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Linear

A Linear Time Series defines a time–history where the load factor Ξ»\lambda varies linearly with time:

Ξ»(t)=cfactor t\lambda(t) = c_\text{factor} \, t

where $c_\text{factor}$ is a constant slope. This is useful when you want loads to ramp up (or down, if negative) at a constant rate as the analysis time increases.

πŸ”§ Grasshopper component

The Linear Time Series (Alpaca4d) component creates an Alpaca4d linear time series that can be connected to load pattern or excitation components.

  • Input

    • LinearFactor: Linear scale factor cfactorc_\text{factor} that multiplies time tt.

      • Type: Number

      • Default: 1.0

      • Effect: The load factor increases (or decreases) proportionally to time: doubling the analysis time doubles the load factor.

  • Outputs

    • TimeSeries: Alpaca4d Linear time series object, to be plugged into components that require a time series.

    • Graph: A list of values representing the time series, typically visualised as a straight line increasing with time.

πŸ“ˆ When to use a linear time series

  • Use it when

    • You want a ramp load that grows from zero to a target value over a given duration.

    • You need to gradually apply loads to avoid sudden jumps (e.g. quasi‑static ramping in nonlinear analysis).

    • You are modelling a linearly increasing excitation intensity.

  • Do not use it when

    • The load should be constant in time β†’ use a Constant time series.

    • The load follows a recorded or arbitrary signal β†’ use a Path / Time History time series.

    • The load is cyclic or periodic β†’ use a Trigonometric time series.

πŸ”— Relation to OpenSees

Alpaca4d’s linear time series is conceptually equivalent to the OpenSees Linear timeSeries:

where cFactor corresponds to the LinearFactor input in the Alpaca4d Grasshopper component.

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