Question

Learning Goal: To analyze a rod assembly in three-dimensional space and determine the support reactions by using the equations of equilibrium for a rigid body. The rod assembly shown has smooth journal bearings at A, B, and C. The forces Fi = 500 N, F = 440 N, F3 = 480 N and FA = 975 N are applied as shown in the figure. The geometry of the rod assembly is given as a = 0.800 m, b=0.550 m , and c= 0.600 m . Neglect the weight of the rod. CA E2

Answer 1

hiven values, f = 500N , f = 440 N , F = 480 N and = 975N and , a=0.800m, b=0.550m ca 0.600m Ak point, À – An and A A B Br and B2 Cy and Cz

consider force equilibrium condition along y direction, Efy = 0 - F + Cy=0 - 480 &lg=0 cy=480N consides moment equilibrium condition along y direction, {My = 0 fxb - Fuxa + C₂x2a = 0 500 x 0.550 - 975 x 0.8 + C₂ X 2 x0.8 = 0 i. C₂=315.625 N er moment equilibrium condition about x-direction EM=0 - f, xa + B₂ x 2a + F₂ x C - F4 x 39 + (₂ X 3a = 0 -500x0.8 + B x2a + 480x0.6 - 975 X 3x 0.8 +315.625x3x0.8. = 0 . Br = 1694.5 = 1059.0625 N = 1059 N 2 X 0.8 Consider moment equilibrium condition about a direction, EM₂=0 f₂ Xa + B x 2a + Fz xa - Cyxa = 0 44080.8+ By x 2 x 0.8 +480 x 0.8 - 480 x 2x0.8 20 Bu-20N

consider force equilibrium condition along a-direction, {f₂=0 A - F, + B2 - Furc=0 A- 500+ 1059 - 975 + 315.625 = 0 & Az = 100.375 N consider force equilibrium condition along redirection, Efn=0 An-F₂ - Buco An- 440-2020 An= 460N ,
I have tried to solve step-by-step. Hope it helps. Thanks for asking questions.