5-74 The bent rod is supported at A, B, and C by smooth journal bearings. Determine the magnitude of F which will cause the positive x component of reaction at the bearing C to be Cx

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answer : The magnitude of the force = 746.27 N

Explanation:

C to be Cx = 50 N

First we have to consider the equilibrium force in the all directions

In x direction

∑ Fx = 0

Fcos60 cos30 - Ax - Cx = 0

hence Ax = 0.433F - 50  ------- (1)

In y direction

∑ Fy = 0

F cos60 sin30 - By - Cy = 0

By + Cy = 0.25 F --------- (2)

In z direction

∑ Fz = 0

-Fsin60 + Az + Bz = 0

    Az + Bz = 0.866 F --------- ( 3 )

Next we consider the equilibrium moments in all directions

In x direction

∑ Mx = 0

Cy(2) - Az(2) = 0

therefore; Cy - Az = 0 ----------- (4)

In y direction

∑ My = 0

Bz (1) - Cx(2) = 0

Bz (1 ) - 50(2) = 0

therefore Bz = 100 N --------------- (5)

In Z direction

∑ Mz = 0

-Ax(2) + By(1) + Cy ( 1.75 ) = 0  ---------- (6)

after solving each equation

Ax = -373.13 N

Az = -746.27 N

By = 559.70 N

Bz = 100 N

Cy = - 746.27 N

and F = -746.27 N

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explanation: