Theoretical and Parametric Studies on the Lateral-Resistant Performance of the Steel Grid Shear Wall

Abstract

This study investigates a novel steel grid shear wall (SGSW) structure with lightweight and discrete lateral-resistance members, focusing on its structural behavior in lateral resistance. By comparing the characteristics of the thin steel plate shear wall, the mechanism of the steel grid components in both the tension zone and compression zone was briefly described. The formulas of lateral-resistant capacity and initial stiffness of the SGSW were derived through the static equilibrium method. Then, the influence laws of the span–height ratio, steel member spacing and section size of the steel members on the lateral-resistant performance of the SGSW were determined through a parametric analysis. In addition, the accuracy of the calculation formula was validated. The results showed that the strains of the steel grid components in different positions were all the same when the bending stiffnesses of the edge members were significantly large. The lateral-resistance capacity of the SGSW increased with the span-to-height ratio, while it decreased as the spacing between the steel components increased. Compared with the effects of web height, web thickness and flange width, increasing the flange thickness exhibited the best effects on improving the lateral capacity. As the flange thickness increased from 7 mm to 13 mm, the lateral-resistant capacity showed an improvement of 35.45%. Additionally, the formula derived in this study demonstrated high accuracy and reliability, with the error not exceeding 8% between the formula calculation and the simulation results.

1. Introduction

A steel plate shear wall (SPSW) is an effective system for resisting lateral loads, commonly used in multi-story and high-rise buildings. The boundary frame and the embedded steel plates work in tandem to resist lateral loads, such as wind and seismic forces. In the past few years, as the theoretical system of steel plate shear walls (SPSWs) has been continuously evolving and maturing, many scholars have put forward various types of SPSWs. Based on the construction methods and load-bearing characteristics, SPSWs can be roughly categorized into the following types: unstiffened thin SPSWs, side-connected SPSWs, stiffened SPSWs and slotted or perforated SPSWs. Montgomery [1] and Elgaaly [2] conducted experiments on the unstiffened SPSW and proved that the thin SPSW had good lateral-resistant behavior and a hysteretic property. To prevent excessive deformation of the frame columns, Mei [3], Chen [4] and Wang [5,6] proposed a series of two-side-connected SPSW structures. Since thin SPSWs are highly susceptible to out-of-plane deformation, a series of stiffened SPSW structures were proposed, such as a cross-stiffened SPSW [7,8], a diagonally stiffened SPSW [9,10,11] and concrete-encased steel shear walls [12]. In order to reduce the steel consumption, different types of slotted or perforated shear wall structures were proposed, including SPSWs with circle openings [13,14], diamond openings [15] and slit panels [16].

However, these commonly used SPSW structures have some shortcomings. The thin SPSW generates noise during the formation of tension zones under horizontal loads, which negatively affects residential comfort. And the load-bearing capacity of thin SPSWs is significantly reduced when it returns to the original position after forming a tension zone and before developing a new tension zone in the opposite direction. As for the thick SPSW, the buckling load of the steel plates must exceed the elastic limit of the steel in design, ensuring that failure occurs due to the yielding of the steel rather than the buckling. This design method cannot fully utilize the strength of the steel and leads to material waste. To enhance the lateral resistance and prevent buckling in thin SPSWs, many types of stiffening ribs are introduced and connected to the thin steel plate by welding, which may easily lead to defects or even burn-through. In addition, due to their relatively small thickness compared to their in-plane dimensions, SPSWs are particularly sensitive to initial imperfections, which may arise during transportation and installation.

To address the existing limitations of the conventional SPSWs, Yan [17,18,19] introduced an innovative steel grid shear wall structure (SGSW), which evolved from the simplified models of SPSWs established by previous researchers [20,21,22]. The specific SGSW is shown in Figure 1. The simplified tension and compression strips model is replaced by steel grid components, where the steel grid components serve as energy dissipation elements instead of steel plates. These steel grid components work in conjunction with the boundary frame to resist horizontal loads. This new lateral-resistant system avoids noise during the formation of tension zones. In addition, the SGSW adopts tangible steel members to resist lateral loads instead of the tension strips in thin SPSWs which are only formed after loading. Therefore, the SGSW does not need to re-form the tension strips when the structure is subjected to cyclic loading, thereby still maintaining good lateral resistance when the loading direction changes. Additionally, the members of SGSWs are discrete and lightweight, which avoids the non-negligible initial defects during the transportation and installation process. The lighter and smaller steel grid components also make it easier for construction workers to install and transport them, which effectively promotes construction efficiency. Moreover, we also compared the SGSW and the traditional SPSW from the perspectives of lateral-resistant capacity and economy in our previous study [17] and found that the SGSW showed stronger lateral-resistant performance after the first circle of cyclic load, and the cost of the SGSW was less.

