You mean for a 254x102x22 UB?Not withstanding the buckling note, thats interesting as I did a quick check using the Blue Book and depending what roof span and loads were taken there seemed to be a possibility that it could suffice. As a matter of interest what loading did you take for the span.
I took half of a 3.5m span (guess) at 0.80kN/m2 Dead and 0.75 Live (for the roof), and 0.9m of cavity wall, on a 7.5m span
Based on that, the deflection of the 254x102x22 beam under dead and live load is 44,5mm. Live load deflection is within limits of span / 360, but 44.5mm combined seems a bit excessive??
The buckling resistance moment is 11.7kNm while the actual bending moment is 63.7kNm. Fully restrained (which it isn't) the capacity of the beam is 91.9kNm.
I'm not actually sure the beam has been designed at all, but maybe the "engineer" checked it as fully restrained and for live load deflection only...