Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums

IJSRD - International Journal for Scientific Research & Development| Vol.4, Issue 04, 2016 | ISSN (online): 2321-0613

Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums Mohammed Abdul Wasiq Salil1 Varnitha M S2 1 Student 2Associate Professor 1,2 The Oxford College of Engineering Abstract— This article presents the comparative study of response of a symmetric and asymmetric structure when they are subjected to response spectrum analysis using the response spectrum developed using the equations provided in the Indian code book IS:1893:2002 and the response spectrum developed using the attenuation equation. The final results are studied to ascertain if there is any variation in the response of the structures subjected to both the response spectrums.

Key words: Response Spectrums, Asymmetric Structures I. INTRODUCTION Seismic hazards are one of the most devastating natural hazards among the various hazards due to their high degree of unpredictability and possibility of large scale damage to life and property in a matter of few seconds. With the advancement in various fields such as construction methods, designing of structures and methods of execution of the various typical projects, a need has been felt for the further revision of the Indian code book IS:1893:2002 which was last revised in the year 2002. Many changes were made in the code book such as updating various cities from zone 2 to zone 3 but the cause of which are still obsolete. The response spectrum provided in the Indian code has been used for a long time and has not been revised as per the needs. This response spectrum provided in the code book is used for every region of the country which appears to be inadequate. Different parts of the country has different seismic conditions and for every region using the same response spectrum is inappropriate as the results obtained may not properly ascertain the seismicity level of the region completely. Hence in order to take into consideration various factors such as the distance of the source from the site i.e., hypocentral distance, a site specific response spectrum is needed. In this article we have developed one such response spectrum using the attenuation equation. The attenuation equation used here is developed by S T G Raghukanth. This attenuation equation has been used for many other research work such as preparation of microzonation map for new Delhi city, preparation of seismic zonation map for Mumbai city and has also been used in the NDMA in the development of probabilistic seismic hazard map of India. The equation has also been used to study the seismicity of Bangalore city. Both the response spectrums acceleration values i.e., one from the code book developed for a certain time period and the other response spectrum developed using attenuation equation for the same time period are entered into the software ETABS 2013 for the symmetric and asymmetric structures. Analysis is carried out for the structures and the results are studied to ascertain whether there are any variations in the results of the structures for both the response spectrums. From the results we try to conclude the importance of updating the

response spectrum of the Indian code such that it can be applied to every region effectively.

II. METHODOLOGY In order to carry out the comparative studies, firstly we have to develop the symmetric and asymmetric models respectively. The dimensions of the various components of the structures are determined by trial and error method.

After the determination of the dimensions the symmetric and asymmetric models are prepared in the software ETABS 2013. The models developed are also checked using equivalent static method by comparing the base shear values obtained in the software with the base shear values calculated manually. Now the response spectrum is developed for a specific period using the equations from the code book IS:1893:2002 and the attenuation relation. It is to be noted that the response spectrum provided in the code book is not considered and the response spectrum is developed for different time period. The acceleration values obtained was using the formula from the IS:1893:2002 which is as follows TABLE 1a Accelerat Acceleration Acceleration ion Periods mm/s²,NFR mm/s²,CRS mm/s²,FF S RS 0 1 0.315 0.0877 0.01 1.015 0.314 0.0873 0.015 1.0225 0.592 0.1635 0.02 1.03 0.679 0.1873 0.03 1.045 0.723 0.2008 0.04 1.06 0.713 0.1985 0.05 1.075 0.687 0.1918 0.06 1.09 0.646 0.1828 0.075 1.1102 0.607 0.1705 0.09 1.135 0.578 0.1627 0.1 2.5 0.542 0.1537 0.15 2.5 0.433 0.1257 0.2 2.5 0.374 0.1096 0.3 2.5 0.287 0.0855 0.4 2.5 0.238 0.0724 0.5 2 0.206 0.0633 0.6 1.666 0.177 0.0542 0.7 1.4286 0.157 0.0489 0.8 1.25 0.14 0.0438 0.9 1.1111 0.124 0.0387 1 1 0.116 0.0364 1.2 0.8333 0.093 0.0295 1.5 0.6667 0.072 0.0232 2 0.5 0.051 0.0167 2.5 0.4 0.04 0.0132 3 0.333 0.03 0.01 4 0.25 0.02 0.0068 Table 1:

