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.     

Some aspects on three-dimensional numerical modelling of reinforced concrete structures using the finite element method

This paper deals with some aspects related to three-dimensional numerical modelling of reinforced concrete structures using the Finite Element Method (FEM). Some subjects such as the solution technique of the non-linear equilibrium equations and the constitutive model for concrete and reinforcement steel are emphasised and commented. A robust method for the evaluation of the intersecting points of the embedded reinforcement bars into the three-dimensional finite element mesh is also presented. The main advantages of the Generalised Displacement Control Method with the Generalised Displacement Parameter to improve the response of the concrete and reinforced concrete analyses are highlighted. Finally, a series of numerical examples related to the above-mentioned aspects are presented.     

Theorem of optimal reinforcement for reinforced concrete cross sections

A theorem of optimal (minimum) sectional reinforcement for ultimate strength design is presented for design assumptions common to many reinforced concrete building codes. The theorem states that the minimum total reinforcement area required for adequate resistance to axial load and moment can be identified as the minimum admissible solution among five discrete analysis cases. Therefore, only five cases need be considered among the infinite set of potential solutions. A proof of the theorem is made by means of a comprehensive numerical demonstration. The numerical demonstration considers a large range of parameter values, which encompass those most often used in structural engineering practice. The design of a reinforced concrete cross section is presented to illustrate the practical application of the theorem.     

The use of topology optimization in disposing carbon fiber reinforcement for concrete structures

A topology optimization procedure is presented as a tool for determining the distribution of external strengthening of concrete slabs, using Carbon Fiber Reinforced Polymer (CFRP). Although the procedure is applied to slabs in this work, the technique can be used in any concrete structure to be reinforced. Numerical simulations are performed using the Finite Element Method, in combination with the automated topology optimization procedure, to indicate the optimal region for placement of the reinforcement. The influence of some aspects of the slab’s structural behavior on the optimization results is presented: concrete cracking, boundary conditions and reinforcement rate. A brief discussion is given of the similarity between the topology optimization results obtained by the maximum stiffness and ultimate strength criteria. Gains are found in the stiffness and strength of reinforced parts. A comparison with conventional reinforcement techniques demonstrates that topology optimization can be a useful tool for defining the region of reinforcement, allowing for material cost savings.     

大体积水工结构配筋CAD研究

以三峡工程临时船闸阀门井的配筋设计为背景，阐述基于积木式模块思想的大体积水工结构参数化配筋CAD软件研制的原理和方法，并就积木式模式化的原理，钢筋图的自动生成技术等问题进行重点论述。     

A plastic damage approach for confined concrete

There are many situations in which it is necessary to increase the capacity of structures in use. This need maybe either for a change of use or because the structures have suffered some damage or have shown little resistance in case of extreme loads such as earthquakes. The most common methods for repair and retrofit of reinforced concrete columns are concrete jacketing, steel jacketing and fiber wrapping. This last type of reinforcement has many advantages as it offers a high-strength, low-weight and corrosion-resistant jacket with easy and rapid installation. The reinforcement with composite materials improves shear and compression strength and ductility as a result of concrete core confinement. The present analytical and numerical ability to quantify the efficiency of fiber confinement is rather limited, especially with respect to ductility.A constitutive model that approximately reproduces the behavior of structural concrete elements under confinement is developed in this paper. The model allows the assessment of concrete columns and bridge piles repaired and/or reinforced with fiber reinforced composites (FRP). The model presented is a modification of an existing coupled plastic damage model. A new definition for the plastic hardening variable and a new yielding surface with curved meridians are proposed. Both improvements enable the adequate reproduction of concrete behavior in high confinement conditions.The comparison of numerical and experimental results shows the model capacity to simulate concrete behavior under triaxial compression conditions like the ones present in concrete columns confined with fiber reinforced composites.     

Behavior of reinforced concrete structures predicted by the finite element method

With current nonlinear analysis computer capabilities, considerable strides are being made in developing procedures, the utilization of which, allows one to analyze reinforced concrete structures while taking into account cracking and other characteristics of the constituent materials. Objective of the analyses is the determination of displacements as well as concrete and steel forces at various stages of loading. Cracking and the consequent loss of tensile strength is a major characteristic that must be modeled in any program for the analysis of reinforced concrete members. The three basic approaches have been employed by various investigators to account for tension cracking are discussed. Advantages and problems associated with these approaches are discussed. The formulation used to delineate compressive stress characteristics of concrete is evaluated. Solution procedures are described. Peculiarities required of solution methods in order to be suitable for the analysis of reinforced concrete systems are noted.     

