Calculate the stress concentration factor (K_t) and maximum stress for a circular hole in a plate of finite width.
Stress concentration occurs when there is a sudden change in the geometry of a component, such as a hole, notch, or fillet. These features cause the internal stress to "bunch up" or concentrate, leading to much higher local stresses than the nominal stress calculated for a uniform cross-section.
The Stress Concentration Factor (K_t) is the ratio of the maximum local stress to the nominal stress. Engineers must account for this factor when designing components to prevent fatigue failure or brittle fracture, especially in materials that don't have high ductility.
Where:
• σ_max is the maximum local stress (MPa)
• K_t is the theoretical stress concentration factor
• σ_nom is the nominal stress calculated for the net cross-section (MPa)
For an infinitely wide plate with a small circular hole, the theoretical stress concentration factor is exactly 3.0. As the hole becomes larger relative to the plate width, the factor actually decreases slightly.
You can reduce stress concentration by making geometric changes more gradual. For example, using a larger fillet radius or adding 'stress-relieving' holes near a sharp corner can help distribute the stress more evenly.
K_t is the theoretical factor based on geometry. K_f is the fatigue notch factor, which accounts for the material's sensitivity to notches under cyclic loading. K_f is usually smaller than K_t.
Yes. Ductile materials like mild steel can undergo local plastic deformation at the stress concentration point, which helps redistribute the stress. Brittle materials like cast iron or ceramics are much more sensitive to stress concentration.
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