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Translation abstract Strut‐and‐tie models for indirectly supported structural concrete beamsFor indirectly supported r.c.‐beams it is recommended to place the required hanging up stirrups within the intersection area of both beam webs. This follows from a clear strut‐and‐tie model. However, about 50 years ago it was discussed to partly place stirrups outside this direct intersection area, and this was eventually allowed in codes. Yet, no strut‐and‐tie model was presented for this case, but only detailing rules were given for placing the hanging up stirrups. In the following two variants for strut‐and‐tie models will be presented for this case. The result is that one cannot really talk of distributing hanging up stirrups in regions outside the direct intersection area of the webs, because altogether the triple amount of stirrups is required. [ABSTRACT FROM AUTHOR]

A practical strengthening strategy for nonseismically designed exterior beam–column joints (BCJs) has been proposed by installing an unsymmetrical chamfer on the soffit of the beam. Its feasibility and effectiveness have been validated by extensive experimental studies. In this study, the load transfer mechanism of an exterior BCJ with chamfer is further analyzed to establish an analytical model for joint shear strength. An additional strut is identified in the chamfer based on finite element analysis results, which serves as the secondary load transfer path in addition to the diagonal strut within the joint area. Furthermore, a parametric study was performed to correlate chamfer size with joint shear strength of a strengthened joint. Width of the diagonal strut is enlarged with increasing chamfer size, whereas the effective width of compression zone in the chamfer is limited. With identified load path of BCJ with chamfer, an analytical model is established based on softened strut-and-tie model (STM) which provides clear load transfer mechanism for rational conception design and reasonable join shear estimation, especially for unreinforced BCJs. Width of the diagonal strut, which is the main parameter in a STM, is redefined accounting for contribution of chamfer. Finally, design procedures and recommendations are provided for application of the strengthening strategy in practice. [ABSTRACT FROM AUTHOR]

The layout of the exterior retaining walls and external thermal insulation demands often introduce an eccentricity between the central axes of the beams and columns, leading to what is termed as an eccentric beam-column joint. Such the beam eccentricity is a key factor in shear failures within the joint region. This study addresses the negative impact of beam eccentricity on the shear capacity of reinforced concrete (RC) eccentric beam-column joints. Current research indicates that in the five prevailing shear capacity formulas of RC eccentric joints, adverse effects are primarily accommodated by either reducing the joint's effective width (b j) or implementing an eccentricity influence factor. The study challenges the validity of these approaches by dissecting the impact of singular and interactive factors, including. Eccentricity (2 e / b c), beam-to-column width ratio (b b/ b c), and the column's aspect ratio (h c/ b c). It was observed that while the influence of 2 e / b c is generally well-accounted for, the effects of b b/ b c and h c/ b c are not adequately considered in the Chinese code and ACI-318. Leveraging the softened strut-and-tie model and insights from these examinations, a refined formula for determining the shear capacity of eccentric joints is introduced. This formula incorporates the detrimental effects of beam eccentricity through a newly conceptualized eccentric influence factor, which is a function of both 2 e / b c and b b/ b c. Compared to existing models, this proposed formula also factors in the beam-to-column depth ratio and the longitudinal reinforcement in the middle of column section. Validation against experimental data from 26 eccentric joints demonstrates that the proposed formula yields predictions with the closest proximity to actual test results and the least variability compared to the five established formulas. This approach to considering the effects of e / b c and b b/ b c proves to be slightly more accurate than Zhou's model, making it a promising alternative for practical applications. [ABSTRACT FROM AUTHOR]

This paper presents a numerical parametric study to examine the structural response of drilled shaft footings (pile caps) presenting different design characteristics, which have not been studied in depth in previous experimental studies. The numerical analyses were conducted with nonlinear finite element models representing typical designs and details of actual footings. The modeling scheme was validated using experimental data from large-scale drilled shaft footings. Key parameters of the numerical study included footing geometric properties, concrete strength, and reinforcement ratios. The results of the parametric studies were examined to identify key behavioral and design aspects to be considered when using 3D strut-and-tie models for the design of drilled shaft footings. The analysis results show that influences associated with footing and column aspect ratios were essentially negligible. However, it was estimated that an increase of the angle of inclination between the compression strut and the vertical axis led to significant reductions in footing stiffness and load capacity. The effect of shaft diameter was also examined in light of lateral concrete confining effects, and it was found that larger shaft diameters provide increased footing capacities. Analyses performed to estimate the influence of concrete compressive strength showed that splitting of the strut controlled the concrete-governed failure mechanism of footings. Finally, the models developed with different amounts of reinforcement revealed that increasing bottom mat reinforcement leads to increased ultimate loads; however, the rate of strength increase decreases with increasing reinforcement ratio. Providing a minimal amount of top mat and side face reinforcement was estimated to impact the structural responses of the footings positively; however, increasing the ratios of the top mat and side face reinforcing bars beyond this minimum did not significantly impact footing strength. [ABSTRACT FROM AUTHOR]

This work was conducted first to devise an explicit equation for the ultimate strength of reinforced concrete dapped-end beams failing in diagonal tension caused by re-entrant corner cracks and second to gain insight into its mechanical behavior. To these ends, we introduce force equilibrium equations that explicitly account for the relevant internal force-resisting components: hanger reinforcement; dowel action of longitudinal reinforcement; concrete compression zone; aggregate interlock; and other reinforcement-related terms. These equations are solved within the framework of a constrained optimization problem. The solution process enables us to quantify the ultimate strength and the contributions of all force transfer actions. Strength prediction validity was confirmed through comparisons with experimentally obtained strength data from 50 specimens collected from the available literature. Our findings indicate the prediction accuracy as superior to that of a strut-and-tie model and design provisions of the Precast/Prestressed Concrete Institute. For practical purposes, a minimalist version of the equilibrium equation is derived to estimate the ultimate strength of diagonal tension failure based on rational simplifications of the force transfer mechanisms. [ABSTRACT FROM AUTHOR]

In this paper, a practical method was proposed to predict the shear capacity of steel reinforced concrete (SRC) deep beams based on the simple strut-and-tie model (STM) for ordinary reinforced concrete (RC) members. Two alternatives were provided to consider the effect of encased steel shape. For Alternative 1, the SRC member is divided into two parts: the RC part and steel shape with inner concrete. The contribution of RC part is determined by the simple STM method, while that of steel shape is calculated with a proposed model from available literature. Alternative 2 directly considers the contribution of steel flanges and web to the ultimate strength of struts and tie of the STM. Totally 48 SRC deep beams were collected to evaluate the proposed method as well as the empirical methods from design codes. The results calculated by the selected code methods are overly conservative. The average test-to-predicted shear strength ratio of code methods ranges from 1.66 to 1.68, and the strengths of at most 2.1% of the specimens are overestimated. The prediction performance of Alternative 1 is close to code methods, with an average test-to-predicted shear strength ratio of 1.59. All the predicted results by Alternative 1 are higher than experimental results. Meanwhile, Alternative 2 provides the most accurate prediction with an average test-to-predicted shear strength ratio of 1.35 and an unsafe prediction ratio of 6.3%. Compared to code methods, the prediction accuracy of Alternative 2 is increased by 14% approximately. Furthermore, the influences of considered failure cases and width of horizontal strut for the STM of Alternative 2 were discussed in depth and the design recommendation was put forward. [ABSTRACT FROM AUTHOR]

