Optimum design of reinforced concrete frames using interactive computer graphics

An integrated approach of the design and optimization problem of reinforced concrete frames, based on the use of interactive computer graphics is presented. The formulation of the optimization problem in terms of all the design variables and constraints is given. The size of the problem is greatly reduced if reinforcement areas are considered as dependent variables. A fully stressed design method is employed to optimize an automatically generated initial design. Analysis and design results plots, including complete reinforcement drawings, are available to designers, helping them to evaluate the current status of the design and allowing them to direct the entire computation process.     

Inelastic dynamic response of reinforced concrete infilled frames

An inelastic finite element model to simulate the behaviour of reinforced concrete frames infilled with masonry panels subjected to static load and earthquake excitation has been presented. Under the loads, the mortar may crack causing sliding and separation at the interface between the frame and the infill. Further, the infill may get cracked and/or crushed which changes its structural behaviour and may render the infill ineffective, leaving the bare frame to take all the load which may lead to the failure of the framing system itself. In this study, a mathematical model to incorporate this behaviour has been presented.     

Artificial intelligence-enhanced seismic response prediction of reinforced concrete frames

Existing physics-based modeling approaches do not have a good compromise between performance and computational efficiency in predicting the seismic response of reinforced concrete (RC) frames, where high-fidelity models (e.g., fiber-based modeling method) have reasonable predictive performance but are computationally demanding, while more simplified models (e.g., shear building model) are the opposite. This paper proposes a novel artificial intelligence (AI)-enhanced computational method for seismic response prediction of RC frames which can remedy these problems. The proposed AI-enhanced method incorporates an AI technique with a shear building model, where the AI technique can directly utilize the real-world experimental data of RC columns to determine the lateral stiffness of each column in the target RC frame while the structural stiffness matrix is efficiently formulated via the shear building model. Therefore, this scheme can enhance prediction accuracy due to the use of real-world data while maintaining high computational efficiency due to the incorporation of the shear building model. Two data-driven seismic response solvers are developed to implement the proposed approach based on a database including 272 RC column specimens. Numerical results demonstrate that compared to the experimental data, the proposed method outperforms the fiber-based modeling approach in both prediction capability and computational efficiency and is a promising tool for accurate and efficient seismic response prediction of structural systems.     

An optimum preliminary strength design of reinforced concrete frames

An optimization procedure is organized for the preliminary design of a multistory-multibay, moment-resisting reinforced concrete frame. A reduced set of collapse mechanisms are used to define the kinematic constraints, special constraints are defined in order to satisfy building code requirements and practical design considerations. In the proposed optimum preliminary design the total volume of reinforcing steel required by the members of the structure is minimized. A strong column—weak beam design results from the optimization study. An example is presented to illustrate the proposed method.     

Modified moment distribution method for reinforced concrete equivalent frames

The purpose of this paper is to enhance and improve the moment distribution method used in solving reinforced concrete equivalent frame problems. In the analysis of a planar building frame which is a vertical cut from the building structure, the horizontal members are tee-sections (tee-beams) and vertical members are usually rectangular columns. When a moment is applied to the end of the tee-beam that creates compression stresses at the flange (top fibers), it can be observed that the tee-beam shows more flexural stiffness than applying the same magnitude of moment to create compression stress at the bottom fibers. In other words, its stiffness is different for applied clockwise and counterclockwise unit moments. In this study, the original moment distribution method (MDM) has been modified and the modified moment distribution method (MMDM) introduced and applied to the American Concrete Institute Equivalent Frame Method (ACI-EFM). The new technique applies different distribution factors for clockwise and counterclockwise moments at a joint and solves the problem accordingly. Several typical problems of reinforced concrete equivalent frame have been solved with the ACI-EFM, new MMDM, and also Portland Cement Association (PCA) computer software ‘Analysis and Design of Slab System’ (ADOSS). The results are found to be about 0–20% different. Considering the fact that the ACI-EFM is itself the approximate method, the results of the introduced method were observed to be close enough to use for preliminary analysis. It is also suitable for long-hand calculations.     

Nonlinear static analysis of reinforced concrete frames by network models

The simulation of reinforced concrete frames by networks, with bars obeying uniaxial stres-strain laws of concrete or steel, is proposed. Formulae for the determination of concrete bar sections are derived. Concrete σ-ε law, including cracking and plastic behavior, is described by 3 constitutive variables; steel σ-ε law, including plastic behavior, is described by 1 constitutive variable. A simple program is presented for the nonlinear static analysis of such network models based on the incremental loading technique. This program is used for the analysis of a plane, one story reinforced concrete frame under cyclic horizontal loading of its girder, for which experimental data are available. The computational results are found in good agreement with the experimental ones.     