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Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums (IJSRD/Vol. 4/Issue 04/2016/174)

Sa/g = 1+1.5T (0.00 ≤ T ≤ 0.10) Sa/g = 2.50 (0.10 ≤ T ≤ 0.40) Sa/g = 1.00/T (0.40 ≤ T ≤ 4.00) Where, T - Time period Sa/g – Acceleration values The acceleration values for the other response spectrum were obtained using the following attenuation equation as given below ln(Sa/g) = C1+C2+C3*M²+C4*r+C5*ln(r+C6e^(C7*M))+C8*log(r)+l n(ε) Where C1, C2, C3, C4, C5, C6, C7, C8, σ(ε) are constants obtained from NDMA report(Development of Probabilistic seismic hazard map of India) Where r – Hypocentral distance in meters, M – Earthquake magnitude.

The hypocentral distance is taken as 12km(r) to obtain near field acceleration values and for far field it is taken as 52km(r). The magnitude M is taken as 7 for both the cases. Using the above two equations the values of accelerations are obtained. The values of acceleration are obtained for a specific time period. The time period and the acceleration values using the code book equations and the acceleration values obtained using attenuation equation for near and far field are shown in the table 1a. These values obtained using the equations are entered in the software ETABS 2013 along with the respective periods for individual symmetric and asymmetric structures. These values are entered in the software in the sub command ‘Response spectrum’ in the command ‘Function’. After defining the response spectrum command we have to define the case RSX and RSY i.e., response spectrum in x – direction and y – direction in the load cases. After defining the load cases analysis is carried out and the required results are extracted for the purpose of comparison.

Table 1 : Story Displacements Symm Str S E CRS NFRS FFRS m mm mm mm 15 49 0.06223 0.00649 0.00213 14 45.8 0.0607 0.00633 0.00208 13 42.6 0.05865 0.00612 0.00201 12 39.4 0.0561 0.00585 0.00192 11 36.2 0.05313 0.00554 0.00182 10 33 0.04977 0.00519 0.00171 9 29.8 0.04606 0.0048 0.00158 8 26.6 0.04205 0.00439 0.00144 7 23.4 0.03776 0.00394 0.00129 6 20.2 0.0332 0.00347 0.00114 5 17 0.0284 0.00296 0.00097 4 13.8 0.02337 0.00244 0.0008 3 10.6 0.01812 0.00189 0.00062 2 7.4 0.01266 0.00132 0.00043 1 4.2 0.00698 0.00073 0.00024 0 0 0 0 0 Table 2:

III. RESULTS After the analysis of all the models is carried out the results are to be extracted for the purpose of comparison of the response of the structures. Here we developed and used three symmetric models and three asymmetric models for the purpose of analysis. One of the symmetric and asymmetric model is analysed using the response spectrum developed using the acceleration values obtained using the equation from the IS:1893:2002. Similarly one of the symmetric and asymmetric model is analysed using the response spectrum developed using the acceleration values obtained using attenuation equation for near field and one symmetric and asymmetric is analysed using the response spectrum for far field. In order to carry out the comparison the results are obtained for the following parameters 1) Story displacements 2) Story drifts 3) Story Shears A. Story Displacements A Story displacement is the amount of displacement that a structure can undergo when it is subjected to response spectrum analysis. Table 1 shows the amount by which each symmetric model subjected to various response spectrums has displaced and the graphs are shown in Fig 1. Similarly the displacements of asymmetric structures are shown in Table 2 and the graphs are shown in Fig 2.

