The document discusses the behavior of materials under stress and strain. It defines stress as the internal resistance of a material to external loads, and strain as the deformation or change in shape of a material under stress. The key types of stress are tensile, compressive, and shear stress. Hooke's law states that stress is proportional to strain within the material's elastic limit, after which plastic deformation occurs. The elastic modulus, shear modulus, and bulk modulus describe a material's response to different types of stress.

1. 1. Essential that engineer understands the behavior of various
materials with respect to strengths and deformations when
subject to various types of loads.
3. Strength of materials basically is a study of behavior of machine
components and structure components when exposed to external
loads.
5. The knowledge of internal reaction that the materials offer to the
external loads, the change that are produced in a body become
the basis of selection of materials for a particular application.

2. Definition of strain and stress
On the application of a load (force), the material of a body undergoes
a change. This change in size or shape is called strain.
Strain, e defined as how much the length of the object has been
changed (ΔL) compared to its original length (Lo).
e = ΔL/Lo
Strain : Percentage that something has
deformed

3. The internal resistance (counterforce) offered by the material of the
body to this change is called stress.
•Counterforce tends to return the atoms to their normal position
•The total resistance developed is equal to the external force
Stress (σ) can be equated to the load per unit area or the force (F)
applied per cross-sectional area (A) perpendicular to the force.
The SI unit for stress is the Pascal
(symbol Pa), which is a shorthand
name for one Newton (Force) per
square metre (Unit Area).
stress on an object defined as the
force per unit area

4. Types of Stress
1. Tensile stress
When a section is subjected to 2 equals and opposite pull, as a
result of which the body tends to lengthen, the stress induced is
called tensile stress.
P P
The corresponding strain is called tensile strain
• ΔL is increase in length
Tensile stress, σt = F/A
• Tensile stress by
Tensile strain, et = ΔL/Lo convention is considered
as positive stress

5. 2. Compressive stress
When a section is subjected to 2 equal and opposite pushes, as a
result of which the body tends to shorten its length, the stress
induced is called compressive stress.
P P
The corresponding strain is called compressive strain
• ΔL is decrease in length
Compressive stress, σc = F/A
• Compressive stress by
Compressive strain, ec = ΔL/Lo convention is considered
as negative stress

6. 3. Shear stress
If the external forces acting on a piece of material tend to slide one
layer of the material over the next layer then stress and strain set up
are called shearing stress and strain.
P
D’ C’
D C
F
Shearing stress, τ =
θ θ
A B
A
Shearing strain is measured by the angular displacement of the block.
If ΔCBC’ or DAD’ = θ, then
γ = CC’/BC

7. Results of Stress
When exert forces on an object, there are three things that can happen:
(3) The object can go back to its original form.
If the object does that then the object was strained within its elastic
limit.
Elastic Limit: The relations below hold, and Hooke’s law is valid.
(2) The object can retain its new shape. If this happens, the object was
strained within its plastic limit.
Plastic Limit: The relations below do not hold and the material is
permanently deformed.
(3) It can break. The object has been strained too much and fractures.
Fracture: Forces exceed maximum limits derived from the
relations below and material breaks.

8. When (1) occurs, the material obeys Hooke’s law F = -kΔL. The
material will retain its original shape when the forces are removed.
How much it moves from its original position when the forces are on it
depend on the size and shape of the body and how the force is applied.
The force can be applied in three ways: tension, compression, and
shear: The change in shape for each of these three ways is determined
from the:
1. elastic modulus for tension and compression, and
2. from the shear modulus for shear
3. If the pressure is distributed on all parts of the object, the volume of
the material changes and the bulk modulus is used
Finally, if the stress exceeds some maximum the object will break. The
maximum stress depends on whether there is a tensile, compressive, or
shear force.

9. Elasticity is a property of an object or material which will restore it to
its original shape after distortion.
A spring is an example of an elastic object - when stretched, it exerts a
restoring force which tends to bring it back to its original length. This
restoring force is in general proportional to the stretch described by
Hooke's Law.
Hooke's Law: One of the properties of elasticity is that it takes about
twice as much force to stretch a spring twice as far. That linear
dependence of displacement upon stretching force is called Hooke's
law which can be expressed as
F = -kΔL
where
F = force in the spring (N)
k = spring constant (N/m)
ΔL = elongation of the spring (m)

10. 1. Tensile Stress or Compressive Stress
Constant: Young’s Modulus, E = FLo /AΔL = Stress/Strain
2. Shear Stress
Constant: Shear Modulus, G = FLo /AΔL = Stress/Strain
3. All directions
Constant: Bulk Modulus, B = -ΔPVo /ΔV

11. Example:
• Find the area of a wire of diameter 0.75 mm in m2. What is the
strain of a 1.5 m wire that stretches by 2 mm if a load is
applied?
• A wire made of a particular material is loaded with a load of
500 N. The diameter of the wire is 1.0 mm. The length of the
wire is 2.5 m, and it stretches 8 mm when under load. What is
the Young Modulus of this material?
• A load of 200 N is applied to a steel wire 2 m long and
diameter 0.5 mm. If the Young Modulus for steel is 2 x 10^11
Pa, the extension is:

12. Hooke’s Law essentially states that stress is proportional to strain
Yield point Ultimate
strength
Elastic
limit
Elastic Plastic
Rupture
region region

13. Elastic Region
•In the context of material behavior, a structural component is said to
behave elastically if during loading/unloading the deformation is
reversible.
•In other words, when the loads are released the specimen will return to
its original, undeformed configuration.
As loads are increased and the stress in the specimen continues to rise,
the material eventually reaches the elastic limit. Beyond this limit, any
additional loading will result in some permanent change to the
specimen geometry upon unloading.
Any increase in stress beyond the yield point will cause the material
to be deformed permanently. Also in this so-called yielding region,
the deformation will be relatively large for small, almost negligible
increases in the stress. This process, characterized by a near-zero
slope to the stress-strain curve, is often referred to as perfect
plasticity.

14. Plastic Region
•When loading is carried beyond the yielding region, the load needs to
increase for additional strain to occur.
•This effect is called strain hardening, and it is associated with an
increased resistance to slip deformation at the microscale (for
polycrystalline materials).
Eventually, the stress-strain curve reaches a maximum at the point of
ultimate stress. For many materials, the decrease in the cross-sectional
area of the specimen is not readily visible to the naked eye until this
limit point is passed.
When the loading is continued beyond the ultimate stress, the cross-
sectional area decreases rapidly in a localized region of the test
specimen.
Since the cross-sectional area decreases, the load carrying capacity of
this region also decreases rapidly. The load (and stress) keeps
dropping until the specimen reaches the fracture point.

15. rst we need to work out
the area:
= πr2 = π × (0.5 × 10-3)2 =
7.85 × 10-7 m2 E = Fl/Ae.
2 x 10^11 = (200 x 2) / 1.96 ^ -3 x
e = (200 x 2 ) / 1.96 ^ -3 x 2 x 10^1
ress = F/A = 500 N ÷ 7.85 ×
e = 0.01 m = 10 mm
10-7 m2 = 6.37 × 108 Pa
rain = e/l = 0.008 ÷ 2.5 =
0.0032
oung’s Modulus =
stress/strain = 6.37 × 108
Pa ÷ 0.0032