Issue 57

M. T. Nawar et alii, Frattura ed Integrità Strutturale, 57 (2021) 259-280; DOI: 10.3221/IGF-ESIS.57.19

   

sin t

1 . d p

p k

1

(8)

у =

(1-cos( ω t)) +

(

-1)

k t

 The plastic range response up to the peak, (t el ≤ t ≤ t m ) is:

 P R m K t m K  1 1 1 2 2 el t P MF d

1 p m k t

' el y ( t - t el )+ у el

(9)

(

( t - t el ) 3 +

) ( t - t el ) 2 +

у =

6

MF

MF d

Several diagrams for the maximum response of SDOF systems exposed to different types of simple load functions have been developed for practical design purposes as presented in Fig. 7. The peak response can be calculated, using the ratio (td/T) and the internal resistance to the applied load ratio (R1/P1). Eqn. 10 calculates the ultimate static pressure load over a simply supported beam based on the ultimate moment capacity (M p ). The ultimate moment capacity can be determined using the corresponding design code:

2 8 p M bL

(10)

q u =

Figure 7: Max deflection of elasto-plastic, one-degree-of-freedom system for triangular load [4].

Figure 8: The dynamic reactions for a simply supported beam.

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