Lateral braces are usually connected to upper flanges of H-shaped beams in the moment resisting frames. Continuous braces such as folded-roof plates may restrain the lateral deformation of H-shaped beams, when they are jointed to the upper flanges of H-shaped beams. If the stress of the flange with continuous braces becomes a tensile, the rotational rigidities of the lateral braces must be increased to obtain sufficient amount of the lateral buckling strength of the beams.
Our previous research (Kimura, Yoshino and Ogawa 2012) clarified the relation between the lateral buckling strength of H-shaped beams and the demands of the lateral and rotational rigidities for continuous braces when a beam is subjected to uniform moment distribution. The elastic buckling strength of the H-shaped beams by formulating energy conservation equations was estimated, considering the lateral and torsional deformation of bracing points of beams.
Then our previous research revealed that the lateral buckling strength of H-shaped beams is effectively increased when lateral braces are attached to compressive flanges, while it is not increased when lateral braces is attached to the tensile flanges.
To consider more realistic conditions, this paper takes the effect of moment gradient along beams into account on the elastic lateral buckling strength of H-shaped beams with continuous braces.
In this paper, three groups of H-shaped beams are adopted as simulation models with a ratio of a flange width to a web depth “
b/h” of 0.33, 0.5, 0.78. Two types of loading conditions are considered: one is that the stress of upper flange become tensile (designated as Type A), and the other is that the stress of upper flange become compressive (designated as Type B), as shown fig, 3, when H-shaped beams is subjected to uniform moment.
The following procedure is adopted: First, the elastic buckling strength of the beams under moment gradient is estimated by formulating energy conservation equations, which are verified by eigenvalue analysis. Then, the effect of lateral and rotational restraint of continuous braces on the lateral buckling strength for the H-shaped beams is examined. In addition, the elasto-plastic buckling behavior of the beams is further simulated by elasto-plastic large deformation analyses.
Finally, the elasto-plastic buckling moment of the beams are evaluated according to the buckling curve provided by Recommendation for Limit State Design of Steel Structure (Architectural Institute of Japan (AIJ)) using the proposing modified equivalent slenderness ratio.
Major findings of this study can be summarized as follows:
1. The elastic lateral buckling strength for H-shaped beams restrained by continuous braces under moment gradient is obtained from Eqs. (12), (15), (19) and (22).
2. For Type A as shown Fig. 3, Eqs. (12), (15) and (19) is applicable as the elastic buckling strength for these beams. Herein, the ratio of bending moment at the ends
M2/
M1 is expressed as the symbol of
m as Fig. 3.
3. For -1.0≦
m<0.4 of Type B as shown Fig. 3, Eqs. (12) and (22) is applicable as the elastic buckling strength for these beams. For
m>0.4, the lower flange with no lateral braces are attached are buckled laterally, and this buckling mode for Type B is same as that for Type A. Therefore, the lateral buckling strength of Type B can be approximately evaluated by that of Type A.
4. The elasto-plastic buckling moment of beams under moment gradient can be sufficiently estimated by the buckling curves provided by Recommendation for Limit State Design of Steel Structure (AIJ) when the proposing modified equivalent slenderness ratio from Eq. (24) is applied.
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