Ok, not sure I should open a new thread (because my post is rather focused on the cold spring) but I try to continue here.

I would like to propose you an exercise.

Let's say a contractor erected a piping system 4"-Std, A53B, CA=0(!) with just 2 anchors, 2 vertical legs (3000mm, 2000 mm) and 2 horizontal legs (5000mm and 3500mm) described as bellow.
100 (anchor)- 200 (bend), 3000 mm up
200- 300 by x=4500m, 300-400 (bend) by x=500 mm
400-500 (bend), 2000 mm up
500-600 (anchor) by x=3500 mm
The above description is the weightless theoretical shape or "as design" shape. The Contractor build it up in shop without any geometrical error. Of course when they erected the system, its shape became "as build shape". The system is deformed under the gravity load.
In node 300, the deflection under gravity is theoretically 10.5 mm and the value is sensitive to the actual capacity of anchors to restrain the rotations. The piping system would be considered as poor sustained vs. common practice, however cannot be classified as out of Code in Sustain case, unless other troubles are foreseen. But this is a "no flow" line, inside located and stayed in place for 6 months with "exactly" 10.5 mm deflection in node 300.


1. A very late inspection revealed the situation and the decision was to place a rest in node 300. A structural beam was available around, it is enough space to use a hydraulic jack, to lift the pipe up in node 300, install the rest and carefully release the jack. The piping rest now on a support as it was better to be from the beginning i.e on the "as designed" geometry. They modified the "as build" shape and now, in node 300, the deflection vs "as designed" shape is zero. But fact is that deformed the old "as-build" system with 10.5 mm in node 300.

2. The theoretical analysis shows that rest load in 300 is a vertical force of 1005 N for Sus case. That means that applying a force of 1005 N reduces to zero the deflection of "as built" shape in node 300. In fact they already applied that force because the hydraulic jack provides a force; the deflection of 10.5 mm is the result of the force applied to allow support installation.

3. The line is used once per year for a special procedure handling hot gas, low pressure. Instead to put a rest in 300 I would prefer to place there a spring support. It may be one with cold load of exactly 1005 N and everybody will start saying that it is not a good procedure. I shall use "the good procedure" that indicates to put there a spring support of 960 N as cold load. When install it, this result in a down deflection of 0.5 mm vs "as designed", but to install it I have to jack up the system with about 10 mm in node 300. And, I repeat, do not be focused on what will happen in hot case, it was analyzed and everything is OK.

4. The Contractor was stupid or clever (the matter is still under debate) and decided to choose a spring support with cold load of 900 N, with different size vs point 3. They can do some structural changes there and they planned to jack the system up to place it. But they purchased one of 1100 N cold load of different size and jack it up there. Let say in both cases the hot analyze still looks well- do not be focused on the details.


5. Let say they purchased the support of case 3 but they succeeded to adjust it (non-recommended by Manufacturer) to 1050 N. They use the same procedure to install it, i.e. jack the pipe up by about 12 mm.

I would like to know in which case of this stupid exercise I introduced the cold spring and how to count it.

The point of this example is that the magnitude of deflection under gravity in absence of the support is greater than the "adjustments" operated by changing "cold load" and to install the support I have to reverse the gravity deflection by applying forces in the elastic system.

Thanks.