224 Mechanics of Materials §10.9 Hoop stresses Rodial stresses Cylinder wall snipo A Externol r2 pressure Internal snipoJ Jaino (an-)ssaJs Cylinder Fig.10.9.Lame line solution for cylinder with internal and external pressures. snipDJ snipo Jeino snipo A External Dr色ssUr色 (negafive 乐0a1 inner rodius 6 Fig.10.10.Lame line solution for cylinder subjected to external pressure only. N.B.-From $10.4 the value of the longitudinal stress oL is given by the intercept A on the o axis. It is not sufficient simply to read off stress values from the axes since this can introduce appreciable errors.Accurate values must be obtained from proportions of the figure using similar triangles. 10.9.Compound cylinders From the sketch of the stress distributions in Fig.10.2 it is evident that there is a large variation in hoop stress across the wall of a cylinder subjected to internal pressure.The material of the cylinder is not therefore used to its best advantage.To obtain a more uniform hoop stress distribution,cylinders are often built up by shrinking one tube on to the outside of another.When the outer tube contracts on cooling the inner tube is brought into a state of224 Mechanics of Materials $10.9 Fig. 10.9. Lam15 line solution for cylinder with internal and external pressures. Fig. 10.10. Lam6 line solution for cylinder subjected to external pressure only. N.B. -From $10.4 the value of the longitudinal stress CT is given by the intercept A on the u axis. It is not sufficient simply to read off stress values from the axes since this can introduce appreciable errors. Accurate values must be obtained from proportions of the figure using similar triangles. 10.9. Compound cylinders From the sketch of the stress distributions in Fig. 10.2 it is evident that there is a large variation in hoop stress across the wall of a cylinder subjected to internal pressure. The material of the cylinder is not therefore used to its best advantage. To obtain a more uniform hoop stress distribution, cylinders are often built up by shrinking one tube on to the outside of another. When the outer tube contracts on cooling the inner tube is brought into a state of