# Linear Time History Analysis

Linear time history analysis is to calculate the linear responses of structures that are subjected to dynamic loads (force excitation) or base accelerations defined by the combination of the applied loads or base acceleration and load curve. The structure responses include nodal displacements, velocities and accelerations as well as element forces and moments etc at the chosen time intervals. If it is force excitation, the magnitude and locations of the dynamic loads are defined in the same way as that for static analysis and the variation of the dynamic loads along with time is defined by load curve in the unit of time versus load factor. If it is base acceleration, the load curve should be acceleration recordings of the ground motions in the unit of time versus acceleration, the ground accelerations varying with time given by the load curve can be scaled by a scaling factor that can be defined in the analysis wizard.

The initial displacements and initial velocities are assumed to be zero in GSA linear time history analysis.

Linear time history analysis utilizes modal dynamic analysis results (frequencies, mode shapes & modal masses etc), so at least one modal dynamic analysis must exist with results before doing linear time history analysis.

## Modelling implications​

Linear time history analysis utilizes modal dynamic analysis results, so the construction of a GSA model for linear time history analysis is the same as that for modal dynamic analysis. See the modelling implications of Modal dynamic analysis for the requirements of building up a model for modal dynamic analysis which also applies to linear time history analysis.

The spatial distribution and magnitude of the dynamic loads are defined in the same way as for defining loads for static analysis. Load combinations (e.g. 1.4L1 + 1.6L2) can also be used in linear time history analysis. The variation of the dynamic loads along with time is defined by load curve in the load curve table.

As linear time history analysis utilizes the results of modal dynamic analysis, at least one modal dynamic analysis task must be analysed before doing linear time history analysis.

## Results​

The results of a linear time history analysis include nodal displacements, velocities and accelerations and element forces and moments at the chosen time intervals. In addition, the nodal displacements, velocities and accelerations can also be plotted against time on the output of chart views.