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The increase in strength of Steel Fiber Reinforced Concrete (SFRC) depends mainly on factors such as the dosage, aspect ratio and number of hooked ends of the fibers. Previous studies proposed models to estimate the flexural and shear strength of SFRC beams, but the shear behavior of SFRC panels has not been extensively studied. The study includes diagonal tension tests on concrete panels to assess the shear performance of SFRC. The experimental program comprises 19 square concrete panels having 600 mm side and 75 mm thickness, including three nominal dosages of steel fibers (20, 40 and 60 kg/m3) and three different number of hooked ends (1, 1.5 and 2). The study proposes models to predict the shear strength and deformation capacity, stiffness degradation and toughness of SFRC panels with different number of hooked ends when subjected to diagonal tension. The models include four characteristic limit states of diagonal cracking, maximum residual strength, code-based acceptable degradation, and maximum deformation. The authors thank to Vicerrectoría de Investigaciones of UMNG for the financial support of the EXT-INV-3575 project. The authors also would like to thank Research Assistants Juan D. Vargas and Diego Silva at Universidad Militar Nueva Granada (UMNG) for data and figure processing. The authors also thank the companies Cemex-Colombia and Proalco-Bekaert-Colombia for supplying the concrete and steel fibers, respectively. All data that support the findings of this study are available from the corresponding author upon reasonable request. The views expressed in this paper are solely those of the authors and do not necessarily reflects the views of the sponsors.

The satisfactory structural behavior observed during large earthquakes and the high seismicity of the country has conditioned the Chilean society to expect immediate occupancy performance level for their buildings under these extreme events, although the seismic design code in Chile mandates only a scope of life safety performance level. Based on observational and statistical evidence from recent strong earthquakes in Chile, it is concluded that the observed seismic resilience of buildings is a consequence of limiting damage, considering that operational performance and life safety are different challenges that require different approaches; furthermore, to provide society with resilient and safe buildings, both challenges must be met simultaneously and not alternatively. The present article describes the concepts, strategies, and future challenges in the context of the Chilean practice, and the authors describe several lessons learned from the design of thousands of concrete buildings that have experienced earthquakes with a magnitude of 8.0 and higher with limited damage; these lessons have proven to be effective in ensuring resilient structural performance under extreme seismic events.

Low cycle fatigue life of high-strength reinforcing steel bars (ASTM A706 Grade 80), using photogrammetry by RGB methodology is evaluated. Fatigue tests are performed on specimens under constant axial displacement with total strain amplitudes ranging from 0.01 to 0.05. The experimental observations indicate that buckling of high-strength reinforcing bars results in a damaging degradation of their fatigue life performance as the slenderness ratio increases, including an early rebar failure as the total strain amplitude increases since it achieves the plastic range faster. In addition to this, the results show that the ratio of the ultimate tensile strength to yield strength satisfies the minimum of 1.25 specified in ASTM A706 for reinforcement. On the other hand, the RGB methodology indicates that the axial strains measured by photogrammetry provide more accurate data since the registered results by the traditional experimental setup do not detect second-order effects, such as slippage or lengthening of the specimens within the clamps. Moreover, the RGB filter is faster than digital image correlation (DIC) because the RGB methodology requires a fewer computational cost than DIC algorithms. The RGB methodology allows to reduce the total strain amplitude up to 45% compared to the results obtained by the traditional setup. Finally, models relating total strain amplitude with half-cycles to failure and total strain amplitude with total energy dissipated for multiple slenderness ratios (L/d of 5, 10, and 15) are obtained.

This paper presents information on development, calibration, and validation of three companion macroscopic modeling approaches for nonlinear analysis of reinforced concrete (RC) structural walls, including: (1) the baseline two-dimensional two-node formulation of the Shear–Flexure-Interaction Multiple-Vertical-Line-Element-Model (SFI-MVLEM), (2) extension of the baseline SFI-MVLEM for modeling of squat walls (SFI-MVLEM-SQ), and (3) extension of the baseline SFI-MVLEM to a three-dimensional four-node element for simulation of non-planar RC walls under multi-directional loading (SFI-MVLEM-3D). The models are implemented in the computational platform OpenSees. Models presented are calibrated and validated against experimental results obtained from tests on RC wall specimens that cover a wide range of physical and behavioral characteristics, including: (1) one slender, two moderately-slender and one medium-rise planar RC walls tested under in-plane loading used for validation of the baseline SFI-MVLEM, (2) three squat planar RC wall specimens tested under in-plane loading used for validation of the SFI-MVLEM-SQ, and (3) one T-shaped and one U-shaped RC wall specimen tested under unidirectional and multi-directional loading, respectively, used for validation of SFI-MVLEM-3D. The comprehensive comparisons between analytically-obtained and experimentally-measured wall responses suggest that the analytical models proposed can accurately simulate both global and local wall responses, within their range of applicability. The models capture load–displacement response features of the walls, including lateral load capacity, lateral stiffness, cyclic stiffness degradation, and pinching characteristics, as well as nonlinear shear deformations and their coupling with flexural deformations during cyclic loading. Comparisons between experimental and analytical results at local response levels suggest that the models can also replicate distributions and magnitudes of wall vertical strains and curvatures at various locations. Overall, the analytical models presented provide robust and reliable tools for nonlinear analysis of RC walls, with a wide range of applicability.

