**2.1. Overpass bridges**

impact of a bridge, especially true of urban overpasses with regard to their more intrusive

Much of the public focus has been centred on several "landmark" bridges [2]. Denn [3] specifies aesthetic guidelines for bridge design, remarking that a careful and early application of aesthetic concepts can make a significant improvement in the appearance of bridges and structures. Every bridge is, to some degree, a historical document, a demonstration of struc‐ tural technique, a performance test of building materials, a comment on the values of a society which produced it and a reflection of the richness or poverty of its designer's imagination. So, the bridge designer must strive to understand the creative process, together with scientific and technical principles. The aesthetic aspects that stimulate the senses in most viewers are proportion, order, simplicity, balance, colour and texture. Design bridges must incorporate these aesthetic principles with the physical and geometric components of the structure.

In this context, the generation of three‐dimensional (3D) geometric models of bridges, which are to be designed and analysed, can play an important role. For this purpose, a computer graphic system, which enables the 3D geometric modelling of decks of the most frequent types of bridges, was developed. With this tool, the geometry of the bridge shape can be directly inserted into the computer application, using the user‐friendly interfaces with geometric parameters of the longitudinal view and cross section of the bridge deck. In this way, the description of the geometry, conceived for each case, is easily achieved. In addition, it satis‐ factorily supports a rapid definition of several suitable alternative solutions for the bridge.

In addition to the 3D model of a bridge allowing its aesthetic analysis, it also supports the creation of 4D (3D + time) interactive models simulating the construction work. In order to create interactive 4D models, simulating the sequence and progress of the construction process, techniques of virtual reality (VR) were used. The designer links each construction task, established in a Gant map, to specific 3D model components, and programs the simula‐ tion of the bridge construction process, using the VR software. The virtual interactive 4D model allows users to view and interact with these construction stages and with the equipment

The incorporation of VR technology into 3D geometric models allows greater realism in the simulations; it is, now, often applied in the field of engineering perhaps because VR technology constitutes a good interface and provides the possibility of finding solutions to real‐life

As aesthetic value is important for civil engineering projects, which impact urban and natural environments, it can be incorporated in curricular programs in engineering schools. However, the attention to structures traditionally dominates in the modern day university education of civil engineering, and the teaching of aesthetics meets obstacles. The main difficulty is the thought that aesthetic values are unfamiliar to engineers. This leads to the need for the

location close to areas of the pedestrian use.

58 Structural Bridge Engineering

involved in the process.

problems in the construction field.

**2. Automatic generation of 3D models**

Overpasses are structural solutions that allow crossroads on different levels. They are usually used when a high‐speed road or a road with intense traffic must be crossed, usually by a secondary road that passes above the dominant one (**Figure 1**).

An overpass has a very significant visual impact but usually, such a careful aesthetic evaluation as that conducted for bridges is not considered necessary/worth the effort. The aesthetic analysis can be organized into two categories [3]: visual design elements and aesthetic design qualities. These structures have a high level of exposure, especially when they are in urban areas, so they should receive a special aesthetic analysis so as to provide a comfortable level of impact. The focus of the analysis is oriented to the shape of the bridge aesthetic aspects such as linearity, setting, brilliance, roughness and smoothness or aggression of shapes.

In the aesthetic study of an urban overpass, the implemented 3D modelling tool allows the easy creation of several solutions for the bridge, with distinct longitudinal shape and different type of deck cross section. The ability to create of 3D models easily, allowing the visualization of each alternative option, supports decision‐making regarding the best solution for the bridge [4]. The interface of the overpass 3D modelling tool is composed of three main windows where the required parameters and supplementary information must be introduced. **Figure 2** shows the interface windows concerning the longitudinal deck shape and two types of cross‐ sectional shapes.

**Figure 2.** Interface of T‐beam and slab section types.

The modelling process is based on geometric parameters allowing the definition of the bridge geometric configuration. It is not needed to indicate the vertices coordinates and the type of drawing element. Based on the parameter's values, the program allows the automatic gener‐ ation of the desired bridge shape. So, the program makes possible to automatically generate 3D models. The parameterization was applied to two types of most used overpass sections, T‐ beam and slab (**Figure 2**); to linear and parabolic longitudinal variations of the deck and to the road geometry in plant and vertical views.

The program was created using Visual Basic programming language, and it is made up of three main windows. The cross‐sectional window is presented in **Figure 2** and the horizontal and vertical alignment windows in **Figure 3**. The interfaces enable the definition of all the possible variations of the geometry of the road. For this purpose, the tool allows the geometric charac‐ terization of all design parameters needed, namely linear alignments, circular curves, transi‐ tion curves and parabolic curves.

