2. Stress and Strain
Outline
1. Stress
2. Strain
3. Stress-strain curve
4. Important definitions
5. Hookโs law
6. Stress strain curve of different materials
4. Stress and Strain
What is stress?
Stress is the resistance force
generated per unit area.
Stress ฯ =
๐น๐๐๐๐ (๐น)
๐ถ๐๐๐ ๐ ๐ ๐๐๐ก๐๐๐๐๐ ๐ด๐๐๐ (๐ด)
5. Stress and Strain
What is strain?
Strain or % Elongation is the ratio of change in length under the
application of force to the initial length.
Strain ฮต =
๐ถโ๐๐๐๐ ๐๐ ๐๐๐๐๐กโ (ฮด๐ฟ)
๐๐๐๐๐๐๐๐ ๐ฟ๐๐๐๐กโ (๐ฟ)
6. Stress and Strain
Types of stress
1. Tensile Stress: Pulling force per unit area
2. Compressive stress: Pushing force per unit
area
3. Shear stress: Parallel force per unit area.
1. Single shear: Failure area is in one
place
2. Double shear: Failure area is in two
place
8. Stress and Strain
Important definitions:
1. Elastic limit(O to A): The elastic limit of a material is the maximum stress that can be
developed within it without causing permanent deformation. Beyond this limit, the material
will not come back to its original shape after force is removed.
2. Upper yield point (B): Material requires maximum stress to initiate plastic
deformation inside the material.
3. Lower yield point (C): Material requires minimum stress to initiate plastic
deformation inside the material.
4. Ultimate tensile stress (D): The maximum amount of stress a material can withstand
before starting to break.
5. Breaking stress (E): At this stress, the material breaks.
9. Stress and Strain
Strain Hardening
The elastic limit of a material is the maximum stress that can be developed within it
without causing permanent deformation
Necking
Necking is a type of plastic deformation observed in ductile materials subjected to tensile stress.
This deformation is characterized by a localized reduction in the cross-sectional area of the
material, giving it a "V" or "neck" shape. Necking begins after ultimate strength is reached. During
necking, the material can no longer withstand the maximum stress and the strain in the specimen
rapidly increases.
10. Stress and Strain
Hookโs law
When a material is loaded within its elastic limit, the stress is proportional to the strain
ฯ โ ฮต
Young Modulus/Modulus of elasticity
The Young's modulus (E) is a property of the material that tells us how easily it can stretch and
deform and is defined as the ratio of tensile stress (ฯ) to tensile strain (ฮต).
E =
๐๐๐๐ ๐๐๐ ๐๐ ๐๐๐๐๐๐๐ ๐ ๐๐ฃ๐ ๐๐ก๐๐๐ ๐
๐๐๐๐ ๐๐๐ ๐๐ ๐๐๐๐๐๐๐ ๐ ๐๐ฃ๐ ๐๐ก๐๐๐๐
=
ฯ
ฮต
11. Stress and Strain
Poissonโs ratio
Poisson's ratio is the ratio of lateral strain to
longitudinal strain in the direction of stretching
force.
Poissonโs ratio, ฮผ =
๐ฟ๐๐ก๐๐๐๐ ๐ ๐ก๐๐๐๐
๐ฟ๐๐๐๐๐ก๐ข๐๐๐๐๐ ๐ ๐ก๐๐๐๐
= -
ฯตt
ฯตl
Lateral strain, ฯตt = โ
๐๐ต
๐ต
Longitudinal strain, ฯตl =
๐๐ฟ
๐ฟ
12. Stress and Strain
Why do we need stress-strain curve?
By seeing the stress strain curve, we can select the proper
material for the manufacturing of a machine. From the stress-
strain curve, we can determine if our selected material will be
able to hold the load properly or not.
14. Stress and Strain Math
A 2.0-m-long steel rod has a cross-sectional area of 0.30cm2. The rod is a
part of a vertical support that holds a heavy 550-kg platform that hangs
attached to the rodโs lower end. Ignoring the weight of the rod, what is
the tensile stress in the rod and the elongation of the rod under the
stress? Youngโs modulus for steel is Y=2.0ร1011Pa.
16. Stress and Strain Math
A 5.0-m-long steel rod has a diameter of 0.1 m2. The rod is a part of a
vertical support that holds a heavy 30000 gm platform that hangs
attached to the rodโs lower end. Ignoring the weight of the rod, what is
the tensile stress in the rod and the elongation of the rod under the
stress? Youngโs modulus for steel is Y=2.0ร1011Pa.
Practice