Optimal Cost Design of RC T-Shaped Combined Footings

This paper shows the optimal cost design for T-shaped combined footings of reinforced concrete (RC), which are subjected to biaxial bending in each column to determine the steel areas and the thickness of the footings assuming a linear distribution of soil pressure. The methodology used in this paper is as follows: First, the minimum contact surface between the footing and the ground is investigated. The design equations for the combined footing are then used to determine the objective function and its constraints to obtain the lowest cost, taking into account the ACI code requirements. Flowcharts are shown for the lowest cost and the use of Maple 15 software. The current model for design is developed as follows: A footing thickness is proposed, and then it is verified that the thickness complies with the effects produced by moments, bending shears, and punching shears. Furthermore, four numerical examples are presented under the same loads and moments applied to each column, with different conditions applied to obtain the optimal contact surface and then the minimum cost design. The results show that the optimal cost design (lowest cost) is more economical and more accurate than any other model, and there is no direct proportion between the minimum contact surface and lowest cost for the design of T-shaped combined footings. In this way, the minimum cost model shown in this work can be applied to the design of rectangular and T-shaped combined footings using optimization techniques.