Mohr's Circle Calculator

Mohr's Circle Formulas:

\[ \text{Center} = \frac{\sigma_x + \sigma_y}{2} \] \[ \text{Radius} = \sqrt{ \left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2 } \]

Center of Mohr's Circle:

Radius of Mohr's Circle:

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1. What is Mohr's Circle?

Mohr's Circle is a graphical representation of the transformation equations for plane stress. It provides a visual method for determining principal stresses, maximum shear stresses, and stresses on any plane.

2. How Does the Calculator Work?

The calculator uses the Mohr's Circle formulas:

\[ \text{Center} = \frac{\sigma_x + \sigma_y}{2} \] \[ \text{Radius} = \sqrt{ \left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2 } \]

Where:

\( \sigma_x \) — Normal stress in x-direction (Pa)
\( \sigma_y \) — Normal stress in y-direction (Pa)
\( \tau_{xy} \) — Shear stress (Pa)

Explanation: The center represents the average normal stress, while the radius determines the maximum shear stress and principal stress difference.

3. Importance of Mohr's Circle

Details: Mohr's Circle is essential in mechanical and civil engineering for stress analysis, failure prediction, and material strength evaluation.

4. Using the Calculator

Tips: Enter all stress values in Pascals (Pa). The calculator will determine the center and radius of Mohr's Circle, which are key to finding principal stresses.

5. Frequently Asked Questions (FAQ)

Q1: What are principal stresses?
A: Principal stresses are the maximum and minimum normal stresses that occur on planes with zero shear stress.

Q2: How do I find maximum shear stress?
A: The maximum shear stress is equal to the radius of Mohr's Circle.

Q3: Can Mohr's Circle be used for 3D stress?
A: While Mohr's Circle is primarily for 2D stress, three circles can represent 3D stress states.

Q4: What's the significance of the center?
A: The center represents the hydrostatic stress component, which affects volume change but not shape distortion.

Q5: How accurate is this calculator?
A: The calculator provides precise results based on the input values, assuming plane stress conditions.