Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected] ENGI 1313 Mechanics I Lecture 23: Equilibrium of a Rigid Body
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Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of [email protected]
ENGI 1313 Mechanics I
Lecture 23: Equilibrium of a Rigid Body
2 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Mid-Term
Thursday October 18Material: Chapter 1 to 4.5 inclusiveTime: 830am-945amLocation: EN 2043, EN 1040, EN 2007,
EN 1001, EN 1003 & EN 1054• Seating arrangements
http://www.engr.mun.ca/undergrad/schedule.php
3 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Quiz #4
Week of October 22-26Section 4.6 through 4.10
Excluding “Reduction to a Wrench”
4 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Chapter 5 Objectives
to develop the equations of equilibrium for a rigid bodyto introduce the concept of the free-body diagram for a rigid bodyto show how to solve rigid body equilibrium problems using the equations of equilibrium
5 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Lecture 23 Objectives
to identify support reactionsto establish the free-body diagram for a rigid body in 2-Dto develop the equations of equilibrium for a 2-D rigid body
6 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Recall – Particle Equilibrium (L10)
Concurrent Force Systems
F1
F2
F3
V = 0, v+Y
+X
∑ =→+ 0Fx
∑ =↑+ 0Fy
2 Equations ∴ Solve for at most 2 Unknowns
7 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body Equilibrium
Forces are Typically not ConcurrentPotential moment or couple moment
∑ =→+ 0Fx
∑ =↑+ 0Fy
∑ = 0Mo
8 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Recall – Particle FBD (L10)
+Y
+X θ = 30°
FAB
W = FAC = mg
FAD
W = (255 kg)(9.806m/s2) = 2.5kN
A
9 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
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
10 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
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
11 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body FBD (cont.)
Drilling Rig200 kg suspended platform on derrick tower
Drill Rig Idealized Model Rigid Body FBD
12 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Rigid Body FBD (cont.)
Cantilever Beam100 kg beam
Idealized Model Rigid Body FBD
13 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Support Reactions
Newton’s 3rd LawExternal loadsSupport specific characteristicsTranslation prevented
⇒ support reaction forceRotation prevented
⇒ support couple moment
14 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Common Structural Supports
Cable
15 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Common Structural Supports (cont.)
Roller
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Common Structural Supports (cont.)
Pin
17 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Common Structural Supports (cont.)
Fixed
18 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Example 23-01
Foot Pedal FBDSpring force is 30 lb
Foot Pedal
Idealized Model Rigid Body FBD
19 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Example 23-02
Dump Truck FBD5000 lb dumpster supported by a pin at A and the hydraulic cylinder BC (short link)
G
W = 5000 lb
20°30°
B
FCB
Ay
Ax
Rigid Body FBD
20 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Comprehension Quiz 23-01
Internal forces are _________ shown on the free body diagram of a whole body.
A) alwaysB) oftenC) rarelyD) never
Answer: D
21 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Comprehension Quiz 23-02The 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 momentB) 3 forces and 1 couple momentC) 3 forcesD) 4 forces
Answer: C Ay
Ax
FBD
22 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
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.
23 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Example 23-03 (cont.)w 40
lbft
=
a 3 ft=
b 4 ft=
θ 30 deg=
Ax, Ay, MA effect of wall on beam.
NB force of roller on beam.
wa2
resultant force of distributed load on beam.
24 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Example 23-04Draw 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 5 Mg= d 1.50 m=
a 0.3 m= e 0.6 m=
b 0.75 m= θ1 20 deg=
c 1 m= θ2 30 deg=
g 9.81m
s2=
25 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Example 23-04 (cont.)
Given:
M 5 Mg= d 1.50 m=
a 0.3 m= e 0.6 m=
b 0.75 m= θ1 20 deg=
c 1 m= θ2 30 deg=
g 9.81m
s2=
NA, NB force of road on car.F force of cable on car.Mg force of gravity on car.
26 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Textbook Problems
27 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Textbook Problems
28 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Textbook Problems
29 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
Textbook Problems
30 ENGI 1313 Statics I – Lecture 23© 2007 S. Kenny, Ph.D., P.Eng.
References
Hibbeler (2007)http://wps.prenhall.com/esm_hibbeler_engmech_1
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