# Structural Engineering & Mechanics

Online ISSN: 1225-4568

Online ISSN: 1225-4568

Publications

Conference Paper

A new vector computational algorithm is presented for calculating the stiffness matrices of multi-layered reinforced concrete shell elements. Each element stiffness matrix is represented in terms of three vector arrays of lengths 78, 96 and 36, respectively. One element stiffness matrix is calculated at a time without interruption in the vector calculations for the uncracked or cracked elements. It is shown that the present algorithm is 1.1 to 7.3 times more efficient then the vector algorithm developed by Min and Gupta on a Cray Y-MP supercomputer

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Article

This paper presents the findings of an experimental study to evaluate retrofit methods which address particular weaknesses that are often found in reinforced concrete structures, especially older structures, namely the lack of sufficient flexural and shear reinforcement within the columns and the lack of adequate shear reinforcement within the joints. Thus, the use of a reinforced concrete jacket and a high-strength fibre jacket for cases of post-earthquake and pre-earthquake retrofitting of columns and beam–column joints was investigated experimentally and analytically. In this paper, the effectiveness of the two jacket styles was also compared.

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Article

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of I-section struts. The so-called exact strip is developed based on the concept that it is effectively a plate. The presented method, which is designated by the name Full-analytical Finite Strip Method, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman's equilibrium equation is solved exactly to obtain the buckling loads and mode shapes for the I-section struts. The investigation of buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. The current post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. Through the solution of the Von-Karman's compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. All the displacement functions are then substituted in the total strain energy expressions. The theorem of minimum total potential energy is subsequently applied to solve for the unknown coefficient. Finally, the developed method is subsequently applied to analyze the initial post-buckling behavior of some representative I-sections for which the results were also obtained through the application of a Semi-energy Finite Strip Method [Ovesy HR. The development and application of a semi-energy post-local buckling finite strip. PhD dissertation, Cranfield University, UK, 1998]. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.

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Article

Three-scale homogenization procedure is proposed in this paper to provide estimates of the effective thermal conductivities of porous carbon-carbon textile composites. On each scale - the level of fiber tow (micro-scale), the level of yarns (meso-scale) and the level of laminate (macro-scale) - a two step homogenization procedure based on the Mori-Tanaka averaging scheme is adopted. This involves evaluation of the effective properties first in the absence of pores. In the next step, an ellipsoidal pore is introduced into a new, generally orthotropic, matrix to make provision for the presence of crimp voids and transverse and delamination cracks resulting from the thermal transformation of a polymeric precursor into the carbon matrix. Other sources of imperfections also attributed to the manufacturing processes, including non-uniform texture of the reinforcements, are taken into consideration through the histograms of inclination angles measured along the fiber tow path together with a particular shape of the equivalent ellipsoidal inclusion. The analysis shows that a reasonable agreement of the numerical predictions with experimental measurements can be achieved.

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Article

This paper presents a comprehensive approach to the evaluation of macroscopic material parameters for natural stone and quarry masonry. To that end, a reliable non-linear material model on a meso-scale is developed to cover the random arrangement of stone blocks and quasi-brittle behaviour of both basic components, as well as the impaired cohesion and tensile strength on the interface between the blocks and mortar joints. The paper thus interrelates the following three problems: (i) definition of a suitable periodic unit cell (PUC) representing a particular masonry structure; (ii) derivation of material parameters of individual constituents either experimentally or running a mixed numerical-experimental problem; (iii) assessment of the macroscopic material parameters including the tensile and compressive strengths and fracture energy.

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Article

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of responses of vibration control systems with the uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of responses of the closed-loop system with uncertain parameters is presented. The upper bounds of responses can be used to estimate the robustness of responses of the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.

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Article

The torsional impact response of a penny-shaped crack in a transversely isotropic strip is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Investigated are the effects of material nonhomogeneity and orthotropy and strip’s highness on the dynamic stress intensity factor. The peak of the dynamic stress intensity factor can be suppressed by increasing the shear moduli’s gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface. The dynamic behavior varies little with the increasing of the strip’s highness.

