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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]

This article introduces an innovative approach to optimize steel reinforcement in reinforced concrete structures using the equilibrium-based formulation described in Ferradi et al. (Comput Struct 286:107095, 2023). The objective is to enhance structural performance and cost-effectiveness by efficiently distributing steel reinforcement within an arbitrary volume representing the concrete, while ensuring external loading equilibrium. To achieve this goal, two approaches are proposed: the first approach focuses on optimizing the cross section of 1D rebars that are already defined in the concrete volume as curves, while the second approach optimizes the steel bulk densities throughout the entire volume, with or without assuming predetermined principal directions for the reinforcement, represented by a steel stress tensor. The latter approach does not rely on any prior knowledge of the geometric distribution of rebars and can be seen as an automated strut and tie method for three-dimensional problems , where the struts are derived from the compression flow, and the ties originate from the tensile flow. Both approaches are formulated as optimization problems, enabling the utilization of the interior point method for effective problem-solving. Numerical examples and comparisons with existing results vividly illustrate the flexibility and potential efficiency gains achievable through the proposed approaches. [ABSTRACT FROM AUTHOR]

The concept of sustainable concrete is aimed at using alternative materials instead of natural resources in concrete production. In recent years, many experimental and numerical studies have been carried out to show that sustainable concrete is an alternative to conventional concrete. In this study, a detailed numerical simulation of reinforced concrete corbels produced with sustainable concrete has been conducted comprehensively. According to the author's best knowledge, the novelty of this study: (1) this is the first time that comprehensive numerical simulation results of sustainable concrete corbels are reported in detail, (2) investigation of the applicability of existing numerical models in sustainable concrete corbels, (3) contribution the realistic simulation of the structural behavior of sustainable concrete corbels. It should also be highlighted that the variables included in the study were the recycled concrete aggregate ratio, the shear span-to-effective depth ratio, the tapering ratio, the angle between strut and tie element, and the amount of reinforcement. Furthermore, the numerical simulation results obtained by the finite element and truss analogy methods were extensively compared with the experimental results. In addition, a structural optimization design was executed on a short corbel to check the suitability of the selected truss analogy model. Based on the study, the simulation results obtained from the finite element method agreed fairly well with the experimental results. Furthermore, the truss analogy method provided relatively accurate and conservative results compared with the experimental results depending on the span-to-depth ratio. Besides, some recommendations for designing sustainable concrete corbels were also discussed. [ABSTRACT FROM AUTHOR]

The reduction in the shear strength accompanied to the increasing in the section depth is characterised as size effect, assuming that all parameters are kept constant. Such behaviour is controlled by many factors. The geometry of the element formed between the load and support points is one of those factors that need to be highlighted. Owing to that, this study aims to assess the impact of the strut geometry on the size effect from the strut and tie method (STM) point of view. As the strut geometry is represented by bearing plates and concrete cover, the current study has focused on those two parameters. Accordingly, two groups of specimens have been examined analytically using STM of the American, European and Canadian codes. In each group, three depths were used of 500, 100, and 1500 mm. The only differences between those two groups are dimensions of bearing plates (loading and supporting) and concrete cover. In the first group, the dimensions of bearing plates and concrete cover have been kept constant with 250 mm and 60 mm, respectively regardless of the section depth. In the second group, those two parameters have been proportioned with the section height to be 15% and 8% of section height, respectively. Furthermore, an experimental database of 25 deep beams reinforced with polymer bars has been compiled from the literature to evaluate the ability of the STM to consider the size effect. The results showed that STM does not consider the size effect. Additionally, the collected data confirmed that the STM of American and European codes overestimated the shear capacity, while the STM of Canadian code gave a conservative prediction, highlighting the need of suitable models for shear strength prediction of FRP reinforced deep elements. [ABSTRACT FROM AUTHOR]

This paper presents optimization of the reliability system for different Strut and Tie models of beams loaded with a torsional and bending moment. In this paper, three STMs depending on the angle of diagonal strut were compared. The presented beam models have a serial system reliability. In the analyses, the full correlation of the top chord of truss - upper reinforcement, full correlation of bottom chord of truss - compression concrete, full correlation of members mapping individual stirrups and concrete in diagonals between stirrups. Estimation of the reliability of the adopted structures was carried out in a software package of Strurel. The variables of concrete, and steel strength as well as concentrated load magnitude were described by a mean value, a standard deviation and a type of distribution. Summing up the results of the analysis, it was noted, that methods for reliability estimation using information about the model’s reliability structure are an excellent alternative to time consuming simulation methods. These methods allow not only to estimate the reliability of the structure, but also to determine the impact of individual members on the reliability of the entire element.

