$10^($th $)$ ed$.$ probs. $4-104$ and $4-105$ABC is suspended in a horizontal position by three A$-36$ steel

rods, each having a diameter of $25$ mm $.$ Treat A$-36$ steel as an elastic$-$

perfectly plastic material. Neglect self$-$weight and buckling effects.

a$.$ Under a load of P$=230$kN$,$ determine...

i$.$ the forces developed in each rod.

ii$.$ the slope of the beam.

b$.$ When the $230$ kN load is removed, determine...

i$.$ the residual stress carried in each rod.

ii$.$ the change in vertical locations of points A&C relative to their positions before the load was

applied.

iii. the slope of the beam.

Answers: $($a$.$i$.)$ F$\_($AD$)=15\mathrm{.}44$kN$,$F$\_($BE$)=91\mathrm{.}84$kN$,$F$\_($CF$)=122\mathrm{.}72$kN; $($a$.$ii$.)-0\mathrm{.}001167$ ;

$($b$.$i$.)\backslash$sigma $\_($AD$)=-35\mathrm{.}49$MPa,$\backslash$sigma $\_($BE$)=53\mathrm{.}23$MPa,$\backslash$sigma $\_($CF$)=-17\mathrm{.}74$MPa; $($b$.$ii$)\backslash$delta $\_($A$)=0\mathrm{.}106$mm upward, $\backslash$delta $\_($C$)=0\mathrm{.}692$mm downward; $($b$.$iii.$)-0\mathrm{.}0006654$