The reliability of multiprocessor systems is now a crucial concern in parallel computing, which can be characterized as connectivity and diagnosability. The s-extra connectivity (s-EC) κ s (G) of a network G is the minimum number of nodes whose deletion disconnects the network G, and every remaining component has no less than s + 1 nodes. The s-extra diagnosability (s-ED) t s (G) of a network G is the maximum cardinality of faulty nodes that can be identified, given that each remaining component has at least s + 1 nodes. This paper investigates the s-EC and s-ED of the complete cubic network CCN(n). Specifically, we initially demonstrate that the s-EC of CCN(n) is κ s (C C N (n)) = (s + 1) (n + 1) - s (s + 3) 2 for n ≥ 3 and 0 ≤ s ≤ n - 2 . Subsequently, we demonstrate that the s-ED under the PMC model is t s (C C N (n)) = (s + 1) (n + 1) - s (s + 3) 2 + s for n ≥ 3 and 1 ≤ s ≤ n - 2 . Similarly, under the MM* model, the s-ED is t s (C C N (n)) = (s + 1) (n + 1) - s (s + 3) 2 + s for n ≥ 6 and 1 ≤ s ≤ n - 2 4 . Finally, we conduct simulation experiments, and the results indicate that the s-EC consistently surpasses other known connectivities, including classical connectivity and s-component connectivity. Additionally, the s-ED consistently outperforms classical diagnosability and s-component diagnosability of CCN(n). [ABSTRACT FROM AUTHOR]

This paper presents the proposed indeterminate strut and tie (IST) method to analyze fiber-reinforced polymer (FRP)-reinforced concrete deep beams with stirrups. The solution of the IST method does not require the assumption of reinforcement yielding and is capable of reflecting the material nonlinearity of concrete. The essential features of the IST methodology for glass FRP-reinforced deep beams are discussed and then analyzed in detail. These features include modeling concrete compressive response, softening concrete compression behavior in struts, and obtaining the depth of compression nodes. For each of these features, several approaches are discussed. The proposed IST methodology is validated by comparing the analysis results with the experimental results, and recommendations for the most suitable modeling methods are proposed. [ABSTRACT FROM AUTHOR]

Corbels are characterized as low shear span-to-depth ratio (a/d) members that transfer vertical and horizontal loads to adjacent members such as columns or walls. Glass fiber–reinforced polymer (GFRP) reinforcement has linear-elastic behavior and a lower modulus of elasticity relative to steel leading to deeper and wider cracks, which is especially critical for low a/d members. Currently, Canadian bridge and building standards provide strut-and-tie modeling provisions to design steel– and GFRP–reinforced concrete (RC) corbels, but the United States (US) code for GFRP–RC structures prohibits the use of this method for GFRP–RC corbels because of lack of research. Eight full-scale GFRP–RC corbels were constructed and tested to failure. The test variables included main tie and secondary reinforcement ratios, a/d ratio, and concrete strength. The experimental results indicated that a/d and concrete strength have a considerable influence on concrete crack width development, deflection, and load-carrying capacity. The Canadian standard for FRP–RC buildings provided conservative shear capacity predictions for all eight corbels. The US code for steel–RC structures overestimated the shear capacity predictions for seven of the eight corbels, suggesting that revisions are required to better predict the capacity of GFRP–RC corbels. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the shear performance of reinforced concrete corbels and to evaluate the accuracy and safety of the Chinese code GB 50010-2010's triangular truss model and the American code ACI 318-19's strut-and-tie model under various design parameters with a specified design load. A total of 22 corbel specimens with different dimensions and reinforcement configurations were designed and simulated using the finite element software ABAQUS 2020, incorporating the microplane M7 material model, which was validated against experimental data. The findings reveal that for corbels with high-strength concrete or larger shear spans, the Chinese code offers a higher safety margin. Conversely, the safety margin according to the American code initially increases and then decreases with the enhancement of concrete strength, while changes in the shear span have an insignificant impact on the safety margin, which tends to decrease as the shear span increases. Additionally, the inclusion of stirrup reinforcement significantly improves the load-bearing capacity of corbels, with an increase ranging from 15% to 46% compared to those without stirrups. [ABSTRACT FROM AUTHOR]

Hammerhead pier is the preferred option in many bridge sites for its limited ground occupation. Since the bearing reactions act on the short cantilever ends of the cap beam, it is usually treated as stress-disturbed region (D region) in structural concrete. Although finite element model (FEM) can predict the response of such structures, the calculation efficiency will be sharply decreased once it enters nonlinearity. Therefore, strut-and-tie model (STM) has been promoted as an alternative approach for analyzing D regions. In this study, a loading pattern was defined to relate the axial force and bending moment of the pier column with the eccentric load ratio. Sectional analysis method and associated codes were developed to generate the STM. In addition, a full-scale hammerhead pier specimen subject to varying eccentric loads was tested. Besides, nonlinear FEM was also established to numerically investigate the response of the pier. The results indicate that the proposed STM has general applicability for modeling the hammerhead pier and shows better prediction than the FEM. The failure pattern of the hammerhead pier with a prefabricated cap beam was defined. Combining the mechanical analysis of STM and experimental results, the recommended design details for hammerhead piers were proposed. [ABSTRACT FROM AUTHOR]

