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## Deflection at the End of Spring Solution

STEP 0: Pre-Calculation Summary
Formula Used
deflection_of_spring = 12*Force Applied at the End of Spring*(Length of Cantilever^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus Of Elasticity*Width of Leaf*Thickness of Leaf^3)
δ = 12*P*(L^3)/((3*nf+2*ng)*E*b*t^3)
This formula uses 7 Variables
Variables Used
Force Applied at the End of Spring - Force Applied at the End of Spring is defined as the net amount of force that is acting on the spring. (Measured in Newton)
Length of Cantilever - Length of Cantilever is defined as half the length of semi-elliptic spring . (Measured in Millimeter)
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.
Modulus Of Elasticity - Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. (Measured in Kilonewton per Square Meter)
Width of Leaf - Width of Leaf is defined as the width of each leaf present in a multi-leaf spring (Measured in Millimeter)
Thickness of Leaf - Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring. (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
Force Applied at the End of Spring: 100 Newton --> 100 Newton No Conversion Required
Length of Cantilever: 50 Millimeter --> 0.05 Meter (Check conversion here)
Number of Full length Leaves: 5 --> No Conversion Required
Number of Graduated Length Leaves: 10 --> No Conversion Required
Modulus Of Elasticity: 10 Kilonewton per Square Meter --> 10000 Pascal (Check conversion here)
Width of Leaf: 10 Millimeter --> 0.01 Meter (Check conversion here)
Thickness of Leaf: 5 Millimeter --> 0.005 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δ = 12*P*(L^3)/((3*nf+2*ng)*E*b*t^3) --> 12*100*(0.05^3)/((3*5+2*10)*10000*0.01*0.005^3)
Evaluating ... ...
δ = 342.857142857143
STEP 3: Convert Result to Output's Unit
342.857142857143 Meter --> No Conversion Required
FINAL ANSWER
342.857142857143 Meter <-- Deflection of Spring
(Calculation completed in 00.048 seconds)

## < 11 Other formulas that you can solve using the same Inputs

Shear Elasticity Modulus when Critical Bending Moment of Simply Supported Open Beam is Given
shear_modulus_of_elasticity = ((Critical Bending Moment^2)*(Unbraced Length of the member^4)-((Modulus Of Elasticity^2)*Moment of Inertia about minor axis*Warping Constant*pi^4))/((pi^2)*(Unbraced Length of the member^2)*Modulus Of Elasticity*Moment of Inertia about minor axis*Torsional constant) Go
Critical Bending Moment for Simply Supported Open Section Beam
critical_bending_moment = (pi/Unbraced Length of the member)*sqrt(Modulus Of Elasticity*Moment of Inertia about minor axis*((Shear Modulus of Elasticity*Torsional constant)+Modulus Of Elasticity*Warping Constant*((pi^2)/(Unbraced Length of the member)^2))) Go
Minor Axis Moment of Inertia when Critical Bending Moment of Simply Supported Open Beam is Given
moment_inertia_about_minor_axis = ((Critical Bending Moment^2)*(Unbraced Length of the member^2))/(((Shear Modulus of Elasticity*Torsional constant)+Modulus Of Elasticity*Warping Constant*((pi^2)/(Unbraced Length of the member^2)))*Modulus Of Elasticity) Go
Unbraced Member Length when Critical Bending Moment of Rectangular Beam is Given
length = (pi/Critical Bending Moment)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)) Go
Critical Bending Moment for Simply Supported Rectangular Beam
critical_bending_moment = (pi/Length)*(sqrt(Modulus Of Elasticity*Moment of Inertia about Minor Axis*Shear Modulus of Elasticity*Torsional constant)) Go
Minor Axis Moment of Inertia when Critical Bending Moment of Rectangular Beam is Given
moment_of_inertia_about_minor_axis = ((Critical Bending Moment*Length)^2)/((pi^2)*Modulus Of Elasticity*Shear Modulus of Elasticity*Torsional constant) Go
Shear Elasticity Modulus when Critical Bending Moment of Rectangular Beam is Given
shear_modulus_of_elasticity = ((Critical Bending Moment*Length)^2)/((pi^2)*Moment of Inertia about Minor Axis*Modulus Of Elasticity*Torsional constant) Go
Maximum and Center Deflection of Simply Supported Beam carrying UDL over its entire Length
deflection = (5*Uniformly Distributed Load*(Length^4))/(384*Modulus Of Elasticity*Area Moment of Inertia) Go
Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center
deflection = (Point Load acting on the Beam*(Length^3))/(48*Modulus Of Elasticity*Area Moment of Inertia) Go
Maximum and Center Deflection of Cantilever Beam carrying Point Load at Free End
deflection = (Point Load acting on the Beam*(Length^3))/(3*Modulus Of Elasticity*Area Moment of Inertia) Go
Stress using Hook's Law
stress_shear = Modulus Of Elasticity*Engineering strain Go

