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For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel:
The formula is also common in the pipeline industry to verify that pipe used for gathering, transmission, and distribution lines can safely withstand operating pressures. The design factor is multiplied by the resulting pressure which gives the maximum operating pressure (MAOP) for the pipeline.
An induction coil is placed around a small section of the pipe at the bend point. It is then induction heated to between 800 and 2,200 degrees Fahrenheit (430 and 1,200 C). While the pipe is hot, pressure is placed on the pipe to bend it. The pipe can then be quenched with either air or water spray or be cooled against ambient air.
This type of loads act throughout the life cycle of pipe. In horizontal pipes, these loads cause bending, and the bending moment is related to Stress (mechanics)#Simple stresses normal and shear stresses. Pipe bending is caused mainly due to two reasons: distributed weight load (e.g. fluid weight) and concentrated weight load (e.g. valve weight).
This results in a constant bending moment between the two supports. Consequently, a shear-free zone is created, where the specimen is subjected only to bending. This has the advantage that no additional shear force acts on the specimen, unlike in the 3-point bending test. [6] The bending modulus for a flat specimen is calculated as follows:
The walls of pressure vessels generally undergo triaxial loading. For cylindrical pressure vessels, the normal loads on a wall element are longitudinal stress, circumferential (hoop) stress and radial stress. The radial stress for a thick-walled cylinder is equal and opposite to the gauge pressure on the inside surface, and zero on the outside ...