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The connection between a prefabricated reinforced concrete column and a pocket foundation is a case treated from a general perspective in the European Standard named EN 1992-1-1 (EC2), and when the structural engineer deals with the dimensioning or verification of the connection, he must tackle several unknowns. The present work aims to fill in the missing information by presenting detailed calculation models based on the strut-and-tie method for four widely used pocket foundations: a pedestal pocket foundation with smooth, rough or keyed internal walls and a pad foundation with a pocket possessing keyed internal walls. In establishing the strut-and-tie models and writing the equation for the internal forces, we consider several standards (EC2, NBR 9062 and DIN 1045-1), good practices (from Austria, England, Germany and Romania) and numerous experimental and numerical investigations. Additionally, detailed design prescriptions applicable to seismic areas are given. This manuscript covers a wide range of design and technology aspects necessary for designing and building columns connected with pocket foundations, information for which is shown only in fragmented form or partially in other publications. Afterward, as a case study, a pocket foundation is designed in all four variations, with the structural design particularities, similitudes and differences being pointed out. Finally, to conclude, we mention the advantages and disadvantages of pocket foundations with respect to the type of internal wall surface used. Quantifiable data based on the case study undertaken are available. [ABSTRACT FROM AUTHOR]

Glass fiber-reinforced polymer (GFRP) reinforcement is a proven noncorrodible alternative to conventional steel reinforcement. Over the past two decades, a deliberate effort has been put toward developing a comprehensive set of design provisions, culminating in the release of ACI CODE-440.11-22. Absent from this Code is the strut-and-tie method commonly used in short shear-span applications due to uncertainty in GFRP-reinforced concrete (RC) behavior. Corbels are short shear-span, shear-controlled elements used to transfer vertical and horizontal loads to columns or walls. This study presents the results of 10 full-scale corbel specimens with varying reinforcement ratios and shear span-depth ratios to better understand the behavior of GFRP-RC corbels under monotonic loading. The results indicate that the cracking behavior, strain development, deflection, capacity, and mode of failure are all dependent on the presence of secondary reinforcement and the shear span-depth ratio. The thermoplastic headed-end bars used were found to be a viable anchorage method. [ABSTRACT FROM AUTHOR]

The use of normal-strength (Grade 60) and high-strength (Grade 80) headed bars as transverse reinforcement can improve the constructability of reinforced concrete structures. However, the ACI 318-19 Code does not allow the use of headed bars as transverse reinforcement in deep beams. ACI 318-19 also does not allow engineers to take advantage of the increased yield strength of Grade 80 reinforcement for use as shear reinforcement. This paper presents an analytical evaluation of shear-critical deep beams that use high-strength headed reinforcement. Six recently conducted largescale experiments are modeled using the two-parameter kinematic theory, the nonlinear finite element tool VecTor2, and strut-and-tie methods described in codes. The predictions are compared with experimental results. A parametric study is conducted to evaluate the influence of the quantity of transverse reinforcement and yield stress of the transverse reinforcement on the response of shearcritical deep beams. [ABSTRACT FROM AUTHOR]

The connection between a prefabricated reinforced concrete column and a pocket foundation is a case treated from a general perspective in the European Standard named EN 1992-1-1 (EC2), and when the structural engineer deals with the dimensioning or verification of the connection, he must tackle several unknowns. The present work aims to fill in the missing information by presenting detailed calculation models based on the strut-and-tie method for four widely used pocket foundations: a pedestal pocket foundation with smooth, rough or keyed internal walls and a pad foundation with a pocket possessing keyed internal walls. In establishing the strut-and-tie models and writing the equation for the internal forces, we consider several standards (EC2, NBR 9062 and DIN 1045-1), good practices (from Austria, England, Germany and Romania) and numerous experimental and numerical investigations. Additionally, detailed design prescriptions applicable to seismic areas are given. This manuscript covers a wide range of design and technology aspects necessary for designing and building columns connected with pocket foundations, information for which is shown only in fragmented form or partially in other publications. Afterward, as a case study, a pocket foundation is designed in all four variations, with the structural design particularities, similitudes and differences being pointed out. Finally, to conclude, we mention the advantages and disadvantages of pocket foundations with respect to the type of internal wall surface used. Quantifiable data based on the case study undertaken are available.