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Article

During the 1995 Hyogoken-Nanbu Earthquake, a reinforced concrete building, called Jeunesse Rokko, suffered intermediate damage by forming a beam-yielding (weak-beam strongcolumn) mechanism, which has been regarded as the most desirable earthquake resisting mechanism throughout the world. High cost to repair damage at many beam ends and poor appearance expected after the repair work made the owner decide to tear down the building. Nonlinear earthquake response analyses were conducted to simulate the behavior of the building during the earthquake. This paper studies correlation between the observed structural damage and response by analyses. INTRODUCTION The 9-story reinforced concrete apartment building was located in the most heavily damaged area in Kobe City. The structure, designed in accordance with the current Building Standard Law of Japan (revised in 1981) and constructed in 1987, consisted of two parallel moment-resisting frames with 6 uniform bays at 5.5 m in the longitudinal...

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Article

Design curves have been prepared for prestressed rectangular beam section based on BS 8110, for determining area of steel for any given cross section, for stresses in concrete and steel and for the design moment. The design moment and the area of steel have been expressed in dimensionless form in terms of cross sectional dimensions and the characteristic strength of concrete. The choice and combination of design parameters result in considerably less number of curves as aid for design of rectangular prestressed beam sections, than those reported in CP 110 (Part 3).

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Article

This study explores a coefficient-based seismic capacity assessment method with a special emphasis on low-rise masonry in-filled (MI) reinforced concrete (RC) buildings subjected to earthquake motion. The coefficient-based method without requiring any complicated finite element analysis is a simplified procedure to assess the maximum spectral acceleration capacity of buildings. This paper first compares the fundamental periods of MI RC structures obtained, respectively, from experimental period data and empirical period-height formulas. The coefficient-based method for low-rise masonry buildings is then calibrated by the published experimental results obtained from shaking table tests. The comparison of the experimental and estimated results indicates that the simplified coefficient-based method can provide good approximations of the maximum spectral accelerations at peak loads of the low-rise masonry reinforced concrete buildings if a proper set of drift factors and initial fundamental vibration periods of structures are used.

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Article

The effects of accumulated strain distributions along the tapered members due to previous loading cycles such as earthquake ground motions were analyzed. Tapered members were used for pin-based portal frames in which maximum moments took place at eaves and decreased to around zero at the supports. It was found that the frame survived the largest intensity at first but failed by lateral buckling when the same loading was applied again. It was observed that 75 percent of the rafter was in the inelastic range before failure.

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Article

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

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Article

Piezoelectric actuators have long been recognised for use in aerospace structures for control of structural shape. This paper looks at active control of the swept shock wave/turbulent boundary layer interaction using smart flap actuators. The actuators are manufactured by bonding piezoelectric material to an inert substrate to control the bleed/suction rate through a plenum chamber. The cavity provides communication of signals across the shock, allowing rapid thickening of the boundary layer approaching the shock, which splits into a series of weaker shocks forming a lambda shock foot, reducing wave drag. Active control allows optimum control of the interaction, as it would be capable of positioning the control region around the original shock position and unimorph tip deflection, hence mass transfer rates. The actuators are modelled using classical composite material mechanics theory, as well as a finite element-modelling program (ANSYS 5.7).

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Article

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

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Article

A novel boundary stress resolution method is suggested in this paper, which is based upon the displacements of finite element analysis and of high precision with stress boundary condition strictly satisfied. The method is used to modify the Zienkiewicz-Zhu () a posteriori error estimator and for the h-version adaptive finite element analysis of crack problems. Successful results are obtained.

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Article

Many types of passive control devices have been recognized as effective tools for improving the seismic resistance of structures. A lot of past research has been carried out to study the response of structures equipped with energy-absorbing devices by assuming that the behavior of the beam-column systems are linearly elastic. However, linear theory may not be adequate for beams and columns during severe earthquakes. This paper presents the results of research on the nonlinear responses of structures with and without added passive devices under earthquakes. A new material model based on the plasticity theory and the two-surface model for beams and columns under six components of forces is proposed to predict the nonlinear behavior of beam-column systems. And a new nonlinear beam element in consideration of shear deformation is developed to analyze the beams and columns of a structure. Numerical results reveal that linear assumption may not be appropriate for beams and columns under seismic loadings, especially for unexpectedly large earthquakes. Also, it may be necessary to adopt nonlinear beam elements in the analysis and design process to assure the safety of structures with or without the control of devices.

