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Force Applied on Spring given Deflection in Spring Formula

GoForce acting on Spring given Resultant Stress Formula

GoForce Applied on Spring given Strain Energy Stored in Spring Formula

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

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

P - Axial Spring Force?δ - Deflection 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?

Force Applied on Spring given Deflection in Spring Example

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Here is how the Force Applied on Spring given Deflection in Spring equation looks like with Values.

Here is how the Force Applied on Spring given Deflection in Spring equation looks like with Units.

Here is how the Force Applied on Spring given Deflection in Spring equation looks like.

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

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

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

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Force Applied on Spring given Deflection in Spring Solution

Follow our step by step solution on how to calculate Force Applied on Spring given Deflection in Spring?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

P = 0.0233m \cdot 8.6E+10Pa \cdot \frac{{0.004m}^{4}}{8 \cdot ({0.036m}^{3}) \cdot 10}

Next Step Prepare to Evaluate

∴

P = 0.0233 \cdot 8.6E+10 \cdot \frac{{0.004}^{4}}{8 \cdot ({0.036}^{3}) \cdot 10}

LAST Step Evaluate

∴

P = 138.2N

Force Applied on Spring given Deflection in Spring Formula Elements

Variables

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

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

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 Axial Spring Force

Go Force acting on Spring given Resultant Stress

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

Go Force Applied on Spring given Strain Energy Stored in Spring

P = 2 \cdot \frac{U h}{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 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}}

Go Shear Stress Correction Factor

K s = (1 + (\frac{.5}{C}))

How to Evaluate Force Applied on Spring given Deflection in Spring?

Force Applied on Spring given Deflection in Spring evaluator uses Axial Spring Force = Deflection 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 Axial Spring Force, Force Applied on Spring given Deflection in Spring formula is defined as the measure of the force exerted on a spring when it is deflected from its original position, which is a critical parameter in determining the stress and deflections in springs, and is essential in designing and analyzing spring-based systems. Axial Spring Force is denoted by P symbol.

How to evaluate Force Applied on Spring given Deflection in Spring using this online evaluator? To use this online evaluator for Force Applied on Spring given Deflection in Spring, enter Deflection of Spring (δ), 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 Force Applied on Spring given Deflection in Spring

What is the formula to find Force Applied on Spring given Deflection in Spring?

The formula of Force Applied on Spring given Deflection in Spring is expressed as Axial Spring Force = Deflection 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- 138.1333 = 0.02332125*86400000000*0.004^4/(8*(0.036^3)*10).

How to calculate Force Applied on Spring given Deflection in Spring?

With Deflection of Spring (δ), 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 Force Applied on Spring given Deflection in Spring using the formula - Axial Spring Force = Deflection 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 Axial Spring Force?

Here are the different ways to Calculate Axial Spring Force-

Axial Spring Force=Shear Stress in Spring*(pi*Diameter of Spring Wire^3)/(Wahl Factor of Spring*8*Mean Coil Diameter of Spring)
Axial Spring Force=2*Strain Energy in Spring/Deflection of Spring

Can the Force Applied on Spring given Deflection in Spring be negative?

No, the Force Applied on Spring given Deflection in Spring, measured in Force cannot be negative.

Which unit is used to measure Force Applied on Spring given Deflection in Spring?

Force Applied on Spring given Deflection in Spring is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Force Applied on Spring given Deflection in Spring can be measured.

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Force Applied on Spring given Deflection in Spring Formula

​GoForce acting on Spring given Resultant Stress Formula

​GoForce Applied on Spring given Strain Energy Stored in Spring Formula

Force Applied on Spring given Deflection in Spring Example

Force Applied on Spring given Deflection in Spring Solution

Force Applied on Spring given Deflection in Spring Formula Elements

Other Formulas to find Axial Spring Force

Other formulas in Stress and Deflections in Springs category

How to Evaluate Force Applied on Spring given Deflection in Spring?

FAQs on Force Applied on Spring given Deflection in Spring

Variable Name

GoForce acting on Spring given Resultant Stress Formula

GoForce Applied on Spring given Strain Energy Stored in Spring Formula