The shaft shown in the figure below is driven by a gear at the right keyway, drives a fan at

the left keyway, and is supported by two deep$-$groove ball bearings. The shaft is made from

AISI $1020$ cold$-$drawn steel with yield strength $=57k(390$MPa$).$ At steady$-$state speed,

the gear transmits a radial load of $230$ lbf and a tangential load of $633$ lbf at a pitch diameter

of $8$ in$.$ Assume $\frac{r}{d}=0\mathrm{.}02$ for keyseat and $R=1$ inch in the figure. Consider room

temperature operating conditions and $99\%$ reliability of the shaft. Use Marin factors, stress

concentration factors, notch sensitivity charts, and other relevant data from Shigley's book.

$($a$)$ Draw shear force and bending moment diagrams using Matlab code provided

$($b$)$ Determine fatigue factors of safety at potentially critical locations, i$.$e$,$ maximum stress

points, shoulders, notches, keyways, etc. Indicate the factor of safety you will choose from

the most critical point.

clc;

clear all;

$\%$ Fill up X array

x$1=[0$:$0\mathrm{.}01$:$2]$;

x$2=[2$:$0\mathrm{.}01$:$5]$;

x$3=[5$:$0\mathrm{.}01$:$6\mathrm{.}75]$;

x$4=[6\mathrm{.}75$:$0\mathrm{.}01$:$8]$;

X$=[$x$1\text{'}$;x$2\text{'}$;x$3\text{'}$;x$4\text{'}]$;

$\%\%$ Fill up Shear force array

V$1(1$:length$($x$1))=7\mathrm{.}47$;

V$2(1$:length$($x$2))=16\mathrm{.}34$;

V$3(1$:length$($x$3))=-36\mathrm{.}53$;

V$4(1$:length$($x$4))=0$;

VF$=[$V$1\text{'}$;V$2\text{'}$;V$3\text{'}$;V$4\text{'}]$;

figure; hold on; grid on;

plot$($X$,$VF$)$;

text$($X$($length$($x$1)),$VF$($length$($x$1)),\text{'}7\mathrm{.}47\text{'})$;

text$($X$($length$($x$1)+$length$($x$2)),$VF$($length$($x$1)+$length$($x$2)),\text{'}16\mathrm{.}34\text{'})$

text$($X$($length$($x$1)+$length$($x$2)+$length$($x$3)),$VF$($length$($x$1)+$length$($x$2)+$length$($x$3)),\text{'}-36\mathrm{.}53\text{'})$;

for k$=2$:length$($X$)$

M$($k$)=$trapz$($X$(1$:k$),$VF$(1$:k$))$;

end

figure; hold on; grid on;

plot$($X$,$M$)$;

text$($X$($length$($x$1)),$M$($length$($x$1)),\text{'}14\mathrm{.}94\text{'})$;

text$($X$($length$($x$1)+$length$($x$2)),$M$($length$($x$1)+$length$($x$2)),\text{'}63\mathrm{.}96\text{'})$

$\%[$Val$,$Loc$]=$max$($M$)$;

$\%$ X$($Loc$)$;

$\%$ Location $=$ find$($X$>5\mathrm{.}99$ & X$<mn>6</mn><mn>.</mn><mn>0</mn><mn>1</mn><mi>)</mi>$;

$\%$ X$($Location$)$

$\%$ M$($Location$)$ this is the matlab code

$(20$ marks$)$