Investigation of the ability of steel plate shear walls against designed cyclic loadings: Benchmarking and parametric study

2.1 Milestone study

Shear wall is used to withstand the building from lateral (earthquake) loads; therefore, cyclic loading is applied. Previous studies averaged based on experimental and analytical results in investigating the dynamic performance of SPSW. Many types of SPSWs have been studied. Emami et al. [5] researched the trapezoidal corrugated geometry. Then, they added layers to the shear wall with gypsum and fiber cement boards, as performed by Mohebbi et al. [11]. Cao et al. [12] modified its geometry by adding X-shaped reinforcement. For more details, see Table 1.

On the basis of research milestones in Table 1, Emami et al. [5] and Lu et al. [14] conducted a study by varying the geometry of the SPSW infill. Meanwhile, Wang et al. [17], Cao et al. [12], Mohebbi et al. [11], Zhang et al. [13], and Zhang et al. [15] focused on conducting research by adding reinforcement to SPSW. Research by Shi et al. [16] strengthens the SPSW column section. Wang et al. [18] conducted a study by adding a damper to the SPSW. Luo et al. [19] researched high-performance CFS materials for SPSW. Most of these studies only added stiffeners. Therefore, this research is carried out by updating the geometry shapes such as circular, cube, and perforated shapes, and infill plate material such as low-carbon steel (LCS), medium-carbon steel (MCS), and high-carbon steel (HCS) that has not reached the milestone to see how much influence the body has on its energy dissipation capability. In addition, the load factor and the mesh size used in this study will be varied, which has never been done in the research milestone to see the difference in the numerical results produced, so that the load factor setting and mesh size used can be used as a reference for future research.

2.2 Finite element analysis (FEA) SPSW

FEA in SPSW was used to analyze the behavior of SPSW when subjected to lateral loads. The SPSW was divided into small interconnected elements, and their behavior was analyzed individually using mathematical equations related to structural mechanics. The equations used were the momentum conservation and elasticity equations related to the SPSW structure. The equations are written in a matrix form, with each matrix element representing the contribution of a tiny component to the overall SPSW system. In this study, FEA was carried out using ABAQUS. One of the elasticity equations used was Hooke’s law. According to Hooke’s law, the relationship between the shear stress τ and the shear strain γ of the steel plate is expressed in Eq. (1) [4].

where G is the shear modulus of steel. Shear stress before yield is expressed in Eq. (2).

where t is the thickness of the infill plate and L is the width of the infill plate. Structural stiffness ( K e ) is expressed in Eq. (3).

2.3 Plate to frame interaction method

Trapezoidal vertical corrugated steel shear wall specimens were made using the plate frame interaction (PFI) method [19]. The PFI method first analyses the thin SPSW, which investigates the behavior of the frame and web plate separately. As a result, it can express a broader view of component interactions. Based on this method, a trilinear interaction diagram is obtained through the superposition principle after calculating and obtaining the shear load transfer diagram for the web and frame [20]. Ultimate strength vertical corrugated steel shear wall or V is obtained from Eq. (4) [5].

where F U is ultimate stress, α is the angle of inclination of the principal tensile stress from the vertical axis to the value 30 ° for these specimens, and h s is the height of the infill plate. Interactive shear buckling of the corrugated infill panel or τ cr is obtained from Eq. (5) [21].

where τ cr , l is local buckling of the corrugated shear panel when a flat subplate between vertical edges buckles and τ cr , G is global buckling of the corrugated shear panel. Then, limiting shear elastic displacement of a corrugated panel frame or U we is obtained from Eq. (6).

where U wcr is shear buckling displacement of the panel, U wpb is a shear displacement of the corrugated panel due to the configuration of the tension field, and σ ty is tension field stress corresponding to the panel yield obtained based on the von Mises yield criterion can be expressed in Eq. (7).

where σ u and σ v are the maximum and minimum principal stresses, respectively, and τ uv is the maximum shear stress value in the plane [22].

