Machinery's Handbook, 31st Edition
290 Plates, Shells, and Cylinders Circular Flat Plates.— In the following formulas, R = radius of plate to supporting edge in inches; W = total load in pounds; and other symbols are the same as used for square and rectangular plates. If metric SI units are used, R = radius of plate to supporting edge in mm, and the values of other symbols are the same as those used for square and rectangular plates. a) Edge supported around the circumference and a uniformly distributed load over the surface of the plate. (15) (16) b) Edge fixed around circumference and a uniformly distributed load over the surface of the plate. (17) (18) c) Edge supported around the circumference and a concentrated load at the center. (19) (20) d) Edge fixed around circumference and a concentrated load at the center. (21) (22) Strength of Cylinders Subjected to Internal Pressure.— In designing a cylinder to with- stand internal pressure, the choice of formula to be used depends on 1) the kind of mate- rial of which the cylinder is made (whether brittle or ductile); 2) the construction of the cylinder ends (whether open or closed); and 3) whether the cylinder is classed as a thin- or a thick-walled cylinder. A cylinder is considered to be thin-walled when the ratio of wall thickness to inside diameter is 0.1 or less and thick-walled when this ratio is greater than 0.1. Materials such as cast iron, hard steel, and cast aluminum are considered to be brittle materials; low- carbon steel, brass, bronze, etc. are considered to be ductile. In the formulas that follow, p = internal pressure, psi; D = inside diameter of cylinder, inches; t = wall thickness of cylinder, inches; μ = Poisson’s ratio, = 0.3 for steel, 0.26 for cast iron, 0.34 for aluminum and brass; and S = allowable tensile stress, psi. Metric SI units can be used in Formulas (23), (25), (26), and (27), where p = internal pressure in N/mm 2 ; D = inside diameter of cylinder, mm; t = wall thickness, mm; μ = Poisson’s ratio, = 0.3 for steel, 0.26 for cast iron, and 0.34 for aluminum and brass; and S = allowable tensile stress, N/mm 2 . For the use of metric SI units in Formula (24), see below. Thin-walled Cylinders: (23) For low-pressure cylinders of cast iron such as are used for certain engine and press ap- plications, a formula in common use is (24) t S Dp 2 = . Dp 2500 03 = + t . S t W 039 2 = . Et WR 0221 3 2 d = . S t W 024 2 = . Et WR 00543 3 2 d = . 048 1 13 W . . 0325 00185 e t . log S t = R R t 2 2 2 + − : D . Et WR 055 3 d 2 = . 062 . 0325 00264 e t . log S t = W R R t 2 2 2 + : D . Et WR 022 3 d 2 =
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