Page 1/15 Optimization of Shear Wall location in C Shaped Reinforced Concrete Framed Building subjected to earthquake loading Mr. Rajiv Banerjee ( [email protected] ) Dr. A.P. J Abdul Kalam Technical University J. B. Srivastava Dr. A.P. J Abdul Kalam Technical University Research Article Keywords: Multi-storey plan irregularity building, Shear wall location, ‘C’ shaped structure, semicircular building, torsion in structures Posted Date: August 8th, 2022 DOI: https://doi.org/10.21203/rs.3.rs-1926210/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Optimization of Shear Wall location in C Shaped Reinforced Concrete Framed Building subjected to earthquake loading
Apr 05, 2023
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Optimization of Shear Wall location in C Shaped Reinforced Concrete Framed Building subjected to earthquake loading Mr. Rajiv Banerjee ( [email protected] )
Dr. A.P. J Abdul Kalam Technical University J. B. Srivastava
Dr. A.P. J Abdul Kalam Technical University
Research Article
Keywords: Multi-storey plan irregularity building, Shear wall location, ‘C’ shaped structure, semicircular building, torsion in structures
Posted Date: August 8th, 2022
DOI: https://doi.org/10.21203/rs.3.rs-1926210/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Page 2/15
Abstract Shear wall provide large strength and stiffness to buildings in the direction of their orientation, which reduces sway of the building signicantly and thereby reduces damage to the structure. When walls are situated in advantageous positions in a building, they may be very ecient in resisting lateral loads originating from wind or earthquakes. A framework is proposed to obtain the optimum location of shear wall for the ‘C’ shaped structure such that the torsional effect arising in the structure due to its plan irregularity is minimized. The proposal is based on the selection of optimum location that converges to the optimum structural and engineering demand parameters for a 'C' shaped structure with a xed length of shear wall. A G + 15 story structure is considered for an illustrative example of the framework considering fourteen models of shear wall location for a ‘C’ shaped structure with a xed length of shear wall (14.5% wall to oor area ratio). The analytical results of each model have been compared with that of bare frame model in terms of base shear, peak story displacement, peak story drift, static eccentricity, time period and torsional moment, and the optimum model is reported. The proposed framework as well as the presented example is expected to serve as the guideline for deciding the optimum location of shear walls for the ‘C’ shaped structure.
1.0 Introduction Environmental and functional conditions, high cost of land, rapid urbanization, and aesthetic requirement of users, sometimes necessitates the architectural plan of the building to be irregular and asymmetric and this result in an asymmetric structure which do not ensure principle of safety in service. Further such high rise building in high earthquake prone regions is not adequate. Even then the construction of such structures is increasing day by day. Issues related to asymmetry were recognized much earlier by Hoerner in the year 1971, and Kan, C.L. and A.K. Chopra in the year 1977. Buildings with irregular plan may undergo a deformed shape due to seismic ground shaking such that there may be very high stress concentration at the corners and other critical places, this may initiate the failure process of the building [8]. The buildings having irregular shape of like ‘Semicircle’, ‘T’,’Z’, ‘L’ and ‘V’ shape and asymmetric form are found to undergo several damages during earthquake (Michoacán Earthquake, Mexico in 1985, Bhuj Earthquake, Gujarat in 2001).
Such buildings exhibit deformed complicated shapes so that tremendous stress concentration occurs at various corners of the building and resulting failure. Further above shape buildings, there is lack of symmetry in the mass and stiffness distribution of buildings. So, it is found invariably that Cm (center of mass) and Cs (center of rigidity) do not coincide with each other. This results in twisting moment in the horizontal plane causing lateral torsion coupled vibration, even if the ground shaking is purely translational in nature.
Ozmen in 2002 investigated geometric and structural aspects of torsional irregularity, according to Turkish Earthquake Code 2007 [6]. Studies have been performed by Response Spectrum Analysis considering various types of irregularities [10]. Nonlinear time history analysis and push over analysis
Page 3/15
were performed for concluding in details about vulnerability of asymmetric structure [2], [3]. Recent damage surveys were conducted after the Gorkha, Nepal Earthquake in 2015 and Imphal in 2016 which reveals that maximum structures were observed to be damaged due to either their lack of symmetry and mainly due to irregularity [8]. The lateral story displacement within the code specied limits and least torsional effect are the major requirement in the seismic design of multi-story irregular asymmetric buildings. The above requirement is dicult to satisfy unless a sucient quantity of shear is provided in the building which improves the lateral stiffness of the building. Tuken and Siddique in 2013 proposed an analytical method to determine the amount of shear wall necessary to make reinforced concrete buildings seismic resistance to severe earthquake [5]. There are several researches on the impact of shear wall on high rise building, mostly on regular buildings. Although research on irregular building is available, the asymmetry and irregularity of the plan considered in this study, the semicircular shaped (‘C’ shaped) building was not considered by any of the researchers. In addition, most research is done on symmetrical building and very few in asymmetric building are mostly done using Indian Standards (1893:2016). Therefore, ‘C’ shaped plan irregular building is taken under consideration to nd suitable position of shear wall under Response Spectrum and Time History Analysis.
