This work extends the theory of limit analysis [2, 5] which consists in computing a structure maximum load bearing capacity to topology optimization problems. Here we aim at finding a structure which maximizes the load-bearing capacity, given some material strength properties, on a fixed computational domain with a given material volume constraint. The problem is relaxed to a convex optimization problem by considering a continuous fictitious density field. We show that this problem is equivalent to minimizing the total volume such that the structure can withstand a given fixed loading [3, 1]. State-ofthe-art conic programming solvers [4] are used for computing the solutions to the convex optimization problems. Finally a SIMP-like penalty method is proposed to obtain discrete topologies. Materials with asymmetric tensile and compressive strengths are considered, with the particular case of no-tension materials. Examples illustrating the efficiency of the proposed method will finally be presented.