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Modulus of Rigidity given Deflection in Spring Formula

GoModulus of Rigidity given Rate of Spring Formula

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Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is. Check FAQs

G = \frac{8 \cdot P \cdot (D^{3}) \cdot N a}{δ \cdot d^{4}}

G - Modulus of Rigidity of Spring Wire?P - Axial Spring Force?D - Mean Coil Diameter of Spring?N_a - Active Coils in Spring?δ - Deflection of Spring?d - Diameter of Spring Wire?

Modulus of Rigidity given Deflection in Spring Example

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Here is how the Modulus of Rigidity given Deflection in Spring equation looks like with Values.

Here is how the Modulus of Rigidity given Deflection in Spring equation looks like with Units.

Here is how the Modulus of Rigidity given Deflection in Spring equation looks like.

86400 = \frac{8 \cdot 138.2 \cdot (36^{3}) \cdot 10}{23.3212 \cdot 4^{4}}

86400N/mm² = \frac{8 \cdot 138.2N \cdot ({36mm}^{3}) \cdot 10}{23.3212mm \cdot {4mm}^{4}}

86400 = \frac{8 \cdot 138.2 \cdot (36^{3}) \cdot 10}{23.3212 \cdot 4^{4}}

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Modulus of Rigidity given Deflection in Spring Solution

Follow our step by step solution on how to calculate Modulus of Rigidity given Deflection in Spring?

FIRST Step Consider the formula

G = \frac{8 \cdot P \cdot (D^{3}) \cdot N a}{δ \cdot d^{4}}

Next Step Substitute values of Variables

∴

G = \frac{8 \cdot 138.2N \cdot ({36mm}^{3}) \cdot 10}{23.3212mm \cdot {4mm}^{4}}

Next Step Convert Units

∴

G = \frac{8 \cdot 138.2N \cdot ({0.036m}^{3}) \cdot 10}{0.0233m \cdot {0.004m}^{4}}

Next Step Prepare to Evaluate

∴

G = \frac{8 \cdot 138.2 \cdot ({0.036}^{3}) \cdot 10}{0.0233 \cdot {0.004}^{4}}

Next Step Evaluate

∴

G = 86399999999.9999Pa

Next Step Convert to Output's Unit

∴

G = 86399.9999999999N/mm²

LAST Step Rounding Answer

∴

G = 86400N/mm²

Modulus of Rigidity given Deflection in Spring Formula Elements

Variables

Modulus of Rigidity of Spring Wire

Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

Symbol: G

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity of Spring Wire

Axial Spring Force

Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Spring Force

Mean Coil Diameter of Spring

The 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

Active Coils in Spring

Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring.

Symbol: N_a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Active Coils in Spring

Deflection of Spring

Deflection of Spring is how much the length of a spring changes when force is applied or released.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of 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

Other Formulas to find Modulus of Rigidity of Spring Wire

Go Modulus of Rigidity given Rate of Spring

G = k \cdot \frac{8 \cdot D^{3} \cdot N a}{d^{4}}

Other formulas in Stress and Deflections in Springs category

Go Resultant Stress in Spring

𝜏 = K \cdot \frac{8 \cdot P \cdot D}{π \cdot d^{3}}

Go Force acting on Spring given Resultant Stress

P = 𝜏 \cdot \frac{π \cdot d^{3}}{K \cdot 8 \cdot D}

Go Mean Coil Diameter given Resultant Stress in Spring

D = 𝜏 \cdot \frac{π \cdot d^{3}}{K \cdot 8 \cdot P}

Go Diameter of Spring Wire given Resultant Stress in Spring

d = {(\frac{K \cdot 8 \cdot P \cdot D}{π \cdot 𝜏})}^{\frac{1}{3}}

How to Evaluate Modulus of Rigidity given Deflection in Spring?

Modulus of Rigidity given Deflection in Spring evaluator uses Modulus of Rigidity of Spring Wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of Spring Wire^4) to evaluate the Modulus of Rigidity of Spring Wire, Modulus of Rigidity given Deflection in Spring formula is defined as a measure of the rigidity of a spring, which is the ratio of shear stress to shear strain within the proportional limit of the material, and is used to determine the stiffness of a spring under various loads. Modulus of Rigidity of Spring Wire is denoted by G symbol.

How to evaluate Modulus of Rigidity given Deflection in Spring using this online evaluator? To use this online evaluator for Modulus of Rigidity given Deflection in Spring, enter Axial Spring Force (P), Mean Coil Diameter of Spring (D), Active Coils in Spring (N_a), Deflection of Spring (δ) & Diameter of Spring Wire (d) and hit the calculate button.

FAQs on Modulus of Rigidity given Deflection in Spring

What is the formula to find Modulus of Rigidity given Deflection in Spring?

The formula of Modulus of Rigidity given Deflection in Spring is expressed as Modulus of Rigidity of Spring Wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of Spring Wire^4). Here is an example- 0.086442 = (8*138.2*(0.036^3)*10)/(0.02332125*0.004^4).

How to calculate Modulus of Rigidity given Deflection in Spring?

With Axial Spring Force (P), Mean Coil Diameter of Spring (D), Active Coils in Spring (N_a), Deflection of Spring (δ) & Diameter of Spring Wire (d) we can find Modulus of Rigidity given Deflection in Spring using the formula - Modulus of Rigidity of Spring Wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of Spring Wire^4).

What are the other ways to Calculate Modulus of Rigidity of Spring Wire?

Here are the different ways to Calculate Modulus of Rigidity of Spring Wire-

Modulus of Rigidity of Spring Wire=Stiffness of Spring*(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)/Diameter of Spring Wire^4

Can the Modulus of Rigidity given Deflection in Spring be negative?

No, the Modulus of Rigidity given Deflection in Spring, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Rigidity given Deflection in Spring?

Modulus of Rigidity given Deflection in Spring is usually measured using the Newton per Square Millimeter[N/mm²] for Pressure. Pascal[N/mm²], Kilopascal[N/mm²], Bar[N/mm²] are the few other units in which Modulus of Rigidity given Deflection in Spring can be measured.

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Modulus of Rigidity given Deflection in Spring Formula

​GoModulus of Rigidity given Rate of Spring Formula

Modulus of Rigidity given Deflection in Spring Example

Modulus of Rigidity given Deflection in Spring Solution

Modulus of Rigidity given Deflection in Spring Formula Elements

Other Formulas to find Modulus of Rigidity of Spring Wire

Other formulas in Stress and Deflections in Springs category

How to Evaluate Modulus of Rigidity given Deflection in Spring?

FAQs on Modulus of Rigidity given Deflection in Spring

Variable Name

GoModulus of Rigidity given Rate of Spring Formula