Elastic bending moment and shear force limit states of steel bridge plate girders considering fatigue crack growth

The passage of vehicular traffic over short-span steel highway bridges generates cumulative fatigue damage within the supporting plate girders. Over time, fatigue crack growth may lead to the untimely occurrence of elastic limit states which may cause a bridge to become structurally deficient or even collapse. It may be useful for structural engineers to be able to design or otherwise modify plate girders for presumed through-thickness fatigue crack configurations so that the premature occurrence of elastic limit states may be averted. The objective of this research was to develop theoretical expressions for the residual bending moment and shear force strengths of I-shaped, transversely stiffened, steel plate girders corresponding to various elastic limit states. Several through-thickness fatigue crack configurations were considered. The formulation of the expressions employed various theories from solid mechanics including elasticity theory, linear elastic fracture mechanics, classical plate theory, and the principle of stationary potential energy. Finite element analyses were then conducted to validate the formulated expressions. The correspondence between the analytical and numerical results was generally in good agreement. Plots of the formulated and validated expressions as functions of crack length and load cycle demonstrated that various elastic limit states influence the overall residual strength of a fatigue-cracked plate girder at varying scales; certain limit states may be neglected in favor of more detrimental limit states. A design procedure for modifying the initial design of a plate girder for prescribed fatigue crack configurations was finally developed and demonstrated by employing the newly formulated and validated expressions.