# Stress Calculator

Created by Luis Fernando
Last updated: Aug 01, 2022

If you're searching for how to calculate stress, you're in the right place! Apart from calculating stress, you can use this calculator for other purposes, such as:

• Calculating Young's modulus (also known as modulus of elasticity);
• Calculating axial strain; and
• Many more!

🙋 The stress of this calculator corresponds to the engineering strain, which is slightly different from the true strain.

## Stress formula and concept

We can think of stress as the internal forces the particles of a continuous material feel and exert on each other. This calculator focuses on the stress occurring when we apply a force, but there are other forms of stress, such as residual and thermal stress.

Mathematically, stress is the force applied per unit area. Then, the stress formula is:

σ =F/A

where:

• σ — Stress resulting from the applied force, in N/m2 (same units of pressure);
• F — Applied force, in N; and
• A — Area of force application, in m2.

The more simple case is the stress that occurs when we apply a force in the axial direction over the area of a bar of uniform cross-section.

The stress (σ) shown in the previous image is an idealization as, in reality, σ is not constant over the cross-section, especially in the extremes where the force is applied:

Therefore, the stress equation σ =F/A is actually the average stress equation.

Applying a force in the axial direction (causing tension or compression) is not the only way to cause stress. In the following image, you can see the other types of loads apart from the axial load. The stress distribution in those cases is even more complicated, and this calculator only focuses on the stress caused by tension and compression forces.

Now that we know how to calculate stress, let's see how to calculate the modulus of elasticity (Young's modulus) and strain.

## Strain formula and Young's modulus

Strain is a measure of the deformation of a material. We calculate the deformation caused by an axial load with something called engineering strain, and its formula is:

ε = ΔL/L₁ = (L₂ - L₁)/L₁

where:

• ε — Strain;
• ΔL — Change in length;
• L — Initial length; and
• L — Final length;

From the strain definition, we can note some points:

• It is a dimensional quantity.
• It doesn't only consider the total change in length but considers it relative to the initial state (before deformation).
• If you multiply the strain formula by 100%, you get the percent change of the bar length.

### Young's modulus

Young's modulus is a material property that measures the resistance to deformation in the presence of axial load in the elastic range. It is related to stress and strain by the following formula:

E = σ/ε

where E is Young's modulus. Young's modulus is a material property often available in advance. We can use it to predict the deformation caused by some stress or the stress required to generate a specific deformation.

Luis Fernando
Area (A)
ft²
Force (F)
lbf
Stress (σ)
psi
Axial strain calculations
Initial length (L₁)
ft
Final length (L₂)
ft
Change in length (ΔL)
ft
Strain (ε)
Young's modulus (E)
psi
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