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# Response Spectrum Analysis Procedure

## Response Spectrum Analysis Procedure

(OP)
I have a question about what is almost the first step in the response spectrum analysis procedure. I live in Canada, so everything I do is based on the National Building Code of Canada (although I would think an RSA would be similar everywhere in the world). In the building code commentary, it outlines a 9 step procedure for calculating the scale factor for use in an RSA. I am unclear about a step at the very beginning. One of the first things it tells you to do is to "restrain all displacements other than those in the direction of earthquake forces, then carry out a linear dynamic analysis to determine the fundamental lateral period, Ta, and the base shear, Ve". What I am unclear about is this: is the base shear, Ve, that they are asking for at this point suppose to be based off of only the fundamental mode which we got our fundamental period, Ta, from? Or are we suppose to base the Ve off of all of the possible modes using a "square root of the sum of squares" type of method? I'm not sure what is the right way to do it. Obviously if we are suppose to base it off of all the modes together, the Ve will generally end up being higher. Any insight would be appreciated. Thanks.

### RE: Response Spectrum Analysis Procedure

The response spectrum base shear is based of the srss or cqc methods usually (usually cqc method as it deals better with closer spaced modes), your code should give you guidance on the appropriate method. Then depending on the code(sorry not familiar with Canadian codes) you may be required to scale the response spectrum base shear up to the base shear determined from the first mode which is why it's telling you to work this out first I think.

In the code I predominantly deal with in New Zealand, the scaling is dependent on how regular the building is, if it's deemed 'regular' then it's scaled up to a minimum of 80% and if it's deemed 'irregular' the base shear is scaled up to a minimum of 100% of the first mode (equivalent static) base shear. There are a number of 'tests' you can do to determine a structures regularity. Again your code probably outlines something similar.

Perhaps scan the full steps referenced for us to review?

### RE: Response Spectrum Analysis Procedure

(OP)
Thanks for responding. I've attached the "Dynamic Analysis" section of the building code here, as well as the commentary which outlines the 9 step procedure for getting the scale factor that I was talking about. As you can see, our code is near identical to your New Zealand code. We also scale up our dynamic loads to at least 80% of the static load if the building is regular, or 100% if it is irregular.

So my question comes in step 2 of the 9 step procedure outlined in the commentary. It says to find the fundamental lateral period (Ta) and base shear (Ve). I understand that Ta is just the period of the first mode of vibration in whichever direction you are investigating. But I am unclear exactly how to calculate Ve. Is Ve suppose to be the dynamic base shear calculated only using the first mode (ie. the same mode that Ta was calculated from)? Or is Ve at this stage suppose to be the dynamic base shear calculated using input from ALL of the relevant modes?

Thanks for any help.

### RE: Response Spectrum Analysis Procedure

Must admit it's not entirely clear based on the way it's phrased, but I think it's the base shear from all modes as it notes you are taking from the analysis the fundamental period and the base shear. It doesn't say to work out the base shear from that period. You then scale the base shear in step 3 to a minimum level.

Step 4 you are working out the equivalent static base shear (I.E. Based on the fundamental period only in this step), and step 5 you scale the response spectrum base shear worked out in step 2 & 3 (Ved) to a minimum of 80/100%V depending on regularity to give you your design base shear Vd.

The above is consistent with the way you would generally approach a response spectrum and base shear scaling.

### RE: Response Spectrum Analysis Procedure

(OP)
I think I agree with you. What you're saying does make sense. Thanks for your input.

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