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An energy based damage index based on a new nonlinear Finite element (FE) approach applicable to RC structures subjected to cyclic, earthquake or monotonic loading is proposed. The proposed method is based on the evaluation of nonlinear local degradation of materials and taking into account of the pseudo-plastic hinge produced in the critical sections of the structure. A computer program is developed, considering local behavior of confined and unconfined concretes and steel elements and also global behavior and damage of reinforced concrete structures under cyclic loading. The segments located between the pseudoplastic hinges at critical sections and the inflection points are selected as base-models through simulation by the proposed FE method. The proposed damage index is based on an energy analysis method considering the primary half-cycles energy absorbed by the structure during loading. The total primary half-cycles absorbed energy to failure is used as normalizing factor. By using the proposed nonlinear analytical approach, the structure's force-displacement data are determined. The damage index is then calculated and is compared with the allowable value. This damage index is an efficient means for deciding whether to repair or demolish structures after an earthquake. It is also useful in the design of new structures as a design parameter for an acceptable limit of damage defined by building codes.  The proposed approach and damage index are validated by results of tests carried out on reinforced concrete columns subjected to cyclic biaxial bending with axial force.

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In this paper a discrete Big Bang-Big Crunch algorithm is applied to optimal design of reinforced concrete planar frames under

the gravity and lateral loads. Optimization is based on ACI 318-08 code. Columns are assumed to resist axial loads and bending

moments, while beams resist only bending moments. Second-order effects are also considered for the compression members, and

columns are checked for their slenderness and their end moments are magnified when necessary. The main aim of the BB-BC

process is to minimize the cost of material and construction of the reinforced concrete frames under the applied loads such that

the strength requirements of the ACI 318 code are fulfilled. In the process of optimization, the cost per unit length of the sections

is used for the formation of the subsequent generation. Three bending frames are optimized using BB-BC and the results are

compared to those of the genetic algorithm.

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The main objective of this study is to drive a simple solution for prediction of steel fiber reinforced concrete (SFRC) behavior

under four point bending test (FPBT). In this model all the force components at the beam section (before and after cracking)

are formulated by applying these assumptions: a bilinear elastic-perfectly plastic stress-strain response for concrete behavior

in compression, a linear response for the un-cracked tension region in a concrete constitutive model, and an exponential

relationship for stress-crack opening in the crack region which requires two parameters.Then the moment capacity of the critical

cracked section is calculated by applying these assumptions and satisfying equilibrium lawat critical cracked section. After that,

parametric studies have been done on the behavior of SFRC to assess the sensitively of model. Finally the proposed model has

been validated with some existing experimental tests.The result shows that the proposed solution is able to estimate the behavior

of SFRC under FPBT with simplicity and proper accuracy.

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This paper describes a methodology in designing high-performance concrete for simply supported beams, using a hybrid optimization strategy based on a variable neighborhood search threshold acceptance algorithm. Three strategies have been applied to discrete optimization of reinforced concrete beams: Variable Neighborhood Descent (VND), Reduced Neighborhood Search (RNS) and Basic Variable Neighborhood Search (BVNS). The problem includes 14 variables: two geometrical one material type one mix design and 10 variables for the reinforcement setups. The algorithms are applied to two objective functions: the economic cost and the embedded CO2 emissions. Firstly, this paper presents the application of these three different optimization strategies, which are evaluated by fitting the set of solutions obtained to a three-parameter Weibull distribution function. The Variable Neighborhood Descent with Threshold Accepting acceptance strategy algorithm (VND-TA) results as the most reliable method. Finally, the study presents a parametric study of the span length from 10 to 20 m in which it can be concluded that economic and ecological beams show a good parabolic correlation with the span length.

