Metaheuristic Optimization of Reinforced Concrete Footings: Optimization of RC Footings

Introduction

As reinforced concrete (RC) columns, footings are also a major component of the structures since failure of them provides the total collapse of structure. Spread footings are the most basic type of footings and these footings are mounted at the bottom of basement columns, but in design of RC spread footings, several structural design limits including the punching effect and geotechnical state limits related to capacity and properties of supporting soil. A safe design providing all strength against all types of stresses is not enough if the stability of footings is not provided according to soil bearing capacity. Comparing to other optimization cases of members, in additional to existing non-linear behavior of RC members, the footing design is more complicated than others since the design variables are both effective on geotechnical and structural state limits.

Nigdeli, Bekdaş and Yang (2018) optimized spread footings by employing several methodologies and the results and these calculations are formulated in this chapter. Differently from the most basic form of spread footing taken as rectangular, a trapezoidal shape to save from the volume of the concrete is presented by using biaxial flexural moments of the mounted column. As additional design variables, orientation (eccentricity respect to the midpoint of footing) of the column is considered to reduce internal forces and to provide minimization of objective function taken as the cost of design. Differently from dimension design variables, quantity of reinforcements in all critical sections are considered as design variables. All design constraints are defined according to ACI 318: Building code requirements for structural concrete. The algorithms with the presented optimum results are Harmony Search (HS) algorithm developed by Geem, Kim and Loganathan (2001), Teaching-Learning Based Optimization (TLBO) developed by Rao, Savsani, and Vakharia (2011), Flower Pollination Algorithm (FPA) developed by Yang (2012), Particle Swarm Optimization (PSO) developed by Kennedy and Eberhart (1995) and Differential Evolution (DE) developed by Storn and Price (1997). Then, a computer code is presented for a simplified methodology.

Optimum Design Of Rc Spread Footings For Columns Under Biaxial Flexural Moment

The design of RC footings involves two different limit states, which are formulated as design constraints in the optimization process. These limit states are namely, geotechnical and structural limit states. These states are separately considered in order to save from the computational effort. Physical mechanic formulations and experimental results are formulated in design codes to represent these limit states.

In the presented methodology, the optimization process related to the assignment of candidate solutions for optimum reinforcement design is not conducted to save from computation time, when selected dimensions of footing is not suitable to provide geotechnical limit states.

As explained in previous chapters, an iterative random search process employing heuristics is done in two phases of optimization, namely global and local optimizations. By these two phases, trapping to a local optimum is prevented via a global search process. In addition to that, the convergence ability is provided via a local search process.