Small displacement theory only.
The cross section or properties of the pipe/beam are not affected by the deformations. The accuracy of an analysis with combined beam and piping will depend on the assumptions made for the small displacement theory and whether these assumptions would cause an error which is with acceptable limits:
a. Displacement is small in comparison to the smallest dimension of the structure
b. Rotations are small and square of rotations is much smaller than unity
c. The strain is small and square of strain can be neglected
d. The equations written for the un-deformed configuration of the structure can be assumed to be valid for the deformed configuration