A rigid beam BCD$,$ shown in Figure $2,$ is supported by a pin at C and $2$ identical cables $($length $=$ Question $1$

For part a$,$

Find the change in length in cable $AB$

$($answer in mm$).$

Question $2$

For part a$,$

Find the normal strain in cable AB$.$

Question $3$

For part a$,$

Find the change in length in cable DE $($in

mm $).$

Question $4$

For part a$,$

Find the normal strain in cable DE$.$

Question $5$

For part b$,$

Find the distributed load intensity q to

produce these displacements $($answer in N$/$

mm $).$

Question $6$

For part c$,$

Find the change in length in cable $AB$

$($answer in mm$).|$ Question $7$

For part c$,$

Find the normal strain in cable AB $.$

Question $8$

$2$ pts

For part c$,$

Find the change in length in cable DE $($answer in mm$).$

Question $9$

$2$ pts

For part c$,$

Find the normal strain in cable DE$.$

Question $10$

$2\mathrm{.}5$ pts

For part d$,$

Find the change in length in cable $AB($answer in mm$).$

Question $11$

For part d$,$

Find the normal strain in cable AB$.$

Question $12$

For part d$,$

Find the change in length in cable DE $($answer in mm$).$

Question $13$

For part d$,$

Find the normal strain in cable DE$.$

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 ODE, 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 $a=0\mathrm{.}8m,L=1\mathrm{.}5m,d=4mm,$ and $=30.$

Take ${}_{DE}=0\mathrm{.}8$GPa,${}_1=12cm,{}_2=24cm.$