MDOF Earthquake Example

MDOF Earthquake Example - CE 573: Structural Dynamics MDOF...

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CE 573: Structural Dynamics MDOF Earthquake Response Spectrum Example Given: A three story building is modeled using shear frames. The mass and stiffness properties are as indicated. Assume 0.02 ξ = for all modes. Each story has a height of 14 ft. Required: Estimate the maximum responses for the displacements, story shears, and story overturning moments. Use the Newmark-Hall design spectrum for your estimates, but assume a maximum ground acceleration of 0.04 g . Combine the modal maxima using the SRSS method. Solution: 1. Obtain the modal information: [] [] 2 15 7000 3000 0 10 kips-sec /in; 3000 5000 2000 kips/in. 5 0 2000 2000 MK ⎡⎤ ⎢⎥ == ⎣⎦ » mmat = diag([15 10 5]); » kmat = [7000 -3000 0; -3000 5000 -2000; 0 -2000 2000]; » dmat = inv(mmat)*kmat; » [vecs,vals] = eig(dmat) vecs = -0.5641 -0.3678 0.3087 -0.0793 0.6891 0.5865 0.8219 -0.6245 0.7488 vals = 438.5707 0 0 0 841.3757 0 0 0 86.7202 » omega = sort( sqrt( diag(vals) ) ) omega = 9.3124 20.9421 29.0065
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» a1 = vecs(:,3); a2 = -vecs(:,1); a3 = -vecs(:,2); » modalmat = [a1 a2 a3] modalmat = 0.3087 0.5641 0.3678 0.5865 0.0793 -0.6891 0.7488 -0.8219 0.6245 {} [] rad sec 9.31 0.3087 0.5641 0.3678 20.94 ; 0.5865 0.0793 0.6891 . 29.01 0.7488 0.8219 0.6245 ω ⎧⎫ ⎪⎪ ⇒= Φ = ⎨⎬ ⎩⎭ 2. Earthquake modal participation factors: {} [ ]{} 1 .
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MDOF Earthquake Example - CE 573: Structural Dynamics MDOF...

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