Stress Distribution
Mathematical framework used to describe the nonuniform distribution of longitudinal stress across the width of a flange or the interface of a fiber and matrix. Applying shear lag theory allows engineers to account for the way stress builds up from the ends of a reinforcement toward its center through shear forces. This approach is fundamental in predicting the load carrying capacity of short fiber composites and wide flange beams.
Analytical Model
Differential equations relate the axial force in the stiffener to the shear strain in the surrounding medium. Under shear lag theory, the assumption of plane sections remaining plane is discarded in favor of a model that captures the warping of the cross section. The results show that the fibers near the point of load application carry less stress than those further along the length where the shear transfer is complete.
Composite Mechanics
Evaluating the aspect ratio and the ratio of elastic moduli determines the efficiency of the reinforcement. If the fibers are too short, shear lag theory predicts that they will never reach their full tensile potential, leading to a composite that is weaker than the sum of its parts. This data determines the critical fiber length required for effective stiffening.
Structural Application
Wide bridge decks and aircraft wing skins often exhibit this phenomenon. Shear lag theory helps in sizing the stiffeners and skin thickness to prevent localized buckling or premature yielding in areas where the stress is most concentrated.
