Bending Moment given Bending Stress Pure Bending Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32
Mb = (σb*pi*d^3)/32
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
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.
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 Stress in Shaft: 177.8 Newton per Square Millimeter --> 177800000 Pascal (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
Mb = (σb*pi*d^3)/32 --> (177800000*pi*0.0469^3)/32
Evaluating ... ...
Mb = 1800.73654796977
STEP 3: Convert Result to Output's Unit
1800.73654796977 Newton Meter -->1800736.54796977 Newton Millimeter (Check conversion here)
FINAL ANSWER
1800736.54796977 1.8E+6 Newton Millimeter <-- Bending Moment in Shaft
(Calculation completed in 00.020 seconds)

Credits

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Osmania University (OU), Hyderabad
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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 Moment given Bending Stress Pure Bending Formula

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

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 Pure Bending?

Bending Moment given Bending Stress Pure Bending calculator uses Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32 to calculate the Bending Moment in Shaft, The Bending Moment given Bending Stress Pure Bending formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. Bending Moment in Shaft is denoted by Mb symbol.

How to calculate Bending Moment given Bending Stress Pure Bending using this online calculator? To use this online calculator for Bending Moment given Bending Stress Pure Bending, enter Bending Stress in Shaft b) & Diameter of Shaft on Strength Basis (d) and hit the calculate button. Here is how the Bending Moment given Bending Stress Pure Bending calculation can be explained with given input values -> 1.8E+9 = (177800000*pi*0.0469^3)/32.

FAQ

What is Bending Moment given Bending Stress Pure Bending?
The Bending Moment given Bending Stress Pure Bending formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend and is represented as Mb = (σb*pi*d^3)/32 or Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32. 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 & 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 Moment given Bending Stress Pure Bending?
The Bending Moment given Bending Stress Pure Bending formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend is calculated using Bending Moment in Shaft = (Bending Stress in Shaft*pi*Diameter of Shaft on Strength Basis^3)/32. To calculate Bending Moment given Bending Stress Pure Bending, you need Bending Stress in Shaft b) & Diameter of Shaft on Strength Basis (d). With our tool, you need to enter the respective value for Bending Stress 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.
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