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Time History Analysis
It provides instrumental measurement of duration, frequencies or accelerations and can be used to understand linear or nonlinear response of a structure for a specific excitation. This method is generally not used to analyze seismic effect as each earthquake is different and the source could be away from the structure under design. However, this method can be used for forensic analysis of a seismic event.
Static Equivalent Method as per ASCE 7
A few mathematical calculations need to be performed in order to obtain seismic response co-efficient Cs. These co-efficient Cs will be used to generate seismic load acting on the system. All calculations and assumptions are done in accordance to the book of standards issued by the American Society of Civil Engineers (ASCE) 7.
The stepwise solution to obtain the static seismic co-efficient’s:

- Step 1: Identify site class based on type of soil from ASCE 7 (Table 20.3-1). Assuming soil type as dense soil let soil class be ‘C’.
- Step 2: Identify short period acceleration, i.e., the acceleration corresponding to 0.2s and spectral response acceleration corresponding to 1s from the response spectrum. (Ss)0.2s = 1.1060 and S1 = 0.8071.
- Step 3: Get short period site coefficient from ASCE 7, (Table 11.4-1). In this case, for (Ss)0.2s =1.1060 and Fa=1 for class C.
- Step 4: Calculate spectral response acceleration at a short period adjusted to site class as: SMS = Fa*Ss = 1*1.1060 = 1.106.
- Step 5: Get long period site coefficient from ASCE 7, (Table 11.4-2) and in this case, for S1 = 0.8071 and Fv = 1.3 for class C.
- Step 6: Calculate spectral response acceleration at period of 1s adjusted to site class as SMS = Fv*S1 = 1.3*0.807 = 1.0491.
- Step 7: Calculate spectral response acceleration parameter at short period of 0.2s defined as: SDS = 2/3* SMS = 2/3*1.106= 0.74
- Step 8: Calculate spectral response acceleration parameter at period of 1s defined as: SD1 = 2/3*SM1 = 2/3*1.0491= 0.7
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