Let’s understand the Normal Stress First

I would like to explain the concept of STRESS with the help of prismatic bars in a more technical and accessible manner.

Imagine we have a prismatic bar, which is basically a straight bar (member) that has a uniform shape throughout its length. (You can check the Below fig. for better understanding) in Fig (a) Axial force produce a uniform stretching of the bar, hence the bar is said to be in tension and in fig (c) force produces uniform compression of the bar, hence the bar is said to be in compression

Now, to understand the internal stress caused by this force in the bar, we make an imaginary cut at a specific point (say sections A and B) perpendicular to the long axis of the bar. This imaginary cut divides the bar into two parts.

Let’s focus on the part on the right side of the cut. When we isolate this part and consider it as a separate “free body”, the force ‘P’ wants to move it in the direction of the applied load. To stop this motion and keep the bar in equilibrium, internal forces (or can say restrain) develop within the bar. These internal forces are spread uniformly over the cross-sectional area of the bar.

The intensity of these internal forces, expressed as force per unit area, is what we call “stress“. It is a way of measuring the force experienced by each small piece of bar material due to an external load.

What is Stress?

Thus, stress can be defined as – Stress is the internal resistance of a material offered against deformation which is the force applied per unit area.

The stress induced in a material depends on the nature of the force, the point of application, and the cross-sectional area of the material. Depending on the nature of the load the nature of stress can be tensile or compressive. Stress is generally represented by the Greek sigma, and we can calculate stress mathematically

σ=P/A

Stress (σ) Unit is N/mm²or MPA

Sign Convention;

Tensile stress +VE
Compression Stress is -VE

Important Note: -

Stress occurs when a bar or any material is prevented from moving freely by external forces or reactions. If a bar is free to rotate or extend without any constraint, Stress does not arise.
Pressure has same unit but pressure is different physical quantity than stress. Pressure external force distributed over surface. E,g Pressure is about how external forces apply to a surface, such as a hand pressing on a table. Stress, on the other hand, is about the internal response of a material to these forces.

On the basis of cross-sectional area considered during calculations of stresses, direct stress ca be following types

Engineering stress or nominal stress
True Stresses or Actual stresses

Engineering Stress (Nominal Stress)

Engineering stress is calculated using the original, unaltered cross-sectional area (A₀) of the material before any deformation. The formula for engineering stress is;

Engineering stress: σ_engg =P/A₀

Where;

σ eng is the engineering stress,

P is the applied Load,

A₀ is the original cross-sectional area of the material.

True Stress (Actual Stress)

True stress takes into account the real-time, changing cross-sectional area (A) of the material as it undergoes deformation. The formula for true stress (σ true) is:

σ true = P/A
where:

σ true is the true stress,
P is the applied Load,
A is the instantaneous cross-sectional area of the material.

Note:

in Tension, True or Actual Stress is always greater than engineering or normal stress
In compression, True or actual stress is always Less than engineering or nominal stress.

Strength of Material: Mechanics of Soilds, RS Khurmi

“Dive into the fascinating world of mechanics with RS Khurmi’s ‘Strength of Materials: Solid Mechanics’. Unlock the secrets of solid mechanics and expand your understanding. Get your copy [here] By Now.

What is Strain?

An Axially load bar undergoes a change in length, becoming longer in tension and shorter when in compression, thus elongation or shortening in axially Loaded per unit length is known as Strain, Starin is represent by

Mathematically, Strain can be calculated as

∈ = Δ/L

Strain = Change in length/Original Length

Unit = Strain is a dimensionless quantity. It always Expressed in the Form of number. If member is in tension the strain is called Tensile strain and If Member is in compression, then strain is called compressive strain.