The major objective of the present study is to determine the optimum position of shear wall for an irregular 'C’ shaped plan story building by comparing the parameters like story displacement, story drift, Time Period, Static Eccentricity, Base Shear, Base Force and Joint Displacement of different proposed models with and without shear wall, which are derived from Response Spectrum Method and Time History analysis.
2.0 Proposed Framework Optimum location is dened as the location of shear wall for a xed structure and length of shear wall that results with minimum static eccentricity and optimum engineering demand parameters (EDPs). Considering a ‘C’ shaped asymmetric structure, the following framework is recommended to obtain a model with optimum location of shear wall:
1. Geometry of the structure is dened: i) Height of structure; ii) number of stories; iii) total oor area; iv) spacing of frames in the radial direction; v) Description of bare frame (structure before inclusion of shear wall)
2. The length and thickness of the shear wall is next xed, for example 14.5% shear wall to oor area and 230 mm thick
Note: The length(/thickness) of shear wall and the building model is rst xed before nding the optimum location of shear wall.
3. Different models are constructed:
Shear wall location is modied along the radial direction
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Shear wall location is modied along the circumferential direction
The modication and alteration are done such that the static eccentricity decreases or is negligibly affected
4. Modal analysis is next analyzed,
Study the behavior of mode shapes: First three mode shapes (at least rst two) in the modal analysis should be translational
The models with any of the rst two mode shapes corresponding to torsion are rejected at this stage
For the optimum positioning of shear wall, the key focus is to reduce the torsional effect arising in the structure due to its plan irregularity. It is desirable to have uniform participation of modal mass in the rst three modes out of which the rst and second modes being the translational mode and third mode acting as torsional mode. This is due to the asymmetrical and irregular conguration and placement of shear walls on the weak and strong axes of the building (15). Symmetrical conguration of shear wall placement x and y direction and time-period play key role on durability of torsion. As torsional mode of vibration in rst and second mode of vibration are not desirable, in this research, only models with at least rst two modes translational are taken into consideration for deciding the best location of shear wall.
5. Further, dynamic analysis is performed for the selected models as follows:
Response Spectrum analysis (RS)
Linear Time history analysis (THA)
6. The remaining models are next examined based on the analysis results for structural parameters (SP) and engineering demand parameters (EDP). The following parameters are used for the examination of the models:
Static eccentricity (SP)
Peak story drift (EDP) (RS)
Base shear (EDP) (RS) and THA)
Story shear (EDP) (RS)
7. The model corresponding to the optimum location of the shear wall is the one giving optimum values of SPs and EDPs in step-6.
3.0 Numerical Example
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3.1 Building description and numerical modeling A G + 14 story structure is considered with a story height of 3m. The total oor area considered is 2260 m2 and radial spacing of frame is 4m. The total shear wall to oor area ratio is xed to 14.5% (slight variations allowed)[11]. The construction material is taken to be concrete (M-25 grade). The diameter of the inner circular columns is 450 mm and the other columns are rectangular of size 450 mm x 750 mm. The exterior beams are of dimensions 300 mm x 450 mm and the interior beams are of dimensions 300 mm x 300 mm. The thickness of slabs is 150 m and the thickness of the shear wall is xed to 230 mm.
A live load of 3.5 kN/m3 is considered on all the oors (except roof) and a live load of 1.5 kN/m3 is considered on the roof (IS 874: Part 1 and 2). The walls other than shear walls are considered to be masonry inll walls of thickness 115 mm. The structure is modelled in E-tabs software without the inll walls. A dead load of 6kN/m is applied on the beams as the proxy of the inll walls. The structure is assumed to be designed based on proper ductile detailing requirements (IS 13920:2016) and is considered as the special moment resisting frame (SMRF) (IS 1893:2016). For numerical ease, the oors are assumed to be in-plane rigid. This rigidity is implemented during the analysis by providing a rigid diaphragm constraint at all oor levels.
3.2 Different models considered based on location of shear wall A total of 14 models are constructed along with one bare frame model for the purpose of comparison (Fig. 2). The considered frame model is symmetric along one principal direction (x-axis) and has a zero static eccentricity and the static eccentricity the other principal direction is 3.76 m. Different combination of location of shear wall in radial and circumferential direction is considered by keeping the static eccentricity minimum. The nalized 14 models are obtained such that the static eccentricity is drastically reduced by the introduction of shear wall (Table 1).
