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 →

There’s Three, Actually

The displacement-based and force-based formulations garner a lot of comparisons for simulating nonlinear frame response. My Google Scholar alerts tell me so. And I even wrote a post comparing the two formulations. Doc Ock from Spider-Man: Into the Spider-Verse There is a third formulation--the mixed formulation. Alemdar and White compared three frame element formulations (displacement-based, … Continue reading There’s Three, Actually →

Discretized Members Only

I wrote a DiscretizeMember procedure in Tcl many years ago--I don't know exactly when, definitely after the 1980s and definitely before moving to Eastchester. "Members Only." by The Semi-Frozen Trombone is licensed under CC BY 2.0 After carrying the function around for years, and probably spawning more variations than uniaxial Concrete models, the procedure went … Continue reading Discretized Members Only →

Global Distributed Loads

Distributed loads on frame elements in OpenSees are defined with respect to the local element axes as opposed to global axes. This choice made the implementation easy, but it can give OpenSees users more shadow work, like bagging your own groceries or pumping your own gas. When global distributed loads act on inclined elements, e.g., … Continue reading Global Distributed Loads →

A Vector in the x-z Plane

Three-dimensional frame elements require user input for the local element axes. Although the local $latex x$ axis points from node I to node J, there is no automatic way to define the local $latex y$ and $latex z$ axes, i.e., how the section axes line up with the element. In two-dimensions, this is not an … Continue reading A Vector in the x-z Plane →

Integration Points with Negative Weight

A colleague in Eastchester once told me that faculty have three, maybe four, good ideas over their career. In other words, a faculty member could have over a hundred papers, but there's only three or four underlying concepts. Perhaps it was "two, maybe three", but you get the point. Playing with integration points and weights, … Continue reading Integration Points with Negative Weight →

Meshing for Column Loads

For material nonlinear analysis of frame models, you can improve the computed response by using more displacement-based elements or more integration points in a force-based element. The material nonlinearity occurs inside the basic system, also known as the natural system or the kernel. To capture geometric nonlinearity due to large displacements, you have to go … Continue reading Meshing for Column Loads →

Better Late than Never

Frame finite elements abound in OpenSees, but something very useful has always been missing--a linear-elastic beam element with moment releases. Sure, you can define two nodes at the release location and use the equalDOF command; however, that can be error prone and you're at the mercy of the constraint handler. On the positive side, this … Continue reading Better Late than Never →

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 →

Behind the Elastic Interior

If VH1 expanded its list of the top one hit wonders of the 2000s to include journal articles in structural engineering, Scott and Fenves (2006) would be right up there with James Blunt and Gnarls Barkley. Actually, Google Scholar puts the article up there with some pretty nice company. Like all journal articles, there's something … Continue reading Behind the Elastic Interior →