Moment of Inertia given Deflection in Leaf Spring Calculator

✖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 in Spring [L]			+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%
✖Deflection of Spring is how a spring responds when force is applied or released.ⓘ Deflection of Spring [δ]			+10% -10%

✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Moment of Inertia given Deflection in Leaf Spring [I]

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Formula

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Moment of Inertia given Deflection in Leaf Spring

Formula

`"I" = ("M"*"L"^2)/(8*"E"*"δ")`

Example

`"0.002158m⁴"=("67.5kN*m"*("4170mm")^2)/(8*"20000MPa"*"3.4mm")`

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Moment of Inertia given Deflection in Leaf Spring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia = (Bending Moment*Length in Spring^2)/(8*Young's Modulus*Deflection of Spring)
I = (M*L^2)/(8*E*δ)
This formula uses 5 Variables

Variables Used

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.
Length in Spring - (Measured in Meter) - Length in Spring is the measurement or extent of something from end to end.
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.
Deflection of Spring - (Measured in Meter) - Deflection of Spring is how a spring responds when force is applied or released.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 67.5 Kilonewton Meter --> 67500 Newton Meter (Check conversion here)
Length in Spring: 4170 Millimeter --> 4.17 Meter (Check conversion here)
Young's Modulus: 20000 Megapascal --> 20000000000 Pascal (Check conversion here)
Deflection of Spring: 3.4 Millimeter --> 0.0034 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (M*L^2)/(8*E*δ) --> (67500*4.17^2)/(8*20000000000*0.0034)

Evaluating ... ...

I = 0.00215763005514706

STEP 3: Convert Result to Output's Unit

0.00215763005514706 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00215763005514706 ≈ 0.002158 Meter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.004 seconds)

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< 5 Leaf Springs Calculators

Length given Deflection in Leaf Spring

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

Deflection in Leaf Spring given Moment

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

Modulus of Elasticity given Deflection in Leaf Spring and Moment

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

Moment of Inertia given Deflection in Leaf Spring

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

Moment given Deflection in Leaf Spring

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

Moment of Inertia given Deflection in Leaf Spring Formula

Area Moment of Inertia = (Bending Moment*Length in Spring^2)/(8*Young's Modulus*Deflection of Spring)
I = (M*L^2)/(8*E*δ)

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 Moment of Inertia given Deflection in Leaf Spring?

Moment of Inertia given Deflection in Leaf Spring calculator uses Area Moment of Inertia = (Bending Moment*Length in Spring^2)/(8*Young's Modulus*Deflection of Spring) to calculate the Area Moment of Inertia, Moment of Inertia given Deflection in Leaf Spring formula is defined as quantity that determines torque needed for desired angular acceleration about rotational axis, akin to how mass determines force needed for desired acceleration. Area Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Deflection in Leaf Spring using this online calculator? To use this online calculator for Moment of Inertia given Deflection in Leaf Spring, enter Bending Moment (M), Length in Spring (L), Young's Modulus (E) & Deflection of Spring (δ) and hit the calculate button. Here is how the Moment of Inertia given Deflection in Leaf Spring calculation can be explained with given input values -> 0.002158 = (67500*4.17^2)/(8*20000000000*0.0034).

FAQ

What is Moment of Inertia given Deflection in Leaf Spring?

Moment of Inertia given Deflection in Leaf Spring formula is defined as quantity that determines torque needed for desired angular acceleration about rotational axis, akin to how mass determines force needed for desired acceleration and is represented as I = (M*L^2)/(8*E*δ) or Area Moment of Inertia = (Bending Moment*Length in Spring^2)/(8*Young's Modulus*Deflection of Spring). Bending Moment is the reaction induced in a structural element when an external force or moment is applied, causing the element to bend, Length in Spring is the measurement or extent of something from end to end, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain & Deflection of Spring is how a spring responds when force is applied or released.

How to calculate Moment of Inertia given Deflection in Leaf Spring?

Moment of Inertia given Deflection in Leaf Spring formula is defined as quantity that determines torque needed for desired angular acceleration about rotational axis, akin to how mass determines force needed for desired acceleration is calculated using Area Moment of Inertia = (Bending Moment*Length in Spring^2)/(8*Young's Modulus*Deflection of Spring). To calculate Moment of Inertia given Deflection in Leaf Spring, you need Bending Moment (M), Length in Spring (L), Young's Modulus (E) & Deflection of Spring (δ). With our tool, you need to enter the respective value for Bending Moment, Length in Spring, Young's Modulus & Deflection of Spring 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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