Nonlinear Plane Frame Analysis 2

[Charlie Delta Whiskey]

I am attempting to program a second order (geometrically nonlinear) plane frame analysis based on the Direct Analysis Method in AISC (reduced stiffness, notional loads, etc.) to use for designing Moment Frames. I already programmed a first order plane frame analysis program in C++ that works perfectly. My question is when doing a second order analysis, how should I apply the loads. I could apply the loads all at once and do Newton-Raphson iterations until I converge on a solution for the displacements, OR I could apply the gravity loads all at once and the lateral loads incrementally like a pushover analysis does, OR I could apply all of the loads incrementally. Computational time is only a little bit of an issue because the moment frames we work with are pretty small BUT I do run 14 or so load combinations and I check several different designs (meaning different W-Shapes). That means if I am checking 20 designs that would be 20 x 14 = 280 analyses and that usually takes my program about 25 seconds or so. Any input would be great because I really am just sort of flying by the seat of my pants on this project and I couldn't find any information that I thought was relevant to my specific project.

 

[Charlie Delta Whiskey]

I will add a second plug for that book, it has really helped me in the process of writing this program, and I have used MASTAN2 to verify my frame results. There was a problem with my tangent stiffness matrix which I fixed and my analysis now converges, whether I increment the loads or not. In the problems I have been doing the analysis converges with ~4-5 iterations when I apply the load all at once and 1-2 iterations when I increment the load 1/10 at a time, so it seems like in my particular case it would be more efficient to just apply the load all at once. This is obviously very dependent on the problems you are doing. I'll probably allow the user to choose the load increment, the maximum number of iterations, and the convergence tolerance. That way if the user sees a "Does not converge" message he can play with the aforementioned parameters.

 

[Charlie Delta Whiskey]

The general principle that should be applied in any non-linear, non-elastic analysis is that the loads should be applied in the same sequence as they will be applied to the actual structure, so in this case apply the dead loads then increment transverse loads.

I think this was the answer I was looking for in my OP. Thanks for the wisdom.