The Moment Magnifier Factor Of Biaxial Bending Beam-columns

Beams and columns of a framework are always in the axial force and biaxial bending state, although the in plane design formula had led to many successful designs, it can't describe the true state of spatial structures. In plane bending has no displacement out of the plane before achieving it's carrying capacity, it is a branch buckling;biaxial bending has two directions of displacement when the moment starts to act, it's the extreme point buckling, the twist effect must be taken into account. The current biaxial bending design formula always use the moment magnifier factor of in plane bending, which based on finite tests data, it's a semi- theoretical -semi-experience formula. In this paper theoretical and finite element analysis methodology are used to study moment magnifier factor of biaxial bending.The first study gaines the balance equation in the energy method, and has proved import part of the boundary conditions to the balance equation before solving it, does not affect the outcome. Derived displacement in three directions, the moment magnifier factor formula and the stress and shearing stress formula of arbitrary points on the cross-section.Changes in a single element method is used to find influential factors of moment magnification factor, and has proved warping rigidity has little impact on the results. Ansys analysis data proves that the theoretical method and program made by own is right, warping restrained has no significant influence on moment magnifier factor and carrying capacity.The carrying capacity and related toroidal of several models are gained whichdemonstrate M_x and L have big influence on moment magnifier factor before it'sbuckling. This paper bring forward two amended factors ζ₁, ζ₂ for the momentmagnifier factor.The research into several models of uniform biaxial bending proves uniform bending has no impact on equivalent bending moment coefficient in plane and out of plane, equivalent bending moment coefficient in plane is suitable for biaxial bending design.