Mechanics: Eccentric torsion + non circular tube

Su Solberg

dear all, i have just received a question about torsion.

1. The problem statement, all variables and given/known data
*************** a graph has been attached as attachment at bottom*************

The objective is to find the torsion shear stress at the cross section of the "dark Grey tube".

Let's have a look:
1.There is a reaction torque acting on the motor M,
2.The force is then transfered to dark grey tube by a light grey carrier.
3. blue cross is the center of the motor
4. purple cross is the centroid of the dark grey tube
5. i have J / Ixx,Iyy of that tube
6. Only the dark grey tube is fixed at 2 ends.
7. carrier is mush shorter than the tube


2. Relevant equations

I think I am finding the suitable eqts. So I miss this section.
Or
You think T/J= shear/R ??

3. The attempt at a solution
So,

#1 i would like to ask whether the following steps are correct
and
#2 What is the torsion equations for irregular hollow section.
#3 how to find the R, outer radius of the shaft, for the case that equation T/J= shear/R is used.


My Methodology:
1. Shear force is acting at the 2 hand sides of the tube as resultant.
2. the Shear force acts like a torque on the hollow section
3. use parallel axis theorem to transform "moment of inertia" from the original centroid to the torque center
4. use a torsion equation that contain J to fix it (<------------#2 that's what i would like to find now)

Thank you very much for your help.

Attached Thumbnails