Dear Dave,

Here is the problem I am facing.

A pipeline is designed according to B31.8 rules. The wall thickness is sufficient to meet the requirements of 841.1.1 and combined stress requirement of 833.4. However when the same is modeled in Caesar (with Bourdon Effects activated, to take care of bending due to pressure expansion), it is showing overstressed in the restrained section. I agree that a restrained line don't require beam bending analysis, but since Caesar is showing over stress, I must explain the difference to the authority approving the stress analysis work.

The combined stress calculated as per 833.4 and reported in "Code Stress" column takes two values i.e SH and SL. SH is coming from the “Hoop Stress” column while SL is the axial stress from “Axial Stress” column + bending stress in "Bending Stress" column. In absence of bending the axial stress column therefore represents SL term of B31.8.

What I feel is that difference is because of the way pressure elongation is handled in Caesar. When Bourdon Effects are activated , the axial stress and hence the combined stress (SH-SL) exceed the true value by a factor of approximately 0.2*SH. On the basis of my guess work, it might be explained as below

Element expansion is calculated as

dL=Alpha*L*(T2-T1)+SH/2*L/E-nu*SH*L/E ----(1)
To completely restrain this expansion, the force exerted at the element is
R=-E*Am*Alpha*(T2-T1)-Am*SH/2+Am*nu*SH
This is the force which is shown in element force report
The axial stress is then calculated by
SA=SL=F/Am+nu*SH --- (2) (As per code equation 833.3a where ST is replaced by R/Am as explained in Caesar documentation)

However in restrained section the only axial deflection is because of poisson contraction, hence 2nd term in (1) above should be ignored. Moreover poisson component has already been taken care by 3rd term in (1) and should not be added twice in (2). The net correction required is therefore
-SH/2+nu*SH=-0.2SH

As stated this is all my guess work to explain the difference and is based upon the observed results

Best regards,

Tanveer Mukhtar