Machinery's Handbook, 31st Edition
Plates, Shells, and Cylinders 291 This formula is based on allowable stress of 1250 pounds per square inch (psi) and will give a wall thickness 0.3 inch greater than Formula (23) to allow for variations in metal thickness that may result from the casting process. If metric SI units are used in Formula (24), t = cylinder wall thickness in mm; D = inside diameter of cylinder, mm; and the allowable stress is in N/mm 2 . The value of 0.3 inches additional wall thickness is 7.62 mm, and the next highest number in preferred metric basic sizes is 8 mm. Thick-walled Cylinders of Brittle Material, Ends Open or Closed: Lamé’s equation is used when cylinders of this type are subjected to internal pressure. (25) The table Ratio of Outside Radius to Inside Radius, Thick Cylinders on page 292 is for convenience in calculating the dimensions of cylinders under high internal pressure without the use of Formula (25). Example, Use of the Table: Assume that a cylinder of 10 inches inside diameter is to withstand a pressure of 2500 psi; the material is cast iron and the allowable stress is 6000 psi. To solve the problem, locate the allowable stress per square inch in the left-hand column of the table and the working pressure at the top of the columns. Then find the ratio between the outside and inside radii in the body of the table. In this example, the ratio is 1.558, and hence the outside diameter of the cylinder should be 10 3 1.558, or about 15 5 ∕ 8 inches. The thickness of the cylinder wall will therefore be (15.58 − 10)⁄2 = 2.79 inches. Unless very high-grade material is used and sound castings assured, cast iron should not be used for pressures exceeding 2000 pounds psi (13.75 N/mm 2 ). It is well to leave more metal in the bottom of a hydraulic cylinder than is indicated by the results of calculations because a hole of some size must be cored in the bottom to permit the entrance of a boring bar when finishing the cylinder, and when this hole is subsequently tapped and plugged it often gives trouble if there is too little thickness. For steady or gradually applied stresses, the maximum allowable fiber stress S may be assumed to be from 3500 to 4000 psi (24–27 N/mm 2 ) for cast iron; from 6000 to 7000 psi (41–48 N/mm 2 ) for brass; and 12,000 psi (82 N/mm 2 ) for steel castings. For intermittent stresses, such as in cylinders for steam and hydraulic work, 3000 psi (20 N/mm 2 ) for cast iron; 5000 psi (34 N/mm 2 ) for brass; and 10,000 psi (69 N/mm 2 ) for steel castings is ordi narily used. These values give ample factors of safety. Note: In metric SI units, 1000 pounds per square inch equals 6.895 newtons per square millimeter (1000 lb/in 2 = 6.895 N/mm 2 ). Also, one newtons per square mil limeter equals one megapascal (1 N/mm 2 = 1 MPa). Thick-walled Cylinders of Ductile Material, Closed Ends: Clavarino’s equation is used: (26) Thick-walled Cylinders of Ductile Material, Open Ends: Birnie’s equation is used: (27) Spherical Shells Subjected to Internal Pressure.— Let: D = internal diameter of shell in inches p = internal pressure in psi S = safe tensile stress per square inch (28) t D S p S p 2 1 1 2 1 µ µ = − + + − − ^ ^ h h = G t D S p S p 2 1 1 1 µ µ = − + + − − ^ ^ h h = G t = thickness of metal in the shell, in inches. Then, t = pD ÷ 4 S t D = S p S p − + 2 1 − d n
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