1
Introduction

Key learnings after reading this chapter:

• What influence do construction activities exert on the climate?
• What are the requirements of a future-oriented way of building?
• How can structural optimization methods contribute to this?

1.1 Preliminaries

Concrete is one of the oldest building materials in the world. The Romans already used it and achieved strengths of up to about 40 MPa [1]. Concrete exhibits an uneven distribution of strengths. Its compressive strength is high, but its tensile strength equals about one tenth of it. Concrete is therefore predominantly stressed in compression while tension is avoided. Structures whose design is oriented toward the material properties take this aspect into account and primarily bear loads via compressive stresses. Thus, this corresponds to the traditional use of concrete for arches, columns, and domes, where compressive forces prevail.

With the advent of reinforced concrete (RC) in the 19th century, the restriction to structures subjected predominantly to compressive stress was lifted [2], since steel was employed to enhance concrete in tension emerging from bending, shear forces, or axial loads. The same applies to local areas of load application or geometric discontinuities such as corbels, openings, and supports.

Due to three factors, namely the technological feasibility of reinforcement, scarcity of human labor and low material costs for concrete itself, the structures changed. Curved shapes disappeared and were widely substituted by simple, rectangular ones, which prevail to the present day. Typical examples are prismatic plates, walls, or beams. The formwork shapes are simplistic and can be easily produced on a large scale. Thus, the structural designs are often motivated by the simpler construction on site, although larger quantities of concrete and steel are needed.

Building is a question of time, its capabilities and the pursuit of goals [3]. Expensive materials lead to rather slender designs. High labor and formwork costs require automation and simplification of shapes. Furthermore, the demand for short construction times favors prefabricated components.

Compared to other building materials, concrete has the advantage of free formability. The initially liquid material hardens and obtains its permanent, solid shape only through hydration. In this respect, concrete structures are open to virtually unlimited outer shapes. In the same way, its inner shape - namely the layout of reinforcement - is freely adjustable and installable. It does not have to adapt to formwork edges in any way, but can easily follow the tensile trajectories instead.

So what is the right shape? What is the right reinforcement (pattern) and where is it located? How does the right cross-section look like? The answers to these questions depend on the defined objectives and constraints to be met. And these conditions change. They change over time, they change depending on the country and the way of life, and they change according to external influences. Because of this mutability, the approaches to find the right shapes must therefore account for the relevant objectives and constraints. This is the only way to find different answers to similar questions, differing only in the underlying boundary conditions. In this way, the range of answers expands and adapts to the scope.

The book develops a generally applicable method for this purpose, namely the Optimization Aided Design (OAD). It is motivated by three fields of investigation. These are:

• the outer shape of structures,
• the inner reinforcement layout, and
• the cross-sectional design.

Briefly, the inner and outer form finding.

1.2 Outer and Inner Shaping

The outer shape of a concrete structure is determined by its intended purpose. This can be, for example, the enclosure of a storeroom, the load-bearing function for a bridge deck, a plane surface of a ceiling, or shielding against soil and groundwater in a tunnel. The shape further characterizes the design.

The outer shape is influenced by the load-bearing and protective function to be met, aspects of economic efficiency, the construction process and the way the structure integrates into the surrounding environment. It is virtually arbitrary due to the ability of free formability, since concrete exhibits the advantage of taking any shape. In this respect, no distinction can be made between "right" and "wrong", since all designs meet the requirements for load-bearing capacity, serviceability, and durability.

In the case of engineering structures such as bridges or tunnels, their outer shape clearly indicates the static load-bearing system. If the outer form follows the dominant internal force flow ("form follows force") and further predominantly orients toward compression, lightweight and, in many cases, bionic-like, curved structures result. Typical examples are arches, shells or even pylons of bridges with inclined cables, which experience a distinctly dominant downward load impact due to the deflecting forces of the cables.

Figure 1.1 Concrete shaped to the flow of forces: pylon of the Pont de Terenez (France). Picture: Thomas Putke-Hohmann.

Figure 1.1 shows such a form finding according to the flow of forces by the bridge "Pont de Terenz", located in France [4]. The bridge layout lies within a narrow circular bend. The pylon is shaped similar to an inverted "Y", with the front leg continuing the slightly inclined column shape above the roadway level in a straight line and orienting toward the lateral forces from the cable deviation. In this way, it is mainly subjected to compressive loads. The lower supports act like two legs in step sequence and provide further stability against lateral loads from wind and centrifugal downforces.

Structures designed according to the flow of forces tend to look aesthetically pleasing and require small amounts of material by avoiding redundant flexural load-bearing effects. In contrast, Figure 1.2 shows a solid bridge designed using simple shapes. It is composed of equal single-span beams, each of which is interchangeable. The external cross-sectional geometry of the superstructure remains constant. This results in two bearing rows per column that are accordingly thick and compact.

The bridge can be built with constant scaffolding and formwork layout. The dominant design aspect here is an effective fabrication with a repetitive sequence, meaning that every single beam is made with the same formwork and scaffolding, the same reinforcement and the same casting concept. The result is a repetitive pattern justified from cost-efficiency in manufacturing. Due to the homogeneous shape across the entire bridge, its beam-like load-bearing behavior and the necessary limitation of distinct rotation angles at the ends of each girder for the train passage, massive, heavy cross-sections result and the spacings between the columns become compact and monotonous. Compared to a structure following the flow of forces, great additional material amount is needed. For the specific case, this is mass concrete, as well as prestressing and reinforcing steel. At the same time, aesthetics suffer due to the obstructed view and consistent pattern of equal spans, equal columns, and the tall and heavy-looking superstructure.

Figure 1.2 Railway concrete bridge with uniform single span girders and compact columns.

Similar to the external shape, the internal load transfer can also be designed intentionally. The reinforcement is typically adapted to the formwork shape and not primarily to the tensile trajectories of the load transfer. For common rectangular cross-sections, reinforcement cages are produced from longitudinal bars and vertical stirrups, thus forming a rectangular grid that follows the formwork's edges (Figure 1.3a). This type of reinforcement suits the convenience of production. Due to the constant orientation, tensile trajectories and reinforcement directions differ, which automatically leads to an increased amount of required reinforcement. In other words, fabrication outweighs material efficiency.

Figure 1.3b shows an alternative layout. Like the outer shape of the concrete cross-section, the reinforcement can also be laid in a virtually arbitrary spatial manner and does not necessarily has to follow a rectangular pattern. The depicted shear force transfer reinforcement layout with shear dowels was developed from a strut-and-tie model adapted to the force flow [6].

Figure 1.3 Reinforcement cages: (a) typical rectangular pattern of longitudinal bars and side aligned stirrups, (b) freely bend reinforcement derived from strut-and-tie modeling [5].

Generally, it can be stated that the outer and the inner shape of RC structures are not limited. If they follow the flow of forces, low material consumption and mostly aesthetic designs result.

The following example of a cross-section choice will illustrate how much the underlying objectives influence the design. A RC cross-section for a beam in axial bending is sought. The cross-section needs to be both sustainable and...