A number of finite element modeling approaches for reinforced concrete (RC) structural walls have recently become available for both research purposes and design applications. Five conceptually-different state-of-the-art finite element models for RC walls are described and evaluated in this paper, including models based on either a fixed-crack or a rotating-crack approach for simulating the biaxial behavior of concrete under plane-stress state, models characterized with either a single- or a multi-layered representation of the wall cross-section, and models with or without consideration of various individual failure mechanisms (e.g., buckling of reinforcement, out-of-plane instability). Modeling approaches were validated against experimental data obtained for five benchmark RC wall specimens, all with rectangular cross-sections, yet are differentiated by a range of salient response characteristics (e.g., aspect ratio, axial load, failure mechanism), in order to assess the capabilities of the models in representing the response of isolated planar walls under uni-directional lateral loading, as well as to identify future research directions. Results presented suggest that the models considered in this study can all capture the lateral load at yield and the peak lateral load capacity of the wall specimens with ±10% accuracy, while the initial stiffness and yield stiffness can be overestimated as much as 3.0 and 1.8 times, respectively. All models can capture nonlinear shear deformations and interaction between flexural and shear responses under cyclic loading, where the analytically-predicted flexural and shear deformations are within ±30% of the experimentally-measured values. Moderate differences between the predicted crack orientations and distributions are noted between the models, and the model results for the magnitudes of principal compressive stresses in concrete and the extent of stress localization are comparable. All models can capture the nonlinear distribution of vertical strains measured along the base of the walls, where the magnitudes of the predicted tensile and compressive strains are within ±50% of experimentally-measured strains for most models. Although some of the model formulations proved to be successful in capturing the experimentally-observed strength loss mechanisms for individual wall specimens, none of the models were capable of comprehensively simulating all of the strength degradation mechanisms observed during the tests.

Slender RC walls are often used in Chile and commonly, due to architectural constraint, the length of walls increases (setback) between floors designated for parking space and upper floors. These types of elements are commonly called flag walls. In this research, the behavior of slender reinforced concrete walls with a constant axial load and a cyclic lateral displacement is numerically studied, in order to compare the results obtained with previous tests. Two different model alternatives are considered: a finite element model and a strut-and-tie model. The selected models allow understanding local response, as well as, distribution of internal forces, which is also relevant information for wall design and detailing. The studied finite element model, based on quadrilateral elements with 3 degrees of freedom per node (2 translational and 1 rotation) and a model of smeared reinforced concrete material based on a rotating angle approach, is able to correctly capture the global response, showing the capacity, degradation and failure mode obtained in the tests. On the other hand, a parametric analysis is performed for models of walls with higher aspect ratio (tall buildings) with small discontinuities, showing a larger impact in deformation capacity due to the high concentration of damage at the discontinuity. These results indicate that in 25-floor high walls (or taller) a reduction of displacement capacity of 40% for discontinuities located at the first floor could be observed. In addition, by incorporating the effect of the slabs into the model, the results indicate that a pure flexure model is an adequate and sufficient tool for analysis. Finally, a strut-and-tie model is also proposed for each direction of the lateral load, whose results are compared with the estimated load calculated with the strains measured by photogrammetry. The considered strut-and-tie model for the case of lateral load with tension in the continuous wall boundary is similar to the wall without discontinuity, which is consistent with the measured strains. For both lateral loading directions, the estimated forces of the horizontally distributed bars and boundary reinforcements are consistent with photogrammetry in the lower zone of the wall, where cracking is relevant. The strut-and-tie model also adequately interprets the effect of the discontinuous bar on the discontinuous boundary of the wall. All these results can help designing and detailing flag walls.

In this article, a simple and accurate quadrilateral thin flat layered shell element formulation for the nonlinear analysis of reinforced concrete (RC) wall systems under static and cycling loads is presented. The 4 node shell element, with 6 degree of freedom (DOF) per node (3 displacements and 3 rotations) is created by superposing the quadrilateral layered membrane element with drilling degrees of freedom (12 DOF, 2 displacement and 1 rotation per node) developed by Rojas et al. (Eng Struct 124:521–538, 2016), and the Discrete Kirchhoff Quadrilateral Element (12 DOF, 1 displacement and 2 rotations) formulated by Batoz and Tahar (Int J Numer Methods Eng 18(11):1655–1677, 1982), to model the in-plane and the out of plane bending behavior of the shell element, respectively. In addition, to model the complex behavior and coupling of the axial, flexural and shear behavior, observed in complex RC wall structures, the transversal section of the shell element consists of a layered system of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with the rotating angle formulation. The formulation used a tangent stiffness matrix approach, which include the coupling of membrane and bending effects. For verification, the shell element formulation is used to model a set of experimental results for T-shaped RC walls that are available in the literature. The proposed element is robust, simple to implement, and it can predict the global results (load vs. displacement and maximum capacity) and also the local behavior (vertical strain at the base level along the web and the flange) observed in RC wall structures.

After the 2010 Maule, Chile, earthquake (Mw 8.8), several reinforced concrete (RC) buildings presented damage in some walls (crushing of concrete, buckling and fracture of steel reinforcement). These buildings had been designed according to the up-to-date seismic standards in the country and were not expected to suffer damage as severe as what was observed. Common features of the damaged walls were: little or no confinement at the wall ends; relatively high axial load; narrow thicknesses (below 200 mm); and discontinuities in height. Slender RC walls are often used in Chile and commonly, due to architectural constraints, the length of the walls changes between floors designated for parking use and the upper floors, creating a setback in the lower levels. These types of walls are commonly called “flag walls”. The problem of discontinuity has not been investigated experimentally and therefore it is necessary to observe its impact in RC walls. Four structural wall specimens were designed, one with no discontinuity and the other three with different sizes of the setback. They were tested under a nominal constant axial load of 0.1f'cAg and cyclic lateral loads increasing at specific drift levels. Conventional instrumentation and photogrammetry were used to monitor the tests. The experimental results show that the impact of the setback, for the sizes tested, is not significant for the strength but it is relevant for the strength degradation and deformation capacity. Strains in the extreme fibers, curvature and principal strains are studied using photogrammetry. It is found that the plastic hinge length increases with drift, but it remains constrained to the setback region. Another discontinuity is found around the reinforcement of the setback where large concentration of strains can cause premature failure of the wall.

