Engineer Boards

# Vertical Distribution of Seimic Force

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I am studying for the SE Lateral portion of test and starting going through Kaplan’s “Seismic Design and Review for the PE Exam” by Alan Williams. The question I have is when the book does example 2.9 explaining the vertical distribution of seismic forces it goes through the steps of calculating the vertical distribution factor (Cv) for each floor the same way I would but when it calculates the total design shear to multiplied by this factor it sums the effective seismic weights for each floor.

The problem I see is by summing the seismic weight for each floor your forgetting to account for the wall weights below the midheight of the first floor. Am I wrong for thinking this needs to be accounted for? ASCE7 states that is should be “total design lateral shear at the base of the structure”.

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I don't have the problem or book you have. However, the walls weights would need to be included in the weight tributary to the frame. This would only be the walls that are perpendicular to the direction of force if the assumption (such as a concrete or masonry shearwall) is that the walls can handle their own inertia and are the LFRS. Once the analysis of the resisting system is in effect, the wall weights get included when you use your load combinations (0.9D + E for example).

Let me know if I'm off track. I don't have the book and am guessing for the most part...

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I believe your talking about when calculating the diaphragm forces you don't need to include the wall weights parrallel the force because of the reasons you stated. The example I am actually having trouble with deals with the vertical distribution of seismic forces from section 12.8.3 in ASCE7. When Williams calculates the total shear at the base (V) for use in equation 12.8-11 he doesn't include the wall weights below the midheight of the first story and I don't know if that is correct.

Hope I'm explaining this all right, thanks.

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I think that Williams is correct. The forces distributed vertically are applicable to that story level. I think the lower half of the first floor is assumed cantilevered to the foundation and easily resisted in that way by anchorage.

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That must be what it is. I have been trying to find other examples but the only ones I find are where the seismic weight assigned to each floor is given so the answers just sum the weights and multiply it by the response coefficient to get the base shear.

I am still a little hesitant as ASCE calls the variable V the "total design shear at the base of the structure". I mean if I was calculating the base shear for a one story building I wouldn't ignore the wall weights below the midheight of the wall in my calculation.

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What helps me is that Cv(sub,o) is at height zero, so no influence on base shear.

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McEngr is correct, IMO. Lower half of the first story is typically taken by your grade beam / foundation system directly. Hoven, for your example of a 1-story frame, all of the effective weight is taken at, and therefore all of the base shear is distributed to, the roof level. Extrapolate that principle for multi-story: all of the base shear is distributed starting at the 2nd floor on up.