User:Eas4200c.f08.WIKI.E/hw7

Mtg 37 Friday 21 November 08
3) Back to Superposition :

$$q_{ij} = q + q_i$$ where $$q_{ij}$$ is true shear flow $$q$$ is the closed cell constant shear flow $$q_i$$ is the open cell piecewise constant shear flow

M.1)W/o stringers


$$R^z=\sum_{i=1}^{n cells}{R^z_i}$$ where $$n=$$ the number of cells

$$R^z_1=0$$

$$R^z=0\;$$

M.2)With Stringers


$$R^z=R^{z1}+R^{z2}\;$$ where $$R^z \;$$ is the resultant of P

$$R^{z1}\;$$ is the resultant of P1 and $$R^{z2}\;$$ is the resultant of P2.

Recalling $$R^z=\sum_{i=1}^{n cells}{R^z_i}=0\;$$ provides us with the formula:

$$R^z=R^{z2}=V_z\neq 0\;$$