A parallel procedure for nonlinear analysis of reinforced concrete three-dimensional frames

The paper discusses the parallelisation of complex three-dimensional software for nonlinear analysis of R/C buildings structures. It presents a comparative study for handling the nonlinear response in different parallel architectures. The nonlinear finite element model adopts a fiber decomposition approach for the cross-section of beam elements to capture nonlinear behavior of concrete. The parallelisation strategy is designed regarding three items: the numerical stability of the nonlinear procedure, the parallel sparse equation solver and the application on heterogeneous hardware: dedicated shared memory machines or clusters of networked personal computers.     

A fibre model for push-over analysis of underdesigned reinforced concrete frames

Most of the existing reinforced concrete buildings were designed according to early seismic provisions or, sometimes, without applying any seismic provision. Some problems of strength and ductility, like insufficient shear strength, pull-out of rebars, local mechanisms, etc., could characterize their structural behaviour. The above mentioned topics lead to a number of problems in the evaluation of the seismic behaviour of reinforced concrete (RC) frames. Therefore the assessment of existing RC structures requires advanced tools. A refined model and numerical procedure for the non-linear analysis of reinforced concrete frames is presented. The current version of the model proposed is capable of describing the non-linear behaviour of underdesigned reinforced concrete frames including brittle modes of failure. Selected results of an experimental–theoretical comparison are presented to show the capabilities of this model. The results show the capacity of the model of describing both the global behaviour and the local deformation at service and ultimate state.     

Numerical simulation study of spallation in reinforced concrete plates subjected to blast loading

In the design of protective structures, concrete walls are often used to provide effective protection against blast from incidental events. With a reasonable configuration and proper reinforcement, the protective structure could sustain a specified level of blast without global failure. However, the concrete wall may generate spallation on the back side of the wall, posing threats to the personnel and equipment inside the structure. For this concern, it is important to establish appropriate concrete spallation criteria in the protective design. Earlier analytical studies have been based on simplified one-dimensional wave theory, which does not consider the complex three-dimensional stress conditions in the case of close-in explosion and the structural effects. This paper presents a numerical simulation study on the concrete spallation under various blast loading and structural conditions. A sophisticated concrete material model is employed, taking into account the strain rate effect. The erosion technique is adopted to model the spallation process. Based on the numerical results, the spallation criteria are established for different levels of spallation. Comparison of the analytical results with experimental data shows a favorable agreement. It is also shown that the structural effects can become significant for relatively large charge weight and longer distance scenarios.     

An interface algorithm for nonlinear reliability analysis of reinforced concrete structures using ADINA

Efficient mechanical models are available for the analysis of reinforced concrete structures considering nonlinear material properties and the bearing capacity of the system. To take the statistical properties of loads and resistances into consideration a reliability analysis is required. The present paper describes an algorithm to approximate the limit state function, which is the condition to evaluate the probabilty of failure. Furthermore, a statistical model and extensions of the ADINA concrete model for use within a reliabilty analysis are presented.     

Fuzzy sets in seismic inelastic analysis and design of reinforced concrete frames

In this paper, a new approach to the problem of estimating the structural response of systems with uncertain characteristics is presented. The approach is based on the theory of fuzzy sets, which allow the designers to describe the uncertain variables. The method is presented briefly in the following. First, the uncertain parameters are expressed as fuzzy numbers with specific characteristics. The concurrent effect of the various uncertainties on the structural response is obtained by applying methodologies of the theory of fuzzy sets. Then the output parameters of the design process as, e.g. the displacements or the stresses of the structure are obtained as new fuzzy numbers expressing the uncertainties of the output parameters. Finally, numerical applications on a number of relatively simple structural systems give an idea of the applicability of the proposed methodology in various aspects of the design process.     

An approximate resizing system for the preliminary design of reinforced concrete frames

Techniques for the preliminary design of a multistorey-multibay, moment-resisting reinforced concrete frames are investigated. Two-level optimization patterns are constructed in this paper. The objective function at the system level is to minimize the total volume of reinforcing steel. The relationship between the area of longitudinal reinforcement and the fully plastic moments of cross-sections will be approximated by a quadratic expression. Once the optimum plastic moments result at the system level, and the member sizes and reinforcement at critical sections within the span of each member will be selected at component level to complete the automatic resizing system. Two examples of reinforced concrete frames are presented to illustrate the features of the proposed method.     

Optimum design of reinforced concrete plane frames based on predetermined section database

For the optimum design of reinforced concrete (RC) structures, predetermined section databases of RC columns and beams are constructed and arranged in order of resisting capacity. Because all the design variables of an RC section are interconnected by a representative design variable of the section identification number, regression equations representing the relation between the section identification number and section resisting capacity are derived to effectively handle all the design variables and to use in determining a continuous solution. An introduction to effective discrete optimization algorithms, which can search for an optimum solution quickly using a direct search method, is followed. Moreover, the investigation for the applicability and effectiveness of the introduced design procedure is conducted through a correlation study for typical example structures. Because of an absence of restrictions on the construction of objective functions, together with very simple optimization processes and fast convergence, the introduced method can effectively be used in the preliminary design of RC frame structures. Especially, the obtained solutions selected from the section database can be applied applicable in practice, because these sections are constructed to satisfy all design code requirements and practical limitations.     

