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Modulus of Rigidity given Deflection in Spring Calculator

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✖Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction.ⓘ Axial Spring Force [P]
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✖The Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring.ⓘ Mean Coil Diameter of Spring [D]
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✖Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring.ⓘ Active Coils in Spring [Na]
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✖Deflection of Spring is how much the length of a spring changes when force is applied or released.ⓘ Deflection of Spring [δ]
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✖Diameter of spring wire is the diameter of the wire of which a spring is made.ⓘ Diameter of spring wire [d]
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✖Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.ⓘ Modulus of Rigidity given Deflection in Spring [G]
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Formula
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Modulus of Rigidity given Deflection in Spring

Formula
`"G" = (8*"P"*("D"^3)*"N"_{"a"})/("δ"*"d"^4)`

Example
`"107924.8N/mm²"=(8*"138.2N"*(("36mm")^3)*"10")/("18.67mm"*("4mm")^4)`

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Modulus of Rigidity given Deflection in Spring Solution

STEP 0: Pre-Calculation Summary
Formula Used
Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4)
G = (8*P*(D^3)*Na)/(δ*d^4)
This formula uses 6 Variables
Variables Used
Modulus of rigidity of spring wire - (Measured in Pascal) - Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
Axial Spring Force - (Measured in Newton) - Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction.
Mean Coil Diameter of Spring - (Measured in Meter) - The Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring.
Active Coils in Spring - Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring.
Deflection of Spring - (Measured in Meter) - Deflection of Spring is how much the length of a spring changes when force is applied or released.
Diameter of spring wire - (Measured in Meter) - Diameter of spring wire is the diameter of the wire of which a spring is made.
STEP 1: Convert Input(s) to Base Unit
Axial Spring Force: 138.2 Newton --> 138.2 Newton No Conversion Required
Mean Coil Diameter of Spring: 36 Millimeter --> 0.036 Meter (Check conversion here)
Active Coils in Spring: 10 --> No Conversion Required
Deflection of Spring: 18.67 Millimeter --> 0.01867 Meter (Check conversion here)
Diameter of spring wire: 4 Millimeter --> 0.004 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
G = (8*P*(D^3)*Na)/(δ*d^4) --> (8*138.2*(0.036^3)*10)/(0.01867*0.004^4)
Evaluating ... ...
G = 107924799143.01
STEP 3: Convert Result to Output's Unit
107924799143.01 Pascal -->107924.79914301 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
107924.79914301 ≈ 107924.8 Newton per Square Millimeter <-- Modulus of rigidity of spring wire
(Calculation completed in 00.004 seconds)
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Home » Physics » Design of Automobile Elements » Design of Springs » Stress and Deflections in Springs » Modulus of Rigidity given Deflection in Spring

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Created by Kethavath Srinath
Osmania University (OU), Hyderabad
Kethavath Srinath has created this Calculator and 1000+ more calculators!
Verified by Urvi Rathod
Vishwakarma Government Engineering College (VGEC), Ahmedabad
Urvi Rathod has verified this Calculator and 1900+ more calculators!

