σx — longitudinal σy — hoop / circumferential τxy — shear (torsion)

Reading it: plot X(σx, τxy) and Y(σy, −τxy); the circle through them has centre C=(σx+σy)/2 and radius R=√[((σx−σy)/2)² + τxy²]. Principal stresses σ₁,₂ = C ± R sit where the circle crosses the σ-axis (shear = 0). A rotation of θ in the element is 2θ on the circle. τmax = R acts on planes 45° from principal planes. For a pressurised pipe with no torsion, σH and σL are already principal — the circle touches them directly.