Prob # 36 E= 200 GPa = 200* 10^9 Pa D= 15 mm = 0.015 m

∆T = 0

Solution

0 x< 0.3

0.3< x < 1

From Bcs

--------------------------------

--------------------------------

So

From Compatibility

-------------------------------------- 1

From macro-equilibrium

Rl Rr

-------------------------2

From 1 &2

Prob # 79 ∆T = 10

0< x < 0.3

0.3< x <0.6

From Bcs

--------------------------------

--------------------------------

From Compatibility

------------------------------------ 1

At joining point

------------------------------- 2

From 1 & 2

Prob # 80

– ------------ I

0.053 < x < 0.293

---------------------------------

0 < x < 0.3

---------------------------------

Subst in I

--------------------------- 1

From macro-equilibrium

---------------------------------- 2

From 1 & 2