Keywords: large displacements, slender structures, reinforced concrete, optimization, experimental results, effective bending stiffness.

One of the pertinent verifications in structural projects is to check if the computed displacements are inside certain limits given by codes. In RC structures, in function of the specificities of this product, such as cracking and cross section stiffness reduction, this calculation becomes sometimes imprecise and, in these cases, the installed structures may present displacements larger than foreseen. In structural design, the cracking phenomena in RC structures are interpreted as physical nonlinearity.

In other words, the stiffness depends on the strength. As a contribution to the studies already accomplished on the determination of effective stiffness in RC cross sections, which will be presented ahead, in the present work we intend: (i) to develop a procedure for the determination of the effective stiffness, and to determine an equation involving the effective stiffness and the bending moment level in a certain section; (ii) to explore the practical and theoretical aspects of the stiffness loss determination, observing that relation exists between the sections where the larger losses happened and the sections that indeed collapsed in a real similar structure.

The methodology of this work bases on comparing the displacements measured in tests in RC structures with data obtained integrating of the elastic line. The quadratic error between the real displacements measured in tests and those provided by the elastic line integration is minimized using optimization techniques. The objective function is the quadratic error, while the design variables are the effective stiffness in each section. Constraints are imposed on the maximum and minimum values of the effective stiffness. Several different formulations are used for the displacements calculation as well as for the optimization methods.

As a consequence of the results of these studies, it will be possible to preview precisely the displacements presented by RC structures composed by beams, besides possible application in forecasting structural collapse.

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