Mohr's Circle Calculator

Advanced Mohr's Circle Calculator for civil engineering applications. Calculate principal stresses, maximum shear stresses, and more with this interactive tool.

Full original guide (expanded)

Mohr's Circle Calculator

Compute principal stresses and Mohrs circle parameters from stress inputs.

Calculator

Results

Principal Stress σ1 0
Principal Stress σ2 0
Maximum Shear Stress τmax 0

Data Source and Methodology

All calculations are based rigorously on the formulas and data provided by the authoritative source "Engineering Mechanics" by Hibbeler, 14th Edition. View Source.

The Formula Explained

Principal Stresses: \( \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)

Maximum Shear Stress: \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)

Glossary of Variables

  • σx: Normal stress in the x-direction.
  • σy: Normal stress in the y-direction.
  • τxy: Shear stress in the xy plane.
  • σ1, σ2: Principal stresses.
  • τmax: Maximum shear stress.

How It Works: A Step-by-Step Example

Consider a material with σx = 100 MPa, σy = 50 MPa, and τxy = 25 MPa. Using the formulas above, you can calculate the principal stresses and maximum shear stress.

Frequently Asked Questions (FAQ)

What is Mohr's Circle?

Mohr's Circle is a graphical representation of the state of stress at a point in a material.

Why use a Mohr's Circle Calculator?

This tool simplifies the complex calculations involved in determining stress transformations in materials.

Can I use this calculator for 3D stress analysis?

No, this calculator is designed for 2D stress analysis only.

What are principal stresses?

Principal stresses are the normal stresses on a plane where the shear stress is zero.

How is maximum shear stress calculated?

Maximum shear stress is determined using the formula \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \).

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
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','
Formula (extracted text)
Principal Stresses: \( \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \) Maximum Shear Stress: \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)
Variables and units
  • T = property tax (annual or monthly depending on input) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Mohr's Circle Calculator

Compute principal stresses and Mohrs circle parameters from stress inputs.

Calculator

Results

Principal Stress σ1 0
Principal Stress σ2 0
Maximum Shear Stress τmax 0

Data Source and Methodology

All calculations are based rigorously on the formulas and data provided by the authoritative source "Engineering Mechanics" by Hibbeler, 14th Edition. View Source.

The Formula Explained

Principal Stresses: \( \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)

Maximum Shear Stress: \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)

Glossary of Variables

  • σx: Normal stress in the x-direction.
  • σy: Normal stress in the y-direction.
  • τxy: Shear stress in the xy plane.
  • σ1, σ2: Principal stresses.
  • τmax: Maximum shear stress.

How It Works: A Step-by-Step Example

Consider a material with σx = 100 MPa, σy = 50 MPa, and τxy = 25 MPa. Using the formulas above, you can calculate the principal stresses and maximum shear stress.

Frequently Asked Questions (FAQ)

What is Mohr's Circle?

Mohr's Circle is a graphical representation of the state of stress at a point in a material.

Why use a Mohr's Circle Calculator?

This tool simplifies the complex calculations involved in determining stress transformations in materials.

Can I use this calculator for 3D stress analysis?

No, this calculator is designed for 2D stress analysis only.

What are principal stresses?

Principal stresses are the normal stresses on a plane where the shear stress is zero.

How is maximum shear stress calculated?

Maximum shear stress is determined using the formula \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \).

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted text)
Principal Stresses: \( \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \) Maximum Shear Stress: \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)
Variables and units
  • T = property tax (annual or monthly depending on input) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Mohr's Circle Calculator

Compute principal stresses and Mohrs circle parameters from stress inputs.

Calculator

Results

Principal Stress σ1 0
Principal Stress σ2 0
Maximum Shear Stress τmax 0

Data Source and Methodology

All calculations are based rigorously on the formulas and data provided by the authoritative source "Engineering Mechanics" by Hibbeler, 14th Edition. View Source.

The Formula Explained

Principal Stresses: \( \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)

Maximum Shear Stress: \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)

Glossary of Variables

  • σx: Normal stress in the x-direction.
  • σy: Normal stress in the y-direction.
  • τxy: Shear stress in the xy plane.
  • σ1, σ2: Principal stresses.
  • τmax: Maximum shear stress.

How It Works: A Step-by-Step Example

Consider a material with σx = 100 MPa, σy = 50 MPa, and τxy = 25 MPa. Using the formulas above, you can calculate the principal stresses and maximum shear stress.

Frequently Asked Questions (FAQ)

What is Mohr's Circle?

Mohr's Circle is a graphical representation of the state of stress at a point in a material.

Why use a Mohr's Circle Calculator?

This tool simplifies the complex calculations involved in determining stress transformations in materials.

Can I use this calculator for 3D stress analysis?

No, this calculator is designed for 2D stress analysis only.

What are principal stresses?

Principal stresses are the normal stresses on a plane where the shear stress is zero.

How is maximum shear stress calculated?

Maximum shear stress is determined using the formula \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \).

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted text)
Principal Stresses: \( \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \) Maximum Shear Stress: \( \tau_{max} = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} \)
Variables and units
  • T = property tax (annual or monthly depending on input) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).