6161103 5.4 two and three-force members

1. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
5
Simplify some equilibrium problems by
recognizing embers that are subjected top only 2
or 3 forces
Two
-
Force Members
Two
-
Force Members
5
When a member is subject to
no couple moments and forces
are applied at only two points
on a member, the member is
called a two-force member

2. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Two-Force Members Example 5
Forces at A and B are summed to
obtain their respective resultants F
A
and
F
A
and
F
B
5
These two forces will maintain
translational and force equilibrium
provided F
A
is of equal magnitude
and opposite direction to F
B
5
Line of action of both forces is
known and passes through A and B

3. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Two-Force Members 5
Hence, only the force
magnitude must be determined
or stated or stated
5
Other examples of the two-
force members held in
equilibrium are shown in the
figures to the right

4. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Three-Force Members 5
If a member is subjected to only three forces, it i s
necessary that the forces be either concurrent or
parallel for the member to be in equilibrium parallel for the member to be in equilibrium
5
To show the concurrency
requirement, consider a body
with any two of the three forces
acting on it, to have line of
actions that intersect at point O

5. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Three-Force Members 5
To satisfy moment equilibrium about O, the third
force must also pass through O, which then
makes the force concurrent makes the force concurrent
5
If two of the three forces parallel,
the point of currency O, is
considered at “infinity”
5
Third force must parallel to
the other two forces to insect
at this “point”

6. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
5
Bucket link AB on the back
hoe is a typical example of a
two-force member since it is
pin connected at its end
provided its weight is provided its weight is neglected, no other force
acts on this member 5
The hydraulic cylinder is pin
connected at its ends, being
a two-force member

7. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
5
The boom ABD is subjected to the
weight of the suspended motor at D,
the forces of the hydraulic cylinder at
B, and the force of the pin at A. If the
boom’s weight is neglected, it is a boom’s weight is neglected, it is a three-force member
5
The dump bed of the truck operates
by extending the hydraulic cylinder
AB. If the weight of AB is neglected,
it is a two-force member since it is
pin-connected at its end points

8. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Example 5.13 The lever ABC is pin-supported
at A and connected to a short
link BD. If the weight of the link BD. If the weight of the members are negligible,
determine the force of the pin
on the lever at A.

9. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Solution FBD 5
Short link BD is a two-force
member, so the resultant
forces at pins D and B must be forces at pins D and B must be equal, opposite and collinear
5
Magnitude of the force is
unknown but line of action
known as it passes through B
and D
5
Lever ABC is a three-force
member

10. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Solution FBD 5
For moment equilibrium, three
non-parallel forces acting on it
must be concurrent at O must be concurrent at O
5
Force F on the lever at B is
equal but opposite to the force
F acting at B on the link
5
Distance CO must be 0.5m
since lines of action of Fand
the 400N force are known

11. 5.4 Two-and Three-Force
Members
5.4 Two-and Three-Force
Members
Solution Equations of
Equilibrium
3
.
60
4
.
0
7.0
tan
1
=


=
−o
θ
Solving,
kN
F
kN F
F F
F
N F F
F
A
A
y
A
x
32
.
1
07.1
0 45 sin 3. 60 sin
;0
0 400 45 cos 3. 60 cos
;0
3
.
60
4
.
0
tan
=
=
= −
= ∑↑+
= + −
= ∑→+
=


=
o o
o o
θ