# Stress Concentrations

JoVE Core
Mechanical Engineering
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JoVE Core Mechanical Engineering
Stress Concentrations

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The equation for stress for a member under pure bending having a plane of symmetry and a uniform cross-section assumes that the stress is evenly distributed across the entire cross-sectional area. However, in real-world applications, the cross-section of a member may vary, or it may have geometric irregularities, such as a flat bar with grooves. In such cases, the maximum stress is expressed using the stress concentration factor. The stress concentration factor is the ratio of the maximum stress to the nominal stress. The maximum stress is the highest stress present at the discontinuity, and the nominal stress is the stress calculated using the composite cross-section. Consider a plate with a U-shaped notch under bending stress. For this scenario, the stress concentration factor increases as the geometry of the notch becomes more pronounced. For a round bar with a circular hole subjected to pure bending, the stress concentration factor is calculated using the ratio of the diameter of the hole to the diameter of the round bar.

## 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.