Question

X Not Correct The cantilever beam consists of a rectangular structural steel tube shape [E = 180 GPa; I = 151 x 106 mm4]. For the loading shown, determine: (a) the beam deflection VA at point A. (b) the beam deflection VB at point B. Assume P = 88 kN, Q = 29 kN, MB = 217 kN-m, w = 60 kN/m, LAB = 1.8 m, LBC = 2.6 m. P w с MB B LAB LBC Answers: X (a) VA = mm. (b) VB = mm.

Answer 1

solution - E= 100gpa EI = V1 A B MB = 217 KN-m E= 1809 Pa = 180kw/mm2 I= 15\xlo-mmy 180x151x106 KN-mm² = 27180 KN-m2 P=180 KN 10=99 KN W = 60 kN/m tes * LAB= LBC= + liom 2.6m Mcx>= -PC1_o) + W (x-032_Q(x-LAB) - Mg (4-68) → EI V"(x)= -88<x-o>+30<x-03-294-1-87-217<*-1-87 EI V'A) = -44<X03 ?Hlock039-24 (2–1832-217<x=187+41 > EIVK) =<=>+ <4-0,4 -22<x+687-934 <--1832 +Gx+62 Applying boundary conditions :- At x= 1.8+216 = 4.4m, vko) » V(x=o) a = 44 x 424 + 10x 4:43 - 21 x 26²_217 x26th ci = 662.22 - 4x4.42 + 1 x Y.y" - 27 x 21 - 217 x 2.62 +662.22 x 4.4 +Ca C2 = -1783.016 VCA) = V(x=0) - EL - 2 <0-es@tbp. co->Y-22<0-18> -217<0-03 +662-22X0-1783.0167 From O from 3 31) 2 = -0.0656 m = -8506 mm ves) = V(x=1-8)= -- [4 x 82 + upxlve *** xo? -* xo ☆ VIAJ= -1783.016 27180 +b68.99. XI.8-1783.61 – 650.312 27100 = -0.0239 m = -23.9 mm