engineering fundamentals Compression Spring Force & Stress
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Calculator
This calculator computes the force exerted by a compression spring (with a known spring constant k) when given the spring length before and after loading.

It also computes the maximum shear stress in the spring from the provided spring geometry.

Inputs
  Spring free length, Lfree:    
  Spring length when deformed, Ldef:    
  Wire diameter, d:    
  Outer diameter of spring, Douter:    
  Spring constant, k:    
Answers
  Force exerted by spring, F:  5.00  lbf
  Maximum Shear Stress, tmax:  242  ksi
 
Equations Behind the Calculator
The force in the compression spring is found from Hooke's Law,

The maximum shear stress tmax in the spring occurs on the inside surface of the coils. It is proportional to the spring force F, and is given by the formula,

where D is the mean diameter of the spring (measured from the centers of the wire cross-sections), W is the Wahl correction factor to account for the spring curvature stress, and C is the spring index (essentially an aspect ratio of the spring cross-section),

Note that W approaches 1 in the limit as C gets large. In other words, as the spring's diameter increases or as its wire diameter decreases, the effect of curvature on the spring shear stress diminishes.

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