Fig. 1: Displacements E CRS NFRS FFRS m mm mm mm 15 49 0.06602 0.00678 0.00223 14 45.8 0.06425 0.0066 0.00217 13 42.6 0.06195 0.00636 0.00209 12 39.4 0.05914 0.00607 0.002 11 36.2 0.05589 0.00574 0.00189 10 33 0.05225 0.00537 0.00176 9 29.8 0.04826 0.00496 0.00163 8 26.6 0.04396 0.00452 0.00148 7 23.4 0.03938 0.00405 0.00133 6 20.2 0.03454 0.00356 0.00117 5 17 0.02946 0.00304 0.00099 4 13.8 0.02415 0.00249 0.00081 3 10.6 0.01862 0.00192 0.00063 2 7.4 0.01288 0.00133 0.00043 1 4.2 0.00694 0.00072 0.00023 0 0 0 0 0 Table 2: Story Displacements Asymm STR S

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Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums (IJSRD/Vol. 4/Issue 04/2016/174)

Fig. 2:

Fig. 3: Crs Drifts Symm

B. Story Drifts The story drifts represent the amount by which each story of a structure subjected to seismic forces has drifted. The story drifts for the symmetric and the asymmetric structures analysed using the various developed response spectrums are shown in Table 3 and Table 4.

C. Story Shears Story shear is the amount of shear developed or experienced at each story of a structure when the structure is subjected to seismic forces. The story shear for the symmetric and the asymmetric structures analysed using the various developed response spectrums are shown in Table 5 and Table 6.

S E CRS NFRS FFRS m 15 49 1.30E-06 5.85E-08 1.877E-08 14 45.8 1.33E-06 8.23E-08 2.637E-08 13 42.6 1.38E-06 1.03E-07 3.284E-08 12 39.4 1.42E-06 1.18E-07 3.783E-08 11 36.2 1.47E-06 1.30E-07 4.193E-08 10 33 1.51E-06 1.40E-07 4.543E-08 9 29.8 1.55E-06 1.48E-07 4.826E-08 8 26.6 1.58E-06 1.55E-07 5.049E-08 7 23.4 1.61E-06 1.61E-07 5.247E-08 6 20.2 1.64E-06 1.66E-07 5.438E-08 5 17 1.67E-06 1.71E-07 5.607E-08 4 13.8 1.69E-06 1.75E-07 5.747E-08 3 10.6 1.71E-06 1.80E-07 5.876E-08 2 7.4 1.71E-06 1.90E-07 6.064E-08 1 4.2 1.66E-06 1.70E-07 5.674E-08 0 0 0 0 0 Table 3: Story Drifts Symm Str

Fig. 4: Nfrs Drifts Symm

Fig. 5: Ffrs Drifts Symm

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Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums (IJSRD/Vol. 4/Issue 04/2016/174)

S 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

E CRS NFRS FFRS m 49 1.3E-06 6.66E-08 2.13E-08 45.8 1.4E-06 9.14E-08 2.92E-08 42.6 1.5E-06 1.12E-07 3.60E-08 39.4 1.5E-06 1.3E-07 4.11E-08 36.2 1.5E-06 1.40E-07 4.52E-08 33 1.6E-06 1.50E-07 4.86E-08 29.8 1.6E-06 1.58E-07 5.12E-08 26.6 1.7E-06 1.63E-07 5.33E-08 23.4 1.7E-06 1.69E-07 5.52E-08 20.2 1.7E-06 1.74E-07 5.69E-08 17 1.7E-06 1.78E-07 5.84E-08 13.8 1.8E-06 1.82E-07 5.97E-08 10.6 1.8E-06 1.86E-07 6.1E-08 7.4 1.7E-06 1.92E-07 6.27E-08 4.2 1.7E-06 1.71E-07 5.56E-08 0 0 0 0 Table 4: Story Drifts Asymm Str

