## Inelastic displacement in P-delta effects

## Inelastic displacement in P-delta effects

(OP)

Hello Folks,

I have elevated vessel mounted on braced legs, for which i am verifying the seismic design. Going through ASCE 7-22, clause 15.4.6 as well as 15.7.10.3, the P-delta effects shall be based on inelastic seismic displacements which does make sense for such inverted pendulum like structure. How can this be achieved in the analysis model (say SAP2000) ? The default non-linear load case with p-delta effects will only consider displacement based on elastic analysis (divided by R), and if Cd was considered in the load case then the loads will increase which is not correct, so how the p-delta can be captured at the inelastic displacement level while maintaining the loads reduced by R ?

Your advise is much appreciated

I have elevated vessel mounted on braced legs, for which i am verifying the seismic design. Going through ASCE 7-22, clause 15.4.6 as well as 15.7.10.3, the P-delta effects shall be based on inelastic seismic displacements which does make sense for such inverted pendulum like structure. How can this be achieved in the analysis model (say SAP2000) ? The default non-linear load case with p-delta effects will only consider displacement based on elastic analysis (divided by R), and if Cd was considered in the load case then the loads will increase which is not correct, so how the p-delta can be captured at the inelastic displacement level while maintaining the loads reduced by R ?

Your advise is much appreciated

## RE: Inelastic displacement in P-delta effects

Look at the image below (which was from a presentation I did maybe 15 years ago).

Vo is whatever lateral loads you originally applied.

P is whatever gravity loads you originally applied.

Delta_o is the initial elastic deflection that results.

H is the height of the column.

The only difference is that you would amplify the Delta_o by Cd so that the secondary shear is really.

Vi = P*Delta_o*Cd / H

Then I'd apply this Vi (for a LINEAR analysis) in combination with my regular loading.

## RE: Inelastic displacement in P-delta effects

I think i might define a non-linear load case with Cd*Eq to get the respective p-delta under inelastic displacement, then subtracted the same from load combination (linear subtract) to remove the load but while keeping p-delta effect. (i have to check it on SDOF model first)

## RE: Inelastic displacement in P-delta effects

Yeah, that would probably work. If your software allows it. I was assuming that your software didn't allow anything so advanced.

## RE: Inelastic displacement in P-delta effects

If you have the thing supported on a braced frame and there's a high center of gravity it's likely that the moment effects from the lateral load significantly govern over anything you're going to get out of P-Delta unless you have some strange stability situation happening.