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The paper continues along the work initiated by the authors in taking into account stress constraints in topology optimization of continuum structures. Revisiting some of their last developments in this field, the authors point out the importance of considering stress constraints as soon as the preliminary design phase, that is, to include stress constraints in the topology optimization problem in order to get the most appropriate structural layout. Numerical applications that can be solved using these new developments make possible to exhibit interesting results related to the specific nature of strength based structural layout for maximum strength compared to maximum stiffness. This particular character of stress design is clearly demonstrated in two kinds of situations: once several load cases are considered and when unequal stress limits in tension and compression are involved.