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.     

Prediction of the moment capacity of reinforced concrete slabs in fire using artificial neural networks

In this study, the application of artificial neural networks (ANN) to predict the ultimate moment capacity of reinforced concrete (RC) slabs in fire is investigated. An ANN model is built, trained and tested using 294 data for slabs exposed to fire. The data used in the ANN model consists of seven input parameters, which are the distance from the extreme fiber in tension to the centroid of the steel on the tension side of the slab (d′), the effective depth (d), the ratio of previous parameters (d′/d), the area of reinforcement on the tension face of the slab (A_s), the fire exposure time (t), the compressive strength of the concrete (f_cd), and the yield strength of the reinforcement (f_yd). It is shown that ANN model predicts the ultimate moment capacity (M_u) of RC slabs in fire with high degree of accuracy within the range of input parameters considered. The moment capacities predicted by ANN are in line with the results provided by the ultimate moment capacity equation. These results are important as ANN model alleviates the problem of computational complexity in determining M_u.     

Efficient finite element modelling of reinforced concrete beams retrofitted with fibre reinforced polymers

This paper presents a new simple and efficient two-dimensional frame finite element (FE) able to accurately estimate the load-carrying capacity of reinforced concrete (RC) beams flexurally strengthened with externally bonded fibre reinforced polymer (FRP) strips and plates. The proposed FE, denoted as FRP–FB-beam, considers distributed plasticity with layer-discretization of the cross-sections in the context of a force-based (FB) formulation. The FRP–FB-beam element is able to model collapse due to concrete crushing, reinforcing steel yielding, FRP rupture and FRP debonding.The FRP–FB-beam is used to predict the load-carrying capacity and the applied load-midspan deflection response of RC beams subjected to three- and four-point bending loading. Numerical simulations and experimental measurements are compared based on numerous tests available in the literature and published by different authors. The numerically simulated responses agree remarkably well with the corresponding experimental results. The major features of this frame FE are its simplicity, computational efficiency and weak requirements in terms of FE mesh refinement. These useful features are obtained together with accuracy in the response simulation comparable to more complex, advanced and computationally expensive FEs. Thus, the FRP–FB-beam is suitable for efficient and accurate modelling and analysis of flexural strengthening of RC frame structures with externally bonded FRP sheets/plates and for practical use in design-oriented parametric studies.     

Non-linear finite element dynamic analysis of two-dimensional concrete structures

This paper presents a numerical procedure for predicting the non-linear dynamic response of plane and axisymmetric reinforced concrete structures. Isoparametric elements with special embedded axial members are used to discretize concrete and steel in space. A summary of a rate and history dependent constitutive model for progressive failure analysis of concrete is given in which the compression behaviour is modelled as a strain rate sensitive elasto-viscoplastic material and in tension as strain rate dependent linear elastic strain softening material. The different rales governing the pre-failure and post-failure behaviour in compression and tension are developed in which the strain rate dependency is included. Steel is modelled as a strain rate dependent uniaxial elasto-viscoplastic material. Explicit central difference scheme in conjunction with an energy balance check is employed for time integration of equations of motion. A computer program for linear and non-linear dynamic analysis of concrete structures is described. Finally, some numerical applications are presented.     

Minimum cost design of RC frames using the DCOC method Part I: Columns under uniaxial bending actions

The paper solves the minimum-cost design problem of RC plane frames. The cost to be minimized includes those of concrete, reinforcing steel and formwork, whereas the design constraints include limits on maximum deflection at a specified node, on bending and shear strengths of beams and on combined axial and bending strength of columns, in accordance with the limit state design (LSD) requirements. The algorithms developed in this work can handle columns under uniaxial bending actions. In the companion paper the numerical procedure is generalized to include columns subjected to biaxial bending. On the basis of discretized continuum-type optimality criteria (DCOC), the design problem is systematically formulated, followed by explicit mathematical derivation of optimality criteria upon which iterative procedures are developed for the solution of design problems when the design variables are the cross-sectional parameters and steel ratios. For practical reasons, the cross-sectional parameters are chosen to be either uniform per member or uniform for several members at a given floor level. The procedure is illustrated on several test examples. It is shown that the DCOC-based methods are particularly efficient for the design of large RC frames.     

A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading

The material point method (MPM) takes advantages of both the Eulerian and Lagrangian methods, so it is capable of handling many challenging engineering problems, such as the dynamic responses of reinforced concrete (RC) subjected to blast and impact loadings. However, it is time-consuming to discretize the steel reinforcement bars (“rebars”) in RC by using MPM because the diameter of the steel bar is very small compared with the size of concrete. A hybrid finite element–material point (FEMP) method is proposed, in which the truss element in the traditional finite element method (FEM) is incorporated into the MPM to model the rebars. The proposed FEMP method is implemented in our three-dimensional material point method code, MPM3D®, and validated by several benchmark problems. Finally, it is applied to simulate the dynamic response of RC slab penetrated by projectile, and the numerical results are in good agreement with the experimental data reported in the literature. The proposed idea is applicable to incorporate other types of finite elements into MPM to take advantages of both FEM and MPM.     

