User:Eas4200c.f08.gator.reger/Week13,14

Meeting 36, Weds 11/19
Upcoming plans:


 * S.) Single-cell Sections
 * S.1) Without Stringers
 * S.2) With Stringers
 * M.) Multi-cell Sections
 * M.1) Without Stringers
 * M.2) With Stingers

S.1) Without Stringers
Can the section from Figure 1 resist transverse shear $$V_x\,$$

$$R^z = R^z_{AB} + R^z_{BA}\,$$ Where $$ R^z_{AB} = q\bar{A'B'} = -R^z_{AB}\,$$ Therefore: $$R^z = 0\,$$

S.2) With Stringers
Looking at Figure 2 (Neglecting contribution of web to bending)

$$ R^z = V_z \,$$ Principal of superposition due to linearity, non-constant shear flow. $$q_{12} = q + \tilde{q_{12}} ,..., q_{ij} = q + \tilde{q_{ij}}\,$$ Where $$ q_{12}\,$$ is not equal to $$ q_{23}\,$$ is not equal to $$ q_{31}\,$$ But $$ q_{ij}(s)\,$$ is constant.

Analytic Algebra
Observation: One unknown $$ q\,$$ (since $$\tilde{q_{ij}}\,$$ is known after solving P2): Need one equation. Method: 1.) Solve problem P2 (Given $$ V_z, V_y\,$$) for all \tilde{q_{ij}}\, 2.) Moment Equation: Take moment about any point in the plane ($$y,z\,$$) 2.1) Superposition: $$ q_{ij} = q + \tilde{q_{ij}}\,$$ 2.2) Select point $$\bar{\theta}\,$$ in plane ($$y,z\,$$) 2.3) $$\Sigma{\theta}\,$$ Moment of ($$ V_z, V_y\,$$)