Identification of the pre-stress force in bridge beams using their first natural frequency

Pre-stressed beams are broadly applied in the highway, urban and railway bridges. In design process of these beams, the pre-stress forces are determined according to the current standards and theoretical formulas but, during the serviceability service life of a bridge, many factors such as relaxation of steel, shrinkage, creep of concrete and ambient temperature can lead to the change of the applied pre-stress forces. Therefore, in order to effectively control the operating state and the bearing capacity of bridges, it is very important to identify the pre-stress losses. The proposed method is the extension of the Simplified Formula of Galef [Galef, 1968] to generic pre-stressed bridge beams for the identification of their pre-stress forces. The procedure is suitable for any slender simply-supported beam of any bridge. Making use of the first natural frequencies of the unloaded and loaded beam under investigation, the Simplified Formula is able to estimate the pre-stress force, knowing the respective buckling load. Most of the existing dynamic methods are particularly sensitive to experimental and model errors in which it is also difficult to select a-priori the best natural frequency that will estimate the pre-stress force. In fact, different natural frequencies values lead different precisions in the estimations. The proposed procedure does not require any selection of the best mode shape to be used in the identification process. Numerical tests on two post-tensioned concrete and steel beams confirm the robustness of the non-destructive method even in the presence of moderate parameter errors.