Question

Hi everybody! can someone please help me with this problem?

The shaft ACB, of constant outer diameter 2R and length 2L, is fixed to walls at both ends A and B. The left half of the shaft (AC)is solid, while the right half (CB) is hollow, with an inner diameter 2R. The right half, CB, is subjected to a uniform distributed torque per unit length q0[N m/m]. The material of the shaft is linear isotropic elastic with shear modulus G.

Obtain symbolic expressions for the x-component of the reaction torques at A and B in terms of q0 and L:

T(ax)=
T(bx)=

Obtain symbolic expressions for the axial torque resultant in the bar Tx (in terms of q0, L, and x), and the position x=0 along the shaft (in terms of L) where this torque resultant goes to zero (T(x0)=0):

0<x<L, T(x) =
L<x<2L, T(x) =
T(x0)=0, T(x) =

Obtain expressions for the maximum absolute value of the shear stress in the shaft,τ, (in terms of q0, L, and R) and its location (rτ, xτ) in terms of R and L:

Tmax =
Ttmax =
Xtmax =

Obtain expressions for the maximum value of the rotation field φx along the shaft, φ (in terms of q0, L, G, and R), and the position along the shaft wherethe maximum rotation occurs, xφ, (in terms of L):

φmax =
xφmax =