Strength of materials

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Define shear stress and shear strain.
The two equal and opposite force act tangentially on any cross sectional plane of the body tending to slide one part of the body over the other part. The stress induced is called shear stress and the corresponding strain is known as shear strain.

Define- Rigidity modulus
The shear stress is directly proportional to shear strain.
N = Shear stress/Shear strain

Define Bulk-modulus
The ratio of direct stress to volumetric strain is called as Bulk modulus.
K    =   Direct stress/ Volumetric strain

Define- lateral strain
When a body is subjected to axial load P, The length of the body is increased. The axial deformation of the length of the body is called lateral strain.

Define- longitudinal strain
The strain right angle to the direction of the applied load is called lateral strain.

Define Poisson’s ratio.
When a body is stressed, within its elastic limit, the ratio of lateral strain to the longitudinal strain is constant for a given material.
Poisson’ ratio (µ or 1/m) = Lateral strain /Longitudinal strain

State the relationship between Young’s Modulus and Modulus of Rigidity.
E = 2G (1+1/m)
Where,
E - Young’s Modulus
G - Rigidity Modulus
1/m - Poisson’s ratio

Give the relationship between Bulk Modulus and Young’s Modulus.
E = 3K (1-2/m)
Where,
E - Young’s Modulus
K - Bulk Modulus
1/m - Poisson’s ratio


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