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UNIT 1.3
Stress & Strain Relationship of Hooke’s Law,
Elastic Moduli, Stress–Strain Diagram
Department of Physics
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
Department of Physics
Stress
Restoringforce F
Stress= =
Area A
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
Department of Physics
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
Department of Physics
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
Department of Physics
The downward force F
causes the displacement x
Types of Modulus
1. Young’s Modulus (Y)
2. Bulk Modulus (K)
3. Rigidity Modulus (n)
Department of Physics
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
Department of Physics
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
=
Department of Physics
F
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
Department of Physics
• 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
Department of Physics
2
Stress strain
Stress E Strain
Stress
E Nm
Strain


= 
=
Poisson’s Ratio (σ)
Lateral strain
σ = ------------------------------- =
Longitudinal strain
β
= a constant
α
Department of Physics
l
d
F
D
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.
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
Department of Physics
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
Department of Physics
-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

  
DISCUSSIONS
Department of Physics

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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 Department of Physics
  • 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 Department of Physics 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 Department of Physics
  • 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 Department of Physics
  • 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 Department of Physics 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) Department of Physics
  • 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 Department of Physics
  • 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 = Department of Physics 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 Department of Physics
  • 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 Department of Physics 2 Stress strain Stress E Strain Stress E Nm Strain   =  =
  • 11. Poisson’s Ratio (σ) Lateral strain σ = ------------------------------- = Longitudinal strain β = a constant α Department of Physics 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 Department of Physics
  • 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 Department of Physics -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    