Modelling the volatility of commodity prices and creating more reliable models for estimating and forecasting commodity price returns are crucial. The body of research on statistical models that can fully reflect the empirical characteristics of commodity price returns is lacking. The main aim of this research was to develop a modelling framework that could be used to accurately estimate and forecast commodity price returns by combining long memory models with heavy-tailed distributions. This study employed dual hybrid long-memory generalised autoregressive conditionally heteroscedasticity (GARCH) models with heavy-tailed innovations, namely, the Student-t distribution (StD), skewed-Student-t distribution (SStD), and the generalised error distribution (GED). Based on the smallest forecasting metrics values for mean absolute error (MAE) and mean squared error (MSE) values, the best performing LM-GARCH-type model for lithium is the ARFIMA (1, o , 1)-FIAPARCH (1, ξ , 1) with normal innovations. For tobacco, the best model is ARFIMA (1, o , 1)-FIGARCH (1, ξ , 1) with SStD innovations. The robust performing model for gold is the ARFIMA (1, o , 1)-FIGARCH (1, ξ , 1)-GED model. The best performing forecasting model for crude oil and cotton returns are the F I A P A R C H   1 , ξ ,   1 − S S t D model and H Y G A R C H   1 , ξ ,   1 − S t D model, respectively. The results obtained from this study would be beneficial to those concerned with financial market modelling techniques, such as derivative pricing, risk management, asset allocation, and valuation. [ABSTRACT FROM AUTHOR]

This study presents a seismic design methodology for precast concrete column-to-pile shaft member socket connections. In designing such connections, the intent was to ensure that the plastic hinge occurs in columns while minimizing the damage to the pile shaft. To achieve this, a strut-and-tie model was developed to represent the force transfer mechanism within the connection region; this model served as the basis for efficient seismic design details, including shaft transverse reinforcement, column embedment length, and shaft size. The predictive accuracy of the strut-and-tie model was validated against both the experimental and finite-element analysis results for a wide variety of connection features. Upon validation, the strut-and-tie model was integrated into a step-by-step seismic design procedure and a case study was conducted to demonstrate the effectiveness of these procedures for determining suitable connection design details. Finally, a computer application with a graphical user interface was developed for the ease of implementation of the strut-and-tie model and reliable interpretation of its analysis results, making it possible to be used routinely in seismic design practice for precast column-to-pile shaft assemblies. [ABSTRACT FROM AUTHOR]

The verification of dapped‐end beams degraded by corrosion is a problem, especially for existing bridges in service. This paper proposes a nonlinear finite element (NLFE) modeling procedure and a simple strut‐and‐tie based procedure for predicting the response of dapped‐end beams subjected to chloride corrosion. Firstly, the finite element modeling strategy, based on the adoption of multilayer shell elements and the PARC_CL 2.1 crack model is described. Then, the degradation effects on concrete, rebars, and steel‐to‐concrete interaction are defined as a function of the propagation period of corrosion. In particular, the effects of corrosion on the reinforcement are modeled by applying a reduction of tensile strength that considers for both the reduction of cross‐section and the ultimate strain caused by pitting. Concrete splitting cracking due to volume expansion during rust formation is modeled by reducing the mechanical properties of concrete. Corrosion effects in steel‐to‐concrete interaction are modeled by applying a bond strength decay to the spring elements connecting corroded rebars—modeled with truss elements—and concrete multilayer shell elements. The proposed finite element procedure is used to study two scenarios based on different spatial distributions of corrosion‐prone areas. Subsequently, a simplified analytical approach based on the strut‐and‐corroded tie method—called S&CT method—is proposed and compared with the finite element outcomes. Finally, the validations of the two proposed methods are presented with respect to a corroded dapped‐end beam, showing that corrosion of rebars affects the resistance mechanisms of the dapped‐end beam, by reducing both resistance and ductility. The proposed simplified analytical S&CT method provides conservative and safe results compared to the numerical NLFE model and to experimental data. [ABSTRACT FROM AUTHOR]

Three scale models of prefabricated piers were designed and manufactured to investigate the impact of staggered longitudinal reinforcement—ultra-high performance concrete (UHPC) connections on seismic performance. The failure modes, hysteresis curves, backbone curves, ductility, stiffness degradation, and energy dissipation capacity of each model were compared and analyzed through quasi-static testing and numerical simulation. The test results demonstrate that the precast assembled pier, incorporating staggered longitudinal reinforcement-UHPC connections, exhibits high bearing capacity and stiffness, effectively enhancing its overall and seismic performance during the early and middle stages; The primary factor contributing to the bond failure of staggered longitudinal reinforcement is the cracking and spalling of UHPC, which directly impacts the ductility and energy dissipation capacity of piers. This paper establishes a prediction formula for the horizontal peak bearing capacity of compression-bending failure piers, based on the strut-and-tie model. The formula takes into account the strength of the staggered longitudinal reinforcement-UHPC connection area, the staggered spacing of the longitudinal reinforcement, the spacing of the stirrups, and the axial compression ratio. By variable parameter analysis and a comparative assessment with the ACI318-19 standard formula, it is evident that the formula proposed in this paper demonstrates desirable accuracy and applicability, offering valuable guidance for the seismic design and structural optimization of prefabricated piers. [ABSTRACT FROM AUTHOR]

In this study, seismic bi–axially loaded RC beam–column joints are investigated. An experimental campaign on shear–critical corner joints is presented, including two as–built specimens and one retrofitted using fully–fastened–haunches (FFHR). Bi–axial tests adopted hexagonal protocol which is essentially to apply load in one direction double with respect to the other. Results obtained for as–built condition were included in a database of corner joints tested bi–axially and discussed in the light of the impact of bi–axial load on joint's shear strength. Further, non–linear finite elements were employed to thoroughly evaluate the bi–axial response. Haunch retrofit was capable to reduce both shear stresses and distortion at joint. Experimentally–derived internal forces were used to validate three–dimensional Strut-and-Tie model of the joints. Such design tool is recommended for practice cases adopting FFHR. [ABSTRACT FROM AUTHOR]

The strength of prestressed steel strands has developed towards high strength, increasing from 1860 MPa to over 2200 MPa. The stress in the prestressed anchorage zone is more concentrated and complex, and the anchor plates for dispersed loads need to be optimized in design. This article proposes a design scheme for adding a middle pressure-bearing step based on the existing anchor plate and then establishes a 1/4 model of the concrete anchoring area of the anchor plate for finite element analysis. Based on the theory of the strut-and-tie model, the position of the middle pressure-bearing step is determined according to the maximum angle of the strut-and-tie model. Then, carry out force transfer tests in the anchorage zone for verification. The research results indicate that after adding a middle pressure bearing step to the anchor plate, the angle between the strut-and-tie model in the anchorage zone increases, and the bearing capacity improves. The position of the middle pressure-bearing step in the anchor plate is different, and the angle between the strut-and-tie models is different. According to the middle step position parameter, λ (the ratio of the effective width of the middle step to the distance from the middle step to the end face of the anchor plate) is 0.533 to optimize the anchor plate, and the bearing capacity of its anchorage zone is relatively high. The main tensile and main compressive stresses of the anchor plate after optimization increased by 6.2% and 5.74%, respectively, compared to the anchor plate before optimization. The main tensile stress of the spiral reinforcement under the anchor plate decreased by 0.59%, the main compressive stress decreased by 2.89%, and the von-Mises stress decreased by 2.32%. The side surface tensile stress of concrete under the anchor plate was reduced by 4.3 percent. Finally, three concrete specimens were poured for force transfer testing in the anchorage zone, verifying the safety and reliability of the optimized anchor plate in the 2200 MPa-level prestressed anchorage zone. [ABSTRACT FROM AUTHOR]

