Derivation of hoop force in terms of unit weight formula
Answers
Answer:
Hoop stress σH varies across the pipe wall from a maximum value on the inner surface to a minimum value on the outer surface of the pipe, as expressed in the hoop stress of Equation (31-1). The equation for the hoop stress is also called the Lame equation and is rewritten as follows:
(31-2)σH=piDi2−peDe2De2−Di2+(pi−pe)Di2De2(De2−Di2)D2
where
σH: Lame hoop stress;
D: diameter at which hoop stress is calculated;
De: external pipe diameter;
Di: internal pipe diameter;
pe: external pressure of pipe;
pi: internal pressure of pipe.
Hoop stress for a thin-wall pipe can be obtained from the force balance below, assuming the hoop stress to be constant in the radial direction:
(31-3)σH=piDi−peDe2t
where t is the minimum wall thickness of the pipeline.
The radial stress σR varies across the pipe wall from a value equal to the internal pressure, pi, on the inside of the pipe wall, to a value equal to the external pressure, pe on the outside of the pipe. The magnitude of the radial stress is usually small when compared with the longitudinal and hoop stresses; consequently it is not specifically limited by the design codes.
According to ASME B31.8 (2010) [8], Hoop stress for a thin wall (D/t > 30) can also be expressed in the following equation:
(31-4)σH=(pi−pe)De2t
Hoop stress for a thick wall (D/t < 30) can be calculated using the following equation:
(31-5)σH=(pi−pe)De−t2t
Depending on which code/standard is used, the hoop stress should not exceed a certain fraction of the specified minimum yield stress (SMYS).