New interaction formula for the plastic resistance of I- and H-sections under combinations of bending moments My,Ed, Mz,Ed and bimoment BEd

Abstract

Three approximate interaction formulae for the plastic resistance of I-shaped cross-sections under bending moment about strong axis My,Ed, bending moment about weak axis Mz,Ed and bimoment BEd were created and analyzed. An interaction formula that takes into account these three internal forces is missing in Eurocodes. For the verification of interaction formulae, the exact interaction curves were obtained by linear programming. A large parametrical study was performed for rolled profiles within size ranges IPE 100–IPE 600 and HEB 100–HEB 900. The differences between those of approximate interaction formulae and results of exact interaction curves were summarized. The results of the best interaction formula valid for three internal forces matched the results of several interaction formulae of other authors, including the formula from prEN1993-1-1:2020, valid only for two internal forces. In the worked example, details of how this interaction formula can be applied in the verification of the cross-section resistance of the beam with real dimensions were shown. The proposed interaction formula can be helpful for hand calculations when designing crane runway beams.