1. Problem 3.154 The force P has a magnitude
of 250 N and is applied at the
end C of a 500 mm rod AC
attached to a bracket at A and
B. Assuming a = 30o and
b = 60o, replace P with (a) an
equivalent force-couple
system at B , (b) an equivalent
system formed by two parallel
forces applied at A and B. a b P C B A
200 mm
300 mm

2. Solving Problems on Your Owna b P C B A
200 mm
300 mm
The force P has a magnitude
of 250 N and is applied at the
end C of a 500 mm rod AC
attached to a bracket at A and
B. Assuming a = 30o and
b = 60o, replace P with (a) an
equivalent force-couple
system at B , (b) an equivalent
system formed by two parallel
forces applied at A and B.
1. Replace a force with an equivalent force-couple system at a
specified point. The force of the force-couple system is equal to
the original force, while the required couple vector is equal to the
moment of the original force about the given point.

3. S F : F = P or F = 250 N 60o S MB : M = _ (0.3 m)(250 N) = _75 N
Problem Solution a b P C B A
200 mm
300 mm
Replace a force with an equivalent
force-couple system at a specified
point.
(a) Equivalence requires:
S F : F = P or F = 250 N o
S MB : M = _ (0.3 m)(250 N) = _75 N
The equivalent force couple system at B is:
F = 250 N o, M = 75 N . m

4. (b) Require: The two force systems are equivalent.
Problem Solution a b P C B A
200 mm
300 mm
(b) Require: The two force systems are equivalent. B A C
60o
250 N
30o F FB FA x y =

5. S Fy : _250 = _ FA sin F _ FB sin F If FA = _ FB then _ 250 = 0 reject
Problem Solution B A C
60o
250 N
30o F FB FA x y =
Equivalence then requires:
S Fx : = FA cos F + FB cos F
FA = _ FB or cos F = 0
S Fy : _250 = _ FA sin F _ FB sin F
If FA = _ FB then _ 250 = reject
Consequently cos F = 0 or F = 90o and FA + FB = 250

6. S MB : _ (0.3 m)( 250 N) = (0.2 m) FA or FA = _ 375 N and FB = + 675 N
Problem Solution B A C
60o
250 N
30o x y C B = F A FB F FA
Also: +
S MB : _ (0.3 m)( 250 N) = (0.2 m) FA
or FA = _ 375 N
and FB = N
FA = 375 N o, FB = 625 N o