Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Comprehensive Study on the Effect of Regular and Staggered Openings on the Seismic Performance of Shear Walls

A Comprehensive Study on the Effect of Regular and Staggered Openings on the Seismic Performance... buildings Article A Comprehensive Study on the Effect of Regular and Staggered Openings on the Seismic Performance of Shear Walls 1 , 2 , 2 3 Ahmed Saeed * , Hadee Mohammed Najm * , Amer Hassan , Shaker Qaidi , 4 5 Mohanad Muayad Sabri Sabri and Nuha S. Mashaan Department of Civil Engineering, Southeast University, Nanjing 211189, China Department of Civil Engineering, Zakir Husain Engineering College, Aligarh Muslim University, Aligarh 202002, India Department of Civil Engineering, College of Engineering, University of Duhok, Duhok 42001, Kurdistan Region, Iraq Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia Faculty of Science and Engineering, School of Civil and Mechanical Engineering, Curtin University, Bentley, WA 6102, Australia * Correspondence: alanessy2015@gmail.com (A.S.); gk4071@myamu.ac.in (H.M.N.) Abstract: Shear walls have high strength and stiffness, which could be used at the same time to resist large horizontal loads and weight loads, making them pretty beneficial in several structural engineering applications. The shear walls could be included with openings, such as doors and windows, for relevant functional requirements. In the current study, a building of G + 13 stories with RC shear walls with and without openings has been investigated using ETABS Software. The seismic analysis is carried out for the determination of parameters like shear forces, drift, base shear, and story displacement for numerous models. The regular and staggered openings of the shear wall have been considered variables in the models. The dynamic analysis is carried out with the help of ETABS software. It has been observed that shear walls without openings models perform better Citation: Saeed, A.; Najm, H.M.; than other models, and this is in agreement with the previous studies published in this area. This Hassan, A.; Qaidi, S.; Sabri, M.M.S.; investigation also shows that the seismic behaviour of the shear wall with regular openings provides Mashaan, N.S. A Comprehensive a close result to the shear wall with staggered openings. At the roof, the displacement of the model Study on the Effect of Regular and with regular openings was 38.99 mm and approximately 39.163 mm for the model with staggered Staggered Openings on the Seismic Performance of Shear Walls. Buildings openings. However, the model without a shear wall experienced a displacement of about 56 mm at 2022, 12, 1293. https://doi.org/ the roof. Generally, it can be concluded that the openings have a substantial effect on the seismic 10.3390/buildings12091293 behaviour of the shear wall, and that should be taken into consideration during the construction design. However, the type of opening (regular or staggered) has a slight effect on the behaviour of Academic Editor: Arslan Akbar shear walls. Received: 20 July 2022 Accepted: 17 August 2022 Keywords: seismic behaviour; opening shear wall; story drift; displacement; base shear Published: 23 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- 1. Introduction iations. Reinforced concrete (RC) buildings considerably resist horizontal and vertical loading. Wind and seismic loads are the most common loads that shear walls are designed to carry [1]. The shear walls are the best and simplest method to sustain these lateral forces as they provide the required strength against seismic forces [2–4]. Shear walls are the components Copyright: © 2022 by the authors. in the external form of a box that provide lateral support to the building. The shear wall Licensee MDPI, Basel, Switzerland. provides strength and stiffness to the building in the lateral direction [5–8]. Since shear This article is an open access article walls carry massive lateral forces, the overturn effects on them are significantly important distributed under the terms and and must be considered in the structural design. Shear walls in buildings are preferred conditions of the Creative Commons to be symmetrical in order to mitigate the negative effects of twists [9–11]. They might be Attribution (CC BY) license (https:// placed symmetrically along with one or both directions in the plan. Shear walls are more creativecommons.org/licenses/by/ effective when provided on the exterior perimeter of the building; therefore, this layout 4.0/). Buildings 2022, 12, 1293. https://doi.org/10.3390/buildings12091293 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 1293 2 of 21 will increase the resistance of the structure against twisting [12]. The shear walls behaviour depends upon the material used, wall length, wall thickness, wall position, and building frame. RC shear walls are used in the design of multi-story buildings located in seismically vulnerable areas because of their rigidity, bearing capacity, and high ductility [13–15]. Obviously, an opening in a shear wall positioned along with in-plane loading is more critical than an opening in a shear wall located along without-of-plane loading because there is a considerable change in displacement noticed after having an opening in a shear wall positioned along with in-plane loading [16]. Shear walls are considered an essential element in the construction of buildings be- cause of their capacity to resist lateral loads such as earthquakes and wind loads. Therefore, research studies have been carried out to understand the structural behaviour of shear walls under different load cases and conditions. Zhang and Wang [17] investigated the seismic performance of prefabricated reinforced masonry shear walls with vertical joint connections, while Dang-Vu et al. [18] studied the seismic fragility assessment of columns in a piloti-type building retrofitted with additional shear walls. Coccia et al. [19] reported the behaviour of masonry walls retrofitted with vertical FRP rebars, and their study showed that the conventional seismic retrofitting techniques on masonry walls influence the seis- mic performance of the element, which is typically modified in an out-of-plane bending behaviour. Further, the study of Jeon et al. [20] investigated the seismic fragility of ordinary reinforced concrete shear walls with coupling beams, and their study showed that high-rise ordinary reinforced concrete shear walls designed using seven pairs of ground motion components and a shear force amplification factor  1.2 were adequate to satisfy the criteria on collapse probability and the collapse margin ratio prescribed in FEMA P695. Reinforced concrete structures with L-shaped walls provide numerous benefits for architects that permit them to design architectures with larger open areas and a lot of versatility [21–23]. However, a lot of experimental tests and numerical models should be done for L-shaped shear walls to ensure compliance with the safety provisions obligatory by the various code standards. What is more, given the necessities of deformability and resistance, L-shaped concrete shear walls are used in multi-story buildings because they possess a high capability of resisting lateral loads and may expend an excellent amount of seismic energy if they are properly designed [24–27]. Openings in shear walls may be required because of municipality or remodeling considerations, similar to elevators, windows, doors, and the placement of staircases [28]. Providing openings in the shear walls decreases the total structural capacity and integrity of the wall, in addition to stress condensation around the openings [27]. The main aim of this study is as follows: to understand the behaviour of staggered and regular openings and to analyze the effectiveness of staggered openings to seismic load when different loads are used. 2. Model Description A 14-story RC structure with shear wall elements and the 14 stories were selected in the model to minimize the analysis time in the software, and the behaviour of shear walls with the openings was the aim of this study and not the effect of the building’s length, shape “L” of RC shear wall without opening, with a vertical and staggered opening in Seismic Zone V, has been considered in this study. Tables 1–3 illustrate the model data, applied loads on the structure, and seismic input data. The plan and geometry of the models are shown in Figures 1–4. Compared to the area of the wall in that story, the shear wall has a 5% opening. Buildings 2022, 12, 1293 3 of 21 Table 1. Models data. Number of Stories 14 Column Size (600  600) mm Beam Size (300  600) mm Slab Depth 150 mm Shear Wall Thickness 300 mm Size of opening (2  1.5) m Story Height 3.5 m Support Fixed Concrete Grade M25 Steel Grade Fe 500 Table 2. Loads. Unit Weight of Concrete 25 kN/m Dead load 3.75 kN/m Live load 3 kN/m Beam Load 11 kN/m Table 3. Seismic data. Seismic Zone V Zone factor (Z) 0.36 Soil Type Medium Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Damping Ratio 5% Response Reduction factor (R) 5 Importance factor (I) 1 Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Buildings 2022, 12, 1293 4 of 21 Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Response spectrum function and time history function (El Centro 1940) have been used in this study for seismic analysis. A response spectrum is a plot of the maximum response amplitude (displacement, velocity or acceleration) versus time period of many linear single degree of freedom oscillators to a give component of ground motion as shown in Figure 5. The resulting plot can be used to choose the response of any linear SDOF oscillator, given its natural time period of oscillation. One such use is in evaluating the peak response of structures to ground motions. The first data listed from an earthquake record are usually the peak ground acceleration (PGA), which expresses the tip of the maximum spike of the acceleration ground motion. Buildings 2022, 12, x FOR PEER REVIEW 4 of 21 Buildings 2022, 12, x FOR PEER REVIEW 4 of 21 Buildings 2022, 12, 1293 5 of 21 Figure 4. The geometry of the structure and 3D structure shear walls with staggered openings. Response spectrum function and time history function (El Centro 1940) have been used in this study for seismic analysis. A response spectrum is a plot of the maximum response amplitude (displacement, velocity or acceleration) versus time period of many linear single degree of freedom oscillators to a give component of ground motion as shown in Figure 5. The resulting plot can be used to choose the response of any linear SDOF oscillator, given its natural time period of oscillation. One such use is in evaluating the peak response of structures to ground motions. The first data listed from an earth- quake record are usually the peak ground acceleration (PGA), which expresses the tip of Fig Figure ure 44. . T The he g geometry eometry of of theth str e uctur struc e tand ure3D anstr d uctur 3D st ershear ucture walls she with ar w stagger alls w ed ith openings. staggered openings. the maximum spike of the acceleration ground motion. Response spectrum function and time history function (El Centro 1940) have been used in this study for seismic analysis. A response spectrum is a plot of the maximum response amplitude (displacement, velocity or acceleration) versus time period of many linear single degree of freedom oscillators to a give component of ground motion as shown in Figure 5. The resulting plot can be used to choose the response of any linear SDOF oscillator, given its natural time period of oscillation. One such use is in evaluating the peak response of structures to ground motions. The first data listed from an earth- quake record are usually the peak ground acceleration (PGA), which expresses the tip of the maximum spike of the acceleration ground motion. Figure 5. Response spectrum function definition. Figure 5. Response spectrum function definition. ETABS Software handles the initial conditions of a time function differently for linear ETABS Software handles the initial conditions of a time function differently for linear and nonlinear time-history load cases. Linear cases always start from zero, thus the and nonlinear time-history load cases. Linear cases always start from zero, thus the corre- corresponding time function must also start from zero and nonlinear cases may either start sponding time function must also start from zero and nonlinear cases may either start from zero or may continue from a previous case. When starting from zero, the time function from zero or may continue from a previous case. When starting from zero, the time func- is simply defined to start with a zero value. When analysis continues from a previous tion is simply defined to start with a zero value. When analysis continues from a previous case, it is supposed that the time function also continues relative to its starting value. A case, it is supposed that the time function also continues relative to its starting value. A long record may be broken into multiple sequential analyses which use a single function long record may be broken into multiple sequential analyses which use a single function with arrival times. This prevents the need to create multiple modified functions. The time history function used in this study is shown in Figure 6. Figure 5. Response spectrum function definition. ETABS Software handles the initial conditions of a time function differently for linear and nonlinear time-history load cases. Linear cases always start from zero, thus the corre- sponding time function must also start from zero and nonlinear cases may either start from zero or may continue from a previous case. When starting from zero, the time func- tion is simply defined to start with a zero value. When analysis continues from a previous case, it is supposed that the time function also continues relative to its starting value. A long record may be broken into multiple sequential analyses which use a single function Buildings 2022, 12, x FOR PEER REVIEW 5 of 21 Buildings 2022, 12, 1293 6 of 21 with arrival times. This prevents the need to create multiple modified functions. The time history function used in this study is shown in Figure 6. Figure 6. Time history function definition. Figure 6. Time history function definition. This study was conducted on a regular plan structure with shear walls containing This study was conducted on a regular plan structure with shear walls containing vertical and staggered openings. The buildings are modelled with a floor area of 690 m vertical and staggered openings. The buildings are modelled