Comparative parametric study of linear and nonlinear behavior of multistory structures
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The document presents a comparative study on the linear and nonlinear seismic analysis of multistorey structures using response spectrum and time history methods. Analyzed structures include G+14, G+17, and G+20 models created with ETABS software, employing Bhuj earthquake data for nonlinear analysis. Results display the storey shear, displacement, and time period across different structures, highlighting the need for accurate seismic design to avoid destruction during earthquakes.
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 822
4. CONCLUSION
The study is based on linear and nonlinear analysis of
multistorey structure for finding base shear, storey
displacement and time period.
1. The storey shear results obtained for G+14, G+17, and G+
20 by response spectrum method are respectively 37%,
30.63%, and 34.24% more than those obtained by time
history method.
2. The storey displacement results obtained for G+14, G+17,
and G+ 20 by response spectrum method are respectively
44.59%, 30.63%, and 34.24% more than those obtained by
time history method.
3. From results it is observed that time period of structure
increases with increase in height.
4. As base shear depends on weight of structure, it is
observed that it increases with increase in height both by
response spectrum and time history method.
4. From results it is recommended that time history analysis
should be performed as it predicts the structural response
more accurately than response spectrum analysis.
REFERENCES
[1] Colin M. Morison, “Dynamic Response of Walls and
Slabs by Single Degree of Freedom Analysis – A
Critical Review and Revision”, International Journal
of Impact Engineering, Elsevier, 2005.
[2] Dang – Guen Lee, Won – Ho Choi, “Evaluation of
Seismic performance of multistory building
structures based on the equivalent responses”
Engineering Structures, Elsevier, 28, 2006.
[3] Paolo Foraboschi, Alessia Vanin, “Nonlinear Static
Analysis of Masonry Buildings Based on a Strut and
Tie Method”, Soil Dynamics and Earthquake
Engineering 55, Elsevier, October 2013
[4] Raja Rizwan Hussain, Mohammed Jameel,
“Nonlinear time domain analysis of base isolated
multistory building under site specific bi – directional
seismic loading” Automation in Construction,
Elsevier, 22, December 2011.
[5] Reza Sehhati, Adrian Rodriguez, “Effects of near
fault ground motions and equivalent pulses on
multistory structure” Engineering structures,
Elsevier, 33, January 2011.
[6] S. M. Wilkinson and R. A. Hiley, “A nonlinear time
history model for the seismic analysis of high rise
framed structures” Computers and Structures,
Elsevier, 84, 2006.
[7] Victor I. Fernandez – Davila, Ernesto F. Cruz,
“Parametric Study of nonlinear seismic response of
three dimensional building models” Engineering
Structures, Elsevier, 28, 2006.](https://image.slidesharecdn.com/comparativeparametricstudyoflinearandnonlinearbehaviorofmultistorystructures-160903053458/85/Comparative-parametric-study-of-linear-and-nonlinear-behavior-of-multistory-structures-8-320.jpg)
Comparative parametric study of linear and nonlinear behavior of multistory structures
- 1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 815 COMPARATIVE PARAMETRIC STUDY OF LINEAR AND NONLINEAR BEHAVIOR OF MULTISTORY STRUCTURES Mrunmayi Gursale1 , P. S. Patil2 1 Student M. Tech Structure, Rajarambapu Institute of Technology, Islampur 2 Professor Civil Engineering Dept, Rajarambapu Institute of Technology, Islampur Abstract The earthquake analysis of multistorey structure is done by linear and nonlinear methods. Response spectrum method of analysis is linear dynamic analysis. For nonlinear dynamic analysis time history method is used. In this paper, response spectrum method is used for linear analysis. For nonlinear analysis, time history method is used. For time history method, time history function of Bhuj earthquake is used. Both the analyses are done using ETABs software. To study seismic behaviour, base shear, time period, storey displacement parameters are studied Keywords: linear analysis, nonlinear analysis, response spectrum method, time history