Ratio of Diameters given Bending Stress of Hollow Shaft 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%
✖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%
✖Bending Stress in Hollow Shaft is the normal stress that is induced at a point in a hollow shaft subjected to loads that cause it to bend.ⓘ Bending Stress in Hollow Shaft [σ_{b 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 Diameters given Bending Stress of Hollow Shaft [C]

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Ratio of Diameters given Bending Stress of Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
C = (1-32*M_{b h}/(pi*d_o^3*σ_{b 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.
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.
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.
Bending Stress in Hollow Shaft - (Measured in Pascal) - Bending Stress in Hollow Shaft is the normal stress that is induced at a point in a hollow shaft subjected to loads that cause it to bend.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Hollow Shaft: 550000 Newton Millimeter --> 550 Newton Meter (Check conversion here)
Outer Diameter of Hollow Shaft: 46 Millimeter --> 0.046 Meter (Check conversion here)
Bending Stress in Hollow Shaft: 120.4 Newton per Square Millimeter --> 120400000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (1-32*M_{b h}/(pi*d_o^3*σ_{b h}))^(1/4) --> (1-32*550/(pi*0.046^3*120400000))^(1/4)

Evaluating ... ...

C = 0.849981810148474

STEP 3: Convert Result to Output's Unit

0.849981810148474 --> No Conversion Required

FINAL ANSWER

0.849981810148474 ≈ 0.849982 <-- 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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< 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 Bending Stress of Hollow Shaft Formula

LaTeX Go

Define Bending Stress

Bending stress is the normal stress that an object encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued. Bending stress occurs when operating industrial equipment and in concrete and metallic structures when they are subjected to a tensile load.

How to Calculate Ratio of Diameters given Bending Stress of Hollow Shaft?

Ratio of Diameters given Bending Stress of Hollow Shaft calculator uses 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) to calculate the Ratio of Inner to Outer Diameter of Hollow Shaft, Ratio of Diameters given Bending Stress of Hollow Shaft formula is defined as a mathematical relationship that determines the ratio of diameters of a hollow shaft based on the bending stress, outer diameter, and other parameters, providing a crucial calculation in the design of hollow shafts for various engineering applications. Ratio of Inner to Outer Diameter of Hollow Shaft is denoted by C symbol.

How to calculate Ratio of Diameters given Bending Stress of Hollow Shaft using this online calculator? To use this online calculator for Ratio of Diameters given Bending Stress of Hollow Shaft, enter Bending Moment in Hollow Shaft (M_{b h}), Outer Diameter of Hollow Shaft (d_o) & Bending Stress in Hollow Shaft (σ_{b h}) and hit the calculate button. Here is how the Ratio of Diameters given Bending Stress of Hollow Shaft calculation can be explained with given input values -> 0.849982 = (1-32*550/(pi*0.046^3*120400000))^(1/4).

FAQ

What is Ratio of Diameters given Bending Stress of Hollow Shaft?

Ratio of Diameters given Bending Stress of Hollow Shaft formula is defined as a mathematical relationship that determines the ratio of diameters of a hollow shaft based on the bending stress, outer diameter, and other parameters, providing a crucial calculation in the design of hollow shafts for various engineering applications and is represented as C = (1-32*M_{b h}/(pi*d_o^3*σ_{b h}))^(1/4) or 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). 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, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & Bending Stress in Hollow Shaft is the normal stress that is induced at a point in a hollow shaft subjected to loads that cause it to bend.

How to calculate Ratio of Diameters given Bending Stress of Hollow Shaft?

Ratio of Diameters given Bending Stress of Hollow Shaft formula is defined as a mathematical relationship that determines the ratio of diameters of a hollow shaft based on the bending stress, outer diameter, and other parameters, providing a crucial calculation in the design of hollow shafts for various engineering applications is calculated using 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). To calculate Ratio of Diameters given Bending Stress of Hollow Shaft, you need Bending Moment in Hollow Shaft (M_{b h}), Outer Diameter of Hollow Shaft (d_o) & Bending Stress in Hollow Shaft (σ_{b h}). With our tool, you need to enter the respective value for Bending Moment in Hollow Shaft, Outer Diameter of Hollow Shaft & Bending 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, Outer Diameter of Hollow Shaft & Bending 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 = (1-16*Torsional Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*Torsional Shear Stress in Hollow Shaft))^(1/4)

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