Definition of Flange Compactness for I-Beams that are Subjected to Combined Primary Bending and Torsion or Lateral Flexure

Abstract

I-shaped flexural members can be subjected to significant lateral forces or torsion combined with major axis bending. This condition commonly occurs with bridge girders that are skewed or curved in plan. Within an elastic range of loading, vector addition of minor axis bending stress or warping normal stress with major axis bending normal stresses results in a linearly varying stress gradient across the flange, which causes a reduction in major axis bending moment at which a slender flange plate buckles. Under combined major axis bending and lateral flange bending, yielding initiates from one edge of the flange and propagates towards the web, which results in the need for compactness and strength definitions that consider the interaction of major-axis and lateral-flange moments. This paper presents a definition of flange strength and slenderness based upon theoretical and analytical models that consider the effect of lateral bending or warping stresses. The effect of stress gradient on elastic flange buckling is quantified using a Galerkin series solution that considers the full width of the flange plate with a variable rotational stiffness along the center of the plate. The coupling of stress gradient and centerline rotation resistance is demonstrated and it is shown that the full flange width must be considered for evaluating buckling capacity of flanges in which the stress varies across the plate. The solution is then used to define the transition point between non-compact and slender flanges subjected to stress gradient. The strength of compact flanges is defined by considering the portion of the plastic flange that is available to resist the vertical moment. Finite element analyses are used to demonstrate the accuracy and applicability of the solution.