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Article

The research and applications of numerical methods of design optimization on structural dynamic behaviors are presented in this paper. The emphasis is focused on the dynamic design optimization of aerospace structures, particularly those composed of composite laminate and sandwich plates. The methods of design modeling, sensitivity analysis on structural dynamic responses, and the optimization solution approaches are presented. The numerical examples of sensitivity analysis and dynamic structural design optimization are given to demonstrate the effectiveness of the numerical methods.

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Article

A hybrid structural design and optimization methodology that combines the strengths of genetic algorithms, local search techniques, and parallel computing is developed to evolve optimal truss systems in this research effort. The primary objective that is met in evolving near-optimal or optimal structural systems using this approach is the capability of satisfying user-defined design criteria while minimizing the computational time required. The application of genetic algorithms to the design and optimization of truss systems supports conceptual design by facilitating the exploration of new design alternatives. In addition, final shape optimization of the evolved designs is supported through the refinement of member sizes using local search techniques for further improvement. The use of the hybrid approach, therefore, enhances the overall process of structural design. Parallel computing is implemented to reduce the total computation time required to obtain near-optimal designs. The support of human-computer interaction during layout optimization and local optimization is also discussed since it assists in evolving optimal truss systems that better satisfy a user's design requirements and design preferences.

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Article

In the present contribution an interface crack model is introduced which is capable of modelling crack initialisation and growth in aluminium as well as in Fibre Metal Laminates. Interface elements are inserted in a finite element mesh with a yield function which bounds all states of stress in the interface. Hardening occurs after a state of stress exceeds the yield stress of the material. The hardening branch is bounded by the ultimate stress of the material. Thereafter, the state of stress is reduced to zero while the inelastic deformations grow. The energy dissipated by the inelastic deformations in this process equals the fracture energy of the material. The model is applied to calculate the onset and growth of cracking in centre cracked plates made of aluminium and GLARE. The impact of the model parameters on the performance of the crack model is studied by comparisons of the numerical results with experimental data.

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Article

This paper provides an analysis of the transient behaviour of a right-angled bent cantilever beam subjected to a suddenly applied force at its tip perpendicular to its plane. Based on a rigid, perfectly plastic material model, a double-hinge mechanism is required to complete the possible deformation under a rectangular force pulse (constant force applied for a finite duration) with a four-phase response mode. The kinematics of the various response phases are described and the partitioning of the input energy at the plastic hinges during the motion is evaluated.

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Article

The problem and its solution of a computer based design procedure for patch loaded interior panel design, in the context of civil engineering, are presented. An Artificial Neural Network (ANN) is trained to predict moment coefficient in short span m 1 for interior panel is proposed. Another ANN is also trained for moment coefficient in long span m2 value. The Bending moment coefficients m1 and m2 for different values of K are calculated and presented in the form of curves. The development of this ANN modeling involves determination of the training set, ANN architecture, training and testing of the network, and generalization capabilities. According to Pigeaud's method the moment along the shorter and longer directions depends on the ratios K, u/B, and v/L. The developed ANN architecture is computationally efficient and has been successfully used in the approximation of Pigeaud's curves.

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Article

Splitting tensile strength (STS) is a respectable mechanical property reflecting ability of the concrete. The STS of concrete is mainly related to compressive strength (CS), water/binder (W/B) ratio and concrete age. In this study, the assessment of STS is made by a novel uncertainty-oriented method which uses least square optimization and then predicts STS of concrete by uncertain (fuzzy) numbers. The approximation method addresses a novel integration of fuzzy set theory and multivariate statistics. The numerical examples showed that the method is applicable with relatively limited data. In addition, the prediction of uncertainty at various levels of possibility can be described. In conclusion, the uncertainty-oriented interval analysis can be suggested an effective tool for appraising the uncertainties in concrete technology.

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Article

This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fixed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.

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Article

In this study, the earthquake damage response of the concrete arch dams was investigated including dam-reservoir interaction. A continuum damage model which is a second-order tensor and includes the strain softening behavior was selected for the concrete material. Fluid-structure interaction problem was modeled by Lagrangian approach. Sommerfeld radiation condition was applied to the truncated boundary of reservoir. The improved form of the HHT- time integration algorithm was used in the solution of the equations of motion. The arch dam Type 5 was selected for numerical application. For the dynamic input, acceleration records of the 10 December 1967 Koyna earthquake were chosen. These records were scaled with earthquake acceleration scale factor (EASF) and then used in the analyses. Solutions were obtained for empty and full reservoir cases. The effects of EASF and damping ratio on the response of the dam were studied.

