PRE-STRESSING IN THICK CYLINDRICAL SHELL
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PRE-STRESSING IN THICK CYLINDRICAL
Pre-stressing means stresses are created during
manufacturing. Thick shells are made from thin shells by
hoop shrinking. Due to hoop shrinking, outer cylinder is put
into tension. The inner cylinder is put into compression.
These pre-stresses make the stress distribution uniform
under fluid pressure.
Refer to Fig. below:
Fig. Pre-stresses Fig. resultant stress variation
PRE-STRESSES IN CYLINDER (due to hoop shrinking)
AB stress = –2psr22/ (r22 –r12) compressive
CD stress = ps(r32+r22)/ (r32 –r22) Tensile
STRESSES DUE TO FLUID PRESSURE
AA’ stress= p((r32+r12)/ (r32 –r12)
CC’ stress= pr12((r32+r22)/[r22(r32 –r12)]
FINAL RESULTANT STRESSES
Final stress at A = AA’ – AB=p((r32+r12)/ (r32 –r12) — 2psr22/ (r22 –r12)
Resultant stress at C = CC’ + CD =pr12((r32+r22)/[r22(r32 –r12)]+ ps(r32+r22)/ (r32 –r22)
Stresses due to fabrication (pre-stresses ) are coupled with stresses due to fluid pressure to get the final distribution of stresses. These are found to be more uniform as compared to stresses in a single walled thick vessel.
ADVANTAGES OF PRE-STRESSING
Stresses are more uniform.
Vessel of less thickness can withstand higher fluid pressures.
For a certain fluid pressure, vessel of lesser thickness will be required.
Less stress will be produced for a certain fluid pressure.
Further, it is applicable when the thick vessel is made from number of thin cylinders.