengthened to some extent, and some cracks on the slab top surface further propagated toward the slab sides.

When the load reached 64.8 kN, the stiffness of the specimen began to decrease, indicating the onset of the elastic–plastic stage. At 70.0 kN, longitudinal through cracks formed along the slab top surface between the supports and the loading points, and the cracks on the slab top near the supports developed in an intersecting pattern. As the load was further increased to 75.0–80.0 kN, several early cracks at the slab bottom extended in length and locally widened, and some cracks on the slab top propagated toward the slab sides. When the load reached 84.8 kN, certain crack openings increased to the millimeter scale, local separation between the steel top plate above the vertical web and the concrete slab was observed at one slab end, and new cracks appeared at the opposite end; at this stage, the midspan deflection was approximately 17.17 mm. Overall, during the elastic–plastic stage, the rate of increase in midspan deflection accelerated distinctly with increasing load, and the major cracks gradually formed and propagated.

When the load reached 89.2 kN, stable loading could no longer be maintained, and the applied load decreased to 85.6 kN after approximately 5 min. At this time, local inward denting of the steel top plate above the vertical web occurred at the slab end, accompanied by concrete spalling; cracks at the slab bottom near the loading points became through cracks, many other cracks widened significantly, and partial debonding of the slab bottom was observed. The control mode was then switched to displacement control. When the load increased to 93.8 kN, an inclined splitting failure occurred in the bending–shear region on the side near one loading point, and the midspan deflection was about 27.49 mm. The specimen was thus judged to have reached the failure stage, after which unloading was carried out and the test was terminated. In this test, the failure of the ST-TVCS was characterized by fracture of the concrete slab and cracking of the welds between the vertical webs and the bottom chord.

After completion of loading on specimens SJ-1 and SJ-2, the crack patterns on the top and bottom surfaces of the concrete slab are shown in Figure 7. It is noted that Figure 7 is intended as a crack-location summary of the slab top and bottom surfaces, focusing on the spatial distribution and orientation of cracking rather than on the stress/strain state of the steel components. The crack map was compiled based on post-test visual inspection and photographic documentation with scale marking, and the crack traces were subsequently projected onto the specimen layout for clarity. The stress/strain response of the steel components is discussed separately in the strain-related sections (e.g., Section 3.3), and is therefore not repeated in Figure 7. It can be seen that they share many common features:

• The number of cracks on the bottom surface of the concrete slab is greater than that on the top surface;
• On the bottom surface of the concrete slab beneath the two loading points, cracks are densely distributed in this region, and the number of cracks within the bending–shear region is relatively large;
• In the bending–shear region, due to the open-web effect of the structure and the presence of secondary bending moments associated with shear in the open-web section, cracking and spalling of the concrete at the slab bottom are comparatively more severe;
• In the pure bending region, few cracks are observed at the bottom of the concrete slab, and they are essentially absent;
• On the top surface of the concrete slab, longitudinal cracks initiate at both slab ends and propagate along the slab length;
• Beneath the two loading points, the bottom surface of the concrete slab exhibits the primary cracks; these cracks are relatively wide and extend laterally toward the slab sides, eventually reaching the top surface. This constitutes one of the key fac-tors leading to fracture of the concrete slab and, consequently, to the overall failure of the structure.

In summary, during the full loading process, stiffness degradation and crack evolution occurred in a broadly synchronous manner. The primary damage zone was concentrated in the bending–shear region near the loading points, where the main cracks on the slab bottom initiated and then propagated toward the slab sides and top surface, eventually forming through cracks and inducing local spalling; this was a key triggering factor for the global failure. In contrast, the cracks in the pure bending region were fine and closely spaced but did not govern the failure.

The failure criterion for the ST-TVCS can be summarized as follows: a pronounced increase in the growth rate of midspan deflection; rapid widening of the main cracks on the slab bottom beneath the loading points; and the occurrence of local spalling and/or cracking of the welds between the vertical webs and the bottom chord. Based on these experimental observations, subsequent design should focus on enhancing the coupled bending–shear resistance and detailing in the bending–shear region.

From the test observations, no local buckling or fracture of the bottom chord or the vertical web members was identified throughout the entire loading history of both specimens. Consistently, the measured strain levels in the steel members indicate that the steel components did not exhibit instability-controlled local failure prior to the global failure. Instead, the structural failure was governed by cracking/fracture of the concrete slab in the bending–shear region, accompanied by local cracking of welds near the end shear–bending blocks.

These observations suggest that the welded joints in the end bending–shear region are sensitive detailing zones. Potential fabrication or welding imperfections at these joints may trigger earlier crack initiation and reduce the safety margin. A systematic defect classification and quantification are beyond the scope of the present study; nevertheless, the above evidence motivates strict quality control (e.g., qualified welding procedures and non-destructive testing (NDT) inspection) and conservative joint detailing in practical design.

