Machinery's Handbook, 31st Edition
Plates, Shells, and Cylinders 293 Example: Find the thickness of metal required in the hemi-spherical end of a cylindrical vessel, 2 feet in diameter, subjected to an internal pressure of 500 pounds per square inch. Solution: The material is mild steel and a tensile stress of 10,000 psi is allowable. , . t 4 10 000 500 2 12 0 3 inch # # # = = Example: A similar example using metric SI units is as follows: find the thickness of metal required in the hemi-spherical end of a cylindrical vessel, 750 mm in diameter, subjected to an internal pressure of 3 newtons/mm 2 . The material is mild steel and a tensile stress of 70 newtons/mm 2 is allowable. . t 4 70 3 750 804mm # # = = If the radius of curvature of the domed head of a boiler or container subjected to internal pressure is made equal to the diameter of the boiler, the thickness of the cylindrical shell and of the spherical head should be made the same. For example, if a boiler is 3 feet in diameter, the radius of curvature of its head should also be 3 feet, if material of the same thickness is to be used and the stresses are to be equal in both the head and cylindrical portion. Collapsing Pressure of Cylinders and Tubes Subjected to External Pressures.— The following formulas may be used for finding the collapsing pressures of lap-welded Besse mer steel tubes: (29) (30) in which P = collapsing pressure in psi; D = outside diameter of tube or cylinder in inches; t = thickness of wall in inches. Formula (29) is for values of P greater than 580 pounds per square inch, and Formula (30) is for values of P less than 580 pounds per square inch. These formulas are substantially correct for all lengths of pipe greater than six diameters between transverse joints that tend to hold the pipe to a circular form. The pressure P found is the actual collapsing pressure, and a suitable factor of safety must be used. Ordinarily, a factor of safety of 5 is sufficient. In cases where there are repeated fluctuations of the pressure, vibration, shocks and other stresses, a factor of safety of from 6 to 12 should be used. If metric SI units are used the formulas are: , D t 86 670 1386 = − , , P D t 50 210 000 3 = ` j P
. D t 5976 9556 = − , P D t 346 200 3 = ` j .
P
(31) (32)
where P = collapsing pressure in newtons per square millimeter; D = outside diame ter of tube or cylinder in millimeters; and t = thickness of wall in millimeters. For mula (31) is for values of P greater than 4 N/mm 2 , and Formula (32) is for values of P less than 4 N/mm 2 . The table Tubes Subjected to External Pressure is based upon the requirements of the Steam Boat Inspection Service of the Department of Commerce and Labor and gives the permissible working pressures and corresponding minimum wall thickness for long, plain, lap-welded and seamless steel flues subjected to external pressure only. The table thicknesses have been calculated from the formula:
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