Ratio of Diameters given Angle of Twist of Hollow Shaft and 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%
✖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 [d_o]			+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 Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity [C]

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Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.

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)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (Check conversion here)
Angle of Twist of Hollow Shaft: 23.58 Degree --> 0.411548637620186 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (1-584*Mt_hollowshaft*L_h/(G_h*d_o^4*θ_hollow))^(1/4) --> (1-584*320*0.33/(70000000000*0.046^4*0.411548637620186))^(1/4)

Evaluating ... ...

C = 0.849953388500584

STEP 3: Convert Result to Output's Unit

0.849953388500584 --> No Conversion Required

FINAL ANSWER

0.849953388500584 ≈ 0.849953 <-- Ratio of Inner to Outer Diameter of Hollow Shaft

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Mechanical » Design of Hollow Shaft » Ratio of Diameters given Angle of Twist of Hollow Shaft and 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

Ratio of Diameters given Angle of Twist of Hollow Shaft and 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 Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity?

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity calculator uses Ratio of Inner to Outer Diameter of Hollow Shaft = (1-584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*Angle of Twist of Hollow Shaft))^(1/4) to calculate the Ratio of Inner to Outer Diameter of Hollow Shaft, Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity formula is defined as a measure of the proportional relationship between the diameters of a hollow shaft, considering the angle of twist and torsional rigidity, which is essential in designing hollow shafts to withstand twisting forces and maintain structural integrity. Ratio of Inner to Outer Diameter of Hollow Shaft is denoted by C symbol.

How to calculate Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity using this online calculator? To use this online calculator for Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity, enter Torsional Moment in Hollow Shaft (Mt_hollowshaft), Length of Hollow Shaft (L_h), Modulus of Rigidity of Hollow Shaft (G_h), Outer Diameter of Hollow Shaft (d_o) & Angle of Twist of Hollow Shaft (θ_hollow) and hit the calculate button. Here is how the Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity calculation can be explained with given input values -> 0.849953 = (1-584*320*0.33/(70000000000*0.046^4*0.411548637620186))^(1/4).

FAQ

What is Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity?

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity formula is defined as a measure of the proportional relationship between the diameters of a hollow shaft, considering the angle of twist and torsional rigidity, which is essential in designing hollow shafts to withstand twisting forces and maintain structural integrity and is represented as C = (1-584*Mt_hollowshaft*L_h/(G_h*d_o^4*θ_hollow))^(1/4) or Ratio of Inner to Outer Diameter of Hollow Shaft = (1-584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*Angle of Twist of Hollow Shaft))^(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, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & 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.

How to calculate Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity?

Ratio of Diameters given Angle of Twist of Hollow Shaft and Torsional Rigidity formula is defined as a measure of the proportional relationship between the diameters of a hollow shaft, considering the angle of twist and torsional rigidity, which is essential in designing hollow shafts to withstand twisting forces and maintain structural integrity is calculated using Ratio of Inner to Outer Diameter of Hollow Shaft = (1-584*Torsional Moment in Hollow Shaft*Length of Hollow Shaft/(Modulus of Rigidity of Hollow Shaft*Outer Diameter of Hollow Shaft^4*Angle of Twist of Hollow Shaft))^(1/4). To calculate Ratio of Diameters given Angle of Twist of Hollow Shaft and 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), Outer Diameter of Hollow Shaft (d_o) & Angle of Twist of Hollow Shaft (θ_hollow). 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, Outer Diameter of Hollow Shaft & Angle of Twist 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 Ratio of Inner to Outer Diameter of Hollow Shaft?

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

Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft
Ratio of Inner to Outer Diameter of Hollow Shaft = sqrt(1-(Axial Force on Hollow Shaft/(pi/4*Tensile Stress in Hollow Shaft*Outer Diameter of Hollow Shaft^2)))
Ratio of Inner to Outer Diameter of Hollow Shaft = (1-32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Bending Stress in Hollow Shaft))^(1/4)

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