Question

The W8x 24 simply supported beam is subjected to the loading shown Part A Using the method of superposition, determine the deflection at its center C. The beam is made of A-36 steel. Take M 3 kip ft and w8 kip/ft (Figure 1) Express your answer with the appropriate units. Figure 1 of 1> AcValue Units Submit Return to Assignment Provide Feedback s t

Answer 1

The method of Superposition Calculation of partialdifferential_1 Sigma M_A = 0 uparrow + Ve R_By (1.6) = 8(8) (4) R_By = 16 Kip Section BA: M_x - 16x - 8 (x - 8)^2/2 = 0 M_x = 16x + 4 (x - 8)^2 M_x = 16x + 4 But +EI d^2y/dx^2 = 16x + 4 (x - 8)^2 -E I d^2y/dx^2 = 8x^2 - 1.5 (x - 8)^3 + C_1 -EIy = 4x^3 - 0.375 (x - 8)^4 + C_1 x+ C_2 -EIy = 4x^3 - 0.375 (x - 8)^4 + X_1 x+ C_2 Boundary condition At x = 0, y = 0 C_2 = 0 At x = 16, y = 0 0 = 3(16)^3 - 0.375 (16)^4 + C_1 (16) C_1 = 768 Therefore EIy = 4x^3 - 0.375 (x - 8)^4 + 768x At 0 deflection at C Cx = 8^1 + EIY = 4(8)^3 + 768 (8) = 8192 Y = 8192/EI For steel E = 29 times 10^6 lb/m^2 For A36 Omega_8 hat 24 section I_xx = 82.8 in^4