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Abstract: This paper presents the influence of adding steel fibers and incorporation of silica fume on the mechanical properties of high-strength concrete. The variables investigated were steel fiber volume fraction (0 to 1.5%), silica fume replacement (5, 10 and 15%) and water-to-binder ratio (0.25, 0.30, 0.35 and 0.40). The influence of fiber content in terms of fiber reinforcing index on the compressive and splitting tensile strengths of high-strength steel fiber reinforce concrete (HSFRC) is presented. The use of silica fume increased both the compressive and splitting tensile strengths of concrete at 28 days. On the other hand, the addition of crimped steel fiber into high-strength concrete improves splitting tensile strength significantly. Based on the test data, using regression analysis, empirical expression to predict 28-day tensile strength of HSFRC in terms of fiber reinforcing index was developed and the absolute variation and integral absolute error (IAE) obtained was 3.1% and 3.3, respectively. The relationship between splitting tensile and compressive strength of SFRC was reported with regression coefficient (r) = 0.9. The experimental values of previous researchers were compared with the values predicted by the model and found to predict the values quite accurately.

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The main cause of structural damage in buildings subjected to seismic actions is lateral drift. In almost all reinforced concrete (RC) structures, whether designed with walls or frames, it is likely to be the code drift limits that control the design drift. The design drift limits and their contribution to damage may be represented indirectly through the material strain limits. The aim of this study is to investigate the seismic design indicators of RC columns using finite element analyses (FEA). The results of FEA have been compared with the results of experimental studies selected from literature. It is observed that the lateral load-deflection curves of analyzed columns are in agreement with the experimental results. Based on these lateral load-deflection curves, the drift limits and the material strain limits, given by the codes as performance indicator, are compared. It is observed that the material strain limits are non-conservative as performance indicator of RC columns, compared to the drift limits.

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An analytical nonlinear stress-strain model and a microscopic damage index for confined and unconfined concretes together with a macroscopic damage index for reinforced concrete (RC) structures under cyclic loading are proposed. In order to eliminate the problem of scale effect, an adjustable finite element computer program was generated to simulate RC structures subjected to cyclic loading. By comparing the simulated and experimental results of tests on the full-scale structural members and concrete cylindrical samples, the proposed stress-strain model for confined and unconfined concretes under cyclic loading was accordingly modified and then validated. The proposed model has a strong mathematical structure and can readily be adapted to achieve a higher degree of precision by modifying the relevant coefficients based on more precise tests. To apply the proposed damage indices at the microscopic and macroscopic levels, respectively, stress-strain data of finite elements (confined and unconfined concrete elements) and moment-curvature data of critical section are employed. The proposed microscopic damage index can easily be calculated by using the proposed simple analytic nonlinear stress-strain model for confined and unconfined concretes. The proposed macroscopic damage index is based on the evaluation of nonlinear local degradation of materials and taking into account the pseudo-plastic hinge produced in the critical section of the structural element. One of the advantages of the macroscopic damage index is that the moment-curvature data of the critical section is sufficient in itself and there is no need to obtain the force-displacement data of the structural member.

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Plan irregularity causes local damages being concentrated in the irregular buildings. Progressive collapse is also the collapse of a large portion or whole building due to the local damages in the structure. The effect of irregularity on the progressive collapse potential of the buildings is investigated in this study. This is carried out by progressive collapse evaluation of the asymmetric mid rise and tall buildings in comparison with the symmetric ones via the nonlinear time history analyses in the 6, 9 and 12 story reinforced concrete buildings. The effect of increasing the mass eccentricity levels is investigated on the progressive collapse mechanism of the buildings with respect to the story drift behavior and the number of beam and column collapsed hinges criteria. According to the results, increasing the mass eccentricity levels causes earlier instability with lower number of the collapsed hinges which is necessary to fail the asymmetric buildings and at the same time mitigates the potential of progressive collapse. Moreover, the decreasing trend of the story drifts of the flexible edges is lower than those of the stiff edges and the mass centers and the amount of decrement in the story drifts of the stiff edges is approximately similar to those of the mass centers.

