Hoop Stress Calculator

Hoop stress is the normal stress in the circumferential direction, acting tangentially to the curve of the vessel wall. For a thin-walled cylinder, the primary hoop stress formula is expressed as sigma_hoop = (P * r) / (t * eta_t), where P represents internal pressure, r is the inner radius, t is the wall thickness, and eta_t denotes joint efficiency. Longitudinal stress, acting parallel to the central axis, is typically half the magnitude of hoop stress under closed-end conditions. Spherical vessels experience uniform membrane stress in all tangential directions, calculated differently due to multi-axial symmetry. Furthermore, material expansion under pressure alters dimensions, which is quantified using Young's modulus and Poisson's ratio.

Consider a cylindrical steel pressure tank with an outer diameter of 1.0 meter (radius r = 0.5 meters) and a wall thickness (t) of 0.01 meters, subjected to an internal pressure (P) of 2.0 MPa (2,000,000 Pa). Assuming a joint efficiency of 1.0, we substitute these values into the hoop stress equation: sigma_hoop = (2,000,000 * 0.5) / (0.01 * 1.0). This yields a hoop stress of 100,000,000 Pa, or 100 MPa. For longitudinal stress under the same conditions, we divide by 2, resulting in 50 MPa. This ensures the material remains well below its yield strength.

Always ensure consistent SI units (meters, Pascals) when inputting parameters to avoid magnitude errors. Remember that the thin-wall assumption only holds true when the radius-to-thickness ratio is greater than 10; thick-walled pressure vessels require Lamé's equations instead of standard membrane formulas. Account for weld joint efficiencies whenever dealing with fabricated commercial tanks.