About Utilization ratio

Hello Guys,I am calculating the deflection and stress  of simply supported beam...with the help of manual calculation formulas.To be sure I checked the same condition with the help of staad pro too.My deflection and stress matches with staad pro.But when i compare my bending stress with yeild stress of steel..i determined a ratio.Which was different from staad pro determined utilization ratio with the constant factor for different loading condition.I dont know how staad pro calculates utilization ratio....can u guys provide formula for calculating utilization ratio in manual calculation which matches to staad pro utilization ratio?