Bending Stress of Circular Shaft given Equivalent Bending Moment Calculator

✖The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a circular shaft a normal stress.ⓘ Equivalent Bending Moment [M_e]			+10% -10%
✖Diameter of circular shaft is denoted by d.ⓘ Diameter of Circular Shaft [Φ]			+10% -10%

✖The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Bending Stress of Circular Shaft given Equivalent Bending Moment [σ_b]

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Formula

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Bending Stress of Circular Shaft given Equivalent Bending Moment

Formula

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

Example

`"0.724332MPa"=(32*"30kN*m")/(pi*(("750mm")^3))`

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Bending Stress of Circular Shaft given Equivalent Bending Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3))
σ_b = (32*M_e)/(pi*(Φ^3))
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Bending Stress - (Measured in Pascal) - The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.
Equivalent Bending Moment - (Measured in Newton Meter) - The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a circular shaft a normal stress.
Diameter of Circular Shaft - (Measured in Meter) - Diameter of circular shaft is denoted by d.

STEP 1: Convert Input(s) to Base Unit

Equivalent Bending Moment: 30 Kilonewton Meter --> 30000 Newton Meter (Check conversion here)
Diameter of Circular Shaft: 750 Millimeter --> 0.75 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_b = (32*M_e)/(pi*(Φ^3)) --> (32*30000)/(pi*(0.75^3))

Evaluating ... ...

σ_b = 724331.829893781

STEP 3: Convert Result to Output's Unit

724331.829893781 Pascal -->0.724331829893781 Megapascal (Check conversion here)

FINAL ANSWER

0.724331829893781 ≈ 0.724332 Megapascal <-- Bending Stress

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< 7 Equivalent Bending Moment & Torque Calculators

Location of Principal Planes

Go Theta = (((1/2)*atan((2*Shear Stress xy)/(Stress along y Direction-Stress along x Direction))))

Diameter of Circular Shaft given Equivalent Bending Stress

Go Diameter of Circular Shaft = ((32*Equivalent Bending Moment)/(pi*(Bending Stress)))^(1/3)

Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress

Go Diameter of Circular Shaft = ((16*Equivalent Torque)/(pi*(Maximum Shear Stress)))^(1/3)

Bending Stress of Circular Shaft given Equivalent Bending Moment

Go Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3))

Equivalent Bending Moment of Circular Shaft

Go Equivalent Bending Moment = Bending Stress/(32/(pi*(Diameter of Circular Shaft^3)))

Maximum Shear Stress due to Equivalent Torque

Go Maximum Shear Stress = (16*Equivalent Torque)/(pi*(Diameter of Circular Shaft^3))

Equivalent Torque given Maximum Shear Stress

Go Equivalent Torque = Maximum Shear Stress/(16/(pi*(Diameter of Circular Shaft^3)))

Bending Stress of Circular Shaft given Equivalent Bending Moment Formula

Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3))
σ_b = (32*M_e)/(pi*(Φ^3))

What is Combined Bending and Torsion?

The Combined bending , direct and torsional stresses in shafts arise when such as in propeller shafts of ships where a shaft is subjected to direct thrust in addition to bending moment and torsion. In such cases the direct stresses due to bending moment and the axial thrust have to be combined into a single resultant.

How to Calculate Bending Stress of Circular Shaft given Equivalent Bending Moment?

Bending Stress of Circular Shaft given Equivalent Bending Moment calculator uses Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3)) to calculate the Bending Stress, The Bending Stress of Circular Shaft given Equivalent Bending Moment formula is defined as 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 is denoted by σ_b symbol.

How to calculate Bending Stress of Circular Shaft given Equivalent Bending Moment using this online calculator? To use this online calculator for Bending Stress of Circular Shaft given Equivalent Bending Moment, enter Equivalent Bending Moment (M_e) & Diameter of Circular Shaft (Φ) and hit the calculate button. Here is how the Bending Stress of Circular Shaft given Equivalent Bending Moment calculation can be explained with given input values -> 7.2E-7 = (32*30000)/(pi*(0.75^3)).

FAQ

What is Bending Stress of Circular Shaft given Equivalent Bending Moment?

The Bending Stress of Circular Shaft given Equivalent Bending Moment formula is defined as 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 and is represented as σ_b = (32*M_e)/(pi*(Φ^3)) or Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3)). The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a circular shaft a normal stress & Diameter of circular shaft is denoted by d.

How to calculate Bending Stress of Circular Shaft given Equivalent Bending Moment?

The Bending Stress of Circular Shaft given Equivalent Bending Moment formula is defined as 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 is calculated using Bending Stress = (32*Equivalent Bending Moment)/(pi*(Diameter of Circular Shaft^3)). To calculate Bending Stress of Circular Shaft given Equivalent Bending Moment, you need Equivalent Bending Moment (M_e) & Diameter of Circular Shaft (Φ). With our tool, you need to enter the respective value for Equivalent Bending Moment & Diameter of Circular 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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