Can anyone direct me to a good discussion on the difference between the algebraic combination method and the scalar? Perhaps something that explains in specific mathematical terms what is going on, when, and why?I've read the User Guide (pages 6-23 and 6-24) and I understand that algebraic combines vectorially. But the scalar is confusing me. Here's the way I interpret what is being said about scalar: if you have a vector v magnitude at angle y and another vector x magnitude at angle z, the result after combining by the scalar method is a scalar of magnitude v+x? Or is the method only used for sets of information that are in the same direction?

I believe this subject was discussed before. I remember offering an illustration to distinguish between algebraic and scalar. (I think it might make more sense if we would call it vector and scalar instead.)
Normally, scalar summation has little use in structural evaluation of piping systems. But Code rules dictate that the stresses due to sustained loads and the stresses due to occasional loads be evaluated. We interpret that to mean that we sum these stresses rather than combine (signed) loads to calculate a total stress. Combining (unsigned) stresses requires the scalar form in CAESAR II speak.

I agree that using the term vector in lieu of algebraic would be helpful. If I can re-iterate what you've said in my terms (and see if you agree) - perhaps the scalar method's sole use is in determining the sustained and occasional stresses. This seems to be a consequence of the fact that these stresses are all longitudinal (that is - along the same line as the centerline of the pipe) and arise from bending (due to weight, wind, etc.) and pressure?

Go Phils.

OK. I'll go with that. But...
Many occasional loads are random - one time to the left and the next time to the right. Adding (unsigned) stresses will accommodate this observation.
On your "longitudinal" point - Code Case 178 offers an equation for longitudinal stress due to sustained loads and it includes the torsion term so the stress calculations are losing a purely longitudinal look.
As general analysis capabilities improve, the slide rule approximations of the Code appear dated. But I still have to admire the Code's ability to assure safe piping installations.

Dave - Thanks for your help.