FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Outer Diameter of Shaft given Torsional Shear Stress Formula

GoOuter Diameter given Ratio of Diameters Formula

GoOuter Diameter of Hollow Shaft given Bending Stress of Hollow Shaft Formula

Fx Copy

LaTeX Copy

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

d o = {(16 \cdot \frac{Mt hollowshaft}{π \cdot 𝜏 h \cdot (1 - C^{4})})}^{\frac{1}{3}}

d_o - Outer Diameter of Hollow Shaft?Mt_hollowshaft - Torsional Moment in Hollow Shaft?𝜏_h - Torsional Shear Stress in Hollow Shaft?C - Ratio of Inner to Outer Diameter of Hollow Shaft?π - Archimedes' constant?

Outer Diameter of Shaft given Torsional Shear Stress Example

With values

With units

Only example

Here is how the Outer Diameter of Shaft given Torsional Shear Stress equation looks like with Values.

Here is how the Outer Diameter of Shaft given Torsional Shear Stress equation looks like with Units.

Here is how the Outer Diameter of Shaft given Torsional Shear Stress equation looks like.

45.9688 = {(16 \cdot \frac{320000}{3.1416 \cdot 35.1 \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

45.9688mm = {(16 \cdot \frac{320000N*mm}{3.1416 \cdot 35.1N/mm² \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

45.9688 = {(16 \cdot \frac{320000}{3.1416 \cdot 35.1 \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Design of Automobile Elements » fx Outer Diameter of Shaft given Torsional Shear Stress

Outer Diameter of Shaft given Torsional Shear Stress Solution

Follow our step by step solution on how to calculate Outer Diameter of Shaft given Torsional Shear Stress?

FIRST Step Consider the formula

d o = {(16 \cdot \frac{Mt hollowshaft}{π \cdot 𝜏 h \cdot (1 - C^{4})})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d o = {(16 \cdot \frac{320000N*mm}{π \cdot 35.1N/mm² \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d o = {(16 \cdot \frac{320000N*mm}{3.1416 \cdot 35.1N/mm² \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Convert Units

∴

d o = {(16 \cdot \frac{320N*m}{3.1416 \cdot 3.5E+7Pa \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d o = {(16 \cdot \frac{320}{3.1416 \cdot 3.5E+7 \cdot (1 - {0.85}^{4})})}^{\frac{1}{3}}

Next Step Evaluate

∴

d o = 0.0459688442234587m

Next Step Convert to Output's Unit

∴

d o = 45.9688442234587mm

LAST Step Rounding Answer

∴

d o = 45.9688mm

Outer Diameter of Shaft given Torsional Shear Stress Formula Elements

Variables

Constants

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

Torsional Moment in Hollow Shaft

Torsional 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 twist.

Symbol: Mt_hollowshaft

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Hollow Shaft

Torsional Shear Stress in Hollow Shaft

Torsional Shear Stress in Hollow Shaft is the shear stress produced in the hollow shaft due to the twisting.

Symbol: 𝜏_h

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Torsional Shear Stress in 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 to find Outer Diameter of Hollow Shaft

Go Outer Diameter given Ratio of Diameters

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

Go Outer Diameter of Hollow Shaft given Bending Stress of Hollow Shaft

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

Go Outer Diameter of Hollow Shaft given Principle Stress

d o = {(16 \cdot \frac{M b h + \sqrt{{M b h}^{2} + {Mt hollowshaft}^{2}}}{π \cdot τ \cdot (1 - C^{4})})}^{\frac{1}{3}}

Go Outer Diameter of Hollow Shaft given Angle of Twist Torsional Rigidity

d o = {(584 \cdot Mt hollowshaft \cdot \frac{L h}{G h \cdot θ hollow \cdot (1 - C^{4})})}^{\frac{1}{4}}

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 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})}

Go Axial Tensile Force given Tensile Stress in Hollow Shaft

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

How to Evaluate Outer Diameter of Shaft given Torsional Shear Stress?

Outer Diameter of Shaft given Torsional Shear Stress evaluator uses Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3) to evaluate the Outer Diameter of Hollow Shaft, Outer Diameter of Shaft given Torsional Shear Stress formula is defined as a measure of the outer diameter of a hollow shaft in a mechanical system, considering the torsional shear stress and other design parameters, to ensure the structural integrity and performance of the shaft. Outer Diameter of Hollow Shaft is denoted by d_o symbol.

How to evaluate Outer Diameter of Shaft given Torsional Shear Stress using this online evaluator? To use this online evaluator for Outer Diameter of Shaft given Torsional Shear Stress, enter Torsional Moment in Hollow Shaft (Mt_hollowshaft), Torsional Shear Stress in Hollow Shaft (𝜏_h) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) and hit the calculate button.

FAQs on Outer Diameter of Shaft given Torsional Shear Stress

What is the formula to find Outer Diameter of Shaft given Torsional Shear Stress?

The formula of Outer Diameter of Shaft given Torsional Shear Stress is expressed as Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). Here is an example- 45968.84 = (16*320/(pi*35100000*(1-0.85^4)))^(1/3).

How to calculate Outer Diameter of Shaft given Torsional Shear Stress?

With Torsional Moment in Hollow Shaft (Mt_hollowshaft), Torsional Shear Stress in Hollow Shaft (𝜏_h) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) we can find Outer Diameter of Shaft given Torsional Shear Stress using the formula - Outer Diameter of Hollow Shaft = (16*Torsional Moment in Hollow Shaft/(pi*Torsional Shear Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3). This formula also uses Archimedes' constant .

What are the other ways to Calculate Outer Diameter of Hollow Shaft?

Here are the different ways to Calculate Outer Diameter of Hollow Shaft-

Outer Diameter of Hollow Shaft=Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft
Outer Diameter of Hollow Shaft=(32*Bending Moment in Hollow Shaft/(pi*Bending Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Outer Diameter of Hollow Shaft=(16*(Bending Moment in Hollow Shaft+sqrt(Bending Moment in Hollow Shaft^2+Torsional Moment in Hollow Shaft^2))/(pi*Maximum Principle Stress in Hollow Shaft*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Can the Outer Diameter of Shaft given Torsional Shear Stress be negative?

No, the Outer Diameter of Shaft given Torsional Shear Stress, measured in Length cannot be negative.

Which unit is used to measure Outer Diameter of Shaft given Torsional Shear Stress?

Outer Diameter of Shaft given Torsional Shear Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Outer Diameter of Shaft given Torsional Shear Stress can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Outer Diameter of Shaft given Torsional Shear Stress Formula

​GoOuter Diameter given Ratio of Diameters Formula

​GoOuter Diameter of Hollow Shaft given Bending Stress of Hollow Shaft Formula

Outer Diameter of Shaft given Torsional Shear Stress Example

Outer Diameter of Shaft given Torsional Shear Stress Solution

Outer Diameter of Shaft given Torsional Shear Stress Formula Elements

Other Formulas to find Outer Diameter of Hollow Shaft

Other formulas in Design of Hollow Shaft category

How to Evaluate Outer Diameter of Shaft given Torsional Shear Stress?

FAQs on Outer Diameter of Shaft given Torsional Shear Stress

Variable Name

GoOuter Diameter given Ratio of Diameters Formula

GoOuter Diameter of Hollow Shaft given Bending Stress of Hollow Shaft Formula