Optimal design of shells against buckling subjected to combined loadings

In this paper, the problem of optimal design of shells against instability is considered. A thin-walled shell is loaded, in general, by overall bending moment, constant or varying along an axis of a shell, by the appropriate shearing force and by an axial force and a constant torsional moment. We look for the shape of middle surface as well as the thickness of a shell, which ensures the maximum critical value of the loading parameter. The volume of material and the capacity of a shell are considered as equality constraints. The concept of a shell of uniform stability is applied.     

Computerized ultimate strength analysis of reinforced concrete sections subjected to axial compression and biaxial bending

This article presents a method of evaluating the ultimate strength capacities of reinforced concrete sections of arbitrary shapes and with or without voids subjected to axial compression and biaxial bending. The concept of load fraction is introduced so as to provide a quantitative measure of structural adequacy. An iterative procedure to determine the load fractions is proposed. Necessary integration over arbitrary domains is dealt with by boundary integration method. This procedure can be computerized readily to high automation. A wide range of reinforced concrete sections are analysed, as examples, using a desk-top computer.     

Computerized modular ratio design of reinforced concrete members subjected to axial load and biaxial bending

A computerized method of analysis and design of reinforced concrete members of arbitrary cross-sections subjected to axial load and biaxial bending is proposed. The design process has been computerized to full automation—in the sense that given the concrete section and the applied loading, the program directly evaluates the amount of reinforcement required and the corresponding stress envelope. The strength of concrete in tension is neglected in the analysis. An iterative process which successively adjusts the section properties according to the stress state is employed. The design process is basically an iterative process of gradually increasing the amount of reinforcement till the permissible stresses are not exceeded. Reinforcement is added at locations of highest mean sequare stress in order to utilize fully the reinforcement added. Multiple loading cases are considered.     

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 requires 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 procedure 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 members. 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.     

Optimal design of dynamically loaded reinforced concrete frames under displacement and rotation constraints

The paper deals with reinforced concrete beams and frames subjected to short-time, high intensity dynamic pressure. The shape and geometry of the structure and the layout of the longitudinal reinforcement are given and the areas of reinforcement are design variables.The determination of the plastic displacements and deformations caused by pressure is based on the plastic hinge theory and on the assumption that during the dynamic response the structure undergoes stationary displacements. The problem is to minimize the total amount of reinforcement such that the plastic displacements do not exceed the allowable displacements prescribed at certain points of the structure, or alternatively, that the plastic rotations in the plastic hinges do not reach the limits at which brittle failure occurs.A variational formulation of the problem is presented and the solution is based on the optimality criteria approach which requires an iterative procedure. A few examples illustrate the application of the method.     

Numerical modeling of masonry-infilled RC frames subjected to seismic loads

The behavior of masonry-infilled reinforced concrete frames under cyclic lateral loading is complicated because a number of different failure mechanisms can be induced by the frame-infill interaction, including brittle shear failures of the concrete columns and damage of the infill walls. In this study, nonlinear finite element models have been used to simulate the behavior of these structures. Diffused cracking and crushing in concrete and masonry are described by a smeared-crack continuum model, while dominant cracks as well as masonry mortar joints are modeled with a cohesive crack interface model. The interface model adopts an elasto-plastic formulation to describe the mixed-mode fracture of concrete and masonry. The model accounts for cyclic crack opening and closing, reversible shear dilatation, and joint compaction due to damage. The constitutive models have been validated with experimental data and successfully applied to the dynamic analysis of a three-story, two-bay, masonry-infilled, non-ductile, reinforced concrete frame tested on a shake table. The results have demonstrated the capabilities of the finite element method in capturing the nonlinear cyclic load–displacement response and failure mechanisms of the structure, and indicated the important contribution of infill walls to the seismic resistance of a non-ductile reinforced concrete frame.     

Predictive modeling of the lateral drift capacity of circular reinforced concrete columns using an evolutionary algorithm

The drift capacity of reinforced concrete (RC) columns is a crucial factor in displacement and seismic based design procedure of RC structures, since they might be able to withstand the loads or dissipate the energy applied through deformation and ductility. Considering the high costs of testing methods for observing the drift capacity and ductility of RC structural members in addition to the impact of numerous parameters, numerical analyses and predictive modeling techniques have very much been appreciated by researchers and engineers in this field. This study is concerned with providing an alternative approach, termed as linear genetic programming (LGP), for predictive modeling of the lateral drift capacity (Δ_max) of circular RC columns. A new model is developed by LGP incorporating various key variables existing in the experimental database employed and those well-known models presented by various researchers. The LGP model is examined from various perspectives. The comparison analysis of the results with those obtained by previously proposed models confirm the precision of the LGP model in estimation of the Δ_max factor. The results reveal the fact that the LGP model impressively outperforms the existing models in terms of predictability and performance and can be definitely used for further engineering purposes. These approve the applicability of LGP technique for numerical analysis and modeling of complicated engineering problems.