Question

3) a) Find the reaction forces at A b) Determine the reaction forces and moments at B c) Find the displacement at 1/2 d) Find the rotation at 1/2 W(x) = wo sin (6)

Answer 1

Answer:

Given that,

Beam length L
=) Using singularity faictions, weget, q=W<X-os - < x-> ARA <*-03-1, + RBLX-13 +MB {X-L3-2 Intergaating both icotina both the the side sides with respect tox, weget, v(x) = wzx-os 'n h 24-032 + RAX-OX + RB X-L> +MB<X-22, Integrating both sides with gespect 40 x, weget, 'M(x) = W cx-o)? W (x-o>3 ARA <x-ostro ex-L)!

+MB<x-L% --) Boundary conditions- MEO at azo VERA at x=0 M=+MB at 8 = V=-RB aut x = For M=-MB at x=L, weget, ++ RAL AR-Me we + Ral -MB - For v= Rp of x=L, weget, we - WL TRA=-RB WE FRA = -RB @ Jutegooting M with respect to x, weget, EID <x-053- 2x-0384 + R$ < x-03? + Red CX-2) ? +MB <x-Lyttc Undegroting both the sides toith gespeel 40% weget, EIY s <x-034-hoc-035 + RA <x-033 + F. 2X-233

- MB [X-L3² + ( X4 (2 Boundary conditiongo- YOU X=0 Y=0 ot x = ay at x=t, For yzo at xzi, weget, WŁ*Watch Race + Col + C2 =0 ... weitet RAL9+(1+4 =0 -- Foa et bono at xth, , wote BAL° +6=0 W1.94 RAL? +6=0 – we get, For Y=0, oot x=0, we get, : 02 0 6 From @.0 weget, Wet Becke - house BALT=0 30 - RA : HW 0

From $ 66, weget, co w achete — focom , weget, wiz I WL% www² - MS 3 MB = - 7WL? 120 From € 6, .. we get, When the RS RB = - que o a) Thus, Reaction force of A, RA= -11WL wo " Reaction force and moment at B; qWL no MB -Twil? . . . 12.0 c) Dis place mout at in

Phkaq 12:30 pment -Rotatidan at -3.6416-X.163 W13 EI W(X) = Wosinca teau, using singularity function, * q = - wosin (AX) + RA CX-o), RB X-L2, +18<x-LX2 followed by to get the s similar procedure can be Solution of this pooble Boundary conditiongo will also remain the same