Damping Is a Sensitive Subject

Dynamic response sensitivity analysis by the direct differentiation method (DDM) works pretty well in OpenSees, minus a couple limitations. First, not all element and material models implement the methods necessary to compute response sensitivity with respect to model parameters. And second, even fewer element and material models implement the methods necessary to compute the sensitivity … Continue reading Damping Is a Sensitive Subject →

Minimal Damper Example

One of the axioms of earthquake engineering simulation is that any shear frame model can be analyzed using simple springs and masses. Even a 40-story shear frame can be economically modeled with 40 zero length elements in series. But what happens when you add dampers to the shear frame? Do you have to start modeling … Continue reading Minimal Damper Example →

A Simple Base-Isolated Model

Although there are several base isolator elements available in OpenSees, I don't know much about base isolation. And when I don't know much about a topic, I look for a simple example to play with--usually something elastic that can be expanded later and that I can return to when I run into issues with nonlinear … Continue reading A Simple Base-Isolated Model →

Sequential Ground Motions

How to impose sequential ground motions while keeping the damaged state of the model from the end of one ground motion to start of the next is a question asked with moderate frequency (including today, which encouraged me to take this post from draft to reality). Below is a minimal working example where two ground … Continue reading Sequential Ground Motions →

Static Analysis with Uniform Excitation

The UniformExcitation defines reference nodal loads in proportion to the mass (nodal plus element contributions), multiplied by negative acceleration, which is specified in a time series. There's nothing inherent in its implementation that ties the UniformExcitation to only dynamic analysis and earthquake excitations. So, if I had known sooner that the UniformExcitation load pattern works … Continue reading Static Analysis with Uniform Excitation →

Earthquake Engineering Experts Hate Me for This One Weird Trick

I was a structural engineer who dabbled in earthquake engineering simulation. Then one day I stumbled upon a weird trick to get ground displacement history from a ground acceleration record. The trick was simple. It worked right away. I couldn't believe it. The trick did not require additional libraries or writing a loop. Just a … Continue reading Earthquake Engineering Experts Hate Me for This One Weird Trick →

Effective Earthquake Forces

There's nothing special about the UniformExcitation load pattern in OpenSees. The pattern is a convenience for defining effective earthquake forces due to uniform ground acceleration as plain 'ol mechanical loads on your model. Consider the equation of motion for uniform ground acceleration, with linear inertia and damping forces, and influence vector $latex {\boldsymbol\iota}$ for the … Continue reading Effective Earthquake Forces →

Spreader Beam Analysis

Problems involving beams are few and far between in Hibbeler 14th edition Engineering Mechanics: Dynamics. The problems mostly deal with springs, friction, pulleys, and things that rotate. So, Problem 15-3 was a welcome sight. A six foot long beam weighing 5000 lb is lifted from rest to a velocity of 8 ft/sec in 1.5 sec … Continue reading Spreader Beam Analysis →

How to Apply Ground Motions in Multiple Directions

A common question is can I apply ground motions in more than one direction to a model in OpenSees? The answer is Yes. Let's say you have files for three ground motion recordings: gm000.txt, gm090.txt, and gmUP.txt. Define a time series for each ground motion, then associate each time series with a uniform excitation load … Continue reading How to Apply Ground Motions in Multiple Directions →