RamSeries manual
Spectrum analysis is used when the dynamic action causes seismic movement at the base of the foundation. In this case, the decoupled motion equation for each mode is expressed as:
where is the seismic
acceleration.
This equation can also be resolved using the response spectra. In this case, only the maximum response of the structure is obtained. If a maximum acceleration of
is assumed for the previous equation, it is evident that the maximum response acceleration of the system would amount to
As a consequence, the maximum displacement is:
Using this answer, we can calculate the maximum displacements in all of the nodes for mode j:
where is the vector of the
modal participation coefficients corresponding to mode j of the vibration.
Supposing that for each degree of freedom the maximum response does not occur
at the same instant in each mode, the maximum response of the structure will
not be equal to the sum of the maxima corresponding to each mode:
Different formulas
for finding the value of through
have been proposed. The most simple and at the same time most
used is that which establishes that the response is equal to the square root of
the sum of the squares of the modal responses. .
As for the stresses, reactions, and in general any response R which is to be determined, we get analogously: