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 →

Pseudo-Time Is Not the Load Factor

In a nonlinear static analysis, the time series associated with lateral loads is typically linear: ops.timeSeries('Linear',1) In this case, the load factor, $latex \lambda$, associated with the time series is equal to the pseudo-time in the domain, i.e., $latex \lambda(t)=t$. Then, when you use the '-time' option in the node and element recorders, you get … Continue reading Pseudo-Time Is Not the Load Factor →

Load Patterns and Time Series

In nonlinear structural analysis, loads add together, just not the load effects. So, the total mechanical load applied to a structural model can be expressed as the sum of time-varying load vectors. $latex {\bf P}(t)={\displaystyle \sum_{i=1}^N} \lambda_i(t){\bf P}_{ref,i}$ Each load vector is the product of a time-varying scalar function, $latex \lambda(t)$, and a non-time-varying reference … Continue reading Load Patterns and Time Series →