In basic studies we undergo 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:-
I. The force of resistance per unit is 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
ii. 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.
SHEAR STRESS:
 Introduction:-
As the beam bends, along with the bending stresses Shear stresses too are generated in the longitudinal direction and transverse direction of the beam. The cause of this shear stress is the transverse shear which acts on the beam due to transverse loading.

 Theory of Shear Stress during Bending:-
Consider a simply supported beam made up of wooden planks which are just kept over one another. Under the action of transverse loads, the different planks slide against each other as seen in figure (a). Now let the planks be glued to each other as shown in figure (b).
On similar loading, the planks do not separate.

This is because shear forces developed at the junctions are now being resisted by the development of resistance shear along the length of the beam and hence longitudinal shear stresses develop in the beam. The longitudinal (horizontal) shear stresses are accompanied by transverse (vertical) shear stresses by the principle of complimentary shear.

In an actual beam, the different longitudinal layers of the beam do not separate or slide against each other due to the development of longitudinal shear stress and thereby the equilibrium of the beam is maintained.

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