This paper primarily investigates the lateral-resistant performance of an SGSW structure. First of all, the force mechanisms in both the tension and compression zones of the SGSW were analyzed. Then, the deformation coordination of the steel grid components in different regions was analyzed, and a formula for calculating the lateral resistance was derived. Finally, through a series of parametric analyses, the effects of the span-to-height ratio, spacing of the steel grid components and the dimensions of the T-shaped steel on the initial stiffness and lateral resistance of the SGSW were investigated, and the reliability of the calculation formula was verified.

2. Force Mechanism Analysis of the SGSW

Thorburn [20] proposed a strip model by studying the post-buckling load-bearing mechanism of unstiffened thin SPSWs and analyzed the influence of different stiffness levels of the boundary steel frame on the stress distribution of the equivalent strip model (Figure 2). When the stiffness of the edge member was infinitely large, the stress in the tension strip, which represented the steel plate tension zone, was uniformly distributed along the whole strip. When the edge members were elastic but still had considerable stiffness, the stress distribution in the tension zone showed a trend of decreasing symmetrically from the central area to both sides. And when the stiffness of the edge members was very small and could not provide sufficient restraint for the plastic development of the thin SPSW, a few pressure zones would appear in the corner areas.

In this paper, the tension strips were materialized as steel grid components. By arranging the steel grid components asymmetrically in the steel frame, the SGSW undertook the hysteretic load by means of the “tension (compression) strip” mechanism. The mechanical mechanisms of the embedded steel grid components in the tension and compression zones were analyzed separately (Figure 3).

2.1. Force Mechanism of Tension Strips

Since the arrangement of the steel grid components was the representation of the post-buckling tension zone, the stress distribution in these grid members should resemble that of the tension strip model. That is, when the stiffness of the edge members was infinitely large, the stress distribution of the strip steel members was uniform, allowing for all tension steel grid components to reach yield. When the stiffness of the edge members was relatively large, the stress of the steel grid member in the central zone was greater and decreased from the center to the sides. So, the central steel grid member would yield first. And when the stiffness of the edge members was significantly insufficient, the lateral-resistant capacity of the SGSW was low, which was detrimental to load transfer and energy dissipation.

2.2. Force Mechanism of Compression Strips

Different from the mechanical mechanism of the steel grid components in tension, the steel grid components in compression would buckle. The critical buckling load and strain varied with the slenderness ratio of the steel grid components. When lateral displacement was small, the compression members did not buckle. The force values in the steel grid components under compression were identical to those of tension but acted in the opposite direction. As the displacement progressively increased, the longest compression steel grid member buckled first, and then, the load-bearing capacity decreased. However, the shorter steel grid components sustained compression, leading to an increase in their load-bearing capacity.

As the research focus of this paper lies in the lateral-resistant performance of the SGSW, the impact of the stiffness of edge members is not considered. In other words, the stiffnesses of the steel beam and column are assumed to be rigid bodies. Therefore, the internal forces of the steel grid components in tension were evenly distributed, and those in compression were also evenly distributed when no buckling occurred.

3. Formula for Calculating the Lateral-Resistant Capacity of the SGSW

3.1. Deformation Coordination Analysis of the SGSW

To simplify the analysis and eliminate the influence of the boundary frame, the following assumptions were made: (1) The stiffnesses of the frame beams and columns were infinite, and the axial deformation and bending deformation of the beams and columns were ignored; (2) The external frame beams and columns were assumed to be connected by hinges.

Under the action of lateral load V, the top point of the SGSW would undergo horizontal displacement U. According to the deformation characteristics of the different steel grid components, the SGSW could be classified into three regions (only the unilateral deformation was analyzed according to the symmetry relationship, Figure 4). The steel grid components in ZONE 1 underwent translation and rotation around the connection joint, while the steel grid components in ZONE 2 and ZONE 3 only underwent rotation. The deformation of the steel grid components in the three regions was analyzed, respectively, below.

3.1.1. ZONE 1

The original length of the member in ZONE 1 is h_i/sinθ, and its translational displacement at the connection point with the beam is U. It can be deduced that the translational displacement at the connection point with the column is

$$U_i=U\times {\displaystyle \frac{H-h_i}{H}}$$

(1)

where H is the height of the frame and h_i is the vertical distance between the top beam and the intersection point of the steel grid member with the column in ZONE 1.

The deformation of the steel grid components in ZONE 1 Δl_i is calculated as follows:

$$\Delta l_i=(U-U_i)\cos \theta ={\displaystyle \frac{h_i}{H}}U\cos \theta$$

(2)

where θ represents the angle between the steel grid components and the horizontal axis.

