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Response Spectrum Analysis

In a response spectrum analysis, the results of a modal analysis are used in terms of a known spectrum to calculate displacements and stresses in the model. For each mode, a response is read from a design spectrum based on the modal frequency and a given damping ratio. All modal responses are then combined to provide an estimate of the total response of the structure.

You can use a response spectrum analysis rather than a time history analysis to estimate the response of structures to random or time-dependent loading environments such as earthquakes, wind loads, ocean wave loads, jet engine thrust or rocket motor vibrations.

Response Spectrum
Plots peak responses over time for a range of single-degree-of-freedom (SDOF) systems subjected to a particular base motion as a function of their natural frequency ωI, or vibration period TI. Each response spectrum curve corresponds to a particular modal damping ratio ξI.
Typical quantities plotted in response spectra are:
  • Maximum displacement Sd(ωI, ξI)
  • Maximum pseudo-velocity Sv(ωI, ξI) = ωI*Sd
  • Maximum pseudo-acceleration Sa (ωI, ξI) = ωI*Sv = ω2I*Sd
The response spectrum is used as base excitation input for a response spectrum analysis.

Relative displacement response spectrum for a particular damping ratio ξ1.

equals the maximum absolute value of the relative displacement time history response for each SDOF oscillator.

Natural circular frequency of vibration for each SDOF oscillator.
  • Analysis Procedure - Response Spectrum Analysis
    The normal modes are calculated first to decouple the equations of motion with the use of generalized modal coordinates. The maximum modal responses are determined from the base excitation response spectrum. With the use of modal combination techniques, the maximum structural response is calculated by summing the contributions from each mode.
  • Mode Combination Techniques
    The maximum structural response is calculated by summing the contributions from each mode. These mode combination techniques are available.
  • Performing a Response Spectrum Analysis
  • Response Spectrum Analysis Options
    The dialog controls the mode combination technique for the calculation of the maximum response in a respose spectrum analysis.
Parent topic: Dynamic Analysis


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