2.4 Functions and applications of shear walls

SPSW is a structural system of vertical steel plate infill panels connected to the building’s perimeter framing. SPSW is designed to withstand lateral loads such as wind and earthquakes and is usually used in high-rise buildings. The primary purpose of the SPSW is to transfer the lateral load from the top floor of the building to the foundation [23]. Steel plates in shear walls can flex and deform under load, dissipating energy and reducing the amount of force transmitted to the structural components of the building. This results in better seismic performance and less structural damage during earthquakes [24].

SPSW is also used to provide rigidity and stability to the lateral systems of a building, which can help prevent excessive deflection and drift. It can be especially important in buildings that are used for critical operations [25]. In addition to its structural benefits, SPSW can also offer architectural benefits. They can be used to create large open spaces with minimal internal columns or walls, increasing the functionality and flexibility of a building’s interior [26].

Overall, the application of SPSW is suitable for tall buildings that receive high lateral loads due to their location or function. This system has been proven effective in increasing seismic performance, reducing structural damage, and providing architectural benefits [28]. An example of a tall building that has used SPSW is the Tianjin Jinta Tower in China [29], and another example can be seen in Figure 1.

Figure 1

Details of the SPSW building and test specimen [27].

3.1 Validation of the research method

Validation used a research basis from the study by Emami et al. [5] who observed cyclic loading behavior on trapezoidal corrugated and unstiffened steel shear wall specimens. Research by Emami et al. [5] was carried out experimentally. The model is formed with a half scale, one floor, and has three forms of shear walls: unstiffened, trapezoidal vertical corrugated, and trapezoidal horizontal corrugated [5]. The series of loads applied is displacement control by increasing or decreasing the amplitude [8]. Therefore, the AC154 protocol was used to evaluate the cyclic behavior more logically [30]. The results are taken from the study by Emami et al. [5] as material for validation results from force–displacement hysteresis in the second specimen, namely, the trapezoidal vertical corrugated SPSW. For validation in this study, trapezoidal vertical corrugated SPSWs were modeled using the finite element model (FEM) with ABAQUS. Following are the modeling results and dimensions of the trapezoidal vertical corrugated SPSW (Figure 2).

Figure 2

Trapezoidal vertical corrugated SPSW: (a) Illustration of the experimental geometry [5], (b) the proposed design, (c) geometrical dimensions of the trapezoidal corrugated plate [5], and (d) 3D modeling of trapezoidal vertical corrugated SPSW (H1). All dimensions are in millimeters (mm).

3.2 Geometrical model

In this study, based on the research by Emami et al. [5], the geometry is half the scale of one floor. The trapezoidal vertical corrugated SPSW itself consists of several parts. The first part consists of a bottom beam using HE-B200 specifications with a length of 3,200 mm, which is given 18 stiffeners, and then at the top, there is a beam with HE-B140 specifications with a length of 2,000 mm with eight stiffeners. A column on each side of the infill has a length of 1,650 mm using HE-B160 specifications and is given four stiffeners. In addition, there are two triangular-shaped stiffeners for each column [5]. Finally, this study has an infill plate with nine variations (Table 2). For the shape of the variation on the plate, see Figure 3. To see the geometry and dimensions of the column, beam, and stiffener, refer to Figure 2(b).

Figure 3

Plate model for the shear walls: (a) H1, (b) H2, (c) H3, (d) V1, (e) V2, (f) V3, (g) D1, (h) D2, and (i) D3. All dimensions are given in millimeters (mm) [32–37].

3.3 Material properties

The material used in this research was steel. Steel has a Poisson ratio of 0.3. On the basis of the research by Emami et al. [5], the mechanical properties of the material (ST12) used were based on the ASTM E8M-04 coupon test. ASTM E8M-04 standard specifies the requirements for performing tensile tests on metallic materials as test pieces of various geometries. The specimen is subjected to a uniaxial tensile load until a fracture occurs. This standard provides details on the preparation of test specimens, test procedures, and calculation of the tensile properties of the tested material, such as yield strength, tensile strength, and elongation [31]. Only one type of infill plate will be varied, namely, code H1. Seven material variations will be various. The seven materials consist of three LCSs, two MCSs, and two HCSs. For more details on the materials used, see Table 3 for the material variation code, Table 4 for material properties for plates, Table 5 for material properties for columns, Table 6 for material properties for beam, and Table 7 for material for stiffener.

