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Buildair S.A. has designed, manufactured and built an inflatable hangar (called hangar H75) for the aeronautical industry at Jeddah Airport, Kingdom of Saudi Arabia. H75 is the largest air-cell inflated structure ever built in the world, finally erected in July 2019. The structural analysis and design of the main body of the hangar has involved complex structural concepts due to the specificity of the structural elements employed, like membranes and straps that lead to a highly nonlinear mechanical problem, or the treatment of wind over the structure without a defined standard for inflatable structures. In this article, the structural concept and specificities of the structure are presented, as well as the design procedure for H75 based on numerical analysis, to fulfil the design requirements in terms of stress and deformation of the main body. [ABSTRACT FROM AUTHOR]