3.2. Load-Deflection Behavior

Compared with specimen SJ-1, specimen SJ-2 has concrete infilled in the four shear–bending blocks located near the two ends. This detailing is primarily intended to investigate whether infilling concrete inside the shear–bending blocks within the bending–shear region influences the development of deflection and the ultimate load-carrying capacity of the structure. The load–midspan deflection curves of the two specimens are shown in Figure 8.

From the onset of loading to final failure, the evolution of deflection indicates that the overall response of the specimen can be divided into three stages: an elastic stage, an elastic–plastic stage, and a failure stage:

Elastic stage: In the elastic stage, the ST-TVCS exhibits typical linear-elastic behavior: the stress level in the cross-section is relatively low, the steel bottom chord primarily resists tension, and the upper concrete slab mainly resists compression. The load–midspan deflection relationship shows a clear linear trend. The shear connectors effectively ensure the composite action between the concrete slab and the steel truss, enabling the structure to maintain a certain initial stiffness. The curves of SJ-1 and SJ-2 in the elastic stage almost coincide, indicating that infilling concrete inside the shear–bending blocks does not enhance the global stiffness of the specimens.

Elastic–plastic stage: For both SJ-1 and SJ-2, the onset of the elastic–plastic stage occurs at a load of 59.6 kN. In this stage, the two specimens display highly consistent mechanical behavior: the tensile stress in the bottom chord increases rapidly, and the load–deflection relationship gradually transitions from linear to nonlinear, exhibiting a progressive process of stiffness degradation. In the later part of this stage, the slope of the load–deflection curve decreases significantly. This phenomenon is mainly attributable to the formation of major cracks in the concrete slab and their subsequent propagation toward the slab sides and top surface.

Failure stage: Once the structure enters the failure stage, the midspan deflection increases rapidly, the stability of the applied load deteriorates markedly, and the global structure shows pronounced stiffness degradation. Prior to failure, repeated spalling occurs at the interface between the concrete slab and the steel top plates of the shear–bending blocks, and the main cracks continuously widen and extend until they reach the slab top, at which point the concrete progressively loses its load-carrying capacity. The ultimate fracture of the concrete slab, accompanied by a rapid drop in the applied load, signifies the complete failure of the composite floor system specimens. The ultimate loads of SJ-1 and SJ-2 are 93.4 kN and 94.8 kN, respectively, and the corresponding deflections at failure are 27.49 mm and 32.90 mm.

According to Design Specifications for Composite Structure (JGJ 138-2016) [30], for a box-type steel–concrete composite slab without openings, having the same geometric configuration and subjected to the same loading conditions, the calculated ultimate load is 128.68 kN. This indicates that the ST-TVCS exhibits excellent mechanical performance and a high load-carrying capacity.

Under identical structural design parameters, infilling concrete inside the shear–bending blocks located in the bending–shear region has only a minor influence on the global stiffness, load-carrying capacity, and flexural deformation of the composite floor system. The slight differences in ultimate load and maximum deflection at failure between the two specimens are likely attributable to fabrication tolerances during specimen preparation.

3.3. Deformation and Strain Behavior of the Structure

3.3.1. Overall Deformation Characteristics

In both the elastic stage and the elastic–plastic stage (i.e., before 59.6 kN), specimens SJ-1 and SJ-2 exhibit a globally symmetric bending configuration about the midspan section, with the midspan corresponding to the point of maximum deflection. Once the structure enters the failure stage, however, the location of maximum deflection shifts away from the midspan toward the fixed hinged support, primarily because failure occurs in the vicinity of the fixed hinged support. In view of the fact that the flexural deformation, failure process, failure mode, and stress distribution of specimens SJ-1 and SJ-2 are essentially similar, the stress–strain analysis in this section focuses only on specimen SJ-2. Figure 9 shows the overall deformation profiles of specimen SJ-2 at different load levels. In the figure, the horizontal axis represents the spanwise direction of the specimen, with the fixed hinged support taken as the origin and the positive direction pointing toward the sliding hinged support, while the vertical axis gives the measured vertical deflections at each measurement point.

For specimen SJ-1, the midspan deflection at the end of the elastic stage is 9.08 mm, and the midspan deflection at failure is 27.49 mm, corresponding to a displacement ductility factor of 3.03. For specimen SJ-2, the midspan deflection at the end of the elastic stage is 9.60 mm, and the midspan deflection at failure is 32.90 mm, corresponding to a displacement ductility factor of 3.43.

3.3.2. Strain Response

Figure 10 shows the strain distributions for the solid-web section and the open-web section at midspan. For the open-web section, the neutral axis remains stably located approximately 0–4 mm above the bottom of the concrete slab, and the strain varies in an almost perfectly linear manner over the depth throughout the elastic stage. This observation confirms the applicability of the plane-section assumption for this type of special cross-sectional configuration. In contrast, the solid-web section exhibits a “bilinear” strain pattern along the depth: within the shear–bending block region, the neutral axis lies in the mid-to-lower portion, while in the concrete slab the neutral axis initially lies close to the slab bottom and gradually shifts upward as the load increases and cracking develops, remaining slightly lower overall than that of the open-web section.

