Plates, Shells, and Cylinders PLATES, SHELLS, AND CYLINDERS Machinery's Handbook, 31st Edition
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Flat Stayed Surfaces.— Large flat areas are often held against pressure by stays distrib uted at regular intervals over the surface. In boiler work, these stays are usually screwed into the plate and the projecting end riveted over to insure steam tightness. The US Board of Supervising Inspectors and the American Boiler Manufacturers Association (ABMA) rules give the following formula for flat stayed surfaces: P S C t 2 2 # = in which P = pressure in pounds per square inch C = a constant, which equals 112 for plates 7 ∕ 16 inch and under 120, for plates over 7 ∕ 16 inch thick 140, for plates with stays having a nut and bolt on the inside and outside 160, for plates with stays having washers of at least one-half the plate thickness, and with a diameter at least one-half of the greatest pitch t = thickness of plate in 16ths of an inch (thickness = 7 ∕ 16 , t = 7) S = greatest pitch of stays in inches Strength and Deflection of Flat Plates.— Generally, the formulas used to determine stresses and deflections in flat plates are based on certain assumptions that can be closely approximated in practice. These assumptions are: 1) the thickness of the plate is not greater than one-quarter the least width of the plate; 2) the greatest deflection when the plate is loaded is less than one-half the plate thickness; 3) the maximum tensile stress resulting from the load does not exceed the elastic limit of the material; and 4) all loads are perpendicular to the plane of the plate. Plates of ductile materials fail when the maximum stress resulting from deflection under load exceeds the yield strength; for brittle materials, failure occurs when the maximum stress reaches the ultimate tensile strength of the material involved. Square and Rectangular Flat Plates.— The formulas that follow give the maximum stress and deflection of flat steel plates supported in various ways and subjected to the loading indicated. These formulas are based upon a modulus of elasticity for steel of 30,000,000 psi and a value of Poisson’s ratio of 0.3. If the formulas for maximum stress, S , are applied without modification to other materials, such as cast iron, aluminum, and brass, for which the range of Poisson’s ratio is about 0.26 to 0.34, the maximum stress cal- culations will be in error by not more than about 3 percent. The deflection formulas may also be applied to materials other than steel by substituting in these formulas the appropri- ate value for E , the modulus of elasticity of the material (see pages 429 and 510 ). The deflections thus obtained will not be in error by more than about 3 percent. In the stress and deflection formulas that follow, p = uniformly distributed load acting on plate, psi W = total load on plate, pounds; W = p 3 area of plate L = distance between supports (length of plate), inches. For rectangular plates, L = long side, l = short side t = thickness of plate, inches
S = maximum tensile stress in plate, psi d = maximum deflection of plate, in. E = modulus of elasticity in tension. E = 30,000,000 psi for steel
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