P-M Interaction by the Book

Find any indeterminate beam, frame, or truss problem from a structural analysis textbook, and you can make OpenSees solve it. But sometimes, replicating the basics is not so easy. Take, for instance, an axial-moment (P-M) interaction diagram of reinforced concrete (RC) sections. The typical approach advocated with OpenSees is to use repeated moment-curvature analyses over … Continue reading P-M Interaction by the Book

Plane Sections Do Remain Plane

Here's another conversation I've had with a concerned user (CU) of OpenSees, not necessarily the same CU that was worried about OpenSees crashing due to non-convergence: CU: "Do plane sections remain plane in the material nonlinear range of response?"PD: "Yes."CU: "What about with force-based frame elements?"PD: "Yes."CU: "How is that possible?"PD: "Because there's no other … Continue reading Plane Sections Do Remain Plane

Hysteretic Damage Parameters

Because the C++ implementation is a straight translation of his FEDEAS subroutine written in FORTRAN, Prof. Filippou receives numerous inquires on the formulation of HystereticMaterial in OpenSees. According to the comments in the FORTRAN files, the bilinear backbone implementation (Hyster1.f) was finalized on November 24, 1994 followed by a trilinear backbone implementation (Hyster2.f) finalized on … Continue reading Hysteretic Damage Parameters

How to Record Section Curvature

I've seen recently a few people compute curvature for an OpenSees fiber section by dividing the difference between top and bottom uniaxial fiber strains by the distance between the fibers. While there's nothing technically wrong with this approach, it's a lot of work and it's error prone. In addition, this approach implies that using a … Continue reading How to Record Section Curvature

Something, Something, Something Fiber

Two recent inquires asked why model response using frame elements with elastic fiber sections, i.e., sections with fibers whose stress-strain response is $latex \sigma=E\varepsilon$, differs from the response with elastic elements, i.e., defined by E, A, Iz, and Iy either with elasticBeamColumn elements or nonlinear elements with elastic sections. I've touched on this subject a … Continue reading Something, Something, Something Fiber

Two Fibers Explain So Much

In a previous post, I asked how well we can capture the moment-curvature response of a rectangular section with EPP material using different integration methods with two fibers. For flexural response, two is the minimum number of fibers necessary to satisfy section equilibrium--one fiber for tension, the other fiber for compression. The previous post showed … Continue reading Two Fibers Explain So Much

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

Repeated Section Modes

If you use a section with linear-elastic response in the displacement-based, force-based, and mixed beam-column elements in OpenSees, you will get the same response from all three elements. TrueFalseIt depends The answer is it depends on the type of "section with elastic response" you use. Also, I wouldn't include "It depends" as a possible answer … Continue reading Repeated Section Modes