24 Stress and Deflections in Springs Calculators

Diameter of Spring Wire given Deflection in Spring
Go Diameter of spring wire = ((8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of rigidity of spring wire*Deflection of Spring))^(1/4)
Mean Coil Diameter given Deflection in Spring
Go Mean Coil Diameter of Spring = (Deflection of Spring*Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Axial Spring Force*Active Coils in Spring))^(1/3)
Number of Active Coils given Deflection in Spring
Go Active Coils in Spring = (Deflection of Spring*Modulus of rigidity of spring wire*Diameter of spring wire^4)/(8*Axial Spring Force*(Mean Coil Diameter of Spring^3))
Modulus of Rigidity given Deflection in Spring
Go Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4)
Deflection of Spring
Go Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of rigidity of spring wire*Diameter of spring wire^4)
Force Applied on Spring given Deflection in Spring
Go Axial Spring Force = Deflection of Spring*Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)
Diameter of Spring Wire given Resultant Stress in Spring
Go Diameter of spring wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3)
Mean Coil Diameter given Resultant Stress in Spring
Go Mean Coil Diameter of Spring = Shear Stress in Spring*(pi*Diameter of spring wire^3)/(Wahl Factor of Spring*8*Axial Spring Force)
Force acting on Spring given Resultant Stress
Go Axial Spring Force = Shear Stress in Spring*(pi*Diameter of spring wire^3)/(Wahl Factor of Spring*8*Mean Coil Diameter of Spring)
Resultant Stress in Spring
Go Shear Stress in Spring = Wahl Factor of Spring*(8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Diameter of spring wire^3)
Diameter of Spring Wire given Rate of Spring
Go Diameter of spring wire = ((Stiffness of Spring*8*Mean Coil Diameter of Spring^3*Active Coils in Spring)/(Modulus of rigidity of spring wire))^(1/4)
Mean Coil Diameter given Rate of Spring
Go Mean Coil Diameter of Spring = (Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Stiffness of Spring*Active Coils in Spring))^(1/3)
Modulus of Rigidity given Rate of Spring
Go Modulus of rigidity of spring wire = Stiffness of Spring*(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)/Diameter of spring wire^4
Rate of Spring
Go Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)
Stress Factor of Spring
Go Wahl Factor of Spring = ((4*Spring Index-1)/(4*Spring Index-4))+(0.615/Spring Index)
Shear Stress Correction Factor given Diameter of Spring Wire
Go Shear Stress Correction Factor of Spring = (1+(.5*Diameter of spring wire/Mean Coil Diameter of Spring))
Mean Coil diameter given Shear Stress Correction Factor
Go Mean Coil Diameter of Spring = 0.5*Diameter of spring wire/(Shear Stress Correction Factor of Spring-1)
Diameter of Spring Wire given Shear Stress Correction Factor
Go Diameter of spring wire = (Shear Stress Correction Factor of Spring-1)*Mean Coil Diameter of Spring/.5
Strain Energy Stored in Spring
Go Strain energy in spring = .5*Axial Spring Force*Deflection of Spring
Force Applied on Spring given Strain Energy Stored in Spring
Go Axial Spring Force = 2*Strain energy in spring/Deflection of Spring
Deflection of Spring given Strain Energy Stored
Go Deflection of Spring = 2*Strain energy in spring/Axial Spring Force
Rate of Spring given Deflection
Go Stiffness of Spring = Axial Spring Force/Deflection of Spring
Spring Index given Shear Stress Correction Factor
Go Spring Index = (0.5)/(Shear Stress Correction Factor of Spring-1)
Shear Stress Correction Factor
Go Shear Stress Correction Factor of Spring = (1+(.5/Spring Index))

Modulus of Rigidity given Deflection in Spring Formula

Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4)
G = (8*P*(D^3)*Na)/(δ*d^4)

Define Modulus of Rigidity?

Shear modulus also known as Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. hear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Young’s modulus a

How to Calculate Modulus of Rigidity given Deflection in Spring?

Modulus of Rigidity given Deflection in Spring calculator uses Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4) to calculate the Modulus of rigidity of spring wire, The Modulus of Rigidity given Deflection in Spring formula is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. Modulus of rigidity of spring wire is denoted by G symbol.

How to calculate Modulus of Rigidity given Deflection in Spring using this online calculator? To use this online calculator for Modulus of Rigidity given Deflection in Spring, enter Axial Spring Force (P), Mean Coil Diameter of Spring (D), Active Coils in Spring (Na), Deflection of Spring (δ) & Diameter of spring wire (d) and hit the calculate button. Here is how the Modulus of Rigidity given Deflection in Spring calculation can be explained with given input values -> 0.107925 = (8*138.2*(0.036^3)*10)/(0.01867*0.004^4).

FAQ

What is Modulus of Rigidity given Deflection in Spring?
The Modulus of Rigidity given Deflection in Spring formula is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ and is represented as G = (8*P*(D^3)*Na)/(δ*d^4) or Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4). Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction, The Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring, Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring, Deflection of Spring is how much the length of a spring changes when force is applied or released & Diameter of spring wire is the diameter of the wire of which a spring is made.
How to calculate Modulus of Rigidity given Deflection in Spring?
The Modulus of Rigidity given Deflection in Spring formula is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ is calculated using Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4). To calculate Modulus of Rigidity given Deflection in Spring, you need Axial Spring Force (P), Mean Coil Diameter of Spring (D), Active Coils in Spring (Na), Deflection of Spring (δ) & Diameter of spring wire (d). With our tool, you need to enter the respective value for Axial Spring Force, Mean Coil Diameter of Spring, Active Coils in Spring, Deflection of Spring & Diameter of spring wire 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 rigidity of spring wire?
In this formula, Modulus of rigidity of spring wire uses Axial Spring Force, Mean Coil Diameter of Spring, Active Coils in Spring, Deflection of Spring & Diameter of spring wire. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Modulus of rigidity of spring wire = Stiffness of Spring*(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)/Diameter of spring wire^4
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