Hello All

What is the right approach in calculating the stress developed in a pipe segment due to thermal expansion of a perpendicular segment (Both connected by 90 deg elbow)

I started with deflection theory assuming the segment under analysis a cantilever and deflection is the growth of the perpendicular segment. The seconed appoach is assuming the perpendicular segment fixed(not allowed to expand),find the stress and load.Allowing the segment to expand ,the same load is used to calculate the moment on the horizontal segment.

Values of moment from both methods varied alot?

Can somebody explain.

Thanks

Your first approach looks a lot like the guided cantilever method which was widely used before martix methods were computerized. Assuming that both ends are anchored, the elbow is a square corner that will not rotate and ignoring the axial load from restrained growth, the thermal load on each leg can be calculated solely on the lateral offset caused by the thermal strain of other leg. This deflection is used with the leg stiffness (the guided cantilever which is 4 times stiffer to transvers end load than a simple cantilever) to compute an end load and from that the bending moment and stress.
I do not understand your second approach. Don't feel too bad though. As I re-read my paragraph above I'm not sure, if you don't already know what I'm saying, that it will make sense!
Focus on the phrase "guided cantilever method", better yet, run it through CAESAR II for a more acceptable result.