Impact Stresses in a Freely Supported Beam

Abstract

The paper reviews various theories used in estimating impact effects on a freely supported beam, and points out the error which may be introduced if the assumption is made that elastic forms are similar under dynamic and static loading.An apparatus is described, in which the beam is a railway rail of 8 feet span, subjected to central impacts, strain measurements being made along the flange by means of small scratch-extensometers. An analysis of records from these instruments gives an indication of the instantaneous bending moment distribution occurring at time intervals of 1/1,000 second during impact, and the bending stresses are shown to be approximately 20 per cent greater than those calculated by assuming “statical equivalence”.The variation of load between weight and beam during impact is recorded by the vertical strain of the rail web under the load, and a complete series of records for various weights and velocities is given. These records demonstrate the occurrence of “sub-impacts”, the weight in certain cases striking the rail five times under what the human eye observes as a single impact. Diagrams of results obtained by calculation from an equation derived by Timoshenko show agreement in form with the load variations recorded by the scratch extensometers. Results obtained by measurement from the area of the ellipse of contact are also given, and loads—obtained by four independent methods—are drawn to a base of impact velocity for various weights. The experimental results are shown in all cases to be at least 2½ times those predicted by the assumption of “statical equivalence”, and (allowing for calibration difficulties) are in fair agreement with those obtained from the Timoshenko equation. Mention is made of the practical significance of the results.