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Maximum Shear Stress Formula

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Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area. Check FAQs

τ max = \frac{\sqrt{{(σ x - σ y)}^{2} + 4 \cdot τ^{2}}}{2}

τ_max - Maximum Shear Stress?σ_x - Stress Along x Direction?σ_y - Stress Along y Direction?τ - Shear Stress in Mpa?

Maximum Shear Stress Example

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Here is how the Maximum Shear Stress equation looks like with Values.

Here is how the Maximum Shear Stress equation looks like with Units.

Here is how the Maximum Shear Stress equation looks like.

55.2675 = \frac{\sqrt{{(95 - 22)}^{2} + 4 \cdot {41.5}^{2}}}{2}

55.2675MPa = \frac{\sqrt{{(95MPa - 22MPa)}^{2} + 4 \cdot {41.5MPa}^{2}}}{2}

55.2675 = \frac{\sqrt{{(95 - 22)}^{2} + 4 \cdot {41.5}^{2}}}{2}

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Maximum Shear Stress Solution

Follow our step by step solution on how to calculate Maximum Shear Stress?

FIRST Step Consider the formula

τ max = \frac{\sqrt{{(σ x - σ y)}^{2} + 4 \cdot τ^{2}}}{2}

Next Step Substitute values of Variables

∴

τ max = \frac{\sqrt{{(95MPa - 22MPa)}^{2} + 4 \cdot {41.5MPa}^{2}}}{2}

Next Step Convert Units

∴

τ max = \frac{\sqrt{{(9.5E+7Pa - 2.2E+7Pa)}^{2} + 4 \cdot {4.2E+7Pa}^{2}}}{2}

Next Step Prepare to Evaluate

∴

τ max = \frac{\sqrt{{(9.5E+7 - 2.2E+7)}^{2} + 4 \cdot {4.2E+7}^{2}}}{2}

Next Step Evaluate

∴

τ max = 55267531.1552814Pa

Next Step Convert to Output's Unit

∴

τ max = 55.2675311552814MPa

LAST Step Rounding Answer

∴

τ max = 55.2675MPa

Maximum Shear Stress Formula Elements

Variables

Functions

Maximum Shear Stress

Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

Symbol: τ_max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress

Stress Along x Direction

Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Along x Direction

Stress Along y Direction

Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Along y Direction

Shear Stress in Mpa

Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: τ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress in Mpa

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity category

Go Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

σ θ = \frac{σ x + σ y}{2} + \frac{σ x - σ y}{2} \cdot \cos (2 \cdot θ plane) + τ \cdot \sin (2 \cdot θ plane)

Go Radius of Mohr's Circle for Two Mutually Perpendicular Stresses of Unequal Intensities

R = \frac{σ major - σ minor}{2}

Go Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

σ t = \frac{σ x - σ y}{2} \cdot \sin (2 \cdot θ plane) - τ \cdot \cos (2 \cdot θ plane)

How to Evaluate Maximum Shear Stress?

Maximum Shear Stress evaluator uses Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2 to evaluate the Maximum Shear Stress, The Maximum Shear Stress formula is defined as half of the difference between major principal stress and minor principal stress. Maximum Shear Stress is denoted by τ_max symbol.

How to evaluate Maximum Shear Stress using this online evaluator? To use this online evaluator for Maximum Shear Stress, enter Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) and hit the calculate button.

FAQs on Maximum Shear Stress

What is the formula to find Maximum Shear Stress?

The formula of Maximum Shear Stress is expressed as Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2. Here is an example- 5.5E-5 = sqrt((95000000-22000000)^2+4*41500000^2)/2.

How to calculate Maximum Shear Stress?

With Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) we can find Maximum Shear Stress using the formula - Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2. This formula also uses Square Root Function function(s).

Can the Maximum Shear Stress be negative?

No, the Maximum Shear Stress, measured in Stress cannot be negative.

Which unit is used to measure Maximum Shear Stress?

Maximum Shear Stress is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Maximum Shear Stress can be measured.

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Maximum Shear Stress Formula

Maximum Shear Stress Example

Maximum Shear Stress Solution

Maximum Shear Stress Formula Elements

Other formulas in Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity category

How to Evaluate Maximum Shear Stress?

FAQs on Maximum Shear Stress

Variable Name