Modulus of Elasticity of Spring given Deflection at end of Spring Solution

STEP 0: Pre-Calculation Summary
Formula Used
Modulus of Elasticity of Spring = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3)
E = 12*P*(L^3)/((3*nf+2*ng)*δf*b*t^3)
This formula uses 8 Variables
Variables Used
Modulus of Elasticity of Spring - (Measured in Pascal) - Modulus of Elasticity of Spring is a quantity that measures the spring's wire resistance to being deformed elastically when a stress is applied to it.
Force Applied at End of Leaf Spring - (Measured in Newton) - Force Applied at End of Leaf Spring is defined as the net amount of force that is acting onto the spring.
Length of Cantilever of Leaf Spring - (Measured in Meter) - The Length of Cantilever of Leaf Spring is defined as half the length of a semi-elliptic spring.
Number of Full length Leaves - Number of Full length Leaves is defined as the total number of extra full length leaves present in a multi-leaf spring.
Number of Graduated Length Leaves - Number of Graduated Length Leaves is defined as the number of graduated-length leaves including master leaf.
Deflection of full leaf at load point - (Measured in Meter) - Deflection of full leaf at load point is how much the leaf of the spring deviates from its position at the load application point.
Width of Leaf - (Measured in Meter) - Width of Leaf is defined as the width of each leaf present in a multi-leaf spring.
Thickness of Leaf - (Measured in Meter) - Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring.
STEP 1: Convert Input(s) to Base Unit
Force Applied at End of Leaf Spring: 37500 Newton --> 37500 Newton No Conversion Required
Length of Cantilever of Leaf Spring: 500 Millimeter --> 0.5 Meter (Check conversion here)
Number of Full length Leaves: 3 --> No Conversion Required
Number of Graduated Length Leaves: 15 --> No Conversion Required
Deflection of full leaf at load point: 36.5 Millimeter --> 0.0365 Meter (Check conversion here)
Width of Leaf: 108 Millimeter --> 0.108 Meter (Check conversion here)
Thickness of Leaf: 12 Millimeter --> 0.012 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
E = 12*P*(L^3)/((3*nf+2*ng)*δf*b*t^3) --> 12*37500*(0.5^3)/((3*3+2*15)*0.0365*0.108*0.012^3)
Evaluating ... ...
E = 211737393053.984
STEP 3: Convert Result to Output's Unit
211737393053.984 Pascal -->211737.393053984 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
211737.393053984 211737.4 Newton per Square Millimeter <-- Modulus of Elasticity of Spring
(Calculation completed in 00.020 seconds)

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Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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25 Extra Full Length Leaves Calculators

