SPRing calculations of F and TAU

SPRing calculations of F and TAU (sprftau) of a circular cross-section spring

SPRing calculations of F and TAU (sprftau) of a circular cross-section spring,
where:
tau = max shear stress produced,
R = radius of coil measured from spring axis to ctr of section,
d = diameter of circular section,
P = load (tensile or compressive),
f = total stretch or shortening of spring,
n = number of active turns in spring,
a = (alpha) pitch angle of spring,
G = the modulus of rigidity of the material (shear modulus),
v = poisson's ratio of the material.

Usage:
1) If the function is called with no input arguments, then a graphical
representation of the equations is produced for publication purposes.
2) If the function is called with only the first 3 input args (R,d,P),
then only the value of tau is returned. f is set to -1.
3) If the function is called with all 7 input args, then both tau and f
are returned.

reference 1:
Roark's Formulas for Stress and Strain, 7th Edition, page 398
Warren C. Young, Richard G. Budynas
(c)2002, 1989 by the McGraw-Hill Companies, Inc.
ISBN 0-07-072542-X

reference 2:
Mechancial Springs, 2nd Edition
A. M. Wahl
(c)1963, 1944 by the McGraw-Hill Book Company, Inc.
Congress Catalog Card Number 62-20725

Rev.1 15Apr2008