Genetic Algorithms in Optimum Concrete Design

Engr. Alden Balili, my graduate thesis advisee did a research on the application of genetic algorithms (GA) in the optimum design of reinforced concrete (RC) space frames considering seismic provisions of the code. The process of GA and its application to the optimization of space frames is in the figure below. Initially, the sizes of the beams and columns of the space frame are randomly selected which becomes the initial population. These sizes are then used by a separate Finite Element Analysis program to determine the member forces which are required in the design of the members including the amount of steel reinforcements. A database of the beam and column sections is used in the design process. The provisions of the National Structural Code of the Philippines (2001) are incorporated in the fitness evaluation of the solution or individual to satisfy the strength and serviceability requirements. The GA procedures of selection, cross-over, mutation and leader reproduction are then applied to generate a new population of solutions. He conducted GA simulations to determine the behavior of the optimization procedure using the different GA procedures like binary vs gray coding, leader reproduction and mutation. Based on his simulations, a new type of leader reproduction called modified leader reproduction was proposed. It was found out that this feature improved the effectiveness and efficiency of the concrete optimization algorithm to acquire the optimal values.

A paper on this study will be presented at the IABSE 2009 Conference at Bangkok, Thailand on Sept. 9-11, 2009.

A Neural Network Model for Shear of RC Beams

Experiments have shown that as the depth of the beam increases, the intensity of shear stress decreases especially in lightly reinforced beams. This phenomenon is referred to as “size effect”. Shear strength is not constant as given by some design codes like the ACI. To understand size effect, an artificial neural network (ANN) model was developed for RC beams without stirrups which fail under diagonal tension.

The ANN model consists of five input nodes representing (1) the compressive strength of concrete, f’c, (2) beam width, b, (3) effective beam depth, d, (4) shear span to depth ratio, a/d, and (5) longitudinal steel ratio. The output is the shear stress, Vu/bd. The graphical user interface of the Visual Basic program of the ANN model is shown.

The figure shows the simulation where the depth (d) was varied from 20 cm to 100 cm for two values of f’c and a/d and constant values for b at 15 cm and r at 2.75%. The size effect is obvious where the shear stress decreases with increasing depth. The experimental results by Kani shows a similar trend as the model. The shear stress also depends on the shear span to depth ratio – a shorter beam (a/d = 2.5) has a larger shear strength than a longer beam (a/d = 5.0).

How safe our our large RC beams with respect to shear failure? Structural engineers must take note of the decrease in shear strength of concrete for large beams so that they can provide adequate shear reinforcements or stirrups.

Reference: Oreta, A.W.C. (2004). "Simulating size effect on shear strength of RC beams without stirrups using neural networks." Eng'g Structures 26(2004) 681-691, Elsevier.