Elastoplastic Behavior

Elastoplastic Behavior - CE 573: Structural Dynamics...

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CE 573: Structural Dynamics Numerical Evaluation of Dynamic Response – Elastoplastic Behavior Example Given: Mass of frame , stiffness k = 20 kips/in, and 2 0.5 kip-sec /in m = 0.02 ξ = . Tank starts at rest and is subjected to pulse F(t) as shown. Assume elastoplastic behavior with yielding occurring at 60 T R = + kips and kips. 35 C R =− Required: Determine the response u(t) from 0.0 sec t = to 1.0 sec t = using Newmark’s linear acceleration method with . 0.1 sec t ∆= Solution: 1. Need to check time step for stability – we will assume that stability is OK. 2. Preliminary Calculations – 2 0.0 in; 0.0 in/sec; 0.0 kips. 0.0 in/sec . ooo oo o Fc uk u o m uu F u −− == = ⇒= = 3. Linear Acceleration Method: If frame is behaving elastically – () ( ) ( ) 2 2 2 kips-sec kips kips-sec in in in kips 63 in 2 3 0.02 0.5 * 20 60 .5 20 0.1 sec 0.1 sec 321.90 kips/in. mc ii t t kk =+ + = + + = If frame is behaving plastically – ( ) ( ) 2 2 2 kips-sec kips kips-sec in in in 2 30 . 0 2 0 . 5 * 2 0 0 0.1 sec 0.1 sec 301.90 kips/in.
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Elastoplastic Behavior - CE 573: Structural Dynamics...

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