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.     

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.     

An iterative procedure for collapse analysis of reinforced concrete plates

An iterative procedure is proposed for evaluating the ultimate load of a laterally loaded plate discretized by finite elements. The procedure regards reinforced concrete plates, but it can be extended to metallic plates without any conceptual change. The stress and displacement fields are approximated by means of a finite element model with constant stress and linear displacement fields. Consequently, any load distribution is represented by the equivalent system of nodal forces for a given mesh. In the set of mechanisms compatible with the assumed discretization the best upper bound to the collapse multiplier of the actual load is obtained via linear programming. By dualization a sequence of linear programming problems is obtained which allows an evaluation of a lower bound of the collapse multiplier for the equivalent load system. When the mesh gets finer and finer, the value obtained does not change substantially anymore. This value can be regarded as an estimate of the collapse multiplier for the original load system. Some numerical examples of plates subjected to uniform pressure confirm the reliability of this approximate multiplier.     

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.     

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.     

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.     

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.     

Nonlinear finite element for modeling reinforced concrete columns in three-dimensional dynamic analysis

A new finite element is proposed for slender, flexure-dominated reinforced concrete columns subjected to cyclic biaxial bending with axial load, and its implementation into a program for the nonlinear static or dynamic analysis of structures in three-dimensions, is described. The element belongs to the class of distributed inelasticity discrete models for the nonlinear dynamic response analysis of frame structures to earthquake ground motions. The element tangent flexibility matrix is constructed at each time step by Gauss-Lobatto integration of the section tangent flexibility matrix along the member length. The tangent flexibility matrix of the cross-section relates the increment of the vector of the three normal stress resultants N, M_y, M_z, to the vector increment of the section deformation measures. ε_o, _y, _z, and is constructed on the basis of the bounding surface of the cross-section, which is defined as the locus of points in the space of the normalized N, M_y, M_z, which correspond to ultimate strength. The bounding surface concept enables the model to produce realistic predictions for the nonlinear response of the cross-section to any arbitrary loading path in the space N-M_y-M_z.The bounding surface is introduced and utilized in a very flexible manner, enabling a variety of cross-sectional shapes to be treated in a unified way. As this flexibility is at the expense of computational simplicity and memory size requirements, emphasis is placed on algorithmic techniques to facilitate numerical implementation and to increase computational efficiency.     

A nonlinear model for static and dynamic transverse load analysis of reinforced concrete highway bridges

The modeling of highway bridge components for the purpose of an inelastic lateral load analysis is discussed. An analytical model incorporating these component models is presented. The computer implementation and the techniques used to develop and store element stiffness matrices are described. The properties of a real bridge are used to illustrate static and dynamic analysis features of the computer model.     

A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems

We present a high-order method employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics, for solving dynamic three-dimensional geometrically nonlinear elasticity problems. We demonstrate that the method has an exponential convergence rate spatially and a second-order accuracy temporally for the four classes of problems of linear/geometrically nonlinear elastostatics/elastodynamics. The method is parallelized through domain decomposition and message passing interface (MPI), and is scaled to over 2000 processors with high parallel performance.     

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.     

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 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.     

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 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.     

A mixed GA-PSO-based approach for performance-based design optimization of 2D reinforced concrete special moment-resisting frames

A mixed genetic algorithm and particle swarm optimization in conjunction with nonlinear static and dynamic analyses as a smart and simple approach is introduced for performance-based design optimization of two-dimensional (2D) reinforced concrete special moment-resisting frames. The objective function of the problem is considered to be total cost of required steel and concrete in design of the frame. Dimensions and longitudinal reinforcement of the structural elements are considered to be design variables and serviceability, special moment-resisting and performance conditions of the frame are constraints of the problem. First, lower feasible bond of the design variables are obtained via analyzing the frame under service gravity loads. Then, the joint shear constraint has been considered to modify the obtained minimum design variables from the previous step. Based on these constraints, the initial population of the genetic algorithm (GA) is generated and by using the nonlinear static analysis, values of each population are calculated. Then, the particle swarm optimization (PSO) technique is employed to improve keeping percent of the badly fitted populations. This procedure is repeated until the optimum result that satisfies all constraints is obtained. Then, the nonlinear static analysis is replaced with the nonlinear dynamic analysis and optimization problem is solved again between obtained lower and upper bounds, which is considered to be optimum result of optimization solution with nonlinear static analysis. It has been found that by mixing the analyses and considering the hybrid GA-PSO method, the optimum result can be achieved with less computational efforts and lower usage of materials.     

Application of ADINA to nonlinear analysis of reinforced concrete shear walls with openings

This paper is concerned with application of ADINA to elasto-plastic analysis of the shear walls with openings. The authors analyzed the types of structures. One is the shear wall with many openings (the model of a secondary shield wall in nuclear power plant), on which scale model experiments were made. The other is the shear wall with openings in concrete rigid frame (the model of a shear wall in a building), on which parametric study was made.

In both cases, concrete is modeled using 8 nodes isoparametric 2 dimensional plane stress elements, reinforcing steels are modeled as truss elements. Concrete and elasto-plastic models are adopted for non-linear material model of concrete and reinforcing steel, respectively. The total numbers of nodes are 248–308, and that of 2D elements are 66–80.

Both analytical results are satisfactory from the view point of structural design. Close agreement to experimental results in the cracking load, crack extension, elasto-plastic stiffness and total strength was verified.     

A simplified damage mechanics approach to nonlinear analysis of frames

This paper presents a general formulation for frame analysis based on ‘lumped dissipation models’ and continuum damage mechanics. A particular model for RC frames based on this framework is proposed and the numerical implementation of simplified damage models in commercial finite element programs is described.     

A parallel mixed time integration algorithm for nonlinear dynamic analysis

This paper presents a parallel mixed time integration algorithm formulated by synthesising the implicit and explicit time integration techniques. The proposed algorithm is an extension of the mixed time integration algorithms [Comput. Meth. Appl. Mech. Engng 17/18 (1979) 259; Int. J. Numer. Meth. Engng 12 (1978) 1575] being successfully employed for solving media-structure interaction problems. The parallel algorithm for nonlinear dynamic response of structures employing mixed time integration technique has been devised within the broad framework of domain decomposition. Concurrency is introduced into this algorithm, by integrating interface nodes with explicit time integration technique and later solving the local submeshes with implicit algorithm. A flexible parallel data structure has been devised to implement the parallel mixed time integration algorithm. Parallel finite element code has been developed using portable Message Passing Interface software development environment. Numerical studies have been conducted on PARAM-10000 (Indian parallel supercomputer) to test the accuracy and also the performance of the proposed algorithm. Numerical studies indicate that the proposed algorithm is highly adaptive for parallel processing.