Dynamic Analysis of Asymmetric Structures

[cancmm]

I am preparing to analyze an existing pile supported structure for earthquake loads. The structure is subject to ship impact loads, so there is an asymmetric pile layout with batter piles angled in one direction. It's been a while since I took my Structural Dynamics course, but I was wondering if anyone could refresh my memory on how the natural frequency is determined for asymmetric structures? In simpler terms, if you have a spring with significantly greater stiffness in one direction than the other, how is this introduced into the stiffness matrix, and subsequently how is the natural frequency affected?

On a side note, I tried running a simple trial with SAP2000 to try and see the effects, but the program won't even run with the batter pile in place. I'm guessing there's a bug in the software.

 

[Denial]

Your problem comes about not because the structure is asymmetric, but because it is nonlinear.[ ] Unless you can somehow simplify your way around it you will probably need to use nonlinear transient dynamic analysis.

 

[JoshPlumSE]

The concept of finding natural periods for asymmetric structures is the same as symmetric structures. You solve for the eigen values of the system. You'll just end up with multiple natural periods / frequencies for the structure. And, the two directions may differ significantly. But, how much difference can you expect?

When I teach our training course (RISA-3D) on dynamics, I am sometimes surprised by how "black box" some engineers think natural period calculations are and how un-prepared they are to do some simple hand calcs on their own to back check program results.

Therefore, I usually start out with a single degree of freedom structure and show how Period = 2*pi*sqrt(Mass/stiffness).

If you look at that SDOF structure and apply it to your case, then you will see that the natural period of your structure in the two different directions should be related to each other (roughly) by the square root of the difference in static stiffnesses for the two directions. So, if one direction is 50% stiffer, then it's natural period will be approximately 1/sqrt(1.5) times the period for the other direction, or 82% of the natural period for the other direction.

Does that help at all? Perhaps that was already obvious to you. But, I find these simple SDOF concepts can be enlightening for these more complex cases.