Question

ngUTU A beam with constant E and I values is loaded as shown. Using method of superposition, find (a) the reaction Rg at point B, (b) the reactions Ra and Ma at fixed support A. Reaction at B can be considered as an external force that makes deflection at B equals zero. Mo L/2

Answer 1

Slope = {-M_0 x/EI: 0 < x lessthanorequalto L/2 slope = R_B L^2/2 EI -M_0L/@ EI: L/2 < x < L Deflection = {-M_0x^2/2EI: 0 < x lessthanorequalto L/2 Max^m Deflection = R_B L^3/3 EI M_0 L/4 EI (L/2 - 2x): L/2 lessthanorequalto x lessthanorequalto L writing eq^n sigma f_y = 0 doublerightarrow R_A + R_B = 0 sigma M_b = 0 doublerightarrow R_A times L - M_a + M_0 = 0 doublerightarrow R_A = M_a - M_0/L -(1) R_B = -R_A = M_0 - M_a/L -(2) M_a = R_A times L + M_0 -(3) Now deflection at B = 0 doublerightarrow delta_1 + delta_2 = 0 doublerightarrow M_0 L/4 EI (L/2 - 2 times L) + R_B L^3/3 EI = 0 doublerightarrow -3L^2 M_0/8 EI + R_B L^3/3 EI = 0 doublerightarrow R_B = 3/8 m_0/L & R_A = -3/8 M_0/L M-a = -3/8 M_0/L times L + M_0 = 5/8 M_0 doublerightarrow M_a = 5/8 m_0