Maximum Shear Stress Calculator

✖Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.ⓘ Stress Along x Direction [σ_x]			+10% -10%
✖Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.ⓘ Stress Along y Direction [σ_y]			+10% -10%
✖Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress in Mpa [τ]			+10% -10%

✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum Shear Stress [τ_max]

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Formula

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Maximum Shear Stress

Formula

`"τ"_{"max"} = sqrt(("σ"_{"x"}-"σ"_{"y"})^2+4*"τ"^2)/2`

Example

`"55.26753MPa"=sqrt(("95MPa"-"22MPa")^2+4*("41.5MPa")^2)/2`

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Maximum Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2
τ_max = sqrt((σ_x-σ_y)^2+4*τ^2)/2
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.
Stress Along x Direction - (Measured in Pascal) - Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.
Stress Along y Direction - (Measured in Pascal) - Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.
Shear Stress in Mpa - (Measured in Pascal) - Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Stress Along x Direction: 95 Megapascal --> 95000000 Pascal (Check conversion here)
Stress Along y Direction: 22 Megapascal --> 22000000 Pascal (Check conversion here)
Shear Stress in Mpa: 41.5 Megapascal --> 41500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_max = sqrt((σ_x-σ_y)^2+4*τ^2)/2 --> sqrt((95000000-22000000)^2+4*41500000^2)/2

Evaluating ... ...

τ_max = 55267531.1552814

STEP 3: Convert Result to Output's Unit

55267531.1552814 Pascal -->55.2675311552814 Megapascal (Check conversion here)

FINAL ANSWER

55.2675311552814 ≈ 55.26753 Megapascal <-- Maximum Shear Stress

(Calculation completed in 00.004 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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National Institute Of Technology (NIT), Hamirpur

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< 4 Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity Calculators

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

Go Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle)

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

Go Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle)

Maximum Shear Stress

Go Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2

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

Go Radius of Mohr's circle = (Major Principal Stress-Minor Principal Stress)/2

< 4 When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses of Unequal Intensity Calculators

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

Go Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle)

Maximum Shear Stress

Go Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2

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

Go Radius of Mohr's circle = (Major Principal Stress-Minor Principal Stress)/2

Maximum Shear Stress Formula

Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2
τ_max = sqrt((σ_x-σ_y)^2+4*τ^2)/2

What is Principal Stress & Normal Stress?

When a stress tensor acts on a body, the plane along which the shear stress terms vanish is called the principal plane, and the stress on such planes is called principal stress.
The intensity of net force acting per unit area normal to the cross-section under consideration is called normal stress.

What is Tangential Force?

The tangential force, also known as the shear force, is the force acting parallel to the surface. When the direction of the deforming force or external force is parallel to the cross-sectional area, the stress experienced by the object is called shearing stress or tangential stress.

How to Calculate Maximum Shear Stress?

Maximum Shear Stress calculator uses Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2 to calculate 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 calculate Maximum Shear Stress using this online calculator? To use this online calculator 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. Here is how the Maximum Shear Stress calculation can be explained with given input values -> 5.5E-5 = sqrt((95000000-22000000)^2+4*41500000^2)/2.

FAQ

What is Maximum Shear Stress?

The Maximum Shear Stress formula is defined as half of the difference between major principal stress and minor principal stress and is represented as τ_max = sqrt((σ_x-σ_y)^2+4*τ^2)/2 or Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2. Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation, Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure & Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Maximum Shear Stress?

The Maximum Shear Stress formula is defined as half of the difference between major principal stress and minor principal stress is calculated using Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2. To calculate Maximum Shear Stress, you need Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ). With our tool, you need to enter the respective value for Stress Along x Direction, Stress Along y Direction & Shear Stress in Mpa and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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