Mathematical Modeling for the Optimal Cost Design of Circular Isolated Footings with Eccentric Column

This article shows a model for the design of circular isolated footings and the column placed anywhere in the footing under minimum cost criteria. Some designs for obtaining the diameter, effective depth, and steel areas of the footing under biaxial bending assume the maximum and uniform pressure at the bottom of the footing supported on elastic soils. All these works consider the column placed at the center of the footing. Three numerical problems are given (each problem presents four variants) to determine the lowest cost to design the circular footings under biaxial bending. Problem 1: Column without eccentricity. Problem 2: Column with eccentricity in the direction of the X axis of one quarter of the diameter of the footing. Problem 3: Column placed at the end furthest from the center of the footing on the X axis. The results are verified by the balance of moments, one-way shear or shear and two-way shear or punching. The new model shows a saving of 17.92% in the contact area with soil and of 31.15% in cost compared to the model proposed by other authors. In this way, the proposed minimum cost design model for circular footings will be of great help for the design when the column is placed on the center or edge of the footing

Electrochemical Corrosion of Galvanized Steel in Binary Sustainable Concrete Made with Sugar Cane Bagasse Ash (SCBA) and Silica Fume (SF) Exposed to Sulfates

This research evaluates the behavior corrosion of galvanized steel (GS) and AISI 1018 carbon steel (CS) embedded in conventional concrete (CC) made with 100% CPC 30R and two binary sustainable concretes (BSC1 and BSC2) made with sugar cane bagasse ash (SCBA) and silica fume (SF), respectively, after 300 days of exposure to 3.5 wt.% MgSO4 solution as aggressive medium. Electrochemical techniques were applied to monitor corrosion potential (Ecorr) according to ASTM C-876-15 and linear polarization resistance (LPR) according to ASTM G59 for determining corrosion current density (icorr). Ecorr and icorr results indicate after more than 300 days of exposure to the sulfate environment (3.5 wt.% MgSO4 solution), that the CS specimens embedded in BSC1 and BSC2 presented greater protection against corrosion in 3.5 wt.% MgSO4 than the specimens embedded in CC. It was also shown that this protection against sulfates is significantly increased when using GS reinforcements. The results indicate a higher resistance to corrosion by exposure to 3.5 wt.% magnesium sulfate two times greater for BSC1 and BSC2 specimens reinforced with GS than the specimens embedding CS. In summary, the combination of binary sustainable concrete with galvanized steel improves durability and lifetime in service, in addition to reducing the environmental impact of the civil engineering structures