method, ETABs. -------------------------------------------------------------------***------------------------------------------------------------------- 1. INTRODUCTION 1.1 General The earthquakes occurred in recent past have indicated that if structures are constructed without considering seismic forces, not properly designed, they will undergo huge destruction and also loss of life. So it is necessary to analyze structure for seismic responses. The analysis is performed on basis of external action, behaviour of structural material, type of structural model selected. Linear static analysis can be used for small structures. Linear dynamic analysis can be done by response spectrum method. In this method peak response of a structure is obtained directly from earthquake response. Nonlinear method gives actual behaviour of structure. In nonlinear static analysis method, to study behaviour of structure, capacity curve is used. Capacity curve is relation between base shear and displacement of roof. It is also called Push over analysis. Nonlinear dynamic analysis is known as time history analysis. For this type of analysis, time history of a particular earthquake for a given structure is required. This method is used to determine seismic behaviour of structure under dynamic load. The seismic responses and seismic performance of structure can be evaluated by dynamic response of equivalent single degree of freedom system obtained from multi degree of freedom system. The second method is obtaining responses by analysis of multi degree of freedom system. 1.2 Linear Dynamic Analysis For linear dynamic analysis, response spectrum method is used. In this method, peak responses of a structure during the earthquake are obtained directly from earthquake responses. The response spectrum is an envelope of upper bound responses based on several different ground motions. The design spectrum given in IS 1893: 2002 Part 1 is used. This spectrum is based on strong motion records of eight Indian earthquakes. In response spectrum method, maximum values of displacements and member forces are calculated for each mode, using design spectra. Response spectra help to calculate peak structural responses under linear range, which can be used to calculate lateral forces developed in structure due to earthquake. This helps for earthquake resistant design. 1.3 Nonlinear Dynamic Analysis Nonlinear method is most accurate method for calculation of seismic responses of structure. For this type of analysis earthquake time history of representative earthquake is required. The base of the structure is subjected to actual ground motion which is representation of ground acceleration verses time. The ground acceleration is determined at small time steps to give ground motion record. In this dynamic analysis of structure is done at each increment of time. Three main parameters for time history are magnitude, distance and soil condition category. For time history analysis, recorded ground motion database from past natural events are used. 2. MODELLING 2.1 General For parametric study of multistorey structure, ETABS software is used. Models for G+14, G+17, and G+20 are generated. These models are analysed by response spectrum and time history method. ETABS is completely integrated software for analysis and design of reinforced structure. Creation of model, modification of model, analysis, all are accomplished using single interface. A single structural model can be used for wide variety of different type analysis and design.
- 2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 816 2.2 Problem Statement Models for G+14, G+17 and G+20 are taken for purpose of study. These models are analysed by both response spectrum and time history method. For time history analysis method, time history record of Bhuj earthquake is used. The typical floor height is taken as 3m. 2.2.1 Dimensions of Proposed Model Table 2.1 Dimensions of Model Sr. No. Property Dimension 1 Plan Dimension in X Direction 16m 2 Plan Dimension in Y Direction 12m 2.2.2 Loads Considered as per IS 1893 – 2002 (Part I) 1. Dead Load 2. Live Load = 2 kN/m2 3. Floor Finish = 1 kN/m2 4. Earthquake force in X direction 5. Earthquake force in Y direction 6. Wind force