Force-Based Element Moment Release

The common approach to adding a moment release at the end of a force-based frame element is to define an extra node then use the equalDOF command to constrain all but the released rotational DOFs. Although this approach is cumbersome, it is fine as long as the element lies within a global plane (X-Y, Y-Z, … Continue reading Force-Based Element Moment Release

Shear Verse, Same as the First

In the same vein as a previous post, this post will show a basic comparison of material nonlinear displacement-based and force-based formulations with axial-flexure-shear interaction in frame elements. The timoshenkoBeamColumn element interpolates constant shear deformation along its length, along with constant axial deformation and linear curvature. Two-point Gauss-Legendre integration over the element is sufficient to … Continue reading Shear Verse, Same as the First

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

Non-Prismatic Frame Elements

Long before the BeamIntegration abstraction, there was only Gauss-Lobatto integration for force-based elements, with a single section model copied to each integration point. This made it impossible to use a single element to simulate the response of an RC member with different reinforcing details along its length, or any member that was inherently non-prismatic. While … Continue reading Non-Prismatic Frame Elements

Failed to Get Compatible …

If you've used the force-based beam-column element in OpenSees, you've likely come across this warning involving element forces and deformations: I've encountered this warning many times and so have others. In fact, I lifted the above image from a recent post on the OpenSees Facebook group. I tried to come up with a MWE to … Continue reading Failed to Get Compatible …

Force-Based Beam-Column Integration Options

I like numerical integration because it allows you to do a lot of interesting things with force-based frame elements--so much more than simulating the response of reinforced concrete moment frames. Numerous numerical integration options are available in OpenSees, so in 2011 I wrote and uploaded to the OpenSees wiki a PDF summarizing those options. According … Continue reading Force-Based Beam-Column Integration Options

A Tale of Two Element Formulations

The question of whether to use the force-based or displacement-based formulation for material nonlinear frame analysis is one that comes up a lot. The answer depends on a few factors, mostly the material and the element length. To get a sense of the basic issues, I will compare the two element formulations with a numerical … Continue reading A Tale of Two Element Formulations