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Length given Deflection in Leaf Spring Formula

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Length in Spring is the measurement or extent of something from end to end. Check FAQs

L = \sqrt{\frac{8 \cdot δ \cdot E \cdot I}{M}}

L - Length in Spring?δ - Deflection of Spring?E - Young's Modulus?I - Area Moment of Inertia?M - Bending Moment?

Length given Deflection in Leaf Spring Example

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Here is how the Length given Deflection in Leaf Spring equation looks like with Values.

Here is how the Length given Deflection in Leaf Spring equation looks like with Units.

Here is how the Length given Deflection in Leaf Spring equation looks like.

3590.9351 = \sqrt{\frac{8 \cdot 3.4 \cdot 20000 \cdot 0.0016}{67.5}}

3590.9351mm = \sqrt{\frac{8 \cdot 3.4mm \cdot 20000MPa \cdot 0.0016m⁴}{67.5kN*m}}

3590.9351 = \sqrt{\frac{8 \cdot 3.4 \cdot 20000 \cdot 0.0016}{67.5}}

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Length given Deflection in Leaf Spring Solution

Follow our step by step solution on how to calculate Length given Deflection in Leaf Spring?

FIRST Step Consider the formula

L = \sqrt{\frac{8 \cdot δ \cdot E \cdot I}{M}}

Next Step Substitute values of Variables

∴

L = \sqrt{\frac{8 \cdot 3.4mm \cdot 20000MPa \cdot 0.0016m⁴}{67.5kN*m}}

Next Step Convert Units

∴

L = \sqrt{\frac{8 \cdot 0.0034m \cdot 2E+10Pa \cdot 0.0016m⁴}{67500N*m}}

Next Step Prepare to Evaluate

∴

L = \sqrt{\frac{8 \cdot 0.0034 \cdot 2E+10 \cdot 0.0016}{67500}}

Next Step Evaluate

∴

L = 3.59093508919541m

Next Step Convert to Output's Unit

∴

L = 3590.93508919541mm

LAST Step Rounding Answer

∴

L = 3590.9351mm

Length given Deflection in Leaf Spring Formula Elements

Variables

Functions

Length in Spring

Length in Spring is the measurement or extent of something from end to end.

Symbol: L

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Length in Spring

Deflection of Spring

Deflection of Spring is how a spring responds when force is applied or released.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Spring

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Young's Modulus

Area Moment of Inertia

Area Moment of Inertia is a moment about the centroidal axis without considering mass.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Bending Moment

Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.

Symbol: M

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Bending Moment

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Leaf Springs category

Go Deflection in Leaf Spring given Moment

δ = (\frac{M \cdot L^{2}}{8 \cdot E \cdot I})

Go Moment of Inertia given Deflection in Leaf Spring

I = \frac{M \cdot L^{2}}{8 \cdot E \cdot δ}

Go Moment given Deflection in Leaf Spring

M = \frac{8 \cdot δ \cdot E \cdot I}{L^{2}}

Go Modulus of Elasticity given Deflection in Leaf Spring and Moment

E = \frac{M \cdot L^{2}}{8 \cdot δ \cdot I}

How to Evaluate Length given Deflection in Leaf Spring?

Length given Deflection in Leaf Spring evaluator uses Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment) to evaluate the Length in Spring, The Length given Deflection in Leaf Spring formula is defined as the end-to-end distance of the spring. Length in Spring is denoted by L symbol.

How to evaluate Length given Deflection in Leaf Spring using this online evaluator? To use this online evaluator for Length given Deflection in Leaf Spring, enter Deflection of Spring (δ), Young's Modulus (E), Area Moment of Inertia (I) & Bending Moment (M) and hit the calculate button.

FAQs on Length given Deflection in Leaf Spring

What is the formula to find Length given Deflection in Leaf Spring?

The formula of Length given Deflection in Leaf Spring is expressed as Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment). Here is an example- 3.590935 = sqrt((8*0.0034*20000000000*0.0016)/67500).

How to calculate Length given Deflection in Leaf Spring?

With Deflection of Spring (δ), Young's Modulus (E), Area Moment of Inertia (I) & Bending Moment (M) we can find Length given Deflection in Leaf Spring using the formula - Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment). This formula also uses Square Root (sqrt) function(s).

Can the Length given Deflection in Leaf Spring be negative?

Yes, the Length given Deflection in Leaf Spring, measured in Length can be negative.

Which unit is used to measure Length given Deflection in Leaf Spring?

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

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Length given Deflection in Leaf Spring Formula

Length given Deflection in Leaf Spring Example

Length given Deflection in Leaf Spring Solution

Length given Deflection in Leaf Spring Formula Elements

Other formulas in Leaf Springs category

How to Evaluate Length given Deflection in Leaf Spring?

FAQs on Length given Deflection in Leaf Spring

Variable Name