with a floor area of 690 m (30 m  23 m) with 7 bays along a 30 m span and 5 bays along a 23 m span. (30 m × 23 m) with 7 bays along a 30 m span and 5 bays along a 23 m span. 3. Modeling and Analysis Table 1. Models data. Four models have been considered in this study. The first model contains a building without shear walls (Figure 1); the second model characterizes a building with shear Number of Stories 14 walls without openings (Figure 2); the third model includes shear walls with vertical Column Size ˑ (600 × 600) mm openings (Figure 3). However, the fourth model includes shear walls with staggered Beam Size ˑ (300 × 600) mm openings (Figure 4). Slab Depth ˑ 150 mm 4. Results & Discussion Shear Wall Thickness ˑ 300 mm 4.1. Story Displacement Size of opening ˑ (2 × 1.5) m Tables 4 and 5 and Figures 7 and 8 demonstrate the maximum displacement in the Story Height 3.5 m case of equivalent static analysis (ESA) (EX&EY). On the top floor, the results show that the Support Fixed building without shear walls produced about 53.089 mm when compared to the building Concrete Grade ˑ M25 with shear walls produced 37.212 mm, i.e., a 30% reduction in the X-direction. It is observed Steel Grade ˑ Fe 500 that the story displacement of the vertical opening at the roof is approximately 38.032 mm and 38.173 mm for staggered openings, respectively. Table Sim 2.i lLo arla yd , i s. n the Y-direction, on the top floor, the results show that the building without shear walls produced 56 mm, while the building with shear walls produced 38.125 mm, a Unit Weight of Concrete 25 kN/m 32% difference. The displacement story of the vertical opening at the roof was also discovered to be 38.99 mm for sDea taggd er e lo da o d p enings and 39.136 mm for unstaggered 3.o 7p 5e kN/ ningm s. T he story displacement in the case of response spectrum analysis (RSA) is shown in Tables 6 and 7 and Live load 3 kN/m Figures 9 and 10. Results show that the building without shear walls produced about 42.006 mm Beam Load 11 kN/m while the building with shear walls produced 28.938 mm, i.e., a 31% decline in the X-direction and a 33% decline in the Y-direction. The displacement story of the vertical opening at the roof is 29.283 mm for staggered openings in the X-direction and 29.434 mm for vertical and staggered openings in the Y-direction, respectively. Tables 8 and 9 and Figures 11 and 12 demonstrate the story displacement in the case of time history analysis (THA). The results appear to show Buildings 2022, 12, 1293 7 of 21 that the building without shear walls produced 45.727 mm, while the building with shear walls produced about 34.72 mm, i.e., a 24% reduction. In the X-direction, the displacement story of the vertical opening at the roof is 28.74 mm for staggered openings and 28.7 mm for unstaggered openings, 32.809 mm and 32.34 mm for vertical and staggered openings in the Y-direction respectively. Table 4. Comparison of the story displacements, ESA and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 53.089 37.212 38.032 38.173 Story 13 51.742 34.488 35.436 35.552 Story 12 49.685 31.614 32.628 32.724 Story 11 46.954 28.609 29.658 29.739 Story 10 43.649 25.48 26.538 26.603 Story 9 39.87 22.259 23.3 23.348 Story 8 35.715 18.987 19.991 20.022 Story 7 31.27 15.723 16.668 16.679 Story 6 26.614 12.532 13.398 13.392 Story 5 21.817 9.489 10.258 10.232 Story 4 16.941 6.681 7.332 7.294 Story 3 12.046 4.205 4.717 4.672 Story 2 7.216 2.171 2.523 2.488 Story 1 2.725 0.707 0.876 0.865 Table 5. Comparison of the story displacements, ESA, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 56.000 38.125 38.99 39.163 Story 13 54.475 35.291 36.281 36.423 Story 12 52.221 32.311 33.364 33.482 Story 11 49.275 29.203 30.287 30.389 Story 10 45.738 25.977 27.065 27.146 Story 9 41.715 22.663 23.731 23.796 Story 8 37.307 19.307 20.332 20.373 Story 7 32.606 15.965 16.927 16.952 Story 6 27.695 12.705 13.585 13.583 Story 5 22.648 9.604 10.382 10.366 Story 4 17.532 6.749 7.405 7.37 Story 3 12.411 4.237 4.752 4.716 Story 2 7.381 2.181 2.534 2.498 Story 1 2.749 0.707 0.875 0.873 The results show that buildings without shear walls have higher story displacement in comparison with other models. The shear wall with staggered openings experiences a higher displacement than vertical openings and shear walls without openings. A shear wall without openings reveals improved performance compared to shear walls with vertical and staggered openings. The same findings have been found in the published literature by Marius [29]. Overall, it can be concluded that the presences of shear walls in the buildings significantly improve the seismic response of the buildings regardless of the openings in that shear wall. Buildings 2022, 12, x FOR PEER REVIEW 7 of 21 Buildings 2022, 12, x FOR PEER REVIEW 7 of 21 Story 7 32.606 15.965 16.927 16.952 Story 7 32.606 15.965 16.927 16.952 Story 6 27.695 12.705 13.585 13.583 Story 6 27.695 12.705 13.585 13.583 Story 5 22.648 9.604 10.382 10.366 Story 5 22.648 9.604 10.382 10.366 Story 4 17.532 6.749 7.405 7.37 Story 4 17.532 6.749 7.405 7.37 Story 3 12.411 4.237 4.752 4.716 Story 3 12.411 4.237 4.752 4.716 Buildings 2022, 12, 1293 8 of 21 Story 2 7.381 2.181 2.534 2.498 Story 2 7.381 2.181 2.534 2.498 Story 1 2.749 0.707 0.875 0.873 Story 1 2.749 0.707 0.875 0.873 Figure 7. Story displacements, ESA in X-direction. Figure 7. Story displacements, ESA in X-direction. Figure 7. Story displacements, ESA in X-direction. Figure 8. Story displacements, ESA in the Y-direction. Figure 8. Story displacements, ESA in the Y-direction. Figure 8. Story displacements, ESA in the Y-direction. Similarly, in the Y-direction, on the top floor, the results show that the building with- Similarly, in the Y-direction, on the top floor, the results show that the building with- Table 6. Comparison of the story displacements, response spectrum, and X-direction (mm). out shear walls produced 56 mm, while the building with shear walls produced 38.125 out shear walls produced 56 mm, while the building with shear walls produced 38.125 mm, a 32% difference. The displacement story of the vertical opening at the roof was also Story without Shear mW malls , a 32% Shear differW ence alls . without The displa Openings cement story Vertical of the Openings vertical openinStaggered g at the roo Openings f was also discovered to be 38.99 mm for staggered openings and 39.136 mm for unstaggered open- discovered to be 38.99 mm for staggered openings and 39.136 mm for unstaggered open- Story 14 42.006 28.938 29.283 29.434 ings. The story displacement in the case of response spectrum analysis (RSA) is shown in ings. The story displacement in the case of response spectrum analysis (RSA) is shown in Story 13 41.105 26.869 27.339 27.468 Tables 6 and 7 and Figures 9 and 10. Results show that the building without shear walls Story 12 39.745Tables 6 and 7 and Figure 24.699 s 9 and 10. Results show 25.251 that the building witho 25.361 ut shear walls Story 11 37.935produced about 42.00622.439 mm while the building with 23.057 shear walls produced 223.15 8.938 mm, i.e., produced about 42.006 mm while the building with shear walls produced 28.938 mm, i.e., Story 10 35.724 20.092 20.759 20.836 a 31% decline in the X-direction and a 33% decline in the Y-direction. The displacement a 31% decline in the X-direction and a 33% decline in the Y-direction. The displacement Story 9 33.152 17.673 18.373 18.433 story of the vertical opening at the roof is 29.283 mm for staggered openings in the X- story of the vertical opening at the roof is 29.283 mm for staggered openings in the X- Story 8 30.252 15.206 15.924 15.964 direction and 29.434 mm for vertical and staggered openings in the Y-direction, respec- direction and 29.434 mm for vertical and staggered openings in the Y-direction, respec- Story 7 27.047 12.722 13.441 13.459 tively. Tables 8 and 9 and Figures 11 and 12 demonstrate the story displacement in the tively. Tables 8 and 9 and Figures 11 and 12 demonstrate the story displacement in the Story 6 23.555 10.262 10.961 10.959 Story 5 19.788 7.878 8.533 8.509 Story 4 15.758 5.634 6.216 6.178 Story 3 11.482 3.61 4.087 4.041 Story 2 7.025 1.905 2.244 2.207 Story 1 2.694 0.641 0.807 0.793 Buildings 2022, 12, 1293 9 of 21 Table 7. Comparison of the story displacements, response spectrum, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 43.769 29.29 29.845 30.009 Story 13 42.743 27.159 27.822 27.96 Story 12 41.252 24.931 25.659 25.776 Story 11 39.305 22.619 23.393 23.493 Story 10 36.951 20.224 21.028 21.11 Story 9 34.23 17.764 18.583 18.648 Story 8 31.179 15.262 16.08 16.122 Story 7 27.822 12.75 13.551 13.574 Story 6 24.178 10.27 11.032 11.03 Story 5 20.264 7.872 8.572 8.554 Story 4 16.093 5.62 6.232 6.194 Story 3 11.681 3.593 4.088 4.049 Story 2 7.101 1.891 2.238 2.2 Buildings 2022, 12, x FOR PEER REVIEW 9 of 21 Buildings 2022, 12, x FOR PEER REVIEW 9 of 21 Story 1 2.688 0.634 0.801 0.796 Figure 9. Story displacement of the models, response spectrum analysis in the X-direction. Figure Figure 9. 9. Story Story displacement displacement of of the the models, models, r response esponse spectr spectrum um analysis analysis in in the the X-dir X-direction. ection. Figure 10. Story displacement of the models, response spectrum analysis, Y-direction. Figure 10. Story displacement of the models, response spectrum analysis, Y-direction. Figure 10. Story displacement of the models, response spectrum analysis, Y-direction. Table 8. Comparison of the story displacements, time history, and X-direction (mm). Table 8. Comparison of the story displacements, time history, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 45.727 34.74 28.749 28.662 Story 14 45.727 34.74 28.749 28.662 Story 13 44.907 32.402 26.854 26.753 Story 13 44.907 32.402 26.854 26.753 Story 12 43.659 29.935 24.805 24.699 Story 12 43.659 29.935 24.805 24.699 Story 11 41.941 27.329 22.651 22.546 Story 11 41.941 27.329 22.651 22.546 Story 10 39.98 24.57 20.405 20.303 Story 10 39.98 24.57 20.405 20.303 Story 9 37.979 21.667 18.09 18 Story 9 37.979 21.667 18.09 18 Story 8 35.546 18.652 15.727 15.644 Story 8 35.546 18.652 15.727 15.644 Story 7 32.594 15.577 13.337 13.266 Story 7 32.594 15.577 13.337 13.266 Story 6 29.044 12.511 10.942 10.87 Story 6 29.044 12.511 10.942 10.87 Story 5 24.855 9.54 8.575 8.51 Story 5 24.855 9.54 8.575 8.51 Story 4 20.043 6.759 6.289 6.214 Story 4 20.043 6.759 6.289 6.214 Story 3 14.698 4.28 4.159 4.096 Story 3 14.698 4.28 4.159 4.096 Story 2 9.009 2.224 2.292 2.23 Story 2 9.009 2.224 2.292 2.23 Story 1 3.454 0.736 0.824 0.807 Story 1 3.454 0.736 0.824 0.807 Buildings 2022, 12, 1293 10 of 21 Table 8. Comparison of the story displacements, time history, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 45.727 34.74 28.749 28.662 Story 13 44.907 32.402 26.854 26.753 Story 12 43.659 29.935 24.805 24.699 Story 11 41.941 27.329 22.651 22.546 Story 10 39.98 24.57 20.405 20.303 Story 9 37.979 21.667 18.09 18 Story 8 35.546 18.652 15.727 15.644 Story 7 32.594 15.577 13.337 13.266 Story 6 29.044 12.511 10.942 10.87 Story 5 24.855 9.54 8.575 8.51 Story 4 20.043 6.759 6.289 6.214 Buildings 2022, 12, x FOR PEER REVIEW 10 of 21 Story 3 14.698 4.28 4.159 4.096 Story 2 9.009 2.224 2.292 2.23 Story 1 3.454 0.736 0.824 0.807 Table 9. Comparison of the story displacements, time history, and Y-direction (mm). Table 9. Comparison of the story displacements, time history, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 46.471 32.91 32.809 32.34 Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 13 45.45 30.694 30.608 30.14 Story 14 46.471 32.91 32.809 32.34 Story 12 43.937 28.363 28.24 27.777 Story 13 45.45 30.694 30.608 30.14 Story 11 41.891 25.903 25.755 25.312 Story 12 43.937 28.363 28.24 27.777 Sto Story ry 10 11 39.3 41.891 27 2 25.903 3.298 25.755 23.168 25.312 22.751 Story 10 39.327 23.298 23.168 22.751 Story 9 36.562 20.554 20.506 20.127 Story 9 36.562 20.554 20.506 20.127 Story 8 33.959 17.697 17.795 17.457 Story 8 33.959 17.697 17.795 17.457 Story 7 30.943 14.778 15.058 14.767 Story 7 30.943 14.778 15.058 14.767 Story 6 27.447 11.865 12.325 12.078 Story 6 27.447 11.865 12.325 12.078 Story 5 23.419 9.039 9.634 9.431 Story 5 23.419 9.039 9.634 9.431 Story 4 18.849 6.397 7.043 6.882 Story 4 18.849 6.397 7.043 6.882 Story 3 13.791 4.043 4.641 4.523 Story 3 13.791 4.043 4.641 4.523 Story 2 8.412 2.095 2.545 2.477 Story 2 8.412 2.095 2.545 2.477 Story 1 3.186 0.686 0.909 0.896 Story 1 3.186 0.686 0.909 0.896 Figure 11. Story displacement of the models, time history analysis, X-direction. Figure 11. Story displacement of the models, time history analysis, X-direction. Figure 12. Displacement of the models, time history analysis, Y-direction. Buildings 2022, 12, x FOR PEER REVIEW 10 of 21 Table 9. Comparison of the story displacements, time history, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 46.471 32.91 32.809 32.34 Story 13 45.45 30.694 30.608 30.14 Story 12 43.937 28.363 28.24 27.777 Story 11 41.891 25.903 25.755 25.312 Story 10 39.327 23.298 23.168 22.751 Story 9 36.562 20.554 20.506 20.127 Story 8 33.959 17.697 17.795 17.457 Story 7 30.943 14.778 15.058 14.767 Story 6 27.447 11.865 12.325 12.078 Story 5 23.419 9.039 9.634 9.431 Story 4 18.849 6.397 7.043 6.882 Story 3 13.791 4.043 4.641 4.523 Story 2 8.412 2.095 2.545 2.477 Story 1 3.186 0.686 0.909 0.896 Buildings 2022, 12, 1293 11 of 21 Figure 11. Story displacement of the models, time history analysis, X-direction. Figure Figure12. 12. Displacement Displacementof of the themodels, models,time time history historyanalysis, analysis,Y Y -dir -diection. rection. 