The motivation of the thesis relates to designing grid shells over existing buildings. Grid shell roofs are a way to enclose an existing space structurally efficiently and have minimal interference with the surroundings from an architectural and environmental perspective. The solution results in less material usage than shell structures, and transparency, allowing for more daylight.
Joints play a significant role in the design of grid shells, including structural and economic efficiency. It is common practice in engineering to design rectangular patterned grid shells with rigid joints. A rectangular shape is easy to deform by applying load; hence, it needs stiffness and rigidity. On the other hand, triangular patterned grid shells are designed with pinned joints as the triangular shape is stiff enough and does not need additional stiffness in the joints. Considering these points, the following research question arises:
How can connection stiffness in the parametric design of grid shell roof structures lead to more efficiency for existing buildings?
To answer this research question, the thesis procedure is divided into five steps. First, a literature study provides a clear understanding of grid shell design principles and their joints. Based on the out-of-plane rotational stiffness, a classification system for joints in grid shells is suggested. The Matrix Method is used to find the boundary for rigid stiffness. The boundary for pinned stiffness is found by studying the influence of the stiffness decreasing in a logarithmic scale over the bending moment distribution.
Furthermore, to explore the influence of the stiffness over the design of the grid shell, a parametric model is created. The study investigates the structural behavior of a triangular and rectangular grid pattern. Therefore, a comparison of the influence of the joint between a rigid and non-rigid shape will be made. The design criteria include the Ultimate Limit State (ULS) and Serviceability Limit State (SLS). To quantify the results, a case study is applied. The C30 Shell project, now designed and completed by Octatube, will be used as a reference to apply the theory of this thesis.
Based on the Eurocode checks, conclusions are drawn related to the effect of the stiffness. The grid shell with rectangular pattern is significantly affected in both Ultimate and Serviceability Limit State with alternation of stiffness in logarithmic scale. However, the stiffness decrease was proved to have no significant effect over the maximum displacements (SLS) but only over the stress distribution for the triangular pattern. Therefore, to find the optimal solution for a grid shell with a triangular pattern, only the ULS unity checks need to be compared. On the contrary, for grid shells with a rectangular pattern, a balance needs to be found between ULS and SLS unity checks.
Following this conclusion, the study is focused on the grid shell with a rectangular pattern. Joints are designed for different stiffness to visualize the difference on how to achieve these stiffness in real-life engineering practice. The FEM software IDEA StatiCa is used to design the joints. The joints follow a similar concept with a rectangular hollow section box in the middle where all the joints are connected. While the required stiffness is decreased approaching semi-rigid and pinned, the dimensions of the joint components are also decreased. The reduction of material used also makes the structure more lightweight and less expensive in terms of material.
Finally, to answer the research question, an optimization procedure has been conducted. Octopus, an optimization algorithm within Grasshopper, is used. The optimization procedure is divided into four steps. The first step was to find an optimal cross-section for each of the stiffness studied. This step focuses on where the solution with the smallest cross-section and lower stiffness can be found. By finding the smallest cross-section, the material used is optimized on a global scale, being one step closer to the smaller self-weight of the roof structure. The second step aims to find the lowest stiffness possible for the cross-section obtained in step 1. This objective is related to design considerations. By lowering the required stiffness, also the dimensions of the components in the joint can be reduced. Thus the material used is decreased on the local scale. In step three, two smaller cross-sections are iterated for different stiffness to verify that the solution obtained is optimal. The last step consisted in giving an optimal design solution for the connections. Other aspects are considered, such as fabrication practicality and transport limitations.
Two types of connections are designed for the grid shell roof. The first connection is designed using only welding and the second connection uses a combination of bolts and welding. The aim is to avoid welding in situ and prefabricate parts of the roof in the factory within the transportation limitations. The fully welded connections allow the prefabrication of roof components off-site. The bolted ones allow connecting these smaller parts in situ.
Based on this investigation, it can be concluded:
The final solution results in a reduction of the total weight of the joints by approximately 50% from fully rigid to optimal stiffness design. Furthermore, an 8% reduction of the self-weight of the structure is achieved by optimizing joint stiffness. Consequently, it results in reduced imposed loading over the existing building and foundation. This reduction is also beneficial for economic and environmental purposes by being more sustainable in terms of material footprint.