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Angle of Twist in Combined Bending and Torsional Stress Formula

GoAngle of Twist in Combined Bending and Torsion Formula

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The Theta is the angle subtended by a plane of a body when stress is applied. Check FAQs

θ = 0.5 \cdot \arctan (2 \cdot \frac{T}{σ b})

θ - Theta?T - Torsion?σ_b - Bending Stress?

Angle of Twist in Combined Bending and Torsional Stress Example

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Here is how the Angle of Twist in Combined Bending and Torsional Stress equation looks like with Values.

Here is how the Angle of Twist in Combined Bending and Torsional Stress equation looks like with Units.

Here is how the Angle of Twist in Combined Bending and Torsional Stress equation looks like.

8.9958 = 0.5 \cdot \arctan (2 \cdot \frac{0.1169}{0.72})

8.9958° = 0.5 \cdot \arctan (2 \cdot \frac{0.1169MPa}{0.72MPa})

8.9958 = 0.5 \cdot \arctan (2 \cdot \frac{0.1169}{0.72})

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Angle of Twist in Combined Bending and Torsional Stress Solution

Follow our step by step solution on how to calculate Angle of Twist in Combined Bending and Torsional Stress?

FIRST Step Consider the formula

θ = 0.5 \cdot \arctan (2 \cdot \frac{T}{σ b})

Next Step Substitute values of Variables

∴

θ = 0.5 \cdot \arctan (2 \cdot \frac{0.1169MPa}{0.72MPa})

Next Step Convert Units

∴

θ = 0.5 \cdot \arctan (2 \cdot \frac{116913Pa}{720000Pa})

Next Step Prepare to Evaluate

∴

θ = 0.5 \cdot \arctan (2 \cdot \frac{116913}{720000})

Next Step Evaluate

∴

θ = 0.157006652162129rad

Next Step Convert to Output's Unit

∴

θ = 8.99581852437023°

LAST Step Rounding Answer

∴

θ = 8.9958°

Angle of Twist in Combined Bending and Torsional Stress Formula Elements

Variables

Functions

Theta

The Theta is the angle subtended by a plane of a body when stress is applied.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Theta

Torsion

Torsion is the twisting of an object due to an applied torque.

Symbol: T

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Torsion

Bending Stress

The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

Symbol: σ_b

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Bending 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)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: ctan(Angle)

arctan

Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x).

Syntax: arctan(Number)

Other Formulas to find Theta

Go Angle of Twist in Combined Bending and Torsion

θ = \frac{\arctan (\frac{T}{M})}{2}

Other formulas in Combined Bending and Torsion Condition category

Go Bending Moment given Combined Bending and Torsion

M = \frac{T}{\tan (2 \cdot θ)}

Go Torsional Moment when Member is subjected to both Bending and Torsion

T = M \cdot (\tan (2 \cdot θ))

Go Torsional Stress given Combined Bending and Torsional Stress

T = (\frac{\tan (2 \cdot θ)}{2}) \cdot σ b

Go Bending Stress given Combined Bending and Torsional Stress

σ b = \frac{T}{\frac{\tan (2 \cdot θ)}{2}}

How to Evaluate Angle of Twist in Combined Bending and Torsional Stress?

Angle of Twist in Combined Bending and Torsional Stress evaluator uses Theta = 0.5*arctan(2*Torsion/Bending Stress) to evaluate the Theta, The Angle of Twist in Combined Bending and Torsional Stress formula is defined as a condition of combined bending and torsion acting on a member. Theta is denoted by θ symbol.

How to evaluate Angle of Twist in Combined Bending and Torsional Stress using this online evaluator? To use this online evaluator for Angle of Twist in Combined Bending and Torsional Stress, enter Torsion (T) & Bending Stress (σ_b) and hit the calculate button.

FAQs on Angle of Twist in Combined Bending and Torsional Stress

What is the formula to find Angle of Twist in Combined Bending and Torsional Stress?

The formula of Angle of Twist in Combined Bending and Torsional Stress is expressed as Theta = 0.5*arctan(2*Torsion/Bending Stress). Here is an example- 2358.324 = 0.5*arctan(2*116913/720000).

How to calculate Angle of Twist in Combined Bending and Torsional Stress?

With Torsion (T) & Bending Stress (σ_b) we can find Angle of Twist in Combined Bending and Torsional Stress using the formula - Theta = 0.5*arctan(2*Torsion/Bending Stress). This formula also uses TangentCotangent Cotangent, Inverse Tangent function(s).

What are the other ways to Calculate Theta?

Here are the different ways to Calculate Theta-

Theta=(arctan(Torsion/Bending Moment))/2

Can the Angle of Twist in Combined Bending and Torsional Stress be negative?

No, the Angle of Twist in Combined Bending and Torsional Stress, measured in Angle cannot be negative.

Which unit is used to measure Angle of Twist in Combined Bending and Torsional Stress?

Angle of Twist in Combined Bending and Torsional Stress is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Twist in Combined Bending and Torsional Stress can be measured.

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Angle of Twist in Combined Bending and Torsional Stress Formula

​GoAngle of Twist in Combined Bending and Torsion Formula

Angle of Twist in Combined Bending and Torsional Stress Example

Angle of Twist in Combined Bending and Torsional Stress Solution

Angle of Twist in Combined Bending and Torsional Stress Formula Elements

Other Formulas to find Theta

Other formulas in Combined Bending and Torsion Condition category

How to Evaluate Angle of Twist in Combined Bending and Torsional Stress?

FAQs on Angle of Twist in Combined Bending and Torsional Stress

Variable Name

GoAngle of Twist in Combined Bending and Torsion Formula