ENGI 1313 Mechanics I - Faculty of Engineering and Applied Science
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Transcript ENGI 1313 Mechanics I - Faculty of Engineering and Applied Science
ENGI 1313 Mechanics I
Lecture 23:
Equilibrium of a Rigid Body
Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]
Mid-Term
Thursday October 18
Material:
Time:
Location:
Chapter 1 to 4.5 inclusive
830am-945am
EN 2043, EN 1040, EN 2007,
EN 1001, EN 1003 & EN 1054
• Seating arrangements
http://www.engr.mun.ca/undergrad/schedule.php
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Quiz #4
Week of October 22-26
Section 4.6 through 4.10
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Excluding “Reduction to a Wrench”
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Chapter 5 Objectives
to develop the equations of equilibrium for
a rigid body
to introduce the concept of the free-body
diagram for a rigid body
to show how to solve rigid body
equilibrium problems using the equations
of equilibrium
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Lecture 23 Objectives
to identify support reactions
to establish the free-body diagram for a
rigid body in 2-D
to develop the equations of equilibrium for
a 2-D rigid body
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Recall – Particle Equilibrium (L10)
Concurrent Force Systems
+Y
V = 0, v
F1
+X
F3
F2
2 Equations
Solve for at most 2 Unknowns
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© 2007 S. Kenny, Ph.D., P.Eng.
F 0
F 0
x
y
ENGI 1313 Statics I – Lecture 23
Rigid Body Equilibrium
Forces are Typically not Concurrent
Potential moment or couple moment
F
F
M
x
0
y
0
o
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© 2007 S. Kenny, Ph.D., P.Eng.
0
ENGI 1313 Statics I – Lecture 23
Recall – Particle FBD (L10)
+Y
FAB
A
= 30
FAD
+X
W = FAC = mg
W = (255 kg)(9.806m/s2) = 2.5kN
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Rigid Body FBD
What is it?
Purpose?
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Sketch or diagram illustrating all external
force and couple vectors acting on a rigid
body or group of rigid bodies (system)
A visual aid in developing equilibrium equation
of motion
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Rigid Body FBD (cont.)
What is the procedure?
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Draw isolated or “free” outlined shape
• Establish idealized model
• Establish FBD
Show all forces and couple moments
• External applied loads
• Rigid body self-weight
• Support reactions
Characterize each force and couple
• Magnitude
• Sense
• Direction
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Rigid Body FBD (cont.)
Drilling Rig
200 kg suspended platform on derrick tower
Drill Rig
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Idealized Model
© 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body FBD
ENGI 1313 Statics I – Lecture 23
Rigid Body FBD (cont.)
Cantilever Beam
100 kg beam
Idealized Model
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© 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body FBD
ENGI 1313 Statics I – Lecture 23
Support Reactions
Newton’s 3rd Law
External loads
Support specific characteristics
Translation prevented
support reaction force
Rotation prevented
support couple moment
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Common Structural Supports
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Cable
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Common Structural Supports (cont.)
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Roller
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Common Structural Supports (cont.)
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Pin
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Common Structural Supports (cont.)
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Fixed
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Example 23-01
Foot Pedal FBD
Spring force is 30 lb
Foot Pedal
Idealized Model
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© 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body FBD
ENGI 1313 Statics I – Lecture 23
Example 23-02
Dump Truck FBD
5000 lb dumpster supported by a pin at A and
the hydraulic cylinder BC (short link)
B
FCB
30
G
20
W = 5000 lb
Rigid Body FBD
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Ax
Ay
Comprehension Quiz 23-01
Internal forces are _________ shown on
the free body diagram of a whole body.
A) always
B) often
C) rarely
D) never
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Answer: D
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Comprehension Quiz 23-02
The beam and the cable (with a frictionless
pulley at D) support an 80 kg load at C. In a
FBD of only the beam, there are how many
unknowns?
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A) 2 forces and 1 couple moment
B) 3 forces and 1 couple moment
C) 3 forces
Ax
D) 4 forces
Answer: C
© 2007 S. Kenny, Ph.D., P.Eng.
FBD
Ay
ENGI 1313 Statics I – Lecture 23
Example 23-03
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Draw the free-body
diagram of the beam
supported at A by a
fixed support and at
B by a roller. Explain
the significance of
each force on the
diagram.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Example 23-03 (cont.)
w 40
lb
ft
a 3 ft
b 4 ft
30 deg
Ax, Ay, MA effect of wall on beam.
NB force of roller on beam.
wa
resultant force of distributed load on beam.
2
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Example 23-04
Draw the free-body
diagram of the
automobile, which is
being towed at
constant velocity up the
incline using the cable
at C. The automobile Given:
M 5 Mg
has a mass M and
center of mass at G.
a 0.3 m
The tires are free to
b 0.75 m
roll. Explain the
c 1m
significance of each
m
g 9.81
force on the diagram.
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d 1.50 m
e 0.6 m
1 20 deg
2 30 deg
s
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Example 23-04 (cont.)
Given:
M 5 Mg
d 1.50 m
a 0.3 m
e 0.6 m
b 0.75 m
1 20 deg
2 30 deg
c 1m
g 9.81
m
s
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NA, NB force of road on car.
F force of cable on car.
Mg force of gravity on car.
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Textbook
Problems
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Textbook
Problems
27
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Textbook
Problems
28
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Textbook
Problems
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
References
Hibbeler (2007)
http://wps.prenhall.com/esm_hibbeler_eng
mech_1
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23