Keywords: optimal design, bridges, box girder.

In this work the problem of optimal design of curved prestressed box girder bridges is addressed. The design variables are the coordinates of the nodes that define the single cell box girder cross-section and the prestressing forces of the internal and external web of the cross-section. The entire design corresponds to a level of preliminary design and takes into account all loading cases specified in DIN 1072 for vehicle SLW 60/30 and the main strength and serviceability constraints based on DIN 4227.

The analysis is based on stresses developed from a longitudinal analysis that considers the bridge as a 3D frame and a lateral analysis that is based on a frame model of the cross-section appropriately supported. The mechanical properties of the box section are determined on the basis of a refined theory based on boundary element method, or simplified formulas. The tendon loads are determined at a number of closed spaced sections by first solving the geometrical problem that defines the projection of a parabola at the vertical chord plane to the internal and external web and then determine the concentrated load in the plane of three consecutive nodes. These nodal loads are transferred to the axis of every section as statically equivalent loads and moments under the assumption of non deformable section. All loading cases that produce min-max stresses are defined and are used to determine the constraints of the problem.

The optimization problem considers a combined objective that accounts for both the cost of the concrete and the cost of the prestressing tendons based on unit prices using a micro GA algorithm. Numerical results are presented that verify the main design rules of thump that exist among experts in bridge design.

1

Ariyawardena, N.; Ghali, A. Prestressing with Unbonded Internal or External Tendons: Analysis and Computer Model, Journal of Structural Engineering, Volume 128, Number 12, December 2002, pp. 1493-1501. doi:10.1061/(ASCE)0733-9445(2002)128:12(1493)

2

Gruttmann, F.; Wagner, W.; Sauer, R. Zur Berechung von Wolbfunktion und Torsionskennwerten beliebiger Stabquerschnitte mit der Methode der Finiten Elemente, Bauingenieur, 73(3), 1998, pp. 138-143.

3

Sampaio, A.Z. Geometric Modelling of Box Girder Deck for Integrated Bridge Graphical System, Automation in Construction, Volume 12, 2003, pp. 55-66. doi:10.1016/S0926-5805(02)00040-7

4

Sapountzakis, E.J. Solution of Non-uniform Torsion of Bars by an Integral Equation Method, Computers & Structures, Volume 77, 2000, pp. 659-667. doi:10.1016/S0045-7949(00)00020-1

5

Sennah, K.M.; Kennedy, J.B. Literature Review in Analysis of Box-girder Bridges, Journal of Bridge Engineering, Volume 7, Number 2, March 2002, pp. 134-143. doi:10.1061/(ASCE)1084-0702(2002)7:2(134)

6

Koumousis, V.K., Georgiou P.G., "Genetic Algorithms in Discrete Optimization of Steel Truss Roofs" Journal of Comp in Civil Engineering 8(3):309-325, 1994. doi:10.1061/(ASCE)0887-3801(1994)8:3(309)

7

Goldberg, D.E., "Genetic algorithms in search, optimization, and machine learning" Addison-Wesley, Reading, Mass., USA, 1989.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £123 +P&P)