12.07.2015 Views

Report - PEER - University of California, Berkeley

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Referring to Eq. (15), the natural period <strong>of</strong> the system without the stiff element isobtained as followsfδYκ1fT0= 2π(32)α gf 1The natural period <strong>of</strong> the system without the flexible element is obtained assδYκ1sT0= 2π(33)α gs1Referring to Eq.(12), the maximum instantaneous period <strong>of</strong> the system withoutflexible element is obtained assTm= aT s⎛⎜Ts=sT0⎜1+⎝− ⎞µ ⎟8⎟⎠swhere s T s is the period <strong>of</strong> the stiff element associated to the secant modulus and-sµ the value <strong>of</strong> - µ in the stiff element. In deriving Eq.(34), the following valueswhich correspond to the elastic-perfectly plastic system are used.−(34)µ1+a =8T, q=1.0 (35)−1+µThe effective period <strong>of</strong> the system without the flexible element is obtained assT0+sTmsTe= (36)2The flexible-stiff mixed structure is a parallel system <strong>of</strong> the flexible and stiffelements. Then, the effective period <strong>of</strong> the total system is obtained from1 1 1= +(37)2 2 2TefT0sTe-Applying the numerical analyses,sµ is obtained by the following two ways.s−10−Σsii=1µ = µ ,−− γ =1 sµ1sµ (38), (39)si∑∑s i is very closely approximated by∑s i =0.36+0.64N (40)The structural system is specified by s δ Y , f δ Y , α s1 and α f1 .shown in Table 2 as - µ s.-sµ obtained by Eq.(38) is394

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