A model of joined beams as limit of a 2D plate

In this paper, we consider an elastic multi-structure composed of two joined beams forming an angle $alpha in ]0, pi/2]$ at the junction, clamped at the three extremities and submitted to forces transverse to the plane containing the skeleton of the multi-structure. We derive the equilibrium configuration of the transverse displacement and the torsional rotation of the multi-structure, via an asymptotic analysis based on a dimensional reduction of a Kirchhoff-Love plate. More generally, we obtain the equilibrium configuration of the transverse displacement and the torsional rotation of a multi-structure whose skeleton is composed of a line and a planar curve joined together.