This paper presents optimization of the reliability system for different Strut and Tie models of beams loaded with a torsional and bending moment. In this paper, three STMs depending on the angle of diagonal strut were compared. The presented beam models have a serial system reliability. In the analyses, the full correlation of the top chord of truss - upper reinforcement, full correlation of bottom chord of truss - compression concrete, full correlation of members mapping individual stirrups and concrete in diagonals between stirrups. Estimation of the reliability of the adopted structures was carried out in a software package of Strurel. The variables of concrete, and steel strength as well as concentrated load magnitude were described by a mean value, a standard deviation and a type of distribution. Summing up the results of the analysis, it was noted, that methods for reliability estimation using information about the model's reliability structure are an excellent alternative to time consuming simulation methods. These methods allow not only to estimate the reliability of the structure, but also to determine the impact of individual members on the reliability of the entire element. [ABSTRACT FROM AUTHOR]

From a design point of view, regions in a structural member can be divided into two regions, namely, B or Bernoulli regions, where the strain distributions are linear, and D or Disturbed regions, where the strain distributions are nonlinear. While the present codal provisions recommend well-defined theories for the design of B regions, thumb rule or empirical equations are still being used to design D regions. It has been recently understood that the strut and tie method is an effective tool for the design of both B and D regions. In a deep beam, the distribution of strain across the depth of the cross-section is nonlinear and hence these structural elements belong to D regions. The existing codal provisions for the design of simply supported deep beams are inadequate and are empirical in nature. Among the available codal provisions, there exists a disparity even in the definition of deep beams. Strut and tie models can be developed using load path method, but more than one model is possible for a given problem, and the designer should have a minimum level of experience to identify the appropriate model. In this paper, a methodology has been developed to identify the optimum model among different possible models. Experimental investigations were carried out to validate the optimum strut and tie model. Further, using this method, the limiting value of span to depth ratio for simply supported beams was found out, so that they could be considered as deep beam. [ABSTRACT FROM AUTHOR]

Generally structural members can be broadly divided into two regions, namely B or Bernoulli regions where the strain distributions are linear and D or Disturbed regions where the strain distributions are nonlinear. A beam whose depth is comparable to span is known as deep beam and these structural elements belong to D regions. It has been recently understood that the strut and tie method (STM) is an effective tool for the design of both B and D regions. The present code recommendations are inadequate for the design of deep beams. In this paper simple equations using STM are developed for finding the area of main steel required to have a balanced type of failure and to find the ultimate capacity of deep beams failing in different failure modes. These equations are compared with experimental results and a good agreement is found. [ABSTRACT FROM AUTHOR]

• Numerical model called Multi-Pier MP for the in-plane pushover analysis of masonry. • Substitution of the 2D continuum with trusses having equivalent mechanical properties. • Possibility to implement directly the model in a commercial software. • Excellent fitting of pushover curves and cracks with very limited computational burden. • Direct utilization in design without the need to implement ad hoc constitutive equations. Several simplified and advanced methods have been proposed to evaluate the behavior of masonrywalls under in-plane loads, but their implementation in standard commercial software remains still an exception. In this paper, a novel 1D approach called Multi-Pier MP method, which has the advantage that can be used in a commercial software and requires only truss elements with a non-linear softening behavior, is presented. In the model, a masonry structure in-plane loaded is transformed in an assemblage of piers (vertical trusses) and diagonal connecting elements (braces), ensuring by elastic stiffness equivalence that a masonry representative element of volume behaves in the same manner as the 1D system constituted by two vertical trusses and two diagonal braces. After a validation at a unit cell level, where geometric and mechanical properties of the trusses are set in order to reproduce correctly masonry behavior respectively under axial loads, combined shear and compression stresses and bending and shear actions, four masonry full scale shear walls with different length to width ratios and presence or absence of openings are analyzed in the non-linear static range. In addition to experimental results, two Heterogeneous Discrete Element and Finite Element Methods were used with validation purposes. Excellent match among MP Method results, experimental evidences and alternative advanced numerical heterogeneous approaches is found, as far as the prediction of ultimate load, post peak behavior, initial stiffness and failure mechanisms is concerned. The model is also capable to follow at each step of loading the spreading and position of tensile and shear cracks. [ABSTRACT FROM AUTHOR]

Este artigo analisa o comportamento estrutural de blocos de concreto armado sobre seis estacas dispostas em arranjo retangular. Considerou-se a deformabilidade do solo de apoio das estacas, diferentes resistências para o concreto e pilares com seções transversais quadradas eretangulares, solicitados por força centrada. O dimensionamento foi feito por um modelo de bielas e tirantes. Realizou-se análise numéricatridimensional por meio do método dos elementos finitos. A configuração do fluxo de tensões e a formação das bielas foram analisadas emperspectiva. Observou-se que quanto mais deformável for o solo, mais uniformes são as distribuições das reações entre as estacas. A seçãotransversal do pilar influenciou na configuração das bielas. A variação da resistência do concreto teve maior influência na resistência dos blocos do que na rigidez. O método analítico utilizado apresentou compatibilidade com os resultados obtidos na simulação numérica.