which theory of failure does WRC 297 applies?
i am not able to understand why we compare
2*Max Shear Stress with 3*Sy,
Sy is yield strength.
where can i find these equations?

Refer to Div. 2 criterion for combination of stresses.

The local bending around the nozzle is classified as secondary hence it is compared to 3 * Saverage and not 3 * Sy (as you wrote in your post).