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Rate of Spring Formula

GoRate of Spring given Deflection Formula

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Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation, every object in this universe has some stiffness. Check FAQs

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

k - Stiffness of Spring?G - Modulus of Rigidity of Spring Wire?d - Diameter of Spring Wire?D - Mean Coil Diameter of Spring?N_a - Active Coils in Spring?

Rate of Spring Example

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Here is how the Rate of Spring equation looks like with Values.

Here is how the Rate of Spring equation looks like with Units.

Here is how the Rate of Spring equation looks like.

5.9259 = 86400 \cdot \frac{4^{4}}{8 \cdot 36^{3} \cdot 10}

5.9259N/mm = 86400N/mm² \cdot \frac{{4mm}^{4}}{8 \cdot {36mm}^{3} \cdot 10}

5.9259 = 86400 \cdot \frac{4^{4}}{8 \cdot 36^{3} \cdot 10}

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Rate of Spring Solution

Follow our step by step solution on how to calculate Rate of Spring?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k = 86400N/mm² \cdot \frac{{4mm}^{4}}{8 \cdot {36mm}^{3} \cdot 10}

Next Step Convert Units

∴

k = 8.6E+10Pa \cdot \frac{{0.004m}^{4}}{8 \cdot {0.036m}^{3} \cdot 10}

Next Step Prepare to Evaluate

∴

k = 8.6E+10 \cdot \frac{{0.004}^{4}}{8 \cdot {0.036}^{3} \cdot 10}

Next Step Evaluate

∴

k = 5925.92592592593N/m

Next Step Convert to Output's Unit

∴

k = 5.92592592592593N/mm

LAST Step Rounding Answer

∴

k = 5.9259N/mm

Rate of Spring Formula Elements

Variables

Stiffness of Spring

Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation, every object in this universe has some stiffness.

Symbol: k

Measurement: Stiffness ConstantUnit: N/mm

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

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

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

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

Other Formulas to find Stiffness of Spring

Go Rate of Spring given Deflection

k = \frac{P}{δ}

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 Rate of Spring?

Rate of Spring evaluator uses Stiffness of Spring = Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring) to evaluate the Stiffness of Spring, Rate of Spring formula is defined as a measure of the stiffness of a spring, which is a critical parameter in determining the stress and deflections of a spring under various loads, and is essential in the design and analysis of spring-based systems in mechanical engineering. Stiffness of Spring is denoted by k symbol.

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

FAQs on Rate of Spring

What is the formula to find Rate of Spring?

The formula of Rate of Spring is expressed as Stiffness of Spring = Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring). Here is an example- 0.005926 = 86400000000*0.004^4/(8*0.036^3*10).

How to calculate Rate of Spring?

With Modulus of Rigidity of Spring Wire (G), Diameter of Spring Wire (d), Mean Coil Diameter of Spring (D) & Active Coils in Spring (N_a) we can find Rate of Spring using the formula - Stiffness of Spring = Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring).

What are the other ways to Calculate Stiffness of Spring?

Here are the different ways to Calculate Stiffness of Spring-

Stiffness of Spring=Axial Spring Force/Deflection of Spring

Can the Rate of Spring be negative?

No, the Rate of Spring, measured in Stiffness Constant cannot be negative.

Which unit is used to measure Rate of Spring?

Rate of Spring is usually measured using the Newton per Millimeter[N/mm] for Stiffness Constant. Newton per Meter[N/mm], Kilonewton per Millimeter[N/mm] are the few other units in which Rate of Spring can be measured.

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Rate of Spring Formula

​GoRate of Spring given Deflection Formula

Rate of Spring Example

Rate of Spring Solution

Rate of Spring Formula Elements

Other Formulas to find Stiffness of Spring

Other formulas in Stress and Deflections in Springs category

How to Evaluate Rate of Spring?

FAQs on Rate of Spring

Variable Name

GoRate of Spring given Deflection Formula