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