ASME VIII Div.1 UG29~30 extenal pressure design does not say anything about local stress. I do not feel the necessity of local stress check for it.
Do you really need to check local stress on the junction of stiffener ring and pipe wall ?
Are there any significant external loads applied on stiffener other than external pressure ? If so, you may use one of 17 equations on Roark's Formulas Table 29 with appropriate stress conception for primary and secondary loads.
However, I am not sure you will find it satisfactory. FEA is best solution

Sun Wee