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
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2D Mickey Mouse problem 2 Mickey mouse <strong>of</strong> weight W<br />
M<br />
st<strong>and</strong>s on<br />
a balcony <strong>of</strong> weight W<br />
B<br />
as shown. The weight <strong>of</strong> strut CB may be<br />
neglected.<br />
This time we need to deal with a structure that has two parts<br />
connected by a joint (the strut BC is connected to the floor AB<br />
through a pin joint). In cases like this you have a choice <strong>of</strong> (a)<br />
treating the two parts together as a single system; or (b) considering<br />
the strut <strong>and</strong> floor as two separate systems. As an exercise, we will<br />
draw free body diagrams for both here.<br />
2L/3 L/3 Romeo, Romeo,<br />
wherefore art thou<br />
j<br />
Romeo?<br />
i<br />
A Pin joint<br />
B<br />
Pin joint<br />
60 o<br />
C<br />
Pin joint<br />
2L/3<br />
L/3<br />
A free body diagram for the balcony <strong>and</strong> strut together is shown on<br />
the right. Note again the convention used to denote the reactions:<br />
the first label denotes the location <strong>of</strong> the force, the second denotes<br />
the direction. Both A <strong>and</strong> C are pin joints, <strong>and</strong> therefore exert both<br />
horizontal <strong>and</strong> vertical forces.<br />
R Ax<br />
R Ay<br />
W B<br />
W M<br />
L/ 3<br />
A<br />
B<br />
R cx<br />
C<br />
The picture shows free body diagrams for both components. Note<br />
the convention we’ve introduced to deal with the reaction force<br />
acting at B – it’s important to use a systematic way to deal with<br />
forces exerted by one component in a system on another, or you<br />
can get hopelessly confused. The recommended procedure is<br />
1. Label the components with numbers – here the balcony is<br />
(1) <strong>and</strong> the strut is (2)<br />
2. Denote reaction forces acting between components with<br />
the following convention. In the symbol R<br />
(1/ 2)<br />
Bx<br />
, the<br />
superscript (1/2) denotes that the variable signifies the<br />
force exerted by component (1) on component (2) (it’s<br />
easy to remember that (1/2) is 1 on 2). The subscript Bx<br />
denotes that the force acts at B, <strong>and</strong> it acts in the positive<br />
x direction.<br />
3. The forces<br />
(1/ 2) (1/ 2)<br />
R<br />
Bx<br />
, R<br />
By<br />
exerted by component (1) on<br />
component (2) are drawn in the positive x <strong>and</strong> y directions on the free body diagram for<br />
component (2).<br />
4. The forces exerted by component (2) on component (1) are equal <strong>and</strong> opposite to<br />
(1/ 2)<br />
R<br />
Bx<br />
,<br />
(1/ 2)<br />
R<br />
By<br />
.<br />
They are therefore drawn in the negative x <strong>and</strong> y directions on the free body diagram for<br />
component (1). You need to think <strong>of</strong> the reaction force components as acting in two directions at<br />
the same time. This is confusing, but that’s the way life is.<br />
R cy<br />
2L/3<br />
L/3<br />
R Ax<br />
Ay<br />
A<br />
R<br />
(1)<br />
B<br />
R (1/2) Bx<br />
W B W M R (1/2) By<br />
R (1/2) Bx<br />
R (1/2) By<br />
(2)<br />
R cx<br />
L/ 3<br />
C<br />
R cy