Weight optimization for flexural reinforced concrete beams with static nonlinear response

The weight optimization of reinforced concrete (RC) beams with material nonlinear response is formulated as a general nonlinear optimization problem. Incremental finite element procedures are used to integrate the structural response analysis and design sensitivity analysis in a consistent manner. In the finite element discretization, the concrete is modelled by plane stress elements and steel reinforcement is modelled by discrete truss elements. The cross-sectional areas of the steel and the thickness of the concrete are chosen as design variables, and design constraints can include the displacement, stress and sizing constraints. The objective function is the weight of the RC beams. The optimal design is performed by using the sequential linear programming algorithm for the changing process of design variables, and the gradient projection method for the calculations of the search direction. Three example problems are considered. The first two are demonstrated to show the stability and accuracy of the approaches by comparing previous results for truss and plane stress elements, separately. The last one is an example of an RC beam. Comparative cost objective functions are presented to prove the validity of the approach.     

The flexural rigidity of reinforced concrete slabs

To allow reliability analyses and design optimisation, two probabilistic models for the flexural rigidity of effectively uncracked reinforced concrete slabs are developed theoretically from a probabilistic model of concrete compliance. A simulation model uses finite difference equations to model concrete and steel stresses and strains, as concrete creeps and shrinks in a slab section. This model accounts for 17 parameters to yield an unbiased estimate of rigidity with a coefficient of variation of 0.23. A simulation study for a normal class of slabs shows that flexural rigidity is effectively independent of steel reinforcement, so rigidity is well represented by the product of a gross moment of inertia and a time-dependent effective gross modulus of elasticity. This modulus is primarily a function of concrete strength, humidity and duration of loading, and it approaches an effective long-term limiting value at about 5000 days. A simplified (design) model approximates this long-term modulus by a simple function of concrete strength and humidity. This model gives an unbiased estimate with a coefficient of variation of 0.27.     

混凝土内应力测量的应变砖传感器设计与应用

针对混凝土内应力传感器匹配误差问题,设计制作埋入式应变砖传感器,将混凝土作为传感器一部分整体进行标定,从而减少实际测量中匹配误差的影响。传感器设计中考虑温度和干扰补偿,并对应变计进行良好防护以确保20MPa压力下传感器绝缘性能良好。进行50kN静态加载试验,得到加载力同传感器输出的函数关系和非线性误差。经过激波管动态加载试验,得出应变砖固有频率大于30kHz,可用于动态加载的混凝土内应力测量。     

Modelling Approaches for Inelastic Behaviour of RC Walls: Multi-level Assessment and Dependability of Results

The severe damage and collapse of many reinforced concrete (RC) wall buildings in the recent earthquakes of Chile (2010) and New Zealand (2011) have shown that RC walls did not perform as well as required by the modern codes of both countries. It seems therefore appropriate to intensify research efforts towards more accurate simulations of damage indicators, in particular local engineering demand parameters such as material strains, which are central to the application of performance-based earthquake engineering. Potential modelling improvements will necessarily build on a thorough assessment of the limitations of current state-of-the-practice simulation approaches for RC wall buildings. This work compares different response parameters obtained from monotonic analyses of RC walls using numerical tools that are commonly employed by researchers and specialized practitioners, namely: plastic hinge analyses, distributed plasticity models, and shell element models. It is shown that a multi-level assessment—wherein both the global and local levels of the response are jointly addressed during pre- and post-peak response—is fundamental to define the dependability of the results. The displacement demand up to which the wall response can be predicted is defined as the first occurrence between the attainment of material strain limits and numerical issues such as localization. The present work also presents evidence to discourage the application of performance-based assessment of RC walls relying on non-regularized strain EDPs.     

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.     

循环载荷作用下两类楼板抗震性能的非线性有限元分析

为比较组合楼板和普通混凝土楼板的抗震性能,采用非线性有限元分析方法研究它们在循环载荷作用下的受力行为,并由此得到两类楼板的滞回曲线、骨架曲线及应力应变分布规律．计算结果表明,采用可靠构造措施的压型钢板与混凝土组合作用明显,在不失较高承载力的同时,组合楼板仍具有良好的抗震性能．将计算结果与试验数据相比较,验证该数值分析方法的有效性。     

A Direct solution of the equivalent frame for two-way slabs

A common procedure for the analysis of concrete buildings with two-way slabs is to reduce the slab along with other components of the building to a series of equivalent frames representing portions of the building between center-lines of spans.This paper presents a direct solution of the equivalent frame. Variations of slab geometry, flexural and torsional beams as well as columns are included in the model considered. The equations derived are cast into a short computer program which can be used for the design of concrete buildings with flat plate, flat slab, and two-way slabs with beams.     

