Second Order Effect in Unbraced Steel Frames at Ultimate State

Abstract

Second order effect is evaluated for unbraced frames at ultimate state. As a case study, an unbraced one bay frame is evaluated using first order elastic, second order elastic, first order plastic and second order plastic analyses. Second order plastic analysis is based on proposed procedures using magnification factor as its basis. These procedures take the effect of formation of plastic hinges and in turn, the softening of the frame on the critical load (buckling load) of the frame into consideration. It has been found by second order plastic analysis that frame strength dramatically deteriorates after formation of the second plastic hinge. While first order plastic analysis puts the strength on the ascending branch, second order analysis puts the strength on the descending branch of load-deformation curve regardless of the level of axial load in the system. It has also been found that while full mechanism failure develops under low levels of axial load, it cannot develop under moderate and high levels of axial loads. Furthermore, it has been found that the strength deteriorate rapidly after formation of the second plastic hinge leads to early collapse before the development of full failure mechanism. The codes are challenged to produce practical procedures for second order effect to account for structure behavior at ultimate state.