4. Finite-Element Analysis

4.1. FEA Modeling

In this study, finite-element analysis (FEA) of the composite floor system was carried out using the ANSYS platform (ANSYS 2021 R1). The constitutive behavior of the steel in the ST-TVCS was modeled by a bilinear kinematic hardening model (BKIN), with the corresponding stress–strain curve shown in Figure 11. The concrete slab was modeled using SOLID65 solid elements. The reinforcing steel in the concrete slab was represented through the embedded (smeared) reinforcement capability of SOLID65 by specifying the rebar material and the reinforcement ratios and orientations via the corresponding real-constant set; two orthogonal reinforcement directions were adopted, and perfect bond between the reinforcement and concrete was assumed. All other steel components, including the steel top plates, shear–bending blocks, the vertical web elements, and the bottom chord, were modeled as three-dimensional solid elements using SOLID65 with the BKIN steel material model. Based on the test results, the bond behavior among the steel top plates, the headed stud shear connectors, and the concrete slab was observed to be satisfactory, with no stud fracture or pull-out; therefore, the studs were not explicitly modeled in the analysis.

Considering the characteristics of the structural system under study and the experimental data, a mesh size of 20 mm was adopted for the concrete solid elements, while a finer 10 mm mesh was used for the bottom chord and the vertical web elements. A bonded contact was defined between the steel top plates and the concrete slab to prevent any relative slipping or separation. In the finite-element model, the spanwise direction of the composite floor system is taken as the Z-axis, the vertical (depth) direction as the Y-axis, and the width direction as the X-axis. For the boundary conditions, the underside of the square-tube bottom chord at the end corresponding to the coordinate origin was fully constrained to simulate a fixed hinged support, whereas at the opposite end only the displacements in the Y and X directions were restrained to simulate a sliding hinged support. A surface load with a width of 160 mm was applied at the loading locations corresponding to the experiment. In addition, to accurately account for the self-weight effect of the structure, a vertical downward acceleration was applied, as illustrated in Figure 12.

4.2. Model Validation and FE Results

4.2.1. Validation of the FE Model and Mesh Sensitivity Analysis

The finite-element analysis results indicate that, in the linear-elastic stage, the load–midspan deflection curve obtained from the model agrees very well with the experimentally measured data, and the global stiffness of the structure remains stable in this range. However, compared with the test results, the finite-element model exhibits a longer elastic working range. In the elastic–plastic stage, the numerical model shows a gradual reduction in stiffness, after which the stiffness tends to stabilize from about 85 kN up to failure; this trend is broadly consistent with the experimental observations.

The ultimate flexural load-carrying capacity predicted by the finite-element model is 93.3 kN, which differs by only 0.5% from the experimental value of 93.8 kN, while the maximum deflection differs by only 5.3%. Overall, the load–deflection curve obtained from the finite-element analysis shows good agreement with the test results, demonstrating that the developed numerical model can effectively capture the mechanical behavior of the ST-TVCS and possesses a high degree of reliability.

To further examine the influence of mesh discretization, a mesh-sensitivity study was performed using three discretizations (baseline, coarse, and refined meshes). The baseline mesh adopted in this study uses an element size of 20 mm for the concrete slab and 10 mm for the steel components. For comparison, a coarser discretization was generated by increasing the element sizes to 30 mm (concrete slab) and 15 mm (steel components), while the refined discretization reduced the element sizes to 15 mm (concrete slab) and 7.5 mm (steel components). Figure 13b compares the resulting global load–deflection responses within the displacement range attainable for all meshes. The responses are close in this comparable range, indicating limited mesh sensitivity of the global behavior. It is noted that the refined mesh becomes numerically unstable in the highly nonlinear stage due to excessive element distortion in the end bottom-chord region, which leads to premature termination; therefore, the baseline mesh is adopted in subsequent analyses as a compromise between accuracy and numerical robustness.

4.2.2. Validation of Sectional Strain Distribution

Under elastic-stage loading, the experimentally measured strain distribution of the midspan solid-web section of specimen SJ-1 was compared with that obtained from the finite-element model, as shown in Figure 14a. The comparison indicates that the test measurements and numerical predictions exhibit a high degree of overall similarity. The corresponding comparison of strain distributions for the midspan open-web section in the elastic stage is presented in Figure 14b. In both the experiment and the simulation, the neutral axis is located within a range of 0–4 mm above the bottom of the concrete slab; therefore, the sectional stress distribution can be evaluated on the basis of the plane-section assumption in classical mechanics of materials. In the later part of the elastic stage, the measured strain at the bottom surface of the bottom chord at midspan is 3.9% higher than the corresponding value from the numerical model.

4.3. Parametric Studies

To investigate the primary factors influencing the load-carrying capacity and deflection of the ST-TVCS, a parametric analysis was conducted using finite-element software, in which ST-TVCS models with different depth-to-span ratios and hole-to-span ratios were established and analyzed.

Unless otherwise stated, all parametric results and the resulting design recommendations are obtained under the same symmetric four-point static loading configuration as the tests. They should be interpreted as guidance for gravity-load-dominated floor applications where the global response is governed by quasi-static bending and bending–shear interaction.

