CE573_Solution_Homework11_2010

CE573_Solution_Homework11_2010 - Graphing the modeshapes...

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1 CE573 – Structural Dynamics Homework #10 1) a)

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2 b) c)
3 d) e)

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4 f)
5

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6 2) 2
7

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8 3) The fundamental modal properties, namely, the approximate fundamental modeshape and corresponding natural frequency, of each structure are estimated using the Rayleigh’s Quotient approach. The initial guess vectors for the modeshapes are estimated using deflections that would be assumed by each structure under mass proportional lateral loading (as in, under unit lateral gravity field). One round of iteration to improve the guess modeshape is made for each structure. In the following pages, the Rayleigh’s Quotient results and the iteration process are given in tabular form. Below, the modeshapes are graphed to illustrate the differences.

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Unformatted text preview: Graphing the modeshapes, normalized to give unit displacement at roof, we see that in the case of the “soft ground story” structure, when the structure is responding in its fundamental mode, the largest interstory drift (i.e. story distortion) takes place at the ground story (65% of total displacement). When the “soft story” structure responds in its first mode, the displacements will concentrate at the soft-story. In the case of “soft third story”, 35% of the total displacement is taken by the soft third story. Note that the “soft ground story” structure has the lowest fundamental frequency. The softening of the third story caused very little change in the fundamental frequency. 9 10 11...
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CE573_Solution_Homework11_2010 - Graphing the modeshapes...

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