This paper investigates the classical linearized model used in the optimization of trussed structures and indicates a method for controlling its approximate nature. It is shown that the expansion of the nodal displacements and axial stresses in two-term Taylor series is equivalent to replacing the axial stiffnesses of the elements by approximate ones called apparent stiffnesses. We can thus evaluate and control the inherent approximation of the model by means of a basic structural quantity: the axial stiffness. This is the "physical" counterpart of the "mathematical" linearization of the equations. In a context of sequential linear programming one has thus at his disposal a mechanical measure to devise suitable move limits for the design variables. Move limits strategies based on limiting the ratios of the apparent stiffnesses to the original stiffnesses can improve the convergence characteristics of a sequential linear programming procedure.