4.3.1. The Impact of High Span-to-Height Ratio

In this study, the span of the steel–concrete composite beam was taken as L = 2 m, with a concrete slab thickness of 50 mm and a bottom chord height of 50 mm. The ratio of the overall sectional depth ℎ of the composite beam to its span L was defined as the depth-to-span ratio. By varying the height of the shear–bending blocks, the beam depth—and thus the depth-to-span ratio—was modified to examine the influence of different depth-to-span ratios on the load-carrying capacity and deflection of the composite beam. Figure 15 shows the effects of the depth-to-span ratio on the ultimate load-carrying capacity and deflection. It can be seen that the ultimate load-carrying capacity of the composite floor system varies only slightly and attains its maximum value when the depth-to-span ratio lies between 1/12 and 1/14. In contrast, the deflection decreases markedly when the depth-to-span ratio is less than 1/15, and becomes essentially insensitive to further increases in depth once the depth-to-span ratio reaches about 1/9.

Taking into account both the ultimate load-carrying capacity and deflection, as well as the demand for spatial utilization in practical engineering applications, it is recommended that the depth-to-span ratio of this type of structural system be taken in the range of 1/11 to 1/14 in design.

4.3.2. The Impact of Hole-to-Span Ratio

In a composite floor system, the web spacing—that is, the length of the openings—is also regarded as an important factor influencing the ultimate load-carrying capacity and deflection. Building on the previous subsection, the total beam depth is taken as h = 190 mm, giving a depth-to-span ratio between 1/12 and 1/13, while the other geometric parameters are kept identical to those in the tests. The ratio of opening length to span is defined as the hole-to-span ratio, and the influence of different hole-to-span ratios on the ultimate load-carrying capacity and deflection of the steel–concrete composite beam is investigated. As shown in Figure 16, the ultimate load-carrying capacity of the composite floor system increases as the hole-to-span ratio decreases; when the hole-to-span ratio is less than 0.07, the incremental gain in ultimate capacity gradually diminishes. Taking into account the space required for service ducts and equipment to pass through, it is recommended that, in design practice, the hole-to-span ratio be selected within the range of 0.04–0.07 in light of actual project conditions.

5. Deformation Analysis

According to the principle of equivalent stiffness, open-web trusses consisting of five or more panels are idealized in this study as equivalent solid-web beams, such that the overall structural depth h, flexural stiffness EI, and shear stiffness C of the open-web truss are taken to be the same as those of the corresponding solid-web beam. This treatment is applied to the basic segments that recur in the truss system and possess identical geometric and mechanical characteristics [31].

Figure 17 illustrates a typical panel i of the ST-TVCS (with dimensions a_i × h), together with the corresponding typical element of the equivalent solid-web beam. Figure 18 shows the cross-sections of the open-web truss and the equivalent solid-web beam. It is noted that A₁ and A₂ denote the cross-sectional areas of the upper concrete slab and the square-tube bottom chord, respectively, in panel i, whereas A_v1 and A_v2 denote the cross-sectional areas of the left and right vertical webs in panel i, respectively.

5.1. Equivalent Flexural Stiffness Analysis

According to the principle of equivalence, by applying a unit bending moment at both ends of the typical panel of the open-web steel truss and at both ends of the corresponding typical element of the equivalent solid-web beam, and requiring that the two elements undergo the same end rotation, the equivalent flexural stiffness EI of the solid-web beam can be determined. A coordinate system is established for the cross-section of the typical panel of the open-web truss, as shown in Figure 19.

On this basis, the equivalent flexural stiffness of a typical panel can be derived from the following expression:

$$EI=E_1{I}_1+E_2{I}_2$$

(1)

where

E₁: elastic modulus of concrete;

E₂: elastic modulus of steel, taken as 2.06 × 10⁵ MPa;

I₁: second moment of area of the concrete slab section;

I₂: second moment of area of the square-tube bottom chord section.

$$EI=E_1\cdot {\displaystyle \frac{b_1{h}_1^3}{12}}+E_1\cdot {\left(h-\overline{y}\right)}^2{A}_1+E_2\cdot {\displaystyle \frac{b_2{h}_2^3-b_3{h}_3^3}{12}}+E_2\cdot {\left(\overline{y}\right)}^2{A}_2$$

(2)

The coordinates of the centroid of the section are given by:

$$\overline{y}={\displaystyle \frac{A_1\times E_1\times h}{A_1\times E_1+A_2\times E_2}}$$

(3)

Substituting into the above expressions and simplifying yields:

$$EI={\displaystyle \frac{E_1{b}_1{h}_1^3}{12}}+{\displaystyle \frac{E_2\left(b_2{h}_2^3-b_3{h}_3^3\right)}{12}}+{\displaystyle \frac{A_1{A}_2{E}_1{E}_2}{A_1{E}_1+A_2{E}_2}}\times h^2$$

(4)

where

A₁: cross-sectional area of the upper concrete slab;

A₂: cross-sectional area of the square-tube bottom chord;

b₁: width of the upper concrete slab;

h₁: height (thickness) of the upper concrete slab;

b₂: outer width of the square-tube bottom chord;

h₂: outer height of the square-tube bottom chord;

b₃: inner hollow width of the square-tube bottom chord;

h₃: inner hollow height of the square-tube bottom chord;

h: overall structural depth.

