18.19:
Stress Concentrations
Stress concentration refers to the amplification of stress in a structural member near points of discontinuity, such as holes or abrupt changes in cross-section. This localized stress often exceeds the average stress within the member.
Consider a flat bar of varying widths connected by fillets. The stress distribution in such a member is independent of the member's size and the material used. It is dependent only on the ratios of geometric parameters.
In structural design, engineers must ensure the maximum stress in a section does not exceed the allowable stress under specific loads, rather than calculating the exact stress distribution.
The ratio of maximum stress and average stress in the critical section of the discontinuity is the stress-concentration factor.
Stress-concentration factors, computed from geometric ratios, help to determine maximum stress near discontinuities under given axial loads.
The process involves multiplying the average stress in the critical section by the appropriate stress concentration factor. However, this is only valid if the maximum stress does not exceed the proportional limit of the material.
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.