References of "Mihaylov, Boyan"
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See detailKinematic-based Approach for Complete Shear Behaviour of Deep FRC Beams
Mihaylov, Boyan ULiege; Liu, Jian ULiege; Tvrznikova, Karolina

Conference (2019, May 27)

While tests of deep fibre-reinforced concrete (FRC) beams have shown that steel fibres enhance the crack control and shear strength, the modelling of these effects in a simple and rational manner remains ... [more ▼]

While tests of deep fibre-reinforced concrete (FRC) beams have shown that steel fibres enhance the crack control and shear strength, the modelling of these effects in a simple and rational manner remains a challenging problem. Because FRC features enhanced tension behaviour, it is not well suited for the traditional strut-and-tie approach which neglects the tension in the concrete. Therefore, this paper proposes an alternative approach which focuses on the displacements in the critical shear cracks. The displacements are described with a kinematic model with two degrees of freedom, and are used with appropriate constitutive relationships to estimate the shear contribution of the fibres. This kinematics-based approach is validated with experimental data, and it is shown to capture adequately the complete pre- and post-peak behaviour of deep FRC beams. [less ▲]

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See detailModelling the Ultimate Shear Behaviour of Deep Beams with Web Openings
Liu, Jian ULiege; Mihaylov, Boyan ULiege

Conference (2019, May 27)

Web openings are inevitably installed in deep beams in practice, while most of the research is focused on the shear behaviour of solid deep beams. The existence of web openings can reduce significantly ... [more ▼]

Web openings are inevitably installed in deep beams in practice, while most of the research is focused on the shear behaviour of solid deep beams. The existence of web openings can reduce significantly the shear capacity of deep beams and therefore cause safety problems. In this study, the typical shear failure modes and load transfer mechanisms of deep beams with web openings are firstly investigated, and based on the investigation a kinematic model is proposed for the shear capacity prediction. This kinematic model stems from the existing two parameter kinematic theory (2PKT), which was shown to provide satisfying predictions on shear capacity of solid deep beams. In the proposed model, one shear span is divided into two sub shear spans below and above the web opening, respectively. The steel layout at beam end beyond the web opening is crucial for resisting shear transferred above the web opening. Twenty seven deep beam specimens with web openings are used for the validation. The proposed kinematic model provides satisfying results, i.e. Vexp/Vpre: Avg=1.14 and COV=7.8%. [less ▲]

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See detailTwo-Parameter Kinematic Approach for complete Shear Behaviour of Deep FRC Beams
Mihaylov, Boyan ULiege; Liu, Jian ULiege; Tvrznikova, Karolina

in Structural Concrete (2019)

While tests of deep fiber-reinforced 1 concrete (FRC) beams have shown that steel fibers enhance the crack control and shear strength, the modeling of these effects in a simple and rational manner remains ... [more ▼]

While tests of deep fiber-reinforced 1 concrete (FRC) beams have shown that steel fibers enhance the crack control and shear strength, the modeling of these effects in a simple and rational manner remains a challenging problem. Because FRC features enhanced tension behavior, it is not well suited for the traditional strut-and-tie approach which neglects the tension in the concrete. Therefore, this paper proposes an alternative approach which focuses on the displacements in the critical shear cracks. The displacements are described with a kinematic model with two degrees of freedom, and are used with appropriate constitutive relationships to estimate the shear contribution of the fibers. This kinematics-based approach is validated with experimental data, and it is shown to capture adequately the complete pre- and post-peak behavior of deep FRC beams. It is also shown that the model predicts well the effect of beam aspect ratio, fiber volume ratio, longitudinal reinforcement ratio and concrete strength on the shear strength of deep FRC beams. [less ▲]

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See detailRéhabilitation et Renforcement de Piles de Pont avec du Béton Fibré à Ultra-Haute Performance
Franssen, Renaud ULiege; Courard, Luc ULiege; Mihaylov, Boyan ULiege

Conference given outside the academic context (2019)

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See detailA Kinematic Approach for the Shear Strength of Short FRC Coupling Beams
Mihaylov, Boyan ULiege

in Engineering Structures (2019)

Short coupling beams are susceptible to brittle shear failures that are typically suppressed with dense transverse and/or diagonal reinforcement. To reduce the amount of shear reinforcement and improve ... [more ▼]

Short coupling beams are susceptible to brittle shear failures that are typically suppressed with dense transverse and/or diagonal reinforcement. To reduce the amount of shear reinforcement and improve the service behavior of the beam, researchers have proposed a solution with steel fiber-reinforced concrete (FRC). However, while this solution is promising, there are no sufficiently simple mechanical models capable of capturing the shear strength and displacement capacity of short FRC coupling beams without diagonal reinforcement. This paper proposes such a model based on first principles: kinematics, equilibrium, and constitutive relationships for the mechanisms of shear resistance. The model accounts in an explicit manner for five shear mechanisms across the critical shear cracks: diagonal compression in the critical loading zones, aggregate interlock, tension in the stirrups and in the steel fibres, and dowel action of the longitudinal reinforcement. These mechanisms are predicted and the results are compared to 20 tests from the literature as well as to FEM predictions. It is shown that the proposed approach models well the effect of beam aspect ratio, concrete strength, stirrup ratio, and amount of steel fibres. Furthermore, the model is used to develop relationships outlining the effectiveness of steel fibres to reduce conventional stirrup reinforcement in coupling beams with various properties. [less ▲]