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Article

Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

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Article

A state-of-the-art report on the new finite elements formulated by the addition of nonconforming displacement modes has been presented. The development of a series improved nonconforming finite elements for the analysis of plate and shell structures is described in the first part of this paper. These new plate and shell finite elements are established by the combined use of different improvement schemes such as; the addition of nonconforming modes, the reduced (or selective) integration, and the construction of the substitute shear strain fields. The improvement achieved may be attributable to the fact that the merits of these improvement techniques are merged into the formation of the new elements in a complementary manner. It is shown that the results obtained by the new elements give significantly improved solutions without any serious defects such as; the shear locking, spurious zero energy mode for the linear as well as nonlinear benchmark problems. Recent developments in the transition elements that have a variable number of mid-side nodes and can be effectively used in the adaptive mesh refinement are presented in the second part. Finally, the nonconforming transition flat shell elements with drilling degrees of freedom are also presented.

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Article

The paper presents a review of the application of the newly proposed mixed finite element model for seismic simulation of different types of composite frame structures. To evaluate the performance of the element, a comparison with displacement-based and force-based models is conducted. The study revealed that the mixed model is superior to the others in terms of both speed of convergence and numerical stability, and is therefore considered the most practical approach for modeling of composite structures. In this model, the element is derived using independent force and displacement shape functions. The nonlinear response of the frame element is based on the section discretization into fibers with uniaxial material models. The interfacial behavior is modeled using an inelastic interface element. Numerical examples to clarify the advantages of the model are presented for the following structural applications: anchored reinforcing bar problems, composite steel-concrete girders with deformable shear connectors, beam on elastic foundation elements, R/C girders strengthened with FRP sheets, R/C beam-columns with bond-slip, and prestressed concrete girders. These studies confirmed that the model represents a major advancement over existing elements in simulating the inelastic behavior of composite structures.

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Article

Presence of high degree of orthotropy enhances shear lag phenomenon in laminated composite box-beams and it persists till failure. In this paper three key parameters governing shear lag behavior of laminated composite box beams are identified and defined by simple expressions. Uniqueness of the identified key parameters is proved with the help of finite element method (FEM) based studies. In addition to this, for the sake of generalization of prediction of shear lag effect in symmetrical laminated composite box beams a feed forward back propagation neural network (BPNN) model is developed. The network is trained and tested using the data base generated by extensive FEM studies carried out for various b/D, b/tF, tF/tW and laminate configurations. An optimum network architecture has been established which can effectively learn the pattern. Computational efficiency of the developed ANN makes it suitable for use in optimum design of laminated composite box-beams.

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Article

The purpose of this paper is to propose a simple analysis method of axial deformation of base-isolation rubber bearings in a building subjected to earthquake loading and present its applicability to the analysis of the bound of the aspect ratio of base-isolated buildings. The base shear coefficient is introduced as a key parameter for the bound analysis. The bound of the aspect ratio of base-isolated buildings is analyzed based on the relationship of the following four quantities; (i) ultimate state of the tensile stress of rubber bearings based on a proposed simple recursive analysis for seismic loading, (ii) ultimate state of drift of the base-isolation story for seismic loading, (iii) ultimate state of the axial compressive stress of rubber bearings under dead loads, (iv) prediction of the overturning moment at the base for seismic loading. In particular, a new recursive analysis method of axial deformation of rubber bearings is presented taking into account the nonlinear tensile behavior of rubber bearings and it is shown that the relaxation of the constraint on the ultimate state of the tensile stress of rubber bearings increases the limiting aspect ratio.

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Article

This paper presents a nonlinear finite element procedure accounting for the effects of geometric as well as material nonlinearities for reinforced concrete bridge piers supported by laminated rubber bearings. Reinforced concrete bridge piers supported by laminated rubber bearings and carrying a cyclic load were analyzed by using a special purpose, nonlinear finite element program, RCAHEST. For reinforced concrete, the proposed robust nonlinear material model captures the salient response characteristics of the bridge piers under cyclic loading conditions and addresses with the influence of geometric nonlinearity on post-peak response of the bridge piers by transformations between local and global systems. Seismic isolator element to predict the behaviors of laminated rubber bearings is also developed. The seismic performance of reinforced concrete bridge piers supported by laminated rubber bearings is assessed analytically. The results show good correlation between the experimental findings and numerical predictions, and demonstrate the reliability and robustness of the proposed analytical model. Additionally, the studies and discussions presented in this investigation provide an insight into the key behavioral aspects of reinforced concrete bridge piers supported by laminated rubber bearings.

