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 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 $$ 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 $.$ It is also

known that the deformation of the cable ED leads to a stress in that cable of $$ DE$,$ whereas the stress

in cable $AB({}_{AB})$ can be calculated as ${}_{AB}=\frac{{}_{DE}}{{}_{DE}}{}_{AB}.$

a$)$ If $={}_1,$ find the strains and changes in length in cables $DE$ and $AB$ using approximate

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

b$)$ If $={}_1,$ find the value of $q$ needed to produce the strains and changes in length in part a$).$

c$)$ If $={}_2,$ find the strains and changes in length in cables DE and AB using approximate

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

d$)$ If $={}_2,$ 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 $$ to be the

change between D$\text{'}$s final and initial positions.

Figure $2$: Rigid beam with cables and distributed load

Take $a=1m,L=2m,d=5mm,$ and $=30.$

Take ${}_{DE}=1$GPa,${}_1=15cm,{}_2=30cm.1$Find the normal strain in cable AB$..)$Find the change in length in cable AB $($answer in mm$).2.)$Find the normal strain in cable AB$.3.)$Find the change in length in cable DEFind the distributed load intensity q to produce these displacements $($answer in N$/$mm$).($in mm$).4.)$Find the normal strain in cable DE$.5.)$ Find the distributed load intensity q to produce these displacements $($answer in N$/$mm$).6.)$Find the change in length in cable AB $($answer in mm$).7.)$Find the normal strain in cable AB$.8.)$ Find the change in length in cable DE $($answer in mm$).9.)$ Find the normal strain in cable DE$.10.)$ Find the change in length in cable AB $($answer in mm$).11.)$Find the normal strain in cable AB$.12.)$ Find the change in length in cable DE