Introduction

In the stress analysis described in the previous chapters, it is presumed that cross-sectional area remains constant and has no discontinuities like holes, etc. In actual parts, it may not be possible to have an area of cross section, which always remains constant. Hence, in these areas, where there is change in cross section, stress concentration takes place. Stress concentration can be defined as increase in stress at the areas of changing cross section and other parameters.

Stress concentration can be due to many reasons: Variation in properties of material from point-to-point, which could be due to non metallic inclusions, blow holes in castings, or cracks or flaws in material. Local bearing pressures between two mating parts, for example, mating gear teeth, ball and races of a rolling bearing, etc. Change in cross section is the most important factor. The areas where there is change in cross section are: a step in diameter, change of cross section either with a fillet or with taper, a hole, a notch, threads, gear teeth, etc.

Stress Concentration Areas

Following are some examples in which change in area causes stress concentration:

• Abrupt change in cross section Area changes abruptly at one section as shown in Figure 9.1(a). This causes severe stress concentration.

• Change of cross section with a fillet A small radius called fillet is given to avoid sharp corners as shown in Figure 9.1(b). Stress concentration is there, but not as severe as in the case of sharp corners.

• Gradual change in cross section Figure 9.1(c) shows gradual change in area. Stress concentration is lesser, even than that of the stress with a fillet.