Length given Deflection in Leaf Spring Calculator

✖Deflection of Spring is how a spring responds when force is applied or released.ⓘ Deflection of Spring [δ]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Area Moment of Inertia [I]			+10% -10%
✖Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.ⓘ Bending Moment [M]			+10% -10%

✖Length in Spring is the measurement or extent of something from end to end.ⓘ Length given Deflection in Leaf Spring [L]

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Length given Deflection in Leaf Spring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment)
L = sqrt((8*δ*E*I)/M)
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

Variables Used

Length in Spring - (Measured in Meter) - Length in Spring is the measurement or extent of something from end to end.
Deflection of Spring - (Measured in Meter) - Deflection of Spring is how a spring responds when force is applied or released.
Young's Modulus - (Measured in Pascal) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.
Bending Moment - (Measured in Newton Meter) - Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.

STEP 1: Convert Input(s) to Base Unit

Deflection of Spring: 3.4 Millimeter --> 0.0034 Meter (Check conversion here)
Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required
Bending Moment: 67.5 Kilonewton Meter --> 67500 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = sqrt((8*δ*E*I)/M) --> sqrt((8*0.0034*20000000000*0.0016)/67500)

Evaluating ... ...

L = 3.59093508919541

STEP 3: Convert Result to Output's Unit

3.59093508919541 Meter -->3590.93508919541 Millimeter (Check conversion here)

FINAL ANSWER

3590.93508919541 ≈ 3590.935 Millimeter <-- Length in Spring

(Calculation completed in 00.004 seconds)

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< Leaf Springs Calculators

Length given Deflection in Leaf Spring

LaTeX Go Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment)

Deflection in Leaf Spring given Moment

LaTeX Go Deflection of Spring = ((Bending Moment*Length in Spring^2)/(8*Young's Modulus*Area Moment of Inertia))

Moment of Inertia given Deflection in Leaf Spring

LaTeX Go Area Moment of Inertia = (Bending Moment*Length in Spring^2)/(8*Young's Modulus*Deflection of Spring)

Moment given Deflection in Leaf Spring

LaTeX Go Bending Moment = (8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Length in Spring^2

Length given Deflection in Leaf Spring Formula

LaTeX Go

Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment)
L = sqrt((8*δ*E*I)/M)

What is Leaf Spring?

A leaf spring takes the form of a slender arc-shaped length of spring steel of rectangular cross-section. In the most common configuration, the center of the arc provides location for the axle, while loops formed at either end provide for attaching to the vehicle chassis. For very heavy vehicles, a leaf spring can be made from several leaves stacked on top of each other in several layers, often with progressively shorter leaves.

How to Calculate Length given Deflection in Leaf Spring?

Length given Deflection in Leaf Spring calculator uses Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment) to calculate 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 calculate Length given Deflection in Leaf Spring using this online calculator? To use this online calculator 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. Here is how the Length given Deflection in Leaf Spring calculation can be explained with given input values -> 3.590935 = sqrt((8*0.0034*20000000000*0.0016)/67500).

FAQ

What is Length given Deflection in Leaf Spring?

The Length given Deflection in Leaf Spring formula is defined as the end-to-end distance of the spring and is represented as L = sqrt((8*δ*E*I)/M) or Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment). Deflection of Spring is how a spring responds when force is applied or released, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Area Moment of Inertia is a moment about the centroidal axis without considering mass & Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend.

How to calculate Length given Deflection in Leaf Spring?

The Length given Deflection in Leaf Spring formula is defined as the end-to-end distance of the spring is calculated using Length in Spring = sqrt((8*Deflection of Spring*Young's Modulus*Area Moment of Inertia)/Bending Moment). To calculate Length given Deflection in Leaf Spring, you need Deflection of Spring (δ), Young's Modulus (E), Area Moment of Inertia (I) & Bending Moment (M). With our tool, you need to enter the respective value for Deflection of Spring, Young's Modulus, Area Moment of Inertia & Bending Moment and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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