in X direction 7. Wind force in Y direction 2.2.3 Earthquake Parameters Based on Structure Location IS 1893 – 2002 (Part I) Table 2.2 Earthquake Parameters Based on Structure Location IS 1893 – 2002 (Part I) Sr. No. Parameters Code Provisions 1 Type of Structure RCC 2 Nature of Building Residential 3 Damping of Concrete 5% 4 Importance Factor 1 5 Response Reduction Factor 5 2.2.4 Sizes of Structural Members Table 2.3 Sizes of Structural Elements Sr. No. Structural Member Size 1 Columns 800mmX800mm 2 Beams 350mmX600mm 3 Thickness of typical slab 125mm 4 Thickness of wall 230mm 5 Grade of Concrete and Steel M20 & Fe415 2.2.5 Seismic and Wind Parameters Table 2.4 Seismic and Wind Parameters Sr. No. Location Seismic Zone Zone Factor (Z) Wind Speed m/s) 1 Bhuj V 0.36 50 2.3 Structural Modelling and Analysis Fig.1 Model of G+ 14 Structures
- 3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 817 Fig.2 Model of G+ 17 Structures Fig.3 Model of G+ 20 Structures 3. RESULTS AND DISCUSSION The results of analysis of multistorey structure by both linear and nonlinear methods are tabulated below. 3.1 Linear Analysis (Response Spectrum Method) 3.1.1 Following Table shows values of Storey Shear for G+14, G+17, G+20 Structures. Table 3.1 Storey Shear of G+14, G+17, G+20 Structures Floor Storey Shear (KN) for G+20 Structure Storey Shear (KN) for G+17 Structure Storey Shear (KN) for G+14 Structure 20F 147.03 - - 19F 328.98 - -
- 4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 818 18F 487.04 - - 17F 619.06 156.11 - 16F 726.99 346.99 - 15F 815.36 510.5 - 14F 888.73 646.49 169.47 13F 950.35 759.71 373.84 12F 1002.49 855.94 547.42 11F 1047.79 939.07 693.89 10F 1089.96 1011.47 820.38 9F 1132.94 1076.11 931.51 8F 1179.32 1137.1 1029.58 7F 1229.63 1197.8 1117.81 6F 1282.98 1259.2 1200.17 5F 1338.2 1320.36 1278.26 4F 1393.96 1380.04 1351.01 3F 1447.68 1436.72 1416.94 2F 1494.68 1486.89 1474.04 1F 1529.04 1524.49 1517.31 GF 1546.53 1544.08 1540.36 PL 1548.08 1545.83 1542.45 3.1.2 Storey Displacement Table 3.4 Storey Displacement of G+14, G+17, G+20 Structures Floor Storey Displacement (m) G+20 Structure Storey Displacement (m) G+17 Structure Storey Displacement (m) G+14 Structure 20F 0.0386 - - 19F 0.0378 - - 18F 0.0369 - - 17F 0.0359 0.0321 - 16F 0.0346 0.0315 - 15F 0.0333 0.0306 - 14F 0.0318 0.0296 0.0259 13F 0.0301 0.0284 0.0253 12F 0.0284 0.027 0.0245 11F 0.0266 0.0255 0.0234 10F 0.0247 0.0238 0.0222 9F 0.0227 0.022 0.0208 8F 0.0206 0.0201 0.0191 7F 0.0184 0.018 0.0174 6F 0.0162 0.0159 0.0154 5F 0.0139 0.0137 0.0133 4F 0.0115 0.0114 0.0111 3F 0.0091 0.009 0.0088 2F 0.0066 0.0065 0.0064 1F 0.0042 0.0041 0.0041 GF 0.0019 0.0019 0.0019 3.1.3 Time Period Table 3.5 Time Period of G+14, G+17, G+20 Structures Sr. No. Model Time Period (sec) 1. G+14 1.22 2. G+17 1.5 3. G+20 1.81
- 5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 819 3.2 Nonlinear Analysis (Time History Method) 3.2.1 Storey Shear Table 3.6 Storey Shear of G+14, G+17, G+20 Structures Floor Storey Shear (KN) for G+20 Structure Storey Shear (KN) for G+17 Structure Storey Shear (KN) for G+14 Structure 20F 61.90 - - 19F 140.24 - - 18F 214.25 - - 17F 272.51 68.72 - 16F 340.96 162.74 - 15F 448.45 280.78 - 14F 538.04 391.39 71.35 13F 661.35 528.68 159.37 12F 710.77 606.86 240.81 11F 749.27 671.53 305.45 10F 785.86 729.27 384.76 9F 837.13 795.14 512.33 8F 880.01 848.50 623.31 7F 934.40 910.21 777.88 6F 978.14 960.01 915.01 5F 1067.75 1053.52 1019.92 4F 1088.46 1086.87 1082.43 3F 1093.24 1091.51 1084.50 2F 1109.78 1105.69 1088.88 1F 1116.84 1106.47 1101.26 GF 1126.84 1120.97 1108.05 PL 1132.09 1123.52 1111.28 3.2.2 Storey Displacement Table 3.7 Storey Displacement of G+14, G+17, G+20 Structures Floor Storey Displacement (m) for G+20 Structure Storey Displacement (m) for G+17 Structure Storey Displacement (m) for G+14 Structure 20F 0.0304 - - 19F 0.0295 - - 18F 0.0288 - - 17F 0.0280 0.0250 - 16F 0.0264 0.0240 - 15F 0.0253 0.0233 - 14F 0.0241 0.0224 0.0196 13F 0.0223 0.0210 0.0187 12F 0.0202 0.0192 0.0174 11F 0.0179 0.0172 0.0158 10F 0.0155 0.0150 0.0140 9F 0.0131 0.0127 0.0120 8F 0.0108 0.0105 0.0100 7F 0.0091 0.0089 0.0086 6F 0.0079 0.0078 0.0075 5F 0.0067 0.0066 0.0064 4F 0.0055 0.0054 0.0053 3F 0.0041 0.0040 0.0039 2F 0.0029 0.0029 0.0028 1F 0.0018 0.0018 0.0018 GF 0.0008 0.0008 0.0008