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See detailEffect of Member Size and Tendon Layout on the Shear Behavior of Post-Tensioned Beams (Accepted)
Mihaylov, Boyan ULiege; Liu, Jian ULiege; Simionopoulos, Konstantine et al

in ACI Structural Journal (2019)

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See detailMixed-Type Modeling of Structures with Slender and Deep Beam Elements (Accepted)
Liu, Jian ULiege; Guner, Serhan; Mihaylov, Boyan ULiege

in ACI Structural Journal (2019)

The nonlinear analysis of reinforced concrete frame structures with slender members can be performed accurately and efficiently with 1D elements based on the plane-sections-remain-plane hypothesis ... [more ▼]

The nonlinear analysis of reinforced concrete frame structures with slender members can be performed accurately and efficiently with 1D elements based on the plane-sections-remain-plane hypothesis. However, if the frame also includes deep beams which require 2D high-fidelity finite element procedures, the analysis of large structures can become very costly. To address this challenge, this paper proposes a mixed-type modeling framework which integrates 1D slender beam elements with a novel 1D macroelement for deep beams. The framework is implemented in an existing nonlinear analysis procedure and is used to model 18 deep beam tests and a 20-story frame. It is shown that the proposed framework provides similarly accurate predictions to the 2D high fidelity procedures but requires a fraction of the time for modeling and analysis. Furthermore, the macroelement improves the post-peak predictions, and therefore the framework is suitable for evaluating the resilience of structures under extreme loading. [less ▲]

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See detailA Kinematic Approach for the Complete Shear Behavior of Short FRC Coupling Beams
Mihaylov, Boyan ULiege; Liu, Jian ULiege; Lobet, Rémy

in ACI Structural Journal (2018), 328

Short coupling beams are susceptible to brittle shear failures that need to be suppressed with dense transverse and diagonal reinforcement. To reduce the amount of shear reinforcement and improve the ... [more ▼]

Short coupling beams are susceptible to brittle shear failures that need to be suppressed with dense transverse and diagonal reinforcement. To reduce the amount of shear reinforcement and improve the service behavior, researchers have proposed a solution with steel fiber-reinforced concrete (FRC). However, while this solution is promising, there are no sufficiently simple mechanical models capable of describing the complete shear behavior of short FRC coupling beams. This paper proposes such a model based on first principles: kinematics, equilibrium, and constitutive relationships for the mechanism of shear resistance. The model is compared with tests from the literature and with a significantly more complex finite element model (FEM). It is shown that, while the proposed kinematic approach requires a straightforward input and negligible time for computations, it also provides a similar (or better) accuracy as the FEM with excellent shear strength predictions. [less ▲]

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See detailMacroelement for Complete Shear Behaviour of Continuous Deep Girders
Liu, Jian ULiege; Mihaylov, Boyan ULiege

in ACI Structural Journal (2018), 115(4), 1089-1100

The evaluation of the serviceability, safety, and resilience of deep girders in bridges and buildings requires accurate models for their pre- and post-peak shear behavior. This paper purposes such a model ... [more ▼]

The evaluation of the serviceability, safety, and resilience of deep girders in bridges and buildings requires accurate models for their pre- and post-peak shear behavior. This paper purposes such a model formulated as a macroelement for deep shear spans under single and double curvature. The element has two nodes with two degrees of freedom per node (translation and rotation). The paper discusses the formulation of the macroelement based on a threeparameter kinematic theory and provides comparisons with tests. It is shown that the macroelement captures the redistribution of forces in continuous members, and in this way predicts their enhanced ductility as compared to simply supported beams. It is also shown that the model captures the opening of the critical shear cracks under loading. The crack predictions can be compared with field measurements to accurately evaluate the safety of the structure, and in this way to avoid potential costly strengthening measures. [less ▲]

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See detailResponse simulation of UHPFRC members
Franssen, Renaud ULiege; Guner, Serhan; Courard, Luc ULiege et al

in BEtter, Smarter, Stronger Proceedings for the 2018 fib Congerss held in Melbourne (2018)

Ultra-high-performance fiber-reinforced concrete (UHPFRC) is a new generation material with outstanding mechanical properties and excellent durability. The uses of UHPFRC have, however, been mostly ... [more ▼]

Ultra-high-performance fiber-reinforced concrete (UHPFRC) is a new generation material with outstanding mechanical properties and excellent durability. The uses of UHPFRC have, however, been mostly limited to demonstration applications and research projects, due to its perceived high cost and the lack of proven analysis procedures. In the past decade, new design provisions have been proposed in France, Switzerland, Japan, and Australia while a proