User:EAS4200C.F08.WIKI.A/My Contribution: HW

=Aircraft Example=

The following figure provides examples of materials used on the F/A-18E Hornet. All of the materials used in this aircraft are light, high in stiffness, and high in strength therefore allowing for optimal performance and long durability. It is desirable however to eliminate all aluminum and titanium and replace them with Fiber Reinforced Composites which would in turn decrease the weight of the aircraft by 30%-40%. In doing so the aircraft would be at its maximum performance. An example of the composites being used in aviation can be seen in the Boeing 787. Fifty percent of this vehicle is made up of these materials making it lighter and more efficient.

The table below gives some examples of parts made of the materials portrayed or not portrayed in the photo.

=Problem 1.1 (Sun 2006)=

Now that some fundamentals have been laid out, it is time to review some concepts that would have been learned in a course known as Mechanics of Materials. It is a course that covers the tendencies of materials under certain forces, bending moments, and torques. To do so a problem from the text "Mechanics of Aircraft Structures" by C.T. Sun will be covered. The problem statement is as follows.

Problem Statement

"The beam of a rectangular thin-walled section (i.e., t is very small) is designed to carry both bending moment M and torque T. If the total wall contour length L = 2(a+b) [(see figure below)] is fixed, find the optimal ratio b/a to achieve the most efficient section if $$M=T$$ and $$\displaystyle\sigma_a=2\displaystyle\tau_a$$ . Note that for closed thin-walled sections such as the one shown below, the shear stress due to torsion is:

$$\displaystyle \tau = T/2abt$$



Problem Solution

The solution to this problem requires the analysis of two separate cases because the question asks for the optimal ratio. The first case assumes that the $$\displaystyle \sigma_m$$ reaches $$\displaystyle \sigma_a$$. In order to judge the correctness of the answers gotten from the analysis, it is imperative that the $$\displaystyle \tau_m $$ < $$\displaystyle \tau_a$$. If for this case $$\displaystyle \tau_m $$ > $$\displaystyle \tau_a $$, than the ratio of b/a is not acceptable.


 * Case 1
 * The first step in solving this problem is to compute the allowable bending moment, M, that corresponds to $$\displaystyle \sigma_m$$ at the location of z = b/2