Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Calculator

✖Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.ⓘ Torsional Moment in Hollow Shaft [Mt_hollowshaft]			+10% -10%
✖Length of Hollow Shaft is the distance between two ends of a hollow shaft.ⓘ Length of Hollow Shaft [L_h]			+10% -10%
✖Modulus of Rigidity of Hollow Shaft 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 of Hollow Shaft [G_h]			+10% -10%
✖Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.ⓘ Angle of Twist of Hollow Shaft [θ_hollow]			+10% -10%
✖The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.ⓘ Ratio of Inner to Outer Diameter of Hollow Shaft [C]			+10% -10%

✖Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity [d_o]

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Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4)
d_o = (584*Mt_hollowshaft*L_h/(G_h*θ_hollow*(1-C^4)))^(1/4)
This formula uses 6 Variables

Variables Used

Outer Diameter of Hollow Shaft - (Measured in Meter) - Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Torsional Moment in Hollow Shaft - (Measured in Newton Meter) - Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist.
Length of Hollow Shaft - (Measured in Meter) - Length of Hollow Shaft is the distance between two ends of a hollow shaft.
Modulus of Rigidity of Hollow Shaft - (Measured in Pascal) - Modulus of Rigidity of Hollow Shaft 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.
Angle of Twist of Hollow Shaft - (Measured in Radian) - Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end.
Ratio of Inner to Outer Diameter of Hollow Shaft - The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

STEP 1: Convert Input(s) to Base Unit

Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Length of Hollow Shaft: 330 Millimeter --> 0.33 Meter (Check conversion here)
Modulus of Rigidity of Hollow Shaft: 70000 Newton per Square Millimeter --> 70000000000 Pascal (Check conversion here)
Angle of Twist of Hollow Shaft: 23.58 Degree --> 0.411548637620186 Radian (Check conversion here)
Ratio of Inner to Outer Diameter of Hollow Shaft: 0.85 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_o = (584*Mt_hollowshaft*L_h/(G_h*θ_hollow*(1-C^4)))^(1/4) --> (584*320*0.33/(70000000000*0.411548637620186*(1-0.85^4)))^(1/4)

Evaluating ... ...

d_o = 0.046002754296788

STEP 3: Convert Result to Output's Unit

0.046002754296788 Meter -->46.002754296788 Millimeter (Check conversion here)

FINAL ANSWER

46.002754296788 ≈ 46.00275 Millimeter <-- Outer Diameter of Hollow Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Mechanical » Design of Hollow Shaft » Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Design of Hollow Shaft Calculators

Tensile Stress in Hollow Shaft when Subjected to Axial Force

LaTeX Go Tensile Stress in Hollow Shaft = Axial Force on Hollow Shaft/(pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2))

Inner Diameter of Hollow Shaft given Ratio of Diameters

LaTeX Go Inner Diameter of Hollow Shaft = Ratio of Inner to Outer Diameter of Hollow Shaft*Outer Diameter of Hollow Shaft

Ratio of Inner Diameter to Outer Diameter

LaTeX Go Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft

Outer Diameter given Ratio of Diameters

LaTeX Go Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity Formula

LaTeX Go

Define Angle of Twist?

For a shaft under torsional loading, the angle through which fixed end of a shaft rotates with respect to the free end is called the angle of twist. As the torque is increased, the outer region of the shaft behaves like a plastic material while the inner core is still linear elastic.

How to Calculate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity calculator uses Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4) to calculate the Outer Diameter of Hollow Shaft, Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, which is critical in determining the shaft's strength and stability under torsional loads, and is influenced by factors such as the shaft's material, length, and twist angle. Outer Diameter of Hollow Shaft is denoted by d_o symbol.

How to calculate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity using this online calculator? To use this online calculator for Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity, enter Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Modulus of Rigidity of Hollow Shaft (G_h), Angle of Twist of Hollow Shaft (θ_hollow) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity calculation can be explained with given input values -> 46002.75 = (584*320*0.33/(70000000000*0.411548637620186*(1-0.85^4)))^(1/4).

FAQ

What is Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, which is critical in determining the shaft's strength and stability under torsional loads, and is influenced by factors such as the shaft's material, length, and twist angle and is represented as d_o = (584*Mt_hollowshaft*L_h/(G_h*θ_hollow*(1-C^4)))^(1/4) or Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4). Torsional Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to twist, Length of Hollow Shaft is the distance between two ends of a hollow shaft, Modulus of Rigidity of Hollow Shaft 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, Angle of Twist of Hollow Shaft is the angle through which the fixed end of a hollow shaft rotates with respect to the free end & The Ratio of Inner to Outer Diameter of Hollow Shaft is defined as the inner diameter of the shaft divided by the outer diameter.

How to calculate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity?

Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, which is critical in determining the shaft's strength and stability under torsional loads, and is influenced by factors such as the shaft's material, length, and twist angle is calculated using Outer Diameter of Hollow Shaft = (584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Angle of Twist of Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/4). To calculate Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity, you need Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Modulus of Rigidity of Hollow Shaft (G_h), Angle of Twist of Hollow Shaft (θ_hollow) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Torsional Moment in Hollow Shaft, Length of Hollow Shaft, Modulus of Rigidity of Hollow Shaft, Angle of Twist of Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft 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 Outer Diameter of Hollow Shaft?

In this formula, Outer Diameter of Hollow Shaft uses Torsional Moment in Hollow Shaft, Length of Hollow Shaft, Modulus of Rigidity of Hollow Shaft, Angle of Twist of Hollow Shaft & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -

Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft
Outer Diameter of Hollow Shaft = (32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

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