A rigid beam ACEF is supported by a pin support at

A and suspended from steel cables

$BC$ and $,$ diameter $10$

mm $)$ which are attached to pin supports

at $B$ and $D$ respectively $($Figure $1).$ Load $P(kN)$ is

applied at point $F.$ The cables BC and DE

were designed to be of lengths $2$ m and $3$ m $,$

respectively, prior to loading. However, an

error in measurement during construction resulted

in Cable DE being $1$ mm longer than

intended, 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 $P=20kN$ is applied. Hint:

Since the cables BC and DE can

transfer only axial force, the reactions at B and D

act vertically $($that is$,$ there are no

horizontal 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 cable

will fail first? Please show all working for this engineering problem.