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Diameter of Shaft given Principle Shear Stress Formula

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Diameter of Shaft From ASME is the required diameter of the shaft according to the American Society of Mechanical Engineers Code for shaft design. Check FAQs

d' = {(\frac{16}{π \cdot 𝜏' max} \cdot \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}})}^{\frac{1}{3}}

d' - Diameter of Shaft From ASME?𝜏'_max - Maximum Shear Stress in Shaft From ASME?M'_s - Torsional Moment in Shaft?k_t' - Combined Shock Fatigue Factor of Torsion Moment?k_b' - Combined Shock Fatigue Factor of Bending Moment?M_s - Bending Moment in Shaft?π - Archimedes' constant?

Diameter of Shaft given Principle Shear Stress Example

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

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

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

48 = {(\frac{16}{3.1416 \cdot 150.51} \cdot \sqrt{{(330000 \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6)}^{2}})}^{\frac{1}{3}}

48mm = {(\frac{16}{3.1416 \cdot 150.51N/mm²} \cdot \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}})}^{\frac{1}{3}}

48 = {(\frac{16}{3.1416 \cdot 150.51} \cdot \sqrt{{(330000 \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6)}^{2}})}^{\frac{1}{3}}

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Diameter of Shaft given Principle Shear Stress Solution

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

FIRST Step Consider the formula

d' = {(\frac{16}{π \cdot 𝜏' max} \cdot \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d' = {(\frac{16}{π \cdot 150.51N/mm²} \cdot \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

d' = {(\frac{16}{3.1416 \cdot 150.51N/mm²} \cdot \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}})}^{\frac{1}{3}}

Next Step Convert Units

∴

d' = {(\frac{16}{3.1416 \cdot 1.5E+8Pa} \cdot \sqrt{{(330N*m \cdot 1.3)}^{2} + {(1.8 \cdot 1800N*m)}^{2}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d' = {(\frac{16}{3.1416 \cdot 1.5E+8} \cdot \sqrt{{(330 \cdot 1.3)}^{2} + {(1.8 \cdot 1800)}^{2}})}^{\frac{1}{3}}

Next Step Evaluate

∴

d' = 0.0480000011387812m

Next Step Convert to Output's Unit

∴

d' = 48.0000011387812mm

LAST Step Rounding Answer

∴

d' = 48mm

Diameter of Shaft given Principle Shear Stress Formula Elements

Variables

Constants

Functions

Diameter of Shaft From ASME

Diameter of Shaft From ASME is the required diameter of the shaft according to the American Society of Mechanical Engineers Code for shaft design.

Symbol: d'

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft From ASME

Maximum Shear Stress in Shaft From ASME

Maximum Shear Stress in Shaft From ASME is the maximum amount of shear stress arising due to shear forces and is calculated using ASME code for shaft design.

Symbol: 𝜏'_max

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress in Shaft From ASME

Torsional Moment in Shaft

Torsional Moment in Shaft is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.

Symbol: M'_s

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional Moment in Shaft

Combined Shock Fatigue Factor of Torsion Moment

Combined Shock Fatigue Factor of Torsion Moment is a factor accounting for the combined shock and fatigue load applied with torsion moment.

Symbol: k_t'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Combined Shock Fatigue Factor of Torsion Moment

Combined Shock Fatigue Factor of Bending Moment

Combined Shock Fatigue Factor of Bending Moment is a factor accounting for the combined shock and fatigue load applied with bending moment.

Symbol: k_b'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Combined Shock Fatigue Factor of Bending Moment

Bending Moment in Shaft

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

Symbol: M_s

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment in 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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in ASME Code for Shaft Desgin category

Go Principle Shear Stress Maximum Shear Stress Theory of Failure

𝜏' max = \frac{16}{π \cdot {d'}^{3}} \cdot \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

Go Equivalent Torsional Moment when Shaft is Subjected to Fluctuating Loads

M t = \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

Go Equivalent Bending Moment when Shaft is Subjected to Fluctuating Loads

M f = k b' \cdot M s + \sqrt{{(M' s \cdot k t')}^{2} + {(k b' \cdot M s)}^{2}}

Go Design of Shaft using ASME Code

𝜏 max = \frac{16 \cdot \sqrt{{(k b \cdot M b)}^{2} + {(k t \cdot M t')}^{2}}}{π \cdot {d s}^{3}}

How to Evaluate Diameter of Shaft given Principle Shear Stress?

Diameter of Shaft given Principle Shear Stress evaluator uses Diameter of Shaft From ASME = (16/(pi*Maximum Shear Stress in Shaft From ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3) to evaluate the Diameter of Shaft From ASME, Diameter of Shaft given Principle Shear Stress formula is defined as the maximum diameter of a shaft that can withstand a given principal shear stress, considering the shaft's torque, bending moment, and material properties, ensuring safe and reliable design according to the ASME code for shaft design. Diameter of Shaft From ASME is denoted by d' symbol.

How to evaluate Diameter of Shaft given Principle Shear Stress using this online evaluator? To use this online evaluator for Diameter of Shaft given Principle Shear Stress, enter Maximum Shear Stress in Shaft From ASME (𝜏'_max), Torsional Moment in Shaft (M'_s), Combined Shock Fatigue Factor of Torsion Moment (k_t'), Combined Shock Fatigue Factor of Bending Moment (k_b') & Bending Moment in Shaft (M_s) and hit the calculate button.

FAQs on Diameter of Shaft given Principle Shear Stress

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

The formula of Diameter of Shaft given Principle Shear Stress is expressed as Diameter of Shaft From ASME = (16/(pi*Maximum Shear Stress in Shaft From ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3). Here is an example- 59758.29 = (16/(pi*150510000)*sqrt((330*1.3)^2+(1.8*1800)^2))^(1/3).

How to calculate Diameter of Shaft given Principle Shear Stress?

With Maximum Shear Stress in Shaft From ASME (𝜏'_max), Torsional Moment in Shaft (M'_s), Combined Shock Fatigue Factor of Torsion Moment (k_t'), Combined Shock Fatigue Factor of Bending Moment (k_b') & Bending Moment in Shaft (M_s) we can find Diameter of Shaft given Principle Shear Stress using the formula - Diameter of Shaft From ASME = (16/(pi*Maximum Shear Stress in Shaft From ASME)*sqrt((Torsional Moment in Shaft*Combined Shock Fatigue Factor of Torsion Moment)^2+(Combined Shock Fatigue Factor of Bending Moment*Bending Moment in Shaft)^2))^(1/3). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Diameter of Shaft given Principle Shear Stress be negative?

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

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

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

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Diameter of Shaft given Principle Shear Stress Formula

Diameter of Shaft given Principle Shear Stress Example

Diameter of Shaft given Principle Shear Stress Solution

Diameter of Shaft given Principle Shear Stress Formula Elements

Other formulas in ASME Code for Shaft Desgin category

How to Evaluate Diameter of Shaft given Principle Shear Stress?

FAQs on Diameter of Shaft given Principle Shear Stress

Variable Name