Determination of the structural efficiency of quadric and cylindrical surfaces when used as reinforced concrete roof structures

Abstract

Modern architecture of civil engineering structures made of reinforced concrete is demanding solutions to problems related to design and construction of roofs shaped as creative forms which require an adequate combination of arts and physical-mathematical models. In that sense, the quadric and cylindrical surfaces offer an attractive based on their volumetric expression, historicity, and mathematical feasibility. In this work, seven cylindrical and quadric surfaces named elliptic cylinder, parabolic cylinder, elliptic cone, elliptic paraboloid, hyperbolic paraboloid, ellipsoid and hyperboloid of two sheets have been analysed to find out which of them show to be more efficient when used as reinforced concrete roof structures. To do so, the configuration of each structure hase been adjusted in terms of similar stiffness, strength parameters and enclosed volume. The structural efficiency was computed using the results of weight/load ratio, available strength, material consumption and relative stiffness. The solution of the model has been achieved using a combination of exact solutions and numerical methods. To compute the model results a Matlab® code was written and validated using the structural software SAP2000®. The best structural efficiency in terms of stiffness, strength, and materials consumption was obtained for roofs configurated using surfaces built from parabolas, i.e., elliptic paraboloid, hyperbolic paraboloid, and parabolic cylinder. The results of this work can be used in future studies and applications related to arhitectural comfort, structural behaviour and material consumption in construction of roofs.