This paper addresses the stress field of reinforced concrete (RC) beam–column joints retrofitted with haunches. Design of such solution currently assumes internal forces evaluated by the so called β‐factor approach, which was originally conceived targeting the enhancement of steel moment‐resisting frames. Extension to RC is subsequent as it emerges from the literature survey. The analytical model is first critically rediscussed. Inconsistencies of the adopted structural scheme, with respect to the actual mechanical behavior, may lie on the compatibility conditions which are imposed between the haunch and concrete beam (or column). In this regard, two‐dimensional finite element models (FEM), using linear‐elastic materials, are employed to study the stress field of two benchmark specimens derived from literature. A partial validation is carried out against experimentally derived internal forces. Results show that, for haunches with extended flat plates and stiff diagonals, compressive diffusion affects the entire haunch region. Consequently, beam's kinematic hypothesis of linear strains is no longer valid. The predicted joint shear demand resulted underestimated by β‐factor approach by 50%. Since 2D FEM may be not efficient for many practical circumstances, an application of Strut‐and‐Tie is alternatively proposed. Finally, both the limitations and possible extensions of the proposed approaches are stated transparently. [ABSTRACT FROM AUTHOR]

Abstract This work introduces a new alternative to obtain strut-and-tie models using the hybrid topology optimization method, which is already proposed in the technical literature and is refined here to use polygonal finite elements and accelerate the solution of the material nonlinearity problem. In this method, concrete is approached as a continuum, using polygonal two-dimensional finite elements, and steel bars as truss elements, using one-dimensional finite elements with two nodes. For a closer representation of reality, an orthotropic constitutive model for concrete was implemented considering different compression and tensile stiffness values, which is one of the advantages of the model. Further, the hybrid method limits the final layout of steel bars, thereby generating better structures from a constructive point of view, while allowing greater freedom for the shape and concrete strut slope. However, this method is more complex, and it increases the computational cost, which was substantially minimized through the implementation of an algorithm. Results obtained for some domains were very close to the results of other methodologies; however, small differences were noted that may be relevant to the final result. Other domains showed results with greater differences, thereby significantly changing the final strut-and-tie model and presenting a new structural design alternative.

Increasing interest in the use of fiber-reinforced polymer (FRP) reinforcement for reinforced concrete (RC) structures has made it clear that insufficient information about the seismic performance of such structures is currently available for practicing engineers. This paper summarizes the results of seven full-scale pseudo-static cyclic tests of squat concrete walls reinforced with glass FRP (GFRP) bars and spirals. Test variables were the wall aspect ratio, the axial load level, and the web reinforcement amount. The test results were analyzed and used to develop a strut-and-tie model (STM) that accurately estimates the peak shear strength and reflects the effects of various influential parameters. The model was achieved by idealizing the shear-transfer mechanism of the web reinforcement using a statically indeterminate truss, and that of the concrete using a direct strut-and-tie system representing the tiedarch action developed through the web. Streamlined expressions were formulated to calculate the shear-transfer capacity of the two mechanisms, and due to lack of a sufficient experimental database, a series of 90 finite element models were conducted to assist in formulating the truss expression. The validity of the developed STM and expressions was examined against the results of the tested walls, showing great accuracy and uniformity. Comparisons were also made with predictions from STMs in ACI 318-19, CSA S806-12, and Eurocode 2 to indicate the accuracy of the developed model. [ABSTRACT FROM AUTHOR]

Reinforced concrete half-joints are susceptible to deterioration mechanisms primarily due to the leakage of surface water, often contaminated with chlorides from de-icing salts, through the expansion joint. Due to the joint geometric form, favourable conditions can be created inside the joint for the corrosion of steel reinforcement. To this end, seven reinforced concrete half-joints were tested to failure under three-point bending to investigate the effect of reinforcement reductions that simulate common deterioration scenarios arising from the corrosion of reinforcement. The results were then compared to the predictions of nonlinear finite element analyses and the strut-and-tie method. The results demonstrated that a reduction in the amount of reinforcement close to the re-entrant corner has major influence on the load-deflection response of reinforced concrete half-joints. The largest reductions in load-carrying capacity were obtained from the half-joints with a full removal of diagonal bars and a combined removal of diagonal and U-bars, both showing reductions in load capacity of more than 50 %. The failure mode in each case of simulated deterioration scenarios involved a shear failure at the nib, except one case which displayed a shear failure in the full depth section due to the reduced anchorage of the bottom reinforcement. Furthermore, it was shown that nonlinear finite element analyses provide accurate predictions of the load-deflection response and failure crack patterns. The strut-and-tie method was found to result in overly conservative predictions, with an average observed-to-predicted load ratio of 1.48 and a coefficient of variation (COV) of 10.2 %. This is considerably higher than an average load ratio of 1.05 and a COV of only 3.1 % obtained from the nonlinear finite element analyses. • Detailed response of seven half-joints, six with reinforcement reductions, presented. • Significance of diagonal reinforcement for limiting the extent of damage at the re-entrant corner highlighted. • Reduced anchorage of the bottom reinforcement led to a full-depth shear failure. • Nonlinear FE analyses provided accurate assessment of load capacity, mode of failure, and internal mechanisms of resistance. • Detailed strain maps provided new insights into damage progression under loading. [ABSTRACT FROM AUTHOR]

