Angle of Twist in Combined Bending and Torsion Calculator

✖Torsion is the twisting of an object due to an applied torque.ⓘ Torsion [T]			+10% -10%
✖Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.ⓘ Bending Moment [M]			+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 Torsion [θ]

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Angle of Twist in Combined Bending and Torsion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta = (arctan(Torsion/Bending Moment))/2
θ = (arctan(T/M))/2
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 Moment - (Measured in Newton Meter) - Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.

STEP 1: Convert Input(s) to Base Unit

Torsion: 0.116913 Megapascal --> 116913 Pascal (Check conversion here)
Bending Moment: 67.5 Kilonewton Meter --> 67500 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (arctan(T/M))/2 --> (arctan(116913/67500))/2

Evaluating ... ...

θ = 0.523597980205553

STEP 3: Convert Result to Output's Unit

0.523597980205553 Radian -->29.9999544273583 Degree (Check conversion here)

FINAL ANSWER

29.9999544273583 ≈ 29.99995 Degree <-- Theta

(Calculation completed in 00.007 seconds)

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Home » Engineering » Civil » Strength of Materials » Principal Stress » Combined Bending and Torsion Condition » Angle of Twist in Combined Bending and Torsion

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National Institute of Technology Karnataka (NITK), Surathkal

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< Combined Bending and Torsion Condition Calculators

Angle of Twist in Combined Bending and Torsional Stress

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

Angle of Twist in Combined Bending and Torsion

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

Torsional Moment when Member is subjected to both Bending and Torsion

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

Bending Moment given Combined Bending and Torsion

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

Angle of Twist in Combined Bending and Torsion Formula

LaTeX Go

Theta = (arctan(Torsion/Bending Moment))/2
θ = (arctan(T/M))/2

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 Torsion?

Angle of Twist in Combined Bending and Torsion calculator uses Theta = (arctan(Torsion/Bending Moment))/2 to calculate the Theta, The Angle of Twist in Combined Bending and Torsion formula is defined as a condition when both torsion and bending moment are acting on the member. Theta is denoted by θ symbol.

How to calculate Angle of Twist in Combined Bending and Torsion using this online calculator? To use this online calculator for Angle of Twist in Combined Bending and Torsion, enter Torsion (T) & Bending Moment (M) and hit the calculate button. Here is how the Angle of Twist in Combined Bending and Torsion calculation can be explained with given input values -> 2536.823 = (arctan(116913/67500))/2.

FAQ

What is Angle of Twist in Combined Bending and Torsion?

The Angle of Twist in Combined Bending and Torsion formula is defined as a condition when both torsion and bending moment are acting on the member and is represented as θ = (arctan(T/M))/2 or Theta = (arctan(Torsion/Bending Moment))/2. Torsion is the twisting of an object due to an applied torque & Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.

How to calculate Angle of Twist in Combined Bending and Torsion?

The Angle of Twist in Combined Bending and Torsion formula is defined as a condition when both torsion and bending moment are acting on the member is calculated using Theta = (arctan(Torsion/Bending Moment))/2. To calculate Angle of Twist in Combined Bending and Torsion, you need Torsion (T) & Bending Moment (M). With our tool, you need to enter the respective value for Torsion & Bending Moment 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 Moment. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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