Angle of twist of hollow cylindrical rod in degrees Calculator

✖Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.ⓘ Torsional moment on shaft [τ]			+10% -10%
✖Length of shaft is defined as the distance between the two opposite ends of a shaft.ⓘ Length of Shaft [l]			+10% -10%
✖Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.ⓘ Modulus of Rigidity [C]			+10% -10%
✖Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section.ⓘ Outer Diameter of Hollow Circular Section [d_ho]			+10% -10%
✖Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.ⓘ Inner Diameter of Hollow Circular Section [d_hi]			+10% -10%

✖Angle of twist of shaft in degree is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of twist of hollow cylindrical rod in degrees [𝜽_d]

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Angle of twist of hollow cylindrical rod in degrees Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180)
𝜽_d = (584*τ*l/(C*((d_ho^4)-(d_hi^4))))*(pi/180)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Angle of twist of shaft in degree - (Measured in Radian) - Angle of twist of shaft in degree is the angle through which the fixed end of a shaft rotates with respect to the free end.
Torsional moment on shaft - (Measured in Newton Meter) - Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.
Length of Shaft - (Measured in Meter) - Length of shaft is defined as the distance between the two opposite ends of a shaft.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
Outer Diameter of Hollow Circular Section - (Measured in Meter) - Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section.
Inner Diameter of Hollow Circular Section - (Measured in Meter) - Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.

STEP 1: Convert Input(s) to Base Unit

Torsional moment on shaft: 51000 Newton Millimeter --> 51 Newton Meter (Check conversion here)
Length of Shaft: 1100 Millimeter --> 1.1 Meter (Check conversion here)
Modulus of Rigidity: 84000 Newton per Square Millimeter --> 84000000000 Pascal (Check conversion here)
Outer Diameter of Hollow Circular Section: 40 Millimeter --> 0.04 Meter (Check conversion here)
Inner Diameter of Hollow Circular Section: 36 Millimeter --> 0.036 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜽_d = (584*τ*l/(C*((d_ho^4)-(d_hi^4))))*(pi/180) --> (584*51*1.1/(84000000000*((0.04^4)-(0.036^4))))*(pi/180)

Evaluating ... ...

𝜽_d = 0.00773217453779084

STEP 3: Convert Result to Output's Unit

0.00773217453779084 Radian -->0.443020967474017 Degree (Check conversion here)

FINAL ANSWER

0.443020967474017 ≈ 0.443021 Degree <-- Angle of twist of shaft in degree

(Calculation completed in 00.020 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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National Institute Of Technology (NIT), Hamirpur

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< Design of Shaft for Torsional Moment Calculators

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

LaTeX Go Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)

Torsional shear stress in shaft due to torsional moment

LaTeX Go Torsional shear stress in twisted shaft = Torsional moment on shaft*Radial Distance from Axis of Rotation/Polar moment of inertia for circular section

Polar moment of inertia of hollow circular cross-section

LaTeX Go Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32

Polar moment of inertia of circular cross section

LaTeX Go Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32

Angle of twist of hollow cylindrical rod in degrees Formula

LaTeX Go

What is angle of twist?

For a shaft under torsional loading, the angle through which the fixed end of a shaft rotates with respect to the free end is called the angle of twist.

How to Calculate Angle of twist of hollow cylindrical rod in degrees?

Angle of twist of hollow cylindrical rod in degrees calculator uses Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180) to calculate the Angle of twist of shaft in degree, The angle of twist of hollow cylindrical rod in degrees formula is defined as the angle through which the hollow cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod. Angle of twist of shaft in degree is denoted by 𝜽_d symbol.

How to calculate Angle of twist of hollow cylindrical rod in degrees using this online calculator? To use this online calculator for Angle of twist of hollow cylindrical rod in degrees, enter Torsional moment on shaft (τ), Length of Shaft (l), Modulus of Rigidity (C), Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi) and hit the calculate button. Here is how the Angle of twist of hollow cylindrical rod in degrees calculation can be explained with given input values -> 25.38323 = (584*51*1.1/(84000000000*((0.04^4)-(0.036^4))))*(pi/180).

FAQ

What is Angle of twist of hollow cylindrical rod in degrees?

The angle of twist of hollow cylindrical rod in degrees formula is defined as the angle through which the hollow cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod and is represented as 𝜽_d = (584*τ*l/(C*((d_ho^4)-(d_hi^4))))*(pi/180) or Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180). Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force, Length of shaft is defined as the distance between the two opposite ends of a shaft, Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is, Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section & Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.

How to calculate Angle of twist of hollow cylindrical rod in degrees?

The angle of twist of hollow cylindrical rod in degrees formula is defined as the angle through which the hollow cylindrical rod is twisted about its central axis when torque is applied onto it or torsion is acting onto the rod is calculated using Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))))*(pi/180). To calculate Angle of twist of hollow cylindrical rod in degrees, you need Torsional moment on shaft (τ), Length of Shaft (l), Modulus of Rigidity (C), Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi). With our tool, you need to enter the respective value for Torsional moment on shaft, Length of Shaft, Modulus of Rigidity, Outer Diameter of Hollow Circular Section & Inner Diameter of Hollow Circular Section 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 Angle of twist of shaft in degree?

In this formula, Angle of twist of shaft in degree uses Torsional moment on shaft, Length of Shaft, Modulus of Rigidity, Outer Diameter of Hollow Circular Section & Inner Diameter of Hollow Circular Section. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angle of twist of shaft in degree = (584*Torsional moment on shaft*Length of Shaft/(Modulus of Rigidity*(Diameter of circular section of shaft^4)))*(pi/180)

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