Hollow rectangular Beam - rigidity and max torque

[10^-3]

Revision that is turning into a learning from scratch session. Some help would be welcome!

- I have a hollow rectangular beam. 0.150m by 0.110m with uniform thickness walls at 0.003m. It is 3m long.
- It has a modulus of rigidity (G) of 27 GigaPascals.
- It has a max permitted shear stress of 200 MegaPascals.

What is the torsional rigidity?
What is max permitted torque (with a safety margin of 2.0)?
What would be the twist angle for the 3m length?

Torsional rigidity = G x second area of inertia. I have G so need 1xx.
1xx =
Each side at ((0.003x0.110^3)/12) = 3.33 E-07
Top & base each at (using parallel axis theory) ((0.003 x 0.144^3)/12) + (0.003 x 0.144 x 0.062^2) = 2.41 E-06
Add 4 sides = 5.48 E-06

Torsional rigidity = 27 E09 x 5.48 E-06 = 148,000 (units?)

Is this right and what are the units?

As for the other 2 parts – I am lost. Any pointers?

 

[Navin A S]

The units for the torsional rigidity are N·m2. Max permitted torque = max allowed shear stress x second area of inertia. Max allowed shear stress = 200MPa Second area of inertia = 5.48E-06 m4 (as calculated above) Max permitted torque = 200MPa x 5.48E-06 m4 = 1.1E-02 N·m With a safety margin of 2.0, the max allowed torque = 2.2E-02 N·m Twist angle = torque applied / torsional rigidity For a 3m length beam, the twist angle = (2.2E-02 N·m) / (148,000 N·m2) = 1.49E-05 radians