6 5 4 3 2 1 0

S 15 14 13 12 11 10 9 8 7 6 5

S 15

E m 49

14

45.8

13

42.6

12

39.4

11

36.2

10

33

9

29.8

8

26.6

7

23.4

Fig. 6: Crs Drifts Asymm L CRS NFRS kN kN Top 0.2332 0.0254 Bottom 0.2332 0.0254 Top 0.4481 0.0482 Bottom 0.4481 0.0482 Top 0.6136 0.0651 Bottom 0.6136 0.0651 Top 0.7366 0.0775 Bottom 0.7366 0.0775 Top 0.834 0.0876 Bottom 0.834 0.0876 Top 0.9177 0.0965 Bottom 0.9177 0.0965 Top 0.9918 0.1042 Bottom 0.9918 0.1042 Top 1.0593 0.1109 Bottom 1.0593 0.1109 Top 1.1243 0.1174 Bottom 1.1243 0.1174

FFRS kN 0.0076 0.0076 0.0147 0.0147 0.0203 0.0203 0.0245 0.0245 0.0279 0.0279 0.0308 0.0308 0.0334 0.0334 0.0358 0.0358 0.0381 0.0381

4 3 2 1 0

20.2

Top 1.1884 0.1243 Bottom 1.1884 0.1243 17 Top 1.2509 0.131 Bottom 1.2509 0.131 13.8 Top 1.3137 0.1374 Bottom 1.3137 0.1374 10.6 Top 1.3809 0.1442 Bottom 1.3809 0.1442 7.4 Top 1.4476 0.1513 Bottom 1.4476 0.1513 4.2 Top 1.4966 0.1569 Bottom 1.4966 0.1569 0 Top 0 0 Bottom 0 0 Table 5: Story Shears Symm Str E L CRS NFRS m kN kN 49 Top 0.2284 0.0247 Bottom 0.2284 0.0247 45.8 Top 0.4348 0.0464 Bottom 0.4348 0.0464 42.6 Top 0.589 0.0621 Bottom 0.589 0.0621 39.4 Top 0.6999 0.0732 Bottom 0.6999 0.0732 36.2 Top 0.7864 0.0821 Bottom 0.7864 0.0821 33 Top 0.8616 0.09 Bottom 0.8616 0.09 29.8 Top 0.9291 0.0966 Bottom 0.9291 0.0966 26.6 Top 0.9909 0.1023 Bottom 0.9909 0.1023 23.4 Top 1.0509 0.108 Bottom 1.0509 0.108 20.2 Top 1.1099 0.1142 Bottom 1.1099 0.1142 17 Top 1.1669 0.1203 Bottom 1.1669 0.1203 13.8 Top 1.2247 0.1263 Bottom 1.2247 0.1263 10.6 Top 1.2889 0.1329 Bottom 1.2889 0.1329 7.4 Top 1.3544 0.1399 Bottom 1.3544 0.1399 4.2 Top 1.4023 0.1453 Bottom 1.4023 0.1453 0 Top 0 0 Bottom 0 0 Table 6: Story Shears Symm Str

0.0403 0.0403 0.0424 0.0424 0.0445 0.0445 0.0468 0.0468 0.0489 0.0489 0.0505 0.0505 0 0 FFRS kN 0.0076 0.0076 0.0145 0.0145 0.0195 0.0195 0.0232 0.0232 0.0262 0.0262 0.0289 0.0289 0.0312 0.0312 0.0331 0.0331 0.0351 0.0351 0.0372 0.0372 0.0392 0.0392 0.0411 0.0411 0.0432 0.0432 0.0453 0.0453 0.0469 0.0469 0 0

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Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums (IJSRD/Vol. 4/Issue 04/2016/174)

Fig. 7: Nfrs Drifts Asymm

IS:1893:2002. Similarly the values of story drifts and the story shears are comparatively higher for the structure analysed using the acceleration values obtained using the equations from IS:1893:2002 as compared to the values obtained for structure analysed using the acceleration values obtained using the attenuation equation. As the response values are higher for the structure analysed using the IS:1893:2002 equation the reinforcement to be provided in the structure are comparatively higher than the minimal amount required which results in higher dead load stresses in the structure and also leads to an uneconomical design.

