Maximum Shear Stress given Member is under Direct and Shear Stress Calculator

✖The stress acting along x-direction.ⓘ Stress acting along x-direction [σ_x]			+10% -10%
✖The Stress acting along y-direction is denoted by the symbol σ_y.ⓘ Stress acting along y-direction [σ_y]			+10% -10%
✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress [𝜏]			+10% -10%

✖Maximum Shear Stress that acts coplanar with cross-section of material, arises due to shear forces.ⓘ Maximum Shear Stress given Member is under Direct and Shear Stress [𝜏_max]

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Maximum Shear Stress given Member is under Direct and Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Shear Stress = sqrt((Stress acting along x-direction-Stress acting along y-direction)^2+4*Shear Stress^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 that acts coplanar with cross-section of material, arises due to shear forces.
Stress acting along x-direction - (Measured in Pascal) - The stress acting along x-direction.
Stress acting along y-direction - (Measured in Pascal) - The Stress acting along y-direction is denoted by the symbol σ_y.
Shear Stress - (Measured in Pascal) - Shear Stress is 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 acting along x-direction: 0.5 Megapascal --> 500000 Pascal (Check conversion here)
Stress acting along y-direction: 0.8 Megapascal --> 800000 Pascal (Check conversion here)
Shear Stress: 2.4 Megapascal --> 2400000 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((500000-800000)^2+4*2400000^2)/2

Evaluating ... ...

𝜏_max = 2404682.93128221

STEP 3: Convert Result to Output's Unit

2404682.93128221 Pascal -->2.40468293128221 Megapascal (Check conversion here)

FINAL ANSWER

2.40468293128221 ≈ 2.404683 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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< Shear Stress Calculators

Maximum Shear Stress given Member is under Direct and Shear Stress

LaTeX Go Maximum Shear Stress = sqrt((Stress acting along x-direction-Stress acting along y-direction)^2+4*Shear Stress^2)/2

Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress

LaTeX Go Plane Angle = 1/2*atan((Stress acting along x-direction-Stress acting along y-direction)/(2*Shear Stress))

Shear Stress using Obliquity

LaTeX Go Shear Stress = tan(Angle of Obliquity)*Normal Stress

Maximum Shear Stress given Major and Minor Tensile Stress

LaTeX Go Maximum Shear Stress = (Major Tensile Stress-Minor Tensile Stress)/2

Maximum Shear Stress given Member is under Direct and Shear Stress Formula

LaTeX Go

Maximum Shear Stress = sqrt((Stress acting along x-direction-Stress acting along y-direction)^2+4*Shear Stress^2)/2
𝜏_max = sqrt((σ_x-σ_y)^2+4*𝜏^2)/2

What is principal 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.

How to Calculate Maximum Shear Stress given Member is under Direct and Shear Stress?

Maximum Shear Stress given Member is under Direct and Shear Stress calculator uses Maximum Shear Stress = sqrt((Stress acting along x-direction-Stress acting along y-direction)^2+4*Shear Stress^2)/2 to calculate the Maximum Shear Stress, The Maximum Shear Stress given Member is under Direct and Shear Stress is half 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 given Member is under Direct and Shear Stress using this online calculator? To use this online calculator for Maximum Shear Stress given Member is under Direct and Shear Stress, enter Stress acting along x-direction (σ_x), Stress acting along y-direction (σ_y) & Shear Stress (𝜏) and hit the calculate button. Here is how the Maximum Shear Stress given Member is under Direct and Shear Stress calculation can be explained with given input values -> 2.4E-6 = sqrt((500000-800000)^2+4*2400000^2)/2.

FAQ

What is Maximum Shear Stress given Member is under Direct and Shear Stress?

The Maximum Shear Stress given Member is under Direct and Shear Stress is half 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 acting along x-direction-Stress acting along y-direction)^2+4*Shear Stress^2)/2. The stress acting along x-direction, The Stress acting along y-direction is denoted by the symbol σ_y & Shear Stress is 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 given Member is under Direct and Shear Stress?

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

How many ways are there to calculate Maximum Shear Stress?

In this formula, Maximum Shear Stress uses Stress acting along x-direction, Stress acting along y-direction & Shear Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum Shear Stress = (Major Tensile Stress-Minor Tensile Stress)/2

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