# Load Patterns and Time Series

In nonlinear structural analysis, loads add together, just not their effects. So, the total mechanical load applied to a structural model can be expressed as the sum of time-varying load vectors.

${\bf P}(t)={\displaystyle \sum_{i=1}^N} \lambda_i(t){\bf P}_{ref,i}$

Each load vector is the product of a time-varying scalar function, $\lambda(t)$, and a non-time-varying reference load vector, ${\bf P}_{ref}$.

The reference load vector is a pattern object in OpenSees. A Plain load pattern forms ${\bf P}_{ref}$ from nodal loads, member loads, and single point (sp) constraints (if you want to impose a nodal displacement history). A UniformExcitation pattern forms the reference load vector from nodal masses based on the direction of ground acceleration, i.e., ${\bf P}_{ref}=-{\bf m}{\boldsymbol \iota}$. You can also define a MultipleSupport load pattern which imposes ground motions at specified nodes.

The scalar function $\lambda(t)$ is a timeSeries object in OpenSees. Several time series are available including Path, Sine, Linear, and Constant. You can assign gravity loads to a constant time series, or you can ramp the gravity loads up in a linear time series then set the loads to constant.

Ground accelerations, $\lambda(t)=\ddot{u}_g(t)$, for a UniformExcitation are typically defined with a Path time series. Most ground acceleration records are in units of g, so you have to scale the time series by g so that you get length and time units that are consistent with your model.

Note that, like a Reese’s peanut butter cup, there is no wrong way to define each load vector. You can embed the load magnitude in either $\lambda(t)$ or ${\bf P}_{ref}$. To reach a peak base shear of 150 in a pushover analysis, both scenarios A and B below will give the same load history. Scenario A places the load magnitude in $\lambda$ while scenario B puts the load magnitude in ${\bf P}_{ref}$.

I prefer scenario A where the reference lateral load sums to 1.0 so that the load factor, $\lambda$, is equal to the base shear. But you can define your loads however best suits your model.

## 2 thoughts on “Load Patterns and Time Series”

1. Dear P.D.
You mentioned that “I prefer scenario A where the reference lateral load sums to 1.0 so that the load factor, is equal to the base shear. ”

But, If a large numerical value is required for the load factor, does it not cause convergence problems?

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1. Hello MSB,
The load factor multiplies the reference loads, so the only thing that matters is the product of the two. A high load factor with low reference loads is the same as a low load factor with high reference loads.
PD

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