Steel and precast columns are commonly designed to transfer moment loads to concrete foundations through cast-in-place headed anchors. In design office practice in the United States, connection strength has been evaluated considering mechanisms emphasizing joint shear, strut-and-tie modeling, and anchoring to concrete. For any given connection, the strengths calculated with these three methods can differ by a wide margin. The application of these methods, including possible enhancements that improve strength estimates, is described. Laboratory tests were performed to provide benchmark physical data to determine the applicability of various design methods. The test specimens consisted of full-scale interior steel-column-to-concrete-foundation connections located away from foundation edges, with details typical of current construction practice on the West Coast of the United States. Strength in both tests was governed by concrete breakout failure. Strategically placed reinforcement increased the strength and displacement capacity of anchored connections governed by breakout. Design recommendations are provided. [ABSTRACT FROM AUTHOR]

When employing the strut-and-tie modelling (STM) method in the conceptual design of reinforced concrete structures, a suitable strut-and-tie (ST) model indicating load transfer mechanisms first needs to be identified. Topology optimization (TO) methods have frequently been used for this purpose. However, although TO methods employing either a ground-structure or a continuum-based TO approach can be used, the performance and effectiveness of these two methods have not been systematically investigated and compared. To obtain a better understanding of the characteristics of both methods, a systematic comparison procedure is proposed to investigate the generation process and the resulting ST designs. Three aspects, relating to structural performance, economic issues, and method applicability are considered in the comparison, with six metrics formulated to quantify these aspects. Based on investigation of designs for three reinforced concrete elements incorporating typical discontinuity regions (two 2D cases and a 3D case), the performance of the two methods is assessed. It is found that both methods result in safe and efficient ST designs, with comparable structural performance, while some differences in terms of computation time and usability are observed. • Quantitative evaluation of strut-and-tie model performance based on six metrics. • Systematic comparison of two different methods for strut-and-tie model generation. • Investigation of the influence of input parameters on generated strut-and-tie models. [ABSTRACT FROM AUTHOR]

On the basis of the modified Kupfer and Gerstle’s biaxial failure criterion ofconcrete, amodified interactive strut-and-tie model (MISTM) to predict the nominal shear strength of RC corbels was derived and is proposed in this paper. The MISTM includes the interaction between the load-carrying capacity of a concrete strut and a tension tie, andthe effects of horizontal force.The numberof horizontal and vertical stirrups wasconsidered. To validate and calibrate the MISTM, a dataset test results for 302 corbelswascollected from the literature. Finally, the predictions obtained from the MISTMwere also compared with those computed usingthe strut-and-tie models in accordance with the ACI 318 code and the state-of-the-art presented in the literature, and arefound to be more accurate and reliable.

An analytical model based on the strut-and-tie method for predicting the shear strength of reinforced concrete (RC) interior beam-column joints is introduced in this paper. Both contributions from truss and strut mechanisms are included in the analytical model. The contributions of concrete and transverse reinforcements based on EC2 [2004] are incorporated in the truss mechanism, whereas the strut mechanism is calculated based on the effective compressive strength of concrete. The deformation compatibility between the truss and strut mechanisms is also incorporated in the proposed model. The proposed model is validated by comparison with available experimental database. The validated results show a satisfactory correlation between the proposed model and available experimental database. The proposed model is also compared with the NZS 3101 [1998]; ACI 318 [2002]; and Hwang and Lee [2000]'s joint shear strength model and an improved performance is found. [ABSTRACT FROM AUTHOR]

Based on the Kupfer failure envelope of concrete, an analytical model called the "interactive strut-and-tie model" (ISTM) for predicting the joint shear capacity of exterior beam–column joints (EBCJs) was formulated and is presented in this study. The ISTM consists of the interaction of the strengths of concrete struts and tension ties, and the strength contributions from shear reinforcements consisting of column ties, intermediate column vertical bars and crossed inclined bars are taken into account. The proposed approach was calibrated and validated using a large dataset of 328 EBCJ test results, covering a broad range of important parameters such as the aspect ratio, axial load ratio, beam reinforcement ratio and horizontal joint reinforcement ratio. Finally, the joint shear strengths computed by the ISTM were also compared against those obtained from state-of-the-art models and were found to have resulted in much more precision and uniformity. [ABSTRACT FROM AUTHOR]

