Flexural-Torsional Buckling of Concrete-Filled Multicellular Steel Tube Walls

Concrete-filled multicellular steel tube walls(CFT-walls) are a newly-developed lateral-force-resisting member in China, it begins with a cold-formed rectangular box, and then added by a series of cold-formed lipped wide-flange U-section in a direction to form a multicellular steel tube wall, concrete is filled-in-situ to form a multicellular CFT-wall.The current equation used in the design of CFT-walls for flexural-torsional buckling is from steel box column, detailed study is lack. This paper presents a study on the flexural-torsional buckling of CFT-walls under axial force and in-plane bending moment, the main works are as follows:1)As the first step of the development, plastic interactive relations are derived for the axial force and bending moments about the strong axis and about the weak axis respectively. When the CFT-walls are degenerated into a sandwich cross-section with two face steel plates and a concrete mid-layer, explicit expressions are obtained for these two interactive relations. Based on these expressions, fitting curves with good accuracy are provided for them. 2)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)Based on the 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. 4)Second-order analysis is carried out for the walls 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. 5)Flexural-torsional buckling of CFT-walls under pure bending is also studied, it is found that as the slenderness for flexural buckling about the weak axis is 1.6, the slenderness for flexural-torsional buckling of the CFT-walls under pure bending is less than 0.5, and the buckling capacity is very close to the plastic bending moment. 6)Introducing the equivalent initial deflection and initial twisting 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, an interactive equation for flexural-torsional buckling of walls is derived. But this is an upper bound solution of the interactive equation because the process of elastic-plastic development has not been included. To achieve the load-carrying capacity of the CFT-walls in reasonable safety, the second-order in-plane bending moment, and further the out-of-plane bending moments and bi-moment must be amplified to consider the elastic-plastic development. 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 higher when the slenderness is increased. The curves are close to the interactive relation for elastic flexural-torsional buckling when the flexural-torsional slenderness is about 2.5. Based on the observation of the derived curves, 3 sets of formulas with different simplicity are proposed, and may be applied on individual preference for simplicity.