Inside the alloy titanium pipe, which is $1$ metcr long and has a cross$-$sectional area of $100m{m}^2,$ there is a steel rod of the same length with a cross$-$sectional area of $50m{m}^2.$ The steel rod is pulled with a force of $85$ KN together with the alloy titanium pipe. Since the elactic modulus of scell is $200$ Mpa and the clastic modulus of the alloy titanium pipe is $100$ M pa$,$ this combined material, $(1$ metre boy unda ve kesit alani $100m{m}^2$ olan alasmh utany um borunun i$$inde kesit alanr $80m{m}^2$ olan aym boydakI $$elik $$ubuk bulunmaktad$$r$.$ Celik cubuk alagrnih titanyum boru ile birlikte $85$ KN bir kuvvet ile $$ekilmektedir$.$ Cellgin Elastik modate $200$ Mpa ve Alagml titanyum bonaman Elastik modata $100$ Mpa olduguna golve bu kombine malzeme$)$:

a$)$ How much ionger in total? Toplam be kadar ura? $(10$ Puan$)$

b$)$ How much plastic deformation occuns? Ne kadar plastik deformasyon olugur? $(10$ Puan$)$

c$)$ How much residual stress remains in the steel ber and ritanium pipe after the force applied to the combined material is removed? $($Kombine matzemeye byguhnas kovvet katdintdkhan sonra $$elik $$ubuk ite titanyum boruda ne kadar artik $($residual$)$ stress kal$$r$)(10$ Puan$)$

Answ$=As=100mm{A}_{\text{e}\text{s}\text{i}}=A_4-50m{m}^2$

Laxple $=1000mm,L_m=L{e}_2=1000mm$

Easn $E_8=100,000Mps.$Eqcos$=E_8-200000$Mpa

$dy$ Bav $m$ yye $=700MpL$ dyena $=0y=500$Mpa