According to Chilean design practice, walls usually have complex geometries and discontinuities in height, mainly in the first story. However, the Chilean design code, similar to many design codes, does not provide special provisions for discontinuities. This paper shows the results of an experimental and numerical study of walls with a central opening at the base. Four slender walls are constructed with the same general dimensions, but with different shapes of the opening (15% and 30% of the length, and 11% and 22% of the wall height). The specimens were tested under constant axial load, while cyclic lateral loading is applied at the top. One of the specimens presents slab elements at the base. Results indicate that lateral strength is similar in all cases; however, displacement capacity varies with opening size. All specimens with openings have less ductility, where the specimen with wider and taller opening had a reduced displacement capacity (∼30% reduction). The width of the opening was more influential than the height in the displacement capacity. Numerical analysis was done through a finite element modeling, where one of the models considered all features of the formulation and a second model considered rigid beams placed in all levels forcing the Bernoulli hypothesis (flexural model). Both models can capture strength, stiffness and displacement capacity, and therefore a flexural model can be used for boundary detailing.

Low-cycle fatigue life of Grade 300E and 500E reinforcing bars including the effect of buckling is evaluated. Low-cycle fatigue tests are carried out on un-machined specimens subjected to constant axial strain loading with strain amplitude ranging from 1% to 5%. The experimental test observations suggest that buckling of reinforcing bars has detrimental effect on its fatigue life and increase in slenderness ratio of the reinforcing bars results in substantial reduction of their low-cycle fatigue life. Equations relating the fatigue life (i.e. number of reversals to failure) with total strain amplitude and total energy dissipated as a function of buckling parameter is proposed. Also, experimental tests are carried out to investigate the influence of mean strain ratio on low-cycle fatigue behaviour of reinforcing bars. Comparative evaluation of the fatigue life models with the results of experimental investigation shows that the proposed model can predict the fatigue life of buckled and unbuckled reinforcing bars with reasonable accuracy.

The Spectrometer/Telescope for Imaging X-rays (STIX) is the instrument of the Solar Orbiter mission conceived for the observation of the hard X-ray flaring emission, with the objective of providing insights on the diagnosis of thermal and non-thermal accelerated electrons at the Sun. The STIX imaging system is composed of 30 pairs of tungsten grids, each one placed in front of a four-pixel detector, and produces as many Fourier components of the angular distribution of the flaring source, via Moiré pattern modulation. Therefore, the data recorded by STIX, named visibilities, can be interpreted as a sparse sampling of the Fourier transform of the X-ray signal and the corresponding image reconstruction problem requires the inversion of the Fourier transform from limited data, usually addressed with regularization techniques. Since the current calibration status of STIX measurements still prevents the use of visibility phases for imaging purposes, here we propose a parameter identification process based on forward fitting just the amplitude of the experimental visibilities. Specifically, we have parameterized the flaring source by means of pre-assigned source shapes (e.g., circular and elliptical bi-variate Gaussian functions), and we relied on several approaches to non-linear optimization in order to estimating the shape parameters. In particular, we have implemented a forward-fit method based on deterministic chi-squared minimization, a stochastic optimization algorithm and a deep neural approach based on ensemble learning, also equipping them with an ad hoc statistical technique for uncertainty quantification. The performances of the three approaches are compared in the case of both microflares and M class events recorded by STIX during its commissioning phase and the validation of results is realized also exploiting the EUV information provided by the Atmospheric Imaging Assembly within the Solar Dynamics Observatory.

A model capable of predicting the shear response of beam-column joints subjected to seismic actions is presented. The analytical model, originally developed for walls and based on a simple physical formulation, is adapted. It considers mean stress and strain fields based on a reinforced concrete panel representing the joint, under the assumption that the principal concrete stress and principal strain directions coincide. Simple constitutive material laws are considered for concrete and steel. To estimate the shear capacity, the model satisfies the equilibrium in the longitudinal (vertical) direction. In order to analyze the accuracy of the model, a database integrated by 92 tests of exterior and interior beam-column joints is collected from the literature. Noting that the original model does not consider the effect of confinement product of adjacent elements to the connection, this effect is introduced through factors that reduce the values of the longitudinal and transverse strain used to calibrate the angle of the strut. In addition, the contribution of the transverse reinforcement in the capacity of the element is included. These modifications together with the influence of the boundary reinforcement, yields a good strength estimate for exterior and interior joints that fail in shear. When comparing with other models from the literature, it is observed that the proposed model provides one of the best correlations.

The capacity of structural systems subjected to shear loads commonly distinguished by discontinuities such as point loads or supports, or abrupt changes of cross section, where complex fields of stresses and strains are generated, is vital information for design. Four structural systems that present stress concentration due to applied shear loads are commonly short walls, deep beams, corbels and beam-column joints. In the present work a model is developed to predict the shear capacity of these elements based on a panel model that considers average strain and stresses in a reinforced concrete orthotropic material, which covers the section of the structural element subjected to stress concentration. In addition, the panel element complies with the longitudinal equilibrium, by equalizing the applied axial load with the internal stresses of the structural element, requiring constitutive material laws for both concrete and steel reinforcement. The original model that has shown good shear strength prediction requires solving the non-linear equation of vertical equilibrium. Thus, this work eliminates the need to solve the iterative problem for the capacity estimation of four possible limit states (failure of concrete in tension and compression, and yielding of longitudinal web and boundary reinforcement). For that, an expression is calibrated for the strain of the model with respect to relevant parameters, for each limit state, that allow the generation of a non-iterative model. The model results in an average predicted capacity over experimental capacity ratio, V model / V test , of 1.0 and a COV of 0.25, with similar performance for all four structural systems. When comparing these results with the general model that requires an iterative method, a similar performance is observed, with an average strength ratio and COV of 0.98 and 0.23, respectively. Likewise, in comparison with the ACI 318, the latter shows worse predictions (on average 24% lower) and with greater scatter (on average 28% higher). The expression in AASHTO code presents better correlation than ACI with predictions closer the proposed model.

