Transcript Introduction

General Equilibrium Problems
Equilibrium Conditions:
F  0
F  0
M  0
x
2D:
y
F  0
z
M  0
3D:
F
F
F
x
0
y
0
z
0
M
M
M
x
0
y
0
z
0
Problem Solving Procedure - Static
Equilibrium
• Draw Free Body Diagram
• Set up equations
• Solve equations
Free Body Diagram
• Decide which body or combination of bodies is to be
shown on the free-body diagram.
• Prepare a drawing or sketch of the outline of this isolated
or free body.
• Carefully trace around the boundary of the free body and
identify all the forces and moments.
• Choose the set of coordinate axes and indicated these
directions on the free-body diagram.
Reactions of Some Common Supports
Roller support
Pin connection
Built-in or fixed support
Hinge
Free-Body Diagram - Examples
Example 1.
P
O
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General Equilibrium - Examples
Example 1: The frame shown supports a part of the roof of a small
building. Knowing that the tension inside the cable is 150 KN,
determine the reactions at the fixed end E.
D
2.25m
A B
C
1.8m
3.75m
20KN
E F
7.2m
4.5m
General Equilibrium –Special Cases
Two-force member: a structural member that is subject to only two forces
F1
F2
Three-force member: a structural member that is subject to only there forces
F2
F1
F3
Example 2: A pin-connected two-bar frame is loaded and
supported as shown in the following figure. Determine
the reactions at supports A and B. The masses of the two
bars are negligible.
1.4m
1.6m
3m
C
3m
A
B
400N/m
Example 3: The device shown in the figure below is a crusher. With a
hand-force H applied as shown, a large force P can be developed onto
material within the enclosure resisting the block moving to the right. Find P
for a given H.
Example 4: In the following figure, find the reactions of (a) roller A onto
bar B1 and (b) roller B onto bar B2.