Design of the Copenhagen Opera House Roof

One of the most expensive opera houses ever built, with construction costs exceeding US$500 million, the Copenhagen Opera House is a donation from the A.P Møller and Chastine Mckinney Møller Foundation to the Danish people. Designed by noted Danish Architect Henning Larsen, the structure’s most distinctive feature is a cantilevered roof, the size of three football pitches, that floats effortlessly over the plaza below. Considered to be one of the largest canopy roof structures in the world, it was constructed using principles taken directly from modern steel bridge design, which provide strength, stability and stiffness to the 43m long cantilever. Ramboll used LUSAS finite element analysis to assist with its innovative design of the structure in order to ensure the necessary strength, stability and dynamic response was achieved.

Project info

Client: A. P. Moller and C. McKinney Moller Foundation Structural Engineer: Ramboll Architect: Henning Larsens Tegnestue A/S, Contractor: Pihl & Son A/S

West roof structure showing main truss girders, inner and outer ring beams, radial beams, extent of box girder construction and perimeter cantilevered beams

Plan of the cantilevered West roof showing area of box construction (light grey) and roof over foyer area (dark grey)

LUSAS modelling of roof displacements caused by differential temperatures

A 3D LUSAS model of the closed box and the girders of the roof structure was used for both static and dynamic analyses. These calculations determined all the normal stresses in the plates, parallel and perpendicular to the stiffeners, as well as the shear stresses and all internal forces in each beam in the girders. The static analysis proved the box structure to be an optimal solution, due to the use of stresses in both directions of the plates in combination with the shear stresses from the large torsional moments in the structure. The results from a wind tunnel test were combined with eigenvalue analyses from LUSAS (which gave mode shapes, natural frequencies and modal masses of the structures) to determine the dynamic response.

We used LUSAS finite element analysis as the main structural analysis tool for the design of the cantilevered roof and it assisted us greatly in the solving of the main design challenges involved.

Hans Exner, Senior Chief Engineer, Ramboll

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