Length of Cantilever given Deflection at end of Spring
Go Length of Cantilever of Leaf Spring = (Deflection at end of leaf spring*((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus of Elasticity of Spring*Width of Leaf*Thickness of Leaf^3)/(12*Force Applied at End of Leaf Spring))^(1/3)
Modulus of Elasticity of Spring given Deflection at end of Spring
Go Modulus of Elasticity of Spring = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3)
Deflection at end of leaf Spring
Go Deflection of full leaf at load point = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus of Elasticity of Spring*Width of Leaf*Thickness of Leaf^3)
Force applied at end of Spring given Deflection at end of Spring
Go Force Applied at End of Leaf Spring = Deflection at end of leaf spring*((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus of Elasticity of Spring*Width of Leaf*Thickness of Leaf^3)/(12*Length of Cantilever of Leaf Spring^3)
Number of Graduated length leaves given Force taken by extra full length leaves
Go Number of Graduated Length Leaves = (3*Pre load for leaf spring*Total Number of Leaves*Number of Full length Leaves)/((2*Number of Full length Leaves*Force Applied at End of Leaf Spring)-(2*Total Number of Leaves*Pre load for leaf spring))
Thickness of each leaf given Bending Stress in extra full length leaves
Go Thickness of Leaf = sqrt(12*Force Applied at End of Leaf Spring*Length of Cantilever of Leaf Spring/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Bending Stress in full leaf))
Length of Cantilever given Deflection of Spring at load point
Go Length of Cantilever of Leaf Spring = (Deflection of full leaf at load point*Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3/(4*Force Taken by Graduated Length Leaves))^(1/3)
Modulus of Elasticity of leaf given Deflection at Load Point Graduated Length Leaves
Go Modulus of Elasticity of Spring = 6*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring^3/(Deflection of graduated leaf at load point*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3)
Deflection at Load Point Graduated Length Leaves
Go Deflection of graduated leaf at load point = 6*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring^3/(Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3)
Width of each leaf of leaf Spring given Deflection of Spring at load point
Go Width of Leaf = 4*Force Taken by Graduated Length Leaves*(Length of Cantilever of Leaf Spring^3)/(Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Deflection of full leaf at load point*Thickness of Leaf^3)
Portion of Force taken by extra full length leaf given deflection of Spring at load point
Go Force Taken by Graduated Length Leaves = Deflection of full leaf at load point*Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3/(4*Length of Cantilever of Leaf Spring^3)
Number of Graduated length leaves given Bending Stress in extra full length leaves
Go Number of Graduated Length Leaves = ((18*Force Applied at End of Leaf Spring*Length of Cantilever of Leaf Spring)/(Bending Stress in graduated leaf*Width of Leaf*Thickness of Leaf^2*2))-(3*Number of Full length Leaves/2)
Modulus of Elasticity of leaf of leaf spring given Deflection of Spring at load point
Go Modulus of Elasticity of Spring = 4*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring^3/(Deflection at end of leaf spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3)
Deflection of leaf Spring at load point
Go Deflection at end of leaf spring = 4*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring^3/(Modulus of Elasticity of Spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3)
Bending Stress on Graduated Length Leaves
Go Bending Stress in graduated leaf = 12*Force Applied at End of Leaf Spring*Length of Cantilever of Leaf Spring/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Thickness of Leaf^2)
Number of extra full length leaves given Bending Stress in extra full length leaves
Go Number of Full length Leaves = ((18*Force Applied at End of Leaf Spring*Length of Cantilever of Leaf Spring)/(Bending Stress in full leaf*Width of Leaf*Thickness of Leaf^2*3))-2*Number of Graduated Length Leaves/3
Number of extra full length leaves given Deflection of Spring at load point
Go Number of Full length Leaves = 4*Force Taken by Full Length Leaves*Length of Cantilever of Leaf Spring^3/(Modulus of Elasticity of Spring*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3)
Force applied at end of Spring given Bending Stress in extra full length leaves
Go Force Applied at End of Leaf Spring = Bending Stress in full leaf*(3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Thickness of Leaf^2/(18*Length of Cantilever of Leaf Spring)
Length of Cantilever given Bending Stress in extra full length leaves
Go Length of Cantilever of Leaf Spring = Bending Stress in full leaf*(3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Thickness of Leaf^2/(18*Force Applied at End of Leaf Spring)
Width of each leaf given Bending Stress in extra full length leaves
Go Width of Leaf = 18*Force Applied at End of Leaf Spring*Length of Cantilever of Leaf Spring/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Bending Stress in full leaf*Thickness of Leaf^2)
Bending Stress in extra full length leaves
Go Bending Stress in full leaf = 18*Force Applied at End of Leaf Spring*Length of Cantilever of Leaf Spring/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Width of Leaf*Thickness of Leaf^2)
Bending Stress in Plate Graduated Length Leaves
Go Bending Stress in graduated leaf = 6*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring/(Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^2)
Bending Stress in Plate Extra Full Length
Go Bending Stress in full leaf = 6*Force Taken by Full Length Leaves*Length of Cantilever of Leaf Spring/(Number of Full length Leaves*Width of Leaf*Thickness of Leaf^2)
Force applied at end of Spring given Force taken by extra full length leaves
Go Force Applied at End of Leaf Spring = Force Taken by Full Length Leaves*(3*Number of Full length Leaves+2*Number of Graduated Length Leaves)/(3*Number of Full length Leaves)
Force taken by extra full length leaves given Force applied at end of Spring
Go Force Taken by Full Length Leaves = 3*Number of Full length Leaves*Force Applied at End of Leaf Spring/(3*Number of Full length Leaves+2*Number of Graduated Length Leaves)

Modulus of Elasticity of Spring given Deflection at end of Spring Formula

Modulus of Elasticity of Spring = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3)
E = 12*P*(L^3)/((3*nf+2*ng)*δf*b*t^3)

Define Young's Modulus?

