Bending Stress for Hollow Shaft Calculator

✖Maximum Bending Moment is the algebraic sum of the moments caused by the internal forces on the shaft and it causes the shaft to rotate.ⓘ Maximum Bending Moment [M_m]			+10% -10%
✖Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Hollow Shaft Outer Diameter [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 [k]			+10% -10%

✖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 for Hollow Shaft [f_b]

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Formula

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Bending Stress for Hollow Shaft

Formula

`"f"_{"b"} = "M"_{"m"}/((pi/32)*("d"_{"o"})^(3)*(1-"k"^2))`

Example

`"156.0005N/mm²"="34000N*mm"/((pi/32)*("20mm")^(3)*(1-("0.85")^2))`

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Bending Stress for Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))
f_b = M_m/((pi/32)*(d_o)^(3)*(1-k^2))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Bending Stress - (Measured in Pascal) - 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.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment is the algebraic sum of the moments caused by the internal forces on the shaft and it causes the shaft to rotate.
Hollow Shaft Outer Diameter - (Measured in Meter) - Hollow Shaft Outer Diameter 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

Maximum Bending Moment: 34000 Newton Millimeter --> 34 Newton Meter (Check conversion here)
Hollow Shaft Outer Diameter: 20 Millimeter --> 0.02 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

f_b = M_m/((pi/32)*(d_o)^(3)*(1-k^2)) --> 34/((pi/32)*(0.02)^(3)*(1-0.85^2))

Evaluating ... ...

f_b = 156000520.79638

STEP 3: Convert Result to Output's Unit

156000520.79638 Pascal -->156.00052079638 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

156.00052079638 ≈ 156.0005 Newton per Square Millimeter <-- Bending Stress

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Process Equipment Design » Agitators » Shaft Subjected to Bending Moment Only » Bending Stress for Hollow Shaft

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< 7 Shaft Subjected to Bending Moment Only Calculators

Diameter of Hollow Shaft Subjected to Maximum Bending Moment

Go Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)

Bending Stress for Hollow Shaft

Go Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))

Diameter of Solid Shaft Subjected to Maximum Bending Moment

Go Diameter of Solid Shaft for Agitator = ((Maximum Bending Moment for Solid Shaft)/((pi/32)*Bending Stress))^(1/3)

Bending Stress for Solid Shaft

Go Bending Stress = (Maximum Bending Moment for Solid Shaft)/((pi/32)*(Diameter of Solid Shaft for Agitator)^3)

Force for Design of Shaft Based on Pure Bending

Go Force = Maximum Torque for Agitator/(0.75*Height of Manometer Liquid)

Maximum Torque of Shaft Subjected to Bending Moment only

Go Maximum Torque for Agitator = Force*(0.75*Radius of Impeller Blade)

Maximum Bending Moment subject to Shaft

Go Maximum Bending Moment = Length of Shaft*Force

Bending Stress for Hollow Shaft Formula

Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))
f_b = M_m/((pi/32)*(d_o)^(3)*(1-k^2))

What is Bending Stress ?

Bending stress is a mechanical engineering concept that describes the internal stress or force that develops within a structural component, such as a beam, shaft, or any elongated structure, when it is subjected to an external load or moment that causes it to bend or undergo deformation. Bending stress occurs in response to forces that create a bending moment in the material.

What is Agitator Shaft?

An agitator shaft, also known as a mixing shaft, is a mechanical component commonly used in industrial equipment and processes for the purpose of mixing, blending, and agitating various substances or materials within a container or vessel. It plays a crucial role in processes across a wide range of industries, including chemical manufacturing, pharmaceuticals, food and beverage production, wastewater treatment, and more.

How to Calculate Bending Stress for Hollow Shaft?

Bending Stress for Hollow Shaft calculator uses Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)) to calculate the Bending Stress, The Bending Stress for Hollow Shaft formula refers to the stress or force that occurs within the shaft when it is subjected to bending loads. Bending Stress is denoted by f_b symbol.

How to calculate Bending Stress for Hollow Shaft using this online calculator? To use this online calculator for Bending Stress for Hollow Shaft, enter Maximum Bending Moment (M_m), Hollow Shaft Outer Diameter (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) and hit the calculate button. Here is how the Bending Stress for Hollow Shaft calculation can be explained with given input values -> 0.000156 = 34/((pi/32)*(0.02)^(3)*(1-0.85^2)).

FAQ

What is Bending Stress for Hollow Shaft?

The Bending Stress for Hollow Shaft formula refers to the stress or force that occurs within the shaft when it is subjected to bending loads and is represented as f_b = M_m/((pi/32)*(d_o)^(3)*(1-k^2)) or Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)). Maximum Bending Moment is the algebraic sum of the moments caused by the internal forces on the shaft and it causes the shaft to rotate, Hollow Shaft Outer Diameter 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 Stress for Hollow Shaft?

The Bending Stress for Hollow Shaft formula refers to the stress or force that occurs within the shaft when it is subjected to bending loads is calculated using Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)). To calculate Bending Stress for Hollow Shaft, you need Maximum Bending Moment (M_m), Hollow Shaft Outer Diameter (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (k). With our tool, you need to enter the respective value for Maximum Bending Moment, Hollow Shaft Outer Diameter & 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.

How many ways are there to calculate Bending Stress?

In this formula, Bending Stress uses Maximum Bending Moment, Hollow Shaft Outer Diameter & Ratio of Inner to Outer Diameter of Hollow Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

Bending Stress = (Maximum Bending Moment for Solid Shaft)/((pi/32)*(Diameter of Solid Shaft for Agitator)^3)

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