This work evaluates experimentally the use of steel or polypropylene fibers in shotcrete as a partial replacement for the traditional reinforcement of electrowelded mesh used at the tunnel support for the subway in Santiago (Chile). For the experimental part, 8 tests were performed on section-scaled (1:2) slender (half-span to depth ratio a/d ∼ 5) specimens under transversal (flexure and shear) and axial loads (0.02f′cAg and 0.07f′cAg) and with different reinforcements layout; and another 4 tests of similar specimens, but with low half-span to depth ratio (a/d ∼ 1.5). The section includes welded mesh (one face), a central reticulated frame and a plane shotcrete with a welded mesh (opposite face) or reinforced shotcrete (steel or polypropylene). The results showed a very important contribution of the reticulated frame in flexion (main internal reinforcement) and a modest contribution of the welded mesh and fibers. A two-dimensional finite element modeling of the tunnel-ground system using OpenSees is also performed using calibrated models for the tunnel section based on the experimental part. The soil is modeled with 9-node quadrilateral elements, the lining is modeled with beam-column elements with fiber sections, and the interaction between the lining and the soil is modeled by the Winkler approach without tension in the direction normal to the contact surface and with perfect adherence in the tangential direction. The model is subjected to the static loads from the excavation, modeled considering the constructive sequence of the tunnel using the α method, and then to a seismic analysis by means of the shear wave method (distortion). The results show that the safety factors implicit in the traditional design are high, implying that the structure remains elastic.

The level of existing research, as well as current code provisions and modeling approaches, are not adequate to characterize the behavior of squat reinforced concrete walls with shear – controlled responses. In this study, an experimental program was conducted to investigate the shear-dominated response attributes of eleven squat wall specimens; including their failure mode, lateral load capacity, ductility, hysteretic response characteristics, and deformation characteristics. Test parameters included the wall aspect ratio, the amounts of vertical and horizontal web reinforcement and longitudinal boundary reinforcement, and the level of axial load. The experimental findings are presented and discussed in this paper, with emphasis on the observed failure mode, shear strength, deformation capacity, and strength degradation characteristics of the walls tested, as well as the contribution of shear, flexural, and sliding deformations to wall lateral displacements. Comparison of the test results with backbone curves specified in performance assessment guidelines is also provided.

RC structural slender walls under large seismic excitation are expected to reach base moment capacity mainly affected by the first vibration mode. However, the base shear could be affected by higher modes once yielding in flexure has occurred, which might result in base shear underestimation in linear design. In this work, an experimental program is carried out on five RC rectangular walls 1:10 scaled. All five specimens considered irregularities at base, common in construction and one specimen did not consider shear reinforcement or boundary detailing. Tests are carried on a unidirectional shaking table and excitation is based on two Chile earthquake records with different intensities. Damage is concentrated at the wall base for all specimens; primary due to flexure with some participation of shear. For one of the records an average amplification of 1.3 is obtained, and a decrease in height of the resultant equivalent lateral force closes to 0.4 hw. By increasing the intensity of the input record, amplification grows to an average of 1.7, while it decreases drastically when subjected to input records with low frequency content. No significant difference is observed in shear amplification in specimens with a base central opening, nor with setback, even though the cracking and failure mode was different for such specimens. Ductility demand shows no correlation when two different earthquakes are considered, whereas the frequency content and Arias intensity (Ia) of the input record directly affected the shear amplification.

A research was conducted to develop a macroscopic modeling approach that integrates axial, flexure, and shear interaction under cyclic loading conditions to obtain reliable predictions of the nonlinear response of reinforced concrete (RC) structural walls. The model, named as Efficient-Shear-Flexure-Interaction (E-SFI), is intended to provide accurate results for squat, medium-rise, and slender planar walls, with a computationally efficient formulation that can be used under generalized conditions. The E-SFI model, which is based on the Shear-Flexure Interaction Multiple-Vertical-Line-Element-Model (SFI-MVLEM), incorporates a two-dimensional RC panel behavior described with a fixed-crack-angle approach. The novel formulation removes the internal degree of freedom per RC panel element of the SFI-MVLEM by incorporating a calibrated expression to compute the horizontal normal strain ( e x ), and therefore removing the assumption of zero resultant horizontal stress ( σ x = 0 ) to increase the range of applicability of the model. Three RC wall specimen tests were selected to calibrate and validate the E-SFI model, as well as to prove the model efficiency, including a slender wall (shear span-to-depth ratio of 3.0), a medium-rise wall (shear span-to-depth ratio of 1.5), and a squat wall (shear span-to-depth ratio of 0.63). Analytical model results reveal the ability of the model to accurately reproduce the hysteretic response for all considered cases, with an important reduction in the runtime and an improved current tangent convergence rate compared with the SFI-MVLEM.

Nonlinear modeling is performed for a reinforced concrete building that presented flexural damage during the 2010 Chile earthquake. The focus of the analysis is the behavior of a wall on the first floor that presented localized damage; the wall is T-shaped, has a web length of 8 m, and a flange length reaching 18 m. An unconfined concrete model and a steel model incorporating buckling were considered, accounting for the poor detailing of the wall boundary element. The walls were modeled using nonlinear fiber elements . A rigid diaphragm was considered, and the slabs were incorporated only in areas where they could generate coupling effects in the walls, being modeled as beams with plastic hinges at their ends. Nonlinear static and dynamic analyses were performed on the building model , utilizing records for Santiago from the 2010 Mw 8.8 earthquake. For relatively low lateral drift values (~0.003), the strain levels observed in the model for the wall suffering damage would lead to flexural damage due to its large size, large amount of longitudinal steel reinforcement in the flange, and poor detailing of the web boundary. Several other nonlinear models were created to compare the impact of the design improvements on the overall performance of the building. From the results, it can be seen that the observed damage would be avoided by implementing design solutions such as increased wall thickness, confinement, or decoupling of the main wall.

