18.19: Stress Concentrations
Stress concentration is when stress intensifies near discontinuities such as holes or abrupt cross-sectional changes in a structural member. This localized stress can often surpass the average stress within the member. The stress distribution in flat bars, either with a circular hole or varying widths connected by fillets, can be determined experimentally using a photoelastic method. The results are based on ratios of geometric parameters like the ratio of the hole's radius to the smaller width in the case of a circular hole and the ratios of the hole's radius to the smaller width and the larger width to the smaller width for fillets.
The structural design aims not to map the exact stress distribution but to ensure that the maximum stress in a given section does not exceed the allowable stress under specific loads with a stress concentration factor. This factor, defined as the ratio between the maximum and the average stresses in the critical section, helps determine the maximum stress near a discontinuity under a given axial load. However, it is important to note that this method is only valid if the maximum stress does not exceed the material's proportional limit because the stress-concentration factors are determined by assuming a linear relationship between stress and strain.
