Two element formulations in OpenSees--forceBeamColumnCBDI and mixedBeamColumn--are capable of handling geometric nonlinearity within the basic system, i.e., P-little-delta effects. The CBDI formulation, described in Neuenhofer and Filippou (1998), approximates the transverse deflection using Lagrange polynomials fit through the curvature at each integration point. Due to the added computational expense and coding details, the forceBeamColumnCBDI element … Continue reading One and Only One
Category: Element Formulations
Flipping Rotation Axes
Zero length rotational springs are a popular approach to model concentrated plasticity in frame members. Although distributed plasticity formulations are not perfect either, the zero length concentrated plasticity approach has a number of issues: implicit plastic hinge length (at best, it's a unitless 1) and having to define equalDOF constraints. There's also the outcomes of … Continue reading Flipping Rotation Axes
You Never Forget
My first journal article was not without some minor drama. Another group of researchers was also in pursuit of the direct differentiation method (DDM) formulation for force-based frame elements. Mutually aware of the parallel efforts, one of those researchers went so far as to call me on a public landline in Davis Hall with a … Continue reading You Never Forget
Converging to Something
Is it better to have converged and lost than never to have converged at all? The displacement-based and force-based frame elements are both distributed plasticity formulations--just one is way better at simulating the spread of plasticity than the other. Despite this fairly well known fact, I still see people use four, five, six, or more … Continue reading Converging to Something
The Three Node Quad
Depending on your experience with finite elements, this post will either be totally obvious or it will blow your mind. The standard bilinear, isoparametric four node quad element degenerates to a three node constant strain triangle when you assign two consecutive element nodes to the same location. This fun fact is due to the math, … Continue reading The Three Node Quad
Transformation Cross-Training
Athletes often cross-train in secondary activities in order to improve performance in their primary sport. For example, football players may practice ballet in order to improve their flexibility and endurance. Using OpenSees, you practically have to be a mathlete to understand the geometric transformation in three dimensions. But instead of fumbling your way through space … Continue reading Transformation Cross-Training
A Rigid Bar Walks Into a Bar
OpenSees has two rigidLink commands that enforce constraints between a primary node (pNode) and a secondary node (sNode). ops.rigidLink('-beam',pNode,sNode) ops.rigidLink('-bar',pNode,sNode) The beam option works well, enforcing linear kinematic constraints as if the two nodes were connected by a beam of infinite axial and flexural stiffness. The bar option should give constraints assuming only infinite axial … Continue reading A Rigid Bar Walks Into a Bar
How to Bend Beams in 3D
Most structural frame models are analyzed in two dimensions (2D), for a variety of legitimate reasons. But sometimes, you have to go to three dimensions (3D). And the most confusing thing about making that jump in OpenSees is the geometric transformation and its "vector in the x-z plane". Instead of going into the details of … Continue reading How to Bend Beams in 3D
Shutting Off the Containment Unit
If you've used OpenSees--even if you're a geotech--you've used the force-based element. When Remo implemented the force-based element, it was the only material nonlinear frame element available in OpenSees (G3 at the time); thus, the original name nonlinearBeamColumn. Only after a standard displacement-based frame element (dispBeamColumn) was added did we change the name from nonlinearBeamColumn … Continue reading Shutting Off the Containment Unit
Eccentrically Loaded Bolt Groups
Tables 7-6 through 7-13 of the AISC Steel Manual contain values for C, the effective number of bolts that resist shear in eccentrically loaded bolt groups. For example, in a bolt group with three vertical rows of 4 bolts spaced s=3 inch with srow=3 inch row spacing and a load at $latex \theta$=30 degrees from … Continue reading Eccentrically Loaded Bolt Groups
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