Reinforced concrete four-pile caps under wall loading occur in heavily loaded foundations in bridge construction. The failure mode of shear across the full width of the cap may occur in these deep structural elements. A statically determinate two-way grillage model, comprising orthogonal deep beam grillage elements obeying a predetermined test observing deflection pattern and boundary conditions, is established to solve the structure's shear capacity. The model gives more accurate and faster solutions than the traditional strut-and-tie method and commercial nonlinear numerical modeling.A key step to solving the model is a linear constitutive (load-deflection) relationship developed for the grillage elements. The grillage model is verified against laboratory experiments for nine pile caps at the University of Southampton (UoS) with the results of a numerical modeling parametric study. A Visual Basic Userform-based design software is developed, incorporating the model and enabling engineers to obtain the shear capacity, full-field reinforcement stress distribution, and cap deflections within seconds. [ABSTRACT FROM AUTHOR]

The effect of development type and length and beam geometry on the behavior of discontinuity regions in concrete deep beams was investigated through experimental testing and numerical study. Observations of cracking patterns and measurements of load and displacement at midspan of four large-scale concrete deep beams tested under a three-point load setup were used to calibrate numerical models. Thirty-five specimens were then modeled in a nonlinear finite element software to evaluate the strength of deep beams with different development lengths, development types, strut angles, and beam geometries. Development length and type of development was found to impact the presence of tensile stress in the support nodes. A rectangular beam geometry was found to cause diagonal tension stresses in the struts, not present in truss-like specimens. The tensile stresses from reinforcement development and diagonal tension were found to not be additive in these rectangular beams. [ABSTRACT FROM AUTHOR]

The strut-and-tie method (STM) is commonly used to design reinforced concrete (RC) pier caps, where the traditional methods of shear and flexural design cannot be used due to nonlinear strain distribution. This paper presents experimental studies on scaleddown pier cap specimens subject to four concentrated loads, to study the influence of various parameters and the applicability of STM. The STM prescribed by ACI 318 and AASHTO are found to give reasonably conservative results only when the beneficial effect of triaxial confinement near the bearing node is invoked; otherwise, the predictions are overly conservative. Variations in bearing plate size, distributed reinforcement, and loading eccentricity did not have much influence on the load capacity, but distributed reinforcement was seen to be beneficial in limiting crack widths. The formation of the assumed STM is validated using strain measurements in concrete and steel, and it is observed that this develops only after significant cracking. [ABSTRACT FROM AUTHOR]

This paper presents findings from laboratory tests on reinforced autoclaved aerated concrete (AAC) thin-panel floor diaphragms. Data were generated through targeted AAC material property tests, out-of-plane testing of reinforced AAC panels, and in-plane testing of light-frame AAC floor diaphragm assemblages. A group of six reinforced panels resting on joists was tested to determine a design load for one-way floor systems subjected to gravity loads. Results of 10 floor diaphragm specimens were used to develop a strutand- tie model that provides a reasonable lower-bound approximation of the ultimate in-plane capacity of one-way floor systems with AAC sheathing. The testing provided reliable design values and the strut-and-tie model fits well with the experimental test data. [ABSTRACT FROM AUTHOR]

Corbels are short, typically shear-controlled cantilevers that transfer loads to columns. Currently, ACI 318-14 provisions allow the structural design of shear-controlled corbels through either an empirical design method or the strut-and-tie method (STM). The objective of this paper is to evaluate STM as an independent design method for corbels and investigate the differences stemming from the use of STM compared with the empirical design method. Four full-scale double-corbel specimens were designed, fabricated, and tested at Ferguson Structural Engineering Laboratory. Two specimens were designed using the empirical method and two specimens were designed using STM, with and without crack-control reinforcement. Measured load-carrying capacities exceeded the capacities calculated using STM for all specimens, and no signs of premature failure were observed in the corbel detailed based on the STM. The results of this study suggest that STM can be used for corbels, and the empirical detailing requirements specific to corbels might not be necessary when using STM. [ABSTRACT FROM AUTHOR]