So, the strain of the steel grid components in ZONE 1 is

$${\epsilon }_i={\displaystyle \frac{\Delta l_i}{h_i/\sin \theta }}={\displaystyle \frac{\frac{h_i}{H}U\cos \theta }{h_i/\sin \theta }}={\displaystyle \frac{U}{2H}}\sin 2\theta$$

(3)

3.1.2. ZONE 2

The original length of the members in ZONE 2 is H/sinθ. Since the stiffness of the steel frame is rigid, the displacement at the intersection points of the steel grid components with the bottom beam is 0. The steel grid components only rotate around the connection point with the bottom beam and experience translational displacement U at the connection point with the top beam. The deformation Δl of the steel grid components in this region can be determined by

$$\Delta l=U\cos \theta$$

(4)

The strain of the steel grid components ε in ZONE 2 is

$$\epsilon ={\displaystyle \frac{\Delta l}{H/\sin \theta }}={\displaystyle \frac{U\cos \theta \sin \theta }{H}}={\displaystyle \frac{U}{2H}}\sin 2\theta$$

(5)

3.1.3. ZONE 3

The original length of the member in the ZONE 3 region is h_j/sinθ, and the steel grid member only rotates around the intersection point with the bottom beam while experiencing the translational displacement U_j at the intersection point with the frame column. The deformation of the steel grid components in this region is calculated as follows:

$$\Delta l_j=(U-U_j)\cos \theta ={\displaystyle \frac{h_j}{H}}U\cos \theta$$

(6)

where h_j is the vertical distance from the bottom beam to the point where the steel grid component intersects with the right column in ZONE 3.

So, the strain of the steel grid components ε in ZONE 3 is

$${\epsilon }_j={\displaystyle \frac{\Delta l_j}{h_j/\sin \theta }}={\displaystyle \frac{\frac{h_j}{H}U\cos \theta }{h_j/\sin \theta }}={\displaystyle \frac{U}{2H}}\sin 2\theta$$

(7)

From Formulas (2), (4) and (6), Δl_i:Δl:Δl_j:= h_i:H:h_j can be derived, while ε_i = ε = ε_j can be derived from Formulas (3), (5) and (7). These demonstrate that the steel grid components embedded in the same side deform proportionally, with strain coordination achieved. Then, the corresponding inter-story displacement angle β can be calculated by

$$\beta ={\displaystyle \frac{U}{H}}={\displaystyle \frac{2{\epsilon }_y}{\sin 2\theta }}$$

(8)

where ε_y is the yield strain of steel.

3.1.4. Summary

In conclusion, when the boundary steel frame stiffness is significantly high, the strains of the embedded steel grid components in tension are uniform, allowing for them to yield simultaneously. Similarly, the steel grid components in compression also have uniform deformation when the lateral displacement is small. However, due to the buckling of the steel grid components in compression, the buckling load-bearing capacity is affected by many complex factors, which need to be analyzed separately.

3.2. The Calculation Method of Lateral-Resistant Capacity

According to the Technical Code for Steel Plate Shear Wall (JGJ/T380-2015) [23], the lateral-resistant capacity V_u calculation formula of the unstiffened SPSW is

$$V_{\mathrm{u}}=0.42\cdot f\cdot t_w{L}_e$$

(9)

where f (N/mm²) is the design strength of steel; t_w (mm) is the thickness of the thin SPSW; and L_e (mm) is the span of the SPSW.

As mentioned above, the SGSW system primarily resists lateral forces through the steel grid components, whereas the thin SPSW depends on the tension strip formed after steel plate buckling to resist lateral loads. The main difference lays in the contribution of the compressed steel grid components. Therefore, it is crucial to include the contribution of these compression components when calculating the lateral-resistant capacity of the SGSW.

Assuming that the arrangement of the steel grid components is established, its elastic stage force is shown in Figure 5. It is shown that a represents the horizontal distance between the column and the point where the steel grid member intersects with the top beam, and d is the spacing between the steel grid components. And θ represents the angle between the steel grid components and the horizontal direction.

For the whole SGSW structure, due to the symmetry of the force distribution, the horizontal force of the two hinged joints at the bottom of the frame is

$$-H_{AB}=H_{DC}=V/2$$

(10)

where H_AB is the horizontal constraint force at point A, H_DC is the horizontal constraint force at point D, and V is the horizontal lateral load on the SGSW structure.

The vertical forces at points A and D can be determined using moment equilibrium at point A:

$$-V_{AB}=V_{DC}={\displaystyle \frac{H}{L}}V$$

(11)

V_AB is the vertical constraint force at point A, while V_DC is the vertical constraint force at point D. L is the span of the SGSW structure.

