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Concept of Stress Concentration

Theoretical stress concentration factor, K t. Maximum stress at the discontinuity. Nominal stress, max stress with no discontinuity. Concept of Stress Concentration. K t is used for normal stresses and K ts for shear stresses. Concept of Stress Concentration.

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Concept of Stress Concentration

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  1. Theoretical stress concentration factor, Kt Maximum stress at the discontinuity Nominal stress, max stress with no discontinuity Concept of Stress Concentration Kt is used for normal stresses and Kts for shear stresses. Mechanical & Aerospace Engr., SJSU

  2. Concept of Stress Concentration Consider an elliptical hole in an infinitely large plate loaded in uniform tension. Using the theory of elasticity the theoretical stress concentration factor is given by the equation below. 2b 2a Elliptical hole • For a circular hole Kt = 3 • The equation can be applied to a longitudinal crack where b << a Mechanical & Aerospace Engr., SJSU

  3. Stress Concentration Factor Stress concentration factor is found using experimental methods. • Photoelasticity – a plane polarized light is passed thru a photelastic material (all transparent plastics) resulting in a colorful fringe pattern indicating the intensity of the stress. Mechanical & Aerospace Engr., SJSU

  4. Stress Concentration Factor • Brittle Coating – a specially prepared lacquers are usually applied by spraying on the actual part. After air drying, the part is subjected to stress. A pattern of small cracks appear on the surface. Data could be used to locate strain gages for precise measurement of the stress. The method is sensitive to temperature and humidity. Mechanical & Aerospace Engr., SJSU

  5. Stress Concentration Factor • Electrical strain gauges The method is the most popular and widely accepted for strain measurements and stress analysis. The strain gauge consists of a grid of strain-sensitive metal foil bonded to a plastic backing material. When the gauge is subjected to a mechanical deformation, its electrical resistance changes proportionally. The change in voltage is converted to strain and the stress is calculated from the strain. Mechanical & Aerospace Engr., SJSU

  6. Stress Concentration Factor • Finite Element method • The CAD model is subdivided into many small pieces of simple shapes called elements. • FEA program writes the equations governing the behavior of each element taking into consideration its connectivity to other elements. • These equations relate the unknowns, for example displacements in stress analysis, to known material properties, restraints and loads. • The program assembles the equations into a large set of simultaneous algebraic equations (thousands or even millions). • These equations are then solved by the program to obtain the stress distribution for the entire model. Mechanical & Aerospace Engr., SJSU

  7. Stress Concentration Factor Mechanical & Aerospace Engr., SJSU

  8. Stress Concentration Factor Round section with a fillet Mechanical & Aerospace Engr., SJSU

  9. Stress Concentration Factor Flat plate with a hole Mechanical & Aerospace Engr., SJSU

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