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

# Category: Element Formulations

# 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

# 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

# Switching Sides

Used for flexible supports and flexible connections, among other things, zero length elements are perhaps the most versatile modeling tools available in OpenSees. One of the confusing things about zero length elements is how to properly define asymmetric response. For example, with a bridge abutment, you want to ensure the zero length element correctly interprets … Continue reading Switching Sides

# A Complicated Equivalent

Whether you use closed-form or numerical integration, the deflection at the free end of a laterally loaded linear-elastic, prismatic column is known to be $latex PL^3/(3EI)$. This result is easily verified in OpenSees with either an elasticBeamColumn element or a material nonlinear element with elastic sections. Now suppose we philosophized a bit then posited the … Continue reading A Complicated Equivalent

# Fuzzy Zero Length Logic

There's a few interpretations floating around regarding the length--real or implied--of zero length elements in OpenSees. So, I made a Twitter poll to assess popular opinion. https://twitter.com/mikusscott/status/1516085441895624705 Despite being an "easy" question, only 50% of respondents chose the correct answer. Like "When was the War of 1812?", the question gives it away--zero length elements have … Continue reading Fuzzy Zero Length Logic

# Inerters Everywhere

Vibration control devices based on relative acceleration, or inerters, are all the rage these days. So it's no surprise that inerter models are making their way into OpenSees. As far as I know, two inerter elements are available: InertiaTruss and Inerter. There has also been a third attempt at inerters, but via a material model. … Continue reading Inerters Everywhere

# 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 …

# 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