Q235 is a plain carbon steel used throughout China. It is also known as Q235A, Q235B, Q235C, and Q235D. Due to mild steel, it is used in production without heat treatment. Q denotes the yield point, and 235 represents the yield strength. This steel has good plasticity and weldability. As the thickness of the material increases, the yield value of Q235 decreases. Due to its moderate carbon content, the performance is comprehensive and sufficient. Q235 is also matched in strength, weldability, and plasticity. This steel is often used in engineering and construction [32].

Q355 steel is a low alloy, high-strength steel used in welded structures that support heavy stresses and loads. Q refers to the yield point, while 355 indicates the yield strength. Q355 is a newer Chinese steel grade designed to replace Q345. The material density is 7.85 g/cm³ and comes in three quality grades, including Q355B, Q355C, and Q355D. This steel has good mechanical properties and hot and cold processing. Q355 steel has excellent mechanical properties, great weldability, and sufficient corrosion resistance. This steel can fabricate and manufacture petroleum storage tanks, high-pressure vessels, boilers, ships, power plants, and many other high-load structural parts. Q355 is also widely used to make shipping, waste storage, weather, offshore, workshop, and toolboxes [33].

ST12 steel is hot-rolled steel that has been further processed. After hot rolled steel has cooled, it is rolled to achieve more precise dimensions and better surface quality. Cold-rolled steel plate is often used to describe various finishing processes – although, technically, “cold rolled” only applies to compressed sheets between rollers. ST12 is usually applied in construction, machine manufacturing, container manufacturing, shipbuilding, and bridge construction [38].

H HEA/HEB steel beams are the most commonly used type of steel profile. Beam, also known as “H” section, continental beam, or HEA/HEB, is available in several material grades, the most common of which are EN 10025, S275, and S355. The H section looks similar to I section, but the flanges are wider [39]. A515Gr70 is a steel grade commonly used in pressure vessel applications. It is a carbon-silicon steel plate with high tensile strength and good weldability. A515Gr70 meets the requirements of ASME and ASTM standards. It is commonly used to manufacture boilers and pressure vessels in the oil, gas, chemical, and power generation industries. The “A” in the designation refers to the fact that it is alloy steel, while the “515” indicates the minimum yield strength of the steel, which is 515 megapascals (MPa). “Gr70” indicates the steel grade, namely, Grade 70 [34].

AISI 1045 is an MCS commonly used in engineering and machining applications. It is also known as 1045 steel and is one of the most popular carbon steel grades due to its exceptional strength, toughness, and wear resistance. The designation “1045” indicates the chemical composition of the steel, which contains about 0.45% carbon and small amounts of other alloying elements such as manganese and sulfur. 1045 steel is often used in high-strength and durability applications, such as gears, shafts, axles, bolts, and studs. It can also be used for parts requiring surface hardening, such as machine and tool parts. 1045 steel can be heat treated to increase its strength and hardness and machined easily [35].

AISI 440SS (or simply 440 stainless steel) is a high-carbon martensitic stainless steel commonly used in applications requiring high strength, hardness, and corrosion resistance. It is part of the 400 series of stainless steels, known for their excellent corrosion resistance and magnetic properties. The “440” in the designation refers to the steel composition, which contains about 16–18% chromium, 0.75% carbon, and small amounts of other alloying elements such as manganese, silicon, and molybdenum. “SS” in designation means “stainless steel.”

440 stainless steel is often used in applications requiring high corrosion resistance, such as surgical and dental instruments, tableware, and bearings. It is also used in applications requiring high strength and hardness, such as valve parts and pump shafts. 440 stainless steel can be heat treated to increase its hardness and strength and is machined and weldable. However, due to its high carbon content, it is prone to brittleness and may require special care during fabrication [36].

