Applies To
	Product(s):	STAAD.Pro
	Version(s):	All
	Environment:	N/A
	Area:	Analysis Solutions
	Subarea:	Response Spectrum Analysis
	Original Author:	SANJIB DAS Bentley Technical Support Group

 

There are few things that we must keep in mind while working with IS:1893 (part-I) Response Spectrum:

 

1. It is a generalised Response Spectrum corresponds to MCE

2. It is an elastic Response Spectrum.

3. PGA of the Response spectrum in 1.0(g)

4. It is not dependent on the building category.

    

While designing a structure, we need to convert the elastic Response Spectrum which corresponds to MCE level to DBE inelastic Response Spectrum. The code has stipulated two methods for seismic analysis:

 

1. Design Lateral Force Method

2. Response Spectrum method

 

Time History method has to be adopted depending on the requirement on the designer.

 

Design Lateral Force Method : In this method, the code has specified a factor Ah  (caluse-6.4.2) which is termed as design horizontal seismic co-efficient. It is (Z/2)*(I/R)*(sa/g). A user who is using this code must have a clear understanding why these factors are considered. The (Sa/g) values obtained from the elastic Response Spectrum depending on the time period obtained from empirical equations. This values has to be scaled down to DBE by taking the average of the values obtained from MCE. That is how the ½ factor comes into picture. The spectrum that is provided by the code is elastic one. One needs to consider ductility off the steel into consideration. By ductility we understand, the ability of structure to undergo inelastic deformation without losing it strength. That is the reason why R comes into the equation. It is called as Response Reduction factor. It is dependent on the following factors.

 

1. Over-strength

2. Ductility

3. Redundancy

 

While designing a member in LSD method, we take into consideration- partial safety factor on material (specifically on steel) and loading. So, we are always overestimating the force. We are not considering ductility of the material- it allows the structure to dissipate the energy imparted on a structure by allowing the members to undergo inelastic deformation but ensuring that the members will not collapse. In such case, the failure mechanism is governed by formation of Plastic Hinges- the concept even is accepted but it is very difficult to achieve the same in case of a concrete member. More redundant is the structure, more plastic hinge formation is required to come to the failure condition. Thus, the factor R is such a factor with which the MCE level Response Spectrum has to be scaled- it will come in the denominator.

 

The generalised response spectrum has a values of 1.0(g) as PGA which indicates a catastrophe in real life structure. It has to be scaled with the site condition that is why the Z- zone factor comes into play. We can consider the highest seismic zone- zone V. Here the zone factor is 0.36. It invariably indicates PGA of that zone is 0.36(g). Thus, zone factor is such a factor with which the Response Spectrum has to be multiplied with.

 

While designing a structure, the designer wants to be in safer sider. Depending on how important the structure is, the designer would like to design the building with higher force. Thus, there comes another factor known as I- importance factor. It has either a value of 1 or 1.5 for IS:1893 Part I.

 

Response Spectrum method: In this method, the code has specified a factor Ak (caluse-7.8.4.5-C) which is termed as Design Horizontal  Acceleration Spectrum- it is the same as Ah. The philosophy of bringing the elastic Response Spectrum which corresponds to MCE level to DBE inelastic Response Spectrum remains the same.

 

Now, coming to STAAD.Pro- the program calculates time period for different mode and (sa/g) value is found out. It has to be scaled down to DBE inelastic spectrum. For this reason- the direction factor should be equal to (Z/2)*(I/R).