Stability of Timber Rib Shells


Funding: EPFL, FNS

Status: Completed, 2005 – 2010

Doctor: Johannes Natterer, engineer, IBOIS EPFL

Thesis director: Prof. Yves Weinand, architect and engineer, IBOIS


Wooden shell structures fascinate the experts as much as the laymen. However, the calculation and the realization of such structures require particular knowledge and experience. Currently the engineer does not have any effective method to calculate these kinds of spatial structures made out of curved screwed lamellate boards. The existing approximations for complex curved structures are not satisfying. The main differences are noticed especially upon the analysis of the stability of structures subject to horizontal loads.

Theories being studied currently are:
The “gamma method”, introduced into DIN in 1969, is based on the differential equations of Möhler and Schelling. It treats straight beams and pillars under compression composed of up to 5 sections that are assembled continuously. For the resolution of the differential equations, a certain number of concessions have been made. The calculated results are exact for a simple beam with a sinusoidal load.

Piotr Krawczyk from the laboratory of mechanics of the structures and continuous mediums developed a finite element method based on FELINA, which allows analysing of layered beams with small interlayer slips. This method is currently in phase of validation. It could be used as a basis for this research.

Appendix F of the German standard E-DIN 1052 presents an approach based on the analogy of shearing. It gives a realistic description of the composite behaviour and makes the dimensioning of spatial structures out of screwed boards possible. The method by analogical modelling separating rigidity from translation and the clean rigidity of the section presents an exact analysis for 2 layers of boards, nevertheless the critical load can show variations up to 26% – under certain edge conditions.

The finite element method (FEM) makes it possible to model each board and each screw. It can give very exact models but the complexity and the number of elements makes impossible to extend it to more complex systems such as ribbed timber shells. FEM will serve as base for comparison and validation of the tests.

The objective of the thesis is the adaptation and the validation of the methods with structural and geometrical requirements of the curved laminated screwed beams as unit for spatial structures. This would offer engineers a tool adapted for an effective dimensioning of spatial and complex structures, which would fill the gap in the standardization and allow a broader diffusion of this type of structures.

The final validation will be the realization of a large structure, which is considered as unstable: a flat spherical shell or a cylinder under compression. On this large scale model, a serie of rigidity tests will be carried out, first without covering and, second, with a stiffening covering. Then, a load bearing test will be made until the structure collapses. This will enable us to compare the measured results with the calculated ones of the digital model.

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