Stiffness Matrix of Free-Standing Helical Stairs

The full, 12×12, stiffness matrix of a free-standing helicoidal stair is constructed in terms of its geometric characteristics. Knowledge of this stiffness matrix allows incorporation of the stair as a single element into a 3-dimensional model of a reinforced concrete building structure, for lateral load analysis. The elements of the stiffness matrix that affect the most the lateral stiffness of the structural system are presented in terms of the following geometric parameters: story height, axis inclination, opening angle in plan, and width and depth of the stairslab. For given story height, the magnitude of these elements is found to depend strongly only on the depth of the stairslab and on the opening angle of the stair. The lateral stiffness of the stair in any horizontal direction is found to be almost negligible for opening angles between 270° and 360°, but becomes quite significant for angles less than 180°. The reduction of stiffness due to axial and shear deformations of the stair is, generally, very small.