FormulaDen.com

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

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Formula

Fx Copy

LaTeX Copy

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

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

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

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Example

With values

With units

Only example

Here is how the Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment equation looks like with Values.

Here is how the Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment equation looks like with Units.

Here is how the Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment equation looks like.

35.0287 = 16 \cdot \frac{320000}{3.1416 \cdot 46^{3} \cdot (1 - {0.85}^{4})}

35.0287N/mm² = 16 \cdot \frac{320000N*mm}{3.1416 \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

35.0287 = 16 \cdot \frac{320000}{3.1416 \cdot 46^{3} \cdot (1 - {0.85}^{4})}

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 Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Solution

Follow our step by step solution on how to calculate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏 h = 16 \cdot \frac{320000N*mm}{π \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

Next Step Substitute values of Constants

∴

𝜏 h = 16 \cdot \frac{320000N*mm}{3.1416 \cdot {46mm}^{3} \cdot (1 - {0.85}^{4})}

Next Step Convert Units

∴

𝜏 h = 16 \cdot \frac{320N*m}{3.1416 \cdot {0.046m}^{3} \cdot (1 - {0.85}^{4})}

Next Step Prepare to Evaluate

∴

𝜏 h = 16 \cdot \frac{320}{3.1416 \cdot {0.046}^{3} \cdot (1 - {0.85}^{4})}

Next Step Evaluate

∴

𝜏 h = 35028728.6575477Pa

Next Step Convert to Output's Unit

∴

𝜏 h = 35.0287286575477N/mm²

LAST Step Rounding Answer

∴

𝜏 h = 35.0287N/mm²

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Formula Elements

Variables

Constants

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

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

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 Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment evaluator uses Torsional Shear Stress in Hollow Shaft = 16*Torsional 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 Torsional Shear Stress in Hollow Shaft, Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment formula is defined as a measure of the shear stress developed in a hollow shaft when it is subjected to a pure torsional moment, which is a critical parameter in the design of hollow shafts to ensure their structural integrity and reliability. Torsional Shear Stress in Hollow Shaft is denoted by 𝜏_h symbol.

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

FAQs on Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment

What is the formula to find Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

The formula of Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment is expressed as Torsional Shear Stress in Hollow Shaft = 16*Torsional 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- 3.5E-5 = 16*320/(pi*0.046^3*(1-0.85^4)).

How to calculate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

With Torsional Moment in Hollow Shaft (Mt_hollowshaft), Outer Diameter of Hollow Shaft (d_o) & Ratio of Inner to Outer Diameter of Hollow Shaft (C) we can find Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment using the formula - Torsional Shear Stress in Hollow Shaft = 16*Torsional 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 Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment be negative?

No, the Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment, measured in Stress cannot be negative.

Which unit is used to measure Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment 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 Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Formula

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Example

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Solution

Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment?

FAQs on Torsional Shear Stress when Shaft is Subjected to Pure Torsional Moment

Variable Name