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Stress ConcentrationAnkush SharmaIn developing a machine it is impossible to avoid changes in cross-section, holes, notches, shoulders etc. Some examples are shown

Any such discontinuity in a member affects the stress distribution in the neighbourhood and the discontinuity acts as a stress raiser.

Consider a plate with a centrally located hole and the plate is subjected to uniform tensile load at the ends.

Stress distribution at a section A-A passing through the hole and another section BB away from the hole are shown in fig.

Stress distribution away from the hole is uniform but at AA there is a sharp rise in stress in the vicinity of the hole.Whenever a machine component changes the shape of its cross-section, the simple stress distribution no longer holds good and the neighbourhood of the discontinuity is different. This irregularity in the stress distribution caused by abrupt changes of form is called stress concentration.

Stress concentration is also, defined as the localization of high stresses due to irregularities present in the component and abrupt changes in the cross section.Theoretical or Form Stress Concentration Factor

The value of Kt depends upon the material and geometry of the part.The cause of Stress concentration are:

Variation in properties of material: Internal cracks and flaws, cavities in welds, air hole in steel components, nonmetallic or foreign inclusions.Load application: contact between meshing teeth of the gears, cam and follower, rail and wheel, crane hook and chainAbrupt changes in sectionDiscontinuities in the component: oil holes or oil grooves, keyways and splines, screw threads.Machining scratches: stamp marks or inspection marks

Consider a plate with transverse elliptical hole and subjected to a tensile load as shown in Fig. 6.6 (a). We see from the stress-distribution that the stress at the point away from the hole is practically uniform and the maximum stress will be induced at the edge of the hole. The maximum stress is given by

and the theoretical stress concentration factor,

When a/b is large, the ellipse approaches a crack transverse to the load and the value of Kt becomes very large.Stress Concentration due to Holes and NotchesWhen a/b is small, the ellipse approaches a longitudinal slit [as shown in Fig. 6.6 (b)] and the increase in stress is small.

When the hole is circular as shown in Fig. 6.6 (c), then a/b = 1 and the maximum stress is three times the nominal value.

The stress concentration in the notched tension member, as shown in Fig. 6.7, is influenced by the depth a of the notch and radius r at the bottom of the notch. The maximum stress, which applies to members having notches that are small in comparison with the width of the plate, may be obtained by the following equation,

Stress Concentration factorsStress concentration factors may also be obtained using any one of the followingexperimental techniques:1. Strain gage method2. Photoelasticity method3. Brittle coating technique4. Grid method

For more accurate estimation numerical methods like Finite element analysismay be employed.

The Charts for stress concentration factors for different geometric shapes and conditions of loading were originally developed b RE Peterson.Methods of Reducing Stress ConcentrationA number of methods are available to reduce stress concentration in machineparts. Some of them are as follows:1. Provide a fillet radius so that the cross-section may change gradually.2. Sometimes an elliptical fillet is also used.3. If a notch is unavoidable it is better to provide a number of small notchesrather than a long one. This reduces the stress concentration to a large extent.4. If a projection is unavoidable from design considerations it is preferable toprovide a narrow notch than a wide notch.5. Stress relieving groove are sometimes provided.