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

 In design standard for steel structures (AIJ 2005), the boundary condition of beams under lateral buckling load is provided as simple support. Meanwhile, beams are often jointed to box-shaped columns with high torsional rigidity as shown in Figure 1. Therefore, beam ends have fork restraint by high torsional rigidity of column on lateral buckling, which is considered the rotational effect between warping and fully fixed supports.

 On the other hand, long span main beams may not possess the full plastic strength due to lateral buckling, so that many lateral braces should be set up along the beams to prevent the lateral buckling deformation (AIJ 2010). When non-structural members such as folded roof plate are directly jointed to beams, they may be used as the continuous braces. However, in Japanese design code, the non-structural members are not considered as braces. Kimura, Yoshino, and Ogawa (2013) clarified the lateral buckling behavior for H-shaped beam with continuous braces when the boundary condition of the beams is simple support.

 This paper evaluates the effect of fork restraint on elastic lateral buckling load for H-shaped beams with continuous braces under the uniform flexural moment and Saint-Venant torsional rigidities in energy conservation equations. In this study, two types of loading conditions are considered, where the upper flange’s compressive load is larger than the lower flange’s one (loading condition, Type A), and where the upper flange’s compressive load is smaller than the lower flange’s one (loading condition, Type B). The continuous braces rigidity is divided into the lateral rigidity, ku, and rotational rigidity, kb, as shown in Fig. 1. In the case of Type A, lateral rigidity is effective for preventing lateral deformation of compressive upper flange, whereas in the case of Type B, rotational rigidity is effective for preventing torsional deformation. Considering fork restraint by column, elastic lateral buckling load of beams with continuous braces are expressed as the loads between warping and fully fixed support.

 This study is conducted by the following procedures:

 ・ The elastic lateral buckling load with warping and fully fixed support under flexural moment is developed by energy method, and can be calculated with Eqs. (11)~(13). Considering fork restraint by column, elastic lateral buckling load of beams with continuous braces are expressed as the loads between warping and fully fixed support. The results are verified by eigenvalue analyses.

 ・ The elasto-plastic lateral buckling behaviors of the beams are simulated by elasto-plastic large deformation analysis. The lower bound of the elasto-plastic lateral buckling stress of the beams are evaluated according to the buckling curve of bending member provided by Recommendation for Limit State Design of Steel Structure (AIJ), using proposing modified equivalent slenderness ratio.

 ・ The relationship between the total value of the stiffing force of the whole continuous braces and the maximum value was grasped. In the case of warping fixed support, the total value is about 60% of the upper bound value. Next, it decreases as the fork rigidity increases, and is about 35% in the case of fully fixed support.

 ・ The upper bound of rotational stiffening moment and lateral stiffening force of continuous braces is evaluated by Eqs. (24) and (25) based on the ratio of flexural and torsional rigidities of beams when the lateral buckling of beams with fork restraint by column occur.