Estimate the Marin loading factor kc for a 1–in-diameter bar that is used as follows. (a) In bending. It is made of steel with Sut = 100LN(1, 0.035) kpsi, and the designer intends to use the correlation S′e =Φ 0.30 ¯Sut to predict S′e.

Question

Estimate the Marin loading factor kc for a 1–in-diameter bar that is used as follows.
(a) In bending. It is made of steel with [latex]S_{ut}[/latex] = 100LN(1, 0.035) kpsi, and the designer intends to use the correlation [latex]S′_{e} =\Phi_{0.30} \overline{S}_{ut}[/latex] to predict [latex]S′_{e} [/latex].
(b) In bending, but endurance testing gave [latex]S′_{e} [/latex]= 55LN(1, 0.081) kpsi.
(c) In push-pull (axial) fatigue, [latex]S_{ut}[/latex] = LN(86.2, 3.92) kpsi, and the designer intended to use the correlation [latex]S′_{e} =\Phi_{0.30} \overline{S}_{ut}[/latex] .
(d) In torsional fatigue. The material is cast iron, and [latex]S′_{e} [/latex] is known by test.

Accepted Answer

(a) Since the bar is in bending,

[latex]k_{c} = (1, 0)[/latex]

(b) Since the test is in bending and use is in bending,

[latex]k_{c} = (1, 0)[/latex]

(c) From Eq. (6–73),

[latex] (k_{c})_{axial} = 1.23 \overline{S}^{−0.0778}_{ut} LN(1, 0.125)[/latex] (6–73)

[latex](k_{c})_{ax} = 1.23(86.2)^{−0.0778}LN(1, 0.125)[/latex]

[latex]\overline {k}_{c} = 1.23(86.2)^{−0.0778}(1) = 0.870[/latex]

[latex]\hat {σ}_{kc} = C \overline {k}_{c} = 0.125(0.870) = 0.109[/latex]

(d) From Table 6–15, [latex]\overline {k}_{c}= 0.90, \hat {σ}_{kc}[/latex] = 0.07,and

[latex]C_{kc} =\frac{0.07}{0.90} = 0.08[/latex]

Table 6–15 Heywood’s Parameter [latex]\sqrt {a}[/latex] and coefficients of variation [latex]C_{Kf}[/latex] for steels

Coefficient of Variation [latex]C_{Kf}[/latex]	[latex]\sqrt{a}(\sqrt {mm}) ,S_{ut}[/latex] in MPa	[latex]\sqrt{a}(\sqrt {in}) ,S_{ut}[/latex] in kpsi	Notch Type
0.10	174/[latex]S_{ut}[/latex]	5/[latex]S_{ut}[/latex]	Transverse hole
0.11	139/[latex]S_{ut}[/latex]	4/[latex]S_{ut}[/latex]	Shoulder
0.15	104/[latex]S_{ut}[/latex]	3/[latex]S_{ut}[/latex]	Groove

Coefficient of Variation $C_{Kf}$	$\sqrt{a}(\sqrt {mm}) ,S_{ut}$ in MPa	$\sqrt{a}(\sqrt {in}) ,S_{ut}$ in kpsi	Notch Type
0.10	174/ $S_{ut}$	5/ $S_{ut}$	Transverse hole
0.11	139/ $S_{ut}$	4/ $S_{ut}$	Shoulder
0.15	104/ $S_{ut}$	3/ $S_{ut}$	Groove

Question 6.17: Estimate the Marin loading factor kc for a 1–in-diameter bar...

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