ME101 (Division III) webpage Notes/ME101-Lecture04-KD.pdf · 2015-02-09 · (c) a single force or resultant Solution: a)Compute the resultant force for the forces shown and the resultant

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ME101 (Division III) webpage

Equivalent Systems: Resultants

Equilibrium

Equilibrium of a body is a condition in which the

resultants of all forces acting on the body is zero.

Condition studied in Statics

When the resultant of all forces on a body is not

zero, acceleration of the body is obtained by

equating the force resultant to the product of the

mass and acceleration of the body.

Condition studied in Dynamics

2ME101 - Division III Kaustubh Dasgupta

Equivalent Systems: Resultants

Vector Approach: Principle of Transmissibility can be used

Magnitude and direction of the resultant force R is obtained by

forming the force polygon where the forces are added head to

tail in any sequence


Resultant of Concurrent Forces

• Two dimensional plane


Equivalent Force and Couple

• Two dimensional plane

• Three dimensional space


Resultant of Two Couples


M = M1 + M2

Resultant of Force System:: 3D

• Three dimensional space


Equivalent

force-couple

systems for

each force

Resultant

equivalent

force-couple

system

Wrench Action

• Coincidence of resultant R and M axes

Positive Wrench Negative Wrench


Wrench Action

• Wrench action or Screw Driver action


Positive Wrench

Replacement of force system by wrench


Resolve M into components

Resolve M2 into a couple Resultant Wrench

For the beam, reduce the

system of forces shown to

(a) an equivalent force-

couple system at A,

(b) an equivalent force

couple system at B, and

(c) a single force or resultant

Solution:

a)Compute the resultant force for

the forces shown and the

resultant couple for the moments

of the forces about A.

b)Find an equivalent force-couple

system at B based on the

force-couple system at A.

c) Determine the point of

application for the resultant

force such that its moment

about A is equal to the

resultant couple at A.

Example on Equivalent System


SOLUTION:

a) Compute the resultant force and the

resultant couple at A.

jjjj

FR

N 250N 100N 600N 150

jR

N600

ji

jiji

FrM R

A

2508.4

1008.26006.1

kM R

A

mN 1880



b) Find an equivalent force-couple system at

B based on the force-couple system at A.

The force is unchanged by the movement

of the force-couple system from A to B.

jR

N 600

The couple at B is equal to the moment

about B of the force-couple system found

at A.

kk

jik

RrMM AB

R

A

R

B

mN 2880mN 1880

N 600m 8.4mN 1880

kM R

B

mN 1000



c)

FR = F1 + F2 + F3 + F4

R = 150-600+100-250 = -650 N

FRd = F1d1 + F2d2 + F3d3 + F4d4

d = 3.13 m


R

d


Example on resultant of a force system

• Determine the resultant of the system of parallel forces

acting on the plate. Solve with a vector approach.


Example on resultant of a force system


Example on Wrench

• Replace the two forces and the negative wrench by a

single force R applied at A and the corresponding

couple M.


Example on Wrench


Example on Wrench


Example on Wrench


Rigid Body Equilibrium

A rigid body will remain in equilibrium provided

• sum of all the external forces acting on the body is

equal to zero, and

• Sum of the moments of the external forces about a

point is equal to zero

x

y

z



Space Diagram: A sketch

showing the physical conditions

of the problem.

Free-Body Diagram: A sketch

showing only the forces on the

selected particle.

Free-Body Diagrams



Support Reactions

Prevention of

Translation or

Rotation of a body

Restraints



Various Supports

2-D Force Systems


Documents

ME101 (Division III) webpage Notes/ME101-Lecture04-KD.pdf · 2015-02-09 · (c) a single force or resultant Solution: a)Compute the resultant force for the forces shown and the resultant