Mechanics of solids

Mechanics of Solids or Solid mechanics is the branch of mechanics which studies about the behavior of solid materials under the action of Forces and Temperature changes.

1. MECHANICS OF SOLIDS - Simple Stress and Strains A PAVAN REDDY

2. Contents Introduction Mechanical properties Stress Strain and Hooke’s law Elastic constants and Poisson’s ratio Factor of safety and Thermal stresses Stress & Strain diagram for ductile material

3. Introduction Mechanics of Solids or Solid mechanics is the branch of mechanics which studies about the behavior of solid materials under the action of Forces and Temperature changes. Applications: To design mechanical parts of machine. To construct beams, pillars, bridges, etc. To manufacture Automobiles, Air crafts, etc

4. Mechanical properties Mechanical properties are the properties which describes the behavior of material under the action of loads acting on it. Some mechanical properties are 1. Strength 2. Elasticity 3. Plasticity 4. Ductility 5. Malleability 6. Durability 7. Toughness 8. Hardness 9. Stiffness 10. Brittleness 11. Fatigue 12. Creep

5. Stress Strain and Hooke’s law Stress: It is the ratio of load applied on the material to the unit cross section area of material. It is denoted by σ . Its units are N/m 2 Strain: It is the ratio of change in dimension to the original dimension of the material. It is denoted with e. It has no units. Hook’s law: It States that with in the elastic limit stress is directly proportional to the strain.

6. Elastic constants Modulus of Elasticity : It is the ratio of Stress and Strain is called modulus of elasticity or elastic modulus or young’s modulus. It is denoted by E. Units N/m 2 Modulus of Rigidity : It is the ratio of shear stress and shear strain is called modulus rigidity or shear modulus. It is denoted by C or N or G. Units N/m 2 Bulk modulus: It is the ratio of direct stress to the volumetric strain. It is denoted by K. Units N/m 2

7. Elastic constants formulae

8. Stress Strain diagram for ductile material A : Proportionality limit B : Elastic limit C : Plastic limit D : Ultimate stress E : Breaking point

9. Thermal stresses Thermal or Temperature stress is the stress induced in a body due to change in temperature. These stress which are developed due raise or fall of temperature of a body. It cause the body to contract or expand.

10. Poisson's ratio It is the ratio of lateral strain to the longitudinal strain is known as Poisson's ratio . It is denoted by µ. The ratio of change in diameter to the original diameter is called Lateral strain or Transverse strain . The ratio of change in length to the original length is called as longitudinal strain or linear strain .

11. Factor of safety Factor of safety or Safety factor is the ratio of ultimate stress to the working stress. It is the term used to describe the load carrying capability of a body beyond actual loads. Ultimate stress is the maximum tensile stress that a material can withstand before breaking. Working or Design stress is the stress developed in the body that doesn’t exceed the elastic limit.

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