Table 1. Static eccentricity in ‘y’ direction
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3.3 Dynamic analysis of the proposed models Modal analysis
Modal analysis is rst performed in the E-tabs for all the proposed models (Section 3.1 and 3.2). The rst three mode shapes are studied, to check if all three are translational. At least, the rst two should be translational else the model is rejected. Table 2 presents the resulting modal shapes for all the 14 + 1 models. Only in models ‘1’, ‘8’,’9’, ‘10’, ‘11’ and ‘14’ have acceptable results for the behavior of rst three mode shapes- Translational-Translational-Rotational (TTR). The rest of the models, including bare model, exhibit rst and second modes as torsional mode of vibration which are not desirable (step-4). For the present study, to achieve approximately 90% of the modal mass participation in vertical direction, seismic analysis is conducted with twelve numbers of modes.
Response spectrum analysis (RS)
The response spectrum analysis is performed as recommended by IS 1893:2016. The structure was assumed to be located in zone ‘V’ and is designed for its corresponding recommendation: i) peak ground acceleration (PGA/zone factor) recommended by IS 1893:2016 is ‘0.36g’; ii) importance factor for the residential building is taken as 1.2 (clause 7.2.3, IS 1893:2016); iii) damping ration of 5% for concrete structure; iv) response reduction factor of 5 for SMRF; v) soil is assumed to be medium stiff (used for selection of respective spectral shape). The CQC rule is used for the modal combination for the corresponding ‘x’ and ‘y’ direction components. The directional combination (100 − 30 percentage rule) was implemented using the load combinations described in Table 3.
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Table 2. Modal behavior of different models
Model Name Behavior in 1st Mode Behavior in 2nd Mode Behavior in 3rd Mode
Bare Model Rotation Translation Translation
Model 1 Translation Translation Rotation
Model 2 Translation Rotation Translation
Model 3 Rotation Translation Translation
Model 4 Rotation Translation Translation
Model 5 Translation Rotation Translation
Model 6 Translation Rotation Translation
Model 7 Rotation Translation Translation
Model 8 Translation Translation Rotation
Model 9 Translation Translation Rotation
Model 10 Translation Translation Rotation
Model 11 Translation Translation Rotation
Model 12 Rotation Translation Translation
Model 13 Rotation Rotation Rotation
Model 14 Translation Translation Rotation
Time history analysis (THA)
Ideally for a complex structure a response history analysis should be performed for a ground-motion set selected based on site-specic target spectra. However, the aim of this research is to propose and explain a framework to obtain the optimum location of shear wall in a ‘C’ shaped structure. Hence, a single time history is selected for the purpose of illustration. Ground acceleration time history record of El Centro, USA (available in CSI ETABS ver. 18.0.2) is used for the implementation of linear time history analysis for the proposed models.
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S. No. Load Combination
4 1.5 DL + 1.5 RSX + 0.45 RSY
5 1.5 DL + 1.5 RSY + 0.45 RSX
6 0.9 DL + 1.5 RSX + 0.45 RSY
7 0.9 DL + 1.5 RSY + 0.45 RSX
8 1.5 DL + 1.5 LL
9 1.2 DL + 1.2 LL + 1.2 RSX
10 1.2 DL + 1.2 LL + 1.2 RSY
11 1.5 DL + 1.5 RSX
12 1.5 DL + 1.5 RSY
13 0.9 DL + 1.5 RSX
14 0.9 DL + 1.5 RSY
In Table 2, DL –Dead Load, LL – Live Load, RSX & RSY – Load from Response Spectrum Analysis along X & Y direction of plan, respectively. 14 load combinations have been considered for Response Spectrum Analysis.
3.4 Selection of Optimum Model based on SPs and EDPs Static Eccentricity (SP)
It is observed that Bare Model shows maximum static eccentricity of 3.76 m and after introduction of shear wall at advantageous position, eccentricity reduces drastically (Table 4). The lowest value is for Model 11 (0.20 m) among T-T-R exhibiting models.
Fundamental Time Period (SP)
Natural time period value depends on mass and exibility of the structure. The more exibility and mass indicate the longer the value of time period (T). From Table 4, it is observed that time period for Model 10 (1.21 sec) and Model 11 (1.27 sec) is very close and lowest among T-T-R exhibiting models. For Model 11, the position of shear wall can be considered appropriate in order to make it more rigid structure for seismic ground motion response.
