Shear Flow in Multi-Cell Sections

Traditional shear flow calculations for thin-walled multi-cell sections subjected to bending have ignored developments in topological algebra that exploit the independence of a network topology from its physical characteristics. By treating the section as a set of thin limbs connected at end nodes, network theory originally developed for electrical circuits can be applied to the problem. Flow rules similar to those formulated by Kirchhoff almost a century and a half ago are derived from conditions of equilibrium and compatibility.

Each limb of the section behaves as a flow generator which drives the flow around the network. A complete solution can be derived for shear flow and for warping displacement in every limb by solving a relatively small number of fundamental circuit equations, equal to the number of independent circuits in the network. Matrices employed in the solution can be formed directly from the section's topological description.