Question

Question 3 Use discontinuity equations to develop the load function w(x) for the beam shown below. Include the beam reaction in this expression. Integrate w(x) to determine V(x), and M(x), Use these functions to plot the shear-force and bending-moment diagrams using excel. Include table data obtained Determine the bending moment M in the beam at the point located 2.12 m to the left of point C 2.0 kN/m 5.0 kN/m 3 m 5 m 4.70 kN 14.30 kN

Answer 1

Given beam reaction are obtained by the by the equilibrium equation Load function w(x) = + 2(x) degree /(+ 4.70 k N degree)/ - 5 x /(+ 14.30 K N) shear force & bending moment (local axis SF_AB (x from A) = + 2(x) S F(A) (x = 0) = + 2(x) (x/2) = + x^2 B M_A(x = 0) = 0 B M_A(x = 0) = 0 , BM_B (x = 3) = (3)^2 = + 9 k N - m s F_BC (x from c) = + 14.30 - 5(x) S F_c(x = 0) = + 14.30 KN, s F_B (x = 5) = -10.7 K N B M_BC (x from C) = + 14.30 - 5(x)(x/2)BM_c(x = 0) BM_B(x = 5) = 71.5 - 62.5 KN shear function s F_x = integral w(x) = + 2(x)/+ 4.70 - 5(x)/+ 14.30 Moment function M_x = integral s F_x = x^2/+ 4.70 (x) - 2.5 x^2 - 2.5 x^2 + 14.30(x) plotting SF_D & B M_D with the obtained results \r\n c) x = 2.1 m from left to point c Mn_x = 14.30 (2.12) - 5(2.12)(2.12)/2 = 30.316 - 11.236 = + 19.08 KN - m S F_BC = 0 = > + 14.80 = 5(x) x = 2.86 cm