- 6. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 820 Following figures show the comparative storey shear graph by both response spectrum and time history method for G+ 14, G+17, G+20 structures. Fig. 4 Storey Shear in KN for G+14 Structure Fig. 5 Storey Shear in KN for G+17 Structure Fig. 6 Storey Shear in KN for G+20 Structure 0 200 400 600 800 1000 1200 1400 1600 1800 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF PL StoreyShear Floor Storey Shear in KN for G+14 Response Spectrum Time History 0 200 400 600 800 1000 1200 1400 1600 1800 17F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF PL StoreyShear Floor Storey Shear in KN for G+17 Response Spectrum Time History 0 500 1000 1500 2000 20F 19F 18F 17F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF PL StoreyShear Floor Base Shear in KN for G+20 Response Spectrum Time History
- 7. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 821 Following figures show the comparative storey shear graph by both response spectrum and time history method for G+ 14, G+17, G+20 structures. Fig. 7 Storey Displacement in M for G+14 structure Fig. 8 Storey Displacement in M for G+17 Structure Fig. 9 Storey Displacement in M for G+20 Structure 0 0.005 0.01 0.015 0.02 0.025 0.03 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF StoreyDisplacement Floor Storey Displacement (M) for G+14 Response spectrum Time History 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 17F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF StoreyDisplacement Floor Storey Displacement (M) for G+17 Response Spectrum Time History 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 20F 19F 18F 17F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F GF StoreyDisplacement Floor Storey Displacement (M) for G+20 Response Spectrum Time History
- 8. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 04 | Apr-2015, Available @ http://www.ijret.org 822 4. CONCLUSION The study is based on linear and nonlinear analysis of multistorey structure for finding base shear, storey displacement and time period. 1. The storey shear results obtained for G+14, G+17, and G+ 20 by response spectrum method are respectively 37%, 30.63%, and 34.24% more than those obtained by time history method. 2. The storey displacement results obtained for G+14, G+17, and G+ 20 by response spectrum method are respectively 44.59%, 30.63%, and 34.24% more than those obtained by time history method. 3. From results it is observed that time period of structure increases with increase in height. 4. As base shear depends on weight of structure, it is observed that it increases with increase in height both by response spectrum and time history method. 4. From results it is recommended that time history analysis should be performed as it predicts the structural response more accurately than response spectrum analysis. REFERENCES [1] Colin M. Morison, “Dynamic Response of Walls and Slabs by Single Degree of Freedom Analysis – A Critical Review and Revision”, International Journal of Impact Engineering, Elsevier, 2005. [2] Dang – Guen Lee, Won – Ho Choi, “Evaluation of Seismic performance of multistory building structures based on the equivalent responses” Engineering Structures, Elsevier, 28, 2006. [3] Paolo Foraboschi, Alessia Vanin, “Nonlinear Static Analysis of Masonry Buildings Based on a Strut and Tie Method”, Soil Dynamics and Earthquake Engineering 55, Elsevier, October 2013 [4] Raja Rizwan Hussain, Mohammed Jameel, “Nonlinear time domain analysis of base isolated multistory building under site specific bi – directional seismic loading” Automation in Construction, Elsevier, 22, December 2011. [5] Reza Sehhati, Adrian Rodriguez, “Effects of near fault ground motions and equivalent pulses on multistory structure” Engineering structures, Elsevier, 33, January 2011. [6] S. M. Wilkinson and R. A. Hiley, “A nonlinear time history model for the seismic analysis of high rise framed structures” Computers and Structures, Elsevier, 84, 2006. [7] Victor I. Fernandez – Davila, Ernesto F. Cruz, “Parametric Study of nonlinear seismic response of three dimensional building models” Engineering Structures, Elsevier, 28, 2006.