Cost optimization of singly and doubly reinforced concrete beams with EC2-2001

A model for the optimal design of rectangular reinforced concrete sections is presented considering the stress–strain diagrams described in EC2-2001 and MC90. The following expressions are developed: economic bending moment; optimal area of steel and optimal steel ratio between upper and lower steel. All the expressions are in nondimensional form. The present model is applied to four different classes of concrete described in MC90. It is concluded that in nondimensional form the equations are nearly coincident for both singly and doubly reinforcement. It is also concluded that the ultimate strain for concrete in the compression zone, ε_cm, lies between the strain for peak stress ε_c1 and the ultimate strain ε_cu. This result is relevant once that the maximum moment is obtained for this value, and not the value ε_cu, as defined in EC2-2001. Cost optimization is implemented in the code and compared with other optimum models based on the ultimate design of ACI.     

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.     

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.     

Damage analysis and numerical simulation for failure process of a reinforced concrete arch structure

This work focuses on the implementation of damage mechanics model to explain and understand failure mechanisms of the concrete structures. A tensorial damage theory and an isotropic application to the arch ribs of a real bridge are presented. Two reinforced concrete arch ribs of a 28 year old bridge has been removed from the field to the laboratory. They were loaded up to failure in order to study the remaining strength of the structure. The damage model involves three independent parameters for simulating the damage behaviors of the concrete material. The damage theory—additional load—finite element method is developed to simulate numerically the failure process of the RC structures based on the proposed damage model. The predicted displacements, strains and failure mode of the RC arch are good agreement with the experimental results. The values of the three material parameters that describe the damage characteristics of concrete were obtained. The numerical calculations revealed the interested behaviors of concrete in a damaging process. The proposed damage model can be used effectively to describe the damage and fracture behaviors of concrete.     

A parametric subdomain discretization for the analysis of the multiaxial response of reinforced concrete sections

The paper presents an improved sectional discretization method for evaluating the response of reinforced concrete sections. The section is subdivided into parametric subdomains that allow the modelization of any complex geometry while taking advantage of the Gauss quadrature techniques. In particular, curved boundaries are dealt with two nested parametric transformations, reducing the modeling approximation. It is shown how the so-called fiber approach is simply a particular case of the present more general method. Many benchmarks are presented in order to assess the accuracy of the results. The influence of the discretization into subdomains and of the quadrature rules, chosen for integration, is discussed. The numerical tests highlight also the effects of spurious stress distributions in the tensile concrete zone, due the interpolation functions adopted for the Gauss integration. It is shown how balancing the number of subdomains and the number of sampling points such spurious effects vanish. The method shows to be accurate, very flexible in the discretization process and robust in analyzing any sectional state. Moreover, it converges faster than the fiber method, reducing the computational demand. All these properties are of great importance when the computations are iteratively repeated, as for the case of the sectional analysis within a computational procedure for a R.C. frame analysis.     

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.     

Least-cost design of singly and doubly reinforced concrete beam using genetic algorithm optimized artificial neural network based on Levenberg–Marquardt and quasi-Newton backpropagation learning techniques

In this work, least-cost design of singly and doubly reinforced beams with uniformly distributed and concentrated load was done by incorporating actual self-weight of beam, parabolic stress block, moment–equilibrium and serviceability constraint besides other constraints. Also, this design expertise was incorporated into a genetically optimized artificial neural network based on steepest descent, Levenberg–Marquardt, and quasi-Newton backpropagation learning techniques. The initial solution for the optimization procedure was obtained using limit state design as per IS: 456-2000.     

钢筋混凝土拱肋劲性骨架爬模施工分析

以国内某主跨300 m的外倾式非对称系杆拱桥为例,采用三维有限元法分析靠拱脚段钢筋混凝土拱肋爬模施工过程中劲性骨架的受力状态. 为简化计算,从结构安全和满足桥梁施工要求出发,合理假定模板系统及劲性骨架的载荷分担率,将劲性骨架简化为空间杆系、载荷简化为节点载荷. 该方法计算模型简单、结果偏于安全,可用于类似结构的工程近似计算.     

Coupled model for the nonlinear analysis of sections made of anisotropic materials, subjected to general 3D loading. Part 2: Implementation and validation

A numerical model for the coupled analysis of cross-sections made of anisotropic materials under general combined loading was formulated in an accompanying paper (1). In this paper, additional aspects concerning its implementation and the scheme for nonlinear analysis are discussed. The model is validated by analyzing several isotropic and anisotropic elastic problems; excellent accuracy was obtained compared to closed-form solutions. Further, the case of a RC section presenting crack-induced anisotropy is investigated. The capability of the model to capture interactions between tangent and normal forces is proved. The conclusion drawn is that the developed model is a suitable sectional constitutive equation for 3D beam elements for realistic structural analysis.