Stress Concentration Factor (Kt)

Last Updated: August 26, 2019

Definition - What does Stress Concentration Factor (Kt) mean?

A stress concentration factor (Kt) is a dimensionless factor that is used to quantify how concentrated the stress is in a material. It is defined as the ratio of the highest stress in the element to the reference stress.

Stress concentration factor (Kt) formula

Reference stress is the total stress within an element under the same loading conditions without the stress concentrators, meaning the total stress on the material where the material is free from holes, cuts, shoulders or narrow passes.

A stress concentration is often called a stress raiser or stress riser.

Corrosionpedia explains Stress Concentration Factor (Kt)

Basic stress analysis calculations assume that the components are smooth, have a uniform section and no irregularities. In practice, virtually all engineering components have at least minimal changes in section and/or shape.

Shoulders on shafts, oil holes, key ways and screw threads all can change the stress distribution so that the basic stress analysis equations no longer apply (as shown in the figure below.) Such discontinuities cause a local increase of stress, referred to as a stress concentration factor.

Abrupt change stress flow lines example

If the material is flawless and has no discontinuity, then the stress concentration factor is "1". If there is great discontinuity, then the stress factor is greater than "1".

Determination of Kt value:

The stress-concentration factor associated with a specific geometry and loading condition of a part can be derived through experimentation, analysis or computational methods.

  • Experimental methods: Optical methods, such as photoelasticity, are very dependable and widely used for experimentally determining the stress concentration at a point on a part. However, several alternative methods that have been used historically include the grid method, brittle coating, brittle model and strain gauge.
  • Analytical methods: The theory of elasticity can be used to analyze certain geometrical shapes to calculate stress-concentration factors.
  • Computational methods: Finite-element techniques provide a powerful and inexpensive computational method of assessing stress-concentration factors.

Characteristics of a stress-concentration factor:

  • Function of the geometry or shape of the part, but not its size or material.
  • Function of the type of loading applied to the part (axial, bending or torsional).
  • Function of the specific geometric stress raiser in the part (such as fillet radius, notch or hole).
  • Always defined with respect to a particular nominal stress.
  • Typically assumes a linear elastic, homogeneous, isotropic material.

Methods of reducing a stress-concentration factor:

A number of methods are available to reduce a stress concentration factor in machine parts, including:

  • Providing a fillet radius so that the cross-section may change gradually.
  • Using an elliptical fillet.
  • Using a number of small notches rather than a long one, if a notch is unavoidable.
  • Using narrow notches rather than wide notches, if a projection is unavoidable.
  • Using stress-relieving grooves.
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