Stresses Produced by Shocks Machinery's Handbook, 31st Edition
278
y.s.
13,000 600
−
25 for diameter less than inches d
p
d
=
20,000
This formula is based on steel having a yield strength, y.s., of 32,000 pounds per square inch. For roller or wheel diameters of up to 25 inches, the Hertz stress (contact stress) resulting from the calculated load p will be approximately 76,000 pounds per square inch. For a 10-inch diameter roller the safe load per inch of roller length is p 20,000 32,000 13,000 600 10 5700lbs per inch of length # = − = Therefore, to support a 10,000 pound load the roller or wheel would need to be 10,000 ∕ 5700 = 1.75 inches wide. Stresses Produced by Shocks Stresses in Beams Produced by Shocks.— Any elastic structure subjected to a shock will deflect until the product of the average resistance developed by the deflection and the dis tance through which it has been overcome has reached a value equal to the energy of the shock. It follows that for a given shock, the average resisting stresses are inversely propor tional to the deflection. If the structure were perfectly rigid, the deflection would be zero and the stress infinite. The effect of a shock is, therefore, to a great extent dependent upon the elastic property (the springiness) of the structure subjected to the impact. The energy of a body in motion, such as a falling body, may be spent in each of four ways: 1) In deforming the body struck as a whole. 2) In deforming the falling body as a whole. 3) In partial deformation of both bodies on the surface of contact (most of this energy will be transformed into heat). 4) Part of the energy will be taken up by the supports, if these are not perfectly rigid and inelastic. How much energy is spent in the last three ways is usually difficult to determine, and for this reason it is safest to figure as if the whole amount were spent as in Case 1. If a reliable judgment is possible as to what percentage of the energy is spent in other ways than the first, a corresponding fraction of the total energy can be assumed as developing stresses in the body subjected to shocks. One investigation into the stresses produced by shocks led to the following conclusions: 1) A suddenly applied load will produce the same deflection, and, therefore, the same stress as a static load twice as great; and 2) the unit stress p (see formulas in Table 1, Stresses Produced in Beams by Shocks ) for a given load producing a shock varies directly as the square root of the modulus of elasticity E and inversely as the square root of the length L of the beam and the area of the section. Thus, for instance, if the sectional area of a beam is increased by four times, the unit stress will diminish only by half. This result is entirely different from those produced by static loads where the stress would vary inversely with the area, and within certain limits be practically independent of the modulus of elasticity. In Table 1, the expression for the approximate value of p , which is applicable whenever the deflection of the beam is small as compared with the total height h through which the body producing the shock is dropped, is always the same for beams supported at both ends and subjected to shock at any point between the supports. In the formulas all dimensions are in inches and weights in pounds.
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