LittleInch, my context is pipe stress engineer in chemicals. The fittings are required to meet the pressure needs of straight pipe. So a S/Std 10" tee must meet the pressure and temperature requirements of the associated straight pipe. Based on X-ray analysis of maybe 3 or 4 piping systems...
Please remember that the tee of a given schedule is targeting a pressure rating and not a thickness. For this reason fittings are usually significantly thicker than the pipe they are attached to.
The weakest point is probably the operating case nozzle loading on the pump. In order to get the allowable, you'll need to assume some ratio of moments and forces and test them. The client's pipe stress engineer should know that the vendor reported allowables are limited by the assumption of...