Mechanical Stress and Strain

Stress:

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When a body is subjected by an external forces or load then it is said to

undergo the deformation. The change in the dimension or shape

increases gradually. At the time of deformation the object material

attacks the tendency of the load to deform the body. When the load is

removed then the internal stress are also removed and it gains its

original shape.

The stress is defined as the internal resistance of the body offers to meet

the load.

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Stress is classified into various types

  • Direct stress
  • Indirect stress
  • Combined stress

Direct Stress:

Direct stress is also known as Simple stress. They are developed under

loading conditions.

They are classified into three types. They are

a) Tension

b) Compression

c) Shear

Tension and Compression stress are developed when the material is

extended or compressed by two opposing forces is known as tensile

stress and compression stress.

Shear stress:

Shear stress is developed when the applied force is parallel to the

resisting area then we can observe the shear stress.

T =F_p / A

T = Shear stress in Pa . N /m^2  or  psi

F_p = parallel component force in Newton or Ibf

A = Area in meters or inches

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Indirect Stress:

Indirect stresses are classified into two types they are Bending stress and

Torsion Stress.

  • Bending
  • Torsion

Combined stress:

Combined stress deals with the both simple stress and indirect stress.

Stress:

Simply stress is defined as the ratio of applied load to the cross sectional

area. The stress is denoted with the symbol ‘\sigma’.The units are  N/mm^2.

Stress (\sigma) = Applied load (L)/ Cross sectional area(A)

Strain:

Strain is known as the deformation that takes place in the solids due to

the stress developed.

(Or )

It is also known as ratio change in length by original length is known as

strain. It is representing by the symbol . For strain there are no units.

\varepsilon= dl /l_0

Percentage of strain = \DeltaL / L \times100 %

dl is known as change in length

l_0  is known as original length.

The equation must be again represented as

stress / young’s modulus = \sigma/ E

E is known as Young’s modulus

Strains are classified into four types they are

  • Tensile Strain
  • Compressive Strain
  • Shear Strain
  • Volumetric strain

Tensile Strain:

A Uniform axial tensile strain is subjected to the uniform cross section at

that case increased in length is observed that is l to (l + δl).

e_t= δl / l

δl = change in length

l = original length

Compressive Strain:

A Uniform axial Compressive Strain is subjected to the uniform cross

section, at that case decreased in length is observed that is l to (l- δl).

e_c= δl / l

δl = change in length

l = original length

Shear Strain:

Shear strain is defined as when the body distorts then it produces an

angle, where the shear strain is measured. We can obtain the equation as

e_s= \tan \Phi

Φ is very small angle and it is measured in radians.

Volumetric strain:

Volumetric strain is defined as the ration between the change in volume

to the original volume.

e_v= change in volume / original volume

e_v= δV / V

Within the elastic limit the stress is directly proportional to the strain.

Stress/Strain = a

a = constant

Young’s modulus:

Modulus of elasticity is defined as the ratio of the stress to the strain.

And it implies that the stress is proportional to the strain. The modulus

of elasticity is denoted by ‘E’. The units are kg/m.

E = stress / strain = \sigma / \ep

Young’s modulus it is also known as Modulus of elasticity.

Modulus of rigidity:

Modulus of rigidity is defines as the ratio of the shear stress to the shear

strain. The modulus of rigidity is denoted by C, G or N. It is also known

as Shear modulus of elasticity.

\tau / e_s= C, G, N

Bulk modulus of rigidity:

The bulk modulus of rigidity is also known as volume modulus of

rigidity. It is defined as the ratio of the normal stress to the volumetric

strain. It is denoted by ‘K’.

\sigma_n/ e_v = K

Proportional limit:

Proportional limit is defined at the stress that is directly proportional to

the strain. In the stress strain diagram the proportional limit is a straight

line. For many metals the proportional limit is equal to elastic limit. The

value of the proportional limit is equal to the young’s modality

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