Despite many investigations on the spatial strut-and-tie mechanical mechanism on pile cap punching failure at present, little has been reported on its application. Meanwhile, compared with the steel-reinforced concrete structure extensively existing in the superstructure, that in the foundation structure is yet seldom seen. The real section steel truss of better material properties was used to replace the virtual truss originally regarded as the concrete stress flow for this reason. Aiming at the punching-force bearing behavior of this kind of the pile cap reinforced by the section steel truss, two series (the first is four six-pile caps and the second is two four-pile caps) of the full-size experimental study and the theoretical analysis have been made. Under the condition of the same reinforcing steel amount, in contrast to the ordinary reinforced pile cap, this kind of the section steel truss pile cap can increase the bearing capacity and ductility. It transfers load according to the spatial strut-and-tie. Before a definite column load, the column load is born jointly by the section steel truss and the concrete spatial strut-and-tie. Then, after the concrete strut is decomposed into the two ones coupled at the two ends, the section steel truss gradually shifts into the bearing main-body. With the total yield of the section steel strut and the complete damage to the concrete strut of the splitting in the midpart plus the shear-compression at the two ends, the punching cone is formed. The failure to the composite strut of the section steel and the concrete is an indication of the loss of the pile cap punching bearing capacity. The bearing capacity calculation formulas were deduced based on this, which agree well with the test results. [ABSTRACT FROM AUTHOR]

• CFRP U-jacketing for the strengthening of exterior reinforced concrete beam-column (B-C) joints. • A two-dimensions finite element model is proposed for strengthened CFRP B-C joints. • Debonding existed on the contact surface of epoxy and concrete are considered. • Effects of concrete compressive strength and column axial load on the strengthened B-C joints shear strength were investigated. • New design equations of shear strength prediction of CFRP strengthened B-C joints. A key part of RC structure seismic performance is the effective distribution of earthquake forces across all resistance elements through reinforced concrete (RC) beam-column (B-C) joints. By virtue of their ease of implementation and convenient material properties, Carbon-Fiber-Reinforced Polymers (CFRP) are highly utilized for strengthening existing structures with inadequate reinforcement or insufficient confinement. Previous experimental research revealed that debonding failure widely occurs on CFRP shear-strengthened B-C joints. The experimental research as well showed the value of column axial load makes a great contribution to such joint's failure mode. Using CFRP U-jacketing to strengthen non-seismically B-C joints, this article presents a non-linear, two-dimensional FE model for investigating shear behavior. The developed FE model considered the adhesive layer between CFRP sheets and concrete to capture the debonding and a bond-slip model was implemented between concrete-to-CFRP sheets using connector elements. The FE results were verified versus experimental works from literature to prove the proposed FE model's accuracy with appreciate to load-deformation relation and failure modes. Depending on the verified FE model, a parametric study on shear-strengthened RC B-C joints with CFRP U-jacketing with free and fixed ends was performed below monotonic loading. In the existing study, several parameters, including column-to-beam flexural strength ratio (over strength ratio), concrete strength, and value of column axial load, were investigated on the structure's strength and ductility. Using the developed strut-and-tie model (STM), new design equations were proposed to calculate strengthened RC B-C joint's shear strength using CFRP. The proposed equations incorporate the interfacial bond among concrete and CFRP effect, as well CFRP sheet end boundary (free or fixed). The developed design equation's ability to estimate shear strengths of strengthened B-C joints with CFRP was verified through experimental works and FE results. It was evident from verification results that the produced design equations were compatible with experimental and FE model results. [ABSTRACT FROM AUTHOR]

The main objective of this study is to propose the Strut-and-Tie method (STM) to predict the shear capacity of simply supported RC deep beams shear-strengthened with carbon fiber reinforced polymers (CFRP). It is assumed that, the total carried shear force by shear-strengthened RC deep beam provided by three independent resistance, namely diagonal concrete strut due to Strut-and-tie mechanism, and the equivalent resisting force resulted by with web reinforcement and FRP layer. The STM approach is regressioned with 104 specimens shear-strengthened with different scheme which are modelled and analyzed through the Non Linear finite elements method and analyzed according under Push over load. For verifying of the accuracy of proposed method, it was used to determine the shear capacity of specimens which have been tested by other researchers. Obtained results were compared with experimental data, that this comparison indicate the proposed method is capable to predict the shear strength of strengthened deep beams with externally bonded (EB) CFRP with acceptable accuracy.

