1. Problem 4-a P The semicircular rod ABCD is a
maintained in equilibrium by
the small wheel at D and the
rollers at B and C. Knowing
that a = 45o, determine the
reactions at B , C , and D.

2. Solving Problems on Your Own
The semicircular rod ABCD is
maintained in equilibrium by
the small wheel at D and the
rollers at B and C. Knowing
that a = 45o, determine the
reactions at B , C , and D.
Problem 4-a P a A O D
45o
45o B C
1. Draw a free-body diagram of the body. This diagram shows
the body and all the forces acting on it.

3. Solving Problems on Your Own
The semicircular rod ABCD is
maintained in equilibrium by
the small wheel at D and the
rollers at B and C. Knowing
that a = 45o, determine the
reactions at B , C , and D.
Problem 4-a P
45o O D C A B a
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.
Problem 4-a Solution P
45o O D C A B a
Draw a free-body diagram
of the body.
45o O D C A B
P sina
P cosa R
C/ 2
B/ 2 P

5. + S Fx = 0: P cosa + B/ 2 _ C / 2 = 0 (2)
Problem 4-a Solution
45o O D C A B
P sina
P cosa R
C/ 2
B/ 2 P
Write three equilibrium
equations and solve
for the unknowns.
+ S MO = 0: (P sina) R _ D (R) = D = P sina (1)
+ S Fx = 0: P cosa + B/ 2 _ C / 2 = (2)
+ S Fy = 0: _P sina + B/ C / 2 _ P sina = 0
_2P sina + B/ C / 2 = (3)

6. (2) + (3) P(cosa _ 2sina) + 2 B/ 2 = 0 B = (2sina _ cosa) P (4) D C A B
P sina
P cosa R
C/ 2
B/ 2
Problem 4-a Solution P
(2) + (3) P(cosa _ 2sina) + 2 B/ 2 = 0
B = (2sina _ cosa) P (4)
(2) _ (3) P(cosa + 2sina) _ 2 C/ 2 = 0
C = (2sina + cosa) P (5) 2 2

7. 45o O D C A B
P sina
P cosa R
C/ 2
B/ 2
Problem 4-a Solution P
For a = 45o
sina = cosa = 1/ 2 2 2 2 1 1 2 1 2
EQ. (4) : B = ( _ ) P = P ; B = P o
EQ. (5) : C = ( _ ) P = P ; C = P o
EQ. (1) : D = P/ D = P/ 2 2 2 2 1 3 2 3 2