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Time-history analysis provides for linear or nonlinear evaluation of dynamic structural response under loading which may vary according to the specified time function. Dynamic equilibrium equations, given by K u(t) + C d/dt u(t) + M d2/dt u(t) = r(t), are solved using either modal or direct-integration methods. Initial conditions may be set by continuing the structural state from the end of the previous analysis. Additional notes include:

  • Step Size – Direct-integration methods are sensitive to time-step size, which should be decreased until results are not affected.
  • HHT Value – A slightly negative Hilber-Hughes-Taylor alpha value is also advised to damp out higher frequency modes, and to encourage convergence of nonlinear direct-integration solutions.
  • NonlinearityMaterial and geometric nonlinearity, including P-delta and large-displacement effects, may be simulated during nonlinear direct-integration time-history analysis.
  • LinksLink objects capture nonlinear behavior during modal (FNA) applications.



Time-history analysis first stepsOverview of the procedure for time-history analysis.SAP2000
Vibrating-machinery steel skid on pilesThis tutorial demonstrates the modeling of vibrating machinery and its connection to a steel-skid structural system.SAP2000

Test Problems

Human-induced vibrationsThe modeling and analysis of human-induced vibrations due to footfalls or another type of impact.SAP2000
Multi-pendulum model (Newton's cradle)Model a pendulum system in SAP2000 using large-displacement time-history analysis.SAP2000
Steady-state vs. time-history analysisTest problems to demonstrate the differences and similarities between steady-state and time-history analyses.SAP2000

See Also