Optimum cost design of reinforced concrete slabs using neural dynamics model

For structural optimization algorithms to find widespread usage among practicing engineering they must be formulated as cost optimization and applied to realistic structures subjected to the actual constraints of commonly used design codes such as the ACI code. In this article, a general formulation is presented for cost optimization of single- and multiple-span RC slabs with various end conditions (simply supported, one end continuous, both ends continuous, and cantilever) subjected to all the constraints of the ACI code. The problem is formulated as a mixed integer-discrete variable optimization problem with three design variables: thickness of slab, steel bar diameter, and bar spacing. The solution is obtained in two stages. In the first stage, the neural dynamics model of Adeli and Park is used to obtain an optimum solution assuming continuous variables. Next, the problem is formulated as a mixed integer-discrete optimization problem and solved using a perturbation technique in order to find practical values for the design variables. Practicality, robustness, and excellent convergence properties of the algorithm are demonstrated by application to four examples.     

Computer analysis of impact behavior of concrete filled steel tube columns

This paper presents a numerical study of the response of axially loaded concrete filled steel tube (CFST) columns under lateral impact loading using explicit non-linear finite element techniques. The aims of this paper are to evaluate the vulnerability of existing columns to credible impact events as well as to contribute new information towards the safe design of such vulnerable columns. The model incorporates concrete confinement, strain rate effects of steel and concrete, contact between the steel tube and concrete and dynamic relaxation for pre-loading, which is a relatively recent method for applying a pre-loading in the explicit solver. The finite element model was first verified by comparing results with existing experimental results and then employed to conduct a parametric sensitivity analysis. The effects of various structural and load parameters on the impact response of the CFST column were evaluated to identify the key controlling factors. Overall, the major parameters which influence the impact response of the column are the steel tube thickness to diameter ratio, the slenderness ratio and the impact velocity. The findings of this study will enhance the current state of knowledge in this area and can serve as a benchmark reference for future analysis and design of CFST columns under lateral impact.     

Analysis of stub-girders using substructuring

This paper deals with the application of the method of substructures to calculate deflections in stub-girders. A stub-girder is a new type of composite beam recently introduced in the United States. It consists of a steel beam and a reinforced concrete slab separated by a series of short steel rolled sections called stubs. The openings between the adjacent stubs are used as service ducts.Since most of the panels of a stub-girder are identical in shape and size, the method of substructures, which requires the physical partitioning of the structure into smaller units, is particularly suitable for its analysis. For the analysis presented herein a substructure, i.e. a smaller unit of the stub-girder, was discretized into an assemblage of plane stress rectangular finite elements. The two dimensional analysis was chosen because a preliminary investigation indicated that the matrix storage requirements for a 3-D analysis were so large that the amount of storage and the cost of the analysis would be prohibitive for most practical cases.The method of analysis is illustrated by application to three stub-girders. The computed results were compared with those determined experimentally. Two different idealizations were used to replace the flanges. The computed deflection values for one of the idealizations showed acceptable agreement with the experimental results. The computer program developed for this investigation can also be used to calculate the deflection in a beam with a series of rectangular openings.     

Design optimization of simply supported concrete slabs by finite element modelling

This paper outlines the finite element prediction process for the development of charts for accurate peak load determination of simply supported, reinforced concrete slabs under uniformly distributed loading. Through a series of parametric studies using a simple concrete model, the simulation of tests on four simply supported slabs was used as a basis for establishing a set of optimum parameter values and computational conditions, which guarantees acceptable solution. The reliability of the established parameter values for prediction purposes was verified by the direct simulation of 11 other slabs. Following the successful reliability check, the finite element model was used for analysing 270 “computer model” slabs, from which charts were developed. These charts serve for quick and reliable peak load determination of arbitrary simply supported slabs. A comparative study of the direct finite element and chart predictions, with values from analytical and design methods, reveals the superiority of the charts over the latter methods, with accuracy comparable to that of the optimised finite element model. The chart prediction is noted to be accurate to within 4% of test results. A strategy for displacement determination is also established, with the same degree of success and the paper discusses possible practical applications of the developed finite element system.     

机场地基反应模量动态识别仿真研究

机场道面是由多块道面板连接在一起共同工作的,Kelvin粘弹性地基上有限尺寸矩形板系统为基础,建立了运动荷载作用下四边弹性支撑的道面板的运动方程,利用变分法、功互等定理等方法求得道面板系统的弯沉解析解.进而根据最小二乘方准则,采用Matlab编程拟合实测动挠度和理论动挠度,从而识别出地基反应模量K.实例计算表明所得结果具有较好的精度.研究结果可为机场道面的板厚设计、参数识别和质量评价等提供理论依据.