AISI 1095 is a high-carbon steel known for its hardness, toughness, and edge retention. It is part of the 10xx series carbon steel, typically used for knives and other cutting tools. The “1095” in the designation refers to the steel composition, which contains about 0.95% carbon and small amounts of other alloying elements such as manganese and phosphorus. AISI 1095’s high carbon content provides excellent hardness and edge retention, making it a popular choice for knives and other cutting tools.

AISI 1095 is also used in various other applications, such as springs, saw blades, and washers. It can be heat treated to increase its strength and hardness and can also be machined and welded. However, due to its high carbon content, AISI 1095 is prone to brittleness and may require special care during fabrication. It is also more susceptible to corrosion than other stainless steel types. It may require a protective coating or regular maintenance to prevent rust and other forms of corrosion [37].

Isotropic hardening is used in infill plate and beam-column analysis. The plasticity model is based on the von Mises yield surface and the associated plastic flow theory [40,41]. The associated flow rule for plasticity can be defined in Eq. (10).

where ε ̇ is plastic strain increment tensor and ε ̇ pl is the equivalent plastic strain rate. PEEQ is the equivalent plastic strain, where ε ̇ pl | 0 is the initial equivalent plastic strain rate [42].

Figure 4

Mechanical properties of H1 SPSW (ST12 plate).

3.4 Initial imperfection

The thickness of the steel plate in the SPSW structure is small, and the corresponding out-of-plane stiffness is also tiny. Therefore, in manufacturing, transporting, and assembling, the initial geometric imperfections in the steel plate are unavoidable [4]. As a result, it is critical in simulation to add initial imperfections to SPSW to approximate experimental results. To account for the initial imperfection of the infill plate, the combined mode shape is considered in the SPSW specimen [41]. Buckling analysis is performed on the specimen using the buckle step in ABAQUS, with geometry in Figure 2(b), and ST12 is used as material (see Figure 4). Then, the result of the first buckling shape mode with eigenvalue is used in the FE model using KEYWORD commands in the ABAQUS application [43]. The magnitude of the imperfection was taken as 1/1,000 of the height of the SPSW [4]. The results before and after applied by initial imperfection are shown in Figure 5.

Figure 5

(a) Before and (b) after applied by initial imperfection.

3.5 FE setting

The FE method is a suitable numerical technique for investigating the global behavior of steel and concrete structures [44]. This study simulated all geometric shapes using the FEM with ABAQUS. The simulation results used as an analysis in this study were hysteresis behavior. In FE modeling, welded joints, fish plates, and bolts that connect the infill plate to the beam and column were ignored. The size of the mesh used varied. The total number of mesh variations used was ten. More details are presented in Table 8. The first boundary condition was applied to the bottom of the specimen, and all degrees of freedom were fixed. The second boundary condition was applied to the top using horizontal dynamic displacement with the amplitude in Figure 6.

Figure 6

(a) Boundary condition of the specimen and (b) applied amplitude in this study.

The load factor applied in the boundary condition of cyclic loading on the specimen was also varied. Like the mesh variation, the load factor varied only in the SPSW specimen with code H1. The steel material used was ST12 with mechanical properties, as shown in Table 4. The material properties of the ST12 material are shown in Figure 4. There were nine variations of the load factor used. More details are presented in Table 9.

4.1 Mesh convergence

The mesh convergence of the buckling simulation results (Figure 7(a)) showed that the mesh was stable in mesh element 129,382 with the first buckling load factor value of 2.9503. The more the mesh elements produced, the more convergent the value of the first buckling load factor would be. In mesh element 2,823, the value of the first buckling load factor was still high at 5.6164. This value dropped dramatically as the number of mesh elements increased.

Figure 7

(a) The first buckling load factor buckling with element mesh and (b) stress static general with element mesh.

