Hi All,

I want to know how Caesar II is calculating the axial stress and axial force for a pipe under pressure (No applied temperature).

In my model I considered 1000 mm pipe (OD = 168.3 mm) and 15.9 mm wall thickness (mill tolerance = 0; corrosion = 0)the pipe is anchored at both side.
Fluid density: 1000 Kg/m3
Internal Pressure: 10 bars.
Material Density 8750 Kg/m3; E = 207000 N/mm²; Poisson ratio = 0.3
First Model (Pipe in air: External Pressure = 0 bars):
load case W+P (OPE or SUS are giving the same results-piping code B31.3 and DNV are giving the same results for axial stress:
Axial stress = 1.92 N/mm²(Stress extended report)
Axial Force = 0 (Restraint summary or local element forces or global element force all these report are given the same axial force = 0)
for B31.3 code the hoop Stress = 5.29 N/mm² (from stress report) => Axial stress due to Poisson effect is Hoop Stress x 0.3 = 5.29 x 0.3 = 1.587 N/mm² (different from 1.92 N/mm² calculated by Caesar II)

for DNV code the hoop Stress = 4.79 N/mm² (from stress report) => Axial stress due to Poisson effect is Hoop Stress x 0.3 = 4.79 x 0.3 = 1.437 N/mm² (different from 1.92 N/mm² calculated by Caesar II)

Second Model (Pipe in water: water depth = 199 m; water density = 1000 Kg/m² wave and current speed are set to 0 ):all other inputs are as the first model (in air):
load case W+P+WAV1 (OPE or SUS are giving the same results-piping code B31.3 and DNV are giving the same results for axial stress:

Axial stress = 1.92 N/mm²(Stress extended report)
Axial Force = 0 (Restraint summary or local element forces or global element force all these report are given the same axial force = 0)

for B31.3 code the hoop Stress = 5.29 N/mm² (from stress report) => Axial stress due to Poisson effect is Hoop Stress x 0.3 = 5.29 x 0.3 = 1.587 N/mm² (different from 1.92 N/mm² calculated by Caesar II)

for DNV code the hoop Stress = 4.79 N/mm² (from stress report) => Axial stress due to Poisson effect is Hoop Stress x 0.3 = 4.79 x 0.3 = 1.437 N/mm² (different from 1.92 N/mm² calculated by Caesar II)

can any one explain to me how Caesar II is calculating the axial stress and why the axial force is not shown in the restraint summary or local element forces. If Caesar II is considering the effective axial Force concept why the axial stress is "0" when the internal and the external pressure are equal cause the true axial force should be equal to (Pi x Ai - Pe x Ae) where:
Pi = Internal pressure
Ai = internal pipe section
Pe = External pressure
Ae = external pipe section

Thanks in advance for your help

Until quite recently, the piping codes simplified the sustained stress calculations by adding a calculated (PD/4t) longitudinal pressure stress to the calculated weight stresses (based on the weight moments and axial force due to weight). Think of trying to do this by hand - PD/4t is close enough.
If your model has no expansion joints and you run a pressure case alone in CAESAR II using default settings, most piping codes (and materials) will show zero structural response - zero load and zero displacement throughout. But you will see a "code stress" that is based on (P*Ain/Axs). (You can change this to PD/4t if you wish.) Pressure, typically, causes no significant structural response. So an add on stress is sufficient.

Also, CAESAR II does not consider the Poisson Effect in the analysis.

Hi Dave

Thank you for your reply but I'm not getting the same results after doing calculation by hand. Here is my result:

Same as the first model with internal pressure = 10 bars (1 N/mm²) (Caesar results for axial stress = 1.92 N/mm² load case SUS P1 (only pressure is applied)

PD/4t = 1*168.3 /4*15.9 = 2.64 N/mm² (far enough from the 1.92 N/mm² shown by Caesar)
P* (Ain/Axs): the term "Ain/Axs" is less than 1 cause the internal section Ai is smaller than the external section Axs therefore the results
of P*(Ain/Axs)= 1*(Ain/Axs) will be less than 1 which is far from PD/4t (2.64 N/mm²) and also far from the 1.92 N/mm² Shown by Caesar II.

The second point is that Caesar II is not taking into account the axial force due to the weight cause Im getting the same results for both model with pipe legth is respectively 1m and 50m the axial stress shown is always 1.92 N/mm²

Hi Dave

After performing some hand calculation I get how Caesar II is calculating the Axial Stress: it's simply the stress due to the end cap force which is approximated by Pi*Ain/A where "A" is the steel Section.

This is correct when the pipe is in air cause the external pressure equal to ~0 bars but it's not correct when the pipe is in deep water where the external pressure is significant the real formula of the end cap force is (Pi*Ain)-(Pe*Axs). In Deep water the term "Pe*Axs" become really significant.

I think Caesar II should take into account the Poisson effect for axial stress calculation and updating the formula of the end cap force in water
Again thank you for your reply

Regards,

Dear Dave,

As per my understanding, Caesar II uses the Poisson Ratio only for:

1. the formulation of the local stiffness matrix (which includes G); and
2. the calculation of the strain when Bourdon Effect is activated.

Is it used for other purposes?

Honestly I don't understand why Caesar II does not consider the Poisson Ratio when calculating the axial stresses. As per B31.8 one of the terms of longitudinal stress is SH*0.3.

Thanks in advance for your support.

If you specify a B31.8 CAESAR II pipe element as "restrained", the program will use 0.3(hoop stress) as the longitudinal stress due to internal pressure in accordance with para. 833.2. That's your Poisson effect. [If you do not declare the pipe as restrained, then longitudinal stress due to pressure is half of the hoop stress - the standard relationship between hoop and long. pressure stress.]

Dear Abdelkader,

Try the formula P*Di^2/(Do^2-Di^2)for axial stress calculation.

For vertical run of pipes, the axial force due to weight of pipe and fluid may add.



Rgds
opinion