Structural Optimization of Stiffened Plates

Abstract

The orthotropic steel deck (OSD) is a deck system applied regularly in steel bridges all around the world. It consists of a steel deck plate which is stiffened by structural elements placed in two orthogonal directions. The deck plate can be used as an integral part of the structure, causing OSDs to achieve a high material efficiency and therefore low self-weight. However, this structural integration requires a large number of welded connections between the deck plate and stiffening members, which also make the system susceptible to fatigue. The fatigue evaluation of these connections is complex and time-consuming, hindering the manual optimization of orthotropic deck designs.

The use of structural optimization could be a solution for this. With parametric optimization, the best possible ratio between structural dimensions may be searched for automatically, while topology optimization could assist in finding new design concepts that could form alternatives to the traditional deck layout. This thesis investigates how these techniques could reduce the self-weight of the design of a case study (the renovated Van Brienenoord bridge) without reducing its fatigue service life. The two methods are treated in separate parts.

In the first part, considering parametric optimization, the traditional OSD concept is maintained and the values of seven selected dimensions are adjusted to obtain a design with a minimized weight. A workflow is developed in which an existing mathematical optimization solver (the artificial bee colony algorithm, a metaheuristic) is coupled to a parametric model, finite element program, and fatigue damage calculator. This enables an iterative process in which designs are generated by the solver and then evaluated in the remainder of the workflow. The information gained from the evaluation is returned to the solver and used to search for lighter designs.

In the second part, the deck remains a stiffened steel plate, but the location and orientation of stiffeners may be changed. Two possible leads for finding new structural concepts are explored. The first considers a topology optimization using the ground structure method, which can find the optimal orientation and size of stiffeners in a plate. This thesis evaluates the method’s current applicability on steel bridge decks. The second lead interprets the results of a topology optimization from existing literature. This gives a new design concept in which the crossbeams curve directly towards the supports instead of being indirectly connected by main girders. A weight minimization using the workflow of the first part and a study of the force transfer in the deck are performed to assess the new concept’s potential.

The first part showed that a 17,4 percent lighter deck structure (280 kg/m2 instead of 339 kg/m2 ) could be obtained for the case study by breaking with the general trend for designing orthotropic steel decks. The optimized design uses smaller and more rectangular troughs than commonly applied, but the largest differences are found in the deck plate thickness and stiffener spacing. For the latter, a value of 300 mm has been in use since the introduction of OSDs in the 1950’s and is present in almost any bridge using an orthotropic steel deck. When fatigue issues started to appear from the 1970’s onward, it was generally decided to increase the deck plate thickness. The results in this thesis strongly suggest that decreasing the stiffener spacing and trough top width is the preferred option when material efficiency is considered. A cost estimation further showed that the price of the optimized design would be comparable to that of the preliminary design that was suggested for the case study.

The topology optimization using the ground structure method showed that the optimal placement of stiffeners for a plate-like bridge deck contains two distinctive zones. Between the supports, the traditional longitudinal-transverse orientation is preferred, while the optimal direction of stiffeners in the middle of the bridge segments is arbitrary. The conventional OSD concept could be seen as optimal based on this result, but for definitive conclusions more research is needed towards a non-linear relation between cross-sectional area and resistance in the applied method. The similar support conditions of decks in other bridges make it likely that these conclusions will apply to those cases as well.

The optimization of the curved crossbeam concept showed the versatility of the workflow developed in the first part of this thesis, as only minor adaptations in the parametric model were needed for the application on a significantly different design. Despite the successful optimization, the potential of the new design to replace the traditional OSD concept is considered low. In its optimized form, the concept was 9,8 percent heavier and less than half as stiff as the best found result in this thesis’ first part. The comparable support conditions for plate girder bridges in general again suggest similar outcomes for other cases, while a different setup of the optimization would not tackle the fundamental stiffness problem of the design. Further research towards the curved crossbeam concept should therefore stick to the original application of box girder decks.