**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Concept of stress

__ Concept of Stress:__Let us introduce the concept of stress as we know that the main problem of engineering mechanics of material is the investigation of the internal resistance of the body, i.e. the nature of forces set up within a body to balance the effect of the externally applied forces.

The externally applied forces are termed as loads. These externally applied forces may be due to any one of the reason.

- due to service conditions
- due to environment in which the component works
- through contact with other members
- due to fluid pressures
- due to gravity or inertia forces.

As we know that in mechanics of deformable solids, externally applied forces acts on a body and body suffers a deformation. From equilibrium point of view, this action should be opposed or reacted by internal forces which are set up within the particles of material due to cohesion.

These internal forces give rise to a concept of stress. Therefore, let us define a stress Therefore, let us define a term stress

**Stress: **

Let us consider a rectangular bar of some cross – sectional area and subjected to some load or force (in Newtons )

Let us imagine that the same rectangular bar is assumed to be cut into two halves at section XX. The each portion of this rectangular bar is in equilibrium under the action of load P and the internal forces acting at the section XX has been shown

Now stress is defined as the force intensity or force per unit area. Here we use a symbol s to represent the stress.

Where A is the area of the X – section

Here we are using an assumption that the total force or total load carried by the rectangular bar is uniformly distributed over its cross – section.

But the stress distributions may be for from uniform, with local regions of high stress known as stress concentrations.

If the force carried by a component is not uniformly distributed over its cross – sectional area, A, we must consider a small area, ‘dA' which carries a small load dP, of the total force ‘P', Then definition of stress is

As a particular stress generally holds true only at a point, therefore it is defined mathematically as

**Units :** The basic units of stress in S.I units i.e. (International system) are N / m^{2} (or Pa)

MPa = 10^{6} Pa

GPa = 10^{9} Pa

KPa = 10^{3} Pa Some times N / mm^{2} units are also used, because this is an equivalent to MPa. While US customary unit is pound per square inch psi.