DrunkEng,
Your question = How pipe shoe length is decided for pipe shoe with stopper?
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Terminology - Stopper is a very confusing term. I do not think it has a common understanding. You are meaning "Restraint". Restraints come in two basic types: Linear and Lateral.
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The Linear restraint prevents movement in the direction (longways) of the pipe run. This type of Restraint is normally called an "Anchor". An Anchor can be created at least three ways; by welding the Shoe base to the top flange of a steel pipe support or the steel Plate embedded in the top of a Concrete pipe support or by attaching steel "Clips" to the bottom of the Shoe and against the side of the pipe support.
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The Lateral restraint prevents movement in the side-to-side direction of the pipe run. This type of Restraint is normally called a "Guide".
All piping subject to Thermal Expansion (large, small, hot or cold) require consideration for the amount of expansion and the type of Shoes, Anchors and Guides.
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Shoe Length - The Shoe length you are using may be okay for your current application but do not automatically consider it okay for the next project. You seem to be using the 650mm shoe for all Shoes that is the right thing to do. It means you can have a supplier make them in mass at a cheaper price and it also helps cut costs in the field when placing them on the pipe and support because the field crew does not have to look for custom length shoes for each pipe support location.
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Shoe Placement - The placement of all shoes (at installation) should be in the center of the pipe support with the pipe at ambient temperature.
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Yes, I know this is more than you needed or wanted. However, your question is posted on a popular website and both your question and answer will be read by many others. Maybe some of these others will benefit from the little extra I have included.
Sometimes its possible to do all the right things and still get bad results