User:Eas4200c.f08.blue.a/Lecture 14

Open Thin Walled Cross Sections Imagine a uniform bar with circular cross section that is said to be non-warping:





The cross section behaves as a rigid disk

The relation we will take as the connection between Torque that is applied and the resulting twist produced with respect to the strength of the material is called Hooke's Law. Hooke's Law can be derived from the equation of torque by setting certain variables as constants.



where



and



which can then be represented as



or



where a=the radius of the circular cross section

You will notice this equation bears a striking resemblance to the equation for the 2nd area moment of inertia of a body. In this case, though, it is in polar coordinates, and is considered the 2nd polar area moment of inertia. The 2nd polar area moment of inertia is also denoted as J.

Hollow Thin Wall Cross Section

Ri = inner radius | Ro = outer radius





 are approximations which give us



or

by arranging the equation this way, we can now see that J is proportional to the area to the 3/2 power.