  The final purpose of this paper is to show that, by inserting a convexity
constraint on the cables of a suspension bridge, the torsional instability of
the deck appears at lower energy thresholds. Since this constraint is suggested
by the behavior of real cables, this model appears more reliable than the
classical ones. Moreover, it has the advantage to reduce to two the number of
degrees of freedom (DOF), avoiding to introduce the slackening mechanism of the
hangers. The drawback is that the resulting energy functional is extremely
complicated, involving the convexification of unknown functions. This paper is
divided in two main parts. The first part is devoted to the study of these
functionals, through classical methods of calculus of variations. The second
part applies this study to the suspension bridge model with convexified cables.
