Question

PRACTICE PROBLEM A For the beam and loading shown, determine (a) the slope at end A, (b) the slope at end B, (c) the deflection at the midpoint C. (Use AMM) Hint: Choose reference section wisely. ANS: A. 256EI El 2El 7wL3 256EI B. 0 5wL4 512E1 C. さ L/2

Answer 1

Moment area method BMP theta_A(l) = Delta_B Delta_B = [Area of M/EI diagram at A and B][Centroide from B] Delta_B = 2/3 times Wl^2/8E times l/2 (l/2 + 3/8(l/2)] + 2/3 times wl^2/16E times l/2 (5/8 times l/2) Delta_B = 11 Wl^4/384 EI + 5Wl^4/758 EI = 9Wl^4/256EI theta_A(l) = 9 Wl^4/256 EI = > theta_A = 9Wl^3/256 EI theta_A/theta_B = Area of M/EI diagram at A and B [Delta AB] Delta AB = 2/3 times wl^2/8EI times l/2 + 2/3 wl^2/16EI times l/2 Delta AB = Wl^3/16 EI theta_A + theta_B = wl^3/16EI 9 Wl^3/256EI + theta_B = Wl^3/16 EI theta_B = 7 Wl^3/256 EI y_c = Delta_c - theta_A (l/2) Delta_c = Area of M/EI diagram A and c[centroid from c] Delta_c = 2/3 times wl^2/8 EI (l/2) [3/8 (l/2)] = wl^4/128 EI = wl^4/128 EI y_c = Delta_c - theta_A (l/2) = Wl^4/128 EI = 9Wl^3/256 EI (l/2) y_c = 5wl^4/512 EI