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This paper aims at finding the long term coupled effect of high temperature and constant high relative humidity on the corrosion rehabilitated patches of chloride contaminated steel reinforced concrete. This paper is an extension of previous research in which the authors experimentally corroborated re-corrosion in the repaired reinforced concrete (RC) patches in the form of macro-cells. In previous research, the coupled effect was investigated by laboratory controlled experimentation at varying temperature of 30, 40 and 50°C and a high ambient relative humidity of 85% in environmental control chambers for duration of one year. The specimens were prepared having total chloride concentration in mixing water 3% and 5 % by mass of binder. In this present research paper, the two year results of the same specimens are presented to get a deep insight of the long term phenomenon of macro-cell corrosion under the coupled effect of high temperature and humidity on repaired RC patches.

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This paper describes experimental and numerical investigations on two specimens of frames composed of steel reinforced concrete beam and angle-steel concrete column under horizontal low cyclic loading. Based on the test results, the relationship curves of the horizontal load-displacement and the failure modes are acquired. Meanwhile the hysteretic behaviors, skeleton curves, stiffness degradation, energy dissipation, residential deformation of the two specimens are studied. Nonlinear structural analysis program OpenSEES is employed to predict the experimental curves. Using the verified numerical model, the influences of slenderness ratio, axial compression ratio, steel ratio of column, cross-section moment resistance of I-shaped steel in beam, ratio of longitudinal rebars of beam and prestressing level on skeleton curves are investigated. The results indicated that the two specimens exhibited the favorable ductility and energy dissipation capacity, and the beam depth could be reduced to improve service function because of the application of the prestress. The ultimate horizontal load decreases with the increase of column slenderness ratio, and firstly increases then decreases with the increase of axial compression ratio. In the meantime, the descent segment of skeleton curve is smooth with the increase of column slenderness ratio, and becomes steeper with the increase of axial compression ratio.

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The contribution of concrete to inelastic deformation capacity and shear strength of reinforced concrete (RC) columns failing in shear has been investigated extensively by various researchers. Although RC members are designed to have shear strengths much greater than their flexural strengths to ensure flexural failure according to the current codes, shear degradation of RC columns failing in flexure has not been studied widely. The aim of this study is to investigate the shear degradation of RC columns using finite element analyses (FEA). The results of FEA are compared with the results of experimental studies selected from literature, and it is observed that the lateral load-deflection curves of analysed columns are compatible with the experimental results. Twenty-six RC columns were analysed under monotonically increasing loads to determine the concrete contribution to shear strength. The results of analyses indicate that increasing the ratio of shear to flexural strength reduces the concrete contribution to shear strength of the columns.

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A fast converging and fairly accurate nonlinear simulation method to assess the behavior of reinforced concrete columns subjected to static oriented pushover force and axial loading (sections under biaxial bending moment and axial loading) is proposed. In the proposed method, the sections of column are discretized into “Variable Oblique Finite Elements” (VOFE). By applying the proposed oblique discretization method, the time of calculation is significantly decreased and since VOFE are always parallel to neutral axis, a uniform stress distribution along each oblique element is established. Consequently, the variations of stress distribution across an element are quite small which increases the accuracy of the calculations. In the discretization of section, the number of VOFE is significantly smaller than the number of “Fixed Rectangular Finite Elements” (FRFE). The advantages of using VOFE compared to FRFE are faster convergence and more accurate results. The nonlinear local degradation of materials and the pseudo-plastic hinge produced in the critical sections of the column are also considered in the proposed simulation method. A computer program is developed to calculate the local and global behavior of reinforced concrete columns under static oriented pushover and cyclic loading. The proposed simulation method is validated by the results of tests carried out on the full-scale reinforced concrete columns. The application of the “Components Effects Combination Method” (CECM) is compared with the proposed “Simultaneous Direct Method” (SDM). The obtained results show the necessity of applying SDM for nonlinear calculations. Especially during the post-elastic phase, which occurs frequently during earthquake loading.

