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Lecture 30: Thin-walled pressure vessels. Design, construction, and maintenance covered by the ASME Boiler and Pressure Vessel Code Can be subjected to internal as well as external pressure Power generation, fuel containers, pressurized gas storage, ... The hoop stress is exactly 2x the axial stress!
Thin Walled Pressure vessels. The cylindrical pressure vessel above has closed ends and contains a fluid at gauge pressure P as shown below. The outer diameter is D and the wall thickness is t. The term ‘thin-wall’ may be taken to mean that D/t > 10.
If there exist an external pressure p o and an internal pressure p i, the formula may be expressed as: $\sigma_L = \dfrac{(p_i - p_o) D}{4t}$ It can be observed that the tangential stress is twice that of the longitudinal stress.
The most common method is based on a simple mechanics approach and is applicable to “thin wall” pressure vessels which by definition have a ratio of inner radius, r, to wall thickness, t, of r/t≥10.
Both for their value in demonstrating two-dimensional effects and also for their practical use in mechanical design, we turn to a slightly more complicated structural type: the thin-walled pressure vessel. Structures such as pipes or bottles capable of holding internal pressure have been very important in the history of science and technology.
Note: The above formulas are good for thin-walled pressure vessels. Generally, a pressure vessel is considered to be "thin-walled" if its radius r is larger than 5 times its wall thickness t (r > 5t). When a pressure vessel is subjected to external pressure, the above formulas are still valid.
The thin-walled pressure vessel expands when it is internally pressurised. This results in three principal strains, the circumferential strain c (or tangential strain t ) in two
