Flexural-Torsional Capacity of Beam-Columns Beam-Columns with Box Section

A theoretical study is carried out for the flexural-torsional buckling capacity of beam-columns with box-section. The main works and developments are as follows: 1) Comparisons are carried out between the formulae used in the codes of GB50017-2017, AISC LRFD 2016, Eurocode 3 part 1-1 and the formulae derived in the flexural-torsional theory, possible improvements are pointed out. 2) As the first step of the development, plastic interactive relations are obtained for the axial force and bending moments about the strong axis and about the weak axis respectively. Fitting curves with good accuracy are provided for interaction equations of axial force-bending moments about the strong axis and about the weak axis. For the general cases of axial force and biaxial bending moments, exact analysis is carried out for the state of spatial plastic hinges and an approximate interactive equation for biaxial bending under a given axial force is also proposed. The effect of bi-moment is incorporated into the proposed equation. 3) Second-order analysis is carried out for the beam-columns with initial deflection and initial twisting, after introducing a specific relation between the initial deflection and initial twisting, simple expressions are obtained for the lateral displacement, twisting angle, lateral bending moments and bi-moments. 4) Based on the well-accepted and codified column strength reduction factor, the equivalent initial out-of-plane deflections are obtained by taking the buckling strength of the column about the weak axis as a plastic hinge state under the axial force and the amplified bending moment due to the second order effect and initial deflection, this equivalent initial deflection includes the effect of residual stress, initial deflection and the additional deflection increment due to plasticity development. 5) Introducing this equivalent initial deflection into the second-order bending moment about the weak axis and into the bi-moment, together with the second-order in-plane bending moment, they are substituted into the spatial interactive equation of the axial force and biaxial bending moments, the interactive equation of beam-column is derived for flexural-torsional buckling. But this is an upper bound solution of the interactive equation because the process of elastic-plastic development has not been included. After amplifying the second order in-plane bending moment, and further amplifying the out-of-plane bending moments and bi-moment to consider the elastic-plastic development, the obtained equation is applicable. A series of curves are provided to show the interaction curves, the curves are close to the interactive relation of strength when the slenderness is small, and the curves are close to the interactive relation for elastic flexural-torsional buckling when the slenderness is increased, and over it when the slenderness is further increased. The paper proposes also a new formula based on the observation of the derived curves. 6) Comparison shows that the in-plane and out-of-plane stability formluae in the current national code GB 50017—2107 govern safety of the beam-columns together, in the case that the out-of-plane formula is on the unsafe side, the in-plane formula will provide the safety.