Interpolation of Ground Acceleration

There was a question on GitHub a few months ago about whether or not OpenSees uses linear interpolation when the analysis time step is smaller than the time step (digitization) of an input ground acceleration. This is a good question as I've used other software that does not interpolate and instead uses the acceleration of … Continue reading Interpolation of Ground Acceleration →

The Little IDA

In Fundamentals of Structural Mechanics, Hjelmstad solves a "little" one-dimensional Boundary Value Problem (BVP) for linear-elasticity before moving on to the three-dimensional BVP, which is full of mathematical difficulties. Hjelmstad's reasoning is sound. "Some of these difficulties are of great importance, while others are simply a nuisance. Reducing the issue to its simplest case helps … Continue reading The Little IDA →

Multiple-Support Excitation

Structural systems typically have different ground accelerations at supports separated by long distances. These systems can be a single structure such as a long span bridge or multiple structures in a region. While most OpenSees analyses use uniform excitation with effective earthquake forces applied to the dynamic DOFs of the model, the framework also accommodates … Continue reading Multiple-Support Excitation →

That’s a Large Mass

After cutting through all the spam, you'll find some good posts on the OpenSees message board. In one such post, Ahmet Alper Parker asked about the large mass method (LMM) and if it can be implemented in OpenSees. I was not familiar with the LMM, so Ahmet pointed me to this paper. The basic idea … Continue reading That’s a Large Mass →

Absolutely, It’s Relative

One of the most frequently asked OpenSees questions is whether node recorders record absolute or relative displacement (relative to the ground) when a model is subjected to a uniform excitation. There's several approaches to find the answer to this question. One solution is to apply a simple uniform excitation--like a constant ground acceleration--to an SDF … Continue reading Absolutely, It’s Relative →

The Rayleigh Quotient

Eigenvalue analysis wasn't giving me what I wanted the other day. So, to make a long story short, I decided to try Rayleigh's method. I won't go through all the details of Rayleigh's method, but the basic idea is you can obtain a very good approximation of the fundamental frequency of a structural model by … Continue reading The Rayleigh Quotient →

Reaction and Unbalance

A confluence of recent inquiries led me to take a look at what the nodeReaction and nodeUnbalance commands return in an OpenSees dynamic analysis. While I have a pretty good handle on nodeReaction, going in to this post, I was unsure about nodeUnbalance. We can learn a lot from a couple springs, so I created … Continue reading Reaction and Unbalance →

Mass and Weight

Many structural analysis software programs will automatically define mass based on the input gravity loads. OpenSees is not one of those programs. You have to define mass and weight separately. Fortunately, using variables for units makes the mass and weight definitions easy. Plus, if using customary units, you won't have to waste time Googling the … Continue reading Mass and Weight →

Last Committed Stiffness

With the rayleigh command, OpenSees allows you to input three stiffness proportional damping factors: 1) the current tangent stiffness, 2) the initial stiffness, and 3) the last committed stiffness. Each option has drawbacks. The current tangent stiffness is problematic because the tangent stiffness can change significantly at each iteration of the equilibrium solution algorithm. The … Continue reading Last Committed Stiffness →

Rayleigh Damping Coefficients

One of the best examples of "offline" calculations you can easily avoid in OpenSees is Rayleigh damping coefficients. I've seen people hard code the mass and stiffness proportional damping coefficients in their OpenSees scripts, after computing said coefficients in another software, e.g., MATLAB, or on paper. Inevitably, it becomes difficult to keep your OpenSees model … Continue reading Rayleigh Damping Coefficients →