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Peak Story Displacement (EDP)
Considering response spectrum analysis (Table 4), for Bare Model, story displacement along X and Y direction are 122.86 mm and 141.57 mm, respectively. Inclusion of Shear Wall drastically reduces the story displacement for Model 11 (50.65 mm in X direction and 65.68 mm in Y direction).
Considering the results of THA (Table 5), for Bare Model, story displacement along X and Y axis is 14.45 mm and 26.5 mm, respectively. For Model 11, the peak story displacement reduces to 6.98 mm and 10.16 mm along X and Y direction, respectively. So, the location of the shear wall as per Model 11 will be appropriate for this type of building.
Peak Story Drift (EDP)
As per IS code 1893:2016, clause 7.11.1.1, story drift in any story shall not exceed 0.004 times the story height (0.004 x 3000 = 12 mm). It is observed from Table 4, story drift for Bare Model along X and Y direction is 4.55 mm and 3.97 mm, which are well within the permissible limit. The values are further reduced for models with shear wall. For Model 11, story drift values are 1.41 mm and 1.82 mm.
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Table 4 Structural parameters and engineering demand parameters for different models
Model Name
Static Eccentricity(Y)
Peak Story Drift (mm)
Bare Model
Model 1 0.75 1.13 63.80 84.60 1.76 2.31
Model 2 0.63 1.44 57.45 90.77 1.58 2.48
Model 3 0.95 1.27 68.39 79.78 1.87 2.18
Model 4 0.3 1.58 51.55 85.41 1.41 2.33
Model 5 0.83 1.25 49.99 74.17 1.35 2.03
Model 6 0.92 1.41 57.99 84.46 1.65 2.31
Model 7 0.33 1.44 60.05 79.04 1.64 2.16
Model 8 0.63 1.33 68.00 71.85 1.72 2.00
Model 9 0.90 1.28 44.70 73.71 1.26 2.18
Model 10 0.59 1.21 52.79 64.69 1.44 1.79
Model 11 0.20 1.27 50.65 65.68 1.41 1.82
Model 12 0.01 1.35 60.48 79.32 1.65 2.15
Model 13 0.04 1.47 67.55 77.73 1.85 2.65
Model 14 0.60 1.29 52.47 96.66 1.43 1.95
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Model Name
Bare Model 6408 7319 6671 7636 14.45 26.50 1526 3061
Model 1 14921 12939 16517 15328 6.18 10.39 1994 3018
Model 2 14152 12457 14304 12625 6.64 12.50 1983 3505
Model 3 15854 12536 15996 12630 4.62 11.90 1521 2931
Model 4 15146 12836 15296 12990 5.38 10.93 1751 3036
Model 5 17919 13656 18064 13791 4.41 9.89 2018 3906
Model 6 17804 12335 17943 12493 5.32 12.43 2673 3132
Model 7 18637 13727 19044 12436 4.80 10.78 1929 2875
Model 8 13835 13468 14020 13588 6.51 9.31 1886 3411
Model 9 16145 13900 16261 14031 4.57 10.26 3154 3916
Model 10 13957 14338 14109 14470 7.10 9.32 2192 4080
Model 11 16692 15127 16902 15267 6.98 10.16 2589 3843
Model 12 18637 13727 18814 13839 5.14 9.36 1927 3713
Model 13 14836 11823 15015 11947 7.36 9.23 1985 3275
Model 14 15922 12430 14304 12625 4.64 10.46 1896 3322
Base Shear and Storey Shear (EDP)
Considering response spectrum analysis (Table 5), base shear for model 11 is 16692 kN and 15127 kN in X and Y direction, respectively. The base shear observed for the other models varies approximately in the range of 14000 ~ 19000 kN and 13000 ~ 15000 kN in X and Y direction, respectively. Overall, model 11 does not depict any outlier and is in acceptable range as all the other models also depict the same order of base shear. The same observation also holds for the story shear considering the response spectrum analysis. Similarly, for THA (Table 5), Model 11 has a base shear of 2589 kN in X direction and 3843 kN in Y direction. Whereas, the other models also have the same order of base shear i.e., 1500 ~ 3200kN and 3000 ~ 4100 kN in X and Y directions, respectively. Therefore, even though model 11 is not optimum for base shear, still it is an acceptable model compared to the other models.
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Comparing all the parameters (SPs and EDPs), the modes of vibration, static eccentricity, time period, peak story displacement, peak story drift, and base shear among the models. Shear Walls located as per Model 11 shows better results on the basis of Time History Analysis and Response Spectrum Analysis. However, the difference between the values of Time Period and Eccentricity of Model 10 was very less. However, the overall performance of the Model 11 in all parameters was observed to be better. Thus, Model 11 is considered optimum and the corresponding location of shear walls in Model 11 are the optimum location of shear wall for the considered ‘C’ shaped structure with 14.5% of shear wall to oor area ratio.
