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

✖Stress Acting Along X Direction is the stress acting along x-direction.ⓘ Stress Acting Along X Direction [σ_x]			+10% -10%
✖Stress Acting Along Y Direction is stress acting along y direction is denoted by σy.ⓘ 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_m]

⎘ Copy

👎

Formula

Reset

👍

Download Principal Stresses Formulas PDF PDF Image

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_m = 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) - Stress Acting Along X Direction is the stress acting along x-direction.
Stress Acting Along Y Direction - (Measured in Pascal) - Stress Acting Along Y Direction is stress acting along y direction is denoted by σy.
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_m = sqrt((σ_x-σ_y)^2+4*𝜏^2)/2 --> sqrt((500000-800000)^2+4*2400000^2)/2

Evaluating ... ...

𝜏_m = 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 00.007 seconds)

You are here -

Home » Physics » Strength of Materials » Stress and Strain » Principal Stresses and Strains » Principal Stresses » Mechanical » Shear Stress » Maximum Shear Stress given Member is under Direct and Shear Stress

Credits

Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< Shear Stress Calculators

Maximum Shear Stress given Member is under Direct and Shear Stress

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

Go Plane Angle = 1/2*atan((Stress Acting Along X Direction-Stress Acting Along Y Direction)/(2*Shear Stress))

Shear Stress using Obliquity

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

Maximum Shear Stress given Major and Minor Tensile Stress

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

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

Maximum Shear Stress = sqrt((Stress Acting Along X Direction-Stress Acting Along Y Direction)^2+4*Shear Stress^2)/2
𝜏_m = 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, Maximum Shear Stress given Member is under Direct and Shear Stress formula is defined as a measure of the maximum shear stress experienced by a member when it is subjected to both direct and shear stresses, providing a critical value for structural analysis and design. Maximum Shear Stress is denoted by 𝜏_m 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?

Maximum Shear Stress given Member is under Direct and Shear Stress formula is defined as a measure of the maximum shear stress experienced by a member when it is subjected to both direct and shear stresses, providing a critical value for structural analysis and design and is represented as 𝜏_m = 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. Stress Acting Along X Direction is the stress acting along x-direction, Stress Acting Along Y Direction is stress acting along y direction is denoted by σy & 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?

Maximum Shear Stress given Member is under Direct and Shear Stress formula is defined as a measure of the maximum shear stress experienced by a member when it is subjected to both direct and shear stresses, providing a critical value for structural analysis and design 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

Home

FREE PDFs

🔍 Search