Stress Formula

Stress is the force that we apply on an object for it to completely deform. Besides, we are aware of human stress but the stress in physics is a little bit complicated to understand. Moreover, in this topic, we will discuss stress, stress formula, its derivation and solved example.

How objects react?

For making origami crane you fold a paper. Also, after finishing the origami it still retains the new shape even after you relief the paper. On the other hand, when you stretch a rubber band, it will snap back when you let go of it. Moreover, there are objects that retain their original shape partially when you stretch them.
Moreover, there are things that change shape when forces are applied to them, but all items do not change in the same way even when we use the same amount of force.

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Stress

Before talking about stress there are few concepts that need to be looked first. Moreover, stress is the amount of force (strength or energy) that we exert on an object, divided by the cross-section area on which the force is acting.

Furthermore, larger object can withstand a higher amount of forces. In addition, by using stress as an alternative of force we are able to use the same yield stress for the same material, no matter how large the object actually is.

Most importantly, stress and strain directly relate with each other and as one increases the other automatically increases. Also, the more stress the object experience, the more it will deform until the object fails.

Besides, all object experience the elastic deformation at first but when the stress on the object exceeds a certain amount, then it will experience plastic deformation and that’s when the switch happens and the object has reached its yield stress.

In addition, in every material the stress and strain bond, though the size of each portion may be different. Also, the elastic deformity is linear. Furthermore, the slope line depends upon the materials of the object is made up of. Moreover, plastic deformation is not linear that makes it more difficult to model.

Stress Formula

The stress formula is the divided product of the force by the cross-section area

Stress = \(\frac{Force}{Area}\)

\(\sigma\) = \(\frac{F}{A}\)

Derivation of the Stress Formula

\(\sigma\) = refers to the amount of stress on the object

F = refers to the force that is acting on the object.
A = refers to the cross-sectional area

Solved Example on Stress Formula

For making the formula more clear to you let’s consider some examples that will help you in understanding them better.

Example 1

Find the stress of an object on which the acting force is 50 Newtons (N) and the cross-section area is 5 \(mm^{2}\)?

Solution:

Let’s write down what is given in the question
Force or F = 50 N (Newtons)
Cross-section area or A = 5 \(mm^{2}\)
Now let’s put values given in the question in the formula

\(\sigma\) = \(\frac{F}{A}\)

\(\sigma\) = \(\frac{50 N}{5 \times 10 ^{-6}}\)

\(\sigma\) = \(10 \times 10^{6} Nm^{2}\)

So, the stress on the object is \(10 \times 10^{6} Nm^{2}\).

Example 2

An elastic spring was given a force of 1000 N over an area of 0.2 \(m^{2}\). So, find the stress on the elastic spring?

Solution:

Firstly, write down what we know from the formula

Force (F) = 1000 N
Area (A) = 0.2 \(m^{2}\)

Now put the values in the formula

\(\sigma\) = \(\frac{F}{A}\)

\(\sigma\) = \(\frac{1000 N}{0.2}\)

\(\sigma\) = \(5000 Nm^{2}\)

So, the stress on the elastic spring is \(5000 Nm^{2}\).