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Question:

I have performed a response spectrum analysis of a multi-DOF structure and the program reports higher acceleration for certain joints than is the maximum acceleration on the response spectrum curve. How is this possible?

Answer:

The response spectrum curve shows the response for a single-DOF structure. When this is applied to a multi-DOF structure, two things must be considered.

(1) For a given mode, an equivalent SDOF system with a modal mass of 1 and a modal stiffness of w^2 (circular frequency squared) responds with the acceleration from the response-spectrum curve. However, this does not mean that every displacement and every joint in the system experiences this acceleration. Some may experience more, some less, depending on the mode shape. To see the actual accelerations, you can plot the mode shape and look at the deflections. The accelerations are w^2 times the displacement for a unit modal displacement. The actual modal displacement for the response spectrum can be obtained from the table Response Spectrum Modal Information, Modal Amplitude value.

(2) Because the structure has multiple modes, these responses are additive in an SRSS way.