The present contribution addresses both the topics of the design of timber-to-timber joints and the design of innovative and structurally efficient timber structures with the aid of a computational tool based on vector-based graphic statics (VGS). First, this manuscript explains how the latest developments of graphic statics and its use applied to both timber joints and structures can improve the design of structures made of this low embodied carbon material. An exhaustive review of timber assemblies focussing on their sustainability and their structural behaviour is presented. Among these is the notch joint specifically identified in the context of digital fabrication and circular use of timber. Afterwards, the theoretical framework of this research is explained. Taking advantage of the lower bound theorem of the theory of plasticity, the main hypotheses that enable the use of graphic statics and strut-and-tie modelling (STM) for timber are then presented. In addition, the structural behaviour of the single notch joint is evaluated using algebraic dimensioning method. The limitations of this method are pointed out and the article proposes an integrated universal approach to investigate the problem using Strut and Tie Modelling (STM) and stress fields. The results of this theoretical framework are validated trough 1/1 scale lab tests. Finally, the third chapter illustrates the potential of VGS via a Research-by-Design approach. In the aim of testing if designing simultaneously creative and efficient timber structures could be effective while using the VGS, architectural engineering student were asked to focus on both the primary load-bearing structure and the joint-systems. [ABSTRACT FROM AUTHOR]

In this paper, the shear behavior of concrete beams reinforced with FRP stirrups is studied. The shear performances of six concrete beams with a size of 150 mm × 300 mm × 3000 mm under four-point loading up to failure were experimentally analyzed. The critical parameters included the shear span to depth ratio (λ) and stirrup spacing (S). The test results revealed that as λ increased from 1 to 2, 3, and 4, the ultimate shear capacity of the beam decreases by 50.5%, 67.7%, and 69.2%, respectively. Meanwhile, as S increased from 100 mm to 150 mm and 200 mm, the ultimate shear capacity decreased by 16.1% and 44.6%, respectively. A new shear capacity calculation model of concrete beam reinforced with FRP stirrups was also proposed, which further considered the shear capacity of the FRP stirrups on the basis of the shear capacity of an RC beam without stirrups using the strut-and-tie model. Finally, the experiment and calculation results of 56 beam specimens reinforced with FRP stirrups extracted from this paper and previous studies were compared using the calculation models proposed in this paper, in order to evaluate the accuracy of these calculation models. [ABSTRACT FROM AUTHOR]

Vertical openings in beams and girders are sometimes used to facilitate the passage of essential services such as HVAC, electricity, and sewage. There is a lack of research on the effects of vertical openings on deep reinforced concrete beams. In this work, 11 RC deep beams were tested to failure, examining key parameters, namely, location of opening, opening shape, and strengthening technique around the opening. The beam ultimate load (Pu) and to a lesser extent stiffness were found to be affected by the presence of openings, wherein those located in the shear span reduced Pu by 12%–19% and those in the constant-moment region contributed to a respective decrease of 8%–13%. The reduction in Pu is also related to the opening shape with rectangular and circular shapes, resulting in the largest and smallest decrease, respectively, and square being in the middle. Two techniques were proposed to mitigate the openings effects, namely, using ultrahigh-performance concrete (UHPC) in the vicinity of the opening, and reinforcing the surrounding opening area with horizontal and vertical steel bars. Both were found effective, with the former resulting in 14% and 10% increase in Pu relative to beams with openings located in the shear and moment regions, respectively, and no strengthening. Additionally, Pu from tests were compared with those calculated using the strut-and-tie model (STM) and an empirical formula from current US standards. Modifications to the STM model, which resulted in better predictions than the expression from current standards, but still needed improvement, were presented, and resulted in an analytical-to-experimental Pu ratio of 0.99 to 1.05. [ABSTRACT FROM AUTHOR]

The present study proposes a novel yet straightforward method for calculating the bearing capacity of deep beams using the theory of lower-bound limit analysis. The equations of the proposed method are obtained from the evaluation of the stresses induced in concrete and reinforcements of deep beams. The modified Mohr-Coulomb yield criterion is utilized to constrain the concrete stress states. Because the proposed method and relevant equations are simple and noniterative, they can be easily employed for design purposes. Moreover, the equations can be applied to beams with and without shear reinforcement. However, the method is limited to deep beams with rectangular cross sections and without openings. In order to assess the accuracy of results, the shear strengths of deep beams obtained by the proposed method are compared with experimental results and the results obtained by the strut-and-tie model. The evaluations of 225 tested deep beams show that the mean ratio of calculated strength to the strength obtained from the test result is 0.94, and the coefficient of variation is 0.22. The variations in results of the proposed method are also investigated for various components, such as the compressive concrete strength, the shear span-to-depth ratio, and the reinforcement ratio. This study shows that the trend of changes in the strength of a deep beam with respect to these components agrees with experimental results. The simplicity of the method is illustrated by an example. [ABSTRACT FROM AUTHOR]

Within the research project ITSAFE, two full-scale structures were built, one consisting of a single-storey, two-span, 7.00 × 14.00 m2 RC frame with a solid slab and another consisting of a two-storey, 7.00 × 7.00 m2 RC frame with solid slabs. In the two-span frame, one of the central supports was first demolished using a pneumatic hammer, resulting in rather limited damage (a 14–15 cm deflection at the removed support location). However, torsional cracks appeared at the interface between a column and slab in one of the outer supports. When the second central support was removed, the structure collapsed with the failure of the support–slab connection. The same type of cracking was observed in the two-storey structure, where the column removal was dynamic, and a 22 cm deflection was measured. These experimental results question current practice in which, for internal supports, alternative load path mobilizing membrane forces in the slab are said to prevent their collapse, or in the cases of edge and corner columns, rupture line analysis is used and suggests that special reinforcement at the column–support connection is also needed to prevent the premature failure of the structure. [ABSTRACT FROM AUTHOR]

