Gekrümmte Spannungsfelder |
M. Bahr 2009 - 2017 |

The constitution of curved surfaces in architecture has changed dramatically since the development of shell construction in the 1920s: from being statically dominated to an increasingly architecturally determined formal language. As a result, the technical investment for realising these free-form structures at times has assumed considerable dimensions. Hence, a method is required which is able to unite the architectural freedom of design with the engineer’s pursuit of efficient structures. Building on the principles of graphic statics and the theory of plasticity is the very purpose of this assignment.

Connecting the supports of a simply supported beam pressure curves can be found analogically. The enclosed area between the connecting line and the pressure curve corresponds to the bending load of the beam.

Under a given load, a thrust line can be developed for arch constructions. Based on a rigid plastic material model, an arch structure is only subjected to compressive stresses, as long as the thrust line remains within the arch section. If it on the other hand would be located outside the cross section, then the arch would additionally be strained by flexural loads. The surface enclosed between the arch and the thrust line corresponds to the bending stress of the arch. As a counterpart to the one-dimensional thrust lines, curved stress fields are to be defined in three-dimensional space in the context of the research. Due to the highly static indeterminacy of surface structures, there are several solutions available in terms of problem statement. On one hand this basic principle allows a broad variety of shapes to be generated, which may serve as a starting point for an architectural draft. On the other hand, the efficiency of the load bearing behaviour can be estimated by means of a graphic comparison of architecturally favoured form and the curved stress field.

Moreover, in a further step of the research, the possibility should be established to conduct a static design for a structure of reinforced concrete, based on a curved stress field. Consequently, a closed method is generated from the development and testing of form up to the constructive itemization of the structure.

Connecting the supports of a simply supported beam pressure curves can be found analogically. The enclosed area between the connecting line and the pressure curve corresponds to the bending load of the beam.

Under a given load, a thrust line can be developed for arch constructions. Based on a rigid plastic material model, an arch structure is only subjected to compressive stresses, as long as the thrust line remains within the arch section. If it on the other hand would be located outside the cross section, then the arch would additionally be strained by flexural loads. The surface enclosed between the arch and the thrust line corresponds to the bending stress of the arch. As a counterpart to the one-dimensional thrust lines, curved stress fields are to be defined in three-dimensional space in the context of the research. Due to the highly static indeterminacy of surface structures, there are several solutions available in terms of problem statement. On one hand this basic principle allows a broad variety of shapes to be generated, which may serve as a starting point for an architectural draft. On the other hand, the efficiency of the load bearing behaviour can be estimated by means of a graphic comparison of architecturally favoured form and the curved stress field.

Moreover, in a further step of the research, the possibility should be established to conduct a static design for a structure of reinforced concrete, based on a curved stress field. Consequently, a closed method is generated from the development and testing of form up to the constructive itemization of the structure.

last modified 30.10.2015