Necessity of P-delta Analysis for a Non-seismic Structure 1

[rilitoma]

Hi everyone,

I've spoken to an engineer recently regarding the necessity of P-delta analysis in a multistorey building. He is practicing structural engineering in an ASEAN country which does not fall into seismic zone. Therefore he only does static analysis in his design. According to him, he does not carry out any P-delta analysis or pushover analysis.

I'm a fresh engineer and it got me thinking,

1. For a static analysis, any code that specifies under what conditions, P-Delta can be ignored?
As far as I know ASCE 7-16 has specified the condition where P-delta analysis can be ignored when stability coefficient falls lower than 0.10. But that is for dynamic analysis.

2. For a static analysis, any code specifies that non-linear (static pushover) analysis shall be carried out?
The engineer informed that he also doesn't carry out any pushover analysis.

 

[Greenalleycat]

Hey mate, I think you might be a little confused about the pushover thing
The pushover analysis is to allow you to mobilise the full capacity of a structure by pushing it until a failure mechanism has formed
As a simple example, a portal frame with gravity and lateral load will have higher demands at one knee than the other, meaning one knee will reach its yield capacity earlier
However, the structure itself is not unstable - it still has one knee able to carry more load, so the pushover allows you to push it further until the second knee yields, at which point you have formed a collapse mechanism and you know your ultimate lateral capacity

Pushover analyses that are only really relevant in the context of a lateral load so you can't really 'pushover' a gravity-loaded structure
I was trying to think of a scenario in which you might consider them, and all I could come up with is some sort of horrible eccentric structure with a large permanent gravity...but if your structure relies on forming one plastic hinge under this load case and then proving that the other hinge hasn't yet formed, that would be one of the worst designs of all time. So don't do that.

P-Delta (big Delta) is similar in that significant lateral deflections generally only form under lateral load cases, hence why it appears in the context of seismic provisions
However, P-delta (small delta) relates to effects such as member imperfections and member deflection - this can be considered and may be relevant in some designs
Some of these effects can be captured by running a non-linear static analysis - this will allow nodes to move, increasing axial load eccentricity to generate more lateral deflection, and so on until the structure converges

 

[rilitoma]

Thanks Greenalleycat.

But as I know, even if the building is not in seismic zone, there are still lateral load input (notional load and equivalent static wind load). However, the said engineer doesn't carry out any pushover or P-Delta (big Delta) checking. So I was trying to research that whether if there's any code provision on this, for static load analysis.

 

[Greenalleycat]

I cannot find any provision for P-Delta effects under any load case other than seismic
My understanding is that P-Delta is primarily a concern for ductile mechanisms, where there is a tendency for deflections to get larger over time as the structure softens due to the plastic deformations
Ductility is typically only utilised in seismic load cases as this fits the nature of the load
Earthquakes typically have a single peak shaking that causes the structure to go ductile followed by repeated smaller cycles that are managed by dissipating energy from the plastic hinge zones
This doesn't work so well in winds - imagine if a hurricane hit the building, caused a ductile mechanism to form, then the hurricane continued to blow past for 12+ hours
It's likely that the building would be shaken apart long before the hurricane got through

With the pushover analysis - I'm still not sure if you are conflating ideas here.
A pushover analysis is a specific type of analysis that aims to utilise all lateral capacity within a structure by forcing a collapse mechanism to form
This is useful for earthquakes to get efficiency in some designs but it is not useful in wind or other lateral cases as you would not typically allow plastic hinges in these load cases, as mentioned previously

If you want to consider the effects of geometric non-linearity then just run a non-linear static case on a model that has both your gravity and lateral (wind or other) loads on it
This way the model will iterate and give you a pseudo P-Delta effect

 

[human909]

Nice explanation first up Greenalleycat. It was clear enough for me.

Thanks Greenalleycat.

But as I know, even if the building is not in seismic zone, there are still lateral load input (notional load and equivalent static wind load). However, the said engineer doesn't carry out any pushover or P-Delta (big Delta) checking. So I was trying to research that whether if there's any code provision on this, for static load analysis.

Rilitoma, I can't speak about your code specific question. But analysis that involves pushing the building where some elements fail generally doesn't apply to non seismic lateral loads. Thus push over analysis is generally not relevant or applicable.

Regarding P-Delta affect. You are likely allowed scope in your code to for suitable rational analysis. For stiff structures P-Delta effects are pretty negligible so it can likely be ignored. For more flexible structures such as moment frames it might well pay to check it. Personally I just run non-linear analysis and call it a day.

(I just checked a heavily loaded moment frame structure that I designed. Deflections and critical stresses in columns increased by 10% but running a non-linear analysis vs linear.)

