Asymptotic Matching Analysis of Scaling of Structural Failure Due to Softening Hinges. I: Theory

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Abstract
Propagation of a crack from the tensile face of a beam causes postpeak softening, i.e., the bending moment decreases at increasing rotation of the hinge. Examples are unreinforced concrete beams and plates, foundations plinths, retaining walls, tunnel linings, or arch dams. Softening in an inelastic hinge is also caused by compression crushing of concrete. This happens in reinforced concrete beams that are prestressed, overreinforced, retrofitted by laminates, or subjected to a large enough axial compressive force, which is typical of columns as well as frames or arches with a large enough horizontal thrust. Hinge softening may also be caused by plastic buckling of flanges in deep thin-wall steel beams. An inevitable consequence of inelastic hinge softening in statically indeterminate structures requiring more than one inelastic hinge to fail is a size effect. Although finite element solutions are possible, general analytical formulas for the size effect in such structures do not exist, because of the com...

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