In shear wall building design, the initial process requires the interaction between the architectural and structural engineering groups to define the adequate wall layout, usually done with a trial-and-error procedure to fulfill architectural and engineering needs, slowing down the design process. For the engineering analysis, first, the wall thickness and length are required to check the building deformation limits, base shear strength, among other parameters. For this reason, the present investigation develops a structural design platform for reinforced concrete wall buildings that uses a deep neural network to predict the wall’s thickness and length based on previous architectural and engineering projects. The study includes, in the first place, the surveying of the architectural and engineering plans for a total of 165 buildings constructed in Chile; the generated database has the geometric and topological definition of the walls and the slabs. As a second stage, a model was trained for the regression of the wall segments’ thickness and length, making use of a feature vector that models the variation between the architectural and the engineering plans for a set of conditions such as the thickness, connectivity (vertical and horizontal), area, wall density, the distance between elements, wall angles, foundation soil type, among other engineering parameters. The regression model results in terms of R2-value are 0.995 and 0.994 for the predicted wall thickness and length, respectively, proving to be a reliable method for the initial engineering wall definition.

In the structural design of shear wall buildings, the initial process requires the interaction between the architecture and engineering teams to define the appropriate distribution of the walls, a stage typically carried out through a trial-and-error procedure, without any consideration of previous similar projects. In previous work, a database of 165 Chilean residential projects of reinforced shear wall concrete buildings was built, which fed a regressive neural network model to predict the wall’s engineering thickness and length values from an architectural 30-feature input vector, which accounts for geometric and topological properties, archiving remarkable results regarding the coefficient of determination ( R 2 ). However, a regressive model of this nature does not incorporate a spatial detail or contextual information of each wall’s perimeter, and also, the prediction of other parameters such as the wall translation has a poor performance. For this reason, the present research proposes a framework based on convolutional neural network (CNN) models to generate the final engineering floor plan by combining two independent floor plan predictions, considering the architectural data as input. The first plan prediction is assembled using two regressive models that predict the wall engineering values of the thickness, the length, the wall translation on both axes from the architectural plan, and the floor bounding box width and aspect ratio. The second plan prediction is assembled using a model that generates a likely image of each wall’s engineering floor plan. Both independently predicted plans are combined to lead the final engineering floor plan, which allows predicting the wall’s rectangles design parameters and propose new structural elements not present in architecture, making the methodology an excellent candidate to accelerate the building wall layout’s early conceptual design.

In this article, the sectional behavior (strain and stress) and the effective width in T-shaped reinforced concrete wall are analytically studied. For the parametric study, a nonlinear quadrilateral thin flat layered shell element with 6 degrees of freedom (DOF) per node for the modeling of reinforced concrete wall structures developed by Rojas et al. (2019) is used, varying the axial load (AL), longitudinal steel ratio of the web (LSRW) and flange (LSRF) boundary, aspect ratio (AR) relative to the length of the web of the wall (lw) and height of the wall (hw), and length of the flange (Lf). The parametric study is used to compare the element response that couple the axial, flexion and shear behavior, with a model that only incorporates the coupling of flexion and axial, maintaining plane sections (flexural model). Based on the parametric study, it is calibrated an analytic model of the strain profile of the tension flange of T-shaped walls. Additionally, by including the effect of shear in the model, amplification of the maximum compression strain and a reduction of the maximum tensile strain in the web is observed, mainly in squat walls. Besides, the parametric study is also used to calculate the effective width of T-shaped walls with the flange in tension, finding that it depends mainly on the length of the flange and the roof drift. After initiation of yielding in the flange, the effective width grows quickly, concluding that independent of the geometry and the slenderness, the effective width of the flange in tension covers the entire section if yielding is expected.

Reinforced concrete structural walls are commonly used to provide lateral strength and stiffness to resist lateral loads from wind or earthquake. Slender walls usually require large amounts of longitudinal reinforcement at wall boundaries to satisfy code lateral strength requirements; therefore, use of structural steel reinforced concrete (SRC) walls, where the boundary longitudinal reinforcement is replaced by a structural steel section, is a potentially attractive alternative. This study presents results of an experimental program involving tests under combined gravity and lateral loading for three, heavily instrumented, moderate-scale SRC slender walls. Primary test variables included varying the size of the embedded structural steel section and the quantity of transverse reinforcement provided at the wall boundaries. Although slip of the structural steel was observed for all specimens, test results reveal good behavior up to and beyond 2% lateral drift, even for a specimen with only modest confinement at the wall boundaries.

Slender walls with discontinuities at their bases, such as flag walls or walls with door openings or access, are common in Chilean practice because of the architectural requirements at facades, first floors, and underground levels. However, there is limited information about the behavior of such elements, and no designs or guidelines in the current codes consider the effects of discontinuities at the base. In this work, two analytical models are presented that estimate the yield displacement, yield curvature, and ultimate curvature of walls with openings, such as flag walls (setback), based on the dimensions of the opening and the longitudinal boundary steel ratio calibrated from a parametric analysis of a nonlinear finite element model. The results indicate that these discontinuities can have a major impact on the elastic displacement, reducing it because of the presence of a more rigid section above the opening, and also on the inelastic component, by increasing the curvature (and the strain) at the wall base because the opening tends to confine the plastic hinge within that area.

A simple yet effective constitutive model-referred to as the “Fixed Strut Angle Model” (FSAM)-is presented in this paper for simulating the nonlinear axial/shear behavior of reinforced concrete membrane (panel) elements subjected to generalized and reversed cyclic loading conditions. In the formulation of the FSAM, normal stresses in cracked concrete are calculated along fixed crack (strut) directions. Shear stresses developing along crack surfaces, which are calculated using a simple friction-based constitutive relationship, are superimposed with the concrete stresses along the struts, for obtaining the total stress field in concrete. Model predictions were compared with panel tests results available in the literature, at various global and local response levels. The model was demonstrated to reasonably capture the overall response characteristics of reinforced concrete panels, including hysteretic shear stress vs. strain behavior, shear stress capacity, hysteretic shear stiffness attributes, ductility, pinching behavior, governing failure mode, principal strain and stress directions, and local deformations.

