Mechanics of Materials · Hoop stress
The stress that unzips a pipe
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The stress that unzips a pipe

Put pressure inside a thin-walled cylinder and the wall is pulled two ways at once. The bigger of the two runs around the girth, and it is called the hoop or circumferential stress: σh=pd2t\sigma_{h} = \dfrac{pd}{2t}. Read aloud: sigma-h equals p d over two t. σh\sigma_{h} is the hoop stress in MPa; pp is the internal gauge pressure in MPa — gauge, so atmospheric pressure outside is already netted off; dd is the internal diameter in mm; and tt is the wall thickness in mm. Solve it for whichever one the question withholds.

You will meet the same relation written σh=prt\sigma_{h} = \dfrac{pr}{t}, with rr the internal RADIUS. Those are the same equation — the 2 in the denominator is exactly the conversion from diameter to radius. What is not the same is feeding a diameter into the pr/t form, which doubles your answer and is the classic wrong number on this topic. Pick one form and read the given carefully.

One quiet gift: with p in MPa and both lengths in mm, the millimetres cancel and the answer arrives in MPa with no conversion owed. That is not luck — a megapascal IS a newton per square millimetre. Thin-wall, incidentally, means d/td/t above about 20; below that the stress varies through the wall and this formula starts telling comfortable lies.