If you want to consider the effects of geometric non-linearity then just run a non-linear static case on a model that has both your gravity and lateral (wind or other) loads on it
This way the model will iterate and give you a pseudo P-Delta effect

Is this really a pseudo P-Delta effect? I am on the understanding that this is a REAL P-Delta effect. Though I'm happy to be educated otherwise.

 

[Greenalleycat]

Hah, fair point there. In my head I separated it out from 'real P-Delta' just because that's how our code kinda does it
I always think of non-linear static analysis as second-order analysis, not as P-Delta...but you're right, it is
The only thing different I suppose is that P-Delta is a broader concept that also requires consideration of inelastic displacements too, which aren't captured in a non-linear static analysis

So all non-linear static is P-Pelta but not all P-Delta is non-linear static..? Maybe?

 

[human909]

Hah, fair point there.

Thanks. For me it wasn't a matter of nit picking it is a matter of cementing my understanding. I'm ignorant in many areas so I'm always questioning things. For me P-Delta as a rigorous analysis theory is that university subject that I skipped because of a hangover!

In my head I separated it out from 'real P-Delta' just because that's how our code kinda does it

And I use a different code and rarely if ever directly consider P-Delta from a hand calculation perspective.

I am just a dumb engineer who knows how to use software. I know how to click the non-linear button!

I always think of non-linear static analysis as second-order analysis, not as P-Delta...but you're right, it is
The only thing different I suppose is that P-Delta is a broader concept that also requires consideration of inelastic displacements too, which aren't captured in a non-linear static analysis

So all non-linear static is P-Pelta but not all P-Delta is non-linear static..? Maybe?

Except that non-static analysis can also consider inelastic displacements, if your analysis approaches and tools support that!

But yes they are different. P-Delta is a specific concept of interactions between displacements and loads orthogonal to those displacements. Non-linear static is a partial description of an analysis approach. Whether "non-linear static" analysis full captures the P-Delta concept depends on the exact details and definitions of both.

But now I AM being pedantic. But only in good humour and with an endeavour to improve my own knowledge and maybe even others at the same time!

 

[Celt83]

The series of "Stability Fun" modules for MASTAN do a great job of running through the topics of secondary effects:

https://www.mastan2.com/stabilityfun.html

I know of at least one location in both ACI 318 and TMS 402 where secondary effects (P-delta) are explicitly noted as a design requirement, slender walls.

 

[JLNJ]

If you are using AISC, then P-delta (big and little) almost certainly apply.

 

[Lomarandil]

(I just checked a heavily loaded moment frame structure that I designed. Deflections and critical stresses in columns increased by 10% but running a non-linear analysis vs linear.)

I agree with this characterization. I've designed a number of concrete moment frame structures in ASEAN, and for the non-seismic countries, this was about right. Where it typically comes into play is the negative moment demand at beam-column connections.

And while 10% doesn't sound like a lot, I think it is both a real effect and important to capture, especially when combined with three other factors common in ASEAN:
1) Poor understanding and application of lateral loading due to wind on nominally "gravity controlled" buildings. Many engineers in the region are already underestimating the negative moment demand for this reason.
2) Poor detailing of beam-column joints to ensure proper rebar development for negative moments, especially in upper levels where you don't get bailed out by clamping force across the joint.
3) The improper use of "pin releases" at the end of concrete beams during FEA analysis, which is pervasive among many engineers in south and southeast Asia.

 

[JoshPlumSE]

I'd like to start over a bit because some countries use different terminology than the US. So, I'm going to use what I think is the most precise language.

LSA = Linear Static Analysis.

GNSA = Geometrically Non-linear Static Analysis. In the US we would often talk about this as a "2nd order analysis". It's just a static analysis that also accounts for the geometric changes in the structure. P-Delta is the most common way to do this. Though P-Delta is an imprecise term because it consists of both p-little delta and P-BIG DELTA. Where p-little delta can often be accounted for with moment amplifiers like (Cm/ 1-Pu/Pe). The P-BIG DELTA portion of this can also be accounted for by adding additional (equal and opposite) story shears to your structure.

MNSA = Material Nonlinearity in a Static Analysis. This is accounting for plastic hinging and yielding in the structure. This is what I would refer to as a push-over analysis. Though many push over analyses would really be the next term.

GMNSA = Geometrical and Material non-linearity in a static analysis. This would be a pushover analysis that also accounts for geometric non-linearity.


