Keywords: spatial deformations, prestressed bridge beam, Grid, lateral deflection, robust algorithm, slight asymmetry.

Prestressed bridge beams with a span over 25 m often suffer unfavorable spatial deformations just after transferring prestress to the beam making erection impossible. The possible reason for this behaviour is the slight asymmetry of the precast technology. Despite the rigorous prescriptions, there is a slight offset between the resultant of the prestressing force and the axis of symmetry of the cross section. Moreover, the inhomogeneous fresh concrete at the time of prestressing can also produce some asymmetry. To the best of our knowledge no reliable method for predicting the lateral deformation is available now. In our paper we apply a previously developed algorithm to predict such unfavorable deflections in the design phase of manufacturing the beam.

In the first section of the paper we describe our algorithm briefly. The core of the algorithm consists of a globally convergent recursion [3] to determine the curvature of the possibly cracked cross section of the beam. The rate of twist is calculated by taking the smaller stiffness of the cracked cross section into account, too. To determine spatial deformations we embedded the iterative procedure into the core of the so called Parallel Hybrid Algorithm (PHA), which is a well established tool to solve boundary value problems [2]. The PHA does not contain corrective iterative steps so the proposed algorithm is robust, although it requires a high computational effort. To reduce the computational time, the PHA algorithm was implemented in the parallel environment (Grid technology). We developed a user interface to provide a simple way of data input and a graphical tool to display the computational results making the algorithm available for industrial users. The algorithm has been extended by some additional subroutines to take the special material properties into account. These subroutines do not affect the robustness of the method and they are based on the Eurocode 2 standard.

In the next section we investigate the lateral torsional buckling of a simply supported, perfect beam under uniform bending moment. Here we compare our numerical results to the analytical solutions [1] and show that in the case of limited tensile strength the bifurcation is subcritical. The prestressing of the beam without tensile strength influences the critical bending moment significantly.

Finally we compare our numerical results to experimental data of asymmetrically prestressed beams. We have found a good agreement between the measured and the calculated deformations of the specimens. Although the critical bending moment of the perfect beam exceeds the ultimate moment of the cross section, the member with high span under its weight is sensitive to asymmetrical prestress.

1

W.F. Chen and E.M. Lui, "Structural stability", Elsevier, 1987.

2

G. Domokos and I. Szeberényi, "A hybrid parallel approach to one-parameter nonlinear boundary value problems", Comp. Assist. Mech. Eng. Sci., 11, 15-34, 2004.

3

A.A. Sipos, "A robust algorithm for calculating the spatial deformations of rods without tensile strength", Proc. Estonian Acad. Sci. Phys. Math., 55(2), 96-111, 2006.

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