4.2 Validation

Judging from the PEEQ contour (Figure 8(b)), the most considerable strain occurred in the infill plate. Compared with the reference contour (Figure 8(a)), the damage on the infill plate was similar. There was a slight difference at the bottom of the column where in the simulation results, there was more deformation. If observed from the hysteresis phenomenon (Figure 9), the hysteresis generated by the simulation had a more excellent energy dissipation than the experimental results. However, the results obtained were pretty close to the experimental results. The maximum shear force achieved in the experimental results was 500 kN. Meanwhile, the maximum shear force in the simulation results was 504.52 kN.

Figure 8

(a) Contour of reference study by Emami et al. [5] and (b) contour of the H1 specimen (PEEQ).

Figure 9

Hysteresis force–displacement pattern.

Judging from Tables 10 and 11, the results from FEM and previous experiments from the stud by Emami et al. [5] are not much different. The specimen’s displacement had an average difference of 1.41%. Meanwhile, the absorbable force had an average difference of 4.57%. These two factors had an average difference of less than 5%. Only a few minor results had differences above 5%, when displacement from Emami et al. [5] was 89.87 mm; and when forced from Emami et al. [5] reached 468.283, 461.02, and 445.495 kN. The maximum absorbed force value in the experiment by Emami et al. [5] was 442.863 kN, while the FEM was 443.91 kN and the difference was 0.24%. The maximum displacement value in the experiment by Emami et al. [5] was 48.649 mm, while the FEM performed was 48.471 mm and had a difference of 0.37%. Then, this FEM method can be used because the FEM solution is generally considered acceptable if the error ranges from 5 to 10% of the actual solution [45–59].

On the displacement contour (Figure 10(a)), it was known that the most significant displacement also occurred in the infill plate section. Its position was opposite the cross with the location of the greatest strain. There was a reasonably large displacement even in the closest location to the largest strain. It happened because when the displacement occurred, the other parts experienced withdrawal, so there was a strain in that location. Displacement also occurred in the beam and column sections on the left because it was in the direction of the applied load. In the stress contour, Figure 10(b) shows the contour when the load had not occurred so that no stress value appeared. In Figure 10(c), there was an increase in stress that occurred in the infill plate area. When loading continued, it can be seen from Figure 10(d) that the highest stress occurred in the column and stiffener triangles. It happened because when the alternating loading took place, the area experienced greater fatigue compared to other locations, and it was evident that there was a large deformation in the area.

Figure 10

(a) Displacement contour, (b) stress step 0 contour, (c) stress step 285 contour, and (d) stress step 1,140 contour.

4.3 Geometry variations

In the geometric variations, there were a total of nine geometric shapes. The first three geometries in Figure 11(a) are H1, H2, and H3. H1 had the best form of hysteresis force–displacement graphics among other geometric shapes, so the H1 specimen had the shape that could dissipate the best energy. Since this geometric shape was chosen to be varied from the material, load factor, and mesh, the H2 specimen can only dissipate energy up to a displacement of 50 mm. In comparison, the smaller H3 specimen can only dissipate energy up to a displacement of 25 mm.

Figure 11

Comparison of the force–displacement hysteresis: (a) specimens H1, H2, and H3; (b) specimen V1, V2, and V3; and (c) specimen D1, D2, and D3.

Geometries V1, V2, and V3 in Figure 11(b) became geometries with fairly good energy dissipation when compared to horizontal and diagonal geometries. For the V1 specimen, it can dissipate energy so that the displacement reaches approximately 20 mm. As for the V2 specimen, it can dissipate energy better up to a displacement of approximately 40 mm. The V3 specimen dissipated energy better than V1 and V2 specimens when the displacement reached approximately 50 mm. For geometries D1, D2, and D3 (Figure 11(c)), geometries with the worst energy dissipation when compared to horizontal and vertical geometries, specimen D1 was the best at dissipating energy with a displacement of up to 38 mm. In comparison, specimen D2 can dissipate energy up to a displacement of 30 mm, and specimen D3 can dissipate energy up to 25 mm displacement. Following are the results of the contours of stress, displacement, and strain for the simulation of geometric variations.

