Induced Stresses in Pipe- Hoop, Longitudinal and Radial Stresses

Topic covered Introduction Circumferential or Hoop Stresses Longitudinal Stresses Radial StressIntroduction to Induced Stresses:When the ends of the pipe ends are closed and pipe is subjected to an internalpressure Pthere are various stresses that develop in the pipe. Each element of pipe are subjected to the below mentioned stresses which act in the direction as shown in the fig.1. Circumferential (hoop) stressH Longitudinal StressL Radial StressR

Fig 1: Different stresses induced in pipeCIRCUMFERENTIAL OR HOOP STRESS:H

The effect of this may split the pipe into two halves as shown in fig.2. The failure of the pipe in two halves in fact is possible across any plane, which contains diameter and axis of the pipe. Elements resisting this type of failure would be subjected to stress and direction of this stress is along the circumference. Hence the above stress is calledCircumferential or Hoop Stress.

If D= Diameter of the pipeL= Length of the pipet= thickness of the pipe.ThenBursting force, FB=Pressure * Area

=P * D * L

Resisting force, FR=Resisting metal area * Stress,H

EquatingFB& FR

P * D * L =2t * L *H

t=(P * D)/2 *H

or H =(P * D) /(2 * t) ______________________(1)

This equation is used for calculating the thickness of pipe so as to withstand pressurePwhereHisallowable circumferential stress.

Fig 2: Circumferential or Hoop stressLONGITUDINAL STRESS:RConsidering that the pipe ends are closed and pipe is subjected toan internal pressure Pthe pipe may fail as shown inFig.3. Elements resisting this type of failure would be subjected to stress and direction of this stress is parallel to the longitudinal direction of the pipe. Hence this stress is calledlongitudinal stress.ThenBursting force, FB =PressureArea

=P *(D * D)/4

Resisting force, FR=Resisting metal areaxStress,L

=D t *L(whentis significantly small as compared toD)

EquatingFB& FR

P * (D * D) /4=D t *L

t =(P D)/4 *L

or L =(P D)/(4 * t) _________________________ (2)

NOTES:1)On comparing equations1 & 2, it is clear that when a pipe having diameterDand thicknesstis subjected to an internal pressureP,the induced circumferential tress is double the induced longitudinal stress.2)Normally, the pipe is considered as a thin wall cylinder i.e.t