**Figure 3.** Vertical and horizontal alignment windows.

The program was tested in a case study. A first 3D model of the bridge was created, followed by several possible alternative solutions (**Figure 4**). The initial solution is a solid slab cross section with constant height, and the alternative options are as follows:


In addition, the program enables the consideration of as many pile forms as the engineer wishes for, with any longitudinal or transversal forms. This versatility made offered by the program facilitates a more thorough aesthetic study. The use of parametric computer programming makes it possible to quickly obtain the 3D model of the overpass and many alternative solutions under analysis. So, it allows users to carry out a more accurate study of the overpasses' aesthetics, supporting the comparative analyses between different possibilities and conse‐ quently the choice of the most suitable option. The modelling process should be done in steps, beginning with a global analysis of all the possible solutions, continuing with the consequent elimination of some of them and going on to more accurate and detailed analysis of a smaller group of possible solutions. This provides the opportunity to choose the solution that presents a good rhythm and a pleasant sense of continuity to the structure.

## **2.2. Box girder bridge**

type of deck cross section. The ability to create of 3D models easily, allowing the visualization of each alternative option, supports decision‐making regarding the best solution for the bridge [4]. The interface of the overpass 3D modelling tool is composed of three main windows where the required parameters and supplementary information must be introduced. **Figure 2** shows the interface windows concerning the longitudinal deck shape and two types of cross‐

The modelling process is based on geometric parameters allowing the definition of the bridge geometric configuration. It is not needed to indicate the vertices coordinates and the type of drawing element. Based on the parameter's values, the program allows the automatic gener‐ ation of the desired bridge shape. So, the program makes possible to automatically generate 3D models. The parameterization was applied to two types of most used overpass sections, T‐ beam and slab (**Figure 2**); to linear and parabolic longitudinal variations of the deck and to the

The program was created using Visual Basic programming language, and it is made up of three main windows. The cross‐sectional window is presented in **Figure 2** and the horizontal and vertical alignment windows in **Figure 3**. The interfaces enable the definition of all the possible variations of the geometry of the road. For this purpose, the tool allows the geometric charac‐ terization of all design parameters needed, namely linear alignments, circular curves, transi‐

sectional shapes.

60 Structural Bridge Engineering

**Figure 2.** Interface of T‐beam and slab section types.

road geometry in plant and vertical views.

tion curves and parabolic curves.

**Figure 3.** Vertical and horizontal alignment windows.

The same application has the capacity to generate 3D box girder deck superstructures [5]. The tool allows the creation of consecutive cross sections, exactly defined and correctly located, along the deck (**Figure 5**). The interface presents diagrams linked to dimensional parameters, in order to facilitate the description of the geometry established for each concrete case of the deck. The 3D model is the result of an appropriate combination of two longitudinal geometric components: the deck morphological evolution and the layout of the road, which acts simul‐ taneously over a cross section, defining the exact deck shape'. The Annex item includes the algorithms used to calculate the 2D coordinates of each vertices of this type of cross section.

The geometric database, needed to create the 3D model of the deck, is formed by a set of geometric parameters, which the bridge designer deals with at the conceptual design stage. To obtain the 3D model of a deck segment, consecutive sections corresponding to the con‐ struction joints are generated using the algorithms of the program and connected to surfaces. The final configuration of the deck is comprised of two longitudinal surfaces: one representing the exterior side of the deck and the other its interior. The top cross sections are finally added to the 3D model (**Figure 5**). As this model uses cross sections correctly defined in shape and in their spatial orientation, it represents the real form of the deck. After the deck, 3D model is completed with the pillars and abutments, and it is inserted into the landscape. The aesthetic evaluation can then be carried out.

**Figure 6.** Longitudinal section and cross sections with different shape and transversal slope.

The implemented software allows the definition of traditional drawing usually required in a bridge project. As the horizontal alignment of the road is normally curved (**Figure 5**) and the road surface is never horizontal, the longitudinal deck section drawing must correspond in order to make a plan of the cut vertical surface defined along the deck axis (**Figure 6**). In this type of drawing, the elevation of the deck at distinct points along it needs to be calculated (**Figure 6**). These values depend on the elevation alignment characteristics. It is also a complex procedure to represent a set of consecutive cross sections with different interior and exterior shapes along the deck.