When viewed from the shape of the contour, H1 occurred the highest stress at the bottom with triangular reinforcement and at the ends of the upper column. The H1 stress contour is shown in Figure 12(a). As for the displacement itself (Figure 12(b)), it was evenly distributed throughout the infill section, and the highest strain (Figure 12(c)) was found in the infill section and was divided at four location points.

Figure 12

Calculation results: (a) stress H1 specimen; (b) displacement H1 specimen; and (c) strain H1 specimen.

When viewed from the shape of the contour, H2 occurred with the highest stress (Figure 13(a)) at the ends of the triangular reinforcement and the lots of the upper column. The displacement (Figure 13(b)) was evenly distributed throughout the infill section but had the highest point in the middle indentation. The highest strain was in the infill section and was divided into three location points, as shown in Figure 13(c).

Figure 13

Calculation results: (a) stress H2 specimen; (b) displacement H2 specimen; and (c) strain H2 specimen.

When viewed from the shape of the contour, H3 (Figure 14(a)) occurred with the highest stress at the ends of the triangular reinforcement and the lots of the upper column. The displacement (Figure 14(b)) was divided into the upper infill beam and the right and left columns. The highest displacement was in the infill indentation in the middle, and the highest strain (Figure 14(c)) was in the infill section, which was not far from the highest displacement.

Figure 14

Calculation results: (a) stress H3 specimen, (b) displacement H3 specimen, and (c) strain H3 specimen.

The stress contour of the V1 specimen (Figure 15(a)) looked more even at the infill and the bottom of the column. The highest stress occurred in the infill section. The highest displacement (Figure 15(b)) was divided into the infill section, spread over eight areas. The highest strain (Figure 15(c)) for the V1 specimen was located in the infill section, similar to the most elevated displacement location.

Figure 15

Calculation results: (a) stress V1 specimen, (b) displacement V1 specimen, and (c) strain V1 specimen.

The stress contour of the V2 specimen (Figure 16(a)) looked more even on the infill. However, the highest stress location occurred at the top end of the column. The highest displacement from the contour in Figure 16(b) was divided into the infill, right and left columns, and the top beam. However, the highest displacement lied in the infill and was in the indentation. The highest strain for the V1 specimen (Figure 16(c)) was located in the infill section close to the most elevated displacement location.

Figure 16

Calculation results: (a) stress V2 specimen, (b) displacement V2 specimen, and (c) strain V2 specimen.

Looking at the stress contour of the V3 specimen (Figure 17(a)), it looked more even on the infill. However, the highest stress locations occurred at the top of the column end and the tip of the triangular reinforcement. The highest displacement from the contour in Figure 17(b) was divided into the infill, right and left columns, and the top beam. However, the highest displacement lied in the infill and was in the indentation. The highest strain for the V3 specimen was located in the infill section close to the most elevated displacement location, as shown in Figure 17(c).

Figure 17

Calculation results: (a) stress V3 specimen, (b) displacement V3 specimen, and (c) strain V3 specimen.

When viewed from the D1 contour (Figure 18), contour Figure 18(a) shows the highest stress locations occurred at the top end of the column and the tip of the triangular reinforcement. Meanwhile, contour Figure 18(b) shows the highest displacement in the infill section. They were located in the top hole. The strain values were spread over the infill area and the triangular reinforcement, as shown in Figure 18(c).

Figure 18

Calculation results: (a) stress D1 specimen, (b) displacement D1 specimen, and (c) strain D1 specimen.

On the D2 contour, the stress contour is shown in Figure 19(a). The highest stress locations occurred at the ends of the upper columns and the ends of the triangular reinforcement. The difference was with the D1 contour; the highest displacement in the D2 specimen was scattered at several points but still in the area close to the hole contour displacement in D2, shown in Figure 19(b). Strain values are shown in Figure 19(c) that were spread over the infill area, with the highest values near the top hole.

