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Engineering Mechanics
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Engineering Mechanics
Lecture 4 & 5
EQUILIBRIUM
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Equilibrium When a body is in equilibrium, the resultant of all forces acting
on it is zero.
Mechanical System
A body or group of bodies which can be conceptually isolated from all other bodies.
Free-Body Diagram: The diagram shows all forces applied to the system by mechanical
contact with other bodies.
The free-body diagram is the most important single step in the solution of problems in mechanics
0.R F 0.M M
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Modeling The Action of Forces
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Modeling The Action of Forces
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Modeling The Action of Forces
Engineering Mechanics5
Lecture 4 & 5
Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Modeling The Action of Forces
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Free-Body Diagram Construction of Free-Body Diagrams
Decide which system to isolate.
Isolate the chosen system by drawing a diagram which represents its complete external boundary
Identify all forces which act on the isolated system as applied by the removed contacting & represent them in their proper positions on the diagram of the isolated system
Show the choice of coordinate axes directly on the diagram.
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Example of Free-Body Diagram
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Example of Free-Body Diagram
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Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
Exercises on Free-Body Diagram
Engineering Mechanics10
Engr.Muhammad Umar FarooqLecture 4 & 5
Equilibrium in Two Dimension0.XF 0.M 0.YF
Engineering Mechanics11
Lecture 4 & 5
Engr.Muhammad Umar FarooqEngineering Mechanics
Equilibrium-Applications Example 1
Determine the magnitudes of the forces C & T.
0.XF 8 cos40 sin 20 16 0o oT C
0.766 0.342 8T C
0.YF sin 40 cos20 3 0o oT C
0.643 0.940 3T C
9.09T kN3.03C kN
16kN 8kN40o
T
C
3kN
. . .F B D
20o
Lecture 4 & 512
Engr.Muhammad Umar FarooqEngineering Mechanics
Equilibrium-Applications Example 2
A 3m ladder rests against a smooth wall. The ladder weighs 10kg. A 90kg man stand on it. Find the reaction
0.XF
0.YF
0.M
1 10 90 0R 1 100R kg
2 0F R
2F R
2 65R kg65F kg
210 1.5cos60 90 2cos60 3cos60 0R
Lecture 4 & 513
Engr.Muhammad Umar FarooqEngineering Mechanics
Equilibrium-Applications Example 3
Determine the tension T in the cable. Pulleys is free to rotate about its bearing. Neglect the weight of all pulleys
Pulley A
Pulley B
0.M 1 2 0T r T r
1 2T T
0.YF 1 2 1000 0T T
1 2 500T T lb
3 4 2 / 2 250T T T lb
3 250T T lb
Lecture 4 & 514
Engr.Muhammad Umar FarooqEngineering Mechanics
Equilibrium-Applications Example 4
Determine the magnitude T of the tension cable and the pin reaction. The beam weights 95kg per meter of length
0.AM ( cos25 )0.25 ( sin 25 )(5 0.12)o oT T
10(5 1.5 0.12) 4.66(2.5 0.12) 0 19.61T kN
0XF 19.61cos25 0o
XA 17.77XA kN
0YF 19.61sin 25 4.66 10 0o
YA
6.37YA kN
Lecture 4 & 515
Engr.Muhammad Umar FarooqEngineering Mechanics
Equilibrium-Applications Example 5
Find the reaction at support A & B 10kN
6m
A B3m
10kN
F.B.D. RYBRYA
RXA
0XF
0YF
0XAR
10 0YA YBR R
0AM 6 10 3 0YBR
5YBR kN
5YAR kN
Lecture 4 & 516
Engr.Muhammad Umar FarooqEngineering Mechanics
Equilibrium-Applications Example 6
Find the reaction at support A & B
0AM
0XF
0YF
1cos45 0oXAR
2.24 3 1sin 45 0oYAR
9 1sin 45 3 3 6 0oYBR
2.24YBR kN
1.47YAR kN
3kN
A B
3m3m3m
45o
1kN
F.B.D. RYBRYA
RXA
3kN
45o
1kN
0.707XAR kN
Lecture 4 & 517
Engr.Muhammad Umar FarooqEngineering Mechanics
Distributed load to concentrated load 2.52 = 5kN
Equilibrium-Applications Example 7
Find the reaction at support A & B
0AM
0XF
0YF 5.17 5 0YAR
6 5 5 6 0YBR
5.17YBR kN
0.17YAR kN
0.XAR
2.5kN/m
A B
2m2m2m
6kN.m
2.5kN/m
F.B.D.RYBRYA
RXA
6kN.m
5kN
Lecture 4 & 518
Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics
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Discussions
Any Question?
HomeworkQ3.1, Q3.3, Q3.6, Q3.7, Q3.11, Q3.13, Q3.15, Q3.17,
Q3.20, Q3.25, Q3.30, Q3.37. Q3.53 (page # 130 to 143)Submit in first 15 minutes of next lecture
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