Bending Moment given Bending Stress in Hollow Shaft Calculator

✖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%
✖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%
✖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%

✖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 given Bending Stress in Hollow Shaft [M_{b h}]

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Bending Moment given Bending Stress in Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32
M_{b h} = σ_{b h}*(pi*d_o^3*(1-(C^4)))/32
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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.
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

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

M_{b h} = σ_{b h}*(pi*d_o^3*(1-(C^4)))/32 --> 120400000*(pi*0.046^3*(1-(0.85^4)))/32

Evaluating ... ...

M_{b h} = 549.948591863872

STEP 3: Convert Result to Output's Unit

549.948591863872 Newton Meter -->549948.591863872 Newton Millimeter (Check conversion here)

FINAL ANSWER

549948.591863872 ≈ 549948.6 Newton Millimeter <-- Bending Moment in 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

Bending Moment given Bending Stress in Hollow Shaft Formula

LaTeX Go

Define Bending Moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

How to Calculate Bending Moment given Bending Stress in Hollow Shaft?

Bending Moment given Bending Stress in Hollow Shaft calculator uses Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32 to calculate the Bending Moment in Hollow Shaft, Bending Moment given Bending Stress in Hollow Shaft formula is defined as a measure of the turning force that causes the shaft to bend, which is essential in designing hollow shafts to withstand external loads and stresses, ensuring the structural integrity of the system. Bending Moment in Hollow Shaft is denoted by M_{b h} symbol.

How to calculate Bending Moment given Bending Stress in Hollow Shaft using this online calculator? To use this online calculator for Bending Moment given Bending Stress in Hollow Shaft, enter Bending Stress in Hollow Shaft (σ_{b h}), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button. Here is how the Bending Moment given Bending Stress in Hollow Shaft calculation can be explained with given input values -> 5.5E+8 = 120400000*(pi*0.046^3*(1-(0.85^4)))/32.

FAQ

What is Bending Moment given Bending Stress in Hollow Shaft?

Bending Moment given Bending Stress in Hollow Shaft formula is defined as a measure of the turning force that causes the shaft to bend, which is essential in designing hollow shafts to withstand external loads and stresses, ensuring the structural integrity of the system and is represented as M_{b h} = σ_{b h}*(pi*d_o^3*(1-(C^4)))/32 or Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32. 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, Outer Diameter of Hollow Shaft is defined as the length of the longest chord of the surface of the hollow circular 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.

How to calculate Bending Moment given Bending Stress in Hollow Shaft?

Bending Moment given Bending Stress in Hollow Shaft formula is defined as a measure of the turning force that causes the shaft to bend, which is essential in designing hollow shafts to withstand external loads and stresses, ensuring the structural integrity of the system is calculated using Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32. To calculate Bending Moment given Bending Stress in Hollow Shaft, you need Bending Stress in Hollow Shaft (σ_{b h}), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C). With our tool, you need to enter the respective value for Bending Stress in Hollow Shaft, Outer Diameter 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.

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