Chapter 2 Review of Forces and Moments - Brown University

2.4.6 Some short-cuts for drawing free body diagrams in systems containing components with
negligible mass
The safest procedure in solving any statics or dynamics problem is to set up and solve equations of
motion for every different part of the structure or machine. There are two particularly common structural
or machine elements that can be treated using short-cuts. These are (i) Two force members in a structure;
and (ii) A freely rotating wheel in a machine.
A Two-force member is a component or structural member that
1. is connected only to two ball-and socket type
joints (in 3D) or pin joints (in 2D).
2. has negligible weight
We’ve seen an example already in one of the Mickey
Mouse examples – it’s shown again in the picture to
remind you. Member BC is a two-force member,
because its weight is negligible, and it has only two
pin joints connecting it to other members. Member
AB is not a two-force member – partly because it’s
weight is not negligible, but also because Mickey
exerts a force on the member.
j
A
2L/3
L/3
Romeo, Romeo,
i
Pin joint
B
Pin joint
60 o
C
Pin joint
wherefore art thou
Romeo?
This is not a 2-force
member
This is a 2-force member
The following rules are very helpful
• Only one component of reaction force acts at the joints on a 2-force member
• The reaction force component acts along a line connecting the two joints.
It’s trivial to show this – if forces act on a body at only two points, and the body is in static equilibrium,
then the forces have to be equal and opposite, and must also act along the same line, to ensure that both
forces and moments are balanced.
A generic 2 force member is shown in the
figure. Note that a 2-force member
doesn’t have to be straight, though it often
is.
A
(3)
B
(2)
(3)
F AB
F AB
B
By convention, a positive reaction force is
normally taken to pull at each end of the
member, as shown. Equal and opposite
reaction forces must act on whatever is
connected to the two force member.
(1)
(1)
A
F AB
F AB
A
(2)