Your approach to designng piping is not correct. Piping wall thickness is only determined by circumferential hoop stress per your program calculation Step 1. Allowable stress is based on the Code allowable stress such as ASME B31.3 for plant piping. The thickness per Step 1 is the thickness to be used throughout the piping system and supports, etc. are placed so that the longitudinal stress also meets the allowable stress requirements. You never increase the pipe wall to accomodate for longitudinal stresses. Only in very rare cases do you increase the wall but only at very local places due to very special forces. For instance at a road crossing to protect against wheel loading you may increase wall of pipe under road. Also if you have a very heavy concentrated load that is causing very high local stresses in the pipe resting on a pipe support you will add reinforcing pads to the pipe to account for the high local wall loads.
Supports are placed such that the piping is not overstressed in the longitudinal direction considering the combmination of all loads that cause stress in the longitudinal direction. This includes the longitudinal pressure stress, weight of the pipe, contents, insulation, etc; wind loads, earthquake loads, possible loads from slug forces, etc are also included. It is customary to consider all loads acting in same direction although wind loads for instance may be acting horizontally while weight may be acting vertically. Also to protect against wind loads guide stops need to be placed on the supports to restrict horizontal movement due to the wind loads. For large diameter thin wall pipe, local stresses at pipe supports need to be considered so this will also go into setting the spacing of supports, or otherwise reinforcing pads may be needed at supports.
An analysis is done with pipe supports placed so that the longitudinal loads do not cause the allowable stress value to be exceeded. The basic allowable stress value for longitudinal loading is the same allowable for the hoop stress, except B31.3 allows 33% increase for occasional loads such as wind.
A piping flexibility analysis is performed which will determine that the longitudinal loading does not cause the allowable stress to be exceeded and to determine stresses due to thermal expansion with the code providing the allowable for thermal expansion using the basic allowable stress value for hoop stress and increasing it to a higher value as indicated in the Code. If there is no significant thermal expansion in the piping then a manual hand calculation can be performed for the longitudinal stress determination.
The piping layout is not good in any case. The piping should not have that much overhang of unsupported piping beyond the pipe supports like you have. Piping is flexible and will vibrate and cause cracking of welds or fatigue failure. There should be a support at all elbows withing a couple of feet. Just visualalize how much overhang you have with a pipe that is out in the air 10' on way and 19' the other way. Also for straight runs of piping supports should be placed to limit deflection to about 1/2" to 1" depending on pipe diameter. This is because if a pipe is sagging between supports too much it is also not stiff enough and will oscillate easy with wind loads. Standard tables for pipe support spacing are available which give maximum recommended spans of pipe supports.
