Effect of lateral-rotational restraint by continuous braces on lateral buckling strength for H-shaped beams with gradient flexural moment and compressive axial force

When steel moment frames are subjected to seismic forces, H-shaped beams carry the gradient flexural moment. 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 1998). 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. On the other hands, there have been many moment resisting frames with dampers to prevent damages of mam frames recently, and then H-shaped beams connected with dampers are subjected to compressive axial forces in addition to gradient flexural moment. If the beam carries the large axial force induced by the damper during earthquake, the lateral-torsional buckling behavior of H-shaped beambecomes more unstable than that under flexural moment only. The axial force which the beams carry is possible to exceed 30% of yield load of the beam. Therefore, in this paper, the lateral buckling behavior for H-shaped beams with continuous braces under gradient flexural moment and compressive axial force is clarified and elasto-plastic lateral buckling stress of the beams or lateral stiffing force and rotational stiffing moment of continuous braces are evaluated by the energy method and numerical analyses. In this study, for H-shaped beams with continuous braces subjected to gradient flexural moment and compressive axial force, two types of loading conditions and two types of bracing rigidities are considered. One of the loading conditions, which is called as Type A, is the case that the upper flange's compressive load is larger than the lower flange's one in the left side of beam as shown in Fig.3(a), and another, which is called as Type B, is that the upper flange's compressive load is smaller than the lower flange's one in the left side of beam as shown in Fig.3(b). Furthermore, the ratio of the compressive axial force, P2 to Pi is represented as an axial force ratio p' in equation of elastic lateral buckling load. The continuous braces are divided into the lateral braces, ku, and rotational braces, kp, as shown in Fig.l. In the case of TypeA, k. is effective for preventing lateral deformation of compressive upper flange, whereas in the case of TypeB, fy, is effective for preventing torsional deformation. This study is conducted by the following procedures: 1. The equations of lateral buckling loads of H-shaped beams with continuous braces under gradient flexural moment and compressive axial force are derived by energy method. To simplify the equations by energy method, the new equations of lateral budding loads are suggested with reference to the terms of the flexural and torsional rigidities of beams, the rigidities of braces, and condition of the loads. 2. The elasto-plastic budding behaviors of the beams are simulated by elasto-plastic large deformation analysis. The lower bound of the elasto-plastic buckling stress of the beams can be evaluated with the interpolated buckling curve between those of bending member and compression member, which are provided by Recommendation for Limit State Design of Steel Structure (AIJ), depending on the axial force ratio. 3. The upper bound of moment and lateral force which continuous braces carry at the lateral buckling of beams is evaluated based on the ratio of the flexural and torsional rigidities of beams, the rigidities of braces, the axial force ratio, and the gradient of flexural moment.