Conclusions Shear wall provide large strength and stiffness to buildings in the direction of their orientation, which reduces sway of the building signicantly and thereby reduce damages to the structure. Shear walls also provide lateral stiffness to prevent the roof or oor from excessive side sway. When walls are situated in advantageous positions in a building, they may be very ecient in resisting lateral loads originating from wind or…
Dr. A.P. J Abdul Kalam Technical University J. B. Srivastava
Dr. A.P. J Abdul Kalam Technical University
Research Article
Keywords: Multi-storey plan irregularity building, Shear wall location, ‘C’ shaped structure, semicircular building, torsion in structures
Posted Date: August 8th, 2022
DOI: https://doi.org/10.21203/rs.3.rs-1926210/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Page 2/15
Abstract Shear wall provide large strength and stiffness to buildings in the direction of their orientation, which reduces sway of the building signicantly and thereby reduces damage to the structure. When walls are situated in advantageous positions in a building, they may be very ecient in resisting lateral loads originating from wind or earthquakes. A framework is proposed to obtain the optimum location of shear wall for the ‘C’ shaped structure such that the torsional effect arising in the structure due to its plan irregularity is minimized. The proposal is based on the selection of optimum location that converges to the optimum structural and engineering demand parameters for a 'C' shaped structure with a xed length of shear wall. A G + 15 story structure is considered for an illustrative example of the framework considering fourteen models of shear wall location for a ‘C’ shaped structure with a xed length of shear wall (14.5% wall to oor area ratio). The analytical results of each model have been compared with that of bare frame model in terms of base shear, peak story displacement, peak story drift, static eccentricity, time period and torsional moment, and the optimum model is reported. The proposed framework as well as the presented example is expected to serve as the guideline for deciding the optimum location of shear walls for the ‘C’ shaped structure.
1.0 Introduction Environmental and functional conditions, high cost of land, rapid urbanization, and aesthetic requirement of users, sometimes necessitates the architectural plan of the building to be irregular and asymmetric and this result in an asymmetric structure which do not ensure principle of safety in service. Further such high rise building in high earthquake prone regions is not adequate. Even then the construction of such structures is increasing day by day. Issues related to asymmetry were recognized much earlier by Hoerner in the year 1971, and Kan, C.L. and A.K. Chopra in the year 1977. Buildings with irregular plan may undergo a deformed shape due to seismic ground shaking such that there may be very high stress concentration at the corners and other critical places, this may initiate the failure process of the building [8]. The buildings having irregular shape of like ‘Semicircle’, ‘T’,’Z’, ‘L’ and ‘V’ shape and asymmetric form are found to undergo several damages during earthquake (Michoacán Earthquake, Mexico in 1985, Bhuj Earthquake, Gujarat in 2001).
Such buildings exhibit deformed complicated shapes so that tremendous stress concentration occurs at various corners of the building and resulting failure. Further above shape buildings, there is lack of symmetry in the mass and stiffness distribution of buildings. So, it is found invariably that Cm (center of mass) and Cs (center of rigidity) do not coincide with each other. This results in twisting moment in the horizontal plane causing lateral torsion coupled vibration, even if the ground shaking is purely translational in nature.
Ozmen in 2002 investigated geometric and structural aspects of torsional irregularity, according to Turkish Earthquake Code 2007 [6]. Studies have been performed by Response Spectrum Analysis considering various types of irregularities [10]. Nonlinear time history analysis and push over analysis
Page 3/15
were performed for concluding in details about vulnerability of asymmetric structure [2], [3]. Recent damage surveys were conducted after the Gorkha, Nepal Earthquake in 2015 and Imphal in 2016 which reveals that maximum structures were observed to be damaged due to either their lack of symmetry and mainly due to irregularity [8]. The lateral story displacement within the code specied limits and least torsional effect are the major requirement in the seismic design of multi-story irregular asymmetric buildings. The above requirement is dicult to satisfy unless a sucient quantity of shear is provided in the building which improves the lateral stiffness of the building. Tuken and Siddique in 2013 proposed an analytical method to determine the amount of shear wall necessary to make reinforced concrete buildings seismic resistance to severe earthquake [5]. There are several researches on the impact of shear wall on high rise building, mostly on regular buildings. Although research on irregular building is available, the asymmetry and irregularity of the plan considered in this study, the semicircular shaped (‘C’ shaped) building was not considered by any of the researchers. In addition, most research is done on symmetrical building and very few in asymmetric building are mostly done using Indian Standards (1893:2016). Therefore, ‘C’ shaped plan irregular building is taken under consideration to nd suitable position of shear wall under Response Spectrum and Time History Analysis.
