Page 64 - Dynamic Loading and Design of Structures
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Page 45
Figure 2.15 (a) Elastoplastic SDOF system, (b) restoring force and (c) loading function.
along with zero initial conditions. The SDOF system response will be divided into three
stages. In the first stage, and thus R(y)=ky. The response is therefore
(2.45)
where and . In the second stage we redefine the time variable as
, where the elastic response time tel is given by the equation
(2.46)
The new form for the equation of motion is
(2.47)
under initial conditions
(2.48)
resulting from the first stage. Integrating eqn (2.47) yields
