Example $8-1$

A compressed$-$air tank having an inner diameter of $5\mathrm{.}5$ m and a wall thickness of $45$ mm is formed by welding two steel hemispheres $($Fig$.8-5).$

a$.$ If the allowable tensile stress in the steel is $93$ MPa $,$ what is the maximum permissible air pressure $p_a$ in the tank?

b$.$ If the allowable shear stress in the steel is $42$ MPa $,$ what is the maximum permissible pressure $p_b?$

c$.$ If the normal strain at the outer surface of the tank is not to exceed $0\mathrm{.}0003,$ what is the maximum permissible pressure $p_c?($Assume that Hooke's law is valid and that the modulus of elasticity for the steel is $210$ GPa and Poisson's ratio is $0\mathrm{.}28.)$

d$.$ Tests on the welded seam show that failure occurs when the tensile load on the welds exceeds $7\mathrm{.}5M\frac{N}{m}$ of weld. If the required factor of safety against failure of the weld is $2\mathrm{.}5,$ what is the maximum permissible pressure $p_b?$

e$.$ Considering the four preceding factors, what is the allowable pressure $p_{\text{e}\text{l}\text{l}\text{o}\text{w}}$ in the tank?

Figure $8-5$

Example $8-1$: Spherical pressure vessel. $($Attachments and supports are shown in photo.$)$