The major objective of the present study is to determine the optimum position of shear wall for an irregular 'C’ shaped plan story building by comparing the parameters like story displacement, story drift, Time Period, Static Eccentricity, Base Shear, Base Force and Joint Displacement of different proposed models with and without shear wall, which are derived from Response Spectrum Method and Time History analysis.
2.0 Proposed Framework Optimum location is dened as the location of shear wall for a xed structure and length of shear wall that results with minimum static eccentricity and optimum engineering demand parameters (EDPs). Considering a ‘C’ shaped asymmetric structure, the following framework is recommended to obtain a model with optimum location of shear wall:
1. Geometry of the structure is dened: i) Height of structure; ii) number of stories; iii) total oor area; iv) spacing of frames in the radial direction; v) Description of bare frame (structure before inclusion of shear wall)
2. The length and thickness of the shear wall is next xed, for example 14.5% shear wall to oor area and 230 mm thick
Note: The length(/thickness) of shear wall and the building model is rst xed before nding the optimum location of shear wall.
3. Different models are constructed:
Shear wall location is modied along the radial direction
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Shear wall location is modied along the circumferential direction
The modication and alteration are done such that the static eccentricity decreases or is negligibly affected
4. Modal analysis is next analyzed,
Study the behavior of mode shapes: First three mode shapes (at least rst two) in the modal analysis should be translational
The models with any of the rst two mode shapes corresponding to torsion are rejected at this stage
For the optimum positioning of shear wall, the key focus is to reduce the torsional effect arising in the structure due to its plan irregularity. It is desirable to have uniform participation of modal mass in the rst three modes out of which the rst and second modes being the translational mode and third mode acting as torsional mode. This is due to the asymmetrical and irregular conguration and placement of shear walls on the weak and strong axes of the building (15). Symmetrical conguration of shear wall placement x and y direction and time-period play key role on durability of torsion. As torsional mode of vibration in rst and second mode of vibration are not desirable, in this research, only models with at least rst two modes translational are taken into consideration for deciding the best location of shear wall.
5. Further, dynamic analysis is performed for the selected models as follows:
Response Spectrum analysis (RS)
Linear Time history analysis (THA)
6. The remaining models are next examined based on the analysis results for structural parameters (SP) and engineering demand parameters (EDP). The following parameters are used for the examination of the models:
Static eccentricity (SP)
Peak story drift (EDP) (RS)
Base shear (EDP) (RS) and THA)
Story shear (EDP) (RS)
7. The model corresponding to the optimum location of the shear wall is the one giving optimum values of SPs and EDPs in step-6.
3.0 Numerical Example
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3.1 Building description and numerical modeling A G + 14 story structure is considered with a story height of 3m. The total oor area considered is 2260 m2 and radial spacing of frame is 4m. The total shear wall to oor area ratio is xed to 14.5% (slight variations allowed)[11]. The construction material is taken to be concrete (M-25 grade). The diameter of the inner circular columns is 450 mm and the other columns are rectangular of size 450 mm x 750 mm. The exterior beams are of dimensions 300 mm x 450 mm and the interior beams are of dimensions 300 mm x 300 mm. The thickness of slabs is 150 m and the thickness of the shear wall is xed to 230 mm.
A live load of 3.5 kN/m3 is considered on all the oors (except roof) and a live load of 1.5 kN/m3 is considered on the roof (IS 874: Part 1 and 2). The walls other than shear walls are considered to be masonry inll walls of thickness 115 mm. The structure is modelled in E-tabs software without the inll walls. A dead load of 6kN/m is applied on the beams as the proxy of the inll walls. The structure is assumed to be designed based on proper ductile detailing requirements (IS 13920:2016) and is considered as the special moment resisting frame (SMRF) (IS 1893:2016). For numerical ease, the oors are assumed to be in-plane rigid. This rigidity is implemented during the analysis by providing a rigid diaphragm constraint at all oor levels.
3.2 Different models considered based on location of shear wall A total of 14 models are constructed along with one bare frame model for the purpose of comparison (Fig. 2). The considered frame model is symmetric along one principal direction (x-axis) and has a zero static eccentricity and the static eccentricity the other principal direction is 3.76 m. Different combination of location of shear wall in radial and circumferential direction is considered by keeping the static eccentricity minimum. The nalized 14 models are obtained such that the static eccentricity is drastically reduced by the introduction of shear wall (Table 1).
