Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

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AxIAL dEFORMATION
A A B
B C
C
A A B
B C
C
(a) (b) (c)
FIGURE 5.12 Typical stress trajectories and normal stress distributions for flat bars with
(a) notches, (b) a centrally located hole, and (c) shoulder fillets.
average stress on the section (termed the nominal stress). We then say that a stress concentration
exists at the discontinuity. The effect of a stress concentration is illustrated in Figure 5.12,
in which a type of discontinuity is shown in the upper figure and the approximate distribution
of normal stress on a transverse plane is shown in the accompanying lower figure.
The ratio of the maximum stress to the nominal stress on the section is known as the
stress-concentration factor K. Thus, the maximum normal stress in an axially loaded member
can be calculated as the product of K and the nominal stress:
s
max
= Ks
(5.13)
nom
Curves similar to those shown in Figures 5.13, 5.14, and 5.15 1 can be found in numerous
design handbooks. It is important that the user of such curves (or tables of factors) ascertain
whether the factors are based on the gross or net section. In this book, the stress-concentration
factors K are to be used in conjunction with the nominal stresses produced at the minimum
or net cross-sectional area, as shown in Figure 5.12. The K factors shown in Figures 5.13,
5.14, and 5.15 are based on the stresses at the net section.
The case of a small circular hole in a wide plate under uniform unidirectional tension
(Figure 5.16) offers an excellent illustration of localized stress redistribution. The theory of
1
Adapted from Walter D. Pilkey, Peterson’s Stress Concentration Factors, 2nd ed. (New York: John Wiley &
Sons, Inc., 1997).