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Question 2.6.16: 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
k_a= aS^b_{ut} LN\left(1, C\right)
a Coefficient of
Variation, C
Surface Finish kpsi MPa b
Ground* 1.34 1.58 −0.086 0.120
Machined or Cold-rolled 2.67 4.45 −0.265 0.058
Hot-rolled 14.5 58.1 −0.719 0.110
As-forged 39.8 271 −0.995 0.145
k_a=4.45\left(520\right)^{-0.265}LN\left(1,0.058\right)

 

\bar{k} _a=4.45\left(520\right)^{-0.265}\left(1\right) =0.848 \bar{\sigma } _{ka}=C\bar{k} _a=\left(0.058\right)4.45\left(520\right) ^{-0.265} =0.049

 

so k_a= LN\left(0.848,0.049\right) .

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