Thinwalled Pressure Vessels
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Thinwalled Pressure Vessels For lessons under hoop tension and other crap

A tank or pipe carrying a fluid or gas under a pressure is subjected to tensile forces, which resist bursting, developed across longitudinal and transverse sections.

TANGENTIAL STRESS, t (Circumferential Stress) Consider the tank shown being subjected to an internal pressure, p. The length of the tank is L and the wall thickness is t. Isolating the right half of the tank:

Tangential Stress Formula

LONGITUDINAL STRESS, L Consider the free body diagram in the transverse section of the tank:

The total force acting at the rear of the tank F must equal to the total longitudinal stress on the wall PT = LAwall. Since t is so small compared to D, the area of the wall is close to Dt.

Longitudinal Stress Formula

SPHERICAL SHELL

Problem 1A cylindrical steel pressure vessel 400 mm in diameter with a wall thickness of 20 mm, is subjected to an internal pressure of 4.5 MN/m2. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value may the internal pressure be increased if the stress in the steel is limited to 120 MN/m2? (c) If the internal pressure were increased until the vessel burst, sketch the type of fracture that would occur.

Solution: Part (a)

Solution continuation

Solution: Part (b)

Fracture Sketch

Problem 2The wall thickness of a 4ftdiameter spherical tank is 5/6 inch. Calculate the allowable internal pressure if the stress is limited to 8000 psi.

Answer

Hoop TensionA vertical cylinder tank is 2m in diameter and 3m high. Its sides are held by means of two steel hoops, one at the top and the other at the bottom. If the tank is filled with water to a depth of 2.1m, determine the tensile stress in each hoop.

Mtop=02T2(3)=F(2.3)T2= 0.3833F
F=ghcgAF=9.81(2.1/2)(2*2.1)=43.26kN
T2= 0.3833(43.26 kN) = 16.58 kN
Fh=02T2+2T1=F2T1=2T2 FT1=5.05 kN

Quiz!A cylindrical container 8m in height and 3m in diameter is reinforced with 2 hoops 1 meter from each end. When it is filled with water, what is the tension in each hoop due to water? (No erasures, no writing at the back, black pen only and provide an accurate FBD) 100 points

AnswerF=ghcgAF= 9.81(8/2)(8*3)F=941.76 kN
Mtophoop=02T2(6)=F(13/3)T2=13F/36=13(941.76)/36=340.08kN
Mbottomhoop=02T1(6)=F(5/3)T1= 5F/36= 5(941.76)/36=130.8kN