1.3 Stress & Strain Relationship of Hooke’s Law.ppt
1. UNIT 1.3
Stress & Strain Relationship of Hooke’s Law,
Elastic Moduli, Stress–Strain Diagram
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2. Restoring force or recovering force per unit area is
called stress.
Stress is expressed in or Pascal.
Types of Stress
•Normal stress
•Tangential stress
-2
Nm
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Stress
Restoringforce F
Stress= =
Area A
3. Canyon Bridge, Los Alamos, NM
o
s =
F
A
Simple compression
Here compressive
structure member
(s < 0 here).
OTHER COMMON STRESS STATES
Ao
Balanced Rock, Arches
National Park
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4. Ratio of the change in dimension produced by an external force
to its original dimension is known as strain.
Strain
Change in volume
Volumetric strain=
Original volume
Change in length
Longitudinal strain=
Original length
Shearing strain=Angular displacement of the plane
perpendicular to the fixed surface
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5. Stress and Strain
Stress refers to the cause of a deformation, and strain
refers to the effect of the deformation.
stress is the force
strain is the elongation
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The downward force F
causes the displacement x
6. Types of Modulus
1. Young’s Modulus (Y)
2. Bulk Modulus (K)
3. Rigidity Modulus (n)
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7. Longitudinal Stress and Strain
L
DL
A
A
F
For wires, rods, and bars, there is
a longitudinal stress F/A that
produces a change in length per
unit length. In such cases:
F
Stress
A
=
L
Strain
L
D
=
Young’s Modulus
'
longitudinal stress
Young s modulus
longitudinal strain
=
/
/
F A FL
Y
L L A L
= =
D D
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8. Shearing Stress and Shearing Strain
A
F
F
f
l
d
A shearing stress alters only the shape of the body, leaving the
volume unchanged.
F
F
f
l
d A
F
Stress
A
=
The strain is the angle expressed in radians
d
Strain
l
f
= =
Shearing Modulus
The shearing modulus
Units are in Pascal.
F A
S
f
=
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F
9. Bulk Modulus
Volume stress F A
K
Volume strain V V
= =
D
Since F/A is generally pressure P, we may write:
/
P PV
K
V V V
= =
D D
Unit is Pascal
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10. • When a spring is
stretched, there is a
restoring force that is
proportional to the
displacement.
• Within the elastic limit,
the ratio of the stress to
the strain is constant (E).
• E is the modulus of
elasticity.
Hooke’s Law
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2
Stress strain
Stress E Strain
Stress
E Nm
Strain
=
=
11. Poisson’s Ratio (σ)
Lateral strain
σ = ------------------------------- =
Longitudinal strain
β
= a constant
α
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l
d
F
D
12. Department of Physics
Elastic Limit
Maximum stress a body can experience without
becoming permanently deformed.
Fatigue
If a body is continuously subjected to Stress or Strain, it
gets fatigued (weak), called Elastic Fatigue.
13. 10 m steel wire stretches 3.08 mm due to the 200 N load.
What is the longitudinal strain?
Srain
3
Data Given :
L 10m; L 3.08 10 m
= =
-3
ΔL 3.08 10
Strain = =
L 10m
m
-4
Longitudinal strain = 3.08×10
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14. Young’s modulus for brass is 8.96 x 1011Pa. A 120N
weight is attached to an 8 m length of brass wire;
the diameter is 1.5 mm. Find the increase in length. .
Area of the wire
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-3
ΔL= 0.6×10 m
11
Y= 8.96 10 Pa, F=120N
-6 2
L=8m A=1.77×10 m
2 -3 2
-6 2
A=πr = 3.14×(0.75×10 m)
=1.77×10 m
-6 11 1
FL
Increase in Length ΔL =
AY
120N 8m
=
(1.77 10 )m (8.96 10 )Nm