Thank you for your respond stanier.
But still I am thinking about the force (the summation of the 2 force vectors parallel to pipe shown in the previous post) that is exerted at the bend.
Consider the pipeline shown on the previous figure to be a free body. The thrust force with NE direction wants to move the bend toward NE. If the pipeline is hanged by ropes from a ceiling, then the bend moves toward NE. But since it's buried and the joints are restrained, the friction between the pipeline surface and soil develops and avoids the bend to move. More thrust force then means more required restrained length. This is what AWWA addresses in its formula.
Recently, I've read an article from ASCE, pipeline 2010 written by ASCE Task Committee on Thrust Restraint Design of Buried Pipelines. It says:
"Current restrained joint design theories for different pipe materials depend on two primary forms of resistance mechanisms to resist the unbalanced thrust forces that arise at a horizontal bend, valve, tee or other similar sources of thrust in a buried pressure pipeline. The first and most commonly recognized form of resistance is from friction and adhesion resistance at the pipe-soil interface; and the second form is from passive and/or bearing resistance of the pipe against the soil surrounding the pipe."
Unified Approach to Thrust Restraint Design, JOURNAL OF TRANSPORTATION ENGINEERING, ASCE / JANUARY 2007, states:"While providing thrust-resisting supports in an above ground pipeline can resist thrust forces, resisting thrust forces in an underground pipeline is usually accomplished with thrust blocks, restrained joint systems, or
a combination of both." And:"and "As an alternative to providing thrust restraint mechanism using thrust blocks, restrained joint systems may be used. In general, the restrained joint system is a mechanical (welded or harnessed) joint providing longitudinal restraint. The objective of the thrust restraint design using a restrained joint system is to determine the length of the pipe that must be restrained on each side of the point of action of the thrust force. The primary objective of the restrained joint system design is to transmit the unbalanced forces to the surrounding soil
without over stressing the pipeline wall and without subjecting the pipeline to joint separations."
Here's a figure under "Restrained Joint System Design":
Still thinking about your explanation, I would be more than happy to see comments about this discussion from you and others since I can see many "senior" names in this post.