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Northrop, E. B.; Chittenden, H. A., Jr. (ed.) / The Wisconsin lumberman, devoted to the lumbering interests of the northwest

(August, 1874)

Steam boilers. Strength of cylinder, sphere and flat surfaces, pp. 513-515 PDF (1.1 MB)

Page 513

The Wisconsin Lumbernman. 513 STEAM BOILERS. Strength of Cylinder, Sphere and Flat Surfaces. In analyzing the various forms of boiler shells they are found to resolve themselves into the cylinder, oval, sphere, chambered and flat surfaces. THE CYLINDER. According to the well known law of hydrostatics, the pressure of steam in a close vessel is exerted equally in all directions. In acting against the circumference of a cylinder, the pressure must therefore be regarded as radiating from the axis, and ex- erting a uniform tensional strain throughout the enclosing material. Its .tendency to cause longitudinal rupture, or to rend the cylinder in lines parallel to its axis, may be con- sidered as a force acting and re-act- ing in opposite directions to divide the cylinder in two. As it must be exerted on equal areas in order that the action and reaction may be equal, this divellant force may be consider- ed as the pressure exerted on the semi-circumference, and tending to rupture the cylinder in a plane drawn through the diameter. It follows, however, from the pressure acting equally in all directions, that the whole amount exerted on the semi- circumference is not equally effective in producing a strain perpendicular to the diameter through which the cylinder may be assumed to rend. If we examine the force tending to cause rupture through the hori- zontal diameter, we shall find the pressure is exerted directly upwards and downwards only along the ver- tical diameter. As we recede right and left from this line, the pressure is exerted diagonally with diminish- ing vertical effect, to produce tension at the extremities of the horizontal diameter, and, unit vanishes alto- gether when we reach these points. The radial pressure at any point, may be resolved into two forces, the one vertical and the other horizontaL It is evident the latter has no ten- sional eftect at there extremities. By taking the component vertical forces at an infinite number of points in the semi-circumference it can be proved that their sum is equal to the full pressure exerted on a line equal in length to the diameter. We may consider the cylinder as composed of a number of rings of a unit's length, placed side by side, each of which resists the pressure in- dependently of the rest. Hence the force, tending to rup- ture the cylinder longitudinally, is represented by multiplying the diam- eter by the pressure on each unite of surface. As this applies only to a cylinder of a unit's length, it is evi- dent that the total amount of force, tending to divide thescylinder in lines parallel to its axis, is found by multi- plying the above product by the length of the cylinder. The practical truth of this has been proved by ex- periment. The retaining force opposed to this pressure, is evidently the resist- ance of the material at the two op- posite sides which bear the strain. The manner in which the strain is borne by the material depends great- ly on its thickness. WVLen this is considerable, compared with the diameter, as in hydraulic presses and cannon, the inner layers of the ma- terial are more severely taxed than those on the outside. This differ- ence may be so great that the latter render no material assistance to the former. If we take two straight bars, of the same material and section but of different lengths, and submit them to the same tensile strain, they will be stretched, within certain limits, in proportion to their length. Suppose a bar 1 foot long is stretched 1-10 inch by a given weight, then a similar bar 10 feet long would be elongated 1 inch by a similar weight, the exten- sion being simply a factor of the length. In a cylnder, say of 3 inches diameter, and 21-2 inches thick, we

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