Problem #$22-$ Stress and Strain Analysis $(10$ points total, $3$ parts$)$

A $24-$foot$-$long steel alloy bar is tensed along its centroidal axis by the forces shown below. The bar has a circular cross$-$section with a radius of $3\mathrm{.}0in.$ The steel is ASTM certified A$992$ steel with a yield stress $y=50$ksi and modulus of elasticity $E=29000$ksi. Show all work and any assumptions clearly. Complete the following:

Part A $(4$ Points$)$: Calculate the axial stress in sections $AB$ and $BC$ of the beam.

Part B $(2$ Points$)$: Based on a standard factor of safety of $1\mathrm{.}67$ calculate the allowable stress in the beam. Does the calculated stress in either section exceed the allowable stress of the steel? Part C $(4$ Points$)$: Calculate the deformation in sections $AB$ and BC of the beam. What is the total axial deformation that the beam experiences? What is the final length of the beam?

Answer Key

$\backslash$table$[[$Answer Key$],[$Section$,\backslash$table$[[$Axial$],[$Stress$],[($ksi$)]],\backslash$table$[[>$ oull$],[$Yes or$],[$No$]],$Deformation, $($in$)],[$AB$,,,],[$BC$,,,],[$Total Deformation, $($in$),,],[$Final Length $($ft$),,]]$