In the paper, an innovative shear wall, which is referred to as steel fiber reinforced concrete (SFRC) shear wall with concrete filled steel tube (CFST) columns, is introduced, based on the high bearing capacity and large stiffness of concrete filled steel tube column (CFSTC) and good cracking resistance and strong toughness of steel fiber reinforced concrete. The loading mechanism of steel fiber reinforced concrete shear wall (SFRCSW) with concrete filled steel tube columns is analyzed, and shear bearing capacity calculation method. A simplified model of the steel fiber reinforced concrete shear wall web softening tension bar is proposed, concrete and distributed web reinforcement to the shear bearing capacity of steel fiber reinforced concrete shear wall web is identified. Furthermore, a new algorithm to obtain the shear bearing capacity of steel fiber reinforced concrete shear wall with concrete filled steel tube columns is established, and then it is validated by using the test results of steel fiber reinforced concrete shear wall with concrete filled steel tube columns under low-cycle repeated loading. The results showed that all tested shear wall specimens exhibited obvious shear failure characteristics and a typical diagonal cracking pattern after test. The steel fibers obviously improved the crack forms of the steel fiber reinforced concrete shear wall web and the seismic behavior of steel fiber reinforced concrete shear wall with concrete filled steel tube columns. In addition, the proposed calculation method is scientific and accurate to analyze and predict the shear bearing capacity of low-rise steel fiber reinforced concrete shear wall with concrete filled steel tube columns. [ABSTRACT FROM AUTHOR]

Reinforced concrete beams reinforced with Fiber Reinforced Polymer (FRP) have several failure patterns, one of which is Concrete Cover Delamination. To prevent this failure, in this study, FRP U-Wrap was installed which was calculated using Strut and Tie Modelling (STM). The specimens of reinforced concrete beams with a length of 3300 mm, a width of 300 mm, and variations in height of 500, 600, and 700 mm were loaded with the two-point load method. Data collection and analysis was carried out using Digital Image Correlation, LVDT, strain gauge, and data logger. The bending behaviour reviewed in this study is ductility, crack pattern, type of failure, flexural capacity, and stiffness. In this study, the addition of U-Wrap did not have a significant effect on flexural behaviour when compared to beams without U-Wrap FRP. All beams experienced a failure pattern of FRP Debonding, so that the Concrete Cover Delamination did not occur. [ABSTRACT FROM AUTHOR]

In this paper, the loading mechanism of steel-fiber-reinforced concrete (SFRC) shear wall (SW) under low-cycle repeated loading is analyzed, and the softened strut-and-tie model (SSTM) of SFRC SW composed of horizontal and vertical resistant members and diagonal strut is proposed, in which the contributions of distributed web reinforcement, concrete, and steel fiber (SF) to the shear bearing capacity (SBC) of SFRC SW is identified. Furthermore, a new algorithm to obtain the SBC of SFRC SW is established, and then it is validated by using the test results of steel-fiber-reinforced high-strength concrete (SFHSC) SW and SFRC SW under low-cycle repeated loading. The results show that the calculated values are in good agreement with the experimental values for the 11 SFRC SWs, and the average strength ratio between calculated and experimental values (Vjh,t/Vjh,c) is 0.958. Therefore, the proposed calculation method is scientific and accurate for analyzing and predicting the SBC of SFRC SW. In addition, the proposed calculation method can scientifically and accurately analyze and predict the SBC of SFRC SW. [ABSTRACT FROM AUTHOR]

Reinforced concrete flat-plate systems are widely adopted in buildings owing to ease of construction and facilitating larger clear story heights. Flat plates are routinely designed for two-way shear to preclude brittle punching failures. Accurate assessment of concrete contribution to shear strength is particularly important for flat plates in carrying out a reliable and economical design. To address this, an efficient analytical method based on the softened strut-and-tie model to estimate punching capacity of flat plates without shear reinforcement under gravity loading is presented. The proposed method can account for the influence of various key parameters such as concrete strength, plate thickness, column geometry, longitudinal reinforcement area, and arrangement of tension reinforcement. The proposed method, when verified against data from 224 specimens reported in the literature, showed reasonably good accuracy with a mean test-to-estimated capacity ratio of 1.20 and a coefficient of variation (CoV) of 0.19. In comparison, average capacity ratios using ACI 318-19 and Eurocode 2 provisions were 1.60 and 1.27 (CoV of 0.34 and 0.29), respectively. A comprehensive discussion on the effects of key parameters on punching behavior of flat plates without shear reinforcement is presented, and suggestions to improve existing design provisions are provided. [ABSTRACT FROM AUTHOR]

With the reliance on ocean resources, the nuclear power powers have set their sights on marine nuclear power plants to break through the bottleneck of energy supply for the development of ocean resources. In this paper, the computational fluid dynamics software ANSYS CFX 2021 is used to simulate the TOSQAN benchmark experiment. Three different turbulence models, the k − ε model, R N G   k − ε model, and S S T model, are selected to analyze the adaptability of the turbulence model. The simulation results are compared with the benchmark experimental results, and the selected numerical calculation model is used to analyze the influence of vapor on the pressure, temperature, hydrogen distribution, and hydrogen risk in the containment space when a hypothetical serious accident occurs in a marine nuclear power plant. The results show that the results simulated with the k − ε turbulence model are closer to the benchmark experimental results. Vapor has no obvious effect on the response speed of pressure balance at each position in the closed containment space, and the condensation of the vapor wall can effectively reduce the pressure peak in the closed containment space. The existence of vapor and the increase in vapor concentration will increase the temperature in the closed containment space. The condensation of vapor on the wall surface will cause the temperature in the containment space to have a peak value, which can effectively reduce the temperature in the containment space. Vapor will promote the mixing of gas in the containment space and make the hydrogen distribution tend to be uniform. The presence of vapor and the increase in vapor concentration can reduce the hydrogen risk in the containment space, but the condensation of vapor may increase the hydrogen risk in the containment space. [ABSTRACT FROM AUTHOR]

The reinforcing steel bars embedded in the concrete of a reinforced concrete (RC) structure in a region with high airborne chloride concentrations may corrode. To avoid overestimating the seismic capacity assessment, it is necessary to understand the residual shear strength of an RC frame with infilled wall and localized corrosion. This work investigates the residual shear strength of an RC frame with infilled wall and localized corrosion by designing five wall specimens with corroded reinforcing steel bars to obtain the residual shear strength of each RC frame with infilled wall with different corrosion zones. Additionally, a model based on the softened strut-and-tie model is proposed to determine the residual shear strength of an RC frame with infilled wall and localized corrosion. The experimental and calculation results are compared to verify the application of the proposed model for the shear strength of an RC frame infilled corroded RC wall. [ABSTRACT FROM AUTHOR]

