Rigid Response Concepts

Rigid and flexible response

A structure or equipment is said to respond rigidly when its natural frequency is well above the amplified region of the response spectrum. In the rigid region, the spectral acceleration equals the zero-period acceleration (ZPA) and the structure moves in phase with the ground. There is no dynamic amplification. Below the rigid boundary, the structure responds flexibly and the spectral acceleration may exceed the ZPA due to dynamic amplification.

Rigid-flexible boundary

The rigid-flexible boundary is the frequency above which the response is considered rigid. It is typically taken at the frequency where the spectral acceleration first equals the ZPA on the high-frequency side of the amplified region. Common values are 33 Hz or the frequency where the spectrum transitions to the ZPA plateau. The boundary depends on the spectrum shape and damping.

Rigid component and missing mass

• When not all modes are extracted, the missing mass responds rigidly at the ZPA
• The rigid component of response is combined with the periodic (modal) component per the standard — typically algebraically or by SRSS
• Some standards separate the rigid and periodic components of each mode and combine them differently
• Equipment classified as rigid (fn above the boundary) can be analysed statically using the ZPA without modal analysis
• The rigid response is in phase across all directions, while the periodic response is not — this affects directional combination