Engineering Fundamentals

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Engineering Fundamentals

• Session 9

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Equilibrium

• A body is in Equilibrium if it moves with
  constant velocity. A body at rest is a special
  case of constant velocity i.e. v 0 constant.
• For a body to be in Equilibrium the resultant
  force (meaning the vector addition of all the
  forces) acting on the body must be zero.
• Resulting force vector addition of force
  vectors
• A Force can be defined as 'that which tends to
  cause a particle to accelerate.

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Equilibrium of Concurrent Forces
Equilibrant E are equal and opposite to Resultant
R
E -R
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Particle Vs Rigid Body

• A particle has dimension 0
• A Rigid body is a non-particle body and it does
  not deform (change shape).

Concurrent forces all forces acting a the same
point
Coplanar forces all forces lie on the same plane
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Conditions for Equilibrium
Explanation Sum of forces 0, Or F1 F2
Fn 0
Example
F1 F2 F3 0
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Conditions for Equilibrium

• Breaking down into x and y components

Example For three forces acting on a particle
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Free Body Diagram

• Free body diagram isolates a rigid body to
  describe the system of forces acting on it.

R
R
mg
R
R
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Free Body Diagram
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Definitions

• System of Particles or BodiesTwo or more bodies
  or particles connected together are referred to
  as a system of bodies or particles.
• External Force External forces are all the
  forces acting on a body defined as a free body or
  free system of bodies, including the actions due
  to other bodies and the reactions due to
  supports.

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Transmissibility of Force
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Load and Reaction

• Loads are forces that are applied to bodies or
  systems of bodies.
• Reactions at points supporting bodies are a
  consequence of the loads applied to a body and
  the equilibrium of a body.

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Tensile and Compressive Forces

• Pushing force on the body -- compressive force
• Pulling force on a body -- a tensile force

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Procedure for drawing a free body diagram

• Step 1 Draw or sketch the body to be isolated
• Step 2 Indicate all the forces that act on the
  particle.
• Step 3 Label the forces with their proper
  magnitudes and directions

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Example 1
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Example 2
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Example 3
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Solution

• Resultant R of the two forces in two ropes

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Solution
Equilibrant E - R
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Solution
Resultant R is the sum of the actions of the tow
ropes on the barge
E - R
Equilibrant E is the reaction of the barge to the
ropes
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Moment and Couple

• Moment of Force
• Moment M of the force F about the point O is
  defined as M F dwhere d is the perpendicular
  distance from O to F
• Moment is directional

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Moment and Couple
Moment Force x Perpendicular Distance
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Resultant of a system of forces
An arbitrary body subjected to a number of forces
F1, F2 F3. Resultant R F1 F2
F3 ComponentsRx F1x F2x F3xRy F1y F2y
F3y
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Resultant Moment
Resultant moment Mo Sum of Moments Mo F1 l1
F2 l2 F3 l3 R l
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Couple

• For a Couple
• R ???F 0
• But Mo ? 0
• Mo F(dl) - Fl Fd
• Moment of couple is the same about every point
  in its plane

Mo F d
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Example 4

• Calculate the total (resultant) moment on the
  body.

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Example 4 (Solution)

• Taking moments about the corner A
• Note that the forces form two couples or pure
  moments 3.6 Nm and 3.0 Nm (resultant force 0,
  moment is the same about any point).

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F 10 N
Exercise
d 3 m
A
1. What is the moment of the 10 N force about
point A (MA)? A) 10 Nm B) 30 Nm
C) 13 Nm D) (10/3) Nm E) 7 Nm
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APPLICATIONS
What is the net effect of the two forces on the
wheel?
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APPLICATIONS
What is the effect of the 30 N force on the lug
nut?
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MOMENT IN 2-D
The moment of a force about a point provides a
measure of the tendency for rotation (sometimes
called a torque).
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Moment
F100
_____________
M
L20
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Moment
F32N
L50cm
L300mm

M27.5N
F55N

M-9.6N
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EXAMPLE 1
Given A 400 N force is applied to the frame and
? 20. Find The moment of the force at
A. Plan
1) Resolve the force along x and y axes. 2)
Determine MA using scalar analysis.
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EXAMPLE 1
Solution ? Fx -400 cos 20 N ? Fy
-400 sin 20 N MA (400 cos 20)(2)
(400 sin 20)(3) Nm 1160 Nm
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GROUP PROBLEM SOLVING
Given A 40 N force is applied to the wrench.
Find The moment of the force at O.
Plan 1) Resolve the force along x and y axes.
2) Determine MO using scalar analysis.