Answer Happy

A custom-designed pressure vessel was fabricated by connecting half of a hollow sphere to each end of a hollow cylinder (see Fig. → ) to become a thin-wall pressure vessel having a cylindrical middle part and semispherical ends. It has inner radius R, wall thickness t, and an inner length =6R. The material has yield strength σ0​, and ultimate strength σu​. If the pressure p inside the vessel keeps on gradually increasing, failure will occur when a certain magnitude of p is reached. A sensor is installed in the room to monitor the surface on the outside of the vessel for any failure that may show up on the outside surface. (a) For yielding on the outside surface: Determine whether yielding will occur first at the cylindrical part or at the semi-spherical part of the pressure vessel. Determine the p that will cause the first yielding. Express your answer of p in terms of R,t, and σ0​. Use the Octahedral Shear Stress Criterion (von Mises Yield Criterion). (b) Show what are the answers if you use the Maximum Shear Stress Yield Criterion (the Tresca Yield Criterion) instead. The stresses in the cylindrical part, and in the semi-spherical part, of the pressure vessel are in terms of the pressure p, as shown below.