RELIABILITY-BASED OPTIMIZATION OF STEEL FRAME STRUCTURES USING MODIFIED GENETIC ALGORITHM

Reliability-based optimization of two and three dimensional frame structures is the subject of this study. For this purpose, a computer program was developed and tested over a number of examples for validation. Since similar studies have been made previously for trusses and reliably documented in the literature, optimization of such structures based on reliability analysis could therefore be confidently relied on, and thus, designing of such structures could be considered with less value for safety factors. This probabilistic optimization technique can well substitute that of the deterministic one where a considerable factor of safety and therefore, a heavy structure as always is a must. For this purpose, one may take into account the probabilistic behavior for load, yield stress, young modulus, etc, using parameters such as standard deviation and variance, through which safety remarks can be embedded into the design procedure by some mathematical relations, resulting to a probabilistic optimization technique. In this technique, one must first define the failure criterion, followed by the computation of safety zone (Z), reliability index (ƒز) and lastly, the failure probability (Pf). In this paper, the applied load and the yield stress are considered probabilistic, while the violation of interior forces from the member ultimate strength is the failure criterion. For each of the interior axial, shear, bending and torsion reactions, the failure probability is calculated and the maximum value is constrained through optimization process. During the optimization process using Genetic Algorithm (GA), the failure probabilities are some boundary constraints and minimizing the weight of structure is the objective of the problem. The profiles of I-shaped cross-sections are selected from a data file. Finally, the probabilistic technique and deterministic one are investigated and compared applied to some structural problems.