This document provides an overview of key concepts in strength of materials including: - Stress is defined as the internal resisting force induced per unit area when an external force is applied. The two basic types of stress are normal stress and shear stress. - Strain is the ratio of deformation to original dimension when a body undergoes stress. The main types of strain are longitudinal, lateral, normal, tensile, compressive, and shear. - Hooke's law states that within the elastic limit, stress is directly proportional to strain for a material. When stress is applied and removed, elastic materials will return to their original state.

1. BIBIN CHIDAMBARANATHAN
STRENGTH
OF
MATERIALS
FOR MECHANICAL ENGINEERS

2. Stress
• Whenever an external force is applied on a body then a
resisting force is induced in the body.
• This resisting force acting per unit area of the body is called
stress.
• Under equilibrium condition this resisting force is equal to the
applied load.
• So the stress is also defined as the ratio of applied force to the
cross sectional area on which this external force is applied.
• The force applied on the body is called load
• Here we use a symbol 𝜎 to represent the stress.
𝜎 =
𝑃
𝐴
=
𝐹
𝐴

3. TYPES OF STRESSES

4. TYPES OF STRESSES
only two basic stresses exists :
• (1) normal stress and
• (2) shear stress.
• Other stresses either are similar to these basic stresses
or are a combination of these
• e.g. bending stress is a combination tensile, compressive
and shear stresses.
• Torsional stress, as encountered in twisting of a shaft is a
shearing stress.

5. Direct stress or Simple stress
• Direct stress is the stress developed due force applied
which is parallel or collinear to the axis of the component.
• Examples for this type of stress are tensile stress,
compressive stress, shear stress.

6. Indirect stress
• If the stress is developed due to moment or torsion then it
is called as indirect stress.
• Example: Bending stress, stress due to torsion

7. Combined stress
• When various types of stress (axial, bending, torsional, shear) act on a single
structure at the same time, then it is called combined stress.
• All possible combinations of these stresses may occur at the same time.
• So for example a structure may be subjected to bending and torsion or
bending and tension simultaneously.
• The most complicated case would include all the specified types of stress

8. Uniaxial state of stress or Normal stress
• The stress that acts in the direction perpendicular to the
area is called normal stress.
• This is also known as uniaxial state of stress, because the
stresses acts only in one direction.
𝑁𝑜𝑟𝑚𝑎𝑙 𝑠𝑡𝑟𝑒𝑠𝑠 𝜎 =
𝑁𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒, 𝑃
𝐴𝑟𝑒𝑎, 𝐴

9. Tensile stress
• The stress-induced in a body when it is subjected to two equal and opposite
pulls as shown in the figure given below is called tensile stress.
• Due to the tensile stress there is an increase in the length of the body and
decrease in the cross section area of the body.
• Tensile stress is a type of normal stress, so it acts perpendicular to the area.
• The strain which is induced due to tensile stress is called tensile strain. It is
equals to the ratio of increase in the length to the original length
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 𝜎 =
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑓𝑜𝑟𝑐𝑒, 𝑃
𝐴𝑟𝑒𝑎, 𝐴

10. Compressive stress
• The stress which induced in a body when it is subjected to two equal and
opposite pushes as shown in the figure given below is called compressive
stress.
• Due to the compressive stress, there is a decrease in the length and increase in
the cross section area of the body.
• Compressive stress is also a type of normal stress and so it also acts
perpendicular to the area.
• The strain which is induced due to compressive stress is called compressive
strain. It is equals to the ratio of decrease in the length to the original length.
𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 𝜎 =
𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑓𝑜𝑟𝑐𝑒, 𝑃
𝐴𝑟𝑒𝑎, 𝐴

11. Biaxial state of stresses
• A two-dimensional state of stress in
which only two normal stresses are
present is called biaxial stress.
• If the stresses acts in two mutually
perpendicular direction, then it is
known as biaxial state of stresses.

12. Triaxial state of stresses
• If the stresses acts in three mutually
perpendicular direction, then it is known
as triaxial state of stresses.
• Triaxial stress refers to a condition where
only normal stresses act on an element
and all shear stresses (𝜏𝑥𝑦, 𝜏𝑥𝑧, and 𝜏𝑦𝑧)
are zero.
• An example of a triaxial stress state is
hydrostatic pressure acting on a small
element submerged in a liquid.

