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Question 6.16: A steel has a mean ultimate strength of 520 MPa and a machin...

A steel has a mean ultimate strength of 520 MPa and a machined surface. Estimate k_{a} .

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From Table 6–10,

Table 6–10   Parameters in Marin Surface Condition Factor

Coefficient of Variation, C k_{a} aS^{b}_{ut} LN(1, C) Surface Finish
b a
MPa kpsi
0.120 −0.086 1.58 1.34 Ground∗
0.058 −0.265 4.45 2.67 Machined or Cold-rolled
0.110 −0.719 58.1 14.5 Hot-rolled
0.145 −0.995 271 39.8 As-forged

*Due to the wide scatter in ground surface data, an alternate function is k_{a}0.878LN(1, 0.120). Note: S_{ut} in kpsi or MPa.

k_{a} = 4.45(520)^{−0.265}LN(1, 0.058)

\overline{k}_{a} = 4.45(520)^{−0.265}(1) = 0.848

\hat {σ}_{ka} = C  \overline{k}_{a}= (0.058)4.45(520)^{−0.265} = 0.049

so k_{a} = LN(0.848, 0.049).

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