Sustainable seismic design of RC frames with structural optimisation techniques

In conventional engineering practice, the sustainable seismic design of reinforced concrete (RC) frames is pursued with the aid of the designer’s experience and/or trial and error approaches. Nevertheless, the complexity of this structural design task, as well as the demand for sustainable solutions in limited time, set the use of automated structural optimization methodologies as an attractive alternative approach. In this study, it is shown that the use of structural optimization techniques in seismic design of RC frames can lead to significant reductions not only in economic costs but also in environmental impacts expressed in terms of embodied CO2 emissions. The latter is significant because in many countries around the world, including most of the top-10 countries in CO2 emissions from cement production, RC structures are designed to resist earthquake loads. Moreover, the trade-offs between the economic costs of earthquake-resistant RC frames and the embodied CO2 emissions are presented. It is concluded that, typically, the designs of RC frames for minimum construction cost and embodied CO2 emissions are closely related. Therefore, both objectives can be achieved almost simultaneously in the framework of optimum seismic design of RC frames

Flower pollination algorithm with pollinator attraction

The Flower Pollination Algorithm (FPA) is a highly efficient optimization algorithm that is inspired by the evolution process of flowering plants. In the present study, a modified version of FPA is proposed accounting for an additional feature of flower pollination in nature that is the so-called pollinator attraction. Pollinator attraction represents the natural tendency of flower species to evolve in order to attract pollinators by using their colour, shape and scent as well as nutritious rewards. To reflect this evolution mechanism, the proposed FPA variant with Pollinator Attraction (FPAPA) provides fitter flowers of the population with higher probabilities of achieving pollen transfer via biotic pollination than other flowers. FPAPA is tested against a set of 28 benchmark mathematical functions, defined in IEEE-CEC’13 for real-parameter single-objective optimization problems, as well as structural optimization problems. Numerical experiments show that the modified FPA represents a statistically significant improvement upon the original FPA and that it can outperform other state-of-the-art optimization algorithms offering better and more robust optimal solutions. Additional research is suggested to combine FPAPA with other modified and hybridized versions of FPA to further increase its performance in challenging optimization problems

Flower pollination algorithm parameters tuning

The flower pollination algorithm (FPA) is a highly efficient metaheuristic optimization algorithm that is inspired by the pollination process of flowering species. FPA is characterised by simplicity in its formulation and high computational performance. Previous studies on FPA assume fixed parameter values based on empirical observations or experimental comparisons of limited scale and scope. In this study, a comprehensive effort is made to identify appropriate values of the FPA parameters that maximize its computational performance. To serve this goal, a simple non-iterative, single-stage sampling tuning method is employed, oriented towards practical applications of FPA. The tuning method is applied to the set of 28 functions specified in IEEE-CEC'13 for real-parameter single-objective optimization problems. It is found that the optimal FPA parameters depend significantly on the objective functions, the problem dimensions and affordable computational cost. Furthermore, it is found that the FPA parameters that minimize mean prediction errors do not always offer the most robust predictions. At the end of this study, recommendations are made for setting the optimal FPA parameters as a function of problem dimensions and affordable computational cost. [Abstract copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.

Efficient optimum seismic design of reinforced concrete frames with nonlinear structural analysis procedures

Performance - based seismic design offers enhanced control of structural damage for different levels of earthquake hazard. Nevertheless, the number of studies dealing with the optimum performance - based seismic design of reinforced concrete frames is rather limited. This observation can be attributed to the need for nonlinear structural analysis procedures to calculate seismic demands. Nonlinear analysis of reinforced concrete frames is accompanied by high computational costs and require s a priori knowledge of steel reinforcement. To address this issue, previous studies on optimum performance-based seismic design of reinforced concrete frames use independent design variables to represent steel reinforcement in the optimization problem. This approach drives to a great number of design variables , which magnifies exponentially the search space undermining the ability of the optimization algorithms to reach the optimum solutions. This study presents a computationally efficient procedu re tailored to the optimum performance-based seismic design of reinforced concrete frames. The novel feature of the proposed approach is that it employs a deformation-based, iterative procedure for the design of steel reinforcement of reinforced concrete frames to meet their performance objectives given the cross-sectional dimensions of the structural me mbers. In this manner, only the cross-sectional dimensions of structural members need to be addressed by the optimization algorithms as independent design variables. The developed solution strategy is applied to the optimum seismic design of reinforced concrete frames using pushover and nonlinear response-history analysis and it is found that it outperforms previous solution approaches

The anchorage-slip effect on direct displacement-based design of R/C bridge piers for limiting material strains

Direct displacement-based design (DDBD) represents an innovative philosophy for seismic design of structures. When structural considerations are more critical, DDBD design should be carried on the basis of limiting material strains since structural damage is always strain related. In this case, the outcome of DDBD is strongly influenced by the displacement demand of the structural element for the target limit strains. Experimental studies have shown that anchorage slip may contribute significantly to the total displacement capacity of R/C column elements. However, in the previous studies, anchorage slip effect is either ignored or lumped into flexural deformations by applying the equivalent strain penetration length. In the light of the above, an attempt is made in this paper to include explicitly anchorage slip effect in DDBD of R/C column elements. For this purpose, a new computer program named RCCOLA-DBD is developed for the DDBD of single R/C elements for limiting material strains. By applying this program, more than 300 parametric designs are conducted to investigate the influence of anchorage slip effect as well as of numerous other parameters on the seismic design of R/C members according to this methodology