Figure 19

Calculation results: (a) stress D2 specimen, (b) displacement D2 specimen, and (c) strain D2 specimen.

On the contour of the D3 specimen, the stress contour in Figure 20(a) shows that stress occurred evenly in the infill section and had the highest value in the upper column area and the triangular reinforcement tip. What was unique about this geometry was that the highest displacement (Figure 20(b)) occurred at the ends of the right and left ovals, which were the areas where the strain (Figure 20(c)) was the highest because there was a large enough shift in the infill so that the strain occurred there. Overall, in Figures 11–19, the stress contours on the geometric variation specimens were similar in the highest stress location, namely, at the top end of the column and the tip of the triangle. However, there were differences in the V1 specimen (Figure 14(a)). The stress contour of the V1 specimen looked more even at the infill. Meanwhile, for displacement contours on specimen geometry variations, all specimens experienced the largest displacement in the infill section. For the strains that occurred, the strain contours that occurred on the specimens of geometric variations all experienced strain on the infill section, especially at the indentations or the ends of the holes for the D1, D2, and D3 geometry variations.

Figure 20

Calculation results: (a) stress D3 specimen, (b) displacement D3 specimen, and (c) strain D3 specimen.

4.4 Mesh variation

In the mesh variation, there were a total of ten meshes used. We started from the size used for 25 mm to increase in multiples of 10 to reach a size of 115 mm. For mesh 25 and mesh 35 (Figure 21(a)), there was no significant difference in value. Judging from the shape of the contours also tended to be similar. Only the location of the points on the graph was different, likewise, for mesh sizes of 45–105 mm (Figure 21(b)–(e)).

Figure 21

Comparison of the force–displacement hysteresis: (a) M25, M35; (b) M45, M55; (c) M65, M75; (d) M85, M95; and (e) M105, M115.

The results looked significantly different when the 115 mm mesh size was used (Figure 21(e)). The highest shear force that can be dissipated in mesh 105 was close to 400 kN. Meanwhile, the highest shear force can be dissipated when mesh 115 reaches close to 600 kN. The difference in this value had gained 33.3%, where this difference figure can no longer be considered rational.

According to the existing contour, for mesh sizes 25 (Figure A1), mesh size 35 (Figure A2), mesh size 45 (Figure A3), mesh size 55 (Figure A4), mesh size 65 (Figure A5), mesh size 75 (Figure A6), mesh size 85 (Figure A7), mesh size 95 (Figure A8), and mesh size 105 (Figure A9), the shape and location of the distribution of stress, strain, and displacement were not much. The difference was striking, on average, only in the displacement and strain contours. The difference occurred at the points of the highest displacement and strain locations. However, overall the largest displacement location was found in infill because infill dissipates energy so that large movements occurred. Because the largest displacement occurred in the infill, the highest strain also occurred. It happened because when a large displacement occurred in several locations, the opposite position will experience a significant strain due to being attracted by the area that experienced the largest displacement. For the M115 contour (Figure A10), it was not much different when compared to other mesh sizes. The difference was striking because the top column, which experienced the highest stress, had a broader area than the various mesh sizes. For detail, contours influenced by mesh are presented in Appendix A.

4.5 Load factor variation

In the variation of the load factor, there were a total of nine that were varied. The multiplier of the load factor that was applied was increased by 0.5 from the previous load factor. The geometry used was H1, and the mesh size used was M25. As shown in Figure 22, LF1.5–LF5 in one round, the displacement value adjusted to the applied load factor. It happened because the load factor represented the fraction of the load applied in each substep.

Figure 22

Comparison of the force–displacement hysteresis: (a) LF1, LF1.5, LF; (b) LF2.5, LF3, LF3.5; and (c) LF4, LF4.5, LF5.

