Selection of Metals for a Compressed Air Tank

You are asked to design a vessel to contain compressed air. Economics and weight are obviously issues to consider, but the primary consideration is safety that is, the tank must not rupture. Specifically, the tank must meet three design criteria  

The maximum stress in the vessel must be below the yield strength of the material used. 

P = p X (area of elemental section) = pSxL = prSOL The vertical component of the pressure is SPp. 

The total upward pressure on the semieireular portion of the cylindrieal shell above the diametral plane XX is obtained by integrating SPy over the entire angle, 0  

Similarly, the total downward pressure on the semicircular portion of the cylindrical shell below the diametral plane XX is also 2prL. These two equal and opposite pressures act to burst the cylinder longitudinally at the plane XX. The resisting force comes from the hoop stress. Thus 

---