Page 243 - Shigley's Mechanical Engineering Design

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218 Mechanical Engineering Design
For materials that strain-strengthen, the critical location in the notch has a higher S y .
The shank area is at a stress level a little below 40 kpsi, is carrying load, and is very
near its failure-by-general-yielding condition. This is the reason designers do not
apply K t in static loading of a ductile material loaded elastically, instead setting
K t = 1.
When using this rule for ductile materials with static loads, be careful to assure
yourself that the material is not susceptible to brittle fracture (see Sec. 5–12) in the
environment of use. The usual definition of geometric (theoretical) stress-concentration
factor for normal stress K t and shear stress K ts is given by Eq. pair (3–48) as
(a)
σ max = K t σ nom
(b)
τ max = K ts τ nom
Since your attention is on the stress-concentration factor, and the definition of σ nom or
τ nom is given in the graph caption or from a computer program, be sure the value of
nominal stress is appropriate for the section carrying the load.
As shown in Fig. 2–2b, p. 33, brittle materials do not exhibit a plastic range. The
stress-concentration factor given by Eq. (a) or (b) could raise the stress to a level to
cause fracture to initiate at the stress raiser, and initiate a catastrophic failure of the
member.
An exception to this rule is a brittle material that inherently contains microdiscon-
tinuity stress concentration, worse than the macrodiscontinuity that the designer has in
mind. Sand molding introduces sand particles, air, and water vapor bubbles. The grain
structure of cast iron contains graphite flakes (with little strength), which are literally
cracks introduced during the solidification process. When a tensile test on a cast iron is
performed, the strength reported in the literature includes this stress concentration. In
such cases K t or K ts need not be applied.
An important source of stress-concentration factors is R. E. Peterson, who com-
1
piled them from his own work and that of others. Peterson developed the style of
presentation in which the stress-concentration factor K t is multiplied by the nominal
stress σ nom to estimate the magnitude of the largest stress in the locality. His approxi-
mations were based on photoelastic studies of two-dimensional strips (Hartman and
Levan, 1951; Wilson and White, 1973), with some limited data from three-dimensional
photoelastic tests of Hartman and Levan. A contoured graph was included in the
presentation of each case. Filleted shafts in tension were based on two-dimensional
strips. Table A–15 provides many charts for the theoretical stress-concentration factors
for several fundamental load conditions and geometry. Additional charts are also avail-
able from Peterson. 2
Finite element analysis (FEA) can also be applied to obtain stress-concentration
factors. Improvements on K t and K ts for filleted shafts were reported by Tipton, Sorem,
and Rolovic. 3

1 R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951;
no. 3, March 1951; no. 5, May 1951; no. 6, June 1951; no. 7, July 1951.
2 Walter D. Pilkey and Deborah Pilkey, Peterson’s Stress-Concentration Factors, 3rd ed, John Wiley & Sons,
New York, 2008.
3 S. M. Tipton, J. R. Sorem Jr., and R. D. Rolovic, “Updated Stress-Concentration Factors for Filleted Shafts in
Bending and Tension,” Trans. ASME, Journal of Mechanical Design, vol. 118, September 1996, pp. 321–327.