Ratio of Diameters given Principle Stress Calculator

✖Bending 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 bend.ⓘ Bending Moment in Hollow Shaft [M_{b h}]			+10% -10%
✖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%
✖Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.ⓘ Maximum Principle Stress in Hollow Shaft [τ]			+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 Principle Stress [C]

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Ratio of Diameters given Principle Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4)
C = (1-16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*d_o^3*τ))^(1/4)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Bending Moment in Hollow Shaft - (Measured in Newton Meter) - Bending 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 bend.
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.
Maximum Principle Stress in Hollow Shaft - (Measured in Pascal) - Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Hollow Shaft: 550000 Newton Millimeter --> 550 Newton Meter (Check conversion here)
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)
Maximum Principle Stress in Hollow Shaft: 129.8 Newton per Square Millimeter --> 129800000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (1-16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*d_o^3*τ))^(1/4) --> (1-16*(550+sqrt(550^2+320^2))/(pi*0.046^3*129800000))^(1/4)

Evaluating ... ...

C = 0.849910063643594

STEP 3: Convert Result to Output's Unit

0.849910063643594 --> No Conversion Required

FINAL ANSWER

0.849910063643594 ≈ 0.84991 <-- Ratio of Inner to Outer Diameter of Hollow Shaft

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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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 Principle Stress Formula

LaTeX Go

Define Principle Stress

It is defined as the normal stress calculated at an angle when shear stress is considered as zero. The normal stress can be obtained for maximum and minimum values.

How to Calculate Ratio of Diameters given Principle Stress?

Ratio of Diameters given Principle Stress calculator uses Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4) to calculate the Ratio of Inner to Outer Diameter of Hollow Shaft, Ratio of Diameters given Principle Stress formula is defined as a dimensionless quantity used in the design of hollow shafts to determine the optimal diameter ratio, considering the principle stresses and material properties, to ensure the structural integrity and performance of the shaft under various loading conditions. Ratio of Inner to Outer Diameter of Hollow Shaft is denoted by C symbol.

How to calculate Ratio of Diameters given Principle Stress using this online calculator? To use this online calculator for Ratio of Diameters given Principle Stress, enter Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Maximum Principle Stress in Hollow Shaft (τ) and hit the calculate button. Here is how the Ratio of Diameters given Principle Stress calculation can be explained with given input values -> 0.84991 = (1-16*(550+sqrt(550^2+320^2))/(pi*0.046^3*129800000))^(1/4).

FAQ

What is Ratio of Diameters given Principle Stress?

Ratio of Diameters given Principle Stress formula is defined as a dimensionless quantity used in the design of hollow shafts to determine the optimal diameter ratio, considering the principle stresses and material properties, to ensure the structural integrity and performance of the shaft under various loading conditions and is represented as C = (1-16*(M_{b h}+sqrt(M_{b h}^2+Mt_hollowshaft^2))/(pi*d_o^3*τ))^(1/4) or Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4). Bending 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 bend, 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 & Maximum Principle Stress in Hollow Shaft is defined as the normal stress calculated at an angle when shear stress is considered zero.

How to calculate Ratio of Diameters given Principle Stress?

Ratio of Diameters given Principle Stress formula is defined as a dimensionless quantity used in the design of hollow shafts to determine the optimal diameter ratio, considering the principle stresses and material properties, to ensure the structural integrity and performance of the shaft under various loading conditions is calculated using Ratio of Inner to Outer Diameter of Hollow Shaft = (1-16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Outer Diameter of Hollow Shaft^3*Maximum Principle Stress in Hollow Shaft))^(1/4). To calculate Ratio of Diameters given Principle Stress, you need Bending Moment in Hollow Shaft (M_{b h}), Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Maximum Principle Stress in Hollow Shaft (τ). With our tool, you need to enter the respective value for Bending Moment in Hollow Shaft, Torsional Moment in Hollow Shaft, Outer Diameter of Hollow Shaft & Maximum Principle 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 Bending Moment in Hollow Shaft, Torsional Moment in Hollow Shaft, Outer Diameter of Hollow Shaft & Maximum Principle 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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