Maximum In-Plane Shear Stress
Find the radius of Mohr’s circle for a plane-stress state.
Try this formula
Calculate maximum in-plane shear stress magnitude or choose another supported quantity.
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Try this formula
Calculate maximum in-plane shear stress magnitude or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Maximum in-plane shear stress magnitude
Enter the known values to see the result.
Use a plane-stress state with consistent signs. This is the maximum shear within the original plane, not necessarily the absolute maximum shear in three dimensions. For absolute maximum shear, include the zero out-of-plane principal stress.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Stress Transformations — Maximum In-Plane Shear Stress. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
The radius of Mohr’s circle measures how large the in-plane shear component can become as the axes rotate. Equal biaxial normal stress alone has zero in-plane shear, even though three-dimensional shear extrema can still be nonzero.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Maximum in-plane shear stress magnitude | ||
| Signed normal stress on the x face | ||
| Signed normal stress on the y face | ||
| Signed in-plane shear stress |
Real-World Applications
Mohr’s circle
Find its radius directly from stress components.
Stress interpretation
Distinguish in-plane from absolute maximum shear.
Worked Example
Problem
For σx = 80 MPa, σy = 20 MPa, and τxy = 30 MPa, find the maximum in-plane shear magnitude.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Stress Transformations — Maximum In-Plane Shear Stress. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use a plane-stress state with consistent signs.
- • This is the maximum shear within the original plane, not necessarily the absolute maximum shear in three dimensions.
- • For absolute maximum shear, include the zero out-of-plane principal stress.
Languages
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