Stiffness of Free-Standing Stairs with 180° Turn

Two types of free-standing stairs, each having an axis that makes a 180° turn in plan, are considered. In the first, the horizontal projection of the axis consists of a central semicircle and two equal straight parts, and in the second, it consists of a straight central part and one quarter-circle at each end. The internal forces of the stair are expressed in terms of the force vector at its top, and its full (12×12) stiffness matrix is constructed in terms of the geometric parameters of the stair. The symmetry of the stair makes it possible to simplify considerably the stiffness matrix and to express all of the elements of the latter in terms of only 13 independent ones. The elements of the stiffness matrix that have the greatest impact on the lateral stiffness of the building structure are presented in terms of the geometric parameters of the stair. In general, for given story height, the magnitude of these elements decreases considerably, only with an increase in the stair-slab depth and a reduction of the length of the central portion of the stair, in favor of that of the end portions. Axial and shear deformations of the stair slab have a negligible influence on its lateral stiffness.