Question

Calculate the deflection and slope at B and the deflection at D for the uniform beam (Stiffness - EI). W kN/m V V V V V V V V V V L/2 Calculate the horizontal deflection of B and the relative rotation of the hinge at B in the frame ABC (member stiffness's shown). W = 2P/L kN/m 2L 4EI L/2 PKN

Answer 1

O Toking moment about B (sight post of B) R -W (+ ) + ) = 0 Re = 2 we aking -x from point . & os shown an figure m= Re (x - 2) - 2x . By maconley's Es = (x - 5) - 20x? Integrating both side w.r.to .x (two times) Es de (-+)2 – 50 + A Ety - he (x-7) - 2 x + Rx+ B Boundary conditions x= 1 4 7.0 x= L = 1.75L, az = 0 : Patting x=1751 of TL Montero OST (1751-4)2-1(1754)" +A => 0 = WL 712 - SALA +A Pulting x= 14 at Ery 0 - RG - - - * * * + 12° ) + 8 123 WLY 124 2048

: Equation of slope Equation of Deflection You te uz (-+)* - *+ we® z - * *? Deflection of point B x=0.75L Yo u MZ (0-75L - ) - 60-752) + E 22° (0.75L) - 4 - 01239 Hot Aing Slope at point B x = 0'75L uz (0.75L - +)*- (075279+ * 22} Dedtection at point o, x=0 204% = - 006494 with Ars Fre sign for upward deflection 2