Equilibrium is a state of a body when at rest or moving

in a straight line with constant velocity. In terms of

force systems, equilibrium occurs when the resultant of all forces acting on a body is zero.

Mathematically, equilibrium is interpreted to have

the following conditions:

(for coplanar equilibrium)

Free Body Diagram (FBD)

A sketch of an object or part of it, completely isolated from all other

objects with which it is in contact

and showing all external forces

(including the dimensions) exerted

by the adjacent bodies.

Here are some supports and their corresponding effects of free-body diagram.

Example 1: A 600lb load is supported by a cable which runs over a

pulley and is fastened to the bar DE. Draw a Free-Body Diagram of bars AC and DE and of the pulley.

Assume all hinges

to be smooth and

neglect the weight

of each bar and

of the pulley.

600lb

D

B

C

A

E

4ft

8ft 8ft

6ft

10ft

Example 2: Draw a Free-Body

Diagram of pulleys E

and D and of the bar AD

shown in the figure.

Assume all hinges to be

smooth and neglect the

weight of each bar and

of the pulleys.

A

E

B

D

F 100lb

100lb

8ft

8ft

30○

60○

120○

Tu

torial C

ircle

Example 3: The uniform rod weighs 420 lb and has its center of

gravity at G. (a) Draw a Free-Body

Diagram of the rod

and determine the

(b) Tension on the

cable and (c) Reactions

at the contact surfaces.

Neglect the thickness of the

rod and assume all

contact surfaces to

be smooth.

Example 4: The cylinder C weighs 1000lb. (a) Draw a Free-body

diagram of cylinder C and of rod AB and determine.

the (b) Tension on the cable and

the (c) Reactions at hinge A.

Assume all contact

surfaces to be smooth. D

B

E

A

C

5ft

3ft

Tu

torial C

ircle

45○

30○ F

Example 5: A cylinder weighing 400 lb is held against a smooth

incline by means of the weightless rod AB in the Figure shown. Determine P (resultant of reactions at B) and N (normal pressure) exerted on the cylinder.

A

B

25○ 35○

Example 6: The figure represents the concurrent force system

acting at a joint of a bridge truss. Determine the value of C and E to maintain equilibrium. (Using the

rotated axes method)

60○

60○

45○

E

C

400 lb 200 lb

300 lb

Example 7: A 300lb box is held at rest on a smooth plane by a force

P inclined at an angle θ with the plane as shown in the figure. If θ = 45, determine the value of P and the normal pressure N exerted by the plane

30○

θ

p

W=300lb

Tutorial Circle

Example 8: Determine the value of the angles α and θ

so that the forces shown will be in equilibrium.

α

θ

20N

40N

30N

Example 9: Three cylinders as shown with corresponding radii,

find the reaction between the walls of cylinders A and B.

r=7m

40N

20N

1m 2m

A B

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Example 10: The cylinders in the figure

below have the indicated weights of 400 lbs and

200 lbs, respectively.

Assuming smooth contact surfaces, (a) Draw the

free-body diagram of the

two cylinder and (b)

Determine the reactions

at F, A, M and S on the

cylinders

Example 11: In the figure below, the bar AB carries a 500 N box. (a)

Draw the Free-body Diagram of the bar and determine (b) the tension in the cord, and (c) the resultant reaction of the hinge at A for equilibrium.

Example 12: The Fink truss shown in the figure below is supported

by a roller at A and a hinge at B. The given loads are normal to the inclined member. Determine the reactions at A and B. (Hint: Replace the loads by their resultant).

Example 13: A bar FM is in

equilibrium under

the action of the

five forces shown

in the figure.

Determine P, R,

and T.

Example 14: Determine the amount and direction of the smallest

force P required to start the wheel over the block. What is the reaction of the block?

Example 15: A 12-ft bar of negligible weight rests in a horizontal

position on the smooth plane shown.

Compute the distance x at which load T=100lb should be placed from point B to keep the bar horizontal.

Q W=20tons

P

Example 16: The weight W of a travelling crane is 20 tons acting as shown. To prevent the crane from tipping to the right when carrying a load P of 20 tons, a counterweight Q is used. Determine the value and position of Q So that the crane will remain in equilibrium both when the maximum load P is applied and when the load P is removed.

Tutorial Circle

x 5ft 9ft 1ft

Example 17: Determine the support reactions.

A B

3m 1m 1m

10KN/m

25KN/m

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Example 18: Determine the external support reactions

(A,B, and C).

A B

C

1m 1m 2m 3m

D

5KN/m

6KN

10KN/m

Tutorial Circle

Example 19: Determine the external support reactions

A B

D

1m 1m 2m 2m

C

100 N/m

400 N/m

1m

Example 20: The truss shown in the figure is supported by a hinged

at A and a roller at B. A load of 2000lb is applied at C. Determine the reactions at A and B.

A

B

C D 10ft

10ft

2000lb

30ft

5ft

30○

Example 21: The truss in the figure below is supported by a roller at

A and a hinge at B. Find the values of the

reactions.

A B

θ=30

1200 lb

1000 lb 1000 lb 1000 lb

1500 lb

15ft

60ft

Example 22: The truss shown in the figure is supported on roller at

A and hinge at B. Solve for the components of the reactions.

Example 23: Compute the total reactions at A and B on the truss

shown.

Example 24: Compute the total reactions at A and B for the truss

shown in the figure below.