Reinforcing bars removed from structural walls that belonged to a damaged building during the 2010 earthquake in Chile are studied under low-cycle fatigue testing. Damage of such walls was characterized by concrete crushing and boundary longitudinal reinforcement buckling. Reinforcement bars are selected from damaged areas, including reinforcement with and without visible buckling. Cyclic load tests are performed with constant strain amplitude in the plastic range (3% and 5%), using an aspect ratio of 20. Fatigue life loss is observed in specimens from reinforcement bars with visible buckling damage with up to 15 cycles less than unaltered bars (3% amplitude tests), and with a fatigue life reduction of at least 40% for bars with and without observed buckling compared to unaltered bars, which indicates a low remaining fatigue capacity. A strain amplitude model also indicates that for a given number of cycles to fatigue failure, the strain amplitude reduces to 36% when comparing bars in buckled zone to unaltered bars. The seismic displacement demand on the building is of about 5 cycles of large amplitude and considering that some longitudinal bars fractured, it indicates that they could have reached 5% strain amplitude.

In this work, the behavior of slender reinforced concrete (rc) walls with different types of discontinuities at the base, under cyclic lateral loading, are experimentally and numerically studied. First, the experimental results of a series of tests of rc walls with setbacks and central openings at the first floor are presented. Second, a robust quadrilateral element with 3 degrees of freedom (dof), 2 displacement and 1 in-plane rotation per node, and a transversal section made of a layered system of fully bonded, nonlinear smeared steel reinforcement and smeared orthotropic concrete material based on a rotating-angle approach, to represent the behavior of rc walls, is reviewed. Finally, the comparison of the experimental results with numerical models of the walls using the robust quadrilateral element is presented. It is observed that the model is able to capture in a good way the global and local response.

The 2010 Chile earthquake of magnitude Mw 8.8 showed the importance of using correct detailing at the wall boundary. Most design methodologies for wall boundary special detailing have been compared to testing, but at the building level have not been validated with evidence from actual earthquakes. For this purpose, two buildings that exhibited flexural wall damage were studied. An additional building that was not damaged, standing less than 100 m from one of the damaged buildings, was also included. The buildings were analyzed using linear–elastic models, as is common practice among designers, and the walls were analyzed in terms of compressive strain demands resulting from roof displacement. The strain demands were determined using a concentrated plasticity model, as well as a model that included the elastic and plastic components of deformation. In this last case, the elastic component was determined by pushing the building model with a pattern consistent with the first mode of lateral vibration until the first wall reached its moment capacity, including a reduced stiffness in the walls and slabs. Results indicate that the damaged walls were expected to reach moment capacity earlier than the other walls, obtaining compressive strain values greater than 0.003. Thus, the walls damaged during the 2010 earthquake correlated well with the estimations of compressive strains, since these were also the first walls to reach maximum capacity. On the other hand, the undamaged building presented generally lower levels of compressive strain values in the walls than those of the damaged buildings.

Reinforced concrete corbels are generally used to transfer loads within a structural system, such as buildings, bridges, and facilities in general. They commonly present low aspect ratio, requiring an accurate model for shear strength prediction in order to promote flexural behavior. The model described here, originally developed for walls, was adapted for corbels. The model is based on a reinforced concrete panel, described by constitutive laws for concrete and steel and applied in a fixed direction. Equilibrium in the orthogonal direction to the shearing force allows for the estimation of the shear stress versus strain response. The original model yielded conservative results with important scatter, thus various modifications were implemented in order to improve strength predictions: 1) recalibration of the strut (crack) direction, capturing the absence of transverse reinforcement and axial load in most corbels, 2) inclusion of main (boundary) reinforcement in the equilibrium equation, capturing its participation in the mechanism, and 3) decrease in aspect ratio by considering the width of the loading plate in the formulation. To analyze the behavior of the theoretical model, a database of 109 specimens available in the literature was collected. The model yielded an average model-to-test shear strength ratio of 0.98 and a coefficient of variation of 0.16, showing also that most test variables are well captured with the model, and providing better results than the original model. The model strength prediction is compared with other models in the literature, resulting in one of the most accurate estimates.

In this article, the formulation and verification of a nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the nonlinear analysis of reinforced concrete (RC) walls under static and cycling loads are presented. The formulation is based on a quadrilateral element with twelve degrees of freedom (DOF), two displacements and one drilling DOF per node, which is defined by a blended field interpolation for the displacements over the element, and a layered system for the element section consisting of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with a rotating angle formulation, and a stiffness tangent approach. The drilling DOF refers to the incorporation of the in-plane rotation as a DOF at each element node. The blended field interpolation has the advantage of producing a smoother strain distribution inside each element, which facilitates element convergence, and the layered section formulation allows for the properties of the concrete and steel over the thickness of the wall to be modified to properly represent the different wall components, such as the concrete cover, steel rebar and confined concrete. Additionally, the formulation introduces a rotational DOF at each node, which allows the membranes to connect directly to beam and column elements. Moreover, this formulation incorporates the coupling of axial, flexural and shear behavior observed on the different configurations of RC wall structures. To verify this formulation, the results of a set of available experimental data reported in the literature for RC wall elements, with different configurations (slender walls, squat walls, wall with irregular disposition of openings) and levels of confinement, under monotonic and reversed loads are compared with the results obtained from the corresponding analytical model. The formulation is notably consistent with the experimental data and can predict the maximum capacity, the global (force vs deformation) and local responses (strain along the wall) and incorporate the coupling of axial, flexural and shear behavior observed in the different configurations of RC wall structures.

