A composite shaft ABC is as shown in fig. A clockwise torque of 2000 Nm is applied at section B common to both the shafts. Plot stress distribution for shaft AB and for shaft BC.

Take Gs=80 GPa and Gc=40 GPa. Calculate the twist of section B.

$J_p ] = \frac{\pi}{32} \times 60^4 = 1.272 \times 10^6 \ mm^4$

$J_p ]_c = \frac{\pi}{32} [ 75^2 – 45^2] = 2.704 \times 10^6 \ mm^4$

ET = 0

$T_A + T_c = 2000$ - [1]

$\theta_s ]_B = \theta_c ]_B$

$\frac{TA \ \times 1200}{80 \times 10^3 \times 1.272 \times 10^6} = \frac{Tc \times 1200}{40 \times 10^3 \times 2.704 \times 10^6}$

$T_A = 0.941 \ Tc$ - [2]

Solving 1 and 2

$T_A = 969.5 \ Nm$

$T_c = 1030.5 \ Nm$

$\theta_3 = \frac{969.5 \times 10^3 \times 1200}{80 \times 10^3 \times 1.272 \times 10^6} = 0.0114$ rad $\hookleftarrow$

$\zeta_s = \frac{969.5 \times 5 \times 10^3 \times 30}{1.272 \times 10^6} = 22.866 \ N/mm^2$

$\zeta_c = \frac{1030.5 \times 10^3 \times 37.5}{2.704 \times 10^6} = 14.29 \ Nmm^2$

Stress distribution diagram