Stress Concentration (2)

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Concept of Stress ConcentrationTheoretical stress concentration factor, Kt

Maximum stress at the discontinuity

Nominal stress, max stress with no discontinuity

Kt is used for normal stresses and Kts for shear stresses.

Stress ConcentrationUniform nominal Stress

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Concept of Stress ConcentrationTheoretical stress concentration factor, Kt

Maximum stress at the discontinuity

Nominal stress, max stress with no discontinuity

tdWP

K

0

0

max

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Stress Concentration for simple geometryIt is possible by using Theory of Elasticity 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.

Elliptical hole

2b

2a

• For a circular hole Kt = 3

• The equation can be applied to a longitudinal crack where b << a

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Stress Concentration FactorStress 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.

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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.

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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.

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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.

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Stress Concentration Factor

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Stress Concentration Factor

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Stress Concentration Factor

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Stress Concentration Factor

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Stress Concentration Factor

Example - 1A Flat plate subjected to a tensile force of 5 KN is shown I fig. The plate material is gray cast iron FG 200 and the factor of safety is 2.5, Determine the thickness of the plate.

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A Non rotating shaft supporting a load of 2.5 KN is shown I fig. The shaft is made of brittle material with an ultimate tensile strength of 300 N/mm2 and the factor of safety is 3. Determine the dimensions of the shaft.

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Example - 2

Methods of Reducing Stress Concentration

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Guidelines for design.Abrupt changes in cross-section should be avoided.

Fillet radii or stress-relieving groove should be provided.

Fig. 11.3(d)

Slot and grooves should be provided with generous run-out radii and with fillet

radii in all corners. Fig. 11.3(b)

Stress relieving grooves or undercut should be provided at the end of threads

and splines. Fig. 11.3(c)

Sharp internal corners and external edges should be avoided

Weakening features like bolt and oil holes, identification marks, and part

number should not be located in highly stressed areas.

Weakening features should be staggered to avoid the addition of their stress

concentration effects, Fig. 11.3(d)

Stress Concentration

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PhotoelasticityCircular Polariscope

Polarizing plates

Model

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Finite Element Analysis701.1

20903556

ave

max

K

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Stress concentration due to hole

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