The contributions of each term in Equation (4) to the total flexural stiffness EI are shown in Figure 20. It can be seen that the magnitude of the third term is much larger than those of the first two. To maintain simplicity of the calculation formula, the contributions of the other two terms may therefore be neglected, and the flexural stiffness EI of the equivalent solid-web beam can be written as:

$$EI={\displaystyle \frac{A_1{A}_2{E}_1{E}_2}{A_1{E}_1+A_2{E}_2}}\times h^2$$

(5)

5.2. Equivalent Shear Stiffness Analysis

According to the equivalence principle, a unit shear force is applied at both ends of the typical panel of the open-web steel truss and the corresponding typical element of the equivalent solid-web beam, such that the two elements develop the same shear angle. On this basis, the equivalent shear stiffness C can be derived. The basic assumptions are as follows: (1) The points of contraflexure of the upper chord and the bottom chord are located at their midpoints, and the vertical webs are rigidly connected to the upper and bottom chords; (2) The locations of the points of contraflexure in the vertical webs are determined in proportion to the line stiffnesses of the upper and bottom chords; (3) Torsional effects are neglected, and only the first-order effects of shear forces and bending moments are considered. Figure 21 presents the unit-force diagram and the corresponding bending moment distribution for a typical panel.

In this figure, ${\mu }_1 \mathrm{and} {\mu }_2$ denote the stiffness ratios of the points of contraflexure in the left and right vertical webs, respectively, and are calculated according to the following expression.

$${\mu }_1={\displaystyle \frac{i_1}{i_1+i_2}};{\mu }_2={\displaystyle \frac{i_2}{i_1+i_2}}$$

(6)

In this study, the line stiffnesses are defined as follows:

i₁: line stiffness of the upper concrete slab;

i₂: line stiffness of the square-tube bottom chord;

i_v1: line stiffness of the left vertical web;

i_v2: line stiffness of the right vertical web.

The shear stiffness $\delta$ of the open-web steel truss is then calculated using the following expression:

$$\begin{gathered} \delta ={\displaystyle \frac{\frac{1}{2}\times \frac{a}{2}\times \frac{a}{2}\times \frac{a{\mu }_1}{3}\times \frac{2}{3}\times \frac{a{\mu }_1}{2}\times 2}{E_1{I}_1}}+{\displaystyle \frac{\frac{1}{2}\times \frac{a}{2}\times \frac{a{\mu }_2}{2}\times \frac{2}{3}\times \frac{a{\mu }_2}{2}\times 2}{E_2{I}_2}} \\ +{\displaystyle \frac{1}{E_2{I}_{v1}}}\left({\displaystyle \frac{1}{2}}\times {\displaystyle \frac{a{\mu }_1}{2}}\times h{\mu }_1\times {\displaystyle \frac{2}{3}}\times {\displaystyle \frac{a{\mu }_1}{2}}+{\displaystyle \frac{1}{2}}\times {\displaystyle \frac{a{\mu }_2}{2}}\times h{\mu }_2\times {\displaystyle \frac{2}{3}}\times {\displaystyle \frac{a{\mu }_2}{2}}\right) \\ +{\displaystyle \frac{1}{E_2{I}_{v2}}}\left({\displaystyle \frac{1}{2}}\times {\displaystyle \frac{a{\mu }_1}{2}}\times h{\mu }_1\times {\displaystyle \frac{2}{3}}\times {\displaystyle \frac{a{\mu }_1}{2}}+{\displaystyle \frac{1}{2}}\times {\displaystyle \frac{a{\mu }_2}{2}}\times h{\mu }_2\times {\displaystyle \frac{2}{3}}\times {\displaystyle \frac{a{\mu }_2}{2}}\right) \\ ={\displaystyle \frac{a^3{\mu }_1^2}{12E_1{I}_1}}+{\displaystyle \frac{a^3{\mu }_2^3}{12E_2{I}_2}}+{\displaystyle \frac{a^{3}h\left({\mu }_1^3+{\mu }_2^3\right)}{12E_2{I}_{v1}}}+{\displaystyle \frac{a^{3}h\left({\mu }_1^3+{\mu }_2^3\right)}{12E_2{I}_{v2}}} \end{gathered}$$

(7)

where

I_v1: second moment of area of the left half of the vertical web in the typical panel;

I_v2: second moment of area of the right half of the vertical web in the typical panel;

a: length of the typical panel;

h: overall structural depth.