13. Shear stresses or Tangential stress
• Shear stress induced in a body when it is subjected to two equal and opposite
forces that acts tangential to the area.
• The strain produced due to the shear stress is called shear strain.
• The shear stress is denoted by the symbol τ (tau). It is a Greek letter.
• It is defined as ratio of shear resistance to the shear area.
• Shear stress is responsible for the change in the shape of the body. It does on
affect the volume of the body.
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 𝜎 =
𝑆ℎ𝑒𝑎𝑟 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 𝑃
𝑆ℎ𝑒𝑎𝑟 𝐴𝑟𝑒𝑎, 𝐴

14. Bending stress
• Bending stress is a more specific type of normal stress.
• When a beam experiences load like that shown in figure one the
top fibers of the beam undergo a normal compressive stress.
• The stress at the horizontal plane of the neutral is zero.
• The bottom fibers of the beam undergo a normal tensile stress

15. Torsional stress
• Torsional shear stress or Torsional stress is the shear stress
produced in the shaft due to the twisting.
• This twisting in the shaft is caused by the couple acting on it

16. Bearing Stress
• When one object presses against
another, it is referred to a bearing
stress
• Bearing stress is the contact pressure
between the separate bodies.
• It differs from compressive stress, as
it is an internal stress caused by
compressive forces

17. Thermal stresses
• If the body is allowed to expand
or contract freely, with the rise
or fall of temperature no stress
is developed, but if free
expansion is prevented the
stress developed is called
temperature stress or strain.

18. Strain
• When an external force is applied on the body then some change in
dimension of the body takes place. The ratio of this change in the dimension
of the body to the original dimension is called strain.
• Strain is a dimensional less quantity as it is the ratio of change in dimension
to the original dimension.
• The strain is denoted by the letter ‘e’. It has no dimensions, it is just a
number.
𝑆𝑡𝑟𝑎𝑖𝑛 𝑒 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛

19. Types of Strain
According to the direction of loading:
❖ Lateral Strain
❖ Longitudinal Strain
According to the loading:
❖ Normal strain
• Compressive strain
• Tensile Strain
❖ Shear Strain
❖ Volumetric strain

20. Longitudinal Strain
• When an axial tensile or compressive load
is applied on a body, then there is an axial
deformation appears in the length of the
body.
• The ratio of axial deformation to the
original length of the body is called as
longitudinal strain.
• It is also defined as the deformation per
unit length in the direction of the applied
load.
𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑙 =
𝑎𝑥𝑖𝑎𝑙 𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
𝛿𝑙
𝑙

21. Lateral Strain
• When an axial tensile load is applied on a
body, there is an increase in the length of the
body.
• But at the same time, other dimensions
which are at right angles to the line of action
of the applied load decreases.
• The strain which produced at right angles to
the direction of the applied load is known as
lateral strain.
𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑡 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑤𝑖𝑑𝑡ℎ
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑤𝑖𝑑𝑡ℎ
=
𝛿𝑏
𝑏

22. Normal strain
• Deformations that are applied perpendicular to the
cross section are normal strains.
𝑁𝑜𝑟𝑚𝑎𝑙 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
𝛿𝑙
𝑙

23. Tensile Strain
• When an external load is applied on
the body and there is increase in the
length of the body.
• Then the ratio of increase in the
length of the body to original length is
called tensile strain.
• Tensile strain is always results in
increase in length.
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒 =
𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
𝛿𝑙
𝑙

24. Compressive strain
• Strain measure under
compressive loading is known as
compressive strain.
• It tends to increase the cross
section area and decrease the
length of the body.
𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒 =
𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
𝛿𝑙
𝑙

25. Shear Strain
• When the shear stress is applied on a body, it tends to deform
the shape of the body as shown in the figure.
• The change in tangential angle in the direction of the loading
is called shear strain
𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒 =
𝛿𝑙
𝑙
= tan 𝜃

26. Volumetric strain or Bulk Strain
• The ratio of change in volume to original volume under
normal loading condition is known as volumetric
strain
𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑉 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑜𝑙𝑢𝑚𝑒
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒
=
𝛿𝑉
𝑉

27. Hooke’s law
❖According to Hooke’s law, when a material is loaded within elastic
limit, the stress induced in the material is directly proportional to
the strain produced.
❖It means that the ratio of stress with the corresponding strain
gives us a constant within elastic limit.
❖When the elastic materials are stretched, the atoms and molecules
deform until stress is been applied and when the stress is
removed they return to their initial state.

28. Thank You