Question

For the beam loaded as shown, write singularity functions for the slope and deflection of the beam and solve for the slope of the beam at A. Use x = 0 starting at the left end of the beam. с B L 1/2—

Answer 1

y 2w A B 42 By SM00 - By x1- (WXL) x_ - (2Wxų) *(1+4) -- 1.75 WL -> By Efy=o * Ay+ By =7 WXL - 24 x L -0 2 2WX * Ag + 1.75 ML - 2WL=0 Ay 0.25 WL Now W<X-oy² + By <x-o> M(O): Ay <X-L>- W ZX-1/2 2 2 - EI v" (3): 025 ML 31-0) - 8 (3-o> +1.75 ML 1-12 - W40-L3² 2 =7 EI V'(X) = 6 0.125 WL <«-07-W <1-078 +0875<2-17 BVL - W - W <X-L>3 ta 1 CS Scanned with CamScanner

7 EI V(2) <X-07 + 0.875 WIL. 0:879 0.125 WL (2-0)3. W 3 24 <0-173 W <a-ly" trix + (z 24 Applying boundary conditions At 1-0 V(X) = 0 from @ (2=0 At 2-L, V(X)=0 from © 0.125 WeL4 3 WL4 + CXL 24 =7 C, -0 =7 V'(U): I ΕΙ 0.125 WL <OC-0)2- W <2-073 + 0.875 WL<X-L8 W <2-293] 0.125 WL <a-033 <3-034 + 0.875 & V(X){0125 - L W (2-174] * 0-81$<x-18 24 24 * Slope at A OA = v' (1=0) [0.125 WIL 10-032 - W 60073 + 0.875 KILSO-LY - W<0-L%3] 6 OA - 0 6 CS Scanned with CamScanner