THE EFFECT OF ACCELERATION TIME ON PLASTIC DEFORMATION OF BEAMS UNDER TRANSVERSE IMPACT LOADING

1954 ◽  
Author(s):  
D. S. GREEN
1956 ◽  
Vol 23 (2) ◽  
pp. 239-243
Author(s):  
M. F. Conroy

Abstract The object of this paper is to consider the plastic deformation of semi-infinite beams subject to dynamic transverse loading at the free end. The type of loading considered is that of a constant bending moment, together with a transverse force the magnitude of which is inversely proportional to the square root of time. Part 1 of the paper consists of a plastic-rigid analysis of the problem, based on the plastic-rigid analysis of infinite beams under transverse, constant velocity, impact loading developed by the author. Part 2 of the paper consists of an elastic-plastic solution of the problem, based on a theoretical analysis of the plastic deformation of infinite beams subject to transverse, constant-velocity impact loading developed by H. F. Bohnenblust. Specific problems are considered for which the deflection solutions obtained by elastic ideally plastic and rigid ideally plastic analyses are compared.


1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.


2008 ◽  
Vol 46 (7-9) ◽  
pp. 898-904 ◽  
Author(s):  
Tomonori Kaneko ◽  
Sadayuki Ujihashi ◽  
Hidetoshi Yomoda ◽  
Shusuke Inagi

1991 ◽  
Vol 33 (2) ◽  
pp. 106-110
Author(s):  
G. V. Klevtsov ◽  
N. A. Gorbatenko ◽  
A. I. Uvarov

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