Table 1. Static eccentricity in ‘y’ direction
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3.3 Dynamic analysis of the proposed models Modal analysis
Modal analysis is rst performed in the E-tabs for all the proposed models (Section 3.1 and 3.2). The rst three mode shapes are studied, to check if all three are translational. At least, the rst two should be translational else the model is rejected. Table 2 presents the resulting modal shapes for all the 14 + 1 models. Only in models ‘1’, ‘8’,’9’, ‘10’, ‘11’ and ‘14’ have acceptable results for the behavior of rst three mode shapes- Translational-Translational-Rotational (TTR). The rest of the models, including bare model, exhibit rst and second modes as torsional mode of vibration which are not desirable (step-4). For the present study, to achieve approximately 90% of the modal mass participation in vertical direction, seismic analysis is conducted with twelve numbers of modes.
Response spectrum analysis (RS)
The response spectrum analysis is performed as recommended by IS 1893:2016. The structure was assumed to be located in zone ‘V’ and is designed for its corresponding recommendation: i) peak ground acceleration (PGA/zone factor) recommended by IS 1893:2016 is ‘0.36g’; ii) importance factor for the residential building is taken as 1.2 (clause 7.2.3, IS 1893:2016); iii) damping ration of 5% for concrete structure; iv) response reduction factor of 5 for SMRF; v) soil is assumed to be medium stiff (used for selection of respective spectral shape). The CQC rule is used for the modal combination for the corresponding ‘x’ and ‘y’ direction components. The directional combination (100 − 30 percentage rule) was implemented using the load combinations described in Table 3.
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Table 2. Modal behavior of different models
Model Name Behavior in 1st Mode Behavior in 2nd Mode Behavior in 3rd Mode
Bare Model Rotation Translation Translation
Model 1 Translation Translation Rotation
Model 2 Translation Rotation Translation
Model 3 Rotation Translation Translation
Model 4 Rotation Translation Translation
Model 5 Translation Rotation Translation
Model 6 Translation Rotation Translation
Model 7 Rotation Translation Translation
Model 8 Translation Translation Rotation
Model 9 Translation Translation Rotation
Model 10 Translation Translation Rotation
Model 11 Translation Translation Rotation
Model 12 Rotation Translation Translation
Model 13 Rotation Rotation Rotation
Model 14 Translation Translation Rotation
Time history analysis (THA)
Ideally for a complex structure a response history analysis should be performed for a ground-motion set selected based on site-specic target spectra. However, the aim of this research is to propose and explain a framework to obtain the optimum location of shear wall in a ‘C’ shaped structure. Hence, a single time history is selected for the purpose of illustration. Ground acceleration time history record of El Centro, USA (available in CSI ETABS ver. 18.0.2) is used for the implementation of linear time history analysis for the proposed models.
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S. No. Load Combination
4 1.5 DL + 1.5 RSX + 0.45 RSY
5 1.5 DL + 1.5 RSY + 0.45 RSX
6 0.9 DL + 1.5 RSX + 0.45 RSY
7 0.9 DL + 1.5 RSY + 0.45 RSX
8 1.5 DL + 1.5 LL
9 1.2 DL + 1.2 LL + 1.2 RSX
10 1.2 DL + 1.2 LL + 1.2 RSY
11 1.5 DL + 1.5 RSX
12 1.5 DL + 1.5 RSY
13 0.9 DL + 1.5 RSX
14 0.9 DL + 1.5 RSY
In Table 2, DL –Dead Load, LL – Live Load, RSX & RSY – Load from Response Spectrum Analysis along X & Y direction of plan, respectively. 14 load combinations have been considered for Response Spectrum Analysis.
3.4 Selection of Optimum Model based on SPs and EDPs Static Eccentricity (SP)
It is observed that Bare Model shows maximum static eccentricity of 3.76 m and after introduction of shear wall at advantageous position, eccentricity reduces drastically (Table 4). The lowest value is for Model 11 (0.20 m) among T-T-R exhibiting models.
Fundamental Time Period (SP)
Natural time period value depends on mass and exibility of the structure. The more exibility and mass indicate the longer the value of time period (T). From Table 4, it is observed that time period for Model 10 (1.21 sec) and Model 11 (1.27 sec) is very close and lowest among T-T-R exhibiting models. For Model 11, the position of shear wall can be considered appropriate in order to make it more rigid structure for seismic ground motion response.
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Peak Story Displacement (EDP)
Considering response spectrum analysis (Table 4), for Bare Model, story displacement along X and Y direction are 122.86 mm and 141.57 mm, respectively. Inclusion of Shear Wall drastically reduces the story displacement for Model 11 (50.65 mm in X direction and 65.68 mm in Y direction).
Considering the results of THA (Table 5), for Bare Model, story displacement along X and Y axis is 14.45 mm and 26.5 mm, respectively. For Model 11, the peak story displacement reduces to 6.98 mm and 10.16 mm along X and Y direction, respectively. So, the location of the shear wall as per Model 11 will be appropriate for this type of building.
