Free-form grid shell with triangular mesh
Project
The business center situated directly on the Zeil in Frankfurt/Main is covered by a spectacular, free-form glass roof with a total area of 12,000 m² which allows natural sunlight to reach all levels of the atrium below. The organic architectural form is inspired by landscapes and ressembles a canyon that stretches between two building volumes. The façade showcases a vortex-like opening into the mall's atrium and is designed with alternating glass and steel panels.
The roof is designed as a shell structure by discretizing the free-form surface into a triangular mesh and exploiting the inherent stiffness of the curved geometry, thereby achieving a filigree and transparent construction.
Design of the grid shell
Initially, the overall geometry was optimized in close coordination with the architect to meet both aesthetic and structural criteria. The exchange of Rhino-files between the engineering team and architect enabled the evaluation of numerous roof geometry alternatives. The meshing of the highly curved 3D surface was studied in great detail and special tools were developed to determine a mesh conductive to the to the flow of forces within the shell. In the subsequent phase, the connections at the node points were designed to be suited to all geometrical and all internal force conditions within the shell.
From digital Geometry to Reality – Construction of the grid shell
Erection of the grid shell
The same geometric data model used for the structural analysis served as a basis for the shop drawings and the fabrication of the hollow box steel members and its nodal connectors. The grid shell is divided into manageable pieces forming so-called ladders. The ladders were prefabricated in the workshop. On site they were lifted into position and connected to the adjacent structure by inserting and welding the lose members. A spatial scaffolding supported the structure during erection and allowed the adjustment of all node positions.
Structural Analsyis of the Grid Shell
Structural Analysis, Boundary Conditions, Mesh Optmization
Wind tunnel and snow drift studies were carried out by the IFI FH Aachen in order to evaluate the loading on the freeform structure. In the end, around 100 linear and non-linear load combinations have been calculated (using 3rd order theory) in order to detect the maximum design stresses of each roof member. The shell structure consists of areas which are mainly under compression (e.g. large column) as well as those mainly under tension (e.g. canyon walls). Each section has been optimized according to its governing load combination.
Project data
Client MAB Projektentwicklung
Architect Massimiliano Fuksas
Finalization 2009
Services structural engineering, special structures
