Question

0.0 Period (s) For the given structure determine the stiffness matrix, mass matrix and construct 7KN/m 3- shape modes. Assume Moment of inertia (I) for one column is: 006 m4 ton Module of elasticity (E): 2 × 106 mm 8 ω2 = 75rad/sec a) 1 = 30 rad/sec

Answer 1

E 2000000 TON/M 19928000 kN/m 0.06 MM4 EACH COLUMN 4 M 3.5 M 7 kN/m 8 kN/m 1 top flooiw 6 und fw Ht of columnn bay 1 bay2 66.5 KN 12tota weight of top floor 13toal weight on bottomfloor76 kN 76 kN M1 66.5 kN M1 0 0 M2 0 kN mass matrix 0 665 STIFFNESS OF COLUMNS

STIFFNESS OF COLUMNS 23 24 K1 STIFFNESS FOR BOTTOM FLOOR 12EI/LA3 224190 kN/m for each column 25 26 total K1 672570 (3 each column) kN/m 27 28 K2 STIFFNESS FOR TOP FLOOR 12EI/LA3 334651 kN/m FOR EACH COLUMN 29 30 1003952.9 (3*each column) kN/m total k2 31 32 1.6765 -1.004 stiffness matrix k1+k2 (-k2) 1676523-1003953 34 k2) k2 1003953 1003953 1000000 -1.004 1.004 35 36 37

37 30 rad/sec 75 rad/sec 900 38 W1 w1A2 5625 w22 39 W2 40 k-wA2M 41 42 43 1608123 -1003953 1.608123 -1.00395 44 for w1 1003953 944102.89 1000000 -1.00395 0.944103 45 46 47 1249023 -1003953 1.249023 -1.00395 48 for w2 1003953 570040.39 1000000 -1.00395 0.57004 49 50 51

18 4676100 176 1.003-1001o td 1003 - 1.003 0 et assume Фе o-626

51 1-626-5625126 10 ot- 2491-003 13 1-003 -003 1-249 0.303