Notes 7 " Torsion << Pt.2>> "

Torsion "Pt.2"

* Example :

 
* Shear stress direction :

For Single Piece :

For Closed Section :

Example :

Structural aluminum tubing of 60x100mm rectangular cross section was fabricated by extrusion . Determine the shearing stress in each of the four walls of a portion of such tubing when it is subjected to a torque of 2.7 KN.m , assuming that :

a) a uniform wall thickness .

b)  as a result of defective fabrication , walls AB and AC are 3-mm thick, and walls BD and CD 5-mm thick .

Solution :

(a) Tubing of uniform wall thickness. 

The area bounded by the center line :

Since the thickness of each of the four walls is t=4mm . We find that the shearing stress in each wall is :

 (b) tubing with variable wall thickness

Observing that the area   bounded by the center line is the same as in part a
And substituting t=3 mm and t=5mm and t=5mm

* We note that the stress in a given wall depends only upon its thickness  .