Taking the CD segment (Figure 6) for analysis, the vertical force at point D can be derived based on the moment equilibrium at point C:

$$H_{DC}=2P_Y\cdot \cos \theta -(P_Y+P_T)\cdot (3d+2a\cdot \sin \theta )/H-P_{YT}\cdot {\displaystyle \frac{(H-2d_y)}{\sqrt{H^2+L^2}}}$$

(12)

In this formula, P_Y and P_T are the counterforces of the SGSW on the frame, which are arranged in the compression and tension zones, respectively. P_YT and P_YY are the reaction forces of the compressed side and tension side fish plate on the frame, respectively.

Taking the BCD segment (Figure 7) for analysis, based on the moment equilibrium at point B, V_DC can be derived as follows:

$$V_{DC}=\sin \theta (5P_T+2P_Y)-(P_T+P_Y)\sin \theta (3a+3d/\sin \theta )/L+P_{YT}\cdot {\displaystyle \frac{H(L+2d_y)}{L\sqrt{H^2+L^2}}}$$

(13)

Taking the ABCD segment (Figure 8) for analysis, V can be calculated based on the moment equilibrium at point A:

$$V=(P_T+P_Y)(5H\cos \theta +4a\sin \theta -6d)/H+P_{YT}\cdot {\displaystyle \frac{{4\mathrm{d}}_{y}L}{H\sqrt{H^2+L^2}}}$$

(14)

The first term of the formula is the reaction force of the tension and compression steel grid components; the second term is the reaction force of the fish plate.

To validate the reliability of Formula (14), various finite element models were created, and qualitative analyses were performed on the different components of the SGSW. The model details are listed in

Table 1. Model details.

Model Number	Details
GWG	L = H = 2700 mm; a = 168 mm; d = 650 mm; dy = 200 mm steel grid components are arranged on both sides
GWG-L	L = H = 2700 mm; a = 168 mm; d = 650 mm; dy = 200 mm; steel grid components are arranged only on the tension side
GWG-Y	L = H = 2700 mm; a = 168 mm; d = 650 mm; dy = 200 mm; steel grid components are arranged only on the compression side
GWG-YWB	L = H = 2700 mm; a = 168 mm; d = 650 mm; dy = 200 mm; only the fishplate is established without steel grid components

.

Based on the above model, monotonic loading simulation analyses were carried out, and the load–displacement curves for the models are shown in Figure 9.

From Figure 9, it is found that the lateral resistances of the different models were generally consistent with the following formula when the inter-story displacement angle reached △:

$$V_{GWG}\approx V_{GWG-L}+V_{GWG-Y}-V_{GWG-YWB}$$

(15)

The total lateral-resistance capacity of each component in the SGSW basically followed the superposition principle, and the reliability of the formula was further verified. In addition, the yield displacements of all models tended to be similar, and the inter-story displacement angle △ (Figure 9) could be used as the yield displacement. The load corresponding to the inter-story displacement angle △ represented the lateral-resistant capacity of the SGSW. According to the derivation in Section 3.1, the yield inter-story displacement angle is

$${\beta }_y={\displaystyle \frac{U}{H}}={\displaystyle \frac{2{\epsilon }_y}{\sin 2\theta }}={\displaystyle \frac{2f_y}{E\cdot \sin 2\theta }}$$

(16)

where ${\epsilon }_y$ is the yield strain, $f_y$ is the design value of steel yield strength, and E is the elastic modulus of steel.

However, it was found that, when the column top displacement of the SGSW reached yield displacement, the flange of the middle T-shaped steel in the compression zone yielded, with no buckling occurring. However, the web of the T-shaped steel did not yield simultaneously (Figure 10). Therefore, a reduction factor of compressed forces in the steel grid components should be introduced.

Through parameter fitting, P_T, P_Y and P_YT are replaced, and the lateral-resistant capacity of the SGSW V_f can be calculated by

$$V_f=1.173(A_Y+0.6A_F)f_y(5H\cos \theta +4a\sin \theta -6d)/H+{\displaystyle \frac{{4\sqrt{2}{\mathrm{d}}^2}_y{tLf}_y}{H\sqrt{H^2+L^2}}}$$

(17)

In the Formula (17), the first term is the lateral-resistant capacity provided by the steel grid steel members, and A_Y and A_F are the area of the web and flange of the T-shaped steel grid member. The second term is the lateral-resistant capacity provided by the fish plate.

The initial lateral stiffness of the SGSW K₀ is

$$K_0={\displaystyle \frac{V_f}{H{\beta }_y}}$$

(18)

4. The Establishment of the Finite Element Model

To validate the proposed formulas in Section 3.2, we conducted a series of finite element parametric analyses and compared the simulation results with the formula calculations. It was crucial that the finite element model used in the following parametric analyses could predict the lateral performance of the SGSWs accurately. Therefore, the finite element model was established in Section 4.1, and the simulation results were compared with the test results in Section 4.2. In addition, the finite element model used for the parametric analysis was improved in Section 4.3 to align with the calculation assumptions of the formula.

