Read about START-PROF pipe stress analysis software
Cold springing of axial expansion joints is made to increase the allowable axial displacement. It doesn't affect fixed anchor loads and stresses much because the expansion joint is much more flexible than piping.
To model the expansion axial joint cold springing, insert the node near the expansion joint and add the prestretch deformation into this node.
Below is shown the result of example model analysis without cold spring.
Example project file: ColdSpringAxialExpJoint.ctp
After we add the cold spring 23.73 * 50% = 11.86 mm after analysis we get slightly different anchor loads and expansion joint deformation 11.96 mm. The difference 11.96 - 11.87 = 0.09 mm is caused by deformations of straight pipes 1-6 and influence of friction forces. The get the exact result we can correct the cold spring value to 11.95 mm instead of 11.86 mm. It will compensate the straight pipes deformations and influence of friction forces.