On the State of Stress in Thick Bars

Abstract

The view is now generally held that in bars containing circular holes or other discontinuities the state of stress ceases to be two-dimensional when the ratio of the radius of the hole r to the thickness of the bar t is less than unity. It is further believed that the factor of stress concentration in thick bars is materially smaller than in thin bars. This view also forms the basis for the doubts which have arisen regarding the reliability of certain theoretical work on stress concentrations produced by very small holes. In this paper results are reported from a photoelastic investigation using both elastic and frozen (see reference 4, Chapter 10) stress patterns and showing that the present point of view is erroneous. Experimental results show that no deviation from a state of plane stress can be found in bars with central circular holes when r/t is of the order of magnitude of about ¼ instead of unity. Experiments further show that the factors of stress concentration remain essentially the same in thick as in thin bars. The present work may also be taken as experimental corroboration of the theoretical value for the factor of stress concentration obtained by Neuber for a very small hole in a bar in tension or compression.