A measurement of the normal strain on the outside of the tank is used to evaluate the internal pressure in the cylinder. Therefore, we will begin by deriving expressions for the normal strains in the x and y directions, using the expressions for the longitudinal stress σlong and the hoop stress σhoop. Since stresses occur in both the x and y directions, the generalized Hooke's Law must be used to determine the strains.
In the x direction (i.e., in the circumferential direction), the normal strain is given by:
Substitute the hoop and longitudinal stress expressions for σx and σy, respectively.
which simplifies to
