# Strength of Materials

In earlier studies we have undergone a basic course in mechanics of Rigid Bodies, more commonly referred to as Engineering Mechanics or Applied Mechanics. Mechanics as such is subdivided into three branches; Mechanics of Rigid bodies, Mechanics of Deformable Bodies and Mechanics of fluids.

Mechanics of Rigid Bodies assumed bodies to be perfectly rigid i.e. there is no deformation of bodies under the action of loads to which they are subjected statics and Dynamics are the two branches of Mechanics Of rigid Bodies involving stationary and moving bodies respectively under the action of loads.

### Stress:

• iThe force of resistances per unit are offered by a body against deformation is known as Stress. When a body is subjected to external loading the body undergoes some deformation. At the same time internal force of resistance is due to the cohesion of molecules inside the body. Thus stress is induced in the body upon external action of load
• If the body is able to resist the external load, it is said to be stable, in equilibrium and therefore for this condition the internal force of resistance should be equal to the external load.

By Definition Stress=force of resistance/cross sectional area

Or Stress=P/A

### Strain:

As the body produce force of resistance to counter the external loading it undergoes some deformation. The extent of deformation depend on the material property like molecular cohesion. The ratio of change in dimension is known as strain.

Since Strain is ratio, it has no units. We shall denote strain by letter e. If L is the original dimension and is change in dimension and then

Strain =Change in dimension/Original dimension

### Types of Stress:

1. Direct Stress and Direct Strain: When the force of resistance acts normal or perpendicular to the area on which it acts, the stress so produced is termed as Direct or Normal Stress and corresponding strain is referred to as Direct Strain. We shall denote direct stress by letter ‘f’. Direct stress could be of tensile nature of compressive nature.
2. Tensile stress: When the force of resistance acts away from the cross sectional area, the direct stress is of tensile nature. Tensile stresses tend to cause an increase in the original dimension.
3. Compressive Stress: When the force of resistance acts towards the cross sectional area, the direct stress is of compressive in nature. Compressive stresses tend to cause a decrease in the original dimension.