Transcript Lecture 23 - 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: Chapter 1 to 4.5 inclusive 830am-945am Location: EN 2043, EN 1040, EN 2007, EN 1001, EN 1003 & EN 1054 • Seating arrangements http://www.engr.mun.ca/undergrad/schedule.php
2 © 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
Excluding “Reduction to a Wrench”
3 © 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
4 © 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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ENGI 1313 Statics I – Lecture 23
6
Recall – Particle Equilibrium (L10)
Concurrent Force Systems
+Y F 1 V = 0, v +X
2 Equations Solve for at most 2 Unknowns © 2007 S. Kenny, Ph.D., P.Eng.
F 3 F 2
F x
F y
0
0
ENGI 1313 Statics I – Lecture 23
Rigid Body Equilibrium
Forces are Typically not Concurrent Potential moment or couple moment
F x
F y
M o
0
0
0
7 © 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Recall – Particle FBD (L10)
+Y F AD A
F AB = 30
+X W = F AC = mg W = (255 kg)(9.806m/s 2 ) = 2.5kN
8 © 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Rigid Body FBD
What is it?
Sketch or diagram illustrating all external force and couple vectors acting on a rigid body or group of rigid bodies (system) Purpose?
A visual aid in developing equilibrium equation of motion
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ENGI 1313 Statics I – Lecture 23
Rigid Body FBD (cont.)
What is the procedure?
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
10 © 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
11 Drill Rig 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
12 Idealized Model © 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body FBD ENGI 1313 Statics I – Lecture 23
Support Reactions
Newton’s 3 rd Law External loads Support specific characteristics Translation prevented support reaction force Rotation prevented support couple moment
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ENGI 1313 Statics I – Lecture 23
Common Structural Supports
Cable
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ENGI 1313 Statics I – Lecture 23
Common Structural Supports (cont.)
Roller
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ENGI 1313 Statics I – Lecture 23
Common Structural Supports (cont.)
Pin
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ENGI 1313 Statics I – Lecture 23
Common Structural Supports (cont.)
Fixed
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ENGI 1313 Statics I – Lecture 23
Example 23-01
Foot Pedal FBD Spring force is 30 lb
Foot Pedal 18 Idealized Model © 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)
19 © 2007 S. Kenny, Ph.D., P.Eng.
F CB G B 30
20
W = 5000 lb Rigid Body FBD A y A x ENGI 1313 Statics I – Lecture 23
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 Answer: D
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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?
A) 2 forces and 1 couple moment B) 3 forces and 1 couple moment C) 3 forces D) 4 forces
A x F BD
Answer: C
A y 21 © 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 23
Example 23-03
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.
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ENGI 1313 Statics I – Lecture 23
Example 23-03 (cont.)
A x
,
A y
,
M A
effect of wall on beam.
N B
force of roller on beam.
w a
resultant force of distributed load on beam.
2
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ENGI 1313 Statics I – Lecture 23
w
40 lb ft
a
3 ft
b
4 ft 30 deg
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 has a mass M and center of mass at G. The tires are free to roll. Explain the significance of each force on the diagram.
Given:
M a b c g
5 Mg 0.3 m 0.75 m 1 m 9.81
m s 2
d
1.50 m
e
0.6 m
1
20 deg
2
30 deg
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ENGI 1313 Statics I – Lecture 23
Example 23-04 (cont.)
25
Given:
M
5 Mg
a
0.3 m
b
0.75 m
c
1 m
g
9.81
m s 2
d
1.50 m
e
0.6 m
1
20 deg
2
30 deg
© 2007 S. Kenny, Ph.D., P.Eng.
N A
,
N B
force of road on car.
F
force of cable on car.
Mg
force of gravity on car.
ENGI 1313 Statics I – Lecture 23
Textbook Problems 26 © 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 29 © 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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ENGI 1313 Statics I – Lecture 23