Timber has long been extensively employed within the construction industry as a famous, environmentally friendly, and low-carbon material. Considering that construction constitutes one of the most significant contributors to carbon emissions throughout the entire life-cycle of a building, there is an urgent desire to incorporate timber into this domain. Nevertheless, the use of timber faces inherent challenges stemming from its anisotropic nature, a result of the natural growth of timber fibers, which makes it challenging for it to function as a primary load-bearing material in coping with the various complex stresses inherent in architectural applications. Numerous designers have attempted to address this limitation through over-sized members and reinforcement at joints; however, none have satisfactorily resolved this issue in an economical manner. In this article, we introduce the Strut-and-Tie models (STM) from Graphic Statics (GS) and a topological optimization algorithm. This algorithm has the capability to generate a 'load-minimizing path' STM based on external load support conditions and the maximum structural path span. Regardless of the complexity of the initial external loads, each load transfer path in the optimized STM bears loads in only one direction, representing an optimal solution with minimal internal loads that align seamlessly with the characteristics of timber. Consequently, we endeavor to adopt this optimization algorithm to propose a structural design methodology, with the aspiration of designing structural systems that harness the unique attributes of timber perfectly and applying them to various architectural scenarios. Ultimately, we conclude that structural systems designed based on optimized STM are adaptable to diverse architectural contexts, and when applied to small-scale buildings, this method can save approximately 20% of material consumption compared to conventional timber frame structures, while in the case of mid-rise to high-rise buildings, it can lead to a material savings of approximately 5%. [ABSTRACT FROM AUTHOR]

For the shear strength of deep beams, most of current design codes adopt the strut-and-tie model. However, since the shear resistance mechanism of deep beams is quite complicated and shear failure could be catastrophic with no prior warning, more reliable and robust shear strength prediction models are required. To this end, in the present study, using the extreme gradient boosting (XGBoost) and Bayesian optimization (BO) algorithms, a BO-XGBoost hybrid model was developed and its hyperparameters were optimized based on a database of 320 test specimens. The prediction accuracy of the proposed BO-XGBoost hybrid model was compared with G-XGBoost (with hyperparameters tuned by grid search), R-XGBoost (with hyperparameters tuned by random search), D-XGBoost (with default hyperparameters), and existing design equations, and the comparison showed that the proposed model can predict most accurately the shear strength of deep beams without any significant and evident bias. The parametric study using the proposed model revealed that the effective depth, beam width, shear span-to-depth ratio, tension reinforcement ratio, and concrete compressive strength are critical to the shear strength of deep beams. For ease and convenience of the utilization of the proposed model, a stand-alone application program was also developed. [ABSTRACT FROM AUTHOR]

Concrete half-joint beams (HJB) are characterised by local reductions in the overall beam depth at the support and are ideal for structural connections. However, the beam joint region is vulnerable to deterioration and design/detailing shortcomings. Non-linear numerical modelling of the behaviour of a series of impaired reinforced concrete HJBs was conducted in this study. The major defects considered were unavailability of diagonal bars/U bars, shear reinforcement inadequacy and reinforcement corrosion. The numerical simulations captured global and local behaviours of the beams. The load capacity prediction discrepancy was in an impressive range of −16.7% to +1.5%, in contrast to the predictions of the commonly used strut-and-tie model in the range of −39.2% to 16.9%. Subsequently, an experimental study was established using finite-element modelling to explore the retrofitting potential of defective HJBs using the deep embedment (DE) technique. The strength enhancement was almost 30% and the internal load paths and the failure mode of the defective beam were favourably altered with the post-installation of the retrofitting element. The DE technique was thus identified as an ideal option for the retrofitting of impaired HJBs. [ABSTRACT FROM AUTHOR]

Based on the experimental results, this paper investigates the shear mechanism of reinforced concrete deep beams without stirrups. By analyzing the kinematics of the critical shear crack, it can be found that the compression of concrete above the critical shear crack causes the crack sliding and that the combined action of the elongation of longitudinal reinforcement and the compression of concrete above the critical shear crack causes the crack opening. Based on the new-found crack kinematics and test data, the aggregate interlock force is calculated by two methods. The dowel action is also calculated. The results reveal that the shear forces transmitted by the aggregate interlock and the dowel action are relatively small, ranging from 0.5% to 9.2%. The uncracked concrete in the compression zone provides the primary resistance. Both the aggregate interlock and the uncracked concrete in the compression zone can cause a size effect. But because of the small proportion of the aggregate interlock, the size effect of shear strength is mainly caused by the size effect of uncracked concrete in the compression zone. A modified strut-and-tie model (STM) is established based on the shear mechanism found in the test. It considers the size effect using the modified size effect law. The modified STM is evaluated by comparing the calculation results with the experimental results of 194 beams. It is shown that the prediction of the modified STM is more accurate than those of the other five models, with a mean value of Vu/Vu,cal of 1.01 and a coefficient of variation value of 0.22. The proposed model well captures the effect of the shear span-to-effective depth ratio and the size effect on the shear strength. The modified STM reflects the actual shear transfer mechanism of deep beams without stirrups and has the advantages of simple calculation and accurate prediction. [ABSTRACT FROM AUTHOR]

This was followed by a special Felicitation session honouring IABSE Honorary Members Prof. S.S. Chakraborty and Dr. B.C. Roy (due to illness, his memento was handed over to Mrs. Dr Roy) and IABSE Vice-President, Dr H. Subbarao. B I Pre-Congress Meetings, Workshop and Congress, 18-22 September 2023 i b Graph The IABSE New Delhi Congress 2023 concluded successfully, attracting over 500 participants from 37 countries. Additionally, the ING-IABSE presented a I "Certificate of Acknowledgement" i to recognise the significant contribution of the OC Chair, Mr. PVVSS R. Prasad and IABSE President Dr. T. Vejrum. [Extracted from the article]

The development of strut-and-tie models (STMs) for the design of reinforced concrete (RC) deep beams considering a general multi-material and multi-volume topology optimization framework is presented. The general framework provides flexibility to control the location/inclination/length scale of the ties according to practical design requirements. Optimality conditions are applied to evaluate the performance of the optimized STM layouts. Specifically, the Michell number Z (or load path) is used as a simple and effective criterion to quantify the STMs. The experimental results confirm that the layout with the lowest load path Z achieves the highest ultimate load. Moreover, significantly reduced cracking is observed in the optimized layouts compared to the traditional layout. This observation implies that the optimized layouts may require less crack-control reinforcement, which would lower the total volume of steel required for the deep beams. [ABSTRACT FROM AUTHOR]

