PROBLEM 5- The building shown has a large reciprocating engine located at level 1. Using the following data, compute the maximum shearing forces that columns must resist on each floor. Using El Centro NS components W3 = 193 k k3 = 100 k/in. W2 = 386 k Weight of engine 100 Kips k2 = 100 k/in. Engine W1 = 386 k k1 = 100 k/in. TTTT TITT Fig. 5 A) Determine the natural frequency, natural periods, and the corresponding mode shapes. B) Verify that the modes are orthogonal as expected. C) Normalize the first mode with respect to the mass matrix q1Tm1 = 1.0 D) Use the normalized first mode (from above) to verify that 1TkQ1 = w2 E) Use the El Centro Response Spectrum and a damping ratio of 5% to estimate the maximum base shear and moment. RESPONSE SPECTRUM IMPERIAL VALLEY EARTHQUAKE MAY 18, 1940 - 2037 PST IIIA001 40.001.0 EL CENTRO SITE IMPERIAL VALLEY IRRIGATION DISTRICT COMP SOOE DAMPING VALUES ARE O. 2. 5. 10 AND 20 PERCENT OF CRITICAL 400 200 F80 Acceleration, g 80 60 40 8884 100 20 20 086 4 VELOCITY (in./sec) .8 201 02 800 006 004 002 الله 2 86 Displacement, in. -20 400 008- 600 400 200 60 200 100 80 60 -800 40 20 20 006 004+ 10 986 F2000 4 2 0013 8000 0006 0004 .8 .6 2 4 6810 PERIOD (secs) .1 .04 .06.08.1 .2 4 .6.81 20 4 2 20 20

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