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Article

The rigid-plastic yield-line analysis of isotropically reinforced concrete slabs acting in conjunction with torsionally weak supporting beams is developed as the lower-bound form of a linear programming formulation. The analysis is extended to consider geometric variation of chosen yield-line patterns by the technique of sequential linear programming. A strategy is followed of using a fine potential yield-line mesh to identify possible collapse modes, followed by analysis using a coarser, simplified mesh to refine the investigation and for use in conjunction with geometric optimization of the yield-line system. The method is shown to be effective for the analysis of three slabs of varying complexity. The modes detected by the fine and simplified analyses are not always similar but close agreement in load factors has been consistently obtained.

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Article

A novel methodology, referred to as Auxiliary Domain Method (ADM), allowing for a very efficient solution of nonlinear reliability problems is presented. The target nonlinear failure domain is first popUlated by samples generated with the help of a Markov Chain. Based on these samples an auxiliary failure domain (AFD), corresponding to an auxiliary reliability problem, is introduced. The criteria for selecting the AFD are discussed. The emphasis in this paper is on the selection of the auxiliary linear failure domain in the case where the original nonlinear reliability problem involves multiple objectives rather than a single objective. Each reliability objective is assumed to correspond to a particular response quantity not exceeding a corresponding threshold. Once the AFD has been specified the method proceeds with a modified subset simulation procedure where the first step involves the direct simulation of samples in the AFD, rather than standard Monte Carlo simulation as required in standard subset simulation. While the method is applicable to general nonlinear reliability problems herein the focus is on the calculation of the probability of failure of nonlinear dynamical systems subjected to Gaussian random excitations. The method is demonstrated through such a numerical example involving two reliability objectives and a very large number of random variables. It is found that ADM is very efficient and offers drastic improvements over standard subset simulation, especially when one deals with low probability failure events.

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Article

The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams on elastic soil is plenty, but the free vibration analysis of Reddy-Bickford beams on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded Reddy-Bickford beam on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of one end fixed and the other end simply supported Reddy-Bickford beam on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the mode shapes are presented in graphs.

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Article

This paper presents a fuzzy optimum design of axisymmetrically loaded thin shells of revolution. This paper consists of two parts, namely: an elastic analysis using the new curved element for finite element analysis developed in this study for axisymmetrically loaded thin shells of revolution, and the volume optimization on the basis of results evaluated from the elastic analysis. The curved element to meridian direction is used to develop the computer program. The results obtained from the computer program are compared by exact solution of each analytic example. The fuzzy optimizations of thin shells of revolution are done using [Model 2] which is in the form of a conventional crisp objective function and constraints with non-membership function, and nonlinear optimum GINO (General Interactive Optimizer) programming. In this paper, design examples show that the fuzzy optimum designs of the steel water tank and the steel dome roof could provide significant cost savings.

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Article

This paper presents a nonlinear analysis of reinforced concrete column with lap splice confined by FRP wrapping in the critical hinging zone. The steel stress-slip model derived from the tri-uniform bond stress model presented in the companion paper is included in the nonlinear frame analysis to simulate the response of reinforced concrete columns subjected to cyclic displacement reversals. The nonlinear modeling is based on a fiber discretization of an RC column section. Each fiber is modeled as either nonlinear concrete or steel spring, whose load-deformation characteristics are calculated from the section of fiber and material properties. The steel spring that models the reinforcing bars consists of three sub-springs, i.e., steel bar sub-spring, lap splice spring, and anchorage bond-slip spring connected in series from top to bottom. By combining the steel stress versus slip of the lap splice, the stress-deformation of steel bar and the steel stress-slip of bars anchored into the footing, the nonlinear steel spring model is derived. The analytical responses are found to be close to experimental ones. The analysis without lap splice springs included may result in an erroneous overestimation in the strength and ductility of columns.