4.2. Story Drift Tables 10 and 11 and Figures 13 and 14 demonstrate the story drifts carried out by using ESA (EX&EY). The results show that the maximum drift that could be found on the fourth floor due to the buildings lack of shear walls is 4.895 mm in X-direction and 5.121 mm in Y-direction. It is also observed that the maximum drift story of the building with shear walls seen on the eighth floor is 3.274 mm, 3.323 mm, and 3.344 mm for the building’s vertical and staggered openings in the X-direction, and 3.358 mm for shear walls without openings and 3.405 mm and 3.425 mm as results of shear walls with a vertical and staggered opening in the Y-direction. Tables 12 and 13 and Figures 15 and 16 demonstrate the story drifts in the case of response spectrum analysis (RSA) in the (X&Y) direction. The results show that the maximum drift seen on the third floor due to the building without shear walls is 4.476 mm in X-direction and 4.6 mm in Y-direction. It is consequently observed that the maximum drift story of the building with shear walls seen on the eighth floor is 2.544 mm, 2.566 mm, and 2.585 mm for the building’s vertical and staggered opening, respectively, in X-direction. However, shear walls without openings have a 2.573 mm thickness, while shear walls with vertical and staggered openings in the Y-direction have 2.614 mm and 2.63 mm thicknesses, respectively. Tables 14 and 15 and Figures 17 and 18 determine the story drifts in the case of time history analysis (THA) in the (X&Y) direction. The results show that the maximum drift found on the third floor is due to the building’s lack of shear walls, 5.689 mm in X-direction and 5.379 mm in Y-direction. Likewise, it was observed that the maximum drift story of the building with shear walls seen on the eighth floor was 3.075 mm, 2.397 mm, and 2.381 mm for the building’s vertical and staggered opening in X-direction, respectively; 2.919 mm for shear walls with no openings, and 2.783 mm and 2.741 mm for shear walls with vertical and staggered Y-direction openings. The results show that the story drift increases from the second story and onwards. It gradually grew and has a tendency to fall back to the top story. The model with a vertical opening and staggered opening shear wall indicates more drift value compared to the shear wall without an opening. The building without shear walls shows a high drift value. The same findings have been found in the published literature by Marius [29]. Buildings 2022, 12, 1293 12 of 21 Table 10. Comparison of the measured story drift, static analysis, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.347 2.725 2.61 2.621 Story 13 2.057 2.874 2.808 2.828 Story 12 2.731 3.005 2.97 2.985 Story 11 3.305 3.129 3.12 3.136 Story 10 3.778 3.222 3.238 3.255 Story 9 4.155 3.271 3.309 3.326 Story 8 4.445 3.274 3.323 3.344 Story 7 4.656 3.192 3.27 3.288 Story 6 4.797 3.043 3.141 3.161 Story 5 4.876 2.808 2.927 2.938 Story 4 4.895 2.476 2.616 2.624 Story 3 4.83 2.034 2.195 2.185 Story 2 4.49 1.463 1.647 1.624 Story 1 2.725 0.707 0.876 0.865 Table 11. Comparison of the story drift, static analysis, Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.526 2.834 2.722 2.74 Story 13 2.253 2.98 2.917 2.941 Story 12 2.946 3.108 3.076 3.094 Story 11 3.538 3.226 3.222 3.242 Story 10 4.023 3.314 3.334 3.352 Story 9 4.408 3.356 3.399 3.423 Story 8 4.701 3.358 3.405 3.425 Story 7 4.911 3.26 3.343 3.368 Story 6 5.047 3.101 3.204 3.22 Story 5 5.116 2.855 2.977 2.997 Story 4 5.121 2.512 2.654 2.658 Story 3 5.103 2.057 2.22 2.218 Story 2 4.632 1.474 1.659 1.631 Buildings 2022, 12, x FOR PEER REVIEW 12 of 21 Story 1 2.749 0.707 0.875 0.873 Figure Figure13. 13. Story Storydrift driftof ofthe the models: models: static static analysis analysis and and X-dir X-dir ection ectionanalysis. analysis. Figure 14. Story drift of the models: static analysis and Y-direction (mm). Tables 12 and 13 and Figures 15 and 16 demonstrate the story drifts in the case of response spectrum analysis (RSA) in the (X&Y) direction. The results show that the max- imum drift seen on the third floor due to the building without shear walls is 4.476 mm in X-direction and 4.6 mm in Y-direction. It is consequently observed that the maximum drift story of the building with shear walls seen on the eighth floor is 2.544 mm, 2.566 mm, and 2.585 mm for the building’s vertical and staggered opening, respectively, in X-direction. However, shear walls without openings have a 2.573 mm thickness, while shear walls with vertical and staggered openings in the Y-direction have 2.614 mm and 2.63 mm thick- nesses, respectively. Buildings 2022, 12, x FOR PEER REVIEW 12 of 21 Buildings 2022, 12, 1293 13 of 21 Figure 13. Story drift of the models: static analysis and X-direction analysis. Figure 14. Story drift of the models: static analysis and Y-direction (mm). Figure 14. Story drift of the models: static analysis and Y-direction (mm). Tables 12 and 13 and Figures 15 and 16 demonstrate the story drifts in the case of response spectrum analysis (RSA) in the (X&Y) direction. The results show that the max- Table 12. Comparison of the story drift, response spectrum, and X-direction (mm). imum drift seen on the third floor due to the building without shear walls is 4.476 mm in X-direction and 4.6 mm in Y-direction. It is consequently observed that the maximum drift Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings story of the building with shear walls seen on the eighth floor is 2.544 mm, 2.566 mm, and Story 14 1.144 2.138 2.038 2.052 2.585 mm for the building’s vertical and staggered opening, respectively, in X-direction. Story 13 1.777 2.256 2.197 2.215 However, shear walls without openings have a 2.573 mm thickness, while shear walls Story 12 2.318 2.355 2.318 2.334 with vertical and staggered openings in the Y-direction have 2.614 mm and 2.63 mm thick- Story 11 2.732 2.443 2.424 2.439 nesses, respectively. Story 10 3.063 2.508 2.503 2.519 Story 9 3.338 2.543 2.552 2.568 Story 8 3.572 2.544 2.566 2.585 Story 7 3.782 2.504 2.542 2.559 Story 6 3.981 2.414 2.472 2.491 Story 5 4.167 2.263 2.345 2.357 Story 4 4.342 2.035 2.145 2.153 Story 3 4.476 1.71 1.852 1.841 Story 2 4.333 1.266 1.44 1.417 Story 1 2.694 0.641 0.807 0.793 Table 13. Comparison of the story drift, response spectrum analysis, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.278 2.201 2.118 2.136 Story 13 1.923 2.316 2.273 2.295 Story 12 2.471 2.41 2.392 2.407 Story 11 2.889 2.493 2.493 2.511 Story 10 3.221 2.551 2.566 2.58 Story 9 3.499 2.58 2.608 2.628 Story 8 3.734 2.573 2.614 2.63 Story 7 3.945 2.526 2.582 2.605 Story 6 4.14 2.429 2.504 2.519 Story 5 4.319 2.271 2.369 2.387 Story 4 4.483 2.037 2.161 2.163 Story 3 4.6 1.707 1.859 1.857 Story 2 4.416 1.26 1.44 1.411 Story 1 2.688 0.634 0.801 0.796 Buildings 2022, 12, x FOR PEER REVIEW 13 of 21 Table 12. Comparison of the story drift, response spectrum, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.144 2.138 2.038 2.052 Story 13 1.777 2.256 2.197 2.215 Story 12 2.318 2.355 2.318 2.334 Story 11 2.732 2.443 2.424 2.439 Story 10 3.063 2.508 2.503 2.519 Story 9 3.338 2.543 2.552 2.568 Story 8 3.572 2.544 2.566 2.585 Story 7 3.782 2.504 2.542 2.559 Story 6 3.981 2.414 2.472 2.491 Story 5 4.167 2.263 2.345 2.357 Story 4 4.342 2.035 2.145 2.153 Story 3 4.476 1.71 1.852 1.841 Story 2 4.333 1.266 1.44 1.417 Story 1 2.694 0.641 0.807 0.793 Table 13. Comparison of the story drift, response spectrum analysis, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.278 2.201 2.118 2.136 Story 13 1.923 2.316 2.273 2.295 Story 12 2.471 2.41 2.392 2.407 Story 11 2.889 2.493 2.493 2.511 Story 10 3.221 2.551 2.566 2.58 Story 9 3.499 2.58 2.608 2.628 Story 8 3.734 2.573 2.614 2.63 Story 7 3.945 2.526 2.582 2.605 Story 6 4.14 2.429 2.504 2.519 Story 5 4.319 2.271 2.369 2.387 Story 4 4.483 2.037 2.161 2.163 Story 3 4.6 1.707 1.859 1.857 Buildings 2022, 12, 1293 14 of 21 Story 2 4.416 1.26 1.44 1.411 Story 1 2.688 0.634 0.801 0.796 Buildings 2022, 12, x FOR PEER REVIEW 14 of 21 Figure Figure 15. 15. Story Story drift drift of of the the models, models, r response esponse spectr spectrum um analysis analysis and and X-dir X-dir ection. ection. Figure Figure 16. 16. Story Story drift, drift, rresponse esponse spectr spectrum um analysis, analysis, and and Y Y -dir -dir ection. ection. Tables 14 and 15 and Figures 17 and 18 determine the story drifts in the case of time Table 14. Comparison of the story drift, time history analysis, X-direction (mm). history analysis (THA) in the (X&Y) direction. The results show that the maximum drift found on the third floor is due to the building’s lack of shear walls, 5.689 mm in X-direc- Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings tion and 5.379 mm in Y-direction. Likewise, it was observed that the maximum drift story Story 14 1.04 2.338 1.907 1.909 of the building with shear walls seen on the eighth floor was 3.075 mm, 2.397 mm, and Story 13 1.624 2.467 2.048 2.054 2.381 mm for the building’s vertical and staggered opening in X-direction, respectively; Story 12 2.206 2.606 2.155 2.154 2.919 mm for shear walls with no openings, and 2.783 mm and 2.741 mm for shear walls Story 11 2.714 2.759 2.246 2.243 Story 10 3.123 with vertical and stagger 2.903 ed Y-direction openings. 2.315 2.305 Story 9 3.533 3.015 2.363 2.356 Story 8 3.862 3.075 2.397 2.381 Table 14. Comparison of the story drift, time history analysis, X-direction (mm). Story 7 4.078 3.066 2.396 2.376 SStory tory 6 without Sh4.233 ear Walls Shear Walls wit 2.972 hout Openings Vertica 2.367 l Openings Staggere 2.364 d Openings Story 5 4.812 2.78 2.287 2.296 Story 14 1.04 2.338 1.907 1.909 Story 4 5.345 2.479 2.131 2.124 Story 13 1.624 2.467 2.048 2.054 Story 3 5.689 2.056 1.869 1.866 Story 12 2.206 2.606 2.155 2.154 Story 2 5.555 1.493 1.47 1.43 Sto Story ry 111 2.71 3.454 4 2 0.736 .759 0.831 2.246 0.807 2.243 Story 10 3.123 2.903 2.315 2.305 Story 9 3.533 3.015 2.363 2.356 Story 8 3.862 3.075 2.397 2.381 Story 7 4.078 3.066 2.396 2.376 Story 6 4.233 2.972 2.367 2.364 Story 5 4.812 2.78 2.287 2.296 Story 4 5.345 2.479 2.131 2.124 Story 3 5.689 2.056 1.869 1.866 Story 2 5.555 1.493 1.47 1.43 Story 1 3.454 0.736 0.831 0.807 Table 15. Comparison of the story drift, time history analysis, Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.197 2.311 2.213 2.201 Story 13 1.817 2.432 2.368 2.363 Story 12 2.446 2.541 2.485 2.466 Story 11 2.994 2.64 2.587 2.561 Story 10 3.491 2.745 2.662 2.626 Buildings 2022, 12, 1293 15 of 21 Table 15. Comparison of the story drift, time history analysis, Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.197 2.311 2.213 2.201 Buildings 2022, 12, x FOR PEER REVIEW 15 of 21 Buildings 2022, 12, x FOR PEER REVIEW 15 of 21 Story 13 1.817 2.432 2.368 2.363 Story 12 2.446 2.541 2.485 2.466 Story 11 2.994 2.64 2.587 2.561 Story 10 3.491 2.745 2.662 2.626 Story 9 3.913 2.856 2.727 2.679 Story 9 3.913 2.856 2.727 2.679 Story 9 3.913 2.856 2.727 2.679 Story 8 4.204 2.919 2.783 2.741 Story 8 4.204 2.919 2.783 2.741 Story 8 4.204 2.919 2.783 2.741 Story 7 4.343 2.914 2.757 2.722 Story 7 4.343 2.914 2.757 2.722 Story 7 4.343 2.914 2.757 2.722 Story 6 4.328 2.826 2.692 2.653 Story 6 4.328 2.826 2.692 2.653 Story 6 4.328 2.826 2.692 2.653 Sto Story ry 55 4.54.57 7 2.642 2.642 2.591 2.591 2.549 2.549 Story 5 4.57 2.642 2.591 2.549 Story 4 5.058 2.354 2.404 2.368 Story 4 5.058 2.354 2.404 2.368 Story 4 5.058 2.354 2.404 2.368 Story 3 5.379 1.947 2.098 2.046 Story 3 5.379 1.947 2.098 2.046 Story 3 5.379 1.947 2.098 2.046 Story 2 5.226 1.41 1.639 1.592 Story 2 5.226 1.41 1.639 1.592 Story 1 3.186 0.686 0.909 0.896 Story 2 5.226 1.41 1.639 1.592 Story 1 3.186 0.686 0.909 0.896 Story 1 3.186 0.686 0.909 0.896 Figure 17. Story drift of the models, time history analysis, X-direction. Figure 17. Story drift of the models, time history analysis, X-direction. Figure 17. Story drift of the models, time history analysis, X-direction. Figure 18. Story drift of the models, time history analysis, Y-direction. Figure Figure 18. 18. Story Story drift drift of of the the models, models, time time history history analysis, analysis, Y Y-dir -direction. ection. The results show that the story drift increases from the second story and onwards. It The results show that the story drift increases from the second story and onwards. It gradually grew and has a tendency to fall back to the top story. The model with a vertical gradually grew and has a tendency to fall back to the top story. The model with a vertical opening and staggered opening shear wall indicates more drift value compared to the opening and staggered opening shear wall indicates more drift value compared to the shear wall without an opening. The building without shear walls shows a high drift value. shear wall without an opening. The building without shear walls shows a high drift value. The same findings have been found in the published literature by Marius [29]. The same findings have been found in the published literature by Marius [29]. Buildings 2022, 12, x FOR PEER REVIEW 16 of 21 Buildings 2022, 12, 1293 16 of 21 4.3. Story Forces 4.3. Story In theFor caces se of the response spectrum, the values of story forces on the first floor are 3558.8 kN for modal without shear walls, 6295.9 kN for building with shear walls, and In the case of the response spectrum, the values of story forces on the first floor are 5906.5 kN, 5871.6 kN for vertical opening, and staggered opening, respectively (as shown 3558.8 kN for modal without shear walls, 6295.9 kN for building with shear walls, and in Figures 19 and 20). As can be seen, the reduction percentage of story force value on the 5906.5 kN, 5871.6 kN for vertical opening, and staggered opening, respectively (as shown in first floor is about 16.3% in buildings without shear walls when compared to buildings Figures 19 and 20). As can be seen, the reduction percentage of story force value on the with shear walls. Figures 21 and 22 demonstrate the story forces in the case of time history first floor is about 16.3% in buildings without shear walls when compared to buildings analysis; the story forces on the first floor due to building without shear walls are 4491.0 with shear walls. Figures 21 and 22 demonstrate the story forces in the case of time history kN when compared to building with shear walls, 7087.7 kN, and 5381.2 kN, 5333.9 kN for analysis; the story forces on the first floor due to building without shear walls are 4491.0 kN shear walls staggered and vertical openings in the case of time history, respectively. Ad- when compared to building with shear walls, 7087.7 kN, and 5381.2 kN, 5333.9 kN for shear ditionally, it is noticed that the difference in story forces in the time history analysis (THA) walls staggered and vertical openings in the case of time history, respectively. Additionally, as compared to the response spectrum analysis (RSA) results are insignificant for the same it is noticed that the difference in story forces in the time history analysis (THA) as compared cases. Overall, it can be said that the displacement and story drift of the building signifi- to the response spectrum analysis (RSA) results are insignificant for the same cases. Overall, ca it can ntly be affsaid ected that by the the displacement height of the st and rucstory tural ele drift men oft, the sto building ry or buil significantly ding. Therefaf ore fected , the sh byea the r wa hei lls ght ope of nin the gs str have uctural a sligelement, ht effect o story n these or m building. echanical Ther prope efor rties e, the as com shear pare walls d to openings have a slight effect on these mechanical properties as compared to the story the story forces. However, the distribution of the