Dynamic response simulation for reinforced concrete slabs

Present investigation comprises development of a new finite element numerical formulation for nonlinear transient dynamic analysis of reinforced concrete slab structures. Depending on many experimental data, new material constitutive relationships for concrete material have been formulated. A regression analysis of available experimental data in the SPSS-statistical program has been employed for formulating the proposed material finite element models, and the appropriateness of the models are confirmed through the histograms and measured indices of determination. Concrete slab structures were analyzed using eight-node serendipity degenerated plate elements. The constitutive models of the nonlinear materials are introduced to take into account the nonlinear stress–strain relationships of concrete. For studying the stress profile of the concrete slab through its thickness, a layered approach is adopted. Elastic perfectly plastic and strain hardening plasticity approaches have been employed to model the compressive behavior of concrete. Assumptions for strain rate effect were included in dynamic analysis by supposing the dynamic yield function as a function of the strain rate, in addition to be the total plastic strain. The yield condition is formulated in terms of the first two stress invariants. Geometrical nonlinearity was considered in analysis as a mathematical model based on the total lagrangian approach taking into account Von Karman assumptions. Implicit Newmark with corrector–predictor algorithm was used for time integration solution of the equation of the motion for slab structures. An incremental and iterative procedure is adopted to trace the entire response of the structure; a displacement convergence criterion is adopted in the present study. A computer program coded in FORTRAN has been developed and used for the dynamic analysis of reinforced concrete slabs. The numerical results show good agreement with other published studies’ results which include deflections.     

Ultimate strength analysis of prestressed reinforced concrete sections under axial force and biaxial bending

A secant approach is illustrated for the ultimate limit state (ULS) analysis of prestressed reinforced concrete sections subjected to axial load and biaxial bending in presence of softening stress–strain laws. The stiffness matrix and the resultant loads are evaluated analytically by a novel methodology, termed fiber-free, which represents a computationally efficient alternative to fiber approaches. Extensive computations of the ULS domains of benchmark test cases show that the robustness of the proposed algorithmic strategy is substantially unaffected by the amount of reinforcement, prestressing and softening, though localized non-convex regions have been occasionally experienced in presence of softening.     

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.     

Nonlinear Formulations of a Four-Node Quasi-Conforming Shell Element

The quasi-conforming technique was introduced in the 1980’s to meet the challenge of inter-elements conforming problems and give a unified treatment of both conforming and nonconforming elements. While the linear formulation is well established, the nonlinear formulation based on the quasi-conforming technique that includes geometric and material nonlinearity is presented in this paper. The formulation is derived in the framework of an updated Lagrangian stress resultant, co-rotational approach. The geometric nonlinear formulation provides solutions to buckling and postbuckling behaviour while the material nonlinear formulation considers the spread of plasticity within the element while maintaining an explicit construction of element matrices. Aside from the elasto-plastic constitutive relation, formulations on laminate composites and reinforced concrete are also presented. The formulations of laminate composite and reinforced concrete material are present based on the layer concept, the material properties can vary throughout the thickness and across the surface of a shell element. The various failure criteria for laminate composite are included in the formulation which makes it possible to analyses the progressive failure of fibre and matrix. For the reinforced concrete material, the nonlinearities as a result of tensile cracking, tension stiffening between cracks, the nonlinear response of concrete in compression, and the yielding of the reinforcement are considered. The steel reinforcement is modeled as a bilinear material with strain hardening.     

Effect of loading types and reinforcement ratio on an effective moment of inertia and deflection of a reinforced concrete beam

In the design of reinforced concrete structures, a designer must satisfy not only the strength requirements but also the serviceability requirements, and therefore the control of the deformation becomes more important. To ensure serviceability criterion, it is necessary to accurately predict the cracking and deflection of reinforced concrete structures under service loads. For accurate determination of the member deflections, cracked members in the reinforced concrete structures need to be identified and their effective flexural and shear rigidities determined. The effect of concrete cracking on the stiffness of a flexural member is largely dependent on both the magnitude and shape of the moment diagram, which is related to the type of applied loading. In the present study, the effects of the loading types and the reinforcement ratio on the flexural stiffness of beams has been investigated by using the computer program developed for the analysis of reinforced concrete frames with members in cracked state. In the program, the variation of the flexural stiffness of a cracked member has been obtained by using ACI, CEB and probability-based effective stiffness model. Shear deformation effect is also taken into account in the analysis and the variation of shear stiffness in the cracked regions of members has been considered by employing reduced shear stiffness model available in the literature. Comparisons of the different models for the effective moment of inertia have been made with the reinforced concrete test beams. The effect of shear deformation on the total deflection of reinforced concrete beams has also been investigated, and the contribution of shear deformation to the total deflection of beam have been theoretically obtained in the case of various loading case by using the developed computer program. The applicability of the proposed analytical procedure to the beams under different loading conditions has been tested by a comparison of the analytical and experimental results, and the analytical results have been found in good agreement with the test results.     

