Influence of upper flange restraint condition on lateral buckling behavior of H-Shaped beam

Abstract

The stiffening effect on the lateral buckling caused by attaching a restraint member such as slab and purlin members to an upper flange of an H-shaped beam is widely known. This stiffening effect occurs not only when the upper flange is the compression side but also when the upper flange is the tensile side, even though to a smaller extent. Considering that the floor slab is attached to the upper flange, the restraint conditions can be considered close to completely restrained. However, depending on the combination between the floor slab and beam cross-section, the upper flange restraint conditions cannot be considered completely restrained. In this study, first, we conducted a comparative analysis between a model that the rotational restraint of the slab is caused by bending resistance and another model that it is caused by torsional resistance, followed by an analysis considering the effect of both. Then, we considered that the rotational restraint is caused by the bending resistance alone and determined how the dimension of rotational restraint influences the buckling strength by conducting a theoretical analysis based on an energy method. When doing so, we summarized it by using a cross-sectional shape index and clarified the relationship between strength increase due to restraint and cross-sectional shape. We also proposed a method to calculate the elastic lateral buckling strength that considers the dimension of the restraint. In addition, we expressed the conditions to achieve complete restraint in terms of the bending stiffness ratio of the slab and web and compared with a realistic bending stiffness ratio of the slab and web. Lastly, we conducted a FEM analysis to determine the stiffening forces that occur in the upper flange. As a result, the following conclusions were obtained: 1) We verified that when the restraint effect caused by both the bending and torsion resistances of the slab is considered, achieving complete restraint is easy compared with when these are considered individually However, the results also showed no significant difference when either of them was considered individually 2) The strength increase caused by the horizontal displacement complete restraint alone can be explained by the cross-sectional shape index R. The strength increases caused by the effect of both the horizontal displacement complete restraint and rotational restraint can be explained by the cross-sectional shape index TS. 3) The decrease rate d of the elastic buckling strength can be explained based on the dimension of the rotational restraint and TS. The elastic lateral buckling strength that considers the dimension of the restraint can be calculated using the elastic lateral buckling strength of complete restraint and the decrease rate d Using the proposed elastic buckling strength, it is possible to evaluate the plastic deformation capacity using a method similar to that of complete restraint. 4) When relying on the bending resistance of the slab, if the bending rigidity ratio of the slab to beam is 10 or higher, it is possible to secure a strength of 95% of the elastic lateral buckling of complete restraint. By using cross-sections with a narrow and medium width as established by JIS and with constant external dimensions, this condition is satisfied in around 75% when the slab thickness is 150mm; this condition is satisfied for almost all when the slab thickness is 200mm. 5) Until the plastic deformation capacity of a beam is satisfied, the dimension of the stiffening force that occur in the upper flange has a correlation with the plastic deformation capacity and therefore, it can be explained using a general slenderness ratio. Further, the maximum value of the stiffening force can be evaluated using a simple approximate equation.