Second-order analysis 1

[abusementpark]

When is it really required?

I keep hearing a lot about people performing second-analysis on all their structures these days. We use RAM Advanse and performing a second-order isn't much of bear, but when I have done it, the difference has almost always been negligible. Maybe, at most, it increase the moments in my columns by a percent or two. Now, the firm I work for mainly works on low-rise buildings.

Do second-order effects really become significant for larger buildings? Can anyone shed some light on the trends here??

 

[asixth]

I don't perform second order analysis for reinforced concrete structures. Dealing with low-rise steel structures, second order analysis does not vary significantly from a first order analysis.

 

[271828]

There are all kinds of examples of situations in which the second-order moments are significantly more (say > 10%) than the first order ones.

Taller buildings are examples.

Low-rise building, a little on the tall side, with non-trivial gravity loads and a loose drift limit.

Tall wind column that also has axial load.

I agree, though, that there are many, many counter-examples. I used to design lots of 5-10 story hospitals that had rigid frames for the LFRS and I seem to remember hte second-order amplifications being small, like 5-8% or less.

 

[Lion06]

I think it also depends on what the lateral system is. If you have a shear wall or braced frame building, the second order effects will be minimal. If you have a moment frame building then second order effects will increase. Something else that is often overlooked is the lateral load. If you have high gravity loads, you will see increased second order effects as your lateral load DECREASES. If you have a one story structure with light gravity loads (as one might expect for a roof - depending where you're located), and not unreasonably low lateral forces, then the second order effects will likely be minimal. Second order effects are the P-delta effects - a small magnitude of P typically means a small amount of P-delta effects.

You should also break your columns along the length to capture P-little delta effects.

 

[JoshPlumSE]

ASCE-7 has some guidance about when a 2nd order analysis must be performed. See section 12.8.7 of the 2005 version. When the ratio of secondary shears to applied shears (theta) is less than 0.10 then they say you can ignore the effect.

Theta = P*Delta / (V*h)

Where:

P = total applied vertical load (at or above the story level)

Delta = the elastic story drift between that floor level and the level below it.

V = The applied lateral force at that level.... NOT the sum of the shear forces from all the floors above that one.

h = story height.

ACI 2002 (section 10.11.4.2) has a similar definition that they use to distinguish between a SWAY frame and a non-sway frame. With a sway frame requiring a more sophisticated P-delta or second order analysis. To some extent 2nd order effects are still required to be considered for non-sway frames.... But, only for very slender members.

Personally, I like the ACI definition better, because their cutoff is a a 5% amplification rather than the 10% that ASCE is recommending.

 

[slickdeals]

If you have high gravity loads, you will see increased second order effects as your lateral load DECREASES

.

Can you explain this? I may be missing a point. Decrease in lateral load = decrease in [Δ] = decrease in P-[Δ] effects?

 

[Lion06]

Decrease in lateral load = decrease in delta is true. But if you have small lateral load, then your first order moments/drifts will be smaller. As a percentage of first order magnitudes, this is likely when you will see the largest second order effects. Think about it on this extreme just to get the idea. Say you have a single story structure (roof only) with very high gravity loads (say 300psf green roof) and no lateral load at all such that you only design for notional loads. First order moments/drifts will be small because of the very small lateral load, but the second order effects will be magnified because you have such a huge P. Delta will typically always be around h/500, so the big driver is really P. As a %, however, the second order effects are most pronounce (typically) with high gravity loads and small lateral loads.

 

[haynewp]

The key is "As a %".