Two Fibers, Five Ways

I occasionally go down rabbit holes of numerical integration. These trips led me to Gauss-Radau integration, all the element integration options available in OpenSees, and, recently, Chebyshev integration. The latest rabbit hole, described in this post, deals with different ways to integrate section moment-curvature response using only two fibers. Consider a rectangular cross-section with EPP … Continue reading Two Fibers, Five Ways

Verifying Will Never Be Easy

A previous post compared the natural periods computed by OpenSees for a relatively simple one-story, one-bay, elastic frame to published ETABS results. Many easy to make modeling choices (mass distribution, rigid joint offsets, relative stiffness, etc.) led to "incorrect" periods. The "correct" modeling choices gave periods from OpenSees that were very close to ETABS--close enough … Continue reading Verifying Will Never Be Easy

The Stiffness Matrix Isn’t Everything

After several deliveries of graduate level courses in linear and nonlinear structural analysis, I have started to think that we over-emphasize the stiffness matrix in linear structural analysis. And this emphasis can lead to conceptual difficulties in nonlinear structural analysis. The steps to a linear analysis are presented as: Form the stiffness matrixForm the load … Continue reading The Stiffness Matrix Isn’t Everything

More Solutions Than Problems

OpenSees has its share of problems: documentation is a work in progress; solid finite element analysis capabilities are not fully developed; benchmarking and verification don't happen too often; and volunteerism drives maintenance and support. Yeah, I know, what support? OpenSees has also generated--or, better yet, been used to generate--more than its fair share of solutions, … Continue reading More Solutions Than Problems

Two Paths You Can Go By

I am confident we can use OpenSees to solve every truss, beam, and frame problem from any statics or structural analysis textbook as well as every single degree-of-freedom and rigid shear frame problem from a structural dynamics textbook. We can also solve any reasonable problem from a finite element textbook. My confidence starts to wane … Continue reading Two Paths You Can Go By