I'd say that anyone who is doing hand calculations is generally doing an LSA (Linear Static Analysis) regardless of what code they're using. They may use some moment amplifiers to account for p-little delta affects in slender members. But, this does little for overall structure stability for lateral loads. This can be dangerous when you have heavy structures with relatively flexible lateral force resisting systems. Shear wall structures (other than high rises) should be fine. But, if you're doing moment frames, then I really think you are required as a responsible engineer to do a GNSA (Geometrically Non-linear static analysis)

1. For a static analysis, any code that specifies under what conditions, P-Delta can be ignored?
As far as I know ASCE 7-16 has specified the condition where P-delta analysis can be ignored when stability coefficient falls lower than 0.10. But that is for dynamic analysis.

This doesn't only apply to Dynamic Analysis (like time history or response spectra). This applies to the Equivalent Static seismic loading procedure as well. Right?

Regardless the ASCE stability coefficient is really a way to check P-Big Delta analysis using the "secondary shears" method. So, it's using a hand-calc method to check to see if P-Delta could be an issue with the structure. That's why you are allowed to ignore it. Though I will point out that material codes (AISC, and ACI) do NOT allow you to ignore P-Delta.

2. For a static analysis, any code specifies that non-linear (static pushover) analysis shall be carried out?
The engineer informed that he also doesn't carry out any pushover analysis.

The only codes that I know of that directly address Push Over analysis is the ASCE 41 "Seismic Evaluation and Retrofit of Existing Structures". This is normally reserved for the retrofit of older buildings that do NOT meet current codes. Where the engineer is trying to do a more advanced "performance based" analysis of the structure to demonstrate that it is still safe to occupy the structure. It certainly can be used (in rare cases) on new building design. But, it is never REQUIRED for new building design. At least not to my knowledge.

 

[Greenalleycat]

Good clarifications, Josh

Our codes are confusing in that the loading codes specify some requirements, and then the material standards add or modify requirements to the whims of the authors (I assume)

P-Delta as an explicit term is only required under the seismic loading code, which I infer to be because they're using it as a broad term to make sure linear and non-linear geometric and material behaviours are being captured
The steel design code requires GNSA / 2nd order analysis for most structures...which I agree is just P-Delta under a different name
Alternatively, as you've mentioned, you can run a linear elastic analysis then factor the loads up by amplification factors, but this is usually much slower and more conservative than code requires

Our codes are the same as yours that the only time Pushovers are specified is for seismic assessmnent, which they term SLAMA (Simplified Lateral Assessment Methodology)

 

[KootK]

It is vitally important to recognize that:

1) For many structures, P-Big-Delta issues are critical even in the absence of any applied lateral load at all. Lateral loads only make matters worse, depending on the load casing.

2) Lateral systems usually stabilize much more gravity load than that applied directly to the lateral systems themselves. Note the significance of the [8P] in the sketch shown below. It should really be [10P] too.

As an experienced engineer, I sometimes allow myself to not consider P-Big-Delta when I am confident that my lateral systems -- including the diaphragms -- are stiff enough render P-Big-Delta insignificant.

I almost always consider P-Big-Delta explicitly for the design of:

1) Moment frames and;

2) Concentrically braced frames tall enough to exhibit meaningful flexural behavior over the height of the structure.

Put another way, I mostly only disregard P-Big-Delta when I'm dealing with stiff diaphragms stabilized by squat, more or less concentric braced frames. Helpfully, this encompasses a lot of buildings. When in doubt, calc it out. And when you're an EIT, make a point of always being in doubt.

 

[RobertHale]

I fully agree with JoshPlumSE, and I would add that some of the US codes have material non-linearities "baked in." Things like the adjustments to Igross in ACI, and the tau factor in AISC direct design. @GreenAlleyCat, I can think of one big scenario for a gravity pushover analysis or "push-down" analysis in this case. The more sophisticated analysis methods (in this case non-linear static analysis) for progressive collapse use the same principle as a pushover analysis. KootK's point about wide squat structures with larger spacing between lateral systems is also important in my mind. In school, distinctly remember the Prof pointing out that fact because it is so counter-intuitive.

 

[DaveAtkins]

For steel structures, those of us old enough to remember the "green" steel manual (Ninth Edition, ASD) will remember that P-big delta analysis and P-little delta analysis were never required. BUT-then when you designed members (especially columns with axial load plus moment), you had to use all sorts of factors. You had to decide what "K" is, you had to reduce the allowable axial stress based on how much moment is combined with the axial load, etc. Now, if you do a P-big delta and P-little delta analysis (using software like RISA-3D), you assume K = 1.0 and the design is fairly simple.

Both methods work, obviously, but once I got used to the new way to do it, I found it to be more realistic. You are directly considering misalignment of members, the secondary horizontal shear introduced when the structure deflects, etc.

DaveAtkins