Elastic Shear Beams in OpenSees

Shear deformations in slender beams are generally not significant compared to flexural deformations. But shear deformation are important in deep beams and short walls, and flexure-shear interaction may be important in the material nonlinear range of response, regardless of aspect ratio. Enough of the perfunctory, non-committal language--you can find that in the latest issue of … Continue reading Elastic Shear Beams in OpenSees

A Simple Solution to a Complicated Equivalent

A previous post posited on the equivalence of discrete flexural springs (moment-rotation) with integration of continuous moment-curvature response. To find the answer, we can use the principle of virtual forces (PVF) and numerical integration of the internal virtual work: $latex {\displaystyle \int_0^L \kappa(x)m(x)\: dx \approx \sum_{i=1}^N \kappa(x_i) m(x_i) w_i}$ where $latex m(x)$ is the "virtual" … Continue reading A Simple Solution to a Complicated Equivalent

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

Get the Accel Out

In OpenSees, a UniformExcitation pattern is functionally equivalent to a regular load pattern, fitting into the framework of a time-varying scalar load factor and constant reference load vector. The scalar load factor is the input ground acceleration, $\latex \ddot{u}_g(t)$, while the reference load vector is $latex {\bf P}_{ref}=-{\bf m}{\boldsymbol \iota}$ where $latex {\bf m}$ is … Continue reading Get the Accel Out

How to Find a Memory Leak in OpenSees

Memory leaks plague virtually all software written in C++ or any other language that requires programmers to manage memory. OpenSees is no exception. With code written by many people with varying knowledge of C++ and very little overall QA/QC, it's fair to say OpenSees has more than its fair share of memory leaks. It's a … Continue reading How to Find a Memory Leak in OpenSees

A Solution, Just Not The Solution

Force-based elements satisfy equilibrium in strong form, even with member loads. However, this does not mean force-based elements always get the exact solution. Consider a simple prismatic, linear-elastic beam with a point load at mid-span. Using a single force-based element with a single point load applied to the element using the eleLoad command. E = … Continue reading A Solution, Just Not The Solution

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