The allowable stress in sustained case is Sh, so it is confirmed that the sustained stresses are within the allowable at that temperature. But due to local yielding because of expansion there may be reduction in pipe diameter(may be minute) because of which the section modulus get disturbed (decreases- as section modulus decreases bending stress increases). Whether the sustained stress calculated considers this effect (section modulus) as it considers other mechanical,erosion and corrosion allowance. If this is not the case then won't the sustained stresses be more in hot condition than calculated.

Thanks in advance,
Rajagopal

You are performing a linear elastic analysis using a 3D beam element. The cross section is assumed to remain constant throughout the analysis.

You might want to perform an analytical study. Consider what the ratio of Sy to Sh is for your material, Then calculate how much ovalization of the pipe is required to reduce the section modulus sufficiently that a moment that would produce Sh on a round pipe would produce Sy on an ovalized pipe. When you've figured this out, you might then want to step back and consider whether this reduction in pipe diameter was "minute."

You could, of course, create local yielding conditions intentionally. You could use knife-edge supports, put weldolets for instruments in high-stress areas, etc. You could size your expansion loops so that operating conditions produce local yielding on at least one elbow in every loop, eventually leading to the phenomenon of stress ratcheting that we all know and love.

Most of the time, though, we can make the expansion loops a little bigger, and we nearly always put instrument connections far enough away from elbows and tees that local yielding in the pipe wall does not occur.

You are right that such a phenomenon could exist. We are using a linearization of a non-linear phenomenon for convenience. Your question hits right on the weakest link of our assumption of linearity.

But I think you will find that you are wrong if you think that "minute" deformations if the pipe due to expansion stresses can be of such magnitude to be of importance analytically to systems that are typically analyzed in CAESAR II. That's one reason why we limit the D/t ratios of the pipe that we analyze.

I recently had to analyze a 96" ID x .5625 wall water line. This is a D/t of about 170; far outside of the valid range for CAESAR II. So we used FEA software to look at the stresses and deflections. We found some interesting things, and made a few small changes to our design, but there was nothing there that one would consider to be potentially catastrophic. Maximum ovalization of the pipe was perhaps 1/4", far less than a 1% reduction in diameter.

It's hard for me to believe that you could create a significant degree of ovalization in a piping system that falls within CAESAR II's normal range of geometric parameters without major overstresses showing up somewhere.