1. Problem 3.156 10 lb A couple of magnitude 30 lb
12 in
8 in
60o
45 lb
30 lb
10 lb
A couple of magnitude
M = 54 lb.in. and the three
forces shown are applied to
an angle bracket. (a) Find the
resultant of this system of
forces. (b) Locate the points
where the line of action of the
resultant intersects line AB
and line BC.

2. Solving Problems on Your Own
A couple of magnitude
M = 54 lb.in. and the three
forces shown are applied to
an angle bracket. (a) Find the
resultant of this system of
forces. (b) Locate the points
where the line of action of the
resultant intersects line AB
and line BC.
Problem M A B C
12 in
8 in
60o
45 lb
30 lb
10 lb
1. Determine the resultant of two or more forces. Determine the
rectangular components of each force. Adding these components
will yield the components of the resultant.

3. M, obtained by adding the moments about the point of the various
Solving Problems on Your Own
A couple of magnitude
M = 54 lb.in. and the three
forces shown are applied to
an angle bracket. (a) Find the
resultant of this system of
forces. (b) Locate the points
where the line of action of the
resultant intersects line AB
and line BC.
Problem M A B C
12 in
8 in
60o
45 lb
30 lb
10 lb
2. Reduce a force system to a force and a couple at a given point.
The force is the resultant R of the system obtained by adding the
various forces. The couple is the moment resultant of the system
M, obtained by adding the moments about the point of the various
forces.
R = S F M = S ( r x F )

4. Solving Problems on Your Own
A couple of magnitude
M = 54 lb.in. and the three
forces shown are applied to
an angle bracket. (a) Find the
resultant of this system of
forces. (b) Locate the points
where the line of action of the
resultant intersects line AB
and line BC.
Problem M A B C
12 in
8 in
60o
45 lb
30 lb
10 lb
3. Reduce a force and a couple at a given point to a single force.
The single force is obtained by moving the force until its moment
about the point (A) is equal to the couple vector MA. A position
vector r from the point, to any point on the line of action of the
single force R must satisfy the equation
r x R = MA R

5. S F : R = ( _ 10 j ) + (_ 45 i ) + ( 30 cos 60o i + 30 sin 60o j ) M A B C
12 in
8 in
60o
45 lb
30 lb
10 lb
Problem Solution
Determine the resultant of
two or more forces.
(a) Adding the components of the forces:
S F : R = ( _ 10 j ) + (_ 45 i ) + ( 30 cos 60o i + 30 sin 60o j )
= _ ( 30 lb ) i + ( lb ) j
R = 34.0 lb o

6. S MB : MB = ( 54 lb.in ) + ( 12 in )(10 lb) _ ( 8 in ) ( 45 lb) A B C
12 in
8 in
60o
45 lb
30 lb
10 lb
Problem Solution
Reduce a force system to
a force and a couple at a
given point.
(b) First reduce the given forces and couple to an equivalent
force-couple system (R, MB) at B. +
S MB : MB = ( 54 lb.in ) + ( 12 in )(10 lb) _ ( 8 in ) ( 45 lb)
= _ 186 lb.in

7. S MB : _ 186 lb.in = _ a ( 15.9808 lb) or a = 11.64 in and with R at E C a c R D E
Problem Solution
Reduce a force and a couple
at a given point to a single force.
With R at D:
S MB : _ 186 lb.in = _ a ( lb) or a = in
and with R at E
S MB : _ 186 lb.in = c ( 30 lb) or c = 6.20 in + +
The line of action of R intersects line AB in. to the left of B
and intersects line BC 6.20 in below B.