The shear angle $\gamma$ of the open-web steel truss can then be expressed as:

$$\gamma ={\displaystyle \frac{F}{C}}={\displaystyle \frac{\delta }{a}}={\displaystyle \frac{a^2{\mu }_1^2}{12E_1{I}_1}}+{\displaystyle \frac{a^2{\mu }_2^2}{12E_2{I}_2}}+{\displaystyle \frac{ah\left({\mu }_1^3+{\mu }_2^3\right)}{12E_2{I}_{v1}}}+{\displaystyle \frac{ah\left({\mu }_1^3+{\mu }_2^3\right)}{12E_2{I}_{v2}}}$$

(8)

Based on the definition of the line stiffness i, by substituting $i_1={\displaystyle \frac{E_1{I}_1}{a}},i_2={\displaystyle \frac{E_2{I}_2}{a}},i_{v_1}={\displaystyle \frac{E_2{I}_{v1}}{h}}{,i}_{v_2}={\displaystyle \frac{E_2{I}_{v2}}{h}},$ together with μ₁ and μ₂ into Equation (8), one obtains:

$$\gamma =a\left[{\displaystyle \frac{1}{12\left(i_1+i_2\right)}}+{\displaystyle \frac{i_1^3+i_2^3}{12i_{v1}{\left(i_1+i_2\right)}^3}}+{\displaystyle \frac{i_1^3+i_2^3}{12i_{v2}{\left(i_1+i_2\right)}^3}}\right]$$

(9)

If the vertical webs on the left and right sides have identical material properties and cross-sections, i.e., i_v1 = i_v2 = i the equivalent shear stiffness C can be simplified as:

$$C={\displaystyle \frac{1}{a\left[\frac{1}{12\left(i_1+i_2\right)}+\frac{i_1^3+i_2^3}{6i_v{\left(i_1+i_2\right)}^3}\right]}}$$

(10)

5.3. Deflection Calculation

Under external loading, the deformation of the ST-TVCS is primarily composed of flexural deformation and shear deformation. According to the equivalent stiffness method, the system is idealized as an equivalent solid-web beam. Once the equivalent flexural stiffness EI and equivalent shear stiffness C are obtained, the deflection can be efficiently evaluated using the diagram-multiplication (unit-force) method from structural mechanics.

$$f=\int {\displaystyle \frac{\overline{M}\cdot M_P}{EI}}ds+\int k{\displaystyle \frac{\overline{F_Q}\cdot F_{QP}}{C}}ds$$

(11)

In this formulation, $\overline{M}$ denotes the bending moment induced by a unit load, $M_P$ denotes the bending moment induced by the actual load, $\overline{F_Q}$ denotes the shear force induced by a unit load, and $F_{QP}$ denotes the shear force induced by the actual load.

Let $m=\int \overline{M}\cdot M_{P}ds,n=\int \overline{F_Q}\cdot F_{QP}ds$, where m and n depend only on the applied vertical load and are independent of the structural stiffness; they can be obtained by the diagram-multiplication method in classical structural mechanics. Substituting Equations (5) and (10) into Equation (11) and integrating yields:

$$\begin{gathered} f=\sum _{i=1}^R\left[m_i\left({\displaystyle \frac{1}{E_{i1}{A}_{i1}}}+{\displaystyle \frac{1}{E_{i2}{A}_{i2}}}\right)\times {\displaystyle \frac{1}{h^2}}\right] \\ +\sum _{i=1}^R \left[ {\displaystyle \frac{k{n}_i}{6}}\left( {\displaystyle \frac{{\left( E_{i1}{I}_{i1} \right)}^3+{\left( E_{i2}{I}_{i2} \right)}^3}{E_{i2}{I}_{iv}{\left( E_{i1}{I}_{i1}+E_{i2}{I}_{i2} \right)}^3}} \right)\times a_i\times h \right] \\ +\sum _{i=1}^R \left[ {\displaystyle \frac{k{n}_i}{12}}\left( {\displaystyle \frac{1}{E_{i1}{I}_{i1}+E_{i2}{I}_{i2}}} \right)\times a_i^2 \right] \end{gathered}$$

(12)

where

R: number of panels in the Top-Chord-Free Vierendeel-truss Composite Slab;

k: sectional shape factor, taken as 1.2;

a_i: element length of panel i;

E_i1: elastic modulus of concrete in section $i$;

E_i2: elastic modulus of steel in section $i$;

I_i1: second moment of area of the upper concrete slab in panel $i$;

I_i2: second moment of area of the bottom chord in panel $i$;

I_iv: second moment of area of the vertical web in panel $i$.

If the material properties, panel lengths, and cross-sectional dimensions are assumed to remain constant along the span of the open-web steel truss, Equation (12) can be rewritten in a simplified form as Equation (13).

$$f=m\left({\displaystyle \frac{1}{E_1{A}_1}}+{\displaystyle \frac{1}{E_2{A}_2}}\right){\displaystyle \frac{1}{h^2}}+\left[{\displaystyle \frac{kn}{6}}\left({\displaystyle \frac{{\left(E_1{I}_1\right)}^3+{\left(E_2{I}_2\right)}^3}{E_2{I}_v{\left(E_1{I}_1+E_2{I}_2\right)}^3}}\right)ah+{\displaystyle \frac{kn}{12}}\left({\displaystyle \frac{1}{E_1{I}_1+E_2{I}_2}}\right)a^2\right]$$

(13)

Substituting the geometric parameters of the ST-TVCS into Equation (13) yields the theoretical midspan deflection, which is then compared with the experimental results and the finite-element predictions, as summarized in

Table 3. Comparison of Elastic-Stage Deflections: Theoretical, Numerical, and Experimental Results.

