Generalized Section Model for Analysis of Reinforced Concrete Chimney Weakened by Openings

In the paper, the general equilibrium equation due to bending moment and normal force is formulated for RC cross-section weakened by an arbitrary number of openings. The governing equations for the normal stresses due to bending moment and normal force are derived for the case when openings are located symmetrically as well as asymmetrically to the bending direction. The normal tensile stresses in concrete are neglected, and the reinforcing steel is continuously spaced at $l$ layers ($l \in N$). The constitutive equations for steel are assumed to be linear elastic, while the concrete is described as an elastic material in compression and brittle in tension. Furthermore, the strains are assumed to be small and their distribution across the section to be linear. The additional reinforcement located in the zone of the flue openings is involved. Basing on the equilibrium equation about the neutral axis, the effective moment of inertia of the cracked annular cross-section with openings is derived, and its influence on the fundamental frequency of the chimney is evaluated. The effects of different parameters on stresses in concrete and steel in the considered annular cross-sections are presented and discussed.