Bending Stress in Shaft Pure Bending Moment Calculator

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Shaft Design on Strength Basis

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Maximum Shear Stress and Principal Stress Theory

Torsional Rigidity

✖Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment in Shaft [M_b]			+10% -10%
✖Diameter of Shaft on Strength Basis is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.ⓘ Diameter of Shaft on Strength Basis [d]			+10% -10%

✖Bending Stress in Shaft is the normal stress that is induced at a point in a shaft subjected to loads that cause it to bend.ⓘ Bending Stress in Shaft Pure Bending Moment [σ_b]

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Formula

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Bending Stress in Shaft Pure Bending Moment

Formula

`"σ"_{"b"} = (32*"M"_{"b"})/(pi*"d"^3)`

Example

`"177.7273N/mm²"=(32*"1.8E6N*mm")/(pi*("46.9mm")^3)`

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Download Design of Automobile Elements Formula PDF

Bending Stress in Shaft Pure Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3)
σ_b = (32*M_b)/(pi*d^3)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Bending Stress in Shaft - (Measured in Pascal) - Bending Stress in Shaft is the normal stress that is induced at a point in a shaft subjected to loads that cause it to bend.
Bending Moment in Shaft - (Measured in Newton Meter) - Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.
Diameter of Shaft on Strength Basis - (Measured in Meter) - Diameter of Shaft on Strength Basis is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Shaft: 1800000 Newton Millimeter --> 1800 Newton Meter (Check conversion here)
Diameter of Shaft on Strength Basis: 46.9 Millimeter --> 0.0469 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_b = (32*M_b)/(pi*d^3) --> (32*1800)/(pi*0.0469^3)

Evaluating ... ...

σ_b = 177727275.186827

STEP 3: Convert Result to Output's Unit

177727275.186827 Pascal -->177.727275186827 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

177.727275186827 ≈ 177.7273 Newton per Square Millimeter <-- Bending Stress in Shaft

(Calculation completed in 00.004 seconds)

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Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 16 Shaft Design on Strength Basis Calculators

Diameter of Shaft given Tensile Stress in Shaft

Go Diameter of Shaft on Strength Basis = sqrt(4*Axial Force on Shaft/(pi*Tensile Stress in Shaft))

Diameter of Shaft given Torsional Shear Stress in Shaft Pure Torsion

Go Diameter of Shaft on Strength Basis = (16*Torsional Moment in Shaft/(pi*Torsional Shear Stress in Shaft))^(1/3)

Torsional Moment given Torsional Shear Stress in Shaft Pure Torsion

Go Torsional Moment in Shaft = Torsional Shear Stress in Shaft*pi*(Diameter of Shaft on Strength Basis^3)/16

Torsional Shear Stress in Shaft Pure Torsion

Go Torsional Shear Stress in Shaft = 16*Torsional Moment in Shaft/(pi*Diameter of Shaft on Strength Basis^3)

Diameter of Shaft given Bending Stress Pure Bending

Go Diameter of Shaft on Strength Basis = ((32*Bending Moment in Shaft)/(pi*Bending Stress in Shaft))^(1/3)

Torsional Shear Stress given Principal Shear Stress in Shaft

Go Torsional Shear Stress in Shaft = sqrt(Principal Shear Stress in Shaft^2-(Normal Stress in Shaft/2)^2)

Normal Stress given Principal Shear Stress in Shaft Bending and Torsion

Go Normal Stress in Shaft = 2*sqrt(Principal Shear Stress in Shaft^2-Torsional Shear Stress in Shaft^2)

Maximum Shear Stress in Shaft Bending and Torsion

Go Maximum Shear Stress in Shaft = sqrt((Normal Stress in Shaft/2)^2+Torsional Shear Stress in Shaft^2)

Bending Stress in Shaft Pure Bending Moment

Go Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3)

Bending Moment given Bending Stress Pure Bending

Go Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32

Tensile Stress in Shaft when it is Subjected to Axial Tensile Force

Go Tensile Stress in Shaft = 4*Axial Force on Shaft/(pi*Diameter of Shaft on Strength Basis^2)

Axial Force given Tensile Stress in Shaft

Go Axial Force on Shaft = Tensile Stress in Shaft*pi*(Diameter of Shaft on Strength Basis^2)/4

Power transmitted by Shaft

Go Power Transmitted by Shaft = 2*pi*Speed of Shaft*Torque transmitted by Shaft

Normal Stress given Both Bending and Torsional act on Shaft

Go Normal Stress in Shaft = Bending Stress in Shaft+Tensile Stress in Shaft

Tensile Stress given Normal Stress

Go Tensile Stress in Shaft = Normal Stress in Shaft-Bending Stress in Shaft

Bending Stress given Normal Stress

Go Bending Stress in Shaft = Normal Stress in Shaft-Tensile Stress in Shaft

Bending Stress in Shaft Pure Bending Moment Formula

Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3)
σ_b = (32*M_b)/(pi*d^3)

Define Bending Stress

Bending stress is a more specific type of normal stress. The stress at the horizontal plane of the neutral is zero. The bottom fibers of the beam undergo a normal tensile stress. It can be concluded therefore that the value of the bending stress will vary linearly with distance from the neutral axis.

How to Calculate Bending Stress in Shaft Pure Bending Moment?

Bending Stress in Shaft Pure Bending Moment calculator uses Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3) to calculate the Bending Stress in Shaft, The Bending Stress in Shaft Pure Bending Moment formula is defined as the compression or tension force acting in a member. If the axial force acts through the centroid of the member it is called concentric loading. Bending Stress in Shaft is denoted by σ_b symbol.

How to calculate Bending Stress in Shaft Pure Bending Moment using this online calculator? To use this online calculator for Bending Stress in Shaft Pure Bending Moment, enter Bending Moment in Shaft (M_b) & Diameter of Shaft on Strength Basis (d) and hit the calculate button. Here is how the Bending Stress in Shaft Pure Bending Moment calculation can be explained with given input values -> 0.000178 = (32*1800)/(pi*0.0469^3).

FAQ

What is Bending Stress in Shaft Pure Bending Moment?

The Bending Stress in Shaft Pure Bending Moment formula is defined as the compression or tension force acting in a member. If the axial force acts through the centroid of the member it is called concentric loading and is represented as σ_b = (32*M_b)/(pi*d^3) or Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3). Bending Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend & Diameter of Shaft on Strength Basis is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

How to calculate Bending Stress in Shaft Pure Bending Moment?

The Bending Stress in Shaft Pure Bending Moment formula is defined as the compression or tension force acting in a member. If the axial force acts through the centroid of the member it is called concentric loading is calculated using Bending Stress in Shaft = (32*Bending Moment in Shaft)/(pi*Diameter of Shaft on Strength Basis^3). To calculate Bending Stress in Shaft Pure Bending Moment, you need Bending Moment in Shaft (M_b) & Diameter of Shaft on Strength Basis (d). With our tool, you need to enter the respective value for Bending Moment in Shaft & Diameter of Shaft on Strength Basis 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 Bending Stress in Shaft?

In this formula, Bending Stress in Shaft uses Bending Moment in Shaft & Diameter of Shaft on Strength Basis. We can use 1 other way(s) to calculate the same, which is/are as follows -

Bending Stress in Shaft = Normal Stress in Shaft-Tensile Stress in Shaft

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