Second-order analysis of plane steel structures using Rankine-Merchant-Wood approach

Plastic analysis of plane steel structures can be conducted for the first order as well as for the second order. The Rankine-Merchant-Wood approach used for the second-order has revealed the importance of the λe/λc ratio (λc being the collapse load factor of simple plastic analysis and λe being the elastic buckling load factor). The field of application, unfortunately, is restricted to a range of values of this ratio. The novelty of the present research makes the Rankine-Merchant-Wood approach applicable for steel frame structures independently of the λe/λc ratio values and without limitation. Thus, λc is replaced by a collapse factor load λM-P which takes into consideration the moment-axial load interaction (M-P). The yield surface method, the initial geometric imperfections, and the residual stresses are taken into consideration. A numerical program has been developed in Matlab language based on the finite element method and the elastic–plastic hinge method. The present approach has been validated for three types of frames, two of them being those of Vogel and one of Chen. The results obtained have been found very close to those of these authors. Thus, the numerical program developed may be considered sufficiently efficient and reliable for this type of analysis.