lateral forces (story forces) on the build- in for g ces. are s However ignifican,tlthe y inf distribution luenced by th of e the weilateral ght of tfor he ces buildin (story g. C for onces) sequentl on the y, tbuilding he openin ar gs e significantly influenced by the weight of the building. Consequently, the openings on the on the shear wall reduced the weight and stiffness of the building and then increased the shear wall reduced the weight and stiffness of the building and then increased the lateral lateral forces. Moreover, compared to other methods of analysis, time history analysis forces. Moreover, compared to other methods of analysis, time history analysis shows that shows that the story forces are higher for all models. That might be attributed to the higher the story forces are higher for all models. That might be attributed to the higher lateral lateral forces applied on the building which generated by earthquake (El Centro). forces applied on the building which generated by earthquake (El Centro). The findings of this study agree with the results of the study by Mosoarca [12]. Figure 19. Story forces of the models, response spectrum analysis, X-direction. Figure 19. Story forces of the models, response spectrum analysis, X-direction. Buildings 2022, 12, x FOR PEER REVIEW 17 of 21 Buildings 2022, 12, 1293 17 of 21 Buildings 2022, 12, x FOR PEER REVIEW 17 of 21 Figure 20. Story forces of the models, response spectrum analysis, Y-direction. Figure 20. Story forces of the models, response spectrum analysis, Y-direction. Figure 20. Story forces of the models, response spectrum analysis, Y-direction. Figure 21. Story forces of the models, time history analysis, X-direction. Figure 21. Story forces of the models, time history analysis, X-direction. Figure 21. Story forces of the models, time history analysis, X-direction. Buildings 2022, 12, x FOR PEER REVIEW 18 of 21 Buil Buildings dings 2022 2022,, 12 12,, 1293 x FOR PEER REVIEW 18 18 oof f 21 21 Figure 22. Story forces of the models, time history analysis, Y-direction. Figure 22. Story forces of the models, time history analysis, Y-direction. Figure 22. Story forces of the models, time history analysis, Y-direction. 4.4. Time Period As shown in Figure 23 the time period of the structure increases with an increase in 4.4. TThe ime P findings eriod of this study agree with the results of the study by Mosoarca [12]. mass. The time period decreases when the shear wall is provided and is a minimum for As shown in Figure 23 the time period of the structure increases with an increase in 4.4. Time Period shear walls on the outer edges of the structure. A building with shear walls indicates that mass. The time period decreases when the shear wall is provided and is a minimum for the time period reduces compared to a building without shear walls. Besides, a building As shown in Figure 23 the time period of the structure increases with an increase in shear walls on the outer edges of the structure. A building with shear walls indicates that with shear walls with a vertical opening, as in Figure 23, shows that the time period de- mass. The time period decreases when the shear wall is provided and is a minimum for the time period reduces compared to a building without shear walls. Besides, a building shear clines walls compa on re the d to outer a staedges ggered of ope the nstr ing uctur . e. A building with shear walls indicates that with shear walls with a vertical opening, as in Figure 23, shows that the time period de- Finally, more or less similar behaviour of using finite element modelling in solving the time period reduces compared to a building without shear walls. Besides, a building clines compared to a staggered opening. with struc shear tures walls and m with atera iavertical ls problem opening, s has be asen in con Figur duc e 23 ted , shows by seve that ral the resea time rchperiod ers, wh declines ich pro- Finally, more or less similar behaviour of using finite element modelling in solving compar vided by liter ed to aastagger ture reports ed opening. [30–37]. structures and materials problems has been conducted by several researchers, which pro- vided by literature reports [30–37]. Figure Figure23. 23. The The time time period period of ofthe the models. models. Figure 23. The time period of the models. Buildings 2022, 12, 1293 19 of 21 Finally, more or less similar behaviour of using finite element modelling in solving structures and materials problems has been conducted by several researchers, which provided by literature reports [30–37]. 5. Conclusions From the analytical study on the effect of openings on the seismic behaviour of shear walls, the following conclusions could be drawn: 1. Based on the ESA method of the models, it can be seen that the model with a shear wall showed improved performance in terms of displacement reduction. Additionally, a building with a shear wall without an opening shows better performance based on displacement reduction. 2. According to the response spectrum analysis, it is observed that the percentage reduction of story force value on the first floor is about 43% in buildings without shear walls when compared to buildings with shear walls and about 28% in buildings with shear walls when compared to shear walls with opening, equally for time history analysis. 3. From time-history analysis, it is concluded that the building with a shear wall showed good quality performance in terms of displacement reduction. Similarly, a build- ing with a shear wall without an opening shows superior performance based on displacement reduction. 4. The results show that using shear walls cuts down on story drift and movement in the X and Y directions by a lot. 5. The maximum story drift in most of the cases produced is found on the seventh floor. 6. In all three analyses (equivalent static analysis, response spectrum, and time his- tory analysis), the results concluded that shear walls without openings show less displacement as compared to the other models. 7. Similarly, it has been found that shear walls without openings show less drift as compared to other models. Thus, in turn, it emphasizes the vital impact of using these models. 8. Compared to other methods of analysis, time history analysis shows that the seismic story forces are higher for all models. Author Contributions: Conceptualization, A.S., A.H., H.M.N., S.Q., M.M.S.S., and N.S.M.; method- ology, A.S, A.H., H.M.N., M.M.S.S., and N.S.M.; software, A.S. and A.H.; validation, H.M.N., S.Q., M.M.S.S., N.S.M.; formal analysis, A.S. and A.H.; investigation, A.S., A.H., H.M.N., S.Q. M.M.S.S., and N.S.M.; resources, A.S., A.H., H.M.N., M.M.S.S., and N.S.M.; data curation, A.S., A.H., H.M.N., M.M.S.S., S.Q., and N.S.M.; writing—original draft preparation, A.S.; writing—review and editing, A.S., A.H., H.M.N., M.M.S.S., and N.S.M.; visualization, A.S. and A.H.; supervision, A.S., A.H., and H.M.N.; project administration, M.M.S.S.; funding acquisition, M.M.S.S. All authors have read and agreed to the published version of the manuscript. Funding: The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program ‘Priority 2030’ (Agreement 075-15-2021-1333 dated 30 September 2021). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data used to support the findings of this study are included in the article. Acknowledgments: The authors extend their thanks to the Ministry of Science and Higher Education of the Russian Federation for funding this work. Conflicts of Interest: The authors declare no conflict of interest. Buildings 2022, 12, 1293 20 of 21 References 1. Lu, X.; Xie, L.; Guan, H.; Huang, Y.; Lu, X. A Shear Wall Element for Nonlinear Seismic Analysis of Super-Tall Buildings Using OpenSees. Finite Elem. Anal. Des. 2015, 98, 14–25. [CrossRef] 2. Najm, H.M.; Ibrahim, A.M.; Sabri, M.M.; Hassan, A.; Morkhade, S.; Mashaan, N.S.; Eldirderi, M.M.A.; Khedher, K.M. Modelling of Cyclic Load Behaviour of Smart Composite Steel-Concrete Shear Wall Using Finite Element Analysis. Buildings 2022, 12, 850. [CrossRef] 3. Pei, S.; Popovski, M.; van de Lindt, J.W. Seismic Design of a Multi-Story Cross Laminated Timber Building Based on Component Level Testing. In Proceedings of the World Conference on Timber Engineering, Auckland, New Zealand, 16–19 July 2012. 4. Esmaili, O.; Epackachi, S.; Samadzad, M.; Mirghaderi, S.R. Study of Structural RC Shear Wall System in a 56-Story RC Tall Building. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. 5. Vigh, L.G.; Deierlein, G.G.; Miranda, E.; Liel, A.B.; Tipping, S. Seismic Performance Assessment of Steel Corrugated Shear Wall System Using Non-Linear Analysis. J. Constr. Steel Res. 2013, 85, 48–59. [CrossRef] 6. Hassan, A.; Pal, S. Effect of Soil Condition on Seismic Response of Isolated Base Buildings. Int. J. Adv. Struct. Eng. 2018, 10, 249–261. [CrossRef] 7. Hassan, A. Optimization of Base Isolation Parameters. LAMBERT Acad. Publ. 2017, 97, 1207–1222. 8. Hassan, A.; Pal, S. Performance Analysis of Base Isolation & Fixed Base Buildings. ISSN (Online) Int. J. Eng. Res. Mech. Civ. Eng. (IJERMCE) 2017, 2, 152–157. 9. Fintel, M. Performance of Buildings with Shear Walls in Earthquakes of the Last Thirty Years. PCI J. 2014, 40, 62–80. [CrossRef] 10. Wallace, J.W.; Thomsen IV, J.H. Seismic Design of RC Structural Walls. Part II: Applications. J. Struct. Eng. 2002, 121, 88–101. [CrossRef] 11. Wu, Y.T.; Kang, D.Y.; Yang, Y.B. Seismic Performance of Steel and Concrete Composite Shear Walls with Embedded Steel Truss for Use in High-Rise Buildings. Eng. Struct. 2016, 125, 39–53. [CrossRef] 12. Mosoarca, M. Failure Analysis of RC Shear Walls with Staggered Openings under Seismic Loads. Eng. Fail. Anal. 2014, 41, 48–64. [CrossRef] 13. Farzampour, A.; Laman, J.A. Behavior Prediction of Corrugated Steel Plate Shear Walls with Openings. J. Constr. Steel Res. 2015, 114, 258–268. [CrossRef] 14. Taranath, B.S. Reinforced Concrete Design of Tall Buildings; CRC Press: Boca Raton, FL, USA, 2009. 15. Galal, K.; El-Sokkarry, H. Recent Advancements in Retrofit of Rc Shear Walls. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. 16. Najm, H.M.; Ibrahim, A.M.; Sabri, M.M.S.; Hassan, A.; Morkhade, S.; Mashaan, N.S.; Eldirderi, M.M.A.; Khedher, K.M. Evaluation and Numerical Investigations of the Cyclic Behavior of Smart Composite Steel–Concrete Shear Wall: Comprehensive Study of Finite Element Model. Materials 2022, 15, 4496. [CrossRef] [PubMed] 17. Zhang, Z.; Wang, F. Experimental Investigation into the Seismic Performance of Prefabricated Reinforced Masonry Shear Walls with Vertical Joint Connections. Appl. Sci. 2021, 11, 4421. [CrossRef] 18. Dang-Vu, H.; Shin, J.; Lee, K. Seismic Fragility Assessment of Columns in a Piloti-Type Building Retrofitted with Additional Shear Walls. Sustainability 2020, 12, 6530. [CrossRef] 19. Coccia, S.; di Carlo, F.; Imperatore, S. Masonry Walls Retrofitted with Vertical FRP Rebars. Buildings 2020, 10, 72. [CrossRef] 20. Jeon, S.H.; Park, J.H. Seismic Fragility of Ordinary Reinforced Concrete Shear Walls with Coupling Beams Designed Using a Performance-Based Procedure. Appl. Sci. 2020, 10, 4075. [CrossRef] 21. Zheng, S.-S.; Yang, W.; Yang, F.; Sun, L.-F.; Hou, P.-J. Seismic Fragility Analysis for RC Core Walls Structure Based on MIDA Method. Zhendong Yu Chongji/J. Vib. Shock 2015, 34, 117–123. [CrossRef] 22. Coronelli, D.; Martinelli, L.; Mulas, M.G. Pushover Analysis of Shaking Table Tests on a RC Shear Wall. In Proceedings of the Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011, Leuven, Belgium, 4–6 July 2011. 23. Wang, Q.; Shi, Q.; Tian, H. Experimental Study on Shear Capacity of SRC Joints with Different Arrangement and Sizes of Cross-Shaped Steel in Column. Steel Compos. Struct. 2016, 21, 267–287. [CrossRef] 24. Lehman, D.E.; Turgeon, J.A.; Birely, A.C.; Hart, C.R.; Marley, K.P.; Kuchma, D.A.; Lowes, L.N. Seismic Behavior of a Modern Concrete Coupled Wall. J. Struct. Eng. 2013, 139, 1371–1381. [CrossRef] 25. Husain, M.; Eisa, A.S.; Hegazy, M.M. Strengthening of Reinforced Concrete Shear Walls with Openings Using Carbon Fiber- Reinforced Polymers. Int. J. Adv. Struct. Eng. 2019, 11, 129–150. [CrossRef] 26. Dou, C.; Jiang, Z.Q.; Pi, Y.L.; Guo, Y.L. Elastic Shear Buckling of Sinusoidally Corrugated Steel Plate Shear Wall. Eng. Struct. 2016, 121, 136–146. [CrossRef] 27. Berman, J.W.; Bruneau, M. Experimental Investigation of Light-Gauge Steel Plate Shear Walls. J. Struct. Eng. 2005, 131, 259–267. [CrossRef] 28. El Ouni, M.H.; Laissy, M.Y.; Ismaeil, M.; Ben Kahla, N. Effect of Shear Walls on the Active Vibration Control of Buildings. Buildings 2018, 8, 164. [CrossRef] 29. Marius, M. Seismic Behaviour of Reinforced Concrete Shear Walls with Regular and Staggered Openings after the Strong Earthquakes between 2009 and 2011. Eng. Fail. Anal. 2013, 34, 537–565. [CrossRef] 30. Najem, H.M.; Ibrahim, A.M. The Effect of Infill Steel Plate Thickness on the Cycle Behavior of Steel Plate Shear Walls. Diyala J. Eng. Sci. 2018, 11, 1–6. [CrossRef] Buildings 2022, 12, 1293 21 of 21 31. Najem, H.M.; Ibrahim, A.M. Influence of Concrete Strength on the Cycle Performance of Composite Steel Plate Shear Walls. Diyala J. Eng. Sci. 2018, 11, 1–7. [CrossRef] 32. Fadhil, H.; Ibrahim, A.; Mahmood, M. Effect of Corrugation Angle and Direction on the Performance of Corrugated Steel Plate Shear Walls. Civ. Eng. J. 2018, 4, 2667–2679. [CrossRef] 33. Ahmed, H.U.; Mohammed, A.S.; Faraj, R.H.; Qaidi, S.M.; Mohammed, A.A. Compressive strength of geopolymer concrete modified with nano-silica: Experimental and modeling investigations. Case Stud. Constr. Mater. 2022, 16, e01036. [CrossRef] 34. Khan, M.; Cao, M.; Ali, M. Cracking behaviour and constitutive modelling of hybrid fibre reinforced concrete. J. Build. Eng. 2020, 30, 101272. [CrossRef] 35. Parvez, I.; Shen, J.; Khan, M.; Cheng, C. Modeling and solution techniques used for hydro generation scheduling. Water 2019, 11, 1392. [CrossRef] 36. Ahmed, H.U.; Mohammed, A.S.; Qaidi, S.M.; Faraj, R.H.; Hamah Sor, N.; Mohammed, A.A. Compressive strength of geopolymer concrete composites: A systematic comprehensive review, analysis and modeling. Eur. J. Environ. Civ. Eng. 2022, 26, 1–46. [CrossRef] 37. Faraj, R.H.; Ahmed, H.U.; Rafiq, S.; Sor, N.H.; Ibrahim, D.F.; Qaidi, S.M. Performance of Self-Compacting Mortars Modified with Nanoparticles: A Systematic Review and Modeling. Clean. Mater. 2022, 4, 100086. [CrossRef] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Buildings Multidisciplinary Digital Publishing Institute

A Comprehensive Study on the Effect of Regular and Staggered Openings on the Seismic Performance of Shear Walls

Loading next page...
