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 00.020 seconds)

Credits

Creator Image
Created by Rithik Agrawal
National Institute of Technology Karnataka (NITK), Surathkal
Rithik Agrawal has created this Calculator and 1300+ more calculators!
Verifier Image
Verified by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

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

Moment of Inertia given Deflection in Leaf Spring Formula

​LaTeX ​Go
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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!