Young’s Modulus (also referred to as the Elastic Modulus or Tensile Modulus), is a measure of mechanical properties of linear elastic solids like rods, wires, and such. There are other numbers that give us a measure of elastic properties of a material, like Bulk modulus and shear modulus, but the value of Young’s Modulus is most commonly used. This is because it gives us information about the tensile elasticity of a material .

How to Calculate Modulus of Elasticity of Spring given Deflection at end of Spring?

Modulus of Elasticity of Spring given Deflection at end of Spring calculator uses Modulus of Elasticity of Spring = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3) to calculate the Modulus of Elasticity of Spring, Modulus of Elasticity of Spring given Deflection at end of Spring formula is defined as the measure of an object's or substance's resistance to being deformed elastically when stress is applied. Modulus of Elasticity of Spring is denoted by E symbol.

How to calculate Modulus of Elasticity of Spring given Deflection at end of Spring using this online calculator? To use this online calculator for Modulus of Elasticity of Spring given Deflection at end of Spring, enter Force Applied at End of Leaf Spring (P), Length of Cantilever of Leaf Spring (L), Number of Full length Leaves (nf), Number of Graduated Length Leaves (ng), Deflection of full leaf at load point f), Width of Leaf (b) & Thickness of Leaf (t) and hit the calculate button. Here is how the Modulus of Elasticity of Spring given Deflection at end of Spring calculation can be explained with given input values -> 0.211737 = 12*37500*(0.5^3)/((3*3+2*15)*0.0365*0.108*0.012^3).

FAQ

What is Modulus of Elasticity of Spring given Deflection at end of Spring?
Modulus of Elasticity of Spring given Deflection at end of Spring formula is defined as the measure of an object's or substance's resistance to being deformed elastically when stress is applied and is represented as E = 12*P*(L^3)/((3*nf+2*ng)*δf*b*t^3) or Modulus of Elasticity of Spring = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3). Force Applied at End of Leaf Spring is defined as the net amount of force that is acting onto the spring, The Length of Cantilever of Leaf Spring is defined as half the length of a semi-elliptic spring, Number of Full length Leaves is defined as the total number of extra full length leaves present in a multi-leaf spring, Number of Graduated Length Leaves is defined as the number of graduated-length leaves including master leaf, Deflection of full leaf at load point is how much the leaf of the spring deviates from its position at the load application point, Width of Leaf is defined as the width of each leaf present in a multi-leaf spring & Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring.
How to calculate Modulus of Elasticity of Spring given Deflection at end of Spring?
Modulus of Elasticity of Spring given Deflection at end of Spring formula is defined as the measure of an object's or substance's resistance to being deformed elastically when stress is applied is calculated using Modulus of Elasticity of Spring = 12*Force Applied at End of Leaf Spring*(Length of Cantilever of Leaf Spring^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Deflection of full leaf at load point*Width of Leaf*Thickness of Leaf^3). To calculate Modulus of Elasticity of Spring given Deflection at end of Spring, you need Force Applied at End of Leaf Spring (P), Length of Cantilever of Leaf Spring (L), Number of Full length Leaves (nf), Number of Graduated Length Leaves (ng), Deflection of full leaf at load point f), Width of Leaf (b) & Thickness of Leaf (t). With our tool, you need to enter the respective value for Force Applied at End of Leaf Spring, Length of Cantilever of Leaf Spring, Number of Full length Leaves, Number of Graduated Length Leaves, Deflection of full leaf at load point, Width of Leaf & Thickness of Leaf and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Modulus of Elasticity of Spring?
In this formula, Modulus of Elasticity of Spring uses Force Applied at End of Leaf Spring, Length of Cantilever of Leaf Spring, Number of Full length Leaves, Number of Graduated Length Leaves, Deflection of full leaf at load point, Width of Leaf & Thickness of Leaf. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Modulus of Elasticity of Spring = 6*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring^3/(Deflection of graduated leaf at load point*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3)
  • Modulus of Elasticity of Spring = 4*Force Taken by Graduated Length Leaves*Length of Cantilever of Leaf Spring^3/(Deflection at end of leaf spring*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3)
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