MecMovies 4.0 : M6.20: Shear Stresses in End-to-end Shafts

Equilibrium equation

$T_{1} - T_{2} = T = 1, 000 N - m$

Compatibility equation

$\frac{T_{1} L_{1}}{J_{1} G_{1}} + \frac{T_{2} L_{2}}{J_{2} G_{2}} = 0$

For shaft $(1)$ :

$L_{1} = 1, 500 mm G_{1} = 75 GPa = 75, 000 N / {mm}^{2} J_{1} = 362, 265 {mm}^{4}$

For shaft $(2)$ :

$L_{2} = 1, 000 mm G_{2} = 40 GPa = 40, 000 N / {mm}^{2} J_{2} = 613, 592 {mm}^{4}$

Substituting these values, the equilibrium and compatibility equations can be solved simultaneously to obtain:

$T_{1} = 424.63 N - m T_{2} = - 575.37 N - m$