Situation $8-$ A $10-$m long precast concrete beam weighing $39kN$ is to be lifted as shown.

Given: Allowable tensile stress of cable $=130$MPa

Modulus of elasticity of cable $=200$GPa

$27.$ If the cable diameter is $16mm,$ which of the following gives the smallest safe value of $H?$

A$.4\mathrm{.}0$

C$.3\mathrm{.}5$

B$.2\mathrm{.}5$

D$.3\mathrm{.}0$

$28.$ If $H=2\mathrm{.}7m,$ what is the smallest safe cable diameter in $mm?$

A$.20$

C$.12$

B$.16$

D$.18$

$29.$ If the cable diameter is $16mm$ and $H=3\mathrm{.}4m,$ determine the elongation $(mm)$ of each cable.

A$.2\mathrm{.}85$

C$.3\mathrm{.}26$

B$.4\mathrm{.}27$

D$.2\mathrm{.}51$

$30.$ If the cable diameter is $16mm$ and $H=3\mathrm{.}4m,$ determine the vertical displacement $(mm)$ of the beam.

A$.4\mathrm{.}36$

C$.3\mathrm{.}17$

B$.3\mathrm{.}74$

D$.3\mathrm{.}34$