Seismic Linear Static Analysis - Relative or Absolute Floor Forces?

[JK7070]

Hi All,

I am trying to figure out whether a seismic static lateral force analysis (or equivalent static analysis or lateral force method) gives absolute or relative storey forces. My aim is to convert the obtained floor forces (Fi) (from the static analysis) into pseudo floor accelerations (pA), where, pA = Fi/m and m is the storey mass. The reason for doing this is so I can compare the codified static analysis results to peak floor accelerations (PFA) obtained from a nonlinear time history analysis. I know that the PFA from the nonlinear analysis are absolute values but I am confused whether the pseudo values from a codified static approach are absolute or relative. Am I comparing apples with apples? I am aware that the PFA's from the nonlinear analysis are maximum absolute values at each floor level and that the PFA's throughout the building height do not all occur simultaneously at the same time.

Any discussion around this would be most welcomed as the more I think about it the more confused I get!

Regards,
JK7070

 

[KootK]

I believe that the storey forces are absolute. That said, with all of the approximations built into the ELF procedure, an apples to apples comparison will indeed be a challenge.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JK7070]

Thanks for the response KootK.

I guess another way to ask the question is this:

When we normally consider the ELF method in terms of obtaining a base shear the storey forces go from a maximum at roof level and vary linearly* to zero at ground. Some codes obviously allow for some increase in the force at roof level to allow for higher modes so the distribution is not entirely a straight line from roof to ground. But when we calculate the pseudo accelerations (pA) from the storey forces should the distribution also go to zero at ground or should we be setting the acceleration at ground equal to the peak ground acceleration (PGA). See plot below of pseudo acceleration for a 10 storey building, I have plotted this going to zero at ground level.

Regards,
JK7070

 

[KootK]

Okay, I see where you're going with this now. And I agree. Try this on for size:

1) Our ELF procedure starts with determining the base shear. That determination is made assuming that the building is an SDOF system with the following properties:

M_sdof = SUM(Wx)

h_sdof = SUM(Wx * hx) / SUM(Wx) <--- vertical location of mass centroid.

a_sdof = V_base / M_sdof <--- acceleration of the SDOF model using base shear and mass (weight really).

2) Now find the acceleration of a particular floor using the code assumptions. We'll stick with a linear k-value to keep it simple.

a_x = h_x / h_sdof * a_sdof = h_x /(SUM(Wx * hx) / SUM(Wx)) * V_base / SUM(Wx) <--- just ratio-ing by height assuming a first mode shear building deformation pattern.

F_x = a_x * W_x = h_x /(SUM(Wx * hx) / SUM(Wx)) * V_base / SUM(Wx) * Wx <--- Back to F=Ma

If you follow the algebra through on that last equation, the two SUM(Wx) cancel out and you'll be left with the code equation for the vertical distribution of base shear.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.