$1.$ A rigid beam ACEF is supported by a pin support at A and suspended from steel cablesBC and DE $($E $=200,000$ MPa, $=0\mathrm{.}3,$ diameter $10$ mm$)$ which are attached to pin supportsat B and D respectively $($Figure $1).$ Load P $($kN$)$ is applied at point F$.$ The cables BC and DEwere designed to be of lengths $2$ m and $3$ m$,$ respectively, prior to loading. However, anerror in measurement during construction resulted in Cable DE being $1$ mm longer thanintended, resulting in some slack prior to loading as shown in Figure $1.($a$)$ Using equilibrium and compatibility considerations determine the support reactions at A$,$B and D when a load of P $=20$ kN is applied. Hint: Since the cables BC and DE cantransfer only axial force, the reactions at B and D act vertically $($that is$,$ there are nohorizontal reaction components at B and D$).($b$)$ Find the normal stress, normal strain and change in diameter of cable BC$,$ when P $=20$kN$.($c$)$ If the cable material fails when the normal stress due to axial load reaches $350$ MPa,determine the load P which must be applied to the beam to cause failure. Which cablewill fail first?