Load/kN	Midspan Deflection (Test)/mm	Midspan Deflection (FEA)/mm	Error of FEA	Midspan Deflection (Theory)/mm	Error of Theory
10	1.42	1.29	9.1%	1.48	4.2%
20	2.68	2.54	5.2%	2.96	10.4%
30	4.01	3.91	2.5%	4.45	10.9%
40	5.37	4.95	8.7%	5.92	10.2%
50	7.01	6.12	12.9%	7.41	5.7%
60	9.08	7.51	17.4%	8.88	2.2%

and

Table 4. Comparison of Elastic-Stage Stiffness: Theoretical, Numerical, and Experimental Results.

-	Test Value	FEA Value	Theoretical Value
Elastic stiffness (kN/mm)	6.608	7.989	6.757
Relative error	-	20.91%	2.25%

.

It can be seen that, in the elastic stage, the theoretical midspan deflections obtained using the equivalent stiffness method agree well with both the test data and the numerical results, indicating that the proposed formulation provides a sound theoretical basis for design.

5.4. Influence of Geometry on Stiffness

From Equation (13), it can be seen that the overall structural depth h affects both the flexural and shear components of the deformation of the composite floor system. As h increases, the flexural deformation decreases in a quadratic manner, while the shear deformation increases approximately linearly. Therefore, there must exist an optimal structural depth at which the global stiffness is maximized and the overall deflection is minimized. Differentiating Equation (13) with respect to h yields:

$${\displaystyle \frac{df}{dh}}=-2m\left({\displaystyle \frac{1}{E_1{A}_1}}+{\displaystyle \frac{1}{E_2{A}_2}}\right){\displaystyle \frac{1}{h^3}}+{\displaystyle \frac{kna}{6}}\left({\displaystyle \frac{{\left(E_1{I}_1\right)}^3+{\left(E_2{I}_2\right)}^3}{E_2{I}_v{\left(E_1{I}_1+E_2{I}_2\right)}^3}}\right)$$

(14)

$${\displaystyle \frac{d^{2}f}{d{h}^2}}=6m\left({\displaystyle \frac{1}{E_1{A}_1}}+{\displaystyle \frac{1}{E_2{A}_2}}\right){\displaystyle \frac{1}{h^4}}>0$$

(15)

From Equation (15), the second derivative is greater than zero, indicating that the function is convex. Setting the first derivative equal to zero gives the stationary point:

$$h_0=\sqrt[3]{{\displaystyle \frac{12I_v\left(E_1{A}_1+E_2{A}_2\right)}{ak{E}_1{A}_1{A}_2}}\times {\displaystyle \frac{{\left(E_1{I}_1+E_2{I}_2\right)}^3}{{\left(E_1{I}_1\right)}^3+{\left(E_2{I}_2\right)}^3}}\times {\displaystyle \frac{m}{n}}}$$

(16)

Accordingly, when the structural depth h = h₀, the deflection of the ST-TVCS attains its minimum value, i.e., f = f_min. The optimal depth h₀ depends on the cross-sectional dimensions of the upper and bottom chords, the cross-sectional dimensions of the vertical members, and the panel length; specifically, h₀ decreases with increasing panel length and increases with increasing cross-sectional size of the vertical webs.

By substituting the material and geometric parameters from the tests into Equation (16), the optimal depth is obtained as h₀ = 182.9 mm, corresponding to a depth-to-span ratio of approximately 1/13. This lies within the range of 1/11–1/14 for the reasonable depth-to-span ratio identified by the finite-element simulations in this study, thereby confirming the accuracy of the proposed formula and supporting its use as a reference for the preliminary design of ST-TVCS.

Based on the optimal depth obtained from Equation (16), the influence of the web spacing on the structural stiffness can be further examined. Substituting Equation (16) into Equation (13) leads to:

$$\begin{gathered} f={\displaystyle \frac{kn}{4E_2{I}_v}}{\left({\displaystyle \frac{12I_v\left(E_1{A}_1+E_2{A}_2\right)}{k{E}_1{A}_1{A}_2}}\times {\displaystyle \frac{m}{n}}\right)}^{{\displaystyle \frac{1}{3}}}\times {\left({\displaystyle \frac{{\left(E_1{I}_1\right)}^3+{\left(E_2{I}_2\right)}^3}{{\left(E_1{I}_1+E_2{I}_2\right)}^3}}\right)}^{{\displaystyle \frac{2}{3}}}\times a^{{\displaystyle \frac{2}{3}}} \\ +{\displaystyle \frac{kn}{12}}\left({\displaystyle \frac{1}{E_1{I}_1+E_2{I}_2}}\right)\times a^2 \end{gathered}$$

(17)

From Equation (17), it can be seen that the deflection of the composite floor system increases gradually with increasing web spacing a. From the viewpoint of mechanical performance, reducing the web spacing is beneficial for decreasing the structural deflection and enhancing the global stiffness. From the perspective of architectural functionality, however, increasing the web spacing is advantageous for the layout and passage of service ducts and equipment. Therefore, the choice of web spacing a must balance structural performance and architectural requirements, while at the same time ensuring that the corresponding h₀ satisfies the structural demands.

