The modelling of complex steel structures under static loading using rigid perfectly plastic material is presented within the framework of second-order cone programming (SOCP). The classic upper and lower bound principles of yield analysis, naturally written as optimization problems, are formulated as a pair of dual second-order cone programs which are then solved using a state-of-the art primal-dual interior point method (IPM). The IPM shows good robustness and efficiency along with reduced computational times especially for limit analysis. The whole process is illustrated first with basic steel structures checks of fillet welds or beams under biaxial bending moment, and second with complex 3D steel assemblies. The results show good agreement with the failures modes and resistance values presented in the Eurocode and allows us to obtain a reliable estimate of the ultimate resistance within a reasonable time.