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Deflection of Spring Formula

GoDeflection of Spring given Strain Energy Stored Formula

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

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

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

Deflection of Spring Example

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

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

Here is how the Deflection of Spring equation looks like.

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

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

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

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Deflection of Spring Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

δ = \frac{8 \cdot 138.2N \cdot ({0.036m}^{3}) \cdot 10}{8.6E+10Pa \cdot {0.004m}^{4}}

Next Step Prepare to Evaluate

∴

δ = \frac{8 \cdot 138.2 \cdot ({0.036}^{3}) \cdot 10}{8.6E+10 \cdot {0.004}^{4}}

Next Step Evaluate

∴

δ = 0.02332125m

Next Step Convert to Output's Unit

∴

δ = 23.32125mm

LAST Step Rounding Answer

∴

δ = 23.3212mm

Deflection of Spring Formula Elements

Variables

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

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

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

Other Formulas to find Deflection of Spring

Go Deflection of Spring given Strain Energy Stored

δ = 2 \cdot \frac{U h}{P}

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 Deflection of Spring?

Deflection of Spring evaluator uses Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4) to evaluate the Deflection of Spring, Deflection of Spring formula is defined as a measure of the maximum displacement of a spring from its original position when a load is applied, providing a way to calculate the spring's stiffness and deformation under various loads and stresses. Deflection of Spring is denoted by δ symbol.

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

FAQs on Deflection of Spring

What is the formula to find Deflection of Spring?

The formula of Deflection of Spring is expressed as Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4). Here is an example- 23321.25 = (8*138.2*(0.036^3)*10)/(86400000000*0.004^4).

How to calculate Deflection of Spring?

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

What are the other ways to Calculate Deflection of Spring?

Here are the different ways to Calculate Deflection of Spring-

Deflection of Spring=2*Strain Energy in Spring/Axial Spring Force

Can the Deflection of Spring be negative?

No, the Deflection of Spring, measured in Length cannot be negative.

Which unit is used to measure Deflection of Spring?

Deflection of Spring is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Deflection of Spring can be measured.

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Deflection of Spring Formula

​GoDeflection of Spring given Strain Energy Stored Formula

Deflection of Spring Example

Deflection of Spring Solution

Deflection of Spring Formula Elements

Other Formulas to find Deflection of Spring

Other formulas in Stress and Deflections in Springs category

How to Evaluate Deflection of Spring?

FAQs on Deflection of Spring

Variable Name

GoDeflection of Spring given Strain Energy Stored Formula