The aim of the article  was to discuss the application of steel-concrete composite structures in bridge engineering in the aspect of structural design, analysis and execution. It was pointed out that the concept of steel-concrete structural composition is far from exhausted and new solutions interesting from the engineering, scientific and aesthetic points of view of are constantly emerging. These latest trends are presented against the background of the solutions executed in Poland and abroad. Particular attention is focused on structures of double composition and steel-concrete structures. Concrete filled steel tubular (CFST) structures are highlighted.
The paper considers some results of creating load-carrying composite systems that have uprated strength, rigidity and safety, and therefore are called geometrically (self-) hardening systems. The optimization mathematic models of structures as discrete mechanical systems withstanding dead load, monotonic or low cyclic static and kinematic actions are proposed. To find limit parameters of these actions the extreme energetic principle is suggested what result in the bilevel mathematic programming problem statement. The limit parameters of load actions are found on the first level of optimization. On the second level the power of the constant load with equilibrium preloading is maximized and/or system cost is minimized. The examples of using the proposed methods are presented and geometrically hardening composite steel-concrete system are taken into account.