20.8 : Stress Concentrations

The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.

The stress concentration factor quantifies the increase in stress at points of discontinuity. It is the ratio of the maximum stress at the discontinuity to the nominal stress calculated for the uniform cross-section. This factor is essential in design engineering to ensure that structures can withstand stresses without failing, especially at points where stress is amplified due to geometrical irregularities.

For example, in a plate with a U-shaped notch under bending stress, the stress concentration factor increases with the sharpness of the notch geometry. Similarly, for a round bar with a circular hole subjected to pure bending, the stress concentration factor depends on the ratio of the hole's diameter to the bar's diameter. This relationship illustrates that as the diameter of the hole increases relative to the diameter of the bar, the stress concentration factor increases.