"[A] shell element will have, in general, 10 unknown internal stress reactants... [B]y making suitable assumptions, we try to obtain simpler a solution... for practical purposes. We first assume that the shell is thin. Such shells are... very flexible for resisting bending moments and shearing forces. ...We would always prefer the shell to resist any loading by development of in-plane forces... we assume that the moments Mx, My, Mx,y and My,x are zero... Then, by taking moments about the x- and y-axes... we conclude that Qy and Qx must also be zero, and by taking moments about the z-axis, we get Nxy = Nyx. Thus there remain only three unknown internal stress resultants, Nx, Ny, and Nxy, to support a given loading. Also... three equations of equilibrium\sum_{} F_x = 0 \quad \sum_{} F_y = 0 \quad \sum_{} F_z = 0...determine the three unknowns. Such simplified theory... is called membrane theory, as opposed to the more general and complex bending theory..."