Timehistoryanalyse

Timehistoryanalyse is a numerical method used in structural dynamics to determine the dynamic response of a structure to transient loads by integrating the equations of motion over time. In a multi-degree-of-freedom system, the response is governed by M x'' + C x' + K x = F(t), where M is mass, C damping, K stiffness, x(t) the vector of displacements, and F(t) the time-dependent external force, such as ground motion during an earthquake.

The procedure involves building a structural model, selecting an appropriate damping model, and choosing a time integration scheme (for example Newmark-beta or Wilson theta). The external load history F(t) is supplied as an acceleration, velocity, or displacement time history, often representing earthquake records or wind gusts. In linear time history analysis, material and geometry are assumed linear; nonlinear time history analysis uses nonlinear constitutive models and may involve stiffness/damping changes during motion.

Outputs are time histories of displacements, velocities, accelerations, floor drifts, interstory forces, and member end forces. Time histories can be used to assess peak responses, damage indicators, and to evaluate performance under specific hazard scenarios. A probabilistic or ensemble approach may involve multiple records to capture variability.

Limitations include dependency on the accuracy of the input record, damping prescription, and structural modeling; high computational cost for nonlinear or large systems; and uncertainties in material behavior and soil-structure interaction. Timehistoryanalyse is widely used in earthquake engineering and performance-based design, complementing response spectrum methods.