Question

The lever PQ is welded to the bent rod QSTU which is supported by a single thrust bearing at S and by the rigid link UV. Link UV is in a plane parallel to the yz plane (it has no x component) and has ball-andsocket connections at each end. Neglect the weights of QSTU, the lever PQ and the link UV. a) Determine the magnitude of the force in UV. b) Find the five support reaction components at S, where the rod is supported by the bearing.

Answer 1

The answer to the questions are as follows

a) The magnitude of the force in UV = 512.41 N

b) The five support reaction components are

1. PQ turning moment force about the z axis

2. PQ turning moment force about the y axis

3. UV turning moment force about the y axis

4. UV turning moment force about the z axis

5. UV turning moment force about the x axis

Please see below

Step-by-step explanation:

When the system is in 3D equilibrium

Sum of forces in x direction = 0

Sum of forces in y direction = 0

Sum of forces in z direction = 0

Also, Sum of moments in x direction = 0

Sum of moments in y direction = 0

Sum of moments in z direction = 0

From the diagram, we have force in the +ve x direction = 600 N

Also moment about y = 600×0.08 = 48 Nm

Moment about z = 600×0.09 = -54 Nm

Moment about x, = 0 Nm

For the support S, taking moment about x = 0.05 × S

taking moment about y = 0

taking moment about z = 0

At point U, taking moment about y = -0.1U

moment about x = -0.05U

moment about z = -0.1U

Summing the moments we have

In the x, y and z directions

0 + 0.04Vy-1.46Vz -0.05Uz= 0.... (1)

48 + 0.1Vz-0.04Vx - 0.1Uz = 0... (2)

-24 + 0.146Vx-0.1Vy + 0.05Ux + 0.01Uy = 0.... (3)

Ux + Vx = 600 ....(4)

Uy = -Vy .....(5)

Uz = -Vz .......(6)

Solving the above 6 equations we get the following values

Ux = 242.28 N

Uy = -366.74

Uz = -10.40

Vx = 357.72N

Vy = 366.74N

Vz = 10.40N

The magnitude of the force in UV =
`\sqrt{357.72^(2) + 366.74^(2) + 10.40^(2) }` = 512.41 N

b) The five support reaction components are

1. PQ turning moment force about the z axis

2. PQ turning moment force about the y axis

3. UV turning moment force about the y axis

4. UV turning moment force about the z axis

5. UV turning moment force about the x axis