## < 11 Other formulas that calculate the same Output

Deflection at the Load Point (Graduated Length Leaves)
deflection_of_spring = 6*Force Taken by Graduated Length Leaves*Length of Cantilever^3/Modulus Of Elasticity*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3 Go
Deflection of the Spring at Load Point
deflection_of_spring = 4*Force Taken by Graduated Length Leaves*Length of Cantilever^3/Modulus Of Elasticity*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3 Go
Deflection of one End of Spring With Respect to Other End
deflection_of_spring = 12*Bending moment*Length of Strip*Distance of Centre of Gravity from Outer End/Modulus Of Elasticity*Width of the strip*Thickness of Strip^3 Go
Deflection of the Spring
deflection_of_spring = (8*Force*(Mean Coil Diameter^3)*Number of Active Coils)/Modulus of rigidity*Diameter of spring wire^4 Go
Deflection of spring
deflection_of_spring = (64*(Axial Load)*(Mean radius spring coil^3)*Coil)/(Modulus of rigidity*(Diameter of spring wire^4)) Go
Deflection of spring when mass m is attached to it
deflection_of_spring = Mass*Acceleration Due To Gravity/Stiffness of spring Go
Axial Deflection of the Spring Due to Axial Load When Stiffness of the Spring is Given
deflection_of_spring = Spring force/Stiffness of spring Go
Deflection of spring in terms of stiffness of spring
deflection_of_spring = Axial Load/Stiffness of spring Go
Deflection of spring in terms of work done on spring
deflection_of_spring = (2*Work Done)/Axial Load Go
Deflection in terms of average load on spring
deflection_of_spring = Work Done/Average Load Go
Deflection of the Spring When Strain Energy Stored is Given
deflection_of_spring = 2*Strain Energy/Force Go

### Deflection at the End of Spring Formula

deflection_of_spring = 12*Force Applied at the End of Spring*(Length of Cantilever^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus Of Elasticity*Width of Leaf*Thickness of Leaf^3)
δ = 12*P*(L^3)/((3*nf+2*ng)*E*b*t^3)

## Define Deflection of the spring?

Spring deflection, also known as spring travel, is the action of a compression spring compressing (being pushed), an extension spring extending (being pulled), or a torsion spring torquing (radially) when a load is applied or released.

## How to Calculate Deflection at the End of Spring?

Deflection at the End of Spring calculator uses deflection_of_spring = 12*Force Applied at the End of Spring*(Length of Cantilever^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus Of Elasticity*Width of Leaf*Thickness of Leaf^3) to calculate the Deflection of Spring, The Deflection at the End of Spring formula is defined as the action of a compression spring compressing (being pushed), an extension spring extending (being pulled), or a torsion spring torquing (radially) when a load is applied . Deflection of Spring and is denoted by δ symbol.

