Condition for Maximum or Minimum Shear Stress given Member 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%

✖The Plane Angle value is the angle made by the plane.ⓘ Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress [θ_plane]

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

Formula

`"θ"_{"plane"} = 1/2*atan(("σ"_{"x"}-"σ"_{"y"})/(2*"𝜏"))`

Example

`"-1.788167°"=1/2*atan(("0.5MPa"-"0.8MPa")/(2*"2.4MPa"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Plane Angle = 1/2*atan((Stress acting along x-direction-Stress acting along y-direction)/(2*Shear Stress))
θ_plane = 1/2*atan((σ_x-σ_y)/(2*𝜏))
This formula uses 2 Functions, 4 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Plane Angle - (Measured in Radian) - The Plane Angle value is the angle made by the plane.
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

θ_plane = 1/2*atan((σ_x-σ_y)/(2*𝜏)) --> 1/2*atan((500000-800000)/(2*2400000))

Evaluating ... ...

θ_plane = -0.0312094049979787

STEP 3: Convert Result to Output's Unit

-0.0312094049979787 Radian -->-1.78816718749901 Degree (Check conversion here)

FINAL ANSWER

-1.78816718749901 ≈ -1.788167 Degree <-- Plane Angle

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Stress and Strain » Principal Stresses and Strains » Principal Stresses » Shear Stress » Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress

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National Institute of Technology (NIT), Tiruchirapalli

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< 4 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

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

Plane Angle = 1/2*atan((Stress acting along x-direction-Stress acting along y-direction)/(2*Shear Stress))
θ_plane = 1/2*atan((σ_x-σ_y)/(2*𝜏))

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

Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress calculator uses Plane Angle = 1/2*atan((Stress acting along x-direction-Stress acting along y-direction)/(2*Shear Stress)) to calculate the Plane Angle, The Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress is when the inverse tangent of the ratio of difference of stress along x and y-axis to twice the value of shear stress is equal to twice the angle of the plane. Plane Angle is denoted by θ_plane symbol.

How to calculate Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress using this online calculator? To use this online calculator for Condition for Maximum or Minimum Shear Stress given Member 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 Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress calculation can be explained with given input values -> -102.454433 = 1/2*atan((500000-800000)/(2*2400000)).

FAQ

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

The Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress is when the inverse tangent of the ratio of difference of stress along x and y-axis to twice the value of shear stress is equal to twice the angle of the plane and is represented as θ_plane = 1/2*atan((σ_x-σ_y)/(2*𝜏)) or Plane Angle = 1/2*atan((Stress acting along x-direction-Stress acting along y-direction)/(2*Shear Stress)). 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 Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress?

The Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress is when the inverse tangent of the ratio of difference of stress along x and y-axis to twice the value of shear stress is equal to twice the angle of the plane is calculated using Plane Angle = 1/2*atan((Stress acting along x-direction-Stress acting along y-direction)/(2*Shear Stress)). To calculate Condition for Maximum or Minimum Shear Stress given Member 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.

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