Fiber models have been developed and applied to various structural elements such as shear walls, beams and columns. Only scarcely have fiber models been applied to circular foundation systems such as cast in drilled holes shafts (CIDH). In pile foundations with constraint head boundary conditions, shear deformations can easily contribute to the lateral pile response. However, soil structure interaction formulations such as the p-y method, commonly used for lateral pile design, do not include structural shear deformations in its traditional derivation method. A fiber model that couples shear and axial-bending behavior, originally developed for wall elements was modified and validated on circular cross sections (columns) before being applied to a 0.61 m diameter reinforced concrete (RC) pile with fixed head boundary conditions. The analytical response was compared to measured test results of a fixed head test pile to investigate the possible impact of pile shear deformations on the displacement, shear, and moment profiles of the pile. Results showed that shear displacements and forces are not negligible and suggest that nonlinear shear deformations for RC piles should be considered for fixed-head or similar conditions. Appropriate sensor layout is recommended to capture shear deformation when deriving p-y curves from field measurements.

SUMMARY Previous earthquakes, such as the 2010 Maule earthquake in Chile, have demonstrated the need to establish suitable predictors of compressive or tensile strains in concrete or steel in reinforced concrete shear walls, which can provide limit states or confinement requirements. Slender walls are commonly controlled by flexural deformations that can be divided into elastic and inelastic components. This study provides calibrated expressions for the elastic and inelastic components of flexural deformations using a fiber model for slender walls. These expressions are obtained for rectangular and T-shaped walls. The elastic component is dependent on the axial load and the boundary steel reinforcement ratio. The impact of wall coupling is investigated, which requires a correction for the elastic component. The investigation of the inelastic component is based on a plastic hinge model, in which the length of the plastic hinge is a function of the lateral inelastic drift of the wall among other parameters. The traditional linear inelastic curvature distribution over the wall height is also modified for cases with steel reinforcement with a long yield plateau or low strain hardening, which results in a larger curvature at the wall base. The distribution is validated with experimental data from the literature. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamic shear amplification has been commonly studied in cantilever reinforced concrete wall systems, however, coupling beams or slabs can generate axial loads that can modify the response. A parametric study is carried out that covers 432 nonlinear time-history analyses (72 models with 6 records) of 2 coupled walls with different length, including variations in the amount of boundary element steel ratio (1%, 3% and 5%), amount of slab steel ratio (0.0%, 0.3% and 0.6% − 0.0% is defined for connected walls without coupling), building height (25 m, 50 m and 75 m), and wall length (2 m, 4 m and 6 m). The walls are represented with nonlinear fiber models; while the coupling slabs are elastic within the length with a rigid-perfectly plastic model at both element ends. The shear amplification values depend on the coupling level, with the highest amplification values ​​being observed for connected (not coupled) systems. The high values ​​for connected walls are due to the rapid plastification of the wall because of the low structural redundancy. The mean shear amplification values are 1.45, 1.10 and 1.35 for coupling slabs with reinforcing steel ratio of 0.0%, 0.3% and 0.6%, respectively. The proposed expression for the dynamic shear amplification also depends on the response modification factor of the walls, a parameter directly related to nonlinearity sources. On the other hand, an expression used by many codes that depends on the number of floors does not necessarily represent the amplification that occurs in tall buildings with moderate coupling, since the plastification at the base in such cases is difficult to achieve given their large elastic displacement capacity, as well as, cases that incorporate a minimum base shear criterion, that reduce the nonlinearity incursions.

Columns that are at the intersection of frames in two different directions are subjected to biaxial shear when lateral loads are simultaneously applied in two directions. Using the resultant shear and evaluating one-way shear strength along the direction of the resultant force, as most design codes do, is unconservative especially when significant shear co-exist about both axes. The conservatism of one-way shear strength in some expressions of ACI 318 (14) balances the not consideration of biaxial shear design in the code. However, the use of more refined or accurate expressions as in ACI 318 (19) makes the consideration of biaxial shear for design a need. Experimental data from the literature is used to compare ACI 318 expressions and validate the trilinear interaction diagram approach included in ACI 318 (19) for biaxial shear loading, showing that it is a simple and reliable method for design.

Masonry walls are structural elements generally used in housing or small buildings. Given their structural configuration, they commonly present shear failure due to seismic actions, characterized by a fragile response. Thus, it is important to have simple, yet reliable tools that correctly estimate the shear capacity of walls. For that, a simple existing model developed for reinforced concrete elements and based on a panel model is used and adapted to masonry walls, providing a novel formulation that can be applicable to both materials. For compression and tension behavior, the prismatic resistance of the panel is used, which, due to the anisotropy of the material, degrades with the angle formed by the load with the vertical mortar joint. Strain values are set for compression and tension failure modes, and a degradation coefficient in compression due to the biaxial strain loading is included. Additionally, bond failure is also incorporated into the model. A database of 41 tests of reinforced masonry walls and 12 tests of confined masonry walls is used for model validation. The strength ratio between the shear strength obtained by the model and the test is compared, giving an average and a coefficient of variation (COV) of 1.0 and 0.15, respectively for reinforced walls, and 1.08 and 0.14 for confined walls, showing a satisfactory performance and better behavior than simple models from the literature. The analysis of general trends of the strength ratio reveals that there is a low dependence between the strength ratio and the studied parameters, implying that the model captures the physical behavior of masonry walls.

This chapter describes the state-of-the-art concerning the use of machine learning methods for solar flare prediction. The general perspective is the one of the Flare Likelihood And Region Eruption foreCASTing (FLARECAST) project, which started in 2015 within the Horizon 2020 framework. The computational aspects of this project are described, with specific focus on the mathematical properties of the algorithms implemented in the FLARECAST pipeline and on the technological services that the project is providing to the heliophysics community.