 
/lp/multidisciplinary-digital-publishing-institute/a-comprehensive-study-on-the-effect-of-regular-and-staggered-openings-QlHa7TfyQ0
Publisher
Multidisciplinary Digital Publishing Institute
Copyright
© 1996-2022 MDPI (Basel, Switzerland) unless otherwise stated Disclaimer The statements, opinions and data contained in the journals are solely those of the individual authors and contributors and not of the publisher and the editor(s). MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Terms and Conditions Privacy Policy
ISSN
2075-5309
DOI
10.3390/buildings12091293
Publisher site
See Article on Publisher Site

Abstract

buildings Article A Comprehensive Study on the Effect of Regular and Staggered Openings on the Seismic Performance of Shear Walls 1 , 2 , 2 3 Ahmed Saeed * , Hadee Mohammed Najm * , Amer Hassan , Shaker Qaidi , 4 5 Mohanad Muayad Sabri Sabri and Nuha S. Mashaan Department of Civil Engineering, Southeast University, Nanjing 211189, China Department of Civil Engineering, Zakir Husain Engineering College, Aligarh Muslim University, Aligarh 202002, India Department of Civil Engineering, College of Engineering, University of Duhok, Duhok 42001, Kurdistan Region, Iraq Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia Faculty of Science and Engineering, School of Civil and Mechanical Engineering, Curtin University, Bentley, WA 6102, Australia * Correspondence: alanessy2015@gmail.com (A.S.); gk4071@myamu.ac.in (H.M.N.) Abstract: Shear walls have high strength and stiffness, which could be used at the same time to resist large horizontal loads and weight loads, making them pretty beneficial in several structural engineering applications. The shear walls could be included with openings, such as doors and windows, for relevant functional requirements. In the current study, a building of G + 13 stories with RC shear walls with and without openings has been investigated using ETABS Software. The seismic analysis is carried out for the determination of parameters like shear forces, drift, base shear, and story displacement for numerous models. The regular and staggered openings of the shear wall have been considered variables in the models. The dynamic analysis is carried out with the help of ETABS software. It has been observed that shear walls without openings models perform better Citation: Saeed, A.; Najm, H.M.; than other models, and this is in agreement with the previous studies published in this area. This Hassan, A.; Qaidi, S.; Sabri, M.M.S.; investigation also shows that the seismic behaviour of the shear wall with regular openings provides Mashaan, N.S. A Comprehensive a close result to the shear wall with staggered openings. At the roof, the displacement of the model Study on the Effect of Regular and with regular openings was 38.99 mm and approximately 39.163 mm for the model with staggered Staggered Openings on the Seismic Performance of Shear Walls. Buildings openings. However, the model without a shear wall experienced a displacement of about 56 mm at 2022, 12, 1293. https://doi.org/ the roof. Generally, it can be concluded that the openings have a substantial effect on the seismic 10.3390/buildings12091293 behaviour of the shear wall, and that should be taken into consideration during the construction design. However, the type of opening (regular or staggered) has a slight effect on the behaviour of Academic Editor: Arslan Akbar shear walls. Received: 20 July 2022 Accepted: 17 August 2022 Keywords: seismic behaviour; opening shear wall; story drift; displacement; base shear Published: 23 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- 1. Introduction iations. Reinforced concrete (RC) buildings considerably resist horizontal and vertical loading. Wind and seismic loads are the most common loads that shear walls are designed to carry [1]. The shear walls are the best and simplest method to sustain these lateral forces as they provide the required strength against seismic forces [2–4]. Shear walls are the components Copyright: © 2022 by the authors. in the external form of a box that provide lateral support to the building. The shear wall Licensee MDPI, Basel, Switzerland. provides strength and stiffness to the building in the lateral direction [5–8]. Since shear This article is an open access article walls carry massive lateral forces, the overturn effects on them are significantly important distributed under the terms and and must be considered in the structural design. Shear walls in buildings are preferred conditions of the Creative Commons to be symmetrical in order to mitigate the negative effects of twists [9–11]. They might be Attribution (CC BY) license (https:// placed symmetrically along with one or both directions in the plan. Shear walls are more creativecommons.org/licenses/by/ effective when provided on the exterior perimeter of the building; therefore, this layout 4.0/). Buildings 2022, 12, 1293. https://doi.org/10.3390/buildings12091293 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 1293 2 of 21 will increase the resistance of the structure against twisting [12]. The shear walls behaviour depends upon the material used, wall length, wall thickness, wall position, and building frame. RC shear walls are used in the design of multi-story buildings located in seismically vulnerable areas because of their rigidity, bearing capacity, and high ductility [13–15]. Obviously, an opening in a shear wall positioned along with in-plane loading is more critical than an opening in a shear wall located along without-of-plane loading because there is a considerable change in displacement noticed after having an opening in a shear wall positioned along with in-plane loading [16]. Shear walls are considered an essential element in the construction of buildings be- cause of their capacity to resist lateral loads such as earthquakes and wind loads. Therefore, research studies have been carried out to understand the structural behaviour of shear walls under different load cases and conditions. Zhang and Wang [17] investigated the seismic performance of prefabricated reinforced masonry shear walls with vertical joint connections, while Dang-Vu et al. [18] studied the seismic fragility assessment of columns in a piloti-type building retrofitted with additional shear walls. Coccia et al. [19] reported the behaviour of masonry walls retrofitted with vertical FRP rebars, and their study showed that the conventional seismic retrofitting techniques on masonry walls influence the seis- mic performance of the element, which is typically modified in an out-of-plane bending behaviour. Further, the study of Jeon et al. [20] investigated the seismic fragility of ordinary reinforced concrete shear walls with coupling beams, and their study showed that high-rise ordinary reinforced concrete shear walls designed using seven pairs of ground motion components and a shear force amplification factor  1.2 were adequate to satisfy the criteria on collapse probability and the collapse margin ratio prescribed in FEMA P695. Reinforced concrete structures with L-shaped walls provide numerous benefits for architects that permit them to design architectures with larger open areas and a lot of versatility [21–23]. However, a lot of experimental tests and numerical models should be done for L-shaped shear walls to ensure compliance with the safety provisions obligatory by the various code standards. What is more, given the necessities of deformability and resistance, L-shaped concrete shear walls are used in multi-story buildings because they possess a high capability of resisting lateral loads and may expend an excellent amount of seismic energy if they are properly designed [24–27]. Openings in shear walls may be required because of municipality or remodeling considerations, similar to elevators, windows, doors, and the placement of staircases [28]. Providing openings in the shear walls decreases the total structural capacity and integrity of the wall, in addition to stress condensation around the openings [27]. The main aim of this study is as follows: to understand the behaviour of staggered and regular openings and to analyze the effectiveness of staggered openings to seismic load when different loads are used. 2. Model Description A 14-story RC structure with shear wall elements and the 14 stories were selected in the model to minimize the analysis time in the software, and the behaviour of shear walls with the openings was the aim of this study and not the effect of the building’s length, shape “L” of RC shear wall without opening, with a vertical and staggered opening in Seismic Zone V, has been considered in this study. Tables 1–3 illustrate the model data, applied loads on the structure, and seismic input data. The plan and geometry of the models are shown in Figures 1–4. Compared to the area of the wall in that story, the shear wall has a 5% opening. Buildings 2022, 12, 1293 3 of 21 Table 1. Models data. Number of Stories 14 Column Size (600  600) mm Beam Size (300  600) mm Slab Depth 150 mm Shear Wall Thickness 300 mm Size of opening (2  1.5) m Story Height 3.5 m Support Fixed Concrete Grade M25 Steel Grade Fe 500 Table 2. Loads. Unit Weight of Concrete 25 kN/m Dead load 3.75 kN/m Live load 3 kN/m Beam Load 11 kN/m Table 3. Seismic data. Seismic Zone V Zone factor (Z) 0.36 Soil Type Medium Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Damping Ratio 5% Response Reduction factor (R) 5 Importance factor (I) 1 Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Buildings 2022, 12, 1293 4 of 21 Figure 1. The geometry of the structure and the 3D of the structure without shear walls. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 2. The geometry of the structure and 3D structure shear wall without opening. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Figure 3. The geometry of the structure and 3D structure shear walls with vertical openings. Response spectrum function and time history function (El Centro 1940) have been used in this study for seismic analysis. A response spectrum is a plot of the maximum response amplitude (displacement, velocity or acceleration) versus time period of many linear single degree of freedom oscillators to a give component of ground motion as shown in Figure 5. The resulting plot can be used to choose the response of any linear SDOF oscillator, given its natural time period of oscillation. One such use is in evaluating the peak response of structures to ground motions. The first data listed from an earthquake record are usually the peak ground acceleration (PGA), which expresses the tip of the maximum spike of the acceleration ground motion. Buildings 2022, 12, x FOR PEER REVIEW 4 of 21 Buildings 2022, 12, x FOR PEER REVIEW 4 of 21 Buildings 2022, 12, 1293 5 of 21 Figure 4. The geometry of the structure and 3D structure shear walls with staggered openings. Response spectrum function and time history function (El Centro 1940) have been used in this study for seismic analysis. A response spectrum is a plot of the maximum response amplitude (displacement, velocity or acceleration) versus time period of many linear single degree of freedom oscillators to a give component of ground motion as shown in Figure 5. The resulting plot can be used to choose the response of any linear SDOF oscillator, given its natural time period of oscillation. One such use is in evaluating the peak response of structures to ground motions. The first data listed from an earth- quake record are usually the peak ground acceleration (PGA), which expresses the tip of Fig Figure ure 44. . T The he g geometry eometry of of theth str e uctur struc e tand ure3D anstr d uctur 3D st ershear ucture walls she with ar w stagger alls w ed ith openings. staggered openings. the maximum spike of the acceleration ground motion. Response spectrum function and time history function (El Centro 1940) have been used in this study for seismic analysis. A response spectrum is a plot of the maximum response amplitude (displacement, velocity or acceleration) versus time period of many linear single degree of freedom oscillators to a give component of ground motion as shown in Figure 5. The resulting plot can be used to choose the response of any linear SDOF oscillator, given its natural time period of oscillation. One such use is in evaluating the peak response of structures to ground motions. The first data listed from an earth- quake record are usually the peak ground acceleration (PGA), which expresses the tip of the maximum spike of the acceleration ground motion. Figure 5. Response spectrum function definition. Figure 5. Response spectrum function definition. ETABS Software handles the initial conditions of a time function differently for linear ETABS Software handles the initial conditions of a time function differently for linear and nonlinear time-history load cases. Linear cases always start from zero, thus the and nonlinear time-history load cases. Linear cases always start from zero, thus the corre- corresponding time function must also start from zero and nonlinear cases may either start sponding time function must also start from zero and nonlinear cases may either start from zero or may continue from a previous case. When starting from zero, the time function from zero or may continue from a previous case. When starting from zero, the time func- is simply defined to start with a zero value. When analysis continues from a previous tion is simply defined to start with a zero value. When analysis continues from a previous case, it is supposed that the time function also continues relative to its starting value. A case, it is supposed that the time function also continues relative to its starting value. A long record may be broken into multiple sequential analyses which use a single function long record may be broken into multiple sequential analyses which use a single function with arrival times. This prevents the need to create multiple modified functions. The time history function used in this study is shown in Figure 6. Figure 5. Response spectrum function definition. ETABS Software handles the initial conditions of a time function differently for linear and nonlinear time-history load cases. Linear cases always start from zero, thus the corre- sponding time function must also start from zero and nonlinear cases may either start from zero or may continue from a previous case. When starting from zero, the time func- tion is simply defined to start with a zero value. When analysis continues from a previous case, it is supposed that the time function also continues relative to its starting value. A long record may be broken into multiple sequential analyses which use a single function Buildings 2022, 12, x FOR PEER REVIEW 5 of 21 Buildings 2022, 12, 1293 6 of 21 with arrival times. This prevents the need to create