Half-joint beams, also referred to as dapped-end beams, have been the subject of several studies, primarily focussing on the design optimisation of new reinforced concrete beams and bridge decks. Existing half-joint structures, however, often show signs of deterioration and can exhibit improper reinforcement detailing. In order to gain a better insight into the impact of local corrosion, anchorage cracking, limited amounts of provided shear reinforcement, and improper reinforcement detailing, a test program was designed. Full-scale tests on nine half-joint beams were performed. The results of the study show that even though the impact of an individual shortcoming on the load carrying capacity of reinforced concrete half-joint beams might not be substantial, inspectors and assessors should pay attention to the possibility of combined effects. When multiple deterioration processes are noted and/or questions are raised with respect to the reinforcement detailing, the impact on the load carrying capacity of the beam might be larger than the linear combination of the individual effects. [ABSTRACT FROM AUTHOR]

The use of headed bars in joints between precast concrete elements allows continuity of reinforcement to be achieved over very short splice lengths. The paper describes a series of flexural tests carried out on specimens consisting of pairs of precast elements connected by overlapping headed bars of 25 mm diameter. The headed bars overlapped by 100 mm within a 200 mm wide in situ concrete joint in which transverse bars and vertical shear studs were installed to provide confinement. This type of joint facilitates the construction of continuously reinforced slabs from precast elements thereby enabling significant reductions in overall construction time and improvements in construction quality due to off-site fabrication. The tests investigated the influence on joint strength, ductility and crack width of concrete strength, out-of-plane offset of precast planks and confining shear studs. Ductile failure with yield of 25 mm diameter high strength headed bars was achieved with joint concrete having a cylinder compressive strength of 39 MPa. A nonlinear finite element model is presented, which gives good predictions of joint strength as well as providing insight into joint behaviour. [ABSTRACT FROM AUTHOR]

Shape Memory Alloy (SMA) material offers an excellent alternative to conventional steel reinforcing bars in the design of smart self-centering structures. This is attributed to its ability to exhibit large deformations, yet sustain low permanent strain upon unloading. Research in the area of designing concrete connections reinforced using SMA bar is scarce. Joint performance and SMA anchorage represent two research areas that require further development. In this research, the performance of concrete joints reinforced using SMA bars anchored using screwlock steel anchors was examined experimentally and analytically to assess the effect of several design variables on the joint response: level of stirrup confinement, anchor position, and anchor orientation. Special screwlock anchors were used and modified in this study. Practical design recommendations with regard to the optimum joint detailing and SMA anchor specification were proposed. [ABSTRACT FROM AUTHOR]

The seventh edition of the AASHTO LRFD Bridge Design Specifications (2016 interim) includes revised provisions for the design of deep beams using the strut-and-tie method. The validity and accuracy of these provisions as applied to simply supported deep beams loaded in a manner that generates an inflection point between the supports was investigated in this research. As part of a course-related laboratory investigation, graduate students at the University of Texas at Austin used these provisions to design two reduced-scale deep beams. The specimens were subsequently constructed and tested. The experimental behaviors of the specimens including governing failure modes, load-displacement curves, and their ultimate capacities were investigated and compared with estimates developed from the strutand-tie method. The results obtained validated the suitability of the revised provisions for the design of deep beams with inflection points located between supports. Additionally, the students developed pre-test estimates for the behaviors and strengths of the two deep beam specimens using the finite element software program VecTor2. While there was some variation among the computed responses, the blind predictions accurately captured governing failure modes and provided reasonable capacity estimates. [ABSTRACT FROM AUTHOR]

For the same disturbed region (D-region) of concrete structures, different strut-and-tie models (STMs) may be verified by different researchers, and the reinforcement layouts thus vary significantly. To assess conveniently the performance of these D-regions designed using different STMs, an evaluation system is proposed in this paper. The numerical procedure of the evaluation system is developed based on the ANSYS parametric design language (APDL) and the computer-aided strut-and-tie (CAST) design tool. The evaluation process of this system is mainly divided into three parts: preliminary evaluation, further evaluation, and final evaluation. At the beginning, in the preliminary evaluation, proper STMs in which the distribution of ties agrees well with the tensile stress regions are initially selected according to a finite element analysis. Furthermore, a crack propagation simulation is qualitatively executed to further evaluate and determine the locations of the most significant ties, where primary cracks may arise. For a rational STM, there should exist corresponding ties at these crack locations. Finally, by a load carrying capacity simulation, the most efficient design can be quantitatively confirmed. A classical dapped beam with openings is adopted to demonstrate the efficiency and reliability of the evaluation system. The analysis results indicate that the evaluation system exhibits more robust characteristics than traditional experimental methods. Moreover, the use of this system in the design of concrete structures will bring about significant economic benefits (e.g., reductions in time and costs) and produce high-performance structures. [ABSTRACT FROM AUTHOR]