The total deformation must also satisfy the allowable deflection requirement of the structure:

$$f\le \left[f\right]$$

(18)

Thus, Equation (18) can be rewritten as:

$$f=\beta a^{{\displaystyle \frac{2}{3}}}+\gamma a^2\le \left[f\right]$$

(19)

where $\beta ={\displaystyle \frac{kn}{4E_2{I}_v}}{\left({\displaystyle \frac{12I_v\left(E_1{A}_1+E_2{A}_2\right)}{k{E}_1{A}_1{A}_2}}\times {\displaystyle \frac{m}{n}}\right)}^{{\displaystyle \frac{1}{3}}}\times {\left({\displaystyle \frac{{\left(E_1{I}_1\right)}^3+{\left(E_2{I}_2\right)}^3}{{\left(E_1{I}_1+E_2{I}_2\right)}^3}}\right)}^{{\displaystyle \frac{2}{3}}}$, $\gamma ={\displaystyle \frac{kn}{12}}\left({\displaystyle \frac{1}{E_1{I}_1+E_2{I}_2}}\right)$.

Which yields:

$$0<a\le \sqrt{{\displaystyle \frac{3\times \left(\frac{\lambda }{6\beta }-\frac{2\beta }{\lambda }\right)+\left[f\right]}{\gamma }}}=a_i$$

(20)

In Equation (20), $\lambda =\sqrt[3]{108\left[f\right]+12\sqrt{3}\times \sqrt{{\left(4{\beta }^3+27\gamma \left[f\right]\right)}^2\times {\gamma }^3}}$.

Consequently, in the design of composite floor systems of this type, the web spacing and structural depth can be determined from Equations (16) and (20) such that the ST-TVCS attains maximum stiffness while satisfying the deformation limits of the structure.

6. Conclusions

This study investigates the ST-TVCS through monotonic static tests, validated finite-element analyses, parametric studies, and theoretical derivations. The main conclusions are as follows:

(1)

The results demonstrate that a top-chord-free open-web composite floor system can still develop stable global flexural resistance through a “concrete slab in compression–bottom chord in tension” force couple, while the open-web region governs the bending–shear transfer near the loading points. This provides experimental and numerical evidence supporting the feasibility of replacing the conventional steel top chord by the concrete slab in such a configuration.

(2)

The experimentally observed damage evolution indicates that cracking and spalling of the slab bottom concentrate in the bending–shear regions adjacent to the loading points, and local cracking of welds near the end shear–bending blocks may trigger rapid capacity loss. These findings identify the end blocks and their weld connections as critical detailing zones in design, and suggest that strengthening efforts should be preferentially targeted there rather than in the pure-bending region.

(3)

The sectional strain measurements show that the midspan open-web section exhibits an approximately linear strain profile over the depth during the elastic stage, supporting the applicability of the plane-section assumption for the proposed special cross-sectional configuration. In contrast, the solid-web (block) region shows a bilinear strain pattern, reflecting combined bending–shear effects. The bottom surface of the bottom chord in the central region is the most likely location to reach yielding first as loading progresses.

(4)

For the investigated specimens, concrete infill in the shear–bending blocks does not lead to a noticeable improvement in global stiffness, ultimate capacity, or failure pattern. From a practical viewpoint, this implies that omitting block infill can be a reasonable option when fabrication simplicity and construction efficiency are prioritized, provided that project-specific detailing requirements are satisfied.

(5)

The validated parametric analysis quantifies how depth-to-span ratio, opening (panel) length, slab thickness, and width-to-span ratio affect ultimate capacity and service deflection, and therefore provides a design-oriented envelope for preliminary proportioning. For the studied system family under the investigated load configuration, depth-to-span ratios of 1/11–1/14 and opening-to-span ratios of 0.04–0.07 achieve a balanced trade-off between strength, stiffness, and service-integration demand.

(6)

A simplified linear-elastic deflection formula based on the equivalent stiffness method is derived and shown to predict the deformation response with good accuracy. The formulation separates flexural and shear components and reveals an optimal structural depth that maximizes global stiffness, enabling rapid preliminary selection of overall depth and web spacing to satisfy serviceability limits without resorting to full numerical analysis.

The present study focuses on the short-term mechanical performance under monotonic static loading. Durability- and reliability-related issues, such as corrosion-induced section loss of steel components, degradation of concrete and bond properties, and their potential influence on local connections and emergency performance, are not explicitly addressed here. These aspects will be investigated in future work to support comprehensive design decisions for practical applications.