Investigation of isostatic slabs in timber

Abstract

The isostatic slab was developed by Pier Nervi and his colleague Aldo Arcangeli to create an elegant and easy to produce floor system, with efficient use of material. These slabs are designed with ribs aligned to the principal bending stress lines that support a flat deck. Concrete isostatic slabs are no longer constructed due to their expensive formwork. However, this system could be advantageous when made from timber as the grain direction will be aligned to the optimal flow of forces. Additionally, isostatic slabs can be designed for any support conditions, so an isostatic timber slab may be more desirable than the typical one-way spanning timber systems. The isostatic timber slab is a new concept and has not been previously used. Therefore, before the system can be applied, there needs to be a greater understanding of the design process. This research achieves this goal by splitting the process into two parts. Firstly, the rib geometry is created by generating the principal bending stress lines. Secondly, the system is designed and analysed for a case study. The aim is achieved by creating a functional design and identifying the critical areas in the design process. An approach for measuring the accuracy of stress lines is developed and used to test different methods for improving the stress line generation process. The improved process uses a more advanced integration method and a holistic seeding method. Additionally, a novel method for interpolating the principal stress trajectories from finite element analysis (FEA) results is established by utilising the shape functions from the theory of FEA. An iterative approach used to select stress lines to create optimised truss geometries in in-plane-loaded plates is tested for its applicability to out-of-plane loaded plates (i.e. slabs). The rib geometry produced was measured by the approximation error and the deck elements' span lengths. This iterative approach does not apply to slabs as it creates clustered areas and excludes symmetries. Analysis of principal stresses under different load cases shows that the most considerable difference from the primary load case is when half of the slab is loaded with a maximum load and half with a minimum load. (The primary load case is the condition used to create the stress lines for the rib geometry). Using FEA to calculate the stresses under each load case shows that uneven loading of the slab does not produce higher stresses than the primary load case. A functional isostatic timber slab design is made for the case study using laminated veneer lumber (LVL) for the ribs and plywood for the deck. Linear elastic FE modelling of the structure shows that increasing the deck thickness and decreasing the rib depth, causes the deck to carry more load and the ribs to carry less and vice versa. Increasing the rib thickness has a small effect on the force distribution due to the available LVL thicknesses. The FE modelling also showed that the torsional load transfer mechanisms are reduced by increasing the rib slenderness. The design is made based on the ultimate limit state (ULS) stress requirements for the elements and three critical connections, and the deflection under the serviceability limit state (SLS). The rib-to-deck joint requirements determine the deck thickness, and the deck has a low utilisation for the stress conditions, meaning that the deck span lengths are not critical. The ribs' depth is heavily dependent on the rib-to-rib moment connection as a large lever is needed. The cross-sectional properties of the ribs are also dependant on the standard LVL sizes. This system is compared to several conventional one-way spanning alternatives based on the total material volume, the structural weight, and the structural depth. The isostatic timber slab has a reduced volume and weight compared to a flat cross-laminated timber (CLT) slab, a Kerto-Ripa slab, and a concrete hollow-core slab; however, the isostatic timber slab has a larger structural depth. A ‘T’-beam equivalent to the two-way spanning isostatic slab has less volume and weight while maintaining the same structural depth, but has a larger average deflection. Timber isostatic slabs are complex to design with a highly connected network of parameters. The system should be designed by minimising the peak moment forces at connections, curating the support conditions to reduce stress line clustering, and selecting stress lines for the rib geometry which ensure sufficient stiffness at the peak deflection location. It is advised to produce a parametric model of the slab that can quickly assess the design performances and efficiently complete design cycles.