Questions $($i$)-(v)$

As Batman approaches closer to the explosive device, he sets the trap off, causing the cable to the beam to release. He immediately uses his grapple hook to support the beam. The grapple hook cable has a diameter of $0\mathrm{.}375$ in$,$ an axial force of $5$ kips, a modulus of elasticity of $29,000$ksi, a length of $20$ ft $,$ and Poisson's ratio of $0\mathrm{.}30.$

Cable Cross Section and Properties

$L=20ft$

$E=29,000$ksi

$P=5$kips

$u=0\mathrm{.}30$

$($i$)$ The axial stress in the cable is most nearly...

$A=r^2$

$(0\mathrm{.}1575)$

$=\frac{P}{A}=\frac{5}{0\mathrm{.}110447}$

$($a$)0\mathrm{.}375$ kN

$($b$)11\mathrm{.}32$ ksi

$($b$)11\mathrm{.}32$ ksi

$($c$)45\mathrm{.}27$ ksi

$($d$)45,000Pa$

$($ii$)$ The resulting diameter of the cable under $5$ kips axial force is most nearly...

$($e$)0\mathrm{.}001561$ in

$($g$)0\mathrm{.}3752$ in

$($f$)0\mathrm{.}3748$ in

$($h$)0\mathrm{.}7496$ in

$($iii$)$ The resulting deflection of the cable is most nearly...

$($i$)0\mathrm{.}001561$ in

$($k$)0\mathrm{.}3752$ in

$($j$)0\mathrm{.}3747$ in

$(1)0\mathrm{.}7496$ in

iv$)$ If the cable is made of steel wire strand with an $F_y=120$ksi and $F_u=150$ksi, which statement is most likely to be true?

$($m$)$ When loaded to failure, the cable will show a significant amount of yielding deformation due to a long yield plateau.

$($n$)$ The yield stress will be obvious to see without the need for the $0\mathrm{.}2\%$ offset method.

$($o$)$ The cable will fracture at a stress between the yield stress and ultimate stress.

$($p$)$ The cable will have less ductility than a similarly sized cable of a lower grade of steel.

The shear stress in the cable due to the axial load is most nearly...

$($q$)0$ psi

$($s$)115\mathrm{.}22$ ksi

$($r$)45\mathrm{.}27$ ksi

$($t$)482\mathrm{.}9$ ksi

Questions $($i$)-($v$)$

As Batman approaches closer to the explosive device, he sets the trap off, causing the cable to the beam to release. He immediately uses his grapple hook to support the beam. The grapple hook cable has a diameter of $0\mathrm{.}375$ in $,$ an axial force of $5$ kips, a modulus of elasticity of $29,000$ksi, a length of $20$ ft $,$ and Poisson's ratio of $0\mathrm{.}30.$

$($i$)$ The axial stress in the cable is most nearly...

$($a$)0\mathrm{.}375$ kN

$($c$)45\mathrm{.}27$ ksi

$($b$)11\mathrm{.}32$ ksi

$($d$)45,000Pa$

$($ii$)$ The resulting diameter of the cable under $5$ kips axial force is most nearly...

$($e$)0\mathrm{.}001561$ in

$($g$)0\mathrm{.}3752$ in

$($f$)0\mathrm{.}3748$ in

$($h$)0\mathrm{.}7496$ in

$($iii$)$ The resulting deflection of the cable is most nearly...

$($i$)0\mathrm{.}001561$ in

$($k$)0\mathrm{.}3752$ in

$($j$)0\mathrm{.}3747$ in

$(1)0\mathrm{.}7496$ in

$($iv$)$ If the cable is made of steel wire strand with an $F_y=120$ksi and $F_u=150$ksi which statement is most likely to be true?

$($m$)$ When loaded to failure, the cable will show a significant amount of yielding deformation due to a long yield plateau.

$($n$)$ The yield stress will be obvious to see without the need for the $0\mathrm{.}2\%$ offset method.

$($o$)$ The cable will fracture at a stress between the yield stress and ultimate stress.

$($p$)$ The cable will have less ductility than a similarly sized cable of a lower grade of steel.

$($v$)$ The shear stress in the cable due to the axial load is most nearly...

$($q$)0$ psi

$($s$)115\mathrm{.}22$ ksi

$($r$)45\mathrm{.}27$ ksi

$($t$)482\mathrm{.}9$ ksi