A rigid beam BCD$,$ shown in Figure $2,$ is supported by a pin at C and $2$ identical cables $($length $=$

L$,$ diameter $=$ d$),$ at B and D$.$ The cable at B is perpendicular to the beam, whereas the cable at D is inclined $0$ from the vertical direction. The beam is loaded with a uniform vertical distributed load with intensity q$,$ which makes the beam rotate such that point D moves down A$.$ It is also known that the deformation of the cable ED leads to a stress in that cable of oDe, whereas the stress

in cable AB $($GAB$)$ can be calculated as $0=$DE $-$

EDE

a$)$ If A $=$ A$1,$ find the strains and changes in length in cables DE and AB using approximate

methods $($i$.$e$.$ using small$-$angle approximation$).$

b$)$ If $4=41,$ find the value of q needed to produce the strains and changes in length in part a$).$

c$)$ If $4=$ A$2,$ find the strains and changes in length in cables DE and AB using approximate

methods $($i$.$e$.$ using small$-$angle approximation$).$

d$)$ If A $=$ A$2,$ find the strains and changes in length in cables DE and AB using exact methods Note: With exact methods, point D will not move directly downwards. Take A to be the

change between D$\text{'}$s final and initial positions.Take a $=1\mathrm{.}2$ m$,$ L $=2\mathrm{.}5$ m$,$ d $=6$ mm$,$ and $\backslash$theta $=30\backslash$deg $.$

Take $\backslash$sigma DE $=1\mathrm{.}2$ GPa, $\backslash$Delta $1=18$ cm$,\backslash$Delta $2=36$ cm$.$