Non-linear geometric analysis (simplified calculations) 1

[Enhineyero]

Hi guys two part question:
1. does anyone know a good resource for simplified calculations for non-linear geometric analysis?

2. Is the second-order effect (P-big delta) moment for a cantilever column with a vertical point load at the tip and is subject to lateral load equal to vertical load times lateral displacement?

 

[Settingsun]

1. How simplified? What are you trying to do? Code moment magnification procedures are simplified procedures, and you may be able to estimate deflection from them if you need that as well.

2. Yes.

 

[Mohanlal0488]

If you want a simplification you can derive equations for specific scenarios. I would look at Krenk's book on non-linear analysis, one of the best written books on the topic in my opinion.

In essence the second order effects are meant to introduce loads due to geometric nonlinearity, however it is a simplification. For the simple case of a column (as you discussed) you could attain the same results as GNL analysis. however if you are dealing with a full on structure The results will deviate as your GNL analysis takes into account far more than your P-delta effects. You can essentially use GNL analysis to evaluate buckling also.

Simple example would be a horizontally curved beam, you can induce your P-delta effects however you would need to perform a few hand calculations to take into account additional moments due to curvature (the AISC has a book that covers this), however with GNL analysis the additional loading will automatically be taken into account.

 

[JoshPlumSE]

There is the B1, B2 method that AISC has had in their code (or commentary) for a long time.

I also like the ASCE-7 "stability coefficient" method, though this is really just a P-Big Delta method.

 

[Enhineyero]

Thanks guys. I will keep this in mind and will browse resources from the AISC (and ASCE mentioned by Josh).

I usually stumble on this when I cant brace the structure or have a beam/column situation. Preference is to do a simple hand computation rather than click a button on a black box.

 

[Settingsun]

It's often the case that computer analysis of the simplified model is the most efficient. Add value by figuring out how to simplify the analysis then let the computer do what it was made to do. You might even use a less-simplified model than would be necessary for hand calculations.

 

[KootK]

If it's a hand calculation that you want, I'd consider an iterative approach as shown below. It probably looks like a lot based on the sketch but truly is not. And it's simple as dirt to understand and execute. In essence, it's the AISC direct analysis method done by hand. Do two or three iterations. If it closes quickly, you'll have your answer. If it doesn't... you'll also have an answer.