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Article

A nonlinear model for time-step analysis of bridges subjected to two orthogonal horizontal components of earthquake motions was developed. The focus of the study was on elastomeric isolators with or without lead cores. The hysteretic behavior of the isolators, the columns, abutments, and shear keys was taken into account. The nonlinear analysis showed that, contrary to linear theory prediction, the use of isolators does not necessarily increase the displacement of the superstructure. Furthermore, it was shown that properly designed isolators can reduce the ductility demand in RC bridge columns substantially.

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Article

This paper presents dynamic responses of structures with sliding base which limits the translation of external loads from ground excitation. A discrete element model based on the discontinuous deformation analysis method is proposed to study this sliding boundary problem. The sliding base is simulated using sets of fictitious contact springs along the sliding interface. The set of contact spring is to translate friction force from ground to superstructure. Validity of the proposed model is examined by the closed-form solutions of an idealized mass-spring structural model subjected to harmonic ground excitation. This model is also applied to a problem of a three-story structural model subjected to the ground excitation of 1940 El Centro earthquake. Analyses of both sliding-base and fixed-base conditions are performed as comparisons. This study shows that using this model can simulate the dynamic response of a sliding structure with frictional cut-off quite accurately. Results reveal that lowering the frictional coefficient of the sliding joint will reduce the peak responses. The structure responses in little deformation, but it displaces at the end of excitation.

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Article

The aim of this discussion is to expose incorrect formulations and terms in the aforementioned paper.

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Article

Experimental studies on the behaviors of box-shape steel reinforced concrete (SRC) composite beams were conducted. Seven 1:3 scale model composite beams were tested to failure. Each of the beams was simply supported at the ends and two concentrated loads were applied at the one-third span and two-thirds span respectively. Experimental results indicate that the flexural strength can be enhanced when the ratio of flexural reinforcements and flange thickness of the shape steel are increased; the shear strength is enhanced with increase of web thickness of the shape steel. Insignificant effects of concrete in the box-shape steel are found on improving the flexural strength and shear strength of the box-shape SRC composite beams, thus concrete inside the box-shape steel can be saved, and the weight of the SRC beams can be decreased. Shear studs can strengthen the connection and co-work effects between the shape steel and the concrete and enhance the shear strength, but stud design for the composite beams should be further improved. Formulas for flexural and shear strength of the composite beams are proposed, and the calculated results are in good agreement with the experimental results. In general, the box-shape SRC composite beam is a kind of ductile member, and suitable for extensive engineering application.

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Article

Exact solution for in-plane displacement of redundant curved beam has been reported. Analytical solutions of internal forces and deformations were derived for plane curved beams with constant curvature under out-of-plane loads, based on traditional mechanics of structures, in which the coupling of flexure and torsion has also been taken into account. The method brings some errors for application without considering the effects of the transverse shear deformation and torsion-related warping. It has been seen that the maximum displacements happen when the point load stresses at the 1/4 to 1/3 position adjacent to the end of the curved beam, while the smaller displacements appear at the area near the midpoint of the curved beam. Various curves have also been provided in support of the experiment.

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Article

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

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Article

This paper reports part of a comprehensive research study conducted at the University of Queensland on the ability of CFRP web-bonded systems in strengthening an exterior beam-column joint subjected to monotonic loads. One 1/2.2 scaled plain and four CFRP repaired/retrofitted joints subjected to monotonic loads were analysed using the nonlinear finite-element program ANSYS and the results were calibrated against experiments. The ANSYS model was employed in order to account for tension stiffening in concrete after cracking and a modified version of the Hognestad's model was used to model the concrete compressive strength. The stress-strain properties of main steel bars were modelled using multilinear isotropic hardening model and the FRPs were modelled as anisotropic materials. A perfect bond was assumed as nodes were shared between adjacent elements irrespective of their type. Good agreement between the numerical predictions and the experimental observation of the failure mechanisms for all specimens were observed. Closeness of these results proved that the numerical analysis can be used by design engineers for the analysis of web-bonded FRP strengthened beam-column joints with confidence.

