Optymalizacja belek sprężonych

W pracy przedstawiono problem optymalizacji dwuprzęsłowych belek sprężonych. Przedstawiono model fizyczny optymalizowanego elementu, a następnie sformułowano problem brzegowy o ściśle określonej strukturze formalnej, umożliwiającej zastosowanie zasady maksimum. Przeprowadzono przykładowe obliczenia mające na celu wyznaczenie optymalnej trasy kabla sprężającego, dla którego ugięcie elementu będzie minimalne.

The paper deals with an optimization problem for double-span pre-stressed beams. The presented methodology can be also applied to the pre-stressed and post-tensioned beams of any cross-section. The physical model of the optimized element is described (Figs. 1, 2). In the problem analyzed there were considered five phases of load (Fig. 2). Then there was formulated the boundary problem with a strictly defined formal structure, allowing use of the maximum principle (Section 3). The attention was paid to the way of formulating the optimization constraints. An example calculation was made to determine the optimal route for a compressing cable ensuring the minimum deflection of the element when simultaneously fulfilling the constraints resulting from the ultimate and serviceability limit state. The presented optimization problem can be transformed in any way by assuming the decision variables to be any dimensions of the cross-section while the objective function as, among others, the volume of concrete, the bending, the compressive stress, the tensile stress. The obtained solution shows the effectiveness of the presented method of calculations.