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. True False It 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 … Continue reading Repeated Section Modes →

Concrete02 with Control of the Initial Stiffness

Although they have the same compressive envelope, Concrete02 offers more features than Concrete01--tension strength, tension stiffening, and compressive unloading/reloading loops. However, one thing Concrete02 (and Concrete01) lacks is control over the initial stiffness, which is fixed at $latex E_c=2f'_c/\varepsilon_{c0}$. To overcome this limitation with Concrete02, Nasser Marafi created Concrete02IS (Concrete02 with control of the Initial … Continue reading Concrete02 with Control of the Initial Stiffness →

Direct Moment-Curvature

That the force-based frame element and fiber sections are in an open relationship should come as no surprise. The displacement-based and mixed frame elements can use fiber sections and all three element formulations can use stress resultant sections. While this post used a coupled stress resultant plasticity model, you can also use the section aggregator … Continue reading Direct Moment-Curvature →

Making Sense Out of Concrete02

Those three extra parameters for Concrete02 are usually enough to make me stick with Concrete01. I struggle to come up with good values for the parameters $latex \lambda$, $latex f_t$, and $latex E_{ts}$ shown in the following image from the OpenSees Concrete02 wiki page. Image developed by Dr. Silvia Mazzoni The four compressive backbone parameters … Continue reading Making Sense Out of Concrete02 →

You Gotta Keep ’em Aggregated

The SectionAggregator was one of my few useful OpenSees ideas. This class gives a flexible way to combine, or aggregate, modes of force-deformation in a single section model. The idea for SectionAggregator came from the Decorator software design pattern, the same pattern from which so many UniaxialMaterial wrappers were spawned (here and here). In fact, … Continue reading You Gotta Keep ’em Aggregated →

Elastoplastic Calibration

You can do a lot with UniaxialMaterials in OpenSees--springs, fibers, trusses, section aggregators, etc. Although over 130 UniaxialMaterials are available, it's likely that only about a dozen see regular use. So, with all due respect to Concrete23, my favorite regular is HardeningMaterial. It's straight out of Simo and Hughes and was the example material for … Continue reading Elastoplastic Calibration →

Stress Resultant Verification

Verifying material nonlinear frame element formulations is pretty difficult. There are only a handful of analytical solutions that do not rely on bilinear uniaxial constitutive response. You're much better off verifying geometric nonlinearity. However, an example based on a relatively straightforward biaxial stress resultant plasticity model has intrigued me over the years. The example, described … Continue reading Stress Resultant Verification →