2. Consider the forces acting on the Shell from Pressure
From pressure
D
L
P
Force = Pressure x Area
= PLD
F = P x L x D
Area = D x L
Here is the
pressure
3. This is resisted by the internal stress
Force = Stress x Area
L
t
Stress S
F = S x L x t x 2
= 2SLt
Area = 2 x t x L
Stress S
4. For equilibrium - Forces must be Equal
From pressure : F = PDL
From internal stress: F = 2SLt
Equating therefore : PDL = 2SLt
Finally : Sh =
PD
2t
This is known as the HOOP STRESS Sh
5. Consider now the Axial or Longitudinal Stress
P
Force = Pressure x Area
Area =
π.D2
4
F =
P.π.D2
4
Pressure
6. Consider now the Axial or Longitudinal Stress
Force = Stress x Area
Area = π.D.t (approx)
S
F = S.π.D.t
Equate F =S.π.D.t =
P.π.D2
4
Thus SL =
P.D
4t
This is kown as the Axial or Longitudinal Stress
Stress
7. Comparison of Hoop and Longitudinal Stress
SL =
P.D
4t
Sh =
PD
2t
What is the relationship between SL and Sh ?
Sh is twice SL or Sh = 2.SL
8. True Stress - Lame Theorem
We have assumed the
stress is like this:
Sh =
PD
2t
In reality it is like this:
Greater
than Sh
9. According to the Lame Theorem (Thick Cylinder Theory)
Ri
Ro
S
S = P .
( Ro2
+ Ri2
)
( Ro2
- Ri2
)
Sh
S > Sh (simple theory)
10. S = P .
( Ro2
+ Ri2
)
( Ro2
- Ri2
)
S =
P.D
2t
We now have three formulae for Hoop Stress
Simple Theory Accurate Lame Equation
Let us now look at the ASME Division 1 Equation
S =
P.( R + 0.6.t )
t
We now have two formulae for the hoop stress
=
P.( D + 1.2.t )
2 t
Notice the similarity
11. Ro/Ri
P/S
This is how the three formulae look
---- Lame (Accurate)
---- ASME (Less Accurate)
---- Simple (Very Inaccurate)
Only half the stress - bad!
12. Simple versus ASME formulae
This little term makes all the difference
t =
P.R
S
t =
P.R
S - 0.6.P
13. Consider the cylinder - ASME Code
This is the formula per UG-27 in the code:
P.R
t =
S.E - 0.6.P
P = Pressure psi
R = Radius inches
S = Design Stress psi
E = Welded Joint Efficiency
Calculations are done the the CORRODED condition
14. Effect of the Corrosion Allowance
R
R+c
All calculations are performed in the CORRODED
state
15. R
R+c
Effect of the Corrosion Allowance
P.(R + c)
t =
S.E - 0.6.P
Equation becomes:
P.(R + c)
t + c =
S.E - 0.6.P
+ cFinally:
