Text-book of mechanics . amp;, and this determines theE m E dangerous equivalent simple stress Pe = Ph Pi =2 —-? m \ ml 2t If the material is wrought iron or steel when— = .3, m we have pe = .83 — Exercise 197. Find the other equivalent simple stressfor the above shell. Exercise 198. A tank is 8 feet in diameter and 16 feetlong. If the shell is 1 inch thick, find the hoop stress,the longitudinal stress, and the equivalent simple stress foran internal pressure of 160 pounds per square inch. Exercise 199. The cast-iron air chamber of a pump isof cylindrical form with hemispherical ends. If the d
Text-book of mechanics . amp;, and this determines theE m E dangerous equivalent simple stress Pe = Ph Pi =2 —-? m \ ml 2t If the material is wrought iron or steel when— = .3, m we have pe = .83 — Exercise 197. Find the other equivalent simple stressfor the above shell. Exercise 198. A tank is 8 feet in diameter and 16 feetlong. If the shell is 1 inch thick, find the hoop stress,the longitudinal stress, and the equivalent simple stress foran internal pressure of 160 pounds per square inch. Exercise 199. The cast-iron air chamber of a pump isof cylindrical form with hemispherical ends. If the diameteris 10 inches and the length of the cylindrical part is 24 inches,what pressure can it withstand with a factor of safety of 5,the wall thickness being inch? i74 MECHANICS OF MATERIALS Spherical Shells under Internal Pressure. — Let r be the internal radius of the shell, t the thickness of the wall,w the internal fluid pressure, p the stress across anyplane passing through the center of the shell. Then. Fig. 89 from the equilibrium of the octant of the shell shown inFig. 89 we have the sum of the vertical forces wr2 sin cos d f dd — — = o. For 02 irrh is approximately the area over which the vertical stress p is assumed uniformly distributed, andthe differential area upon which w acts is (rd(t>) (r sin dd).Thus wr p=Vt COMPOUND STRESSES 175 This, according to the first theory of elastic failure(page 162), is the dangerous stress, while according tothe third theory the equivalent simple stress is \ ml wr— j 2t or as — = .3 for wrought iron and steelm wr Pe = -35T--• * Exercise 200. Sketch an element of the above shell as afree body and deduce the above value of pe. Exercise 201. A force of 500 pounds applied to theplunger of a force pump is transferred to a hollow cast-ironsphere 10 inches in internal diameter. What should be thethickness of the shell if the plunger is 1 inch in diameterand the factor of safety is to be 6 ? Cylindrical
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