Helical and Elliptic Springs (Classic Reprint)

Excerpt from Helical and Elliptic Springs

Fig. 4 shows the curve of two similar springs of different lengths similarly loaded. AO represents the curve when the length is double that of ae. Suppose we divide AE into a number of small parts and call these elements, and divide ac' into the same number of parts; each of these will contain two elements, that is, for each element of AE there will be two corresponding elements of ac, and the distance of any two such elements from the end of the spring will be twice the distance of the corresponding element of AE from E. That is, the arm and the moment of bending of any two elements of AO will be twice the arm and moment of bending of the corresponding element of ab. The deflection of spring AC will therefore be 2 x 2 x 2 23 8 times the deflection of spring ae. If the deflection of spring AB is inch, the deflection of spring AC will be 23 x r: 3 inches. If the deflection of AE is inch, the deflection of AC will be 23 x 10 inches, provided it is strong enough to carry the load.

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