# Summary

In this course, we explained how a response spectrum analysis is conducted along with the important considerations and techniques in mode combination.

Let’s summarize the key takeaways from each lesson.

How to Perform Response Spectrum Analysis

• Response spectrum is a mode superposition analysis that uses the results of a modal analysis with a known spectrum to calculate displacements and stresses in the model.
• The input spectrum is a graph of spectral value vs frequency that captures the intensity and frequency content of time-history excitation.
• For base excitation by a single-point response spectrum, at least one allowed boundary condition must be defined, and the input excitation must act uniformly on all support points
• Three types of input excitation spectrum are supported: displacement, velocity, and acceleration.

Understanding Mode Combination Methods in Response Spectrum Analysis

• There are multiple mode combination methods, but most of them evolved from one general equation.
• If there are no closely-spaced modes, the dependency between the modes can be neglected. The square root sum of squares (SRSS ) method can be used to combine the modal results.
• If there are closely spaced modes for a structure, we can use either the Rosenblueth (ROSE) method or the complete quadratic combination (CQC) method to include the correlation effects between the modes.
• For the CQC method, damping input is required.

Understanding the Rigid Response and Missing Mass Effects in Response Spectrum Analyses

• In a response spectrum analysis, we would combine periodic responses with the mode combination methods.
• For rigid response, we’d prefer to add them algebraically since they may be in-phase.
• The input spectrum is divided into three regions: high-frequency rigid response region, low-frequency periodic response region and transition region.
• In the transition region, both the rigid response and periodic response exit and the Lindley Yow or Gupta method can be used to define the combination of the two types of responses.
• The missing mass method calculates how much mass is missing from the modal analysis and accounts for this quantity in the response spectrum analysis.
• The missing mass response is combined with the previously calculated rigid response by algebraic summation.