EXTENSION SPRINGS DESIGN FOR STATIC LOADING
This calculator has been developed to calculate shear and tensile stresses on
ordinary helical extension springs with full twisted end. The calculator can be
used for static loading case.
Calculations are done with the knowledge of extension spring wire
diameter, spring diameter and maximum working load. Calculation results generated by the calculator are shear and tensile
stress at extension spring end, shear stress at spring body, factor of safety values for
the points where the stress values are calculated.
The points where
maximum stresses occurred on extension spring twisted end are shown in the following figure. At
point A, maximum tensile stress is occurred due to bending moment and axial
force. At point B, maximum torsion stress is occurred. In addition to these
points, high shear stresses are occured at the body of the extension spring.


Location of Maximum Bending and Torsion
Stresses in Twisted Loops 

Extension Spring Design
with Twisted End 
For the extension springs which works under static loading, first define the design
parameters with the " Dimensional Design of Extension Spring " calculator. Then
use "Stress Analysis of Extension Spring for Static Loading" calculator to check spring against yielding.
The formulas and parameters used in the calculator are given in " List of Equations " section of this page.
Note: This calculator has been
developed by mainly using Shigley's Mechanical Engineering Design book. For
further information on subject , this reference source can be used.
Calculator:
Note 1 : ^{x} Material properties are from Ref2 except "User defined" selection.
Note 2 : ^{+} See supplements for reference values.
Note 3 : ^{o} The design factor value that used for all of the points
of interest ( Tensile stress at pointA, shear stress at pointB and shear
stress at spring body).
RESULTS 
Parameter 
Symbol 
Value 
Unit 
STRESS RELEATED PARAMETERS 
Maximum working load 
F_{max} 



STRESS PARAMETERS AT POINT B 
Shear stress at point B for maximum working load 
τ_{B} 



Allowable torsional strength at point B 
S_{all_B} 


Safety factor at point B ^{+} 
fos_{B} 


 
STRESS PARAMETERS AT POINT A 
Tensile stress at point A for maximum working load 
σ_{A} 



Allowable tensile strength at point A 
S_{A} 


Safety factor at point A ^{+} 
fos_{A} 


 
STRESS PARAMETERS AT SPRING BODY 
Shear stress at spring body for maximum working load 
τ_{sb} 



Allowable torsional strength for spring body 
S_{sb} 


Safety factor at spring body ^{+} 
fos_{sb} 


 
SPRING MATERIAL PARAMETERS 
Ultimate tensile strength of material 
S_{ut} 



Material ASTM No. 


Note 1 : ^{+} Green color means, fos ≥ n_{s}, red color means fos ≤ n_{s}
Definitions:
Extension spring: Extension /
tension springs
are coil springs which work under tensile loading. In order to carry and transfer tensile loads, extension springs require special ends in the form of hooks or loops. These special ends are generally produced by using the last coil of the spring or a separate component like screwed inserts. Generally, extension springs are connected to other component via these ends. If there is a motion to extend extension spring, it exerts force to component to move it back.
Extension springs are usually
coiled with an initial tension which keeps the extension spring coils closed. Due to initial tension incorporated into spring, spring can’t be extended theoretically until a force that is greater than initial tension. In practice, extension springs extends slightly with smaller forces than initial tension due to deflection of end loops.
Tension springs are generally used to return back the component to its default position by providing return force.
Design factor (nd): The ratio of failure stress to allowable stress.
The design factor is what the item is required to withstand .The design factor is defined for an application
(generally provided in advance and often set by regulatory code or policy) and is not an actual calculation.
Factor of Safety (Safety Factor):
The ratio of failure stress to actual/expected stress. The difference between the factor of safety (safety factor)
and design factor is: The factor of safety gives the safety margin of designed part against failure. The design factor
gives the requirement value for the design. Safety factor shall be greater than or equal to design factor.
Spring rate: A parameter which shows relation between applied force and deflection. In other words, reaction force per unit deflection or spring resistance to length change.
Spring index: The ratio of spring
mean diameter to coil diameter.
Static/Quasistatic Loading:
Following loading cases are defined as Static/Quasistatic loading:
• A constant loading

• A cycling loading with torsional shear stress range up to 10 % of fatigue
strength (or endurance strength)

• A cycling loading with torsional shear stress range more than 10 % of fatigue
strength (or endurance strength) up to 10^{4}
cycles

Supplements:
Reference: