Question

AL EXAM Na i roblem #3-0-1, 1 December 2018 GIVEN: E 29,000 ksi 1 1000 int IOR 40 K 33.3K 16.1K 30' FIND: Find the deflection at point D by virtual work. (Mm) Answer will be in inches, and give direction.

Answer 1

Sigma m_A = 0 R_c(30) - 40(15) - 10(40) = 0 R_c = 33.33k. sigma F_y = 0: R_A + R_C = 50k. R_A = 16.67k. mu_AC = 16.67x - 40(x - 15) mu_AC = -23.33x + 600. mu_CD = 10(x). Apply unit vertical load @ 'D' sigma M_A = 0: R_C(30) - 1(40) = 0. R_C = 1.33. R_A = 0.33. m_AC = -0.33x. m_CD = 1(x). delta_D = sigma integral_0^2 mmdx/EI = integral_0^30 (-23.33x + 600)(- 0.33x) dx/EI + integral_0^10 10(x) middot (x) dx/EI = (7.6989x^3/3 - 198x^2/2)_0^30 1/EI + 10x^3/3)_0^10 1/EI = -16476.56/EI = -16476.56 times 12^3/29000(1000) = -0.9817 inch. Delta_DV = -0.9817 inch. Delta_DV = 0.9817 in. uparrow (upward)