1. Problem 4-b 4 in 4 in 20 lb 40 lb The T-shaped bracket shown is
supported by a small wheel at E
and pegs at C and D. Neglecting
the effect of friction, determine
the reactions at C , D , and E
when q = 30o. A B
2 in C D
3 in
3 in E q

2. 4 in
4 in
Solving Problems on Your Own
The T-shaped bracket shown is
supported by a small wheel at E
and pegs at C and D. Neglecting
the effect of friction, determine
the reactions at C , D , and E
when q = 30o.
Problem 4-b
20 lb
40 lb A B
2 in C D
3 in
3 in E q
1. Draw a free-body diagram of the body. This diagram shows
the body and all the forces acting on it.

3. 4 in
4 in
Solving Problems on Your Own
The T-shaped bracket shown is
supported by a small wheel at E
and pegs at C and D. Neglecting
the effect of friction, determine
the reactions at C , D , and E
when q = 30o.
Problem 4-b
20 lb
40 lb A B
2 in C D
3 in
3 in E q
2. Write equilibrium equations and solve for the unknowns.
For two-dimensional structure the three equations might be:
SFx = SFy = SMO = 0
where O is an arbitrary point in the plane of the structure
or SFx = SMA = 0 SMB = 0
where point B is such that line AB is not parallel to the y axis
or SMA = 0 SMB = 0 SMC = 0
where the points A, B , and C do not lie in a straight line.

4. Draw a free-body diagram of the body. 2 in C D 3 in 4 in 4 in 3 in E
Problem 4-b Solution
20 lb
40 lb A B
Draw a free-body diagram of the body.
2 in C D
3 in
4 in
4 in
3 in E
20 lb
40 lb q A B C
2 in C D
3 in D
3 in E E
30o

5. + S Fy = 0: E cos 30o _ 20 _ 40 = 0 E = = 69.28 lb 60 lb
4 in
4 in
Problem 4-b Solution
20 lb
40 lb A B C
2 in
Write equilibrium equations and
solve for the unknowns. C D
3 in D
3 in E E
30o
+ S Fy = 0: E cos 30o _ 20 _ 40 = 0
E = = lb
E = 69.3 lb o
60 lb
cos 30o

6. ( 20 lb)( 4 in) _ ( 40 lb)( 4 in) _ C ( 3 in) + E sin 30o ( 3 in) = 0
Problem 4-b Solution
20 lb
40 lb A B C
2 in C D
3 in D
3 in E E
+ S MD = 0:
( 20 lb)( 4 in) _ ( 40 lb)( 4 in) _ C ( 3 in) + E sin 30o ( 3 in) = 0
_ 80 _ 3C ( 0.5 )( 3 ) = 0
C = lb C = 7.97 lb
30o

7. 4 in
4 in
Problem 4-b Solution
20 lb
40 lb A B C
2 in C
+ S Fx= 0:
E sin 30o + C _ D = 0
( lb )( 0.5 ) lb _ D = 0
D = 42.6 lb D
3 in D
3 in E E
30o