4.1. Model Details

The finite element model of the SGSW is shown in Figure 11a. The dimension of each component in the model was taken according to the specimen in Section 4.2. The boundary steel frame was modeled using the S4R element, while the C3D8R element was used to simulate the embedded steel grid components and the fish plate. The mesh size of the boundary beam and column was 50 mm, and that of the steel grid components was 30 mm. The influence of welding residual stress was ignored, and all the components in the structure were connected by *Tie. The base of the SGSW was fully fixed to the ground, and the out-of-plane displacement was restricted. The material properties of steel were simulated by the elastoplastic model (Figure 11b), and the data in the constitutive model were obtained from the tensile test at room temperature.

4.2. Comparison Between Experiment and Simulated Results

In order to validate the accuracy of the established simulation model, the test results were compared with the finite element results based on References [17,18], respectively. The dimensions of the specimens are listed in

Table 2. The size of the test specimens.

Specimen	Cross-Section Dimension/mm
	Column	Beam	T-Shaped Steel Grid Member
GWG1 [17]	H 200 × 200 × 8 × 12	H 300 × 200 × 8 × 12	T 150 × 40× 4 × 4
GWG2 [18]	H 200 × 200 × 8 × 12	H 320 × 200 × 10 × 12	T 60 × 60 × 6 × 6

. The span of the two specimens was 1700 mm, and the layer height was 1450 mm.

The test setup is shown in Figure 12, and the cyclic loading protocol is illustrated in Figure 13; the lateral cyclic load applied to the finite element model is also consistent with Figure 13.

The comparison of the test and simulation results are illustrated in Figure 14 and

Table 3. Comparison of the peak load between test and FEA results.

Specimen	Peak Load/kN
	Test	FEA	Error
GWG1	1066.20	1076.84	−1.00%
GWG2	1291.44	1258.12	2.58%

. It could be found that the hysteresis curves obtained by the experiments and simulation agreed well, and the results of the finite element calculation could accurately reflect the whole and local deformation of both the structure and each component. And the error in the peak load was also minimal, indicating that the finite element model was able to accurately predict the lateral-resistant capacity of the SGSW. Overall, the finite element model demonstrated high accuracy in predicting the structural performance.

4.3. Improved Finite Element Model

The reliability of the finite element model established based on the actual state of the specimens had been confirmed in Section 4.2. However, this model did not fully comply with the assumptions of the formula derivation in Section 3. Since this paper emphasizes the lateral-resistant capacity of the SGSW as an independent lateral-resisting system, some adjustments to the model were necessary to align it with the calculation assumptions. The assumptions were as follows:

(1) The bending stiffnesses of the beam and column were sufficiently high, ensuring that the steel grid components could fully develop plasticity. It could also be found from Table 3 that the peak load of GWG1 was lower than that of GWG2, even if the steel consumption of GWG1 was significantly greater than that of GWG2. This was because the steel grid components of GWG1 could not due to the insufficient stiffness of the edge frame, and the obvious column deformation of GWG1 can be found in Figure 14. This further proved that edge members with insufficient bending stiffness were detrimental to the lateral-resistant capacity and should be avoided in practical applications.

(2) The frame beam and column connections were ideal hinge joints, which only served as the edge members of the SGSWs. The formula derived in this paper essentially calculated the lateral-resistant capacity provided by the steel grid components when they all fully developed, without considering the contribution of the steel frame. Therefore, the beam–column joints were set as ideal hinges to eliminate the effect of the frame.

(3) The embedded steel grid components were reliably welded to the steel frame, and the fish plate would not fail throughout the entire loading process.

Based on the above assumptions, the finite element model was improved, as shown in Figure 15. The boundary frame was replaced by rigid members. The ideal hinge of the beam and column connections were achieved by MPC/Pin constraint. The ideal bilinear model was adopted for the Q235 steel with a yield strength of 235 Mpa, and the elastic modulus E was 2.06 × 105 MPa. The main dimension of the model was set with the column height H = 2700 mm, the span L = 3240 mm and spacing between the steel grid member d = 650 mm.

5. Parametric Analyses of the SGSWs

Parametric analyses were conducted to obtain the influence of the span-to-height ratio, spacing of the steel grid components and the T-shaped steel dimension on the lateral-resistant capacity and initial stiffness of the SGSW. And the lateral-resistant capacities obtained from the simulation were then compared with the results of the formula to verify its reliability.

5.1. The Influence of Span-to-Height Ratio

The influence of the span-to-height ratio on the performance of the SGSW was investigated. The span-to-height ratio of the SGSW was adjusted by changing the span, and the height of the steel frame was kept at 2700 mm. The corresponding relationship between the span and span-to-height ratio is listed in

Table 4. Span-to-height ratio parameter table.