multiple modified functions. The time history function used in this study is shown in Figure 6. Figure 6. Time history function definition. Figure 6. Time history function definition. This study was conducted on a regular plan structure with shear walls containing This study was conducted on a regular plan structure with shear walls containing vertical and staggered openings. The buildings are modelled with a floor area of 690 m vertical and staggered openings. The buildings are modelled with a floor area of 690 m (30 m  23 m) with 7 bays along a 30 m span and 5 bays along a 23 m span. (30 m × 23 m) with 7 bays along a 30 m span and 5 bays along a 23 m span. 3. Modeling and Analysis Table 1. Models data. Four models have been considered in this study. The first model contains a building without shear walls (Figure 1); the second model characterizes a building with shear Number of Stories 14 walls without openings (Figure 2); the third model includes shear walls with vertical Column Size ˑ (600 × 600) mm openings (Figure 3). However, the fourth model includes shear walls with staggered Beam Size ˑ (300 × 600) mm openings (Figure 4). Slab Depth ˑ 150 mm 4. Results & Discussion Shear Wall Thickness ˑ 300 mm 4.1. Story Displacement Size of opening ˑ (2 × 1.5) m Tables 4 and 5 and Figures 7 and 8 demonstrate the maximum displacement in the Story Height 3.5 m case of equivalent static analysis (ESA) (EX&EY). On the top floor, the results show that the Support Fixed building without shear walls produced about 53.089 mm when compared to the building Concrete Grade ˑ M25 with shear walls produced 37.212 mm, i.e., a 30% reduction in the X-direction. It is observed Steel Grade ˑ Fe 500 that the story displacement of the vertical opening at the roof is approximately 38.032 mm and 38.173 mm for staggered openings, respectively. Table Sim 2.i lLo arla yd , i s. n the Y-direction, on the top floor, the results show that the building without shear walls produced 56 mm, while the building with shear walls produced 38.125 mm, a Unit Weight of Concrete 25 kN/m 32% difference. The displacement story of the vertical opening at the roof was also discovered to be 38.99 mm for sDea taggd er e lo da o d p enings and 39.136 mm for unstaggered 3.o 7p 5e kN/ ningm s. T he story displacement in the case of response spectrum analysis (RSA) is shown in Tables 6 and 7 and Live load 3 kN/m Figures 9 and 10. Results show that the building without shear walls produced about 42.006 mm Beam Load 11 kN/m while the building with shear walls produced 28.938 mm, i.e., a 31% decline in the X-direction and a 33% decline in the Y-direction. The displacement story of the vertical opening at the roof is 29.283 mm for staggered openings in the X-direction and 29.434 mm for vertical and staggered openings in the Y-direction, respectively. Tables 8 and 9 and Figures 11 and 12 demonstrate the story displacement in the case of time history analysis (THA). The results appear to show Buildings 2022, 12, 1293 7 of 21 that the building without shear walls produced 45.727 mm, while the building with shear walls produced about 34.72 mm, i.e., a 24% reduction. In the X-direction, the displacement story of the vertical opening at the roof is 28.74 mm for staggered openings and 28.7 mm for unstaggered openings, 32.809 mm and 32.34 mm for vertical and staggered openings in the Y-direction respectively. Table 4. Comparison of the story displacements, ESA and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 53.089 37.212 38.032 38.173 Story 13 51.742 34.488 35.436 35.552 Story 12 49.685 31.614 32.628 32.724 Story 11 46.954 28.609 29.658 29.739 Story 10 43.649 25.48 26.538 26.603 Story 9 39.87 22.259 23.3 23.348 Story 8 35.715 18.987 19.991 20.022 Story 7 31.27 15.723 16.668 16.679 Story 6 26.614 12.532 13.398 13.392 Story 5 21.817 9.489 10.258 10.232 Story 4 16.941 6.681 7.332 7.294 Story 3 12.046 4.205 4.717 4.672 Story 2 7.216 2.171 2.523 2.488 Story 1 2.725 0.707 0.876 0.865 Table 5. Comparison of the story displacements, ESA, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 56.000 38.125 38.99 39.163 Story 13 54.475 35.291 36.281 36.423 Story 12 52.221 32.311 33.364 33.482 Story 11 49.275 29.203 30.287 30.389 Story 10 45.738 25.977 27.065 27.146 Story 9 41.715 22.663 23.731 23.796 Story 8 37.307 19.307 20.332 20.373 Story 7 32.606 15.965 16.927 16.952 Story 6 27.695 12.705 13.585 13.583 Story 5 22.648 9.604 10.382 10.366 Story 4 17.532 6.749 7.405 7.37 Story 3 12.411 4.237 4.752 4.716 Story 2 7.381 2.181 2.534 2.498 Story 1 2.749 0.707 0.875 0.873 The results show that buildings without shear walls have higher story displacement in comparison with other models. The shear wall with staggered openings experiences a higher displacement than vertical openings and shear walls without openings. A shear wall without openings reveals improved performance compared to shear walls with vertical and staggered openings. The same findings have been found in the published literature by Marius [29]. Overall, it can be concluded that the presences of shear walls in the buildings significantly improve the seismic response of the buildings regardless of the openings in that shear wall. Buildings 2022, 12, x FOR PEER REVIEW 7 of 21 Buildings 2022, 12, x FOR PEER REVIEW 7 of 21 Story 7 32.606 15.965 16.927 16.952 Story 7 32.606 15.965 16.927 16.952 Story 6 27.695 12.705 13.585 13.583 Story 6 27.695 12.705 13.585 13.583 Story 5 22.648 9.604 10.382 10.366 Story 5 22.648 9.604 10.382 10.366 Story 4 17.532 6.749 7.405 7.37 Story 4 17.532 6.749 7.405 7.37 Story 3 12.411 4.237 4.752 4.716 Story 3 12.411 4.237 4.752 4.716 Buildings 2022, 12, 1293 8 of 21 Story 2 7.381 2.181 2.534 2.498 Story 2 7.381 2.181 2.534 2.498 Story 1 2.749 0.707 0.875 0.873 Story 1 2.749 0.707 0.875 0.873 Figure 7. Story displacements, ESA in X-direction. Figure 7. Story displacements, ESA in X-direction. Figure 7. Story displacements, ESA in X-direction. Figure 8. Story displacements, ESA in the Y-direction. Figure 8. Story displacements, ESA in the Y-direction. Figure 8. Story displacements, ESA in the Y-direction. Similarly, in the Y-direction, on the top floor, the results show that the building with- Similarly, in the Y-direction, on the top floor, the results show that the building with- Table 6. Comparison of the story displacements, response spectrum, and X-direction (mm). out shear walls produced 56 mm, while the building with shear walls produced 38.125 out shear walls produced 56 mm, while the building with shear walls produced 38.125 mm, a 32% difference. The displacement story of the vertical opening at the roof was also Story without Shear mW malls , a 32% Shear differW ence alls . without The displa Openings cement story Vertical of the Openings vertical openinStaggered g at the roo Openings f was also discovered to be 38.99 mm for staggered openings and 39.136 mm for unstaggered open- discovered to be 38.99 mm for staggered openings and 39.136 mm for unstaggered open- Story 14 42.006 28.938 29.283 29.434 ings. The story displacement in the case of response spectrum analysis (RSA) is shown in ings. The story displacement in the case of response spectrum analysis (RSA) is shown in Story 13 41.105 26.869 27.339 27.468 Tables 6 and 7 and Figures 9 and 10. Results show that the building without shear walls Story 12 39.745Tables 6 and 7 and Figure 24.699 s 9 and 10. Results show 25.251 that the building witho 25.361 ut shear walls Story 11 37.935produced about 42.00622.439 mm while the building with 23.057 shear walls produced 223.15 8.938 mm, i.e., produced about 42.006 mm while the building with shear walls produced 28.938 mm, i.e., Story 10 35.724 20.092 20.759 20.836 a 31% decline in the X-direction and a 33% decline in the Y-direction. The displacement a 31% decline in the X-direction and a 33% decline in the Y-direction. The displacement Story 9 33.152 17.673 18.373 18.433 story of the vertical opening at the roof is 29.283 mm for staggered openings in the X- story of the vertical opening at the roof is 29.283 mm for staggered openings in the X- Story 8 30.252 15.206 15.924 15.964 direction and 29.434 mm for vertical and staggered openings in the Y-direction, respec- direction and 29.434 mm for vertical and staggered openings in the Y-direction, respec- Story 7 27.047 12.722 13.441 13.459 tively. Tables 8 and 9 and Figures 11 and 12 demonstrate the story displacement in the tively. Tables 8 and 9 and Figures 11 and 12 demonstrate the story displacement in the Story 6 23.555 10.262 10.961 10.959 Story 5 19.788 7.878 8.533 8.509 Story 4 15.758 5.634 6.216 6.178 Story 3 11.482 3.61 4.087 4.041 Story 2 7.025 1.905 2.244 2.207 Story 1 2.694 0.641 0.807 0.793 Buildings 2022, 12, 1293 9 of 21 Table 7. Comparison of the story displacements, response spectrum, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 43.769 29.29 29.845 30.009 Story 13 42.743 27.159 27.822 27.96 Story 12 41.252 24.931 25.659 25.776 Story 11 39.305 22.619 23.393 23.493 Story 10 36.951 20.224 21.028 21.11 Story 9 34.23 17.764 18.583 18.648 Story 8 31.179 15.262 16.08 16.122 Story 7 27.822 12.75 13.551 13.574 Story 6 24.178 10.27 11.032 11.03 Story 5 20.264 7.872 8.572 8.554 Story 4 16.093 5.62 6.232 6.194 Story 3 11.681 3.593 4.088 4.049 Story 2 7.101 1.891 2.238 2.2 Buildings 2022, 12, x FOR PEER REVIEW 9 of 21 Buildings 2022, 12, x FOR PEER REVIEW 9 of 21 Story 1 2.688 0.634 0.801 0.796 Figure 9. Story displacement of the models, response spectrum analysis in the X-direction. Figure Figure 9. 9. Story Story displacement displacement of of the the models, models, r response esponse spectr spectrum um analysis analysis in in the the X-dir X-direction. ection. Figure 10. Story displacement of the models, response spectrum analysis, Y-direction. Figure 10. Story displacement of the models, response spectrum analysis, Y-direction. Figure 10. Story displacement of the models, response spectrum analysis, Y-direction. Table 8. Comparison of the story displacements, time history, and X-direction (mm). Table 8. Comparison of the story displacements, time history, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 45.727 34.74 28.749 28.662 Story 14 45.727 34.74 28.749 28.662 Story 13 44.907 32.402 26.854 26.753 Story 13 44.907 32.402 26.854 26.753 Story 12 43.659 29.935 24.805 24.699 Story 12 43.659 29.935 24.805 24.699 Story 11 41.941 27.329 22.651 22.546 Story 11 41.941 27.329 22.651 22.546 Story 10 39.98 24.57 20.405 20.303 Story 10 39.98 24.57 20.405 20.303 Story 9 37.979 21.667 18.09 18 Story 9 37.979 21.667 18.09 18 Story 8 35.546 18.652 15.727 15.644 Story 8 35.546 18.652 15.727 15.644 Story 7 32.594 15.577 13.337 13.266 Story 7 32.594 15.577 13.337 13.266 Story 6 29.044 12.511 10.942 10.87 Story 6 29.044 12.511 10.942 10.87 Story 5 24.855 9.54 8.575 8.51 Story 5 24.855 9.54 8.575 8.51 Story 4 20.043 6.759 6.289 6.214 Story 4 20.043 6.759 6.289 6.214 Story 3 14.698 4.28 4.159 4.096 Story 3 14.698 4.28 4.159 4.096 Story 2 9.009 2.224 2.292 2.23 Story 2 9.009 2.224 2.292 2.23 Story 1 3.454 0.736 0.824 0.807 Story 1 3.454 0.736 0.824 0.807 Buildings 2022, 12, 1293 10 of 21 Table 8. Comparison of the story displacements, time history, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 45.727 34.74 28.749 28.662 Story 13 44.907 32.402 26.854 26.753 Story 12 43.659 29.935 24.805 24.699 Story 11 41.941 27.329 22.651 22.546 Story 10 39.98 24.57 20.405 20.303 Story 9 37.979 21.667 18.09 18 Story 8 35.546 18.652 15.727 15.644 Story 7 32.594 15.577 13.337 13.266 Story 6 29.044 12.511 10.942 10.87 Story 5 24.855 9.54 8.575 8.51 Story 4 20.043 6.759 6.289 6.214 Buildings 2022, 12, x FOR PEER REVIEW 10 of 21 Story 3 14.698 4.28 4.159 4.096 Story 2 9.009 2.224 2.292 2.23 Story 1 3.454 0.736 0.824 0.807 Table 9. Comparison of the story displacements, time history, and Y-direction (mm). Table 9. Comparison of the story displacements, time history, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 46.471 32.91 32.809 32.34 Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 13 45.45 30.694 30.608 30.14 Story 14 46.471 32.91 32.809 32.34 Story 12 43.937 28.363 28.24 27.777 Story 13 45.45 30.694 30.608 30.14 Story 11 41.891 25.903 25.755 25.312 Story 12 43.937 28.363 28.24 27.777 Sto Story ry 10 11 39.3 41.891 27 2 25.903 3.298 25.755 23.168 25.312 22.751 Story 10 39.327 23.298 23.168 22.751 Story 9 36.562 20.554 20.506 20.127 Story 9 36.562 20.554 20.506 20.127 Story 8 33.959 17.697 17.795 17.457 Story 8 33.959 17.697 17.795 17.457 Story 7 30.943 14.778 15.058 14.767 Story 7 30.943 14.778 15.058 14.767 Story 6 27.447 11.865 12.325 12.078 Story 6 27.447 11.865 12.325 12.078 Story 5 23.419 9.039 9.634 9.431 Story 5 23.419 9.039 9.634 9.431 Story 4 18.849 6.397 7.043 6.882 Story 4 18.849 6.397 7.043 6.882 Story 3 13.791 4.043 4.641 4.523 Story 3 13.791 4.043 4.641 4.523 Story 2 8.412 2.095 2.545 2.477 Story 2 8.412 2.095 2.545 2.477 Story 1 3.186 0.686 0.909 0.896 Story 1 3.186 0.686 0.909 0.896 Figure 11. Story displacement of the models, time history analysis, X-direction. Figure 11. Story displacement of the models, time history analysis, X-direction. Figure 12. Displacement of the models, time history analysis, Y-direction. Buildings 2022, 12, x FOR PEER REVIEW 10 of 21 Table 9. Comparison of the story displacements, time history, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 46.471 32.91 32.809 32.34 Story 13 45.45 30.694 30.608 30.14 Story 12 43.937 28.363 28.24 27.777 Story 11 41.891 25.903 25.755 25.312 Story 10 39.327 23.298 23.168 22.751 Story 9 36.562 20.554 20.506 20.127 Story 8 33.959 17.697 17.795 17.457 Story 7 30.943 14.778 15.058 14.767 Story 6 27.447 11.865 12.325 12.078 Story 5 23.419 9.039 9.634 9.431 Story 4 18.849 6.397 7.043 6.882 Story 3 13.791 4.043 4.641 4.523 Story 2 8.412 2.095 2.545 2.477 Story 1 3.186 0.686 0.909 0.896 Buildings 2022, 12, 1293 11 of 21 Figure 11. Story displacement of the models, time history analysis, X-direction. Figure Figure12. 12. Displacement Displacementof of the themodels, models,time time history historyanalysis, analysis,Y Y -dir -diection. rection. 