EFFECT OF WARPING RESTRAINT OF BEAMS TO COLUMN JOINT ON LATERAL BUCKLING BEHAVIOR FOR H-SHAPED BEAMS WITH CONTINUOUS BRACES UNDER GRADIENT FLEXURAL MOMENT

Abstract

 Large cross-section beams are used as main beams to design structural members effectively in real large space structures. Long span beams may not possess the plastic strength due to lateral buckling, so that many lateral braces along the beams should be set up to prevent the lateral bucking deformation (AIJ 2010). Most of beams in frames are connected by continuous braces such as folded-roof plates, which are effective to prevent the lateral buckling of beams. However, in the Japanese design code, non-structural members are not considered as the braces. Kimura (2013) clarified the lateral buckling behavior for H-shaped beams with continuous braces when the boundary condition of the beams is simple support.

 On the other hands, in design standard for steel structures (AIJ 2005), the boundary condition of beams against lateral buckling is provided as simple support. Meanwhile, beams are often jointed to box-shaped columns with high torsional rigidity as shown in Fig. 1. Therefore, it is considered that beam-to-column joints have effect of warping restraint on lateral buckling for beams. Suzuki and Kimura (2000) elucidated that the lateral buckling load with the warping restraint of the column is larger than that with simple support and the torsional rigidity of box sectional columns is corresponding to warping fixed support. Furthermore, it is shown that elastic lateral buckling load for H-shaped beams with continuous braces under the uniform flexural moment are expressed as the loads between simple support and warping prevention for Kimura (2018). Actually, H-shaped beams carry the gradient flexural moment, when steel moment frames are subjected to seismic forces.

 This paper evaluates the effect of continuous braces on elastic lateral buckling load for H-shaped beams under the gradient flexural moment, considering warping and Saint-Venant torsional rigidities in energy conservation equations. In this study, two types of loading conditions are considered. The continuous braces rigidities are consisting of the lateral and the rotational rigidities as shown in Fig. 1. In the case of Type A, the lateral rigidity is effective for preventing lateral deformation of the compressive upper flange, whereas in the case of Type B, the rotational rigidity is effective for preventing torsional deformation of the beams.

 This study is conducted by the following procedures:

 1. The equations of the elastic lateral buckling load for H-shaped beams with warping restraint and continuous braces under gradient flexural moment is developed by the energy method and numerical analyses. To simplify the equations, the closed from solution of lateral buckling loads are suggested with reference to the terms of the flexural and torsional rigidities of beams and loading conditions.

 2. The elasto-plastic buckling behaviors of the beams are simulated by elasto-plastic large deformation analyses. The lower bound of the buckling stress for the beams are evaluated by the buckling curve of bending member in Recommendation for Limit State Design of Steel Structure (AIJ) with proposing modified equivalent slenderness ratio with the elastic buckling load of the beams with warping restraint and continuous braces.

 3. The upper bound of rotational stiffening moment and lateral stiffening force which continuous braces is evaluated based on the ratio of the flexural and torsional rigidities of beams, the rigidities of braces, the warping restraint ratio, and the gradient of flexural moment.