Diameter of Spring Wire given Resultant Stress in Spring Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diameter of spring wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3)
d = ((K*8*P*D)/(pi*๐œ))^(1/3)
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Diameter of spring wire - (Measured in Meter) - Diameter of spring wire is the diameter of the wire of which a spring is made.
Wahl Factor of Spring - Wahl Factor of Spring is simply a measure of the degree to which external stress is amplified at the curvature of the spring coil.
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.
Shear Stress in Spring - (Measured in Pascal) - Shear Stress in Spring is the force tending to cause deformation of spring by slippage along a plane or planes parallel to the imposed stress.
STEP 1: Convert Input(s) to Base Unit
Wahl Factor of Spring: 1.162 --> No Conversion Required
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)
Shear Stress in Spring: 230 Newton per Square Millimeter --> 230000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = ((K*8*P*D)/(pi*๐œ))^(1/3) --> ((1.162*8*138.2*0.036)/(pi*230000000))^(1/3)
Evaluating ... ...
d = 0.0040001503651821
STEP 3: Convert Result to Output's Unit
0.0040001503651821 Meter -->4.0001503651821 Millimeter (Check conversion here)
FINAL ANSWER
4.0001503651821 โ‰ˆ 4.00015 Millimeter <-- Diameter of spring wire
(Calculation completed in 00.020 seconds)

Credits

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Osmania University (OU), Hyderabad
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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))

Diameter of Spring Wire given Resultant Stress in Spring Formula

Diameter of spring wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3)
d = ((K*8*P*D)/(pi*๐œ))^(1/3)

Define a Spring?

A spring is an elastic object that stores mechanical energy. Springs are typically made of spring steel. There are many spring designs. In everyday use, the term often refers to coil springs. The rate or spring constant of a spring is the change in the force it exerts, divided by the change in deflection of the spring.

How to Calculate Diameter of Spring Wire given Resultant Stress in Spring?

Diameter of Spring Wire given Resultant Stress in Spring calculator uses Diameter of spring wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3) to calculate the Diameter of spring wire, The Diameter of Spring Wire given Resultant Stress in Spring formula is defined as the thickness or the diameter of the wire by which the spring is made. Diameter of spring wire is denoted by d symbol.

How to calculate Diameter of Spring Wire given Resultant Stress in Spring using this online calculator? To use this online calculator for Diameter of Spring Wire given Resultant Stress in Spring, enter Wahl Factor of Spring (K), Axial Spring Force (P), Mean Coil Diameter of Spring (D) & Shear Stress in Spring (๐œ) and hit the calculate button. Here is how the Diameter of Spring Wire given Resultant Stress in Spring calculation can be explained with given input values -> 4000.15 = ((1.162*8*138.2*0.036)/(pi*230000000))^(1/3).

FAQ

What is Diameter of Spring Wire given Resultant Stress in Spring?
The Diameter of Spring Wire given Resultant Stress in Spring formula is defined as the thickness or the diameter of the wire by which the spring is made and is represented as d = ((K*8*P*D)/(pi*๐œ))^(1/3) or Diameter of spring wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3). Wahl Factor of Spring is simply a measure of the degree to which external stress is amplified at the curvature of the spring coil, 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 & Shear Stress in Spring is the force tending to cause deformation of spring by slippage along a plane or planes parallel to the imposed stress.
How to calculate Diameter of Spring Wire given Resultant Stress in Spring?
The Diameter of Spring Wire given Resultant Stress in Spring formula is defined as the thickness or the diameter of the wire by which the spring is made is calculated using Diameter of spring wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3). To calculate Diameter of Spring Wire given Resultant Stress in Spring, you need Wahl Factor of Spring (K), Axial Spring Force (P), Mean Coil Diameter of Spring (D) & Shear Stress in Spring (๐œ). With our tool, you need to enter the respective value for Wahl Factor of Spring, Axial Spring Force, Mean Coil Diameter of Spring & Shear Stress in Spring 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 Diameter of spring wire?
In this formula, Diameter of spring wire uses Wahl Factor of Spring, Axial Spring Force, Mean Coil Diameter of Spring & Shear Stress in Spring. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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)
  • Diameter of spring wire = (Shear Stress Correction Factor of Spring-1)*Mean Coil Diameter of Spring/.5
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