Pressure Vessel Calculator

Wall thickness for a pressure vessel follows from a force balance on a cut section. Slice a cylinder lengthwise and the internal pressure acting on the projected area must be carried by two wall sections, giving hoop stress equal to pressure times radius divided by thickness. Cut it across and the same pressure is carried by the full circumference, giving axial stress of half that value. Hoop stress therefore governs cylindrical design, and it is the reason a sphere, which has no preferred direction and carries only the lower value, needs about half the thickness of a cylinder at the same radius and pressure. The ASME UG-27 formulas are these relations rearranged with correction terms, the 0.6P for cylinders and 0.2P for spheres, that keep them accurate as walls become moderately thick. Three inputs carry most of the engineering judgment. Allowable stress S is a code assigned value that already includes a safety margin against tensile and yield strength at temperature; SA-516 Grade 70 carbon steel is about 138 MPa near ambient and falls as temperature rises. Joint efficiency E derates the weld relative to the parent plate, taking 1.0 for a fully radiographed double welded butt joint, 0.85 for spot radiography and 0.70 with none, so inspection cost trades directly against plate thickness. Corrosion allowance, commonly 1.5 to 3 mm for carbon steel, is estimated from a corrosion rate times the intended service life. The formulas assume a thin wall, meaning a radius to thickness ratio above about 10; below roughly 4 the stress gradient through the wall makes them unconservative and Lame thick wall analysis or ASME Division 2 methods apply. They also cover the shell only, not heads, nozzles or external pressure buckling.

Pressure vessel codes were written in response to a long record of fatal boiler explosions. Through the nineteenth century steam boilers failed regularly and lethally: the 1865 loss of the steamboat Sultana on the Mississippi, following a boiler rupture, killed well over a thousand people and remains the deadliest maritime disaster in United States history. Explosions in factories and mills were common enough that insurance inspection companies emerged specifically to examine boilers, but there was no uniform design rule and no legal requirement to follow one. The decisive event was the explosion at the Grover Shoe Factory in Brockton, Massachusetts, in March 1905, where a boiler failure collapsed the building and started a fire, killing 58 workers. Massachusetts passed the first state boiler law in 1907, and other states followed with incompatible requirements, creating a patchwork that manufacturers could not build to economically. The American Society of Mechanical Engineers established its Boiler Code Committee in 1911, and the first edition of the Boiler and Pressure Vessel Code appeared in 1914 and 1915. Section VIII, covering unfired pressure vessels, was added in 1925, and its design by rule provisions became what is now Division 1. Division 2, offering design by analysis with higher allowable stresses in exchange for more detailed calculation and inspection, was introduced in 1968. The U stamp, applied by manufacturers under third party Authorized Inspector oversight, made code compliance verifiable and is now referenced in law across most North American jurisdictions.