Statical Hysteresis in the Flexure of Bars (Classic Reprint)

This book explores the phenomenon of hysteresis in the bending of elastic bars. Hysteresis is the energy lost when a material is subjected to a cyclic load, such as the bending of a bar. The author develops a theory of statical hysteresis, which is the hysteresis that occurs when the stress on the bar is within the proportional limit. The theory is based on the assumption that the stress-strain relationship for an elastic bar in a cyclic state is symmetrical about a straight line. The author then applies the theory to the bending of rectangular bars and shows that the energy loss due to statical hysteresis is proportional to the fourth power of the length of the bar and the third power of the maximum load. The author also shows that the ratio of the width of the hysteresis loop to the average width is independent of the length of the bar and the maximum load. The theory is verified by experiments on rectangular bars of Armco iron. The results of the experiments show that the theory is valid for small ranges of stress within the proportional limit. The significance of the findings is that they reveal the fundamental mechanisms underlying hysteresis in the bending of elastic bars.