Geodesic Lines on Free-Form Surfaces - Optimized Grids for Timber Rib Shells
In addition to glue-laminated timber, screw-laminated timber has increasingly been applied to rib shells. The ribs are made from laminated timber boards, which are joined together with the aid of pin-like fasteners such as screws or nails. The current research is meant to optimize these grids on free-form surfaces with regard to the bending stress due to initial curvature of the boards. This can be done by arranging the ribs according to geodesic lines which allows the application of straight boards, subjected only to bending about their week axis and to torsion. The determination of such geodesic grids on free-form surfaces, currently enjoying great popularity in contemporary architecture, is quite complex. In order to satisfy this demand and to improve automation of the production process, the software GEOS has been developed in close collaboration with the Laboratory of Timber Construction (EPFL/IBOIS) and the chair of Geometry (EPFL/GEOM). This software calculates grids of geodesic lines on free-form surfaces and provides all geometrical data necessary for computer-controlled sawing. Free-form surfaces are treated as Bézier surfaces. In order to proved the reliability of the assumptions the program is based upon, a timber rib shell prototype (length/width/height: 8000 mm x 3000 mm x 2060 mm) was build. Thin timber laths (12/60 mm) were used. All laths were sawn and predrilled by means of computer-controlled sawing. The prototype could thus be built in relatively short time. In general, it can be stated that even after assembly of the fourth layer the predrilled holes at the intersections fitted precisely about 85% of the time. This confirms the reliability of the calculation and shows that the demanded precision is kept even for significant curvatures. For a better understanding of the load-bearing behavior of the structure load tests were carried out. The comparison of the measured deformations with the calculated deformations enabled us to evaluate the calculation model, based on a framed load-bearing system. For small charges, good accordance between calculation and reality could be noticed. The software GEOS provides an important tool for the design and the realization of timber rib shells. It contributes to clarifying current uncertainties in the design planning process and will highly improve the confidence of engineers and architects in conceiving and realizing this type of challenging lightweight spatial structures.