User:Eas4200c.f08.blue.a/Lecture 11

How Ahead We Have Been
While the pace of the course seems to be slow, we have actually been covering material several chapters ahead of where we are currently at. An example is found when comparing problems 1.1 and 3.5. As it turns out, problem 1.1 is just a specific case of problem 3.5.



For the first case, the box, $$tau = T/2abt$$. In the second case, T = 2qA, where A is the average area and $$q = tau*t$$. This is a case where the first example, the box is a specific case of the second figure. The box problem is solved using the ad-hoc method and the generic shape is solved using a method based on the elasticity of the object.

Getting back to the airplane stringer problem, the question was posed last time as to why the walls of the stringer are sloped outward rather than being parallel as shown below. Also the question of why an open cross section is used rather than a closed cross section.



First off, there are 2 reasons why an open cross section is used. 1) Manufacturing - sheet metal is used to make the stringer. It is much easier to stamp an open cross section than to extrude a closed cross section. 2) Airplane construction - stringers are rivited to the outside skin of the plane and it is next to impossible to rivit a closed cross section. To use a closed cross section, spot wels would be needed.



Next, why are the walls of the stringer not parallel. It was suggested that the reason why they are not parallel is for storage purposes. Stringers can be stacked vertically when being stored prior to construction which saves a lot of space in a factory.



Shear Panels, Shear Stress/Strain
Engineering Shear Strain (not torsional shear strain)



The angle between the original and deformed box is gamma which is defined as dv/dx. Using small angle approximations, alpha = tan(alpha).

Tensorial shear strain is defined as (1/2)gammaxy.