Blast Loading of Fully Clamped Beams with Transverse Shear Effects

A theoretical analysis is presented for a fully clamped beam made from a rigid, perfectly plastic material, which is subjected to a uniformly distributed blast loading with a magnitude that decreases with time. The influence of the transverse shear force as well as the bending moment is retained in the yield condition. It is observed that when the dimensionless transverse shear parameter v in the present paper is substituted by 2v, the dimensionless results, except for the bending moment, are the same as those obtained by Nonaka for a simply supported beam subjected to the same external loading. However, the bending moment mc(ξ), for a fully clamped beam, may be expressed in the present paper in the form mc(ξ) = 1 + 2m5(ξ), where m5(ξ)(— 1 ≤ m5 ≤ 0) is the corresponding bending moment for a simply supported beam. It is shown that the correlation parameters proposed by Youngdahl are also suitable for eliminating the effects of the pulse loading shape on the final deformations of beams when transverse shear effects are retained in the yield condition. The conditions for the onset of a transverse shear failure, which develops at the supports of beams for sufficiently severe dynamic loads, are also predicted for the various pulse shapes. It is found that the upper and lower bound estimates of a theorem for an impulsively loaded, rigid, perfectly plastic continuum bound the maximum permanent transverse displacements of the present analysis for a fully clamped beam with transverse shear effects.