In doing a analysis for which the supports are to be taken from the
existing towers. we found one tower foundation where i considered axial restraint is failing due to the more Pipe axial force. There is no provision to put up a new tower next to that one.

I tried out all the possibilities but axial restraint is must in that
location.

I have put up a small vertical loop between the two axial restraints
located at a distance of 110M. The pipe size is 2000 Dia.

For understanding please see below,

Location
1. DX(Horizontal) - 24000 mm (Axail restraint)
2. DX - 24000 mm +Y restraint
Bend
3. DY(Vetical) - -7000 mm
Bend
4. DX - 13000 mm
Bend
5. +DY - +7000 mm
Bend
6. DX -24000 mm
7. DX -6000 mm
8. DX -80mm (Cold Spring)
9. DX - 17920 (Axial Restraint)

The axial force at location 9 is too high, if i introduce a cold pull
at location between 6 to 9 of 80mm the loads at location 9 is resonably low.

The allowed cold pull is only 2/3rd of the total displacement.

The total displacement means is it between Location 1 to 9 or 6 to 9.

Kindly help me.

If you are talking about the Code's 2/3 limit to cold pull - that's 2/3's of the actual cold pull. If you are planning to install an 80mm pull, you analyze using 53.3mm.

Appendix P takes this one step further and has you look at both 2/3 and 4/3.

These extremes are checked because it's a hard thing to get right in the field.

These checks are for load, not for stress range. Cold pull does not affect stress range.

In my case, i have two operating conditions, one at 300 deg.C & another at 150deg.C.

How to arrive Cold spring in this situation ?. If i take 150 deg.C, the 80mm cold pull considered is around 2times the actual movement.

But in the both the case, if i consider 80mm cold pull, the loads are resonably low.

Is it correct ?

The cut short (CS) element as used in CAESAR II is the gap (or overlap) that will exist in the field when the system is assembled. You decide what that will be. You will use the same CS length for all load cases, 150C and 300C.

The Code says use 2/3 of actual CS in the analysis.

It's up to you to decide how much to pull your system.