Peak Story Drift (EDP)
As per IS code 1893:2016, clause 7.11.1.1, story drift in any story shall not exceed 0.004 times the story height (0.004 x 3000 = 12 mm). It is observed from Table 4, story drift for Bare Model along X and Y direction is 4.55 mm and 3.97 mm, which are well within the permissible limit. The values are further reduced for models with shear wall. For Model 11, story drift values are 1.41 mm and 1.82 mm.
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Table 4 Structural parameters and engineering demand parameters for different models
Model Name
Static Eccentricity(Y)
Peak Story Drift (mm)
Bare Model
Model 1 0.75 1.13 63.80 84.60 1.76 2.31
Model 2 0.63 1.44 57.45 90.77 1.58 2.48
Model 3 0.95 1.27 68.39 79.78 1.87 2.18
Model 4 0.3 1.58 51.55 85.41 1.41 2.33
Model 5 0.83 1.25 49.99 74.17 1.35 2.03
Model 6 0.92 1.41 57.99 84.46 1.65 2.31
Model 7 0.33 1.44 60.05 79.04 1.64 2.16
Model 8 0.63 1.33 68.00 71.85 1.72 2.00
Model 9 0.90 1.28 44.70 73.71 1.26 2.18
Model 10 0.59 1.21 52.79 64.69 1.44 1.79
Model 11 0.20 1.27 50.65 65.68 1.41 1.82
Model 12 0.01 1.35 60.48 79.32 1.65 2.15
Model 13 0.04 1.47 67.55 77.73 1.85 2.65
Model 14 0.60 1.29 52.47 96.66 1.43 1.95
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Model Name
Bare Model 6408 7319 6671 7636 14.45 26.50 1526 3061
Model 1 14921 12939 16517 15328 6.18 10.39 1994 3018
Model 2 14152 12457 14304 12625 6.64 12.50 1983 3505
Model 3 15854 12536 15996 12630 4.62 11.90 1521 2931
Model 4 15146 12836 15296 12990 5.38 10.93 1751 3036
Model 5 17919 13656 18064 13791 4.41 9.89 2018 3906
Model 6 17804 12335 17943 12493 5.32 12.43 2673 3132
Model 7 18637 13727 19044 12436 4.80 10.78 1929 2875
Model 8 13835 13468 14020 13588 6.51 9.31 1886 3411
Model 9 16145 13900 16261 14031 4.57 10.26 3154 3916
Model 10 13957 14338 14109 14470 7.10 9.32 2192 4080
Model 11 16692 15127 16902 15267 6.98 10.16 2589 3843
Model 12 18637 13727 18814 13839 5.14 9.36 1927 3713
Model 13 14836 11823 15015 11947 7.36 9.23 1985 3275
Model 14 15922 12430 14304 12625 4.64 10.46 1896 3322
Base Shear and Storey Shear (EDP)
Considering response spectrum analysis (Table 5), base shear for model 11 is 16692 kN and 15127 kN in X and Y direction, respectively. The base shear observed for the other models varies approximately in the range of 14000 ~ 19000 kN and 13000 ~ 15000 kN in X and Y direction, respectively. Overall, model 11 does not depict any outlier and is in acceptable range as all the other models also depict the same order of base shear. The same observation also holds for the story shear considering the response spectrum analysis. Similarly, for THA (Table 5), Model 11 has a base shear of 2589 kN in X direction and 3843 kN in Y direction. Whereas, the other models also have the same order of base shear i.e., 1500 ~ 3200kN and 3000 ~ 4100 kN in X and Y directions, respectively. Therefore, even though model 11 is not optimum for base shear, still it is an acceptable model compared to the other models.
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Comparing all the parameters (SPs and EDPs), the modes of vibration, static eccentricity, time period, peak story displacement, peak story drift, and base shear among the models. Shear Walls located as per Model 11 shows better results on the basis of Time History Analysis and Response Spectrum Analysis. However, the difference between the values of Time Period and Eccentricity of Model 10 was very less. However, the overall performance of the Model 11 in all parameters was observed to be better. Thus, Model 11 is considered optimum and the corresponding location of shear walls in Model 11 are the optimum location of shear wall for the considered ‘C’ shaped structure with 14.5% of shear wall to oor area ratio.
Conclusions Shear wall provide large strength and stiffness to buildings in the direction of their orientation, which reduces sway of the building signicantly and thereby reduce damages to the structure. Shear walls also provide lateral stiffness to prevent the roof or oor from excessive side sway. When walls are situated in advantageous positions in a building, they may be very ecient in resisting lateral loads originating from wind or…
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