# Determination of Warping Function for Thin-walled Multi-cellular Beams

I am trying to find warping function $$\mathcal{T}$$ for a thin-walled multi-cellular beam. There are four rectangular cells. The governing differential equation for $$\mathcal{T}$$ is Eq. 8.98 as shown in attached figure. But I don't know the boundary condition.

• In practice, the fact that you don't know the boundary condition makes these warping function corrections fairly useless, because it is a situation where St Venant's Principle does not apply. IMO, if you need to include this level of detail in a structural analysis, you shouldn't be using beam elements anyway. Apr 8 '19 at 9:49
• … and this is a good example of the engineering principle "design structures that you can analyse easily" If a design only functions correctly because of the exact amount multi-cell beam warping, there is something seriously wrong at the conceptual level, IMO. Apr 8 '19 at 9:53