4.2. Story Drift Tables 10 and 11 and Figures 13 and 14 demonstrate the story drifts carried out by using ESA (EX&EY). The results show that the maximum drift that could be found on the fourth floor due to the buildings lack of shear walls is 4.895 mm in X-direction and 5.121 mm in Y-direction. It is also observed that the maximum drift story of the building with shear walls seen on the eighth floor is 3.274 mm, 3.323 mm, and 3.344 mm for the building’s vertical and staggered openings in the X-direction, and 3.358 mm for shear walls without openings and 3.405 mm and 3.425 mm as results of shear walls with a vertical and staggered opening in the Y-direction. Tables 12 and 13 and Figures 15 and 16 demonstrate the story drifts in the case of response spectrum analysis (RSA) in the (X&Y) direction. The results show that the maximum drift seen on the third floor due to the building without shear walls is 4.476 mm in X-direction and 4.6 mm in Y-direction. It is consequently observed that the maximum drift story of the building with shear walls seen on the eighth floor is 2.544 mm, 2.566 mm, and 2.585 mm for the building’s vertical and staggered opening, respectively, in X-direction. However, shear walls without openings have a 2.573 mm thickness, while shear walls with vertical and staggered openings in the Y-direction have 2.614 mm and 2.63 mm thicknesses, respectively. Tables 14 and 15 and Figures 17 and 18 determine the story drifts in the case of time history analysis (THA) in the (X&Y) direction. The results show that the maximum drift found on the third floor is due to the building’s lack of shear walls, 5.689 mm in X-direction and 5.379 mm in Y-direction. Likewise, it was observed that the maximum drift story of the building with shear walls seen on the eighth floor was 3.075 mm, 2.397 mm, and 2.381 mm for the building’s vertical and staggered opening in X-direction, respectively; 2.919 mm for shear walls with no openings, and 2.783 mm and 2.741 mm for shear walls with vertical and staggered Y-direction openings. The results show that the story drift increases from the second story and onwards. It gradually grew and has a tendency to fall back to the top story. The model with a vertical opening and staggered opening shear wall indicates more drift value compared to the shear wall without an opening. The building without shear walls shows a high drift value. The same findings have been found in the published literature by Marius [29]. Buildings 2022, 12, 1293 12 of 21 Table 10. Comparison of the measured story drift, static analysis, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.347 2.725 2.61 2.621 Story 13 2.057 2.874 2.808 2.828 Story 12 2.731 3.005 2.97 2.985 Story 11 3.305 3.129 3.12 3.136 Story 10 3.778 3.222 3.238 3.255 Story 9 4.155 3.271 3.309 3.326 Story 8 4.445 3.274 3.323 3.344 Story 7 4.656 3.192 3.27 3.288 Story 6 4.797 3.043 3.141 3.161 Story 5 4.876 2.808 2.927 2.938 Story 4 4.895 2.476 2.616 2.624 Story 3 4.83 2.034 2.195 2.185 Story 2 4.49 1.463 1.647 1.624 Story 1 2.725 0.707 0.876 0.865 Table 11. Comparison of the story drift, static analysis, Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.526 2.834 2.722 2.74 Story 13 2.253 2.98 2.917 2.941 Story 12 2.946 3.108 3.076 3.094 Story 11 3.538 3.226 3.222 3.242 Story 10 4.023 3.314 3.334 3.352 Story 9 4.408 3.356 3.399 3.423 Story 8 4.701 3.358 3.405 3.425 Story 7 4.911 3.26 3.343 3.368 Story 6 5.047 3.101 3.204 3.22 Story 5 5.116 2.855 2.977 2.997 Story 4 5.121 2.512 2.654 2.658 Story 3 5.103 2.057 2.22 2.218 Story 2 4.632 1.474 1.659 1.631 Buildings 2022, 12, x FOR PEER REVIEW 12 of 21 Story 1 2.749 0.707 0.875 0.873 Figure Figure13. 13. Story Storydrift driftof ofthe the models: models: static static analysis analysis and and X-dir X-dir ection ectionanalysis. analysis. Figure 14. Story drift of the models: static analysis and Y-direction (mm). Tables 12 and 13 and Figures 15 and 16 demonstrate the story drifts in the case of response spectrum analysis (RSA) in the (X&Y) direction. The results show that the max- imum drift seen on the third floor due to the building without shear walls is 4.476 mm in X-direction and 4.6 mm in Y-direction. It is consequently observed that the maximum drift story of the building with shear walls seen on the eighth floor is 2.544 mm, 2.566 mm, and 2.585 mm for the building’s vertical and staggered opening, respectively, in X-direction. However, shear walls without openings have a 2.573 mm thickness, while shear walls with vertical and staggered openings in the Y-direction have 2.614 mm and 2.63 mm thick- nesses, respectively. Buildings 2022, 12, x FOR PEER REVIEW 12 of 21 Buildings 2022, 12, 1293 13 of 21 Figure 13. Story drift of the models: static analysis and X-direction analysis. Figure 14. Story drift of the models: static analysis and Y-direction (mm). Figure 14. Story drift of the models: static analysis and Y-direction (mm). Tables 12 and 13 and Figures 15 and 16 demonstrate the story drifts in the case of response spectrum analysis (RSA) in the (X&Y) direction. The results show that the max- Table 12. Comparison of the story drift, response spectrum, and X-direction (mm). imum drift seen on the third floor due to the building without shear walls is 4.476 mm in X-direction and 4.6 mm in Y-direction. It is consequently observed that the maximum drift Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings story of the building with shear walls seen on the eighth floor is 2.544 mm, 2.566 mm, and Story 14 1.144 2.138 2.038 2.052 2.585 mm for the building’s vertical and staggered opening, respectively, in X-direction. Story 13 1.777 2.256 2.197 2.215 However, shear walls without openings have a 2.573 mm thickness, while shear walls Story 12 2.318 2.355 2.318 2.334 with vertical and staggered openings in the Y-direction have 2.614 mm and 2.63 mm thick- Story 11 2.732 2.443 2.424 2.439 nesses, respectively. Story 10 3.063 2.508 2.503 2.519 Story 9 3.338 2.543 2.552 2.568 Story 8 3.572 2.544 2.566 2.585 Story 7 3.782 2.504 2.542 2.559 Story 6 3.981 2.414 2.472 2.491 Story 5 4.167 2.263 2.345 2.357 Story 4 4.342 2.035 2.145 2.153 Story 3 4.476 1.71 1.852 1.841 Story 2 4.333 1.266 1.44 1.417 Story 1 2.694 0.641 0.807 0.793 Table 13. Comparison of the story drift, response spectrum analysis, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.278 2.201 2.118 2.136 Story 13 1.923 2.316 2.273 2.295 Story 12 2.471 2.41 2.392 2.407 Story 11 2.889 2.493 2.493 2.511 Story 10 3.221 2.551 2.566 2.58 Story 9 3.499 2.58 2.608 2.628 Story 8 3.734 2.573 2.614 2.63 Story 7 3.945 2.526 2.582 2.605 Story 6 4.14 2.429 2.504 2.519 Story 5 4.319 2.271 2.369 2.387 Story 4 4.483 2.037 2.161 2.163 Story 3 4.6 1.707 1.859 1.857 Story 2 4.416 1.26 1.44 1.411 Story 1 2.688 0.634 0.801 0.796 Buildings 2022, 12, x FOR PEER REVIEW 13 of 21 Table 12. Comparison of the story drift, response spectrum, and X-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.144 2.138 2.038 2.052 Story 13 1.777 2.256 2.197 2.215 Story 12 2.318 2.355 2.318 2.334 Story 11 2.732 2.443 2.424 2.439 Story 10 3.063 2.508 2.503 2.519 Story 9 3.338 2.543 2.552 2.568 Story 8 3.572 2.544 2.566 2.585 Story 7 3.782 2.504 2.542 2.559 Story 6 3.981 2.414 2.472 2.491 Story 5 4.167 2.263 2.345 2.357 Story 4 4.342 2.035 2.145 2.153 Story 3 4.476 1.71 1.852 1.841 Story 2 4.333 1.266 1.44 1.417 Story 1 2.694 0.641 0.807 0.793 Table 13. Comparison of the story drift, response spectrum analysis, and Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.278 2.201 2.118 2.136 Story 13 1.923 2.316 2.273 2.295 Story 12 2.471 2.41 2.392 2.407 Story 11 2.889 2.493 2.493 2.511 Story 10 3.221 2.551 2.566 2.58 Story 9 3.499 2.58 2.608 2.628 Story 8 3.734 2.573 2.614 2.63 Story 7 3.945 2.526 2.582 2.605 Story 6 4.14 2.429 2.504 2.519 Story 5 4.319 2.271 2.369 2.387 Story 4 4.483 2.037 2.161 2.163 Story 3 4.6 1.707 1.859 1.857 Buildings 2022, 12, 1293 14 of 21 Story 2 4.416 1.26 1.44 1.411 Story 1 2.688 0.634 0.801 0.796 Buildings 2022, 12, x FOR PEER REVIEW 14 of 21 Figure Figure 15. 15. Story Story drift drift of of the the models, models, r response esponse spectr spectrum um analysis analysis and and X-dir X-dir ection. ection. Figure Figure 16. 16. Story Story drift, drift, rresponse esponse spectr spectrum um analysis, analysis, and and Y Y -dir -dir ection. ection. Tables 14 and 15 and Figures 17 and 18 determine the story drifts in the case of time Table 14. Comparison of the story drift, time history analysis, X-direction (mm). history analysis (THA) in the (X&Y) direction. The results show that the maximum drift found on the third floor is due to the building’s lack of shear walls, 5.689 mm in X-direc- Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings tion and 5.379 mm in Y-direction. Likewise, it was observed that the maximum drift story Story 14 1.04 2.338 1.907 1.909 of the building with shear walls seen on the eighth floor was 3.075 mm, 2.397 mm, and Story 13 1.624 2.467 2.048 2.054 2.381 mm for the building’s vertical and staggered opening in X-direction, respectively; Story 12 2.206 2.606 2.155 2.154 2.919 mm for shear walls with no openings, and 2.783 mm and 2.741 mm for shear walls Story 11 2.714 2.759 2.246 2.243 Story 10 3.123 with vertical and stagger 2.903 ed Y-direction openings. 2.315 2.305 Story 9 3.533 3.015 2.363 2.356 Story 8 3.862 3.075 2.397 2.381 Table 14. Comparison of the story drift, time history analysis, X-direction (mm). Story 7 4.078 3.066 2.396 2.376 SStory tory 6 without Sh4.233 ear Walls Shear Walls wit 2.972 hout Openings Vertica 2.367 l Openings Staggere 2.364 d Openings Story 5 4.812 2.78 2.287 2.296 Story 14 1.04 2.338 1.907 1.909 Story 4 5.345 2.479 2.131 2.124 Story 13 1.624 2.467 2.048 2.054 Story 3 5.689 2.056 1.869 1.866 Story 12 2.206 2.606 2.155 2.154 Story 2 5.555 1.493 1.47 1.43 Sto Story ry 111 2.71 3.454 4 2 0.736 .759 0.831 2.246 0.807 2.243 Story 10 3.123 2.903 2.315 2.305 Story 9 3.533 3.015 2.363 2.356 Story 8 3.862 3.075 2.397 2.381 Story 7 4.078 3.066 2.396 2.376 Story 6 4.233 2.972 2.367 2.364 Story 5 4.812 2.78 2.287 2.296 Story 4 5.345 2.479 2.131 2.124 Story 3 5.689 2.056 1.869 1.866 Story 2 5.555 1.493 1.47 1.43 Story 1 3.454 0.736 0.831 0.807 Table 15. Comparison of the story drift, time history analysis, Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.197 2.311 2.213 2.201 Story 13 1.817 2.432 2.368 2.363 Story 12 2.446 2.541 2.485 2.466 Story 11 2.994 2.64 2.587 2.561 Story 10 3.491 2.745 2.662 2.626 Buildings 2022, 12, 1293 15 of 21 Table 15. Comparison of the story drift, time history analysis, Y-direction (mm). Story without Shear Walls Shear Walls without Openings Vertical Openings Staggered Openings Story 14 1.197 2.311 2.213 2.201 Buildings 2022, 12, x FOR PEER REVIEW 15 of 21 Buildings 2022, 12, x FOR PEER REVIEW 15 of 21 Story 13 1.817 2.432 2.368 2.363 Story 12 2.446 2.541 2.485 2.466 Story 11 2.994 2.64 2.587 2.561 Story 10 3.491 2.745 2.662 2.626 Story 9 3.913 2.856 2.727 2.679 Story 9 3.913 2.856 2.727 2.679 Story 9 3.913 2.856 2.727 2.679 Story 8 4.204 2.919 2.783 2.741 Story 8 4.204 2.919 2.783 2.741 Story 8 4.204 2.919 2.783 2.741 Story 7 4.343 2.914 2.757 2.722 Story 7 4.343 2.914 2.757 2.722 Story 7 4.343 2.914 2.757 2.722 Story 6 4.328 2.826 2.692 2.653 Story 6 4.328 2.826 2.692 2.653 Story 6 4.328 2.826 2.692 2.653 Sto Story ry 55 4.54.57 7 2.642 2.642 2.591 2.591 2.549 2.549 Story 5 4.57 2.642 2.591 2.549 Story 4 5.058 2.354 2.404 2.368 Story 4 5.058 2.354 2.404 2.368 Story 4 5.058 2.354 2.404 2.368 Story 3 5.379 1.947 2.098 2.046 Story 3 5.379 1.947 2.098 2.046 Story 3 5.379 1.947 2.098 2.046 Story 2 5.226 1.41 1.639 1.592 Story 2 5.226 1.41 1.639 1.592 Story 1 3.186 0.686 0.909 0.896 Story 2 5.226 1.41 1.639 1.592 Story 1 3.186 0.686 0.909 0.896 Story 1 3.186 0.686 0.909 0.896 Figure 17. Story drift of the models, time history analysis, X-direction. Figure 17. Story drift of the models, time history analysis, X-direction. Figure 17. Story drift of the models, time history analysis, X-direction. Figure 18. Story drift of the models, time history analysis, Y-direction. Figure Figure 18. 18. Story Story drift drift of of the the models, models, time time history history analysis, analysis, Y Y-dir -direction. ection. The results show that the story drift increases from the second story and onwards. It The results show that the story drift increases from the second story and onwards. It gradually grew and has a tendency to fall back to the top story. The model with a vertical gradually grew and has a tendency to fall back to the top story. The model with a vertical opening and staggered opening shear wall indicates more drift value compared to the opening and staggered opening shear wall indicates more drift value compared to the shear wall without an opening. The building without shear walls shows a high drift value. shear wall without an opening. The building without shear walls shows a high drift value. The same findings have been found in the published literature by Marius [29]. The same findings have been found in the published literature by Marius [29]. Buildings 2022, 12, x FOR PEER REVIEW 16 of 21 Buildings 2022, 12, 1293 16 of 21 4.3. Story Forces 4.3. Story In theFor caces se of the response spectrum, the values of story forces on the first floor are 3558.8 kN for modal without shear walls, 6295.9 kN for building with shear walls, and In the case of the response spectrum, the values of story forces on the first floor are 5906.5 kN, 5871.6 kN for vertical opening, and staggered opening, respectively (as shown 3558.8 kN for modal without shear walls, 6295.9 kN for building with shear walls, and in Figures 19 and 20). As can be seen, the reduction percentage of story force value on the 5906.5 kN, 5871.6 kN for vertical opening, and staggered opening, respectively (as shown in first floor is about 16.3% in buildings without shear walls when compared to buildings Figures 19 and 20). As can be seen, the reduction percentage of story force value on the with shear walls. Figures 21 and 22 demonstrate the story forces in the case of time history first floor is about 16.3% in buildings without shear walls when compared to buildings analysis; the story forces on the first floor due to building without shear walls are 4491.0 with shear walls. Figures 21 and 22 demonstrate the story forces in the case of time history kN when compared to building with shear walls, 7087.7 kN, and 5381.2 kN, 5333.9 kN for analysis; the story forces on the first floor due to building without shear walls are 4491.0 kN shear walls staggered and vertical openings in the case of time history, respectively. Ad- when compared to building with shear walls, 7087.7 kN, and 5381.2 kN, 5333.9 kN for shear ditionally, it is noticed that the difference in story forces in the time history analysis (THA) walls staggered and vertical openings in the case of time history, respectively. Additionally, as compared to the response spectrum analysis (RSA) results are insignificant for the same it is noticed that the difference in story forces in the time history analysis (THA) as compared cases. Overall, it can be said that the displacement and story drift of the building signifi- to the response spectrum analysis (RSA) results are insignificant for the same cases. Overall, ca it can ntly be affsaid ected that by the the displacement height of the st and rucstory tural ele drift men oft, the sto building ry or buil significantly ding. Therefaf ore fected , the sh byea the r wa hei lls ght ope of nin the gs str have uctural a sligelement, ht effect o story n these or m building. echanical