  We reconsider the minimization of the compliance of a two dimensional elastic
body with traction boundary conditions for a given weight. It is well known how
to rewrite this optimal design problem as a nonlinear variational problem. We
take the limit of vanishing weight by sending a suitable Lagrange multiplier to
infinity in the variational formulation. We show that the limit, in the sense
of $\Gamma$-convergence, is a certain Michell truss problem. This proves a
conjecture by Kohn and Allaire.
