User:Eas4200c.f08.gator.edwards/Problem 1.1

Problem 1.1
 Team gator, you need to register user "Eas4200c.f08.gator.edards" so that this wiki page can be preserved. I also moved the figure up so that it does not block the link to "show" your first collapsible table. Eml4500.f08 12:52, 18 September 2008 (UTC)



Problem 1.1 is taken from the textbook Mechanics of Aircraft Structures by C.T.Sun, copyright 2006.

Find the optimum ratio of $$b/a$$ to maximize the load carrying ability of the beam. Assume $$M=T$$ and $$\displaystyle \sigma_{allowable}=2\displaystyle \tau_{allowable}$$.

The question is asking for the optimal cross section carrying the maximum bending moment and maximum torque.

Since the cross section walls are very thin, assume shear stress distribution in the thin walls of the beam are distributed uniformly. This results in the equation $$\displaystyle \tau=\frac{T}{2abt}$$.

Case 1: Assume $$\displaystyle \sigma$$ (bending moment stress) reaches $$\displaystyle \sigma_{allowable}$$ first. Verify $$\displaystyle \tau \le 2\displaystyle \tau$$.

From Mechanics of Materials, the normal stress caused by a bending moment is $$\displaystyle \sigma=\frac{Mz}{I}$$