Helical Springs
When close-coiled helical spring, composed of a wire of round rod of diameter d wound into a helix of mean radius R with n number of turns, is subjected to an axial load P produces the following stresses and elongation:
The maximum shearing stress is the sum of the direct shearing stress ?1 = P/A and the torsional shearing stress ?2 = Tr/J, with T = PR.
This formula neglects the curvature of the spring. This is used for light spring where the ratio d/4R is small.
For heavy springs and considering the curvature of the spring, a more precise formula is given by: (A.M.Wahl Formula)
where m is called the spring index and (4m – 1) / (4m – 4) is the Wahl Factor.
The elongation of the bar is
Notice that the deformation ? is directly proportional to the applied load P. The ratio of P to ? is called the spring constant k and is equal to
SPRINGS IN SERIES
For two or more springs with spring laid in series, the resulting spring constant k is given by
where k1, k2,… are the spring constants for different springs.
SPRINGS IN
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