Multi-objective optimum selection of ground motion records with genetic algorithms

Existing ground motion selection methods for the seismic assessment of structural systems consider only spectral compatibility as selection objective. Other important earthquake parameters such as those related to regional seismicity, local soil conditions, strong ground motion intensity and duration are considered indirectly by setting them as selection constraints. This study presents a new framework for the optimum selection of earthquake ground motions, where more than one objectives are considered explicitly in the selection procedure including objectives that are not directly related to spectral matching. To address the multi-objective nature of the optimization problem examined herein, the weighted sum method is used that supports decision making both in the pre-processing and post-processing phase of the selection procedure. The optimum selections are conducted by the use of a mixed-integer genetic algorithm that is able to track near-global optimal solutions of constrained problems with both discrete and continuous design variables. It is found that proposed methodology is able to select ground motion sets that are both spectrum compatible and representative of the seismic conditions of the structural system under investigation

Selection of earthquake ground motions for multiple objectives using genetic algorithms

Existing earthquake ground motion (GM) selection methods for the seismic assessment of structural systems focus on spectral compatibility in terms of either only central values or both central values and variability. In this way, important selection criteria related to the seismology of the region, local soil conditions, strong GM intensity and duration as well as the magnitude of scale factors are considered only indirectly by setting them as constraints in the pre-processing phase in the form of permissible ranges. In this study, a novel framework for the optimum selection of earthquake GMs is presented, where the aforementioned criteria are treated explicitly as selection objectives. The framework is based on the principles of multi-objective optimization that is addressed with the aid of the Weighted Sum Method, which supports decision making both in the pre-processing and post-processing phase of the GM selection procedure. The solution of the derived equivalent single-objective optimization problem is performed by the application of a mixed-integer Genetic Algorithm and the effects of its parameters on the efficiency of the selection procedure are investigated. Application of the proposed framework shows that it is able to track GM sets that not only provide excellent spectral matching but they are also able to simultaneously consider more explicitly a set of additional criteria

A combined damage index for seismic assessment of non-ductile reinforced concrete structures

Existing seismic damage indices have been formulated and verified almost exclusively on the basis of flexural damage mechanisms. In this paper, a local damage index proposed previously by the authors for assessing existing reinforced concrete (RC) structures is described. According to its formulation, deterioration caused by all deformation mechanisms (flexure, shear, anchorage slip) is treated separately for each mechanism. Moreover, the additive character of damage arising from the three response mechanisms, as well as the increase in degradation rate caused by their interaction, are fully taken into consideration. The proposed local damage index is first calibrated against experimental recordings and then is applied to predict seismic damage response of one RC column and one frame test specimen with substandard detailing. It is concluded that in all cases and independently from the prevailing mode of failure, the new local damage index predicts well the damage pattern of the analysed specimens

Seismic damage analysis including inelastic shear-flexure interaction

The paper focusses on seismic damage analysis of reinforced concrete (R/C) members, accounting for shear-flexure interaction in the inelastic range. A finite element of the beam-column type for the seismic analysis of R/C structures is first briefly described. The analytical model consists of two distributed flexibility sub-elements which interact throughout the analysis to simulate inelastic flexural and shear response. The finite element accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding. Based on this model, a seismic damage index is proposed taking into account both inelastic flexural and shear deformations, as well as their interaction. The finite element and the seismic damage index are used to analyse the response of R/C columns tested under cyclic loading and failing either in shear or in flexure. It is shown that the analytical model and damage index can predict and describe well the hysteretic response of R/C columns with different types of failure

A gradual spread inelasticity model for R/C beam-columns, accounting for flexure, shear and anchorage slip

A new beam-column model is developed for the seismic analysis of reinforced concrete (R/C) structures. This finite element consists of two interacting, gradual spread inelasticity sub-elements representing inelastic flexural and shear response and two rotational springs at the ends of the member to model anchorage slip effects. The flexural sub-element is able to capture gradual spread of flexural yielding in plastic hinge regions of R/C members. The shear sub-element interacts throughout the analysis with the flexural sub-element, in the location of the plastic hinge regions, in order to capture gradual spread of inelastic shear deformations as well as degradation of shear strength with curvature ductility demand based on an analytical procedure proposed herein. The skeleton curves and hysteretic behaviour in all three deformation mechanisms are determined on the basis of analytical procedures and hysteretic models found to match adequately the experimental results. Empirical formulae are proposed for the shear distortion at onset of stirrup yielding and onset of shear failure. The proposed element is implemented in the general finite element code for damage analysis of R/C structures IDARC and is validated against experimental results involving R/C column and frame specimens failing in shear subsequent to yielding in flexure. It is shown that the model can capture well the hysteretic response and predict reliably the type of failure of these specimens