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288 Mechanical Engineering Design
Table 6–2
Factor a Exponent
Parameters for Marin Surface Finish S ut, kpsi S ut, MPa b
Surface Modification Ground 1.34 1.58 −0.085
Factor, Eq. (6–19) Machined or cold-drawn 2.70 4.51 −0.265

Hot-rolled 14.4 57.7 −0.718
As-forged 39.9 272. −0.995

From C.J. Noll and C. Lipson, “Allowable Working Stresses,” Society for Experimental
Stress Analysis, vol. 3, no. 2, 1946 p. 29. Reproduced by O.J. Horger (ed.) Metals
Engineering Design ASME Handbook, McGraw-Hill, New York. Copyright © 1953 by
The McGraw-Hill Companies, Inc. Reprinted by permission.

EXAMPLE 6–3 A steel has a minimum ultimate strength of 520 MPa and a machined surface.
Estimate k a .

Solution From Table 6–2, a = 4.51 and b =−0.265. Then, from Eq. (6–19)

Answer k a = 4.51(520) −0.265 = 0.860

Again, it is important to note that this is an approximation as the data is typically
quite scattered. Furthermore, this is not a correction to take lightly. For example, if in
the previous example the steel was forged, the correction factor would be 0.540, a sig-
nificant reduction of strength.

Size Factor k b
15
The size factor has been evaluated using 133 sets of data points. The results for bend-
ing and torsion may be expressed as
⎧ −0.107 −0.107
⎪ (d/0.3) = 0.879d 0.11 ≤ d ≤ 2in
⎪
⎪
0.91d 2 < d ≤ 10 in
⎨ −0.157
k b = (6–20)
⎪ (d/7.62) −0.107 = 1.24d −0.107 2.79 ≤ d ≤ 51 mm
⎪
⎪
⎩ −0.157
1.51d 51 < d ≤ 254 mm
For axial loading there is no size effect, so
k b = 1 (6–21)
but see k c .
One of the problems that arises in using Eq. (6–20) is what to do when a round bar
in bending is not rotating, or when a noncircular cross section is used. For example,
what is the size factor for a bar 6 mm thick and 40 mm wide? The approach to be used

15 Charles R. Mischke, “Prediction of Stochastic Endurance Strength,” Trans. of ASME, Journal of Vibration,
Acoustics, Stress, and Reliability in Design, vol. 109, no. 1, January 1987, Table 3.