Notice of RetractionShear response of a clamped beam subjected to intense dynamic loading with considering weakening effect of the shear sliding cross-section
The present paper, adopting a rigid, perfectly plastic idealization material model and a square yield locus, with the consideration of two conditions of weakening and non-weakening effects of transverse shear sliding section, analyses the shear response of a clamped beam in the initial plastic deformation stage subject to a uniformly distributed impulsive loading and the precondition of possible shear failure mode, writes the shear's movement equation, puts forward the expressions of shear velocity and shear sliding volume, finally the conclusion of the availability of different shear response model for weakening effect is drawn.
A further study of plastic shear failure of impulsively loaded clamped beams
Abstract As early as in 1973, Menkes and Opat (Exp Mech 1973; 13:480–6) conducted an experimental investigation on the dynamic plastic response and failure of fully clamped metal beams subjected to a uniformly distributed impulsive loading and identified three basic failure modes: large inelastic deformation (Mode I), tensile tearing (Mode II) and transverse shear failure at the supports (Mode III). A rigid-plastic analysis was later carried out by Jones (Trans ASME J Eng Ind 1976; 98 (B1): 131–6), in which an elementary failure criterion was adopted to estimate the threshold impulsive velocities at the onset of Mode II or Mode III failure. A deep understanding of these three basic failure modes is of fundamental importance to failure analyses of various structures under intense dynamic loading. The present paper re-examines the plastic shear failure (Mode III) of impulsively loaded clamped beams, with focus on two effects: (i) the interaction between the shear force and bending moment; and (ii) the weakening of the sliding sections during the failing process. A dimensional analysis is first performed to obtain a general form of the threshold impulsive velocity, which overlooks succeeding concrete analyses. The elementary failure criterion is then modified to incorporate the sliding sections’ weakening effect. Interaction between the shear force and the bending moment at the supporting ends is considered by using circular yield curve (Robinson, Int J Solids Struct 1973; 9:819), Hodge's curve (J Appl Mech 1957; 24:453–6), or a yield condition based on slip-line solutions. By taking into account the variation with time of the shear force and the bending moment over the failing cross-sections, the plastic deformation and failure process of the beams are traced and the ratio of plastic shear dissipation to the total plastic dissipation is thus calculated. This is followed by a discussion on a shear strain failure criterion. Finally, the predictions from various approaches are compared with each other as well as with relevant experimental results.
Double-hinge modes in the dynamic response of plastic cantilever beams subjected to step loading
Abstract In this paper, double-hinge modes are introduced to analyse the response of a stepped or bent cantilever beam subjected to step loading at its free end. The material of the beams is assumed to be rigid-perfectly plastic, and complete solutions are constructed for four cases, which are summarized in tables. An analogy is found between the responses of stepped and bent cantilevers. For the bent cantilevers, the results herein provide a replacement for the ‘unstable hinge’ solutions previously derived, which violate the yield criterion. The results obtained are also useful for estimating the effects of imperfections in beams during dynamic loading.