Squat reinforced concrete walls require enough shear strength in order to promote flexural yielding, which creates the need for designers of an accurate method for strength prediction. In many cases, especially for existing buildings, strength estimates might be insufficient when more accurate analyses are needed, such as pushover analysis. In this case, estimates of load versus displacement are required for building modeling. A model is developed that predicts the shear load versus shear deformation of squat reinforced concrete walls by means of a panel formulation. In order to provide a simple, design-oriented tool, the formulation considers the wall as a single element, which presents an average strain and stress field for the entire wall. Simple material constitutive laws for concrete and steel are used. The developed models can be divided into two categories: (i) rotating-angle and (ii) fixed-angle models. In the first case, the principal stress/strain direction rotates for each drift increment. This situation is addressed by prescribing the average normal strain of the panel. The formation of a crack, which can be interpreted as a fixed principal strain direction is imposed on the second formulation via calibration of the principal stress/strain direction obtained from the rotating-angle model at a cracking stage. Two alternatives are selected for the cracking point: fcr and 0.5fcr (post-peak). In terms of shear capacity, the model results are compared with an experimental database indicating that the fixed-angle models yield good results. The overall response (load-displacement) is also reasonable well predicted for specimens with diagonal compression failure.

Buckling of longitudinal reinforcement in reinforced concrete (RC) columns or walls is commonly seen with a length equal to the spacing between stirrups (local buckling), but experimental observations have shown that the length of buckling can span a larger length, deforming several stirrups within the buckling length (global buckling). The behavior of the longitudinal reinforcement under compression resulting in global buckling is studied in this work, based on a concentrated plasticity fiber model that considers four (4) plastic hinges. The model was originally validated for local buckling and here is extended to global buckling by introducing the effect of transversal reinforcement and expansion of the core concrete in the analysis. Modeling of the forces from the stirrups acting on the longitudinal bar assumes that part of the force is transferred directly to the expanding concrete core and the remaining force is balanced by internal stresses in the longitudinal bar. The bar buckling behavior is evaluated for different buckling length values and the length is chosen such that it delivers the lowest maximum stress. The proposed model is validated by comparison of the predicted buckling mode with experimental test results from the literature. The average error in the mode prediction is −0.59 (about half the space between stirrups), which is a reasonably good value considering that the database of tests used covers buckling modes from 1 to 7 (stirrup spacing). Besides of providing good critical buckling length predictions, it allows obtaining the stress versus strain curve for the overall buckling bar. Analysis of three column specimens from the literature indicates that the overall stress versus strain response can be obtained with a reasonable accuracy. Peak stress is obtained within an error of about 10% compared to the test result for a strain well represented by the model. The post-peak slope also gives a good estimate for the degradation stage.

This work validated a model of shear–flexure interaction for prestressed self-consolidating concrete beams with varied shear span-to-depth ratios, which were tested under four-point bending as part of this work. The interaction between flexure and shear was introduced by a panel element’s biaxial behavior in a modified fiber element formulation. Two different assumptions were considered for the interaction model implementation: (i) zero transverse normal stress perpendicular to the beam axis in any cross section, and (ii) a prescribed transverse normal strain profile along the beam based on the model calibrated for cantilever members. The interaction model with a prescribed transverse strain profile and with a consideration of flexure-induced deformations had better predictions of capacity and deformation for the tested beams, as well as the transverse normal strain profile, compared to the other models.

The Mw 8.8 earthquake in 2010 in Chile provided valuable information regarding the damage and potential design code changes for reinforced concrete (RC) structures. Many modern RC buildings suffered severe damage, mainly in the form of concrete cover spalling, followed by longitudinal boundary bar buckling and concrete crushing. The absence of wall boundary detailing explains such behavior, but older structures and thousands of other buildings suffered minor or no damage at all. An analysis of some potential factors that influenced the damage caused is carried out and the fundamental principles for the Chilean RC design code changes are exposed. Currently, a displacement-based approach is used for detailing of the wall boundary elements as well as for establishing damage limitation. Compressive concrete strain cannot exceed 0.008, limiting indirectly the axial load, which is one of the potential precursors of the damage. Transversal reinforcement is also provided in zones of potential yielding of the longitudinal reinforcement such that buckling due to compression preceded by tension is minimized; this buckling is more likely in asymmetric cross-sections, such as T-shaped sections, where usually the web goes into larger tensile and compressive strains given the variation of location of the neutral axis for the web under tension or compression.

The p-y method is one of the most popular methods in pile design and has been calibrated for various boundary conditions using numerical and experimental studies during recent years. Most studies on reinforced concrete (RC) piles have included the impact of flexural nonlinearity, (e.g. nonlinear moment–curvature relations) but not considered associated pile shear deformations when deriving p-y curves from field data. Common p-y curves may be better applicable for piles with flexure dominated failures (e.g. piles with free- head boundary conditions). For piles with fixed head boundaries (i.e. rotation restrained piles) shear deformations could be of significant influence. To study this problem, a coupled shear flexure interaction model for axial-bending-shear behavior coded in OpenSees was applied to a 0.61 m (2 ft) diameter flagpole and a 0.61m (2 ft) diameter fixed head pile specimen to investigate the possible influence of shear deformations to the overall pile responses. The surrounding soil wa...

Reinforced concrete buildings utilizing structural walls for lateral load resistance are the predominant form of construction in Chile for buildings over four stories. Typical buildings include a large number of walls, with ratios of wall cross-sectional area to floor plan area of roughly 3% in each principal direction. Based on the good performance of RC buildings in the March 1985 earthquake, requirements for closely spaced transverse reinforcement at wall boundaries were excluded when Chile adopted a new concrete code in 1996 based on ACI 318-95. In recent years, use of three-dimensional linear models along with modal response spectrum analysis has become common. Since 1985, nearly 10,000 new buildings have been permitted. Although the newer buildings have similar wall area to floor plan areas as older buildings, newer walls are thinner and buildings are taller, leading to significantly higher wall axial load ratios.