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Beyond Constant Cross Sections

Mechanical parts and structural elements often have features that cause sudden changes in geometry. Under loads, these changes in geometry increase the local stress fields of the parts quite significantly, and they usually represent locations from which parts start to fail. This localization of high stresses is called stress concentration. Features such as holes, notches, shoulders, grooves, and threads that often cause this phenomenon are called stress concentrators.

Definition of Stress Concentration Factor

A dimensionless factor, known as stress concentration factor K, is used to quantify how "concentrated" the stress is. It is defined as the ratio of the highest stress in the element to the reference stress (nominal stress).

One of the most commonly used reference stress is just the (gross) stress in the same element under the same loading conditions without the stress concentrators (holes, notches, shoulders and so on). Stress concentration factor defined this way is denoted as Kg; another commonly used reference stress is the nominal stress over the cross section area at the location of the stress concentrator. Stress concentration factor defined in this fashion is called Kn.

The stress concentration factor calculators presented in this section calculate both Kg and Kn, whenever possible. One needs to extra attention as to which reference/nominal stress is used before applying these stress concentration factors. Likewise, the same is true for using formulas in failure criteria and fatigue analysis.

Calculators of Stress Concentration Factor
Slab with a pair of opposite U-shaped notches
Slab with a center hole Slab with an off-center hole
Shaft with a circumferential u-shaped groove
Shaft with shoulder fillet
Hollow square beam
Right angle beam