Ther prope efor rties e, the as com shear pare walls d to openings have a slight effect on these mechanical properties as compared to the story the story forces. However, the distribution of the lateral forces (story forces) on the build- in for g ces. are s However ignifican,tlthe y inf distribution luenced by th of e the weilateral ght of tfor he ces buildin (story g. C for onces) sequentl on the y, tbuilding he openin ar gs e significantly influenced by the weight of the building. Consequently, the openings on the on the shear wall reduced the weight and stiffness of the building and then increased the shear wall reduced the weight and stiffness of the building and then increased the lateral lateral forces. Moreover, compared to other methods of analysis, time history analysis forces. Moreover, compared to other methods of analysis, time history analysis shows that shows that the story forces are higher for all models. That might be attributed to the higher the story forces are higher for all models. That might be attributed to the higher lateral lateral forces applied on the building which generated by earthquake (El Centro). forces applied on the building which generated by earthquake (El Centro). The findings of this study agree with the results of the study by Mosoarca [12]. Figure 19. Story forces of the models, response spectrum analysis, X-direction. Figure 19. Story forces of the models, response spectrum analysis, X-direction. Buildings 2022, 12, x FOR PEER REVIEW 17 of 21 Buildings 2022, 12, 1293 17 of 21 Buildings 2022, 12, x FOR PEER REVIEW 17 of 21 Figure 20. Story forces of the models, response spectrum analysis, Y-direction. Figure 20. Story forces of the models, response spectrum analysis, Y-direction. Figure 20. Story forces of the models, response spectrum analysis, Y-direction. Figure 21. Story forces of the models, time history analysis, X-direction. Figure 21. Story forces of the models, time history analysis, X-direction. Figure 21. Story forces of the models, time history analysis, X-direction. Buildings 2022, 12, x FOR PEER REVIEW 18 of 21 Buil Buildings dings 2022 2022,, 12 12,, 1293 x FOR PEER REVIEW 18 18 oof f 21 21 Figure 22. Story forces of the models, time history analysis, Y-direction. Figure 22. Story forces of the models, time history analysis, Y-direction. Figure 22. Story forces of the models, time history analysis, Y-direction. 4.4. Time Period As shown in Figure 23 the time period of the structure increases with an increase in 4.4. TThe ime P findings eriod of this study agree with the results of the study by Mosoarca [12]. mass. The time period decreases when the shear wall is provided and is a minimum for As shown in Figure 23 the time period of the structure increases with an increase in 4.4. Time Period shear walls on the outer edges of the structure. A building with shear walls indicates that mass. The time period decreases when the shear wall is provided and is a minimum for the time period reduces compared to a building without shear walls. Besides, a building As shown in Figure 23 the time period of the structure increases with an increase in shear walls on the outer edges of the structure. A building with shear walls indicates that with shear walls with a vertical opening, as in Figure 23, shows that the time period de- mass. The time period decreases when the shear wall is provided and is a minimum for the time period reduces compared to a building without shear walls. Besides, a building shear clines walls compa on re the d to outer a staedges ggered of ope the nstr ing uctur . e. A building with shear walls indicates that with shear walls with a vertical opening, as in Figure 23, shows that the time period de- Finally, more or less similar behaviour of using finite element modelling in solving the time period reduces compared to a building without shear walls. Besides, a building clines compared to a staggered opening. with struc shear tures walls and m with atera iavertical ls problem opening, s has be asen in con Figur duc e 23 ted , shows by seve that ral the resea time rchperiod ers, wh declines ich pro- Finally, more or less similar behaviour of using finite element modelling in solving compar vided by liter ed to aastagger ture reports ed opening. [30–37]. structures and materials problems has been conducted by several researchers, which pro- vided by literature reports [30–37]. Figure Figure23. 23. The The time time period period of ofthe the models. models. Figure 23. The time period of the models. Buildings 2022, 12, 1293 19 of 21 Finally, more or less similar behaviour of using finite element modelling in solving structures and materials problems has been conducted by several researchers, which provided by literature reports [30–37]. 5. Conclusions From the analytical study on the effect of openings on the seismic behaviour of shear walls, the following conclusions could be drawn: 1. Based on the ESA method of the models, it can be seen that the model with a shear wall showed improved performance in terms of displacement reduction. Additionally, a building with a shear wall without an opening shows better performance based on displacement reduction. 2. According to the response spectrum analysis, it is observed that the percentage reduction of story force value on the first floor is about 43% in buildings without shear walls when compared to buildings with shear walls and about 28% in buildings with shear walls when compared to shear walls with opening, equally for time history analysis. 3. From time-history analysis, it is concluded that the building with a shear wall showed good quality performance in terms of displacement reduction. Similarly, a build- ing with a shear wall without an opening shows superior performance based on displacement reduction. 4. The results show that using shear walls cuts down on story drift and movement in the X and Y directions by a lot. 5. The maximum story drift in most of the cases produced is found on the seventh floor. 6. In all three analyses (equivalent static analysis, response spectrum, and time his- tory analysis), the results concluded that shear walls without openings show less displacement as compared to the other models. 7. Similarly, it has been found that shear walls without openings show less drift as compared to other models. Thus, in turn, it emphasizes the vital impact of using these models. 8. Compared to other methods of analysis, time history analysis shows that the seismic story forces are higher for all models. Author Contributions: Conceptualization, A.S., A.H., H.M.N., S.Q., M.M.S.S., and N.S.M.; method- ology, A.S, A.H., H.M.N., M.M.S.S., and N.S.M.; software, A.S. and A.H.; validation, H.M.N., S.Q., M.M.S.S., N.S.M.; formal analysis, A.S. and A.H.; investigation, A.S., A.H., H.M.N., S.Q. M.M.S.S., and N.S.M.; resources, A.S., A.H., H.M.N., M.M.S.S., and N.S.M.; data curation, A.S., A.H., H.M.N., M.M.S.S., S.Q., and N.S.M.; writing—original draft preparation, A.S.; writing—review and editing, A.S., A.H., H.M.N., M.M.S.S., and N.S.M.; visualization, A.S. and A.H.; supervision, A.S., A.H., and H.M.N.; project administration, M.M.S.S.; funding acquisition, M.M.S.S. All authors have read and agreed to the published version of the manuscript. Funding: The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program ‘Priority 2030’ (Agreement 075-15-2021-1333 dated 30 September 2021). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data used to support the findings of this study are included in the article. Acknowledgments: The authors extend their thanks to the Ministry of Science and Higher Education of the Russian Federation for funding this work. Conflicts of Interest: The authors declare no conflict of interest. Buildings 2022, 12, 1293 20 of 21 References 1. Lu, X.; Xie, L.; Guan, H.; Huang, Y.; Lu, X. A Shear Wall Element for Nonlinear Seismic Analysis of Super-Tall Buildings Using OpenSees. Finite Elem. Anal. Des. 2015, 98, 14–25. [CrossRef] 2. Najm, H.M.; Ibrahim, A.M.; Sabri, M.M.; Hassan, A.; Morkhade, S.; Mashaan, N.S.; Eldirderi, M.M.A.; Khedher, K.M. Modelling of Cyclic Load Behaviour of Smart Composite Steel-Concrete Shear Wall Using Finite Element Analysis. Buildings 2022, 12, 850. [CrossRef] 3. Pei, S.; Popovski, M.; van de Lindt, J.W. Seismic Design of a Multi-Story Cross Laminated Timber Building Based on Component Level Testing. In Proceedings of the World Conference on Timber Engineering, Auckland, New Zealand, 16–19 July 2012. 4. Esmaili, O.; Epackachi, S.; Samadzad, M.; Mirghaderi, S.R. Study of Structural RC Shear Wall System in a 56-Story RC Tall Building. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. 5. Vigh, L.G.; Deierlein, G.G.; Miranda, E.; Liel, A.B.; Tipping, S. Seismic Performance Assessment of Steel Corrugated Shear Wall System Using Non-Linear Analysis. J. Constr. Steel Res. 2013, 85, 48–59. [CrossRef] 6. Hassan, A.; Pal, S. Effect of Soil Condition on Seismic Response of Isolated Base Buildings. Int. J. Adv. Struct. Eng. 2018, 10, 249–261. [CrossRef] 7. Hassan, A. Optimization of Base Isolation Parameters. LAMBERT Acad. Publ. 2017, 97, 1207–1222. 8. Hassan, A.; Pal, S. Performance Analysis of Base Isolation & Fixed Base Buildings. ISSN (Online) Int. J. Eng. Res. Mech. Civ. Eng. (IJERMCE) 2017, 2, 152–157. 9. Fintel, M. Performance of Buildings with Shear Walls in Earthquakes of the Last Thirty Years. PCI J. 2014, 40, 62–80. [CrossRef] 10. Wallace, J.W.; Thomsen IV, J.H. Seismic Design of RC Structural Walls. Part II: Applications. J. Struct. Eng. 2002, 121, 88–101. [CrossRef] 11. Wu, Y.T.; Kang, D.Y.; Yang, Y.B. Seismic Performance of Steel and Concrete Composite Shear Walls with Embedded Steel Truss for Use in High-Rise Buildings. Eng. Struct. 2016, 125, 39–53. [CrossRef] 12. Mosoarca, M. Failure Analysis of RC Shear Walls with Staggered Openings under Seismic Loads. Eng. Fail. Anal. 2014, 41, 48–64. [CrossRef] 13. Farzampour, A.; Laman, J.A. Behavior Prediction of Corrugated Steel Plate Shear Walls with Openings. J. Constr. Steel Res. 2015, 114, 258–268. [CrossRef] 14. Taranath, B.S. Reinforced Concrete Design of Tall Buildings; CRC Press: Boca Raton, FL, USA, 2009. 15. Galal, K.; El-Sokkarry, H. Recent Advancements in Retrofit of Rc Shear Walls. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. 16. Najm, H.M.; Ibrahim, A.M.; Sabri, M.M.S.; Hassan, A.; Morkhade, S.; Mashaan, N.S.; Eldirderi, M.M.A.; Khedher, K.M. Evaluation and Numerical Investigations of the Cyclic Behavior of Smart Composite Steel–Concrete Shear Wall: Comprehensive Study of Finite Element Model. Materials 2022, 15, 4496. [CrossRef] [PubMed] 17. Zhang, Z.; Wang, F. Experimental Investigation into the Seismic Performance of Prefabricated Reinforced Masonry Shear Walls with Vertical Joint Connections. Appl. Sci. 2021, 11, 4421. [CrossRef] 18. Dang-Vu, H.; Shin, J.; Lee, K. Seismic Fragility Assessment of Columns in a Piloti-Type Building Retrofitted with Additional Shear Walls. Sustainability 2020, 12, 6530. [CrossRef] 19. Coccia, S.; di Carlo, F.; Imperatore, S. Masonry Walls Retrofitted with Vertical FRP Rebars. Buildings 2020, 10, 72. [CrossRef] 20. Jeon, S.H.; Park, J.H. Seismic Fragility of Ordinary Reinforced Concrete Shear Walls with Coupling Beams Designed Using a Performance-Based Procedure. Appl. Sci. 2020, 10, 4075. [CrossRef] 21. Zheng, S.-S.; Yang, W.; Yang, F.; Sun, L.-F.; Hou, P.-J. Seismic Fragility Analysis for RC Core Walls Structure Based on MIDA Method. Zhendong Yu Chongji/J. Vib. Shock 2015, 34, 117–123. [CrossRef] 22. Coronelli, D.; Martinelli, L.; Mulas, M.G. Pushover Analysis of Shaking Table Tests on a RC Shear Wall. In Proceedings of the Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011, Leuven, Belgium, 4–6 July 2011. 23. Wang, Q.; Shi, Q.; Tian, H. Experimental Study on Shear Capacity of SRC Joints with Different Arrangement and Sizes of Cross-Shaped Steel in Column. Steel Compos. Struct. 2016, 21, 267–287. [CrossRef] 24. Lehman, D.E.; Turgeon, J.A.; Birely, A.C.; Hart, C.R.; Marley, K.P.; Kuchma, D.A.; Lowes, L.N. Seismic Behavior of a Modern Concrete Coupled Wall. J. Struct. Eng. 2013, 139, 1371–1381. [CrossRef] 25. Husain, M.; Eisa, A.S.; Hegazy, M.M. Strengthening of Reinforced Concrete Shear Walls with Openings Using Carbon Fiber- Reinforced Polymers. Int. J. Adv. Struct. Eng. 2019, 11, 129–150. [CrossRef] 26. Dou, C.; Jiang, Z.Q.; Pi, Y.L.; Guo, Y.L. Elastic Shear Buckling of Sinusoidally Corrugated Steel Plate Shear Wall. Eng. Struct. 2016, 121, 136–146. [CrossRef] 27. Berman, J.W.; Bruneau, M. Experimental Investigation of Light-Gauge Steel Plate Shear Walls. J. Struct. Eng. 2005, 131, 259–267. [CrossRef] 28. El Ouni, M.H.; Laissy, M.Y.; Ismaeil, M.; Ben Kahla, N. Effect of Shear Walls on the Active Vibration Control of Buildings. Buildings 2018, 8, 164. [CrossRef] 29. Marius, M. Seismic Behaviour of Reinforced Concrete Shear Walls with Regular and Staggered Openings after the Strong Earthquakes between 2009 and 2011. Eng. Fail. Anal. 2013, 34, 537–565. [CrossRef] 30. Najem, H.M.; Ibrahim, A.M. The Effect of Infill Steel Plate Thickness on the Cycle Behavior of Steel Plate Shear Walls. Diyala J. Eng. Sci. 2018, 11, 1–6. [CrossRef] Buildings 2022, 12, 1293 21 of 21 31. Najem, H.M.; Ibrahim, A.M. Influence of Concrete Strength on the Cycle Performance of Composite Steel Plate Shear Walls. Diyala J. Eng. Sci. 2018, 11, 1–7. [CrossRef] 32. Fadhil, H.; Ibrahim, A.; Mahmood, M. Effect of Corrugation Angle and Direction on the Performance of Corrugated Steel Plate Shear Walls. Civ. Eng. J. 2018, 4, 2667–2679. [CrossRef] 33. Ahmed, H.U.; Mohammed, A.S.; Faraj, R.H.; Qaidi, S.M.; Mohammed, A.A. Compressive strength of geopolymer concrete modified with nano-silica: Experimental and modeling investigations. Case Stud. Constr. Mater. 2022, 16, e01036. [CrossRef] 34. Khan, M.; Cao, M.; Ali, M. Cracking behaviour and constitutive modelling of hybrid fibre reinforced concrete. J. Build. Eng. 2020, 30, 101272. [CrossRef] 35. Parvez, I.; Shen, J.; Khan, M.; Cheng, C. Modeling and solution techniques used for hydro generation scheduling. Water 2019, 11, 1392. [CrossRef] 36. Ahmed, H.U.; Mohammed, A.S.; Qaidi, S.M.; Faraj, R.H.; Hamah Sor, N.; Mohammed, A.A. Compressive strength of geopolymer concrete composites: A systematic comprehensive review, analysis and modeling. Eur. J. Environ. Civ. Eng. 2022, 26, 1–46. [CrossRef] 37. Faraj, R.H.; Ahmed, H.U.; Rafiq, S.; Sor, N.H.; Ibrahim, D.F.; Qaidi, S.M. Performance of Self-Compacting Mortars Modified with Nanoparticles: A Systematic Review and Modeling. Clean. Mater. 2022, 4, 100086. [CrossRef]

Journal

BuildingsMultidisciplinary Digital Publishing Institute

Published: Aug 23, 2022

Keywords: seismic behaviour; opening shear wall; story drift; displacement; base shear

There are no references for this article.