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Principle Shear Stress Maximum Shear Stress Theory of Failure Formula

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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. Check FAQs

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

𝜏'_max - Maximum Shear Stress in Shaft From ASME?d' - Diameter of 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?

Principle Shear Stress Maximum Shear Stress Theory of Failure Example

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Here is how the Principle Shear Stress Maximum Shear Stress Theory of Failure equation looks like with Values.

Here is how the Principle Shear Stress Maximum Shear Stress Theory of Failure equation looks like with Units.

Here is how the Principle Shear Stress Maximum Shear Stress Theory of Failure equation looks like.

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

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

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

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Principle Shear Stress Maximum Shear Stress Theory of Failure Solution

Follow our step by step solution on how to calculate Principle Shear Stress Maximum Shear Stress Theory of Failure?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

𝜏' max = \frac{16}{π \cdot {48mm}^{3}} \cdot \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}}

Next Step Substitute values of Constants

∴

𝜏' max = \frac{16}{3.1416 \cdot {48mm}^{3}} \cdot \sqrt{{(330000N*mm \cdot 1.3)}^{2} + {(1.8 \cdot 1.8E+6N*mm)}^{2}}

Next Step Convert Units

∴

𝜏' max = \frac{16}{3.1416 \cdot {0.048m}^{3}} \cdot \sqrt{{(330N*m \cdot 1.3)}^{2} + {(1.8 \cdot 1800N*m)}^{2}}

Next Step Prepare to Evaluate

∴

𝜏' max = \frac{16}{3.1416 \cdot {0.048}^{3}} \cdot \sqrt{{(330 \cdot 1.3)}^{2} + {(1.8 \cdot 1800)}^{2}}

Next Step Evaluate

∴

𝜏' max = 150510010.712373Pa

Next Step Convert to Output's Unit

∴

𝜏' max = 150.510010712373N/mm²

LAST Step Rounding Answer

∴

𝜏' max = 150.51N/mm²

Principle Shear Stress Maximum Shear Stress Theory of Failure Formula Elements

Variables

Constants

Functions

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

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

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 Diameter of Shaft given Principle Shear Stress

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

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 Principle Shear Stress Maximum Shear Stress Theory of Failure?

Principle Shear Stress Maximum Shear Stress Theory of Failure evaluator uses Maximum Shear Stress in Shaft From ASME = 16/(pi*Diameter of Shaft From ASME^3)*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) to evaluate the Maximum Shear Stress in Shaft From ASME, Principle Shear Stress Maximum Shear Stress Theory of Failure formula is defined as a method to determine the maximum shear stress in a shaft according to the ASME Code for Shaft Design, considering the torque and bending moment acting on the shaft, and providing a safe design criterion to prevent failure. Maximum Shear Stress in Shaft From ASME is denoted by 𝜏'_max symbol.

How to evaluate Principle Shear Stress Maximum Shear Stress Theory of Failure using this online evaluator? To use this online evaluator for Principle Shear Stress Maximum Shear Stress Theory of Failure, enter Diameter of Shaft From ASME (d'), 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 Principle Shear Stress Maximum Shear Stress Theory of Failure

What is the formula to find Principle Shear Stress Maximum Shear Stress Theory of Failure?

The formula of Principle Shear Stress Maximum Shear Stress Theory of Failure is expressed as Maximum Shear Stress in Shaft From ASME = 16/(pi*Diameter of Shaft From ASME^3)*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). Here is an example- 0.000151 = 16/(pi*0.048^3)*sqrt((330*1.3)^2+(1.8*1800)^2).

How to calculate Principle Shear Stress Maximum Shear Stress Theory of Failure?

With Diameter of Shaft From ASME (d'), 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 Principle Shear Stress Maximum Shear Stress Theory of Failure using the formula - Maximum Shear Stress in Shaft From ASME = 16/(pi*Diameter of Shaft From ASME^3)*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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Principle Shear Stress Maximum Shear Stress Theory of Failure be negative?

No, the Principle Shear Stress Maximum Shear Stress Theory of Failure, measured in Stress cannot be negative.

Which unit is used to measure Principle Shear Stress Maximum Shear Stress Theory of Failure?

Principle Shear Stress Maximum Shear Stress Theory of Failure 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 Principle Shear Stress Maximum Shear Stress Theory of Failure can be measured.

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Principle Shear Stress Maximum Shear Stress Theory of Failure Formula

Principle Shear Stress Maximum Shear Stress Theory of Failure Example

Principle Shear Stress Maximum Shear Stress Theory of Failure Solution

Principle Shear Stress Maximum Shear Stress Theory of Failure Formula Elements

Other formulas in ASME Code for Shaft Desgin category

How to Evaluate Principle Shear Stress Maximum Shear Stress Theory of Failure?

FAQs on Principle Shear Stress Maximum Shear Stress Theory of Failure

Variable Name