When is P-Delta Calculation required? 1

[structurebeton]

Can someone tell clearly when is a P-Delta Analysis required to be done? I seldom perform such calculations in steel buildings.

Thanks,

 

[JAE]

Under AISC, Chapter C in the specification is pretty clear that considering second order effects are always required.

 

[asixth]

AS4100 which is in limit state format, allows a first-order analysis to be carried out but requires the design actions to be maginfied.

Best to carry out a second order analysis, particular when members are required to resist large compression forces combined with bending such as sway frames, a second order analysis can add significantly to the drift.

 

[Mackowitz]

ASCE7-05, Section 12.8.7 has an exception that may get you out of it. But JAE is right, AISC doesn't have an exception.

 

[structurebeton]

One reason it typically doesn't matter checking P-delta is the fact that there is very little movement when X-Bracing is used as lateral resisting system. In moment frames, it is a different story, and I very seldom design moment frames.

 

[JAE]

structurebeton,

You are correct that X-bracing means little lateral deflection of the X-brace. But with large warehouse structures, the metal deck diaphragm can have significant lateral second-order deflections between the brace lines and this can significantly add to the lateral loading of the structure and should be checked.

 

[csd72]

You can get second order effects between the nodes even if the ends are braced.

 

[civeng80]

Yes asixth thats true, but why for deflections does one use first order analysis and not the more accurate 2nd order analysis, Ive always wondered about that one.

Cheers!

 

[WillisV]

civeng80 - there is nothing saying you can't use 2nd order analysis under service load conditions to predict deflections. Typically it is not common practice, but if I see that 2nd order effects are considerable in a particular structure then I would certainly check deflections under a P-delta with service loads.

 

[Lion06]

I always check drift using P-delta with service loads. I don't see the point of ever checking a beam deflection using P-delta. If there is no P, then there is no P-delta. Only in rare occasions (in the braced frames) will you get axial load in the beams. You will get some axial load in moment frame beams, but very, very small values. Second order effects are most pronounced with a large P and a small M, not a small P and a large M. The reason for that is that if M is already large, a small P with the deflected shape will add a small percentage of the moment. If P is large with a small M, that percentage is likely to be much higher.

 

[Lexatus]

You can always check P-delta effects, but in some cases it is really necessary to do it. If you consider a cantilever beam with vertical P force and an horizontal one, this last will give you a displacement equal to F H^3 / 3EI, so you will have:

Mtot = F H + P (FH^3/3EI) = F H [1 + (P H^2/3EI)] =>

Approximately: Mtot = M1 (1 + P/Pcrit)

Because for a cantilever beam:
Pcrit = (pi^2 EI) / (2H)^3 = (9 EI) / (4 H^2)

So you can notice that if P is quite similar to Pcrit (Euler’s load) the Mtot is twice bigger than M1.

In other words, with a little P you have little 2nd order effects, maybe negligible. But watch out if your element has a big axial load. In that case you MUST verify second order effects.

 

[asixth]

In frame action under gravity loads, the foundations resit an outwards thrust therefore, the beam will be under a minimal compression force due to frame action, but this will not produce any significant P-delta displacements.