P-Delta Analysis 1

[dimmm]

Greeting everyone.
This is the first time I use this forum.
May i ask how to do P-Delta analysis?
Thanks for your action.

 

[ash060]

Usually you would use a computer program. As anything but the most simple structures would be too time consuming and rigorous to do by hand.

 

[SteelPE]

Yes, people mostly use computer programs to analyze these types of problems for complex structures. However, you need to make sure your computer program is doing the calculation correctly. In the commentary of appendix 7 of the AISC they give two simple structures that you can easily hand calculate to check your program.

Otherwise I believe you are stuck using the B1,B2 factors to get around this problem.

 

[dimmm]

Thanks for your reply.
it is because i am required to do both software and manual analysis.
May I show you a picture here?
its a cantilever circular steel column, fixed - free.
I show you the picture to give you a better understanding.


thanks

 

[Teguci]

Don't bother with a program, just do it by hand.

1. Calculate your lateral deflection due to your side load.
2. Add a P delta moment to the model using your lateral deflection "+ a little" per engineering judgement. Also need to consider foundation overturning.
3. Recalculate deflections with both the P delta and lateral moments applied and check to see if you are close to your "+ a little" estimate.
4. Redo again if you want a closer number.

 

[dimmm]

Thanks for your advice.
I have never done this problem before. Could you recommend me that something I can refer? Or an example?
To be honest, I do not know how to start it.

 

[ron9876]

Check with your mentor if possible.

 

[dimmm]

Alright. Thank you guys.

 

[JoshPlumSE]

Rather than running multiple iterations of hand calculations (as Teguci suggested), I'd recommend using the Theta method described in seismic chapter of ASCE 7 (12.8.7). It just allows you to achieve the same answer in one iteration...

Theta = axial force * Delta / (Shear * story height)

Where Delta is the initial deflection due to the applied shear.

This is a ratio of P-Delta shears to the original story shears. The additional deflections due to the 2nd, 3rd, 4th iterations of deflection would then be:

Theta*Delta + Theta^2 * Detla + Theta^3 * Delta +....

The infinite sum of this series becomes:

Delta total = Delta /(1-theta)

In the end, this is really just an approximate hand calculation. Doing the P-Delta analysis with a computer program will normally provide a better result. Even so, it is never a bad idea to give computer results a sanity check using these types of approximate hand calculations.

 

[dimmm]

Thank you JoshPlum, I try to go through these.