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# 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 ?

Replies continue below

### RE: Inelastic displacement in P-delta effects

You've posed a really good question. I don't think there is a simple answer. Maybe someone has a better idea than I do. But, I would probably do the following:

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

(OP)
Thanks Josh, the problem is that i need to do it at each time the loads are changed as the design progress.

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

#### Quote:

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)

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

Why don't you just reduce your R so that your deflections are realistic and then divide your stresses out by R for evaluation (or increase your allowables). Or do both runs and look at your comparative reactions and forces to see if it's even significant enough to worry about.

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.

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