Introduction

Seismic analysis is a subset of structural analysis and is the calculation of response of a building structure to earthquake. In usual case normal buildings less than 3 stories doesn’t require earthquake analysis (except japan).

Engineer know that everything has a natural frequency. A building also has a natural frequency and this is belong to modal analysis of a building.

Fundamental mode has the lowest frequency of building response.  Most buildings, however, have higher modes of response, which are uniquely activated during earthquakes. This modal frequencies are the basis of the earthquake analysis procedure.

There are 2 common methods of doing earthquake analysis

1. Equivalent Static Analysis

This approach defines a series of forces acting on a building to represent the effect of earthquake ground motion, typically defined by a seismic design response spectrum. It assumes that the building responds in its fundamental mode. For this to be true, the building must be low-rise and must not twist significantly when the ground moves. This method we can calculate the response with hand calculation.

The response is read from a design response spectrum. We will discuss how to design a response spectrum in next posts.

2. Response Spectrum Analysis

This approach permits the multiple modes of response of a building to be taken into account in the frequency domain. This is the method using in many structural analysis softwares like sap2000. I will do a separate post on how we can do earthquake analysis in Sap2000.

Computer analysis can be used to determine these modes for a structure. For each mode, a response is read from the design spectrum, based on the modal frequency and the modal mass, and they are then combined to provide an estimate of the total response of the structure. In this we have to calculate the magnitude of forces in all directions i.e. X, Y & Z and then see the effects on the building.Combination methods include the following:

• absolute – peak values are added together
• square root of the sum of the squares (SRSS)
• complete quadratic combination (CQC) – a method that is an improvement on SRSS for closely spaced modes

The result of a response spectrum analysis using the response spectrum from a ground motion is typically different from that which would be calculated directly from a linear dynamic analysis using that ground motion directly, since phase information is lost in the process of generating the response spectrum.

Earthquake Design in Brief ( According to Australian code)

Please refer AUS 1170 for the detailed Design. Here i will discuss the importance of parameters. Please read response spectrum post before continue.

Factors to be considered for earthquake design ( Static Method)

Below factors are useful when doing the earthquake analysis in sap2000 or etabs.

Probability Factor (Kp)

Kp for the annual probability of exceedance can be found from table 3.1 of aus 1170. This will depends on the time. Typically Earthquake design will carried out to 50 years , 500 years and 2500 years of retaining periods. Which gives 1/50,1/500,1/2500 annual probability exceedance.

Hazard Coefficient Factor (Z)

Hazard coefficient factor can be taken from table 3.2 of aus 1170. This is actually a factor of peak ground acceleration. Usually take as 0.1g for Sri Lanka and it should not be less than 0.08 g. (g= Gravitational acceleration)

Ductility Factor ( μ )

This is a factor use to determine how ductile is structure. Typical value is varying from 1 to 4. can be found from table 6.5(A)

Performance Factor (Sp)

This has only two values. 0.77 and 0.67. can be found from table 6.5(A) ,

Spectral Shape factor (Ch(T)

This will depend on the soil and it will be use to design the required response spectrum.