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

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The Plane Angle value is the angle made by the plane. Check FAQs

θ pl = \frac{1}{2} \cdot a \tan (\frac{σ x - σ y}{2 \cdot 𝜏})

θ_pl - Plane Angle?σ_x - Stress Acting Along X Direction?σ_y - Stress Acting Along Y Direction?𝜏 - Shear Stress?

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

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Here is how the Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress equation looks like with Values.

Here is how the Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress equation looks like with Units.

Here is how the Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress equation looks like.

-1.7882 = \frac{1}{2} \cdot a \tan (\frac{0.5 - 0.8}{2 \cdot 2.4})

-1.7882° = \frac{1}{2} \cdot a \tan (\frac{0.5MPa - 0.8MPa}{2 \cdot 2.4MPa})

-1.7882 = \frac{1}{2} \cdot a \tan (\frac{0.5 - 0.8}{2 \cdot 2.4})

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

Follow our step by step solution on how to calculate Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress?

FIRST Step Consider the formula

θ pl = \frac{1}{2} \cdot a \tan (\frac{σ x - σ y}{2 \cdot 𝜏})

Next Step Substitute values of Variables

∴

θ pl = \frac{1}{2} \cdot a \tan (\frac{0.5MPa - 0.8MPa}{2 \cdot 2.4MPa})

Next Step Convert Units

∴

θ pl = \frac{1}{2} \cdot a \tan (\frac{500000Pa - 800000Pa}{2 \cdot 2.4E+6Pa})

Next Step Prepare to Evaluate

∴

θ pl = \frac{1}{2} \cdot a \tan (\frac{500000 - 800000}{2 \cdot 2.4E+6})

Next Step Evaluate

∴

θ pl = -0.0312094049979787rad

Next Step Convert to Output's Unit

∴

θ pl = -1.78816718749901°

LAST Step Rounding Answer

∴

θ pl = -1.7882°

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

Variables

Functions

Plane Angle

The Plane Angle value is the angle made by the plane.

Symbol: θ_pl

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Plane Angle

Stress Acting Along X Direction

Stress Acting Along X Direction is the stress acting along x-direction.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Acting Along X Direction

Stress Acting Along Y Direction

Stress Acting Along Y Direction is stress acting along y direction is denoted by σy.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Acting Along Y Direction

Shear Stress

Shear Stress is 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

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.

Syntax: 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.

Syntax: atan(Number)

Other formulas in Shear Stress category

Go Shear Stress using Obliquity

𝜏 = \tan (ϕ) \cdot σ n

Go Maximum Shear Stress given Major and Minor Tensile Stress

𝜏 m = \frac{σ 1 - σ 2}{2}

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

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

How to Evaluate 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 evaluator uses Plane Angle = 1/2*atan((Stress Acting Along X Direction-Stress Acting Along Y Direction)/(2*Shear Stress)) to evaluate the Plane Angle, Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress formula is defined as a measure that determines the angle at which the maximum or minimum shear stress occurs in a member subjected to both direct and shear stresses, providing critical information for structural analysis and design. Plane Angle is denoted by θ_pl symbol.

How to evaluate Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress?

The formula of Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress is expressed as Plane Angle = 1/2*atan((Stress Acting Along X Direction-Stress Acting Along Y Direction)/(2*Shear Stress)). Here is an example- -102.454433 = 1/2*atan((500000-800000)/(2*2400000)).

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

With Stress Acting Along X Direction (σ_x), Stress Acting Along Y Direction (σ_y) & Shear Stress (𝜏) we can find Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress using the formula - Plane Angle = 1/2*atan((Stress Acting Along X Direction-Stress Acting Along Y Direction)/(2*Shear Stress)). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress be negative?

Yes, the Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress, measured in Angle can be negative.

Which unit is used to measure 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 is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Condition for Maximum or Minimum Shear Stress given Member under Direct and Shear Stress can be measured.

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

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

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

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

Other formulas in Shear Stress category

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

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

Variable Name