Horizontal beam $AB$ is supported by pin A and cable $BC$ as shown. Pin $A$ is in single shear and has diamete

$d_A=12\mathrm{.}5mm.$ Cable $BC$ has diameter $d_{BC}=8mm.$ Determine the yield safety factors of cable $BC$ against

tensile stress $(S{F}_{BC})$ and pin A against shear stress $(S{F}_A).$

Both the pin and the cable are made out of $6061-$T$6$ aluminum. Assume the shear strength of $6061-$T$6$

aluminum is $50\%$ of its tensile yield strength.

Take $=40,L=2m,F=750N,$ and $q_o=250\frac{N}{m}.$

$S{F}_{BC}=$ number $($rtol $=0\mathrm{.}01,$ atol $\{$:$=1e-05)$

$S{F}_A=$ number $($rtol $=0\mathrm{.}01,$ atol $=1e-05)$ TENSILE PROPERTIES OF COMMON STRUCTURAL MATERIALS

$\backslash$table$[[$MATERIAL$,\backslash$table$[[$ULTIMATE$],[$TENSILE$],[$STRENGTH$,],[$S$\_(9)]],$YIELD STRENGTH, Sy$,$ DENSITY,

$\backslash$rho $],[$ksi$,$MPa,ksi,MPa,lb$/$ in$.^(3),$Mg$/$m$^(3)],[$CARBON & ALLOY STEELS$],[1010$ A$,44,303,29,200,0\mathrm{.}284,7\mathrm{.}87],[1018$ A$,49\mathrm{.}5,341,32,221,0\mathrm{.}284,7\mathrm{.}87],[1020$ HR$,66,455,42,290,0\mathrm{.}284,7\mathrm{.}87],[1045$ HR$,92\mathrm{.}5,638,60,414,0\mathrm{.}284,7\mathrm{.}87],[1212$ HR$,61\mathrm{.}5,424,28,193,0\mathrm{.}284,7\mathrm{.}87],[4340$ HR$,151,1041,132,910,0\mathrm{.}283,7\mathrm{.}84],[52100$ A$,167,1151,131,903,0\mathrm{.}284,7\mathrm{.}87],[],[302$ A$,92,634,34,234,0\mathrm{.}286,7\mathrm{.}92],[303$ A$,87,600,35,241,0\mathrm{.}286,7\mathrm{.}92],[304$ A$,83,572,40,276,0\mathrm{.}286,7\mathrm{.}92],[440$ C A$,117,807,67,462,0\mathrm{.}286,7\mathrm{.}92],[$CAST IRON$],[$Gray$,25,170,-,-,0\mathrm{.}260,7\mathrm{.}20],[$Malleable$,50,340,32,220,0\mathrm{.}266,7\mathrm{.}37],[$ALUMINUM ALLOYS$],[1100-0,12,83,4\mathrm{.}5,31,0\mathrm{.}098,2\mathrm{.}71],[2024-$T$4,65,448,43,296,0\mathrm{.}100,2\mathrm{.}77],[6061-$T$6,38,260,35,240,0\mathrm{.}098,2\mathrm{.}71],[7075-0,34,234,14\mathrm{.}3,99,0\mathrm{.}100,2\mathrm{.}77],[7075$ T$6,86,593,78,538,0\mathrm{.}100,2\mathrm{.}77],[$MAGNESIUM ALLOYS$],[$HK$31$XA$-0,25\mathrm{.}5,176,19,131,0\mathrm{.}066,1\mathrm{.}83],[$HK$31$XA$-$H$24,36\mathrm{.}2,250,31,214,0\mathrm{.}066,1\mathrm{.}83],[$NICKEL ALLOYS$],[$Monel $400$ A$,80,550,32,220,0\mathrm{.}319,8\mathrm{.}83]]$