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Angle of Obliquity Formula

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The Angle of Obliquity is the angle made by resultant stress with the normal of the oblique plane. Check FAQs

ϕ = a \tan (\frac{𝜏}{σ n})

ϕ - Angle of Obliquity?𝜏 - Shear Stress?σ_n - Normal Stress?

Angle of Obliquity Example

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With units

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Here is how the Angle of Obliquity equation looks like with Values.

Here is how the Angle of Obliquity equation looks like with Units.

Here is how the Angle of Obliquity equation looks like.

89.7327 = a \tan (\frac{2.4}{0.0112})

89.7327° = a \tan (\frac{2.4MPa}{0.0112MPa})

89.7327 = a \tan (\frac{2.4}{0.0112})

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Angle of Obliquity Solution

Follow our step by step solution on how to calculate Angle of Obliquity?

FIRST Step Consider the formula

ϕ = a \tan (\frac{𝜏}{σ n})

Next Step Substitute values of Variables

∴

ϕ = a \tan (\frac{2.4MPa}{0.0112MPa})

Next Step Convert Units

∴

ϕ = a \tan (\frac{2.4E+6Pa}{11196Pa})

Next Step Prepare to Evaluate

∴

ϕ = a \tan (\frac{2.4E+6}{11196})

Next Step Evaluate

∴

ϕ = 1.56613136063471rad

Next Step Convert to Output's Unit

∴

ϕ = 89.7327171274671°

LAST Step Rounding Answer

∴

ϕ = 89.7327°

Angle of Obliquity Formula Elements

Variables

Functions

Angle of Obliquity

The Angle of Obliquity is the angle made by resultant stress with the normal of the oblique plane.

Symbol: ϕ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle of Obliquity

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

Normal Stress

Normal Stress is stress that occurs when a member is loaded by an axial force.

Symbol: σ_n

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Normal 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 Stress Relations category

Go Resultant Stress on Oblique Section given Stress in Perpendicular Directions

σ R = \sqrt{{σ n}^{2} + 𝜏^{2}}

Go Stress along Maximum Axial Force

σ = \frac{P a}{A}

Go Maximum Axial Force

P a = σ \cdot A

Go Safe Stress given Safe Value of Axial Pull

σ = \frac{P s}{A}

How to Evaluate Angle of Obliquity?

Angle of Obliquity evaluator uses Angle of Obliquity = atan(Shear Stress/Normal Stress) to evaluate the Angle of Obliquity, Angle of Obliquity formula is defined as a measure of the angle between the principal stress direction and the horizontal plane in a three-dimensional stress state, providing a way to quantify the orientation of principal stresses in a material or structure. Angle of Obliquity is denoted by ϕ symbol.

How to evaluate Angle of Obliquity using this online evaluator? To use this online evaluator for Angle of Obliquity, enter Shear Stress (𝜏) & Normal Stress (σ_n) and hit the calculate button.

FAQs on Angle of Obliquity

What is the formula to find Angle of Obliquity?

The formula of Angle of Obliquity is expressed as Angle of Obliquity = atan(Shear Stress/Normal Stress). Here is an example- 5141.306 = atan(2400000/11196).

How to calculate Angle of Obliquity?

With Shear Stress (𝜏) & Normal Stress (σ_n) we can find Angle of Obliquity using the formula - Angle of Obliquity = atan(Shear Stress/Normal Stress). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Angle of Obliquity be negative?

Yes, the Angle of Obliquity, measured in Angle can be negative.

Which unit is used to measure Angle of Obliquity?

Angle of Obliquity is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Obliquity can be measured.

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