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Wind in Warped Sails

Original Post - 28 Mar 2021 - Michael H. Scott

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The Island of Unfinished OpenSees Business grows every year. I own a few acres on that island and I’m sure you do too. Occasionally, items make their way off the island and get shipped to the mainland, i.e., the OpenSees GitHub repository.

Take, for example, the warping frame elements developed at the University of Sydney in 2011. One element is small strain, linear-elastic and the other element accounts for large strain and material nonlinearity. Both elements use 7 DOFs/node and 9 basic deformations. The nonlinear element is able to model inelastic lateral-torsional buckling (LTB).

Every few years, these elements pop up, i.e., someone asks about them specifically or someone asks generally about modeling LTB in OpenSees. A few years ago, a couple colleagues in Eastchester were able to compile the warping elements using the 2011 snap shot zip file provided by the University of Sydney researchers.

Ultimately, my colleagues graduated an M.S. student who used the nonlinear element to model the seismic response of steel slit panel frames. It was good work, but we never got the code into “official” OpenSees. The elements remained on the island.

After a recent LTB question, I decided to give the warping elements another look. I created a new branch then incorporated the elastic warping element and corotational warping 3D transformation. Minimal cleanup was required for post-2011 changes in OpenSees.

Here is an example from Figure 13 of the report. The W10x100 beam is in symmetric bending about its strong axis with a small perturbation moment about its weak axis. The beam is discretized into four elastic warping elements.

The applied moment vs. midspan out-of-plane displacement relationship shown below matches the results from the report pretty well.

I added the code to the OpenSees repository via PR #558. The elastic warping element works. The nonlinear element compiles.

I will tackle the nonlinear displacement-based element next and get it from compiling to working. It’s doable, but it’s going to take some work to get it up to current OpenSees snuff because the element has the added cargo of a 3D warping fiber section and a few complications therein. Let’s just hope the code don’t get stuck at sea, or in a canal.