Angle of Twist in Combined Bending and Torsional Stress Calculator

✖Torsion is the twisting of an object due to an applied torque.ⓘ Torsion [T]			+10% -10%
✖The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Bending Stress [σ_b]			+10% -10%

✖The Theta is the angle subtended by a plane of a body when stress is applied.ⓘ Angle of Twist in Combined Bending and Torsional Stress [θ]

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Formula

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Angle of Twist in Combined Bending and Torsional Stress

Formula

`"θ" = 0.5*arctan(2*"T"/"σ"_{"b"})`

Example

`"8.995819°"=0.5*arctan(2*"0.116913MPa"/"0.72MPa")`

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Angle of Twist in Combined Bending and Torsional Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta = 0.5*arctan(2*Torsion/Bending Stress)
θ = 0.5*arctan(2*T/σ_b)
This formula uses 3 Functions, 3 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)
ctan - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., 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)., arctan(Number)

Variables Used

Theta - (Measured in Radian) - The Theta is the angle subtended by a plane of a body when stress is applied.
Torsion - (Measured in Pascal) - Torsion is the twisting of an object due to an applied torque.
Bending Stress - (Measured in Pascal) - The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

STEP 1: Convert Input(s) to Base Unit

Torsion: 0.116913 Megapascal --> 116913 Pascal (Check conversion here)
Bending Stress: 0.72 Megapascal --> 720000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = 0.5*arctan(2*T/σ_b) --> 0.5*arctan(2*116913/720000)

Evaluating ... ...

θ = 0.157006652162129

STEP 3: Convert Result to Output's Unit

0.157006652162129 Radian -->8.99581852437023 Degree (Check conversion here)

FINAL ANSWER

8.99581852437023 ≈ 8.995819 Degree <-- Theta

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< 6 Combined Bending and Torsion Condition Calculators

Angle of Twist in Combined Bending and Torsional Stress

Go Theta = 0.5*arctan(2*Torsion/Bending Stress)

Angle of Twist in Combined Bending and Torsion

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

Torsional Stress given Combined Bending and Torsional Stress

Go Torsion = (tan(2*Theta)/2)*Bending Stress

Bending Stress given Combined Bending and Torsional Stress

Go Bending Stress = Torsion/(tan(2*Theta)/2)

Torsional Moment when Member is subjected to both Bending and Torsion

Go Torsion = Bending Moment*(tan(2*Theta))

Bending Moment given Combined Bending and Torsion

Go Bending Moment = Torsion/(tan(2*Theta))

Angle of Twist in Combined Bending and Torsional Stress Formula

Theta = 0.5*arctan(2*Torsion/Bending Stress)
θ = 0.5*arctan(2*T/σ_b)

What is Torsional Bending?

Torsional bending is the twisting of a beam under the action of a torque. It occurs when external loads act far away from the vertical plane of bending, and the beam is subjected to twisting about its longitudinal axis, known as torsion, in addition to the shearing force and bending moment.
Torsion on structural elements may be classified into two types: statically determinate, and statically indeterminate.

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

Angle of Twist in Combined Bending and Torsional Stress calculator uses Theta = 0.5*arctan(2*Torsion/Bending Stress) to calculate 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 calculate Angle of Twist in Combined Bending and Torsional Stress using this online calculator? To use this online calculator for Angle of Twist in Combined Bending and Torsional Stress, enter Torsion (T) & Bending Stress (σ_b) and hit the calculate button. Here is how the Angle of Twist in Combined Bending and Torsional Stress calculation can be explained with given input values -> 2358.324 = 0.5*arctan(2*116913/720000).

FAQ

What is Angle of Twist in Combined Bending and Torsional Stress?

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 and is represented as θ = 0.5*arctan(2*T/σ_b) or Theta = 0.5*arctan(2*Torsion/Bending Stress). Torsion is the twisting of an object due to an applied torque & The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

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

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 is calculated using Theta = 0.5*arctan(2*Torsion/Bending Stress). To calculate Angle of Twist in Combined Bending and Torsional Stress, you need Torsion (T) & Bending Stress (σ_b). With our tool, you need to enter the respective value for Torsion & Bending 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 Theta?

In this formula, Theta uses Torsion & Bending Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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