Ratio of Diameter given Torsional Shear Stress in Hollow Shaft 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%
✖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%
✖Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.ⓘ Torsional Shear Stress in Hollow Shaft [𝜏_h]			+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 Diameter given Torsional Shear Stress in Hollow Shaft [C]

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Ratio of Diameter given Torsional Shear Stress in Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in Hollow Shaft))^(1/4)
C = (1-16*Mt_hollowshaft/(pi*d_o^3*𝜏_h))^(1/4)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
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 Shear Stress in Hollow Shaft - (Measured in Pascal) - Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.

STEP 1: Convert Input(s) to Base Unit

Torsional Moment in Hollow Shaft: 320000 Newton Millimeter --> 320 Newton Meter (Check conversion here)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (Check conversion here)
Torsional Shear Stress in Hollow Shaft: 35.1 Newton per Square Millimeter --> 35100000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (1-16*Mt_hollowshaft/(pi*d_o^3*𝜏_h))^(1/4) --> (1-16*320/(pi*0.046^3*35100000))^(1/4)

Evaluating ... ...

C = 0.85039483049206

STEP 3: Convert Result to Output's Unit

0.85039483049206 --> No Conversion Required

FINAL ANSWER

0.85039483049206 ≈ 0.850395 <-- Ratio of Inner to Outer Diameter of Hollow Shaft

(Calculation completed in 00.004 seconds)

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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 Diameter given Torsional Shear Stress in Hollow Shaft Formula

LaTeX Go

Define Torsion

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.

How to Calculate Ratio of Diameter given Torsional Shear Stress in Hollow Shaft?

Ratio of Diameter given Torsional Shear Stress in Hollow Shaft calculator uses Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in Hollow Shaft))^(1/4) to calculate the Ratio of Inner to Outer Diameter of Hollow Shaft, Ratio of Diameter given Torsional Shear Stress in Hollow Shaft formula is defined as a measure of the diameter of a hollow shaft in relation to the torsional shear stress it can withstand, providing a critical design parameter for engineers to ensure the structural integrity of hollow shafts in various mechanical systems. Ratio of Inner to Outer Diameter of Hollow Shaft is denoted by C symbol.

How to calculate Ratio of Diameter given Torsional Shear Stress in Hollow Shaft using this online calculator? To use this online calculator for Ratio of Diameter given Torsional Shear Stress in Hollow Shaft, enter Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Torsional Shear Stress in Hollow Shaft (𝜏_h) and hit the calculate button. Here is how the Ratio of Diameter given Torsional Shear Stress in Hollow Shaft calculation can be explained with given input values -> 0.850395 = (1-16*320/(pi*0.046^3*35100000))^(1/4).

FAQ

What is Ratio of Diameter given Torsional Shear Stress in Hollow Shaft?

Ratio of Diameter given Torsional Shear Stress in Hollow Shaft formula is defined as a measure of the diameter of a hollow shaft in relation to the torsional shear stress it can withstand, providing a critical design parameter for engineers to ensure the structural integrity of hollow shafts in various mechanical systems and is represented as C = (1-16*Mt_hollowshaft/(pi*d_o^3*𝜏_h))^(1/4) or Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in 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, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.

How to calculate Ratio of Diameter given Torsional Shear Stress in Hollow Shaft?

Ratio of Diameter given Torsional Shear Stress in Hollow Shaft formula is defined as a measure of the diameter of a hollow shaft in relation to the torsional shear stress it can withstand, providing a critical design parameter for engineers to ensure the structural integrity of hollow shafts in various mechanical systems is calculated using Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in Hollow Shaft))^(1/4). To calculate Ratio of Diameter given Torsional Shear Stress in Hollow Shaft, you need Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Torsional Shear Stress in Hollow Shaft (𝜏_h). With our tool, you need to enter the respective value for Torsional Moment in Hollow Shaft, Outer Diameter of Hollow Shaft & Torsional Shear Stress in 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, Outer Diameter of Hollow Shaft & Torsional Shear Stress in 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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