The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

Abstract

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

Shear and bending response of a rigid-plastic beam subjected to impulsive loading

“…The influence of the rotatory inertia and transverse shear forces on the dynamic plastic response of rigid-plastic beams has been examined by Jones and de Oliveira [10,11]. Jones [12] has…”

Hollow and concrete filled steel hollow sections under transverse impact loads

“…It was shown by Liu Jones [8], Shen and Jones [9] and Wen et al [10] that transverse shear effects must also be considered in beam impact problems, however Jones [11], Liu and Jones [8] and Shen and Jones [9] showed that the influence of the transverse shear force is not particularly important for impacts at the mid-span, while there is a strong influence when the impact is close to a support. Jones and de Oliveira [12], de Oliveira [13], Liu and Jones [10] and Wen et al [10] considered square bending moment-transverse shear (M-Q) interaction curves, and Nonaka [5] and Shen and Jones [9] studied the more general case where plastic flow is controlled by the simultaneous influence of bending moment, membrane force and transverse shear. Strain-rate sensitivity of the material was considered in [1,5,7,9,10] and strain hardening in [10].…”

Post-failure behaviour of impulsively loaded circular plates

“…In fact, Eqs. (11) and (12) give or M r ¼ M 0 at n ¼ 3=2 and r ¼ 0. Thus, for nZ3=2, it is likely that a plastic hinge would form at the plate centre, as shown in Fig.…”

“…The kinematic admissibility of the velocity field used in the present solution has been analysed elsewhere [3], as has the static admissibility for the case when the plate does not fail at the supports [11].…”