This paper presents the technical causes of the collapse of the Annone overpass, a reinforced concrete half-joint bridge built in the early 1960s in northern Italy, occurred in October 2016. This work provides a detailed description of the geometry of the bridge and its conceptual design, highlighting the differences between the original design and the as-built situation. The condition of the bridge before the collapse and the event that triggered the collapse are also described. The paper highlights the critical issues occurring concurrently with the passage of a heavy truck. After a brief presentation concerning the characterization of the materials (concrete and steel), the work presents strut-and-tie models for the estimation of the ultimate capacity of the half-joints, which are considered to be the critical point of the entire structure. The strut-and-tie models are validated through comparison with experimental data obtained by testing a half-joint extracted directly from the bridge after collapse. The structural behavior of the bridge, the assessment of its safety, and the reasons that led to the collapse of the structure are also discussed through the use of simplified linear elastic and nonlinear finite-element models. Some weak points of the national infrastructural managing system, mainly referring to exceptional transports, are also discussed. The study highlights the methods that could be used to prevent future accidents in the absence of macrodesign mistakes and the main lessons learnt. [ABSTRACT FROM AUTHOR]

To improve the seismic behavior and thermal property of traditional cold-formed steel (CFS) walls for satisfying the requirements multistory structures, a new type of fiber-reinforced lightweight concrete (FLC)-filled CFS shear wall strengthened using horizontal reinforcement is proposed in this study. Four full-scale specimens were tested under reversed cyclic loading to investigate the seismic behavior, including failure mode, hysteresis curve, shear capacity, deformability, stiffness degradation, and energy-dissipating capacity. Test results indicated that the restrictive effect of FLC on the studs and its diagonal-bracing effect improved the wall's hysteretic behavior, making the wall exhibit the ductile shear failure. Increasing the wall thickness increased the shear strength, lateral stiffness, and energy-dissipating capacity, whereas installing the coupling-section interior studs enhanced the ductility. Finally, a simplified strut-and-tie model was proposed to evaluate the shear capability of FLC-filled walls, and the calculated values exhibited good agreement with the test results, but the further verification is required. [ABSTRACT FROM AUTHOR]

As a transfer member at the discontinuous place of vertical load, the deep beam has a complex stress mechanism and many influencing factors, such as compressive strength of concrete, shear span ratio, and reinforcement ratio. At the same time, the stress analysis principle of traditional shallow beams is no longer applicable to the design and calculation of deep-beam structure. The main purpose of this paper was to use the strut-and-tie model to analyze its stress mechanism, and to verify the applicability of the model. Nine high-strength concrete deep-beam specimens with longitudinal reinforcement with an anchor plate of the same size were tested by two-point concentrated loading method. The effects of shear span ratio (0.3, 0.6, and 0.9), longitudinal reinforcement ratio (0.67%, 1.05%, and 1.25%), horizontal reinforcement ratio (0.33%, 0.45%, and 0.50%), and stirrup reinforcement ratio (0.25%, 0.33%, and 0.50%) on the failure mode, deflection curve, characteristic load, crack width, steel bar, and concrete strain of the specimens were analyzed. The results showed that the failure mode of deep-beam specimens was diagonal compression failure. The normal section cracking load was about 15 to 20% of the ultimate load, and the inclined section cracking load was about 30~40% of the ultimate load. The shear span ratio increased from 0.3 to 0.9, and the bearing capacity decreased by 32.9%. When the longitudinal reinforcement ratio increased from 0.67% to 1.25%, the ultimate load increased by 42.6%. The shear span ratio and longitudinal reinforcement ratio have a significant effect on the bearing capacity of the high-strength concrete deep beams with longitudinal reinforcement with an anchor plate. The shear capacity of nine high-strength concrete deep-beam specimens with longitudinal reinforcement with an anchor plate was calculated by national standards, and the results were compared with the calculation results of the Tan–Tang model, the Tan–Cheng model, SSTM, and SSSTM. The analysis showed that the softened strut-and-tie model takes into account the softening effect of compressive concrete, and is a more accurate mechanical model, which can be applied to predict the shear capacity of high-strength concrete deep-beam members with longitudinal reinforcement with an anchor plate. [ABSTRACT FROM AUTHOR]

Reinforced concrete corbels were examined in this study for the cracking behavior and strength evaluation, focusing on defects typically found in these structures. A total of 11 corbel specimens were tested, including healthy specimens (HS), specimens with lower concrete strength (LC), specimens with less reinforcement ratio (LR), and specimens with more concrete cover than specifications (MC). The HS specimens were designed using the ACI conventional method. The specimens were tested under static loading conditions, and the actual strengths along with the crack patterns were determined. In the experimental tests, the shear capacity of the HS specimens was 28.18% and 57.95% higher than the LR and LC specimens, respectively. Similarly, the moment capacity of the HS specimens was 25% and 57.52% greater than the LR and LC specimens, respectively. However, in the case of the built-up sections, the shear capacity of the HS specimens was 9.91% and 37.51% higher than the LR and LC specimens, respectively. Likewise, the moment capacity of the HS specimens was 39.91% and 14.30% higher than the LR and LC specimens, respectively. Moreover, a detailed nonlinear finite element model (FEM) was developed using ABAQUS, and a more user-friendly strut and tie model (STM) was investigated toward its suitability to assess the strengths of the corbels with construction defects. The results from FEM and STM were compared. It was found that the FEM results were in close agreement with their experimental counterparts. [ABSTRACT FROM AUTHOR]

The construction of strut‐and‐tie models (STMs) is the key, but also the difficulty when the model is used to describe the force mechanism and guide the reinforcement layout design of concrete disturbed regions (D‐regions). Topology optimization is a promising way to guide STMs construction. Different from the existing construction methods of predetermining nodes, the angle of inclination of the truss elements is first determined to ensure that it is consistent with that of the principal stresses in a 2D finite element model of the structure. The constructed model can well reflect the force transmission path of structural members, and it is better than the existing methods when it is evaluated through the principle of minimum strain energy. To verify the validity of the STM, a reinforcement layout scheme is adopted completely according to the position of the tension ties. On this basis, another reinforcement layout scheme adds additional transverse reinforcements in the bottle‐shaped stress field. The nonlinear finite element comparative analysis of an irregular deep beam designed by the two schemes is carried out. The results show that the two ultimate loads are close. Brittle failure occurs in the former, while the latter has higher deformability and eventually ductile failure occurs. [ABSTRACT FROM AUTHOR]

The fanning compression stress pattern in RC deep beams under uniform load presents a challenge to formulating the configuration of strut‐and‐tie model (STM). To this end, this paper proposes an alternative method for creating a graphical discontinuous stress field model (DSFM) to fill up the whole beam continuum. It comprises a certain number of trapezoidal stress‐bands with varying bandwidths, and their stress values can be calculated based on force equilibrium conditions. Several stress subfields are defined through a certain stress combination from several directions. The DSFM is implementable for both service limit state (SLS) and ultimate limit state (ULS) in that its configuration is primarily oriented by elastic stress field and only a limited plastic redistribution is allowed for plastic failure. The graphical procedure of DSFM is demonstrated and examined by a test deep beam example, which shows that the predictions are fairly in good agreement with the test results. [ABSTRACT FROM AUTHOR]

