Problem #$2-$ Stress and Strain Analysis $(15$ points total, $3$ parts$)$

A $20-$foot$-$long structural steel bar is tensed along its centroidal axis. Point B is tensed by $47$ kips of force and point C is tensed by $147$ kips of force. The bar has a rectangular cross$-$section with a base of $1\mathrm{.}8$ inches and height of $3$ inches. The steel is ASTM HSLC steel with a yield stress, ${}_y=50$ ksi and modulus of elasticity, $E=30,000$ksi. Show all work and any assumptions on the provided calculation sheet. Record your answers on the answer key. Complete the following:

Part A $(6$ Points$)$: Calculate the axial stress in sections AB and BC of the beam. Does the calculated stress in either section exceed the yield stress of the steel?

Part B $(6$ 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?

Part C $(3$ Points$)$: The allowable stress in the beam is $29\mathrm{.}9$ ksi $,$ calculate the factor of safety the beam was designed for.

Answer Key

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