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Bending Stress for Hollow Shaft Formula

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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. Check FAQs

f b = \frac{M m}{(\frac{π}{32}) \cdot {(d o)}^{3} \cdot (1 - k^{2})}

f_b - Bending Stress?M_m - Maximum Bending Moment?d_o - Hollow Shaft Outer Diameter?k - Ratio of Inner to Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Bending Stress for Hollow Shaft Example

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With units

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Here is how the Bending Stress for Hollow Shaft equation looks like with Values.

Here is how the Bending Stress for Hollow Shaft equation looks like with Units.

Here is how the Bending Stress for Hollow Shaft equation looks like.

156.0005 = \frac{34000}{(\frac{3.1416}{32}) \cdot {(20)}^{3} \cdot (1 - {0.85}^{2})}

156.0005N/mm² = \frac{34000N*mm}{(\frac{3.1416}{32}) \cdot {(20mm)}^{3} \cdot (1 - {0.85}^{2})}

156.0005 = \frac{34000}{(\frac{3.1416}{32}) \cdot {(20)}^{3} \cdot (1 - {0.85}^{2})}

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Bending Stress for Hollow Shaft Solution

Follow our step by step solution on how to calculate Bending Stress for Hollow Shaft?

FIRST Step Consider the formula

f b = \frac{M m}{(\frac{π}{32}) \cdot {(d o)}^{3} \cdot (1 - k^{2})}

Next Step Substitute values of Variables

∴

f b = \frac{34000N*mm}{(\frac{π}{32}) \cdot {(20mm)}^{3} \cdot (1 - {0.85}^{2})}

Next Step Substitute values of Constants

∴

f b = \frac{34000N*mm}{(\frac{3.1416}{32}) \cdot {(20mm)}^{3} \cdot (1 - {0.85}^{2})}

Next Step Convert Units

∴

f b = \frac{34N*m}{(\frac{3.1416}{32}) \cdot {(0.02m)}^{3} \cdot (1 - {0.85}^{2})}

Next Step Prepare to Evaluate

∴

f b = \frac{34}{(\frac{3.1416}{32}) \cdot {(0.02)}^{3} \cdot (1 - {0.85}^{2})}

Next Step Evaluate

∴

f b = 156000520.79638Pa

Next Step Convert to Output's Unit

∴

f b = 156.00052079638N/mm²

LAST Step Rounding Answer

∴

f b = 156.0005N/mm²

Bending Stress for Hollow Shaft Formula Elements

Variables

Constants

Bending Stress

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.

Symbol: f_b

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress

Maximum Bending Moment

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.

Symbol: M_m

Measurement: Bending MomentUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment

Hollow Shaft Outer Diameter

Hollow Shaft Outer Diameter is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Hollow Shaft Outer Diameter

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.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Ratio of Inner to Outer Diameter of Hollow Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Bending Stress

Go Bending Stress for Solid Shaft

f b = \frac{M solidshaft}{(\frac{π}{32}) \cdot {(d solidshaft)}^{3}}

Other formulas in Shaft Subjected to Bending Moment Only category

Go Force for Design of Shaft Based on Pure Bending

F m = \frac{T m}{0.75 \cdot h m}

Go Maximum Torque of Shaft Subjected to Bending Moment only

T m = F m \cdot (0.75 \cdot R b)

Go Maximum Bending Moment subject to Shaft

M m = l \cdot F m

Go Diameter of Solid Shaft Subjected to Maximum Bending Moment

d solidshaft = {(\frac{M solidshaft}{(\frac{π}{32}) \cdot f b})}^{\frac{1}{3}}

How to Evaluate Bending Stress for Hollow Shaft?

Bending Stress for Hollow Shaft evaluator 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 evaluate 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 evaluate Bending Stress for Hollow Shaft using this online evaluator? To use this online evaluator 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.

FAQs on Bending Stress for Hollow Shaft

What is the formula to find Bending Stress for Hollow Shaft?

The formula of Bending Stress for Hollow Shaft is expressed as Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)). Here is an example- 0.000156 = 34/((pi/32)*(0.02)^(3)*(1-0.85^2)).

How to calculate Bending Stress for Hollow Shaft?

With Maximum Bending Moment (M_m), Hollow Shaft Outer Diameter (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (k) we can find Bending Stress for Hollow Shaft using the formula - Bending Stress = Maximum Bending Moment/((pi/32)*(Hollow Shaft Outer Diameter)^(3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Bending Stress?

Here are the different ways to Calculate Bending Stress-

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

Can the Bending Stress for Hollow Shaft be negative?

No, the Bending Stress for Hollow Shaft, measured in Stress cannot be negative.

Which unit is used to measure Bending Stress for Hollow Shaft?

Bending Stress for Hollow Shaft is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Bending Stress for Hollow Shaft can be measured.

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Bending Stress for Hollow Shaft Formula

​GoBending Stress for Solid Shaft Formula

Bending Stress for Hollow Shaft Example

Bending Stress for Hollow Shaft Solution

Bending Stress for Hollow Shaft Formula Elements

Other Formulas to find Bending Stress

Other formulas in Shaft Subjected to Bending Moment Only category

How to Evaluate Bending Stress for Hollow Shaft?

FAQs on Bending Stress for Hollow Shaft

Variable Name

GoBending Stress for Solid Shaft Formula