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Bending Moment given Bending Stress in Hollow Shaft Formula

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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. Check FAQs

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

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

Bending Moment given Bending Stress in Hollow Shaft Example

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

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

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

549948.5919 = 120.4 \cdot \frac{3.1416 \cdot 46^{3} \cdot (1 - ({0.85}^{4}))}{32}

549948.5919N*mm = 120.4N/mm² \cdot \frac{3.1416 \cdot {46mm}^{3} \cdot (1 - ({0.85}^{4}))}{32}

549948.5919 = 120.4 \cdot \frac{3.1416 \cdot 46^{3} \cdot (1 - ({0.85}^{4}))}{32}

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Bending Moment given Bending Stress in Hollow Shaft Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

M b h = 120.4N/mm² \cdot \frac{π \cdot {46mm}^{3} \cdot (1 - ({0.85}^{4}))}{32}

Next Step Substitute values of Constants

∴

M b h = 120.4N/mm² \cdot \frac{3.1416 \cdot {46mm}^{3} \cdot (1 - ({0.85}^{4}))}{32}

Next Step Convert Units

∴

M b h = 1.2E+8Pa \cdot \frac{3.1416 \cdot {0.046m}^{3} \cdot (1 - ({0.85}^{4}))}{32}

Next Step Prepare to Evaluate

∴

M b h = 1.2E+8 \cdot \frac{3.1416 \cdot {0.046}^{3} \cdot (1 - ({0.85}^{4}))}{32}

Next Step Evaluate

∴

M b h = 549.948591863872N*m

Next Step Convert to Output's Unit

∴

M b h = 549948.591863872N*mm

LAST Step Rounding Answer

∴

M b h = 549948.5919N*mm

Bending Moment given Bending Stress in Hollow Shaft Formula Elements

Variables

Constants

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

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

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 Moment given Bending Stress in Hollow Shaft?

Bending Moment given Bending Stress in Hollow Shaft evaluator uses Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32 to evaluate the Bending Moment in Hollow Shaft, Bending Moment given Bending Stress in Hollow Shaft formula is defined as a measure of the turning force that causes the shaft to bend, which is essential in designing hollow shafts to withstand external loads and stresses, ensuring the structural integrity of the system. Bending Moment in Hollow Shaft is denoted by M_{b h} symbol.

How to evaluate Bending Moment given Bending Stress in Hollow Shaft using this online evaluator? To use this online evaluator for Bending Moment given Bending Stress in Hollow Shaft, enter Bending Stress in Hollow Shaft (σ_{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 Moment given Bending Stress in Hollow Shaft

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

The formula of Bending Moment given Bending Stress in Hollow Shaft is expressed as Bending Moment in Hollow Shaft = Bending Stress in Hollow Shaft*(pi*Outer Diameter of Hollow Shaft^3*(1-(Ratio of Inner to Outer Diameter of Hollow Shaft^4)))/32. Here is an example- 5.5E+8 = 120400000*(pi*0.046^3*(1-(0.85^4)))/32.

How to calculate Bending Moment given Bending Stress in Hollow Shaft?

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

Can the Bending Moment given Bending Stress in Hollow Shaft be negative?

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

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

Bending Moment given Bending Stress in Hollow Shaft is usually measured using the Newton Millimeter[N*mm] for Torque. Newton Meter[N*mm], Newton Centimeter[N*mm], Kilonewton Meter[N*mm] are the few other units in which Bending Moment given Bending Stress in Hollow Shaft can be measured.

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Bending Moment given Bending Stress in Hollow Shaft Formula

Bending Moment given Bending Stress in Hollow Shaft Example

Bending Moment given Bending Stress in Hollow Shaft Solution

Bending Moment given Bending Stress in Hollow Shaft Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Bending Moment given Bending Stress in Hollow Shaft?

FAQs on Bending Moment given Bending Stress in Hollow Shaft

Variable Name