1. The pole is subjected to the two forces shown. Determine the components of

reaction of A assuming it to be a ball-and-socket joint.

“Ball-and-socket joint”

FF

2. The shaft assembly (consisting of welded pieces AB, ED and CD) is supported

by a thrust bearing at A and a radial bearing at B. The assembly is subjected to a

force at C and a couple . If it is known that the y component of the reaction

at bearing B is (N), determine the vector expressions of the force , couple

and the bearing reactions at A and B. Link ED lies in the yz plane. ED=250 mm.

F

M

j104

F

M

Radial Bearing

Thrust Bearing

Ax

Az

Ay

Bz

By

3. Under the action of the 40 N·m torque

applied to the vertical shaft, the

restraining cable AC limits the rotation of

the arm OA and attached shaft to an angle

of 60° measured from the y axis. The

collar D fastened to the shaft prevents

downward motion of the shaft in its

bearing. Calculate the bending moment

M, the compression P and the shear force

V in the shaft at section B. (Bending

moment, expressed as a vector, is normal

to the shaft axis and shear force is also

normal to the shaft axis.)

Bx Bz

By

My

Mx

T B

4. Structure ABCD is supported by a collar at D that can rotate and slide along bar EF which is

fixed and is frictionless. Structure ABCD makes contact with smooth surfaces at A and C

where normal direction to the surface at A lies in a plane that is parallel to the xy plane.

Force P is parallel to the y axis. If P=10 kN, determine the reactions at A, C and D. Note that

collar D acts like a wide radial bearing.

n

Dy

Dz

NC

NA

NAx NAy

My

Mz

5. Because of friction a very large force T is required to raise the 10 kg body when the cable

is wound around a fixed rough cylinder as shown. For the static equilibrium values shown,

determine all of the reactions at point O. The 0.3 m dimension refers to the point A where

the cable loses contact with the cylinder. Neglect the weight of the fixed cylinder.

6. Two rods are welded to form a T-shaped structure. The end D of the structure rests

against a frictionless vertical wall, while ends A and B are supported by radial bearings.

When a 600 N magnitude vertical force P is applied to the midpoint E of the part DC of the

structure, determine the reactions at D.

25 cm 15 cm

15 cm

40 cm

50 cm

50 cm

7. The uniform 900- by 1200-mm trap door has a mass of 200 kg and is propped open by the

light strut AB at the angle q=tan-1(3/4). Calculate the compression FB in the strut and the force

supported by the hinge D normal to the hinge axis. Assume that the hinges act at the extreme

ends of the lower edge.

z

y

x

W

Dz

Dy

Dx

FB Cz Cy

Cx

G W=200(9.81) N

8. The electric sander has a mass of 3 kg with

mass center at G and is held in a slightly tilted

position (z-axis vertical) so that the sanding

disk makes contact at its top with the surface

being sanded. The sander is gripped by its

handles at B and C. If the normal force R

against the disk is maintained at 20 N and is

due entirely to the force component Bx (i.e., Cx

= 0), and if the friction force F acting on the

disk is 60 percent of R, determine the

components of the couple M which must be

applied to the handle at C to hold the sander in

position. Assume that half of the weight is

supported at C.

Cy

Cz

29.43 N

My Mx

Mz

Nm.MNm.MNm.M

kMjMiM

k.k.i.

k.ik.j.i.

jik.i.

M

zyx

zyx

C

56241118571

0

432930040

71514203020040

122040120

0

N.CB

CBWF

NC

CF

NB

BF

N..W

CC

NFNR

zz

zzz

y

yy

x

xx

zx

71514

00

12

0120

20

0200

715142

8193

20

12100

602020