## Mechanical Properties of Solids

# Application of Elastic Behavior of Material

- Railway tracks and bridges declared unsafe after long use due to Elastic fatigue.
- If the material breaking after Elastic limit it is called brittle material.
- Brittle material is used to make Glass.
- If the material breaking point and Elastic limit are far it is called ductile material.
- Ductile material is used to make thin wires.
- Elastic property of a material increase with addition of impurity.
- Slow cooling of material after heating called Annealing.
- For invar steel Elasticity is independent of temperature.
- Springs are made of steel because it is more Elastic
- Young's modulus of a material does not depend up on Dimensions of body but depends upon nature of material.
- Young's modulus (Y) of a material is the ratio of linear stress to linear strain.
- Shear modulus (n) is defined as the ratio of shear stress to shear strain.
- Bulk modulus (k) is defined as the ratio of Bulk stress to bulk strain.
- Y. nk are having same units = N/m
^{2} - When a wire is stretched young's modulus, When twisted rigidity modulus involved.

### View the Topic in this video From 01:10 To 58:27

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1. For a beam with circular cross-section depression is given by \tt \delta=\frac{WL^{3}}{12\pi r^{4}Y}

2. Torque required to produce a unit twist in a solid shaft

\tau_{solid}=\frac{\pi\eta\ r^{4}}{2l}

3. Torque required to produce a unit twist in a hollow shaft

\tau_{hollow}=\frac{\pi\eta(r_2^4-r_1^4)}{2l}