User:Eas4200c.f08.blue.a/Lecture 8

The motivation for this problem is that we are trying to study a box beam with a rectangular cross-section as a model for aerospace structures. These structures have a variety of applications in the aerospace industry such as in the fuselage and the wings, for example.

In continuation of problem 1.1, we left off on lecture 7 discussing the results of the Case 1 example. We saw that the strongest structure ended up having a height that was 3 times longer than it was wide.

Lecture 8 presented the idea of looking into the shear stress caused by Tmax(1). Where:



Recalling that we allow this equivalences due to Assumption 2. Furthermore:



Recalling that this is due to Assumption 3. As you can see, this is not acceptable.



The Mohr's Circle defines the region by which sigma and tau interact on this beam. Notice that tau is exactly half of sigma.

CASE 2:

Now, let's assume the maximum shear stress reaches the allowable shear stress first.



This is valid due to the assumption that there is a uniform stress distribution throughout the member.



It is clear to see that the only way to maximize T is by maximizing (ab), since thickness and allowable shear stress are fixed.



where (ab)max is the maximized value of (ab), which coincidentally is only when a=b=L/4