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Article

With the advent of computer, the finite element method has become a most powerful numerical method for structural analysis. However, bridge designers are reluctant to use it in their designs because of its complex nature and its being time consuming in the preparation of the input data and analyzing the results. This paper describes the development of a computer based finite element model using the idea of eccentric beam elements for the analysis of slab-on-girder bridges. The proposed method is supported by a laboratory test using a reinforced concrete bridge model. Other bridge analytical schemes are also introduced and compared with the proposed method. The main aim of the comparison is to prove the effectiveness of the shell and eccentric beam modelling in the studies of lateral load distribution of slab-on-girder bridges. It is concluded that the proposed finite element method gives a closer to real idealization and its developed computer program, SHECAN, is also very simple to use. It is highly recommended to use it as an analytical tool for the design of slab-on-girder bridges.

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Article

A nonlinear semi-three-dimensional layered finite element procedure is developed for cracking and failure analysis of reinforced concrete beams and the spandrel beam-column-slab connections of flat plates. The layered element approach takes the elasto-plastic failure behaviour and geometric nonlinearity into consideration. A strain-hardening plasticity concrete model and a smeared steel model are incorporated into the layered element formulation. Further, shear failure, transverse reinforcement, spandrel beams and columns are successfully modelled. The proposed method incorporating the nonlinear constitutive models for concrete and steel is implemented in a finite element program. Test specimens including a series of reinforced concrete beams and beam-column-slab connections of flat plates are analysed. Results confirm the effectiveness and accuracy of the layered procedure in predicting both flexural and shear cracking up to failure.

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Article

An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.

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Article

Reinforced concrete (RC) interior beam-column joints with high-strength materials: concrete compressive strength of 100 MPa and the yield strength of longitudinal bars of 685 MPa, were analyzed using three-dimensional (3-D) nonlinear finite element method (FEM). Specimen OKJ3 of joint shear failure type was a plane interior joint, and Specimen 12 of beam flexural failure type was a 3-D interior joint with transverse beams. Though the analytical initial stiffness was higher than experimental one, the analytical results gave a good agreement with the test results on the maximum story shear forces, the failure mode.

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Article

Cyclic loading tests were carried out on six half-scale reinforced concrete beam-column subassemblages designed to the current Chinese Seismic Design Code for Buildings. The deformation behavior and restoring force characteristics of the subassemblages were studied. Emphasis was directed on their seismic behavior and deformation components. Based on test data and a simplified analysis model of the global and local deformation, the contribution of the deformation components due to beam flexure, column flexure, joint shear, and slippage of longitudinal reinforcement in the joint to the global deformation of subassemblages at different displacement amplitudes of cyclic loading was investigated.

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Article

A method for computing the elastic buckling prestressing force of a post-tensioned composite steel-concrete tee-beam is presented. The method is based on a virtual work formulation, and incorporates the restraint provided by the concrete slab to the buckling displacements of the steel beam. The distortional buckling solutions are shown to be given by a quadratic equation. The application of the analysis to calculation buckling strengths is given, based on codified rules for beam-columns. Conclusions are then drawn on the importance of distortional buckling when a post-tensioned composite beam is stressed during jacking.

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Article

Seismic performance of coupling beams not designed for ductility is examined. Eight 1:4 scale coupling beam specimens, with seven reinforced concrete sections and one composite section, were tested under cycles of push-pull action. Characteristics of the specimens include moderate shear span ratio in the range of 2.5-3.5, high main reinforcement ratio at 3-4% and small to large stirrup spacing with 90- degree hooks. All the reinforced concrete specimens failed in a brittle manner. Displacement ductility of specimens with large stirrup spacing (140 mm) is in the range of 3 to 5. Seismic performance of the specimens is also examined using the ultimate drift angle and the amount of energy dissipated. Correlating the test data, an empirical relationship is proposed to estimate the ultimate drift angle of a class of coupling beams considered in the study not designed for ductility.

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Article

A study has presented analytical solutions for lower and upper bounds of free vibrations of axially compressed beams with two delaminations. The study also investigated the linear relation between the square of the natural frequency of a simple supported delaminated beam and the axial compressive load. A model is developed with the delaminated portion of the beam is modeled as an undelaminated beam with a reduced bending stiffness. The study assumed that a delaminated beam of constrained mode is an undelaminated beam with a reduced stiffness at the location of the delamination. The results show that for simply supported beams, the square of the constrained mode fundamental frequency varies linearly with the axial compressive load. The discussions suggested that identification of natural frequency and the buckling load of the delaminated beam may lead to an estimate of the fundamental frequency of the delaminated beam under axial compressive loading can be obtained.

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