Untitled Lesson

21ME202 – STRENGTH OF MATERIALS FOR MECHANICAL ENGINEERS
MATERIALS

UNIT I STRESS, STRAIN AND DEFORMATION OF SOLIDS

Rigid bodies and deformable solids

In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is

zero or negligible.

The distance between any two given points on a rigid body remains constant in time regardless

of external forces or moments exerted on it.

Deformable solids, externally applied forces acts on a body and body suffers a deformation.

From equilibrium point of view, this action should be opposed or reacted by internal forces

which are set up within the particles of material due to cohesion.

Stress is the measure of what the material feels from externally applied forces.

It is simply a ratio of the external forces to the cross sectional area of the material.

Strain is the deformation of a material from stress.

 It is simply a ratio of the change in length to the original length.

Deformations that are applied perpendicular to the cross section are normal strains, while

deformations applied parallel to the cross section are shear strains.

Tensile stress is simply the force per unit area acting on the material in an outward normal

direction (pulling).

Tensile strength, however, is the maximum tensile stress that a material can withstand before

breaking.

Compressive stress is the force that is responsible for the deformation of the material such

that the volume of the material reduces.

It is the stress experienced by a material which leads to a smaller volume. High compressive

stress leads to failure of the material due to tension.

Shearing Stress is defined as: “A type of stress that acts coplanar with cross section of

material.”

Shear stress arises due to shear forces.

They are the pair of forces acting on opposite sides of a body with the same magnitude and

opposite direction.

Longitudinal strain It is defined as the change in the length of an object relative to its original

length

Lateral strain: The ratio of change in radius to the original radius is called lateral strain.

Poisson’s ratio The ratio of lateral strain to longitudinal strain is called Poisson’s ratio

Elasticity is the ability of a material to return to its previous shape after stress is released.

In many materials, the relation between applied stress is directly proportional to the resulting

strain (up to a certain limit), and a graph representing those two quantities is a straight line.

Elastic limit is the maximum stress a material can withstand before the permanent

deformation.

It is the material's highest limit before the material's plastic deformation can occur.

 Once the stress or force is removed from the material, the material comes back to its original

shape

Hooke’s Law states that the strain of the material is proportional to the applied stress within

the elastic limit of that material.

Mathematically, Hooke’s law is commonly expressed as:

F = –k.x

Where F is the force, x is the extension in length, and k is the constant of proportionality known

as the spring constant in N/m.

Modulus of Elasticity, As per Hooke’s law, up to the proportional limit, “for small

deformation, stress is directly proportional to strain.”

Mathematically, Hooke’s Law is expressed as follows: Stress α Strain

The factor of safety is defined as the ratio of ultimate stress to the working stress.

Elastic constants are the constants which describe the mechanical response of an elastic

material when it is subjected to different kinds of loads.

Based on the type of stress and strain, Elastic constants can be classified into 4 types.

oYoung’s Modulus of elasticity (E)

oBulk Modulus (K)

oModulus of rigidity (G)

oPoisson’s ratio (μ)

Young’s modulus of elasticity is an elastic constant that is defined as the ratio of Longitudinal

stress to longitudinal strain.

When an axial load P is applied along the bar’s longitudinal axis, the bar’s length will be

increased in the direction of the applied load, and stress (σ) is induced in the bar

The bulk modulus of elasticity is an elastic constant showing a material’s incompressibility.

When a body is subjected to three mutually perpendicular stresses of equal intensity (σ).

 Then the ratio of direct stress (σ) to the corresponding volumetric strain (ϵv) is defined as the

bulk modulus (K) for the material of the body.

Modulus of Rigidity is an elastic constant that measures a deformable body’s rigidity.

The shear modulus or modulus of rigidity expresses the relation between shear stress and shear

strain. Modulus of rigidity can be defined as the ratio of shear stress to shear strain.

Poisson’s ratio is an elastic constant which is defined as the ratio of lateral strain to

longitudinal strain. Poisson’s ratio is a unitless quantity, and it is generally denoted as μ or

1/m.

Poisson’s ratio = -Lateral Strain/Longitudinal Strain

Volumetric strain is defined as the change in volume divided by the original volume,

Thermal stress is the stress produced by any change in the temperature of the material.

Thermal stress is induced in a body when the temperature of the body is raised or lowered and

the body is not allowed to expand or contract freely.

Thermal stress includes both heat and cold stress.

Principle stress: The magnitude of normal stress, acting on a principal plane is known as

principal stresses.

 Principle plane: The planes which have no shear stress are known as principal planes.

Mohr's circlerepresents stress and strain at different planes for a stressed body in a two-

dimensional space

Reference

https://byjus.com/physics/stress-and-strain/