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Shear Stress Factor for Spring given Torsional stress amplitude Formula

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Wahl Factor of Spring is simply a measure of the degree to which external stress is amplified at the curvature of the spring coil. Check FAQs

K = σ m \cdot \frac{π \cdot d^{3}}{8 \cdot P a \cdot D}

K - Wahl Factor of Spring?σ_m - Mean Shear Stress in Spring?d - Diameter of Spring Wire?P_a - Spring Force Amplitude?D - Mean Coil Diameter of Spring?π - Archimedes' constant?

Shear Stress Factor for Spring given Torsional stress amplitude Example

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Here is how the Shear Stress Factor for Spring given Torsional stress amplitude equation looks like with Values.

Here is how the Shear Stress Factor for Spring given Torsional stress amplitude equation looks like with Units.

Here is how the Shear Stress Factor for Spring given Torsional stress amplitude equation looks like.

2.1772 = 156 \cdot \frac{3.1416 \cdot {4.0047}^{3}}{8 \cdot 50.2 \cdot 36}

2.1772 = 156N/mm² \cdot \frac{3.1416 \cdot {4.0047mm}^{3}}{8 \cdot 50.2N \cdot 36mm}

2.1772 = 156 \cdot \frac{3.1416 \cdot {4.0047}^{3}}{8 \cdot 50.2 \cdot 36}

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Shear Stress Factor for Spring given Torsional stress amplitude Solution

Follow our step by step solution on how to calculate Shear Stress Factor for Spring given Torsional stress amplitude?

FIRST Step Consider the formula

K = σ m \cdot \frac{π \cdot d^{3}}{8 \cdot P a \cdot D}

Next Step Substitute values of Variables

∴

K = 156N/mm² \cdot \frac{π \cdot {4.0047mm}^{3}}{8 \cdot 50.2N \cdot 36mm}

Next Step Substitute values of Constants

∴

K = 156N/mm² \cdot \frac{3.1416 \cdot {4.0047mm}^{3}}{8 \cdot 50.2N \cdot 36mm}

Next Step Convert Units

∴

K = 1.6E+8Pa \cdot \frac{3.1416 \cdot {0.004m}^{3}}{8 \cdot 50.2N \cdot 0.036m}

Next Step Prepare to Evaluate

∴

K = 1.6E+8 \cdot \frac{3.1416 \cdot {0.004}^{3}}{8 \cdot 50.2 \cdot 0.036}

Next Step Evaluate

∴

K = 2.17721136315677

LAST Step Rounding Answer

∴

K = 2.1772

Shear Stress Factor for Spring given Torsional stress amplitude Formula Elements

Variables

Constants

Wahl Factor of Spring

Wahl Factor of Spring is simply a measure of the degree to which external stress is amplified at the curvature of the spring coil.

Symbol: K

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wahl Factor of Spring

Mean Shear Stress in Spring

Mean Shear Stress in Spring is defined as the amount of mean stress acting when spring is subjected to fluctuating stress.

Symbol: σ_m

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Mean Shear Stress in Spring

Diameter of Spring Wire

Diameter of Spring Wire is the diameter of the wire of which a spring is made.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Spring Wire

Spring Force Amplitude

The Spring Force Amplitude is defined as the amount of force deviation from the mean force and is also called the alternating component of force in fluctuating loads.

Symbol: P_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Spring Force Amplitude

Mean Coil Diameter of Spring

Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Mean Coil Diameter of Spring

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 Against Fluctuating Load category

Go Mean Force on spring

P m = \frac{P min + P max}{2}

Go Maximum Force on Spring given Mean Force

P max = 2 \cdot P m - P min

Go Minimum Force on Spring given Mean Force

P min = 2 \cdot P m - P max

Go Force Amplitude of Spring

P a = .5 \cdot (P max - P min)

How to Evaluate Shear Stress Factor for Spring given Torsional stress amplitude?

Shear Stress Factor for Spring given Torsional stress amplitude evaluator uses Wahl Factor of Spring = Mean Shear Stress in Spring*(pi*Diameter of Spring Wire^3)/(8*Spring Force Amplitude*Mean Coil Diameter of Spring) to evaluate the Wahl Factor of Spring, Shear Stress Factor for Spring given Torsional stress amplitude formula is defined as a dimensionless quantity used to determine the effect of fluctuating loads on the spring's performance, providing a critical value to ensure the spring's reliability and safety in various engineering applications. Wahl Factor of Spring is denoted by K symbol.

How to evaluate Shear Stress Factor for Spring given Torsional stress amplitude using this online evaluator? To use this online evaluator for Shear Stress Factor for Spring given Torsional stress amplitude, enter Mean Shear Stress in Spring (σ_m), Diameter of Spring Wire (d), Spring Force Amplitude (P_a) & Mean Coil Diameter of Spring (D) and hit the calculate button.

FAQs on Shear Stress Factor for Spring given Torsional stress amplitude

What is the formula to find Shear Stress Factor for Spring given Torsional stress amplitude?

The formula of Shear Stress Factor for Spring given Torsional stress amplitude is expressed as Wahl Factor of Spring = Mean Shear Stress in Spring*(pi*Diameter of Spring Wire^3)/(8*Spring Force Amplitude*Mean Coil Diameter of Spring). Here is an example- 2.177211 = 156000000*(pi*0.004004738^3)/(8*49.95129*0.036).

How to calculate Shear Stress Factor for Spring given Torsional stress amplitude?

With Mean Shear Stress in Spring (σ_m), Diameter of Spring Wire (d), Spring Force Amplitude (P_a) & Mean Coil Diameter of Spring (D) we can find Shear Stress Factor for Spring given Torsional stress amplitude using the formula - Wahl Factor of Spring = Mean Shear Stress in Spring*(pi*Diameter of Spring Wire^3)/(8*Spring Force Amplitude*Mean Coil Diameter of Spring). This formula also uses Archimedes' constant .

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Shear Stress Factor for Spring given Torsional stress amplitude Formula

Shear Stress Factor for Spring given Torsional stress amplitude Example

Shear Stress Factor for Spring given Torsional stress amplitude Solution

Shear Stress Factor for Spring given Torsional stress amplitude Formula Elements

Other formulas in Design Against Fluctuating Load category

How to Evaluate Shear Stress Factor for Spring given Torsional stress amplitude?

FAQs on Shear Stress Factor for Spring given Torsional stress amplitude

Variable Name