A measurement of the normal strain in the longitudinal direction on the outside of the tank is used to evaluate the stresses produced in the wall of the cylinder by the internal fluid pressure in the tank. Therefore, we will begin by deriving an expression for the normal strain in the longitudinal direction (i.e., the x direction), 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 strain.
In the x direction (i.e., in the longitudinal direction), the normal strain is given by:
Substitute the longitudinal and hoop stress expressions for σx and σy, respectively.
which simplifies to