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Observations and investigations have proved that using traditional fire curves such as stand-ard fire curves and natural fire curves should be limited to small/medium compartments. In addition, when using the traditional fire curves, a uniform temperature is assumed throughout the compartment. However, for large open compartments, assuming uniform temperature is not compatible with real fires. To overcome this limitation, a non-uniform fire method named as travelling fire is employed as an alternative. A study is performed here on a seismic-damaged large plan 3-story reinforced concrete structure designed to meet the life safety level of performance when exposed to a travelling fire. To draw a comparison, the structural fire analysis is also performed using the traditional methods. The results show a notable difference – while the fire resistance based on the travelling fire is around 91 minutes, it is around 140 minutes when based on a uniform temperature. This shows that the structure studied is more susceptible to failure when subjected to the non-uniform fire than the uniform fire.

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Complex nature of diagonal tension accompanied by formation of new cracks as well as closing and propagating preexisting cracks has deterred researchers to achieve an analytical and mathematical procedure for accurate predicting shear behavior of reinforced concrete, and there is the lack of a unique theory accepted universally. Shear behavior of reinforced concrete is studied in this paper based on recently developed constitutive laws for normal strength concrete and mild steel bars using nonlinear finite element method. The salient feature of these stress-strain relations is to account the interactive effects of concrete and embedded bars on each other in a smeared rotating crack approach. Implementing the considered constitutive laws into an efficient secant-stiffness based finite element algorithm, a procedure for nonlinear analysis of reinforced concrete is achieved. The resulted procedure is capable of predicting load-deformation behavior, cracking pattern, and failure mode of reinforced concrete. Corroboration with data from shear-critical beam test specimens with a wide range of properties showed the model to predict responses with a good accuracy. The results were also compared with those from the well-known theory of modified compression field and its extension called disturbed stress field model which revealed the present study to provide more accurate predictions. 

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A nonlinear Finite Element (FE) algorithm is proposed to analyze the Reinforced Concrete (RC) columns subjected to Cyclic Biaxial Bending Moment and Axial Loading (CBBMAL). In the proposed algorithm, the following parameters are considered: uniaxial behavior of concrete and steel elements, the pseudo-plastic hinge produced in the critical sections, and global behavior of the columns. In the proposed numerical simulation, the column is discretized into two Macro-Elements (ME) located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections are discretized into Fixed Rectangular Finite Elements (FRFE). The basic equilibrium is justified over a critical hypothetical cross-section assuming the Kinematics Navier’s hypothesis with an average curvature. The method used qualifies as a “Strain Plane Control Process” that requires the resolution of a quasi-static simultaneous equations system using a triple iteration process over the strains in each section. In order to reach equilibrium, three main strain parameters (the strains in the extreme compressive point, the strains in the extreme tensile point and the strains in another corner of the section) are used as three main variables. The proposed algorithm has been validated by the results of tests carried out on full-scale RC columns. The application of the Components Effects Combination Method (CECM) is also compared with the proposed Simultaneous Direct Method (SDM). The results obtained show the necessity of applying SDM for the post-elastic phase, which occurs frequently during earthquake loading.

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A formwork is a structure used to contain poured concrete and to mold it to the required dimensions. Different formwork systems provide a wide range of concrete construction solutions that can be chosen to suit the needs of a particular structure. The selection of panels and the design of the formwork layout for concrete structures, especially if the panels are to be reused many times to form different work zones, is one of the most complex tasks in formwork construction. It influences the quality of work, construction time, site safety and cost. The formwork costs account for a significant part of the total costs for concrete works. The problem of the selection and layout of reusable panel forms is solved mainly based on the intuitive judgment of experienced engineers in collaboration with the form system supplier. This study proposes a mixed integer linear programming modeling approach to support the formwork planning process. The problem consists in determining the number and sizes of the panels according to the geometry of the concrete elements in order to minimize the rental cost of wall shuttering in a building divided into work zones that are to be completed in sequence, reusing the chosen panels. The model can be solved using typical software dedicated to mixed integer linear programs. A simple example is used to illustrate the efficiency of the proposed approach, where the formwork rental costs is 7.31% lower than the rental costs of panels and corners optimized without consideration of the reuse in consecutive zones.