Flexural analysis of reinforced fibrous concrete members using the finite element method

A numerical procedure based on the finite element method is developed for the geometric and material nonlinear analysis of reinforced concrete members containing steel fibres and subjected to monotonic loads. The proposed procedure is capable of tracing the displacements, strains, stresses, crack propagation, and member end actions of these structures up to their ultimate load ranges. A frame element with a composite layer system is used to model the structure. An iterative scheme based on Newton-Raphson's method is employed for the nonlinear solution algorithm. The constitutive models of the nonlinear material behaviour are presented to take into account the nonlinear stress-strain relationships, cracking, crushing of concrete, debonding and pull-out of the steel fibres, and yielding of the reinforcement. The geometric nonlinearity due to the geometrical change of both the structure and its elements are also represented. The numerical solution of a number of reinforced fibrous concrete members are compared with published experimental test results and showed good agreement.     

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.     

Numerical study of confinement effectiveness in solid and hollow reinforced concrete bridge piers: Methodology

A consistent methodology is suggested for modelling confinement in both solid and hollow reinforced concrete bridge pier sections, within the computational framework of three-dimensional nonlinear finite element analysis. The ultimate goal is to suggest the most convenient transverse reinforcement arrangements in terms of enhanced strength and ductility, as well as ease of construction and cost-effectiveness. The present study is particularly relevant with respect to confinement of hollow sections, for which previous experimental and analytical research is limited. Constitutive laws, modelling techniques, post-processing issues and preliminary applications are first introduced, and a large parametric model setup for circular and rectangular bridge piers of solid and hollow section, is subsequently presented. A detailed discussion follows on various issues concerning confinement modelling, aiming to broaden the scope and applicability of the suggested methodology. The respective numerical results and their interpretation and evaluation will be presented in a companion paper.     

A layered cylindrical quadrilateral shell element for nonlinear analysis of RC plate structures

This paper proposes a simple and accurate 4-node, 24-DOF layered quadrilateral flat plate/shell element, and an efficient nonlinear finite element analysis procedure, for the geometric and material nonlinear analysis of reinforced concrete cylindrical shell and slab structures. The model combines a 4-node quadrilateral membrane element with drilling or rotational degrees of freedom, and a refined nonconforming 4-node 12-DOF quadrilateral plate bending element RPQ4, so that displacement compatibility along the interelement boundary is satisfied in an average sense. The element modelling consists of a layered system of fully bonded concrete and equivalent smeared steel reinforcement layers, and coupled membrane and bending effects are included. The modelling accounts for geometric nonlinearity with large displacements (but moderate rotations) as well as short-term material nonlinearity that incorporates tension, cracking and tension stiffening of the concrete, biaxial compression and compression yielding of the concrete and yielding of the steel. An updated Lagrangian approach is employed to solve the nonlinear finite element stiffness equations. Numerical examples of two reinforced concrete slabs and of a shallow reinforced concrete arch are presented to demonstrate the accuracy and scope of the layered element formulation.     

Nonlinear optimal design model of a concrete reinforcement truss plank

The reinforced concrete truss plank is one kind of specially-shaped reinforcement concrete composite slab that has been used in bridge structures, building structures, etc. in Hong Kong, Japan, America and European countries. Because of its complicated reinforcement distribution, this truss plank is analysed and designed by simplified methods that neglect the contributions from a combined reinforcement truss mechanism and the design is over-conservative. This paper describes a non-linear optimal design model for this plank, considering reinforcement truss action by a strain compatible method from a refined finite element model and experiment analysis.Communicated by J. Sobieski     

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.     

An efficient generation method of embedded reinforcement in hexahedral elements for reinforced concrete simulations

In this paper, an automatic procedure for the generation of embedded steel reinforcement inside hexahedral finite elements is presented. The automatic mapping of the entire reinforcement network inside the concrete hexahedral finite elements is performed using the end-point coordinates of the rebar reinforcement macro-elements. By introducing a geometrical constraint, this procedure decreases significantly the computational effort for generating the input data of the embedded rebar elements in three-dimensional finite-element analysis, particularly when dealing with relatively large-scale reinforced concrete models. The computational robustness and efficiency of the proposed mesh generation method are demonstrated through numerical experiments.     

分层强化学习中的动态分层方法研究

分层强化学习中现有的自动分层方法均是在对状态空间进行一定程度探测之后一次性生成层次结构,不充分探测不能保证求解质量,过度探测则影响学习速度,为了克服学习算法性能高度依赖于状态空间探测程度这个问题,本文提出一种动态分层方法,该方法将免疫聚类及二次应答机制融入Sutton提出的Option分层强化学习框架,能对Option状态空间进行动态调整,并沿着学习轨迹动态生成Option内部策略,以二维有障碍栅格空间内两点间最短路径规划为学习任务进行了仿真实验,结果表明,动态分层方法对状态空间探测程度的依赖性很小,动态分层方法更适用于解决大规模强化学习问题.