Question

For the cantilever beam and loading shown, use the method of superposition to determine (a) the slope at point A, (b) the deflection at point A. Use E 200 GPa. Hint: Use the expression found in Problem 1 for the tri angular load. 120 kN/m W360 × 64 20 kN 2.1 m

Answer 1

the cantilever beam and loading (a) for 20 KN load: By using separation of rules t = 178 times 10^6 mm^4 = 178 times 10^-6 m^4 EI = 200 times 10^9 times 178 times 10^-6 = 35600 KN m^2 \r\n For 120 KN/M loading A_1 = 1/2 times 2.1 times 1.17978 times 10^-3 M_1/F__I = 20 times 2.1/35600 = 1.7478 times 10^-3 m^-1 M_2 = -1/2 times 120 times 3 times 1/35600 = -5.0562 times 10^-3 M^4 A_2 = 1/4 times 3 times -5.0562 times 10^-3 = 3.7921 (b) Reference tangent at c theta_c = 0 theta_A = -theta_CA = -A_1 -A_2 = -1.23876 times 10^-3 - (- 3.7921 times 10^-3) = 2.55 times 10^-3 rad yA = t A/C = A_1 (3.07) + AC (3 - 3/5) = 1.23876 times 10^-3 (2.3) + (- 3.792 times 10^-3) times 2.4 = -6.25 times 10^-3 M = 6.25 MM