Span (L)/mm	2160	2430	2700	3240	3780
Span to height ratio (L/H)	0.8	0.9	1.0	1.2	1.4

.

Figure 16a shows the load–displacement curves of the SGSW with different span height ratios, and the yield load of each model was extracted and is illustrated in Figure 16b. It was obvious that the increase in the span-to-height significantly enhanced the load-bearing capacity of the SGSW. As the span-to-height ratio increased from 0.8 to 1.4, the lateral-resistant capacity of the SGSW increased by 37.25%. However, it could be found that the SGSW structures with lower span-to-height ratios (L/H = 0.8, 0,9) exhibited slightly larger yield displacements compared to those with higher span-to-height ratios. That was because the length of the steel grid components increased with the span, making the members more prone to instability due to the larger slenderness ratio, which in turn caused the structure to reach yielding earlier.

The tangent stiffness–displacement curves are shown in Figure 16c, and the change trend of the initial lateral stiffness with span-to-height ratio is illustrated in Figure 16d. The analyzed models configured with span-to-height (L/H) ratios of 0.8, 0.9, 1.0, 1.2 and 1.4 exhibited initial tangent stiffness values of 131 kN/mm, 150 kN/mm, 161 kN/mm, 185 kN/mm and 207 kN/mm, respectively. This indicated that the initial stiffness increased almost linearly as the span-to-height ratio increased. As the span-to-height ratio increased from 0.8 to 1.4, the initial stiffness of the SGSW increased by 58.02%.

The calculation results from the formula were compared with those from the finite element analysis for different span-to-height ratios, as shown in

Table 5. The comparison of the formula results and simulation outcomes with different L/H.

L/H	Simulation Value		Calculated Value		Error in K0 (%)	Error in Vf (%)
	Initial Stiffness K0 (kN/mm)	Yield Load Vf (kN)	Initial Stiffness K0′ (kN/mm)	Yield Load Vf′ (kN)
0.8	131	1039	134	1166	2.00	1.60
0.9	150	1167	181	1285	0.60	2.60
1.0	161	1185	164	1297	0.40	1.10
1.2	185	1295	186	1319	0.50	0.70
1.4	207	1426	207	1467	0.20	2.90

. It could be observed that the maximum error between the formula calculation and simulation results did not exceed 3%, indicating a good agreement between the formula and simulation and confirming the accuracy of the calculation formula.

5.2. The Influence of the Spacing of the Steel Grid Components

To investigate the effect of the spacing between the steel grid components on the lateral-resistant performance and stiffness of the whole structure, the parameterized models were built, and the model sizes are listed in

Table 6. Steel member spacing parameter table.

Model Number	KCL-d−10	KCL-d−5	KCL-d	KCL-d+5	KCL-d+10
Steel spacing (d)/mm	550	600	650	700	750

.

Figure 17a shows the load–displacement curves of the SGSWs with different spacing between the steel grid components, while Figure 17b shows the variation in the lateral-bearing capacities as the spacing increased. The tangent stiffness–displacement curves are shown in Figure 17c,d illustrates the evolution of initial lateral stiffness as the function of the spacing.

It could be found that the initial stiffness decreased as the spacing of the steel grid components increased. The initial stiffness decreased by 10.82% when the spacing of the steel grid components increased from 550 mm to 750 mm. When the inter-story displacement angle reached 0.3%, the tangent stiffness began to decrease. As the horizontal load increased continuously, buckling occurred on the compression steel grid components. When the inter-story displacement angle reached 0.5%, the tangent stiffness significantly decreased, and the load-bearing capacity tended to stabilize. At this point, the lateral-bearing capacities of the models were 1395 kN, 1342 kN, 1308 kN, 1283 kN and 1231 kN, which decreased by 8.03% as the spacing increasing from 550 mm to 750 mm. This indicated that, as the spacing between steel grid components increased, the lateral-resistant capacity of the SGSW decreased obviously. Therefore, a denser arrangement of steel grid components could enhance the lateral-resistant capacity and initial stiffness of the SGSW to some extent.

The results calculated by the formula and the simulation results with different steel member spacing are listed in

Table 7. The comparison of the formula results and simulation outcomes with different steel spacing.

Steel Spacing	Simulation Value		Calculated Value		Error in K0 (%)	Error in Vf (%)
	Initial Stiffness K0 (kN/mm)	Yield Load Vf (kN)	Initial Stiffness K0′ (kN/mm)	Yield Load Vf′ (kN)
550	194	1395	198	1405	2.00	0.70
600	188	1342	191	1357	1.60	1.10
650	185	1308	184	1308	0.40	0.00
700	183	1283	177	1260	3.00	1.80
750	176	1231	171	1212	3.00	1.60

. It could be found that the maximum error between the simulation and calculated results was only 3%.

