Write and test computer subroutines or procedures that will implement ( a ) Table 6–2, returning a , b , C , and [latex]{\bar{k}}_{a}[/latex] . ( b ) Equation (6–20) using Table 6–4, returning [latex]k_{b}[/latex]. ( c ) Table 6–11, returning α, β, C , and [latex]\bar k_{c}[/latex]. ( d ) Equations (6–27) and (6–75), returning [latex]\bar k_{d}[/latex] and [latex]C_{kd}[/latex]. [latex]k_{b}={\left\{\begin{array}{l l}{(d/0.3)^{-0.107}=0.879d^{-0.107}}&{0.11\leq d\leq2\operatorname*{in}}\\ {0.91d^{-0.157}}&{2\lt d\leq10\operatorname{in}}\\ {(d/7.62)^{-0.107}=1.24d^{-0.107}}&{2.79\leq d\leq51\ \operatorname*{mm}}\\ {1.51d^{-0.157}}&{51\lt 254\operatorname*{mm}}\end{array}\right.}[/latex] (6-20) [latex]k_{d}=0.975+0.432(10^{-3})T_{F}-0.115(10^{-5})T_{F}^{2}+0.104(10^{-8})T_{F}^{3}-0.595(10^{-12})T_{F}^{4} [/latex] (6-27) [latex]{k}_{d}=\bar{k}_{d}{{L N}}(1,0.11)[/latex] (6-75)

The results of Probs. 6-41 to 6-44 will be the basis of a class computer aid for fatigue problems. The codes should be made available to the class through the library of the computer network or main frame available to your students.

Question 6.44: Write and test computer subroutines or procedures that will ......

Shigley’s Mechanical Engineering – Solutions Manual [1575090]

Write and test computer subroutines or procedures that will implement

(a) Table 6–2, returning a, b, C, and ${\bar{k}}_{a}$ .

(b) Equation (6–20) using Table 6–4, returning $k_{b}$ .

(d) Equations (6–27) and (6–75), returning $\bar k_{d}$ and $C_{kd}$ .

$k_{b}={\left\{\begin{array}{l l}{(d/0.3)^{-0.107}=0.879d^{-0.107}}&{0.11\leq d\leq2\operatorname*{in}}\\ {0.91d^{-0.157}}&{2\lt d\leq10\operatorname{in}}\\ {(d/7.62)^{-0.107}=1.24d^{-0.107}}&{2.79\leq d\leq51\ \operatorname*{mm}}\\ {1.51d^{-0.157}}&{51\lt 254\operatorname*{mm}}\end{array}\right.}$ (6-20)

$k_{d}=0.975+0.432(10^{-3})T_{F}-0.115(10^{-5})T_{F}^{2}+0.104(10^{-8})T_{F}^{3}-0.595(10^{-12})T_{F}^{4}$ (6-27)

${k}_{d}=\bar{k}_{d}{{L N}}(1,0.11)$ (6-75)

Table 6–2 Parameters for Marin Surface Modification Factor, Eq. (6–19) $k_{a}=a S_{u t}^{b}$ (6-19)	Surface Finish	Factor a		Exponent b
	Surface Finish	$S_{u t}$ , kpsi	$S_{u t}$ , Mpa	Exponent b
	Ground	1.34	1.58	-0.085
	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

Table 6–4 Effect of Operating Temperature on the Tensile Strength of Steel.* ( $S_{T}$ = tensile strength at operating temperature; $S_{R T}$ = tensile strength at room temperature; $0.099\leq{\hat{\sigma}}\leq0.110)$	Temperature, °C	$S_{T}/S_{R T}$	Temperature, °F	$S_{T}/S_{R T}$
	20	1.000	70	1.000
	50	1.010	100	1.008
	100	1.020	200	1.020
	150	1.025	300	1.024
	200	1.020	400	1.018
	250	1.000	500	0.995
	300	0.975	600	0.963
	350	0.943	700	0.927
	400	0.900	800	0.872
	450	0.843	900	0.797
	500	0.768	1000	0.698
	550	0.672	1100	0.567
	600	0.549
	*Data source: Fig. 2–9.

Table 6–11 Parameters in Marin Loading Factor	Mode of Loading	$\mathrm{k_{c}}=\alpha\,\mathrm{S_{ut}^{-\beta}}\,\mathrm{LN}(1,{C})$				Average $K_{c}$
		$\alpha$		${{{\beta}}}$	C
		kpsi	Mpa	${{{\beta}}}$	C
	Bending	1	1	0	0	1
	Axial	1.23	1.43	-0.0778	0.125	0.85
	Torsion	0.328	0.258	0.125	0.125	0.59

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