How to calculate Deflection at the End of Spring using this online calculator? To use this online calculator for Deflection at the End of Spring, enter Force Applied at the End of Spring (P), Length of Cantilever (L), Number of Full length Leaves (nf), Number of Graduated Length Leaves (ng), Modulus Of Elasticity (E), Width of Leaf (b) and Thickness of Leaf (t) and hit the calculate button. Here is how the Deflection at the End of Spring calculation can be explained with given input values -> 342.8571 = 12*100*(0.05^3)/((3*5+2*10)*10000*0.01*0.005^3).

### FAQ

What is Deflection at the End of Spring?
The Deflection at the End of Spring formula is defined as the action of a compression spring compressing (being pushed), an extension spring extending (being pulled), or a torsion spring torquing (radially) when a load is applied and is represented as δ = 12*P*(L^3)/((3*nf+2*ng)*E*b*t^3) or deflection_of_spring = 12*Force Applied at the End of Spring*(Length of Cantilever^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus Of Elasticity*Width of Leaf*Thickness of Leaf^3). Force Applied at the End of Spring is defined as the net amount of force that is acting on the spring, Length of Cantilever is defined as half the length of 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, Modulus Of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, Width of Leaf is defined as the width of each leaf present in a multi-leaf spring and Thickness of Leaf is defined as the thickness of each leaf present in a multi-leaf spring.
How to calculate Deflection at the End of Spring?
The Deflection at the End of Spring formula is defined as the action of a compression spring compressing (being pushed), an extension spring extending (being pulled), or a torsion spring torquing (radially) when a load is applied is calculated using deflection_of_spring = 12*Force Applied at the End of Spring*(Length of Cantilever^3)/((3*Number of Full length Leaves+2*Number of Graduated Length Leaves)*Modulus Of Elasticity*Width of Leaf*Thickness of Leaf^3). To calculate Deflection at the End of Spring, you need Force Applied at the End of Spring (P), Length of Cantilever (L), Number of Full length Leaves (nf), Number of Graduated Length Leaves (ng), Modulus Of Elasticity (E), Width of Leaf (b) and Thickness of Leaf (t). With our tool, you need to enter the respective value for Force Applied at the End of Spring, Length of Cantilever, Number of Full length Leaves, Number of Graduated Length Leaves, Modulus Of Elasticity, Width of Leaf and 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 Deflection of Spring?
In this formula, Deflection of Spring uses Force Applied at the End of Spring, Length of Cantilever, Number of Full length Leaves, Number of Graduated Length Leaves, Modulus Of Elasticity, Width of Leaf and Thickness of Leaf. We can use 11 other way(s) to calculate the same, which is/are as follows -
• deflection_of_spring = Mass*Acceleration Due To Gravity/Stiffness of spring
• deflection_of_spring = Work Done/Average Load
• deflection_of_spring = (2*Work Done)/Axial Load
• deflection_of_spring = (64*(Axial Load)*(Mean radius spring coil^3)*Coil)/(Modulus of rigidity*(Diameter of spring wire^4))
• deflection_of_spring = Axial Load/Stiffness of spring
• deflection_of_spring = Spring force/Stiffness of spring
• deflection_of_spring = (8*Force*(Mean Coil Diameter^3)*Number of Active Coils)/Modulus of rigidity*Diameter of spring wire^4
• deflection_of_spring = 2*Strain Energy/Force
• deflection_of_spring = 12*Bending moment*Length of Strip*Distance of Centre of Gravity from Outer End/Modulus Of Elasticity*Width of the strip*Thickness of Strip^3
• deflection_of_spring = 6*Force Taken by Graduated Length Leaves*Length of Cantilever^3/Modulus Of Elasticity*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3
• deflection_of_spring = 4*Force Taken by Graduated Length Leaves*Length of Cantilever^3/Modulus Of Elasticity*Number of Graduated Length Leaves*Width of Leaf*Thickness of Leaf^3 Let Others Know
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