5.3. The Influence of T-Shaped Steel Dimension Size

The effect of dimension size on the lateral-resistant performance of the SGSW was studied by separately altering the width and thickness of the flanges and web of the T-shaped steel components. The T-shaped steel with a cross-section of T125 × 125 × 6 × 9 was selected as the control group. The correspondence between the T-shaped steel parameters and model numbers is shown in

Table 8. The size of steel members parameter table.

Group	Model Number	T-Shaped Steel Dimension/mm	Change in Section Area/mm2
Control Group	KCL-T	T125 × 125 × 6 × 9	0
Group-Ⅰ	KCL-T-F−10	T115 × 125 × 6 × 9	−60
	KCL-T-F−5	T120 × 125 × 6 × 9	−30
	KCL-T-F+5	T130 × 125 × 6 × 9	+30
	KCL-T-F+10	T135 × 125 × 6 × 9	+60
Group-Ⅱ	KCL-T-FH+1	T125 × 125 × 7 × 9	+114
	KCL-T-FH+2	T125 × 125 × 8 × 9	+228
	KCL-T-FH+3	T125 × 125 × 9 × 9	+352
	KCL-T-FH+4	T125 × 125 × 10 × 9	+364
Group-Ⅲ	KCL-T-Y−10	T125 × 115 × 6 × 9	−90
	KCL-T-Y−5	T125 × 120 × 6 × 9	−45
	KCL-T-Y+5	T125 × 130 × 6 × 9	+45
	KCL-T-Y+10	T125 × 135 × 6 × 9	+90
Group-Ⅳ	KCL-T-YH−2	T125 × 125 × 6 × 7	+125
	KCL-T-YH−1	T125 × 125 × 6 × 8	+250
	KCL-T-YH+2	T125 × 125 × 6 × 11	+375
	KCL-T-YH+4	T125 × 125 × 6 × 13	+500

. Additionally, the changes in the T-section area caused by the variation in each sectional dimension relative to the control group are provided in the last column of Table 8.

The load–displacement curves of each group are shown in Figure 18a–Figure 21a. The lateral-resistant capacity of each model was extracted from the load–displacement curves, and the relationships between the value with different cross-section sizes of T-shaped steel are illustrated in Figure 18b–Figure 21b. Figure 18c–Figure 21c show the tangent stiffness–displacement curves of the SGSW of each group, and Figure 18d–Figure 21d present the change trend of the initial stiffness with the variation in width and thickness of the flanges and web, respectively.

5.3.1. The Influence of Web Height

It can be found from Figure 18 that the tangential stiffness decreased sharply when the inter-layer displacement angle reached 0.3% but stabilized once the displacement angle reached 0.5%. The lateral-resistant capacity and initial stiffness demonstrated 8.22% and 5.56% enhancement, respectively, as the web height increased from 115 mm to 135 mm.

5.3.2. The Influence of Web Thickness

From Figure 19, it can be seen that the load-bearing capacity and initial stiffness of the SPSW both increased linearly with the increase in web thickness. As the web thickness increased from 6 mm to 10 mm, the lateral-resistant capacity of the structure was elevated by 10.40%, while the initial stiffness demonstrated an improvement of 5.61%. A comparison of the effects of web height and web thickness on the performance of the SGSW revealed that increasing the web height of the steel grid components enhanced the lateral-resistance capacity of the SGSW more effectively with the same increment in steel consumption.

5.3.3. The Influence of Flange Width

As shown in Figure 20, increasing the flange width effectively improved both the initial stiffness and lateral-resistance capacity of the SGSW. Specifically, when the flange width increased from 115 mm to 135 mm, the lateral-resistant capacity and initial stiffness of the structure rose by 10.46% and 9.66%, respectively. Compared to an increase in web height, increasing the flange width had a slightly greater enhancement effect on the structure’s lateral-resistant capacity. However, increasing the flange width required more steel consumption since the thickness of the flange was larger than that of the web.

5.3.4. The Influence of Flange Thickness

Increasing the flange thickness was an effective method to enlarge the cross-sectional area of the T-shaped steel grid components. Meanwhile, Figure 21 shows that the increase in flange thickness significantly improved the initial stiffness and lateral-resistant capacity of the SGSW. As the flange thickness increased from 7 mm to 13 mm, the lateral-resistant capacity showed an improvement of 35.45%, while the initial thickness grew by 30.91%.

