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Bending Stress in Hollow Shaft Formula

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Bending Stress in Hollow Shaft is the normal stress that is induced at a point in a hollow shaft subjected to loads that cause it to bend. Check FAQs

σ b h = 32 \cdot \frac{M b h}{π \cdot {d o}^{3} \cdot (1 - C^{4})}

σ_{b h} - Bending Stress in Hollow Shaft?M_{b h} - Bending Moment in Hollow Shaft?d_o - Outer Diameter of Hollow Shaft?C - Ratio of Inner to Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Bending Stress in Hollow Shaft Example

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

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

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

120.4113 = 32 \cdot \frac{550000}{3.1416 \cdot 46^{3} \cdot (1 - {0.85}^{4})}

120.4113N/mm² = 32 \cdot \frac{550000N*mm}{3.1416 \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

120.4113 = 32 \cdot \frac{550000}{3.1416 \cdot 46^{3} \cdot (1 - {0.85}^{4})}

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Bending Stress in Hollow Shaft Solution

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

FIRST Step Consider the formula

σ b h = 32 \cdot \frac{M b h}{π \cdot {d o}^{3} \cdot (1 - C^{4})}

Next Step Substitute values of Variables

∴

σ b h = 32 \cdot \frac{550000N*mm}{π \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

Next Step Substitute values of Constants

∴

σ b h = 32 \cdot \frac{550000N*mm}{3.1416 \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

Next Step Convert Units

∴

σ b h = 32 \cdot \frac{550N*m}{3.1416 \cdot {0.046m}^{3} \cdot (1 - {0.85}^{4})}

Next Step Prepare to Evaluate

∴

σ b h = 32 \cdot \frac{550}{3.1416 \cdot {0.046}^{3} \cdot (1 - {0.85}^{4})}

Next Step Evaluate

∴

σ b h = 120411254.76032Pa

Next Step Convert to Output's Unit

∴

σ b h = 120.41125476032N/mm²

LAST Step Rounding Answer

∴

σ b h = 120.4113N/mm²

Bending Stress in Hollow Shaft Formula Elements

Variables

Constants

Bending Stress in Hollow Shaft

Bending Stress in Hollow Shaft is the normal stress that is induced at a point in a hollow shaft subjected to loads that cause it to bend.

Symbol: σ_{b h}

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress in Hollow Shaft

Bending Moment in Hollow Shaft

Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend.

Symbol: M_{b h}

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in Hollow Shaft

Outer Diameter of Hollow Shaft

Outer Diameter of Hollow Shaft 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 Outer Diameter of Hollow 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.

Symbol: C

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 in Design of Hollow Shaft category

Go Ratio of Inner Diameter to Outer Diameter

C = \frac{d i}{d o}

Go Inner Diameter of Hollow Shaft given Ratio of Diameters

d i = C \cdot d o

Go Outer Diameter given Ratio of Diameters

d o = \frac{d i}{C}

Go Tensile Stress in Hollow Shaft when Subjected to Axial Force

σ tp = \frac{P ax hollow}{\frac{π}{4} \cdot ({d o}^{2} - {d i}^{2})}

How to Evaluate Bending Stress in Hollow Shaft?

Bending Stress in Hollow Shaft evaluator uses Bending Stress in Hollow Shaft = 32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)) to evaluate the Bending Stress in Hollow Shaft, Bending Stress in Hollow Shaft formula is defined as a measure of the maximum stress that a hollow shaft can withstand without deforming or breaking, considering the moment of inertia and the outer diameter of the shaft, and is a critical parameter in the design of hollow shafts for various mechanical applications. Bending Stress in Hollow Shaft is denoted by σ_{b h} symbol.

How to evaluate Bending Stress in Hollow Shaft using this online evaluator? To use this online evaluator for Bending Stress in Hollow Shaft, enter Bending Moment in Hollow Shaft (M_{b h}), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button.

FAQs on Bending Stress in Hollow Shaft

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

The formula of Bending Stress in Hollow Shaft is expressed as Bending Stress in Hollow Shaft = 32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). Here is an example- 0.00012 = 32*550/(pi*0.046^3*(1-0.85^4)).

How to calculate Bending Stress in Hollow Shaft?

With Bending Moment in Hollow Shaft (M_{b h}), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) we can find Bending Stress in Hollow Shaft using the formula - Bending Stress in Hollow Shaft = 32*Bending Moment in Hollow Shaft/(pi*Outer Diameter of Hollow Shaft^3*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)). This formula also uses Archimedes' constant .

Can the Bending Stress in Hollow Shaft be negative?

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

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

Bending Stress in 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 in Hollow Shaft can be measured.

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Bending Stress in Hollow Shaft Formula

Bending Stress in Hollow Shaft Example

Bending Stress in Hollow Shaft Solution

Bending Stress in Hollow Shaft Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Bending Stress in Hollow Shaft?

FAQs on Bending Stress in Hollow Shaft

Variable Name