Machinery's Handbook, 31st Edition
280 Stresses Produced by Shocks bar. It is, therefore, more economical to use round stock for springs which must withstand shocks, due to the fact that the deflection for the same fiber stress for a square bar spring is smaller than that for a round bar spring, the ratio being as 4 to 5. The round bar spring is therefore capable of storing more energy than a square bar spring for the same stress. Table 2. Stresses Produced in Springs by Shocks
Form of Bar from Which Spring is Made
Fiber (Unit) Stress f Produced by Weight Q Dropped a Height h on a Helical Spring
Approximate Value of f
d QD QD n Ghd 8 1 1 4 3 3 4 π + + c
. Dd n QhG 127 2 Dd n QhG 134 2 .
f
f
Round
m
=
=
Square = G = modulus of elasticity for torsion; d = diameter or side of bar; D = mean diameter of spring; n = number of coils in spring. . 09 f d QD 4 9 1 1 QD n 3 Ghd 3 4 π = + + c m f Shocks from Bodies in Motion.— The formulas given can be applied, in general, to shocks from bodies in motion. A body of weight W moving horizontally with the velocity of v feet per second has a stored-up energy: E g Wv g Wv 6 foot-pounds or inch-pounds K 2 2 # = This expression may be substituted for Qh in the tables in the equations for unit stresses containing this quantity, and the stresses produced by the energy of the moving body thereby determined. The formulas in the tables give the maximum value of the stresses, providing the de- signer with some definitive guidance even where there may be justification for assuming that only a part of the energy of the shock is taken up by the member under stress. The formulas can also be applied using metric SI units. The stored-up energy of a body of mass M kilograms moving horizontally with the velocity of v meters per second is: E Mv 2 1 newton meters K 2 = - This expression may be substituted for Qh in the appropriate equations in the ta bles. For calculation in millimeters, Qh = 1000 E K newton-millimeters. 2 1 Fatigue Stresses.— So-called “fatigue ruptures” occur in parts that are subjected to con tinually repeated shocks or stresses of small magnitude. Machine parts that are subjected to continual stresses in varying directions, or to repeated shocks, even if of comparatively small magnitude, may fail ultimately if designed from a mere knowledge of the behavior of the material under a steady stress, such as is imposed upon it by ordinary tensile stress testing machines. Examinations of numerous cases of machine parts, broken under ac- tual working conditions, indicate that at least 80 percent of these ruptures are caused by fatigue stresses. Most fatigue ruptures are caused by bending stresses, and frequently by a revolving bending stress. Hence, to test materials for this class of stress the tests should be made to stress the material in a manner similar to that in which it will be stressed under actual working conditions. See Fatigue Properties on page 209 for more on this topic.
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