Since only the sectional sizes of the T-shaped steel members were modified in Chapter 5.3, the variation in steel consumption among the different models was proportional to the change in sectional area; the proportionality coefficient is the total length of the steel grid components. Summarizing the above simulation results, increasing the web height to enlarge the sectional area by 120 mm² could enhance the lateral-bearing capacity by 8.22%, while increasing the web thickness to enlarge the sectional area by 364 mm² could improve the lateral-bearing capacity by 10.4%. And increasing the sectional area by 180 mm² through modifying the flange width led to a 10.46% improvement in lateral-resistant capacity, while increasing the sectional area by 500 mm², while modifying the flange thickness led to a 35.45% improvement. Therefore, compared with the effects of web height, web thickness and flange width mentioned above, increasing the flange thickness proved to be the most effective method for enhancing the lateral-resistance capacity and initial stiffness of the SGSW.

Increasing the thickness of flanges would also significantly increase the steel consumption. Therefore, a comprehensive consideration of steel consumption and the lateral-resistance capacity of the SGSW was essential to enhance structural efficiency while ensuring economic feasibility and reliability in practical engineering applications.

5.3.5. Comparison Between Simulation Results and Calculation Results

To verify the accuracy of the formula derived in Section 3, the results obtained by the formula were compared with the simulation results in

Table 9. The comparison of the formula calculation and the simulation results.

Parameter	Value	Simulation Value		Calculated Value		Error in K0 (%)	Error in Vf (%)
		Initial Stiffness K0 (kN/mm)	Yield Load Vf (kN)	Initial Stiffness K0′ (kN/mm)	Yield Load Vf′ (kN)
Web height /mm	115	180	1253	181	1285	0.60	2.60
	120	182	1283	183	1297	0.40	1.10
	125	185	1308	184	1308	0.40	0.00
	130	187	1334	186	1320	0.60	1.10
	135	190	1356	188	1331	1.30	1.80
Web thickness /mm	6	185	1308	184	1308	0.40	0.00
	7	188	1343	191	1356	1.60	1.00
	8	191	1376	198	1404	3.50	2.10
	9	194	1413	205	1452	5.40	2.80
	10	196	1444	211	1500	7.80	3.90
Flange height /mm	115	176	1243	176	1251	0.10	0.60
	120	181	1277	180	1280	0.40	0.20
	125	185	1308	184	1308	0.40	0.00
	130	189	1341	188	1337	0.40	0.30
	135	193	1373	192	1366	0.30	0.50
Flange thickness /mm	7	165	1134	162	1148	2.00	1.30
	8	176	1231	173	1228	1.70	0.20
	9	185	1308	184	1308	0.40	0.00
	11	202	1442	207	1468	2.40	1.80
	13	216	1536	229	1628	6.20	6.00

. The results calculated using the formula showed good agreement with the finite element analysis results, with an error within 8%. This indicated that the formula could accurately predict the lateral-resistant capacity and initial stiffness of the SGSW.

6. Conclusions and Prospects

This paper focuses on a new lateral-resistance system, SGSW. Firstly, the force mechanism of steel grid components with different frame stiffness was analyzed. The SGSW was then divided into three regions, and the deformations of the steel grid components in each region were analyzed individually. Next, based on the static equilibrium, the lateral-resistant capacity calculating method of the SGSW was established. Finally, a series of parametric analyses were conducted to determine the influence of the span-to-depth ratio, spacing of the steel grid components and cross-section size on the lateral-resistant capacity of the SGSW, and the reliability of the calculation formula was verified. The specific conclusions are as follows:

(1) The steel grid components located at different positions of the SGSW could meet the deformation compatibility condition. The theoretical formula for calculating the lateral-resistant capacity of the SGSW demonstrated good accuracy, and the error value between the theoretical formula and simulated results could be controlled within 8%.

(2) As the span-to-height ratio increased, both the lateral-resistant capacity and initial lateral stiffness of the SGSW showed significant improvement. Specifically, when the span-to-height ratio increased from 0.8 to 1.4, the lateral-resistance capacity and initial stiffness of the SGSW increased by 37.25% and 58.02%, respectively. However, increasing the spacing between the steel grid components from 550 mm to 750 mm resulted in a decrease of 10.72% in lateral-resistance capacity and 8.03% in initial lateral stiffness.

(3) Increasing the web and flange size of the T-shaped steel grid components effectively improved the lateral-resistant capacity and initial stiffness of the SGSW. Among these parameters, enlarging the flange proved to be the most effective method for enhancing the load-bearing capacity of the SGSW, although it also led to a significant increase in steel consumption. In actual engineering, it was essential to balance both steel consumption and the lateral-resistance capacity of the SGSW.

(4) During the derivation of the calculation formula in this paper, the steel beam and column were treated as rigid bodies, and the contribution of the steel frame was not considered. However, previous experimental results indicated that frame columns might undergo deformation when their flexural rigidity is insufficient to withstand the tensile or compressive forces exerted by the steel grid components. In practical applications, it is essential to avoid this situation to ensure that the steel grid components can fully develop plasticity as much as possible. Therefore, it is necessary to further specify requirements for the flexural stiffness of the edge members in the future.