Stress Concetration 1h5m5e

Stress Concentration Ankush Sharma

In 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 ing 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 Theoretical or Form Stress Concentration Factor abrupt changes in the cross section.  

The value of Kt depends upon the material and geometry of the part.

The cause of Stress concentration are: i. Variation in properties of material: Internal cracks and flaws, cavities in welds, air hole in steel components, nonmetallic or foreign inclusions. ii. Load application: between meshing teeth of the gears, cam and follower, rail and wheel, crane hook and chain iii. Abrupt changes in section iv. Discontinuities in the component: oil holes or oil grooves, keyways and splines, screw threads. v. Machining scratches: stamp marks or inspection marks

Stress Concentration due to Holes and Notches Consider a plate with transverse elliptical hole and subjected to a tensile load as shown in Fig. 6.6 (a). We see from the stressdistribution 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.

 When 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

applies notches

to that

stress,

are

which having

small

in

comparison with the width of the plate, may be obtained by the following equation,

Stress Concentration factors Stress concentration factors may also be obtained using any one of the following experimental techniques: 1. Strain gage method 2. Photoelasticity method 3. Brittle coating technique 4. Grid method For more accurate estimation numerical methods like Finite element analysis may 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 Concentration A

number

of

methods

are

available

to

reduce

stress

concentration in machine parts. 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 notches rather 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 to