Engineering | Finite Element Analysis | Stress
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Response Spectrum Analysis
Response spectrum analysis (RSA) is a procedure for computing the statistical maximum
response of a structure to a ground bourne excitation. Each vibration mode considered
may be assumed to respond independently as a single-degree-of-freedom system. Design
guideline codes specify response spectra that determine the base acceleration applied
to each mode according to its period (the number of seconds required for a cycle
of vibration). The design response spectrum is then usually obtained by multiplying
the basic acceleration coefficient by a factor based on required structural performance,
risk & location.
Having determined the response of each vibration mode to the excitation,
it is necessary to obtain the response of the structure by combining the effects
of each vibration mode. Because the maximum response of each mode will not necessarily
occur at the same instant, the statistical maximum response, where damping is zero,
is taken as the square root of the sum of the squares of the individual responses.
Response spectrum analysis produces a set of results for each excitation load case
which is in the form of an envelope. All results are absolute values, each value
represents the maximum absolute value of displacement, moment, shear, etc. that is
likely to occur during the event which corresponds to the input response spectrum.
Shakedown Analysis
If load intensities on a structure remain sufficiently low, the response of the body
is purely elastic (with the exception of stress singularities). If the load intensities
become sufficiently high, the instantaneous load-carrying capacity of the structure
becomes exhausted (unconstrained plastic flow and damage evolution occurs) & collapses.
If the plastic strain increments in each load cycle are of the same sign then, after
a sufficient number of cycles, the total strains (and therefore displacements) become
so large that the structure departs from its original form and becomes unserviceable.
This phenomenon is called incremental collapse or ratcheting. If the strain increments
change sign in every cycle, they tend to cancel each other and total deformation
remains small leading to alternating plasticity. In this case, however, the material
at the most stressed points begins to fails due to low-cycle fatigue.
If, after some
time plastic flow and damage evolution cease to develop further and the accumulated
dissipated energy in the whole structure remains bounded such that the structure
responds purely elastically to the applied variable loads, one says that the structure
shakes down .
Dynamic Impulse - RSA
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