A geometric discontinuity caused by abrupt changes in cross-sectional dimensions and a force discontinuity caused by concentrated loads results in discontinuity regions due to the disturbance in the flow of internal forces. A softened strut-and-tie model has been developed for determining the shear strength of discontinuity regions that fail under diagonal compression. The softened strut-and-tie model requires complicated computations, consequently making it challenging to apply in engineering practice. In this paper, a further simplification of the softened strut-and-tie model is proposed to facilitate design practice. Strength predictions of the simplified model correlate well with 449 test results of deep beams, corbels, squat walls, and beam-column joints available from the literature. The simplified model incorporates the shear-resisting mechanisms as postulated by the softened strut-and-tie model, and it is a function of the concrete compressive strength, steel yield strength, shear reinforcement ratio, and geometric configuration of the discontinuity region. [ABSTRACT FROM AUTHOR]

The paper presents typical examples of brittle failure that reinforced concrete structures continue to suffer to date in spite of the advances in shear design claimed to have been made in recent years. The key concepts underlying the development of shear design methods are concisely presented and it is shown that the cause of the apparent inability of the methods to consistently achieve their aim is the incompatibility between the assumed mechanisms of load transfer underlying the methods and fundamental concrete behavior. Simpler and more efficient design methods are presented, which have been developed on the basis of alternative mechanisms of load transfer compatible with fundamental concrete behavior at the structure's ultimate limit state. [ABSTRACT FROM AUTHOR]

The paper addresses the design and behaviour of narrow cast in-situ joints between precast concrete elements in which continuity of reinforcement is achieved through overlapping headed bars. Using headed bars minimises the lap length required within the cast-in-situ joint region. Confining reinforcement in the form of transverse bars and vertical shear studs is also installed in the joint. The paper describes a series of tensile tests which were carried out to simulate the tensile zone of a joint loaded in pure flexure. The headed bars used in the tests were 25 mm in diameter with 70 mm square heads and yield strength of 530 MPa. The tests studied the influences of concrete strength, headed bar spacing, splice length, transverse reinforcement and confining shear studs on joint strength. A lap length of 100 mm in concrete with 28 MPa cylinder strength was found to be sufficient to develop the full strength of the headed bars. A strut-and-tie model (STM) is presented for determining joint strength. Analysis shows that the STM gives safe results even though it does not fully capture the observed joint behaviour. An upper bound plasticity model is found to give relatively good predictions of joint strength in most cases, although it also does not always capture the correct failure mechanism. The tests provide insights into joint behaviour which, in conjunction with numerical modelling, will facilitate the development of an improved design method. Widespread use of this system would lead to improvements in buildability, sustainability and health and safety in the construction of concrete structures. [ABSTRACT FROM AUTHOR]

In this study, a reinforcement detailing approach based on strut-and-tie modeling is presented. This method is mostly preferred instead of conventional methods in order to overcome the calculation and design difficulties at the regions of reinforced concrete (RC) structures where shear effect is dominant. Topology optimization algorithm has been improved from various aspects, integrated with strut-and-tie method and applied on an RC cantilever beam. At the experimental stage of the study, reinforcement layout of test specimens have been designed by conventional method as well as integrated design method and a structural behavior comparison has been performed. Based on the results obtained, it has been concluded that superior results could be achieved for the design of RC structural members and provide convenience to the design engineers by eliminating the experience required in case topology optimization and strut-and-tie methods are applied together. [ABSTRACT FROM AUTHOR]

Mainstream approaches to design spatial architectural forms that are structurally relevant consist either in adapting well-known and catalogued conventional types or in searching for close-to-optimum solutions of well-defined problems. Few means exist to explore structural forms detached from these routines. The approach in this paper generates diverse non-triangulated structural topologies that do not result from optimization procedures. The process incrementally transforms interim networks of bars and forces by means of a parametric policy (–) that maintains the static equilibrium of the network at every single step, (–) that ensures growth of the network within specified (non-)convex geometric boundaries, and (–) whose high-level abstract description controls all design parameters. The successive policy application aims at decreasing the number of interim forces while increasing the number of nodes and bars in compression or tension. The entire process ends when no interim force exists anymore, which is always achievable thanks to the permanence of the static equilibrium condition. From a designer perspective, the approach opens up the generative design black box by providing geometrical and topological control and partial automation of the generation process, while not resorting to common topology patterns – e.g. triangulated bar networks. This paper describes the conceptualization and its implementation into a computational framework, named Policy-based Exploration of Equilibrium Representations (PEER). It illustrates the potential of the approach to unveil unprecedented, unexpected, but statically-valid, structural topologies. Opportunities for further development are eventually discussed. • Generate bar networks in static equilibrium within specified non-convex geometric bounds. • Generation through a parametric policy to allow broader design space exploration. • Policy syntax, incepted and implemented by the authors, integrates static equilibrium. • This integration frees generated networks from equilibrium imposing post-processing. • The policy only considers geometric bounds to generate topologies for any given loads. • The network topology is not known a priori. Generating numerous topologies is the goal. • Generated networks not deemed optimum; rather inspire conceptual structural design. [ABSTRACT FROM AUTHOR]