The design of reinforcement of concrete pylons in cable‐stayed bridges is a challenging task. Usually, only the influence of the strong horizontal component of the cable force is considered during the reinforcement design of the concrete tower, while the bursting forces caused by the vertical components of the cable forces are ignored. However, the latter is also an important factor for concrete cracking in bridge towers. In this paper, the concrete tower of a single cable plane cable‐stayed bridge is considered. The strut‐and‐tie model (STM) of the pylon wall subject to the vertical components of one single cable force was derived. Based on the minimum strain energy principle, an equation for predicting the bursting force was given. Then, the STMs of a concrete pylon with two cable forces with different vertical distances between cables were proposed. A series of equations for predicting the bursting force in different STMs were presented. The STMs of a concrete pylon with multiple cables were subsequently obtained from the STM for two cable forces. The analysis results show that the vertical distance between cables has a great influence on the STM configuration of the tower. When the cable distance is less than 0.7 times the width of the tower wall, the bursting force is larger than that when the cable distance is larger than 0.7 times the width of the tower wall. This study was expected to provide a reference in the design and applications of pylons of concrete cable‐stayed bridges. [ABSTRACT FROM AUTHOR]

In this study, ultrahigh-performance concrete (UHPC) was utilized in precast segmental beams to reduce the self-weight, shorten the construction time, and improve the performance and durability of bridges. Owing to the discontinuity in the joints, shear behavior plays a critical role in the overall structural performance of precast UHPC segmental beams (PUSBs). Therefore, four dry-jointed segmental specimens along with one monolithic specimen were designed and tested under a two-point concentrated load with various joint types, shear span-to-depth ratios (λ), and numbers of shear keys. Two types of shear failure modes were observed in the tests: shear compression failure of the web (λ = 1.44 and 2.56) and local shear failure of the flanges at the joint (λ = 3.67). The shear capacity, stiffness, and cracking load of the dry-jointed segmental specimens were lower than those of the monolithic specimen, and the single-keyed specimen exhibited better shear behavior than the three-keyed specimen. Increasing λ decreased the shear strength and stiffness of the segmental beams and considerably affected their failure modes and crack distributions. Additionally, four UHPC design codes were evaluated for their accuracy in estimating the shear strength of the specimens, and a simplified strut-and-tie model was developed to predict the shear strength of externally pre-stressed PUSBs. Finally, several design recommendations were proposed. This study is expected to facilitate the research and application of PUSBs. [ABSTRACT FROM AUTHOR]

This paper investigates the effectiveness of engineering cementitious composites (ECC) thin layers for seismic strengthening of reinforced concrete (RC) short walls with high axial load ratios. Three RC short walls with an aspect ratio of 1.1 were tested under cyclic loading: one control wall and two ECC strengthened walls, adopting two different strengthening layer schemes. The results showed that the failure mode, damage tolerance, lateral stiffness, shear strength, and energy dissipation of the strengthened walls were improved to certain extents. The mesh grid ECC layer was proved an effective and applicable technique, the shear strength and energy dissipation of the corresponding strengthened wall were improved by 37.2% and 33.5%, respectively, and the addition of mesh grid and tie bars in the ECC layer prevented the debonding failure at the ECC/concrete interface. Besides, the shear resistance mechanisms of the test specimens were idealized by the strut-and-tie model, the contribution of cracked ECC tensile strength to shear was considered in the horizontal and vertical mechanisms. The predicted shear strengths of the RC walls agreed well with the test values. [ABSTRACT FROM AUTHOR]

B Engineering for Sustainable Development b Graph Introduction IABSE Congress New Delhi 2023 with the main theme of "Engineering for Sustainable Development" will be held from 20 to 22 September 2023. IABSE Congress New Delhi 2023 will provide an excellent opportunity to both domestic and international professional organisations / companies to display and promote their products and services in this ever-growing market called India. Registration Registration includes access to the Opening and Closing Ceremonies, all Parallel/Technical Sessions, Welcome Reception, Entry to the onsite Congress, Commercial Exhibition, Delegate Bag, Congress Proceedings, Lunches and Coffee Breaks. [Extracted from the article]

According to the shear capacity test results of six steel-fiber-reinforced high-strength concrete (SFHSC) corbels with welded-anchorage longitudinal reinforcement under concentrated load, the effects of shear span ratio and steel fiber volume fraction on the failure mode, cracking load and ultimate load of corbel specimens were analyzed. On the basis of experimental research, the shear transfer mechanism of corbel structure was discussed. Then, a modified softened strut-and-tie model (MSSTM), composed of the diagonal and horizontal mechanisms, was proposed, for steel-fiber-reinforced high-strength concrete corbels. The contributions of concrete, steel fiber and horizontal stirrups to the shear bearing capacity of the corbels were clarified. A calculation method for the shear bearing capacity of steel-fiber-reinforced high-strength concrete corbels was established and was simplified on this basis. The calculation results of the model were compared with the test values and calculation results of the GB50010-2010 code, the ACI318-19 code, the EN 1992-1-1 code and the CSA A23.3-19 code. The results showed that the concrete corbel with small shear span ratio mainly has two typical failure modes: shear failure and diagonal compression failure. With the increase in shear span ratio, the shear capacity of corbels decreases. Steel fiber can improve the ductility of a reinforced concrete corbel, but has little effect on the failure mode of the diagonal section. The calculated values of the national codes were lower than the experimental values, and the results were conservative. The theoretical calculation values of the shear capacity calculation model of the corbels were close to the experimental results. In addition, the model has a clear mechanical concept considering the tensile properties of steel-fiber-reinforced high-strength concrete and the influence of horizontal stirrups, which can reasonably reflect the shear transfer mechanism of corbels. [ABSTRACT FROM AUTHOR]

The strut-and-tie model is widely used for the analysis and design of reinforced concrete structures under a plane stress state. To apply this model, it is necessary to define strut-and-tie systems that represent the flow of stresses generated in the analysed structure. To make the concept of the model less dependent on designer experience for regions or structures with geometric or static discontinuity, this strut-and-tie model is defined through an evolutionary structural optimisation (ESO) considering linear isotropic material, which provides the automatic generation of strut-and-tie models. The evolution criterion adopted by the topological optimisation method considers the elimination of less requested elements in terms of tension, based on the elastic-linear analysis. The aim of this study is to develop and implement various strategies to control the removal of these elements, which leads to different final configurations. In this context, optimised solutions to complex problems involving reinforced concrete structures can be obtained. The results of two out of the three practical applications presented were compared with the results provided in the literature to validate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]