The main advantage of the attenuation equation is that it takes into consideration the hypocentral distance as well as the magnitude of the earthquake event consider, as a result of which we get the values with respect to the amount of seismicity felt in a specific region due to a certain magnitude of earthquake from the earthquake source.

Depending upon these values the structural steel can be designed properly to incorporate the amount of seismicity felt in that specific region which also results in economical design. Hence it is very important that the Response spectrum provided in the IS:1893:2002 be revised appropriately so that it can accommodate each and every region of the country effectively.

V. SUMMARY & CONCLUSIONS

Fig. 8: Ffrs Drifts Asymm IV. TERMS USED AND THEIR FULL FORMS S – Story, E – Elevation, L – Location, CRS – Code book response spectrum (developed using IS:1893:2002 equations), NFRS – Near field response spectrum (developed using attenuation equation for a lower value of hypocentrals distance), FFRS – Far field response spectrum(developed using attenuation equation for a higher value of hypocentral distance) The results have been obtained and the comparative study is carried out. It can be seen that the values of displacements for the structures analysed using the attenuation equation has lesser amount of displacement for both the near and far field response spectrum analysis as compared to the displacement values obtained for the structure analysed using the equation provided in the

In this article response spectrum analysis has been carried by separately developing the response spectrums using the equations provided in the IS:1893:2002 and the attenuation equation. First the dimensions of the models to be developed are ascertained by trial and error method. The models developed are checked by using equivalent static method by comparing the base shear values obtained for the models developed in the software ETABS 2013 and the base shear values obtained manually. Now the acceleration values obtained using code book equations and the far field and near field acceleration values obtained from the attenuation equation are entered in 3 separate symmetric and asymmetric models and analysis is carried out. After the completion of analysis the results for the parameters displacements, drifts and shears are obtained. From the comparative study of the these parameters for various structures we obtain that the values obtained using IS:1893:2002 equations are comparatively higher as compared to the values for the far and near field equations.

The values will lead to an uneconomical design of the structure and also develop extra stresses for the acceleration values of IS:1893:2002 equation, whereas the attenuation equation values gives results as per the seismic condition of the site and the distance from the source of seismic action which helps in providing economical design of structures and no extra stresses would be bared by the structure.

REFERENCES [1] Development Of Probabilistic Seismic Hazard Map Of India Final Report Technical Report [2] Of The Working Committee of Experts (Wce) Constituted By Natural Disaster Management Authority Govt Of India, New Delhi.

[3] Seismic Hazard Estimation For Mumbai City. S. T. G. Raghu Kanth And R. N. Iyengar.

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Comparative Study of Response of Symmetric and Asymmetric Structures using Response Spectrums (IJSRD/Vol. 4/Issue 04/2016/174)

[4] Seismic Hazard Mapping Of Delhi City. R.N.Iyengar1 And S.Ghosh, 13th World Conference On Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004, Paper No. 180.

[5] Seismic Hazard Analysis For Bangalore Region, T.G.Sitharam And P.Anbazhagan, Natural Hazards (2007) 40:261 – 278, Doi 10.1007/S11069 – 006 – 0012 – Z. [6] Estimating Seismic Hazard For Central And Southern India, K.S. Jaiswal And R. Sinha., The 14 th, World Conference On Earthquake Engineering, October 12-17, 2008, Beijing, China.

[7] Probabilistic Seismic Hazard Studies Of East Coast Region Of India., L. Kanagarathinam [8] , G. R. Dodagoudar And A. Boominathan, The 14 th, World Conference On Earthquake Engineering, October 12-17, 2008, Beijing, China.

[9] Site Specific Seismic Hazard Assessment For Hyderabad City. K. Tirumala Reddy, P. Sreenivas Sarma And S. Jayaprakash Narayana, International Journal Of Earth Sciences And Engineering, Issn 0974 – 5904, Vol.03,No.05, October 2010, Pp.696 – 707.

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