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A reinforced concrete half-joint beam has a complex geometry that includes both a locally disturbed nib region and a full depth section. While this configuration simplifies the design and construction procedures, half joint structures rely on the internal steel reinforcement to transfer force from the nib into the bulk of the beam. When assessing existing reinforced concrete half-joints, engineers can be confronted with internal reinforcement layouts that do not correspond to the as-designed drawings and/or do not comply with current design practice. Bars may be missing or the location, percentage and spacing of the steel reinforcing bars may be non-compliant. To provide a better understanding of the contribution of the internal steel reinforcing bars found in a typical half joint detail, an experimental test program on full-scale half-joint beams was undertaken. Four different scenarios were tested to identify the impact of specific reinforcing bars. A reference specimen was designed in accordance with existing practice. The reference beam, and beams with either missing diagonal reinforcement, missing horizontal reinforcement or a reduced amount of shear reinforcement were tested. All the beams exhibited nib failures with the exception of the beam where the shear reinforcement was reduced. In this case, the failure mode changed from a nib failure to a full-depth failure. The results indicated that if certain bars are missing the overall load bearing capacity of a half-joint could be approximately 40% lower than that of a properly designed detail, but that a redistribution of forces was noted. [ABSTRACT FROM AUTHOR]

Strut-and-tie modelling constitutes a powerful tool for the design of complex structural reinforced concrete elements. It has been proved numerically that strut-and-tie (ST) models obtained using structural optimization methods produce designs that are more efficient. However, to the best of the authors' knowledge, no experimental evidence of such results has been published. This paper presents experimental results for nine test specimens; five of them were designed using optimal models derived from a full homogenization structural optimization algorithm, and the remaining four using conventional ST models for comparison purposes. Although all specimens carry loads higher than the factored design load, specimens based on ST models derived using full homogenization with reinforcement parallel to the ties exhibit better structural performance regarding crack growth control, more ductile modes of failure and a greater increase in load capacity. [ABSTRACT FROM AUTHOR]

Strut-and-tie modeling involves simplifying the dispersion of compressive stress within a concrete member. In this paper, an experimental study has been conducted to determine the strength of compressed struts and the dispersion of compression in bottleshaped struts focusing on the effect of aspect ratio. Sixteen reinforced concrete isolated struts as plain panels were tested up to failure under in-plane point loading. The tested specimens were prepared with various aspect ratios. The behavior of tested beams was investigated and the dispersion of compressive stresses have been examined and compared with an analytical equation of isostatic lines of compression (ILCs) and the provisions of ACI 318-11. The overall shape formed by strut-and-tie modeling (STM) can be useful for designers to estimate the magnitude of the transverse tensile force and more adequate arrangement of required reinforcement in the various geometrical conditions. The results indicate that the dispersion of compression and the shape of the strut-and-tie model are influenced by the aspect ratio of struts. The angle between strut and maximum tensile stress are closer to the results of investigated analytical method than the angle provided by ACI 318-11. Current ACI 318-11 provisions indicate a constant slope of 1:2 for flow of compressive stress without considering the effect of aspect ratio or geometrical properties of strut. [ABSTRACT FROM AUTHOR]

Strut-and-tie models (STM) have been developed for original and repaired precast reinforced concrete (RC) bridge assemblies tested under quasi-static cyclic loads. The original assemblies, built using accelerated bridge construction techniques, are half-scale column-to-footing and column-to-pier cap specimens connected using grouted splice sleeves. The repaired assemblies are strengthened over the plastic hinge region using a unidirectional carbon fiber reinforced polymer (CFRP) shell, post-installed headed steel bars, and non-shrink concrete. The repair technique was successful and the load and displacement capacities of the damaged assemblies were restored. Generic modeling parameters are established for the STM procedure, enabling the models to be adapted to new repair applications. Special attention is focused on the struts within the CFRP shell. All assemblies are modeled using sectional analysis in conjunction with the predicted STM load to estimate a bilinear force–displacement response. The STM and bilinear force–displacement response envelopes obtained from the models show satisfactory agreement with the experiments of the original and repaired bridge assemblies in terms of initial stiffness, lateral load and displacement capacity. [ABSTRACT FROM AUTHOR]