Stability analysis of a large span timber dome
Abstract: The aim of this thesis is to study the feasibility of building a timber dome with a span of 300 metres, concerning elastic stability. The load-bearing members were modelled with the properties of glued laminated timber GL30c with the dimensions 0.8×1.6 m2. The design loads were 2 kN/m2 and 4 kN/m2 in symmetrical and asymmetrical load cases, respectively. The numerical calculations were performed using the software Abaqus FEA, and compared with analytical equations, modified using empirical data. There are many ways to arrange the surface members in a braced dome. Common arrangements include Ribbed, Schwedler, Lattice, Kiewitt, Geodesic and Three-way grid. The three latter arrangements were compared in terms of global linear elastic stability, constructability and stiffness, in order to find the pattern most suitable to span 300 metres. It was concluded that the Geodesic geometry had the most suitable arrangement, primarily due to the slightly higher critical load in symmetrical and asymmetrical load scenarios, fewer number of unique elements lengths, and smaller deviation in the member length distribution. The non-linear global elastic stability was studied concerning initial geometrical imperfections using linear buckling mode shapes and creep was studied by reducing the Young’s modulus for permanent loads. These two phenomena were also looked studied in combination. The effect of radial and differential settlements on elastic stability, both in combination with initial geometrical imperfections, was also studied. It was found that the structure was highly sensitive to initial imperfections with a lower bound critical value of only 0.135 q/qcr, corresponding to a uniformly distributed load equal to 8.9 kN/m2, when the structure was loaded symmetrically. This critical load value represents an outlier, over 95 % of the critical loads were above 15 kN/m2. This was compared to the empirical formula, only applicable in the symmetrical load case, which estimated the global failure load to 19.6 kN/m2. Creep reduced the capacity down to 0.394 q/qcr of the linear buckling load in an asymmetrical load case covering 20 % of the dome area in the xy-plane. This corresponded to a uniformly distributed load of 29.9 kN/m2. Neither radial nor differential settlements caused any decrease of the critical load. Combining creep and initial imperfections reduced the capacity further, from a lower bound value of 0.135 q/qcr to 0.081 q/qcr, the latter corresponding to 5.4 kN/m2. No synergistic effect was found. It was therefore concluded that global stability likely will not cause the dome to collapse, given that the design loads were significantly lower that the stability critical failure loads. Material failure was also investigated in relation to initial geometrical imperfections as well as the combined effect of creep and imperfections. It was found that the stress level in the most critical beam would cause material failure if the maximum imperfection was larger than 0.8 metres, or D/375, leading to the conclusion that, perhaps, the primary cause for concern would be imperfection induced stresses, not imperfection induced global stability failure.
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