12 EQulIBRIUM OF A DEFORMABLE BODY 19 118 The shaft is suppo

1.2 EQulIBRIUM OF A DEFORMABLE BODY 19 1-18. The shaft is supported at its ends by two bearings A and B and is subjected to the forces applied to the pulleys fixed to the shaft. Determine the resultant internal loadings acting on the cross section at point C.The 400-N forces act in the -z direction and the 200-N and 80-N forces act in the ty direction. The journal bearings at A and B exert only y and z components of force on the shaft. 400 mm 150 mm 150 mm 200 mm 200 mm\" 80 N 300 mm S0 N 200 N 200 N 400 N 400N Prob. 1-18

Solution

let us determine the internal forces due to force 400 N separately and 200N and 80 N separately and then superpose the results

internal forces due to 400N:

let us consider moment equilibrium at support B

800*(0.2+0.2+0.15+0.15+0.4)-A_z*(0.2+0.2+0.15+0.15+0.4+0.3)=0

A_z = 628.57 N

Shear force at C in z direction = 800-628.57=171.43 N

bending moment at C about y axis = 628.57*(0.3+0.2)-(800*0.2) = 154.285 Nm

internal forces due to 200N and 80N forces:

let us consider moment equilibrium at support B

400*(0.15+0.15+0.4)+160*0.4+A_y*(0.2+0.2+0.15+0.15+0.4+0.3)=0

A_y = -245.71 N

Shear force at C in y direction = 245.71 N

bending moment at C about z axis = 245.71*(0.3+0.2) = 122.855 Nm