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One kind of the irregularities in structures, with considerable effect on seismic performance, is setback in elevation that causes large damage especially in the vicinity of the irregularity. The main objective of this research is to propose and develop drift based index to estimate damage to Reinforced Concrete Moment Resisting Frames (RCMRFs) with setback. For this purpose, first, inelastic dynamic time-history analysis is performed on several frames with different types of setbacks subjected to various earthquake records and damage to them is computed by the Park-Ang damage index. Then two relations between the damage and drift are derived by applying irregularity indices to account for setback effects. It is shown that the proposed damage indices are capable to estimate the damage index of setback frames.

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Among important issues in progressive collapse behavior of a building is tracking down the type and location of the damaged elements. This paper deals with identifying the distribution of collapse from the first element to the entire building due to earthquake loads. Here, 3D collapse propagations in symmetric and asymmetric reinforced concrete buildings are compared using nonlinear time history analyses. The variables of such analyses are earthquake load intensity and the level of in plan one directional mass eccentricity. Results show that collapse distribution is dependent on the degree of asymmetry in building. Some patterns to predict progressive collapse scenarios in similar symmetric and asymmetric buildings are also determined. One main pattern shows that the propagation of collapse is horizontal through the stories, but not vertical through the height of the buildings. Spread of the collapse is independent of the earthquake records also according to the results, damage concentration is larger in places with larger mass concentration.

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This paper describes both global and local versions of an energetic analytical model to quantify the damage caused to reinforced concrete (RC) structures under monotonic, cyclic or fatigue loading. The proposed model closely represents the damage to structures and yields a damage index (DI) for the RC members. The model is cumulative and is based on the energy absorbed. The energy under the monotonic envelope curve at the failure of the member is taken as a reference capacity. The data required to apply the model in any given situation or member can be obtained either by numerical simulation or from experimental tests. An analytical computer program was developed to simulate numerically the response of RC members taking into account the nonlinear behavior of the materials and structures involved. The proposed model was verified by comparison with practical tests undertaken by other researchers on over 20 RC columns. The comparison demonstrates that the model provides a realistic estimation of the damage of the RC structural members. The comparison between values of the proposed DI calculated based on experimental test data and numerical simulation results for a cyclic loading case shows that to calculate DI, it is not necessary to perform expensive experimental tests and that using a nonlinear structural analytical simulation is sufficient. The results are also compared to a damage model proposed by Meyer (1988).

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Minimum reinforcement ratios provided in the standards are remaining at very low levels especially at large systems subject to the effects of earthquake. Thus, arranging the reinforcement ratios intended for preliminary design can provide significant ease and safety in project design phase, and speed and simplicity in the project control phase. Moreover, a more realistic limitation becomes ensured compared to general minimum reinforcement ratios given in the standards. System characteristics which may affect the reinforcement ratios can be specified by general and simple parameters. As the result of many extensive studies, expressions for reinforcement ratios intended for preliminary design which will cover systems having different parameters can be composed. Today, thanks to the development levels of finite elements programs which can perform reinforced concrete modeling, meeting this requirement is much more possible compared to the past. Structure of parameters should neither be very special nor very general. Otherwise, reinforcement ratios intended for preliminary design will either be valid for a single system or they will remain at very low limits such as the minimum reinforcement ratios given in the standards. For this reason, in this study it was tried to follow a route in between these two extreme conditions. Today, it is possible to perform many studies on the systems having different and comprehensive inclusive parameters and to determine practical ratios which will constitute a recommendation for the project designs. For this purpose, an eight storey reinforced concrete system with single spacing whose shear wall cross-section is 25x250cm, column cross-section is 25x30cm, and beam cross-section is 25x50cm was addressed, and its non-linear planary analyses under static earthquake loads were performed through the ANSYS finite elements program for 13 different reinforcement case. The reinforcement ratios to be recommended for the addresses system and similar systems were tried to be revealed. The examined system was arranged as to get the most critical and extreme values for many parameters which can be considered, but it was tried for the reinforcement ratios to be recommended to be valid not only for this system but also for the general system network having similar properties to this system. In the future researches, expressions of general and inclusive preliminary design reinforcement ratios can be obtained as per the results of many studies to be made on systems having different parameters.