These expressions for strains in the longitudinal and circumferential directions in terms of the internal pressure p must now be related to the strain gage measurement.
The general strain transformation equation is:
The strain gage is oriented at 30° from the longitudinal axis (i.e., the y axis). In the strain transformation equation, θ is measured from the x axis; therefore, θ = 60° for this gage.
Substitute the expressions for εx, εy, γxy, and θ into the strain transformation equation.