Lec 04 & 5

Engr.Muhammad Umar FarooqLecture 4 & 5 Engineering Mechanics

Engineering Mechanics

Lecture 4 & 5

EQUILIBRIUM

1


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

2


Modeling The Action of Forces

3



4



Engineering Mechanics5

Lecture 4 & 5



6


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.

7


Example of Free-Body Diagram

8


Example of Free-Body Diagram

9


Exercises on Free-Body Diagram


Engr.Muhammad Umar FarooqLecture 4 & 5

Equilibrium in Two Dimension0.XF 0.M 0.YF


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



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



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



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



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



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


Distributed load to concentrated load 2.52 = 5kN


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


19

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

Documents

Lec 04 & 5