By determining the LF2, the load that occurred was doubled in each substep compared to the load factor 1. Likewise with the other load factor values, in this analysis, there was no variation in the load factor that had completed the simulation due to the inability of the computing hardware. Observed from the contours (see Appendix B), LF1 experienced the highest stress (Figure A11(a)) on the upper column and the triangular reinforcement. However, this specimen experienced displacement (Figure A11(b)) centered on the infill displacement outside the infill arch. The strain (Figure A11(c)) on this specimen occurred in the infill section, precisely at the outer end of the infill arch between the highest displacements. It happened because when the highest displacement occurred, the middle part of the infill experienced strain. There was only a slight difference in the contour of the LF1.5 specimen (Figure A12). The location of the highest stress was the same as LF1 (Figure A12(a)), with a smaller distribution of the most increased stress. The displacement (Figure A12(b)) that occurred touched the upper beam with a moderate value. Whereas the strain contour in the LF1.5 (Figure A12(c)) indicated the same highest value but with a smaller distribution. On the contour of the LF2 specimen (Figure A13), there was no significant difference with LF1, whereas for LF2.5 (Figure A14), LF3(Figure A15), LF 4.5 (Figure A18), and LF5(Figure A19), the distribution of stress, displacement, and strain was not much different from the LF1.5 contour. The LF 4 (Figure A16) and LF 4.5 (Figure A17) contours experienced stress and strain similar to LF 1.5, but there was a slight difference in the displacements. The location of the displacements that occurred in the upper beam had a relatively low value. For detail, contours influenced by load factor are presented in Appendix B.

4.6 Material variation

In the material variation, there were a total of seven variations. The seven existing materials were varied only in infill to see which material was most suitable for dissipating earthquake energy. The material used in the study by Emami et al. [5] was used in the LCS 3 specimen (Figure 23(a)). If we look at it as a whole, the HCS material (Figure 23(c)) can accept loads up to close to 1,000 kN. Although it was an LCS material that touched up to 1,000 kN more, it stabilized at around 500 kN. Thus, HCS had an excellent ability to dissipate energy compared to other materials. It was appropriate because HCS has higher strength and hardness than LCS and MCS (Figure 23(b)). It makes them more resistant to wear and tear and more suitable for applications requiring high strength and rigidity.

Figure 23

Comparison of the force–displacement hysteresis: (a) LCS1, LCS2, LCS3; (b) MCS1, MCS2; and (c) HCS1, HCS2.

However, HCS is more brittle than LCS, which means it is more prone to fracture if subjected to large deformations. Then the suitable material again depends on the design requirements and the building itself. LCS is commonly used because of its good ductility, weldability, affordability, and corrosion resistance, which are essential for SPSW. However, HCS is more suitable for specific applications requiring high strength and rigidity.

Judging from the contours (Appendix C), the highest stress LCS material (as displayed in Figures A20(c), A21(c), and A22(c)) was spread at the same point, namely, at the top of the column and the triangular reinforcement. For the highest displacement of the LCS material tested (Figures A20(d), A21(d), and A22(d)), the distribution points were similar at the top of the circular section, but the peaks were not always in the same place. For the highest strain of LCS material (Figures A20(e), A21(e), and A22(e)) occurred between the peaks of the highest displacement distribution. Because at the location of the highest displacement, no strain occurred, and this was because the strain occurred at the base of the displacement. The MCS material was slightly different. MCS1 experienced the most increased stress on the upper column, triangular reinforcement, and region touched the infill (Figure A23(c)), while the MCS2 specimen only experienced the highest stress on the infill (Figure A24(c)). The highest displacement occurred similarly in the infill section, but the difference was that if MCS1 (Figure A23(d)) occurred on the sides of the infill, while for MCS2 (Figure A34(d)), it was in the middle of the infill. The highest strain in the MCS material (as displayed in Figures A23(e) and A24(e)) occurred in the middle of the infill, the same as the LCS. The HCS material experienced the highest stress, displacement, and strain in the infill section (Figures A25 and A26). It was because only the infill uses the HCS material, so the highest stress was experienced on the infill. For detail, contours influenced by the material are presented in Appendix C.