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Pseudo-Time Is Not the Load Factor

Original Post - 07 Nov 2022 - Michael H. Scott

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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, \(\lambda\), associated with the time series is equal to the pseudo-time in the domain, i.e., \(\lambda(t)=t\). Then, when you use the -time option in the node and element recorders, you get the load factor “for free”, i.e., without any additional effort.

However, the load factor is not always equal to the pseudo-time in a static analysis. For example, a little-used option lets you supply a factor to the linear time series:

ops.timeSeries('Linear',1,'-factor',0.8)

In this case, the load factor is \(\lambda(t)=0.8t\). In other words, for every pseudo-time step of 1.0, the load factor will increase by 0.8 (or whatever factor you give).

There are other time series, e.g., Trig, Pulse, and Path, where the pseudo-time and load factor are not equal. But using a factor with the Linear time series was the most notable counter-example that came to mind.