Mohr’s Circle Calculator

What is Mohr’s Circle?

Mohr’s Circle is a graphical representation used in engineering and materials science to analyze the stress state at a point in a material under load. It provides a visual method for understanding the relationships between normal and shear stresses acting on different planes passing through a point in a stressed body. This tool is particularly useful for determining principal stresses, maximum shear stress, and stress transformations for different orientations.

How to Use the Mohr’s Circle Calculator

Step 1: Enter the stress components

Input the known stress components in the designated fields. These include:

• σx (sigma x): Normal stress in the x-direction
• σy (sigma y): Normal stress in the y-direction
• τxy (tau xy): Shear stress in the xy-plane

Ensure you use consistent units, preferably in MPa (megapascals).

Step 2: Specify the angle of rotation

Enter the angle θ (theta) in degrees for which you want to calculate the transformed stresses. This angle represents the rotation of the stress element from its original orientation.

Step 3: Click the “Calculate” button

After entering all required values, click the “Calculate” button to process the input and generate results.

Step 4: Interpret the results

The calculator will display the following results:

• Principal stresses (σ1 and σ2): The maximum and minimum normal stresses
• Maximum shear stress (τmax): The largest shear stress value
• Principal angle (θp): The angle at which principal stresses occur
• Transformed stresses (σx’, σy’, τx’y’): Stress components at the specified angle θ

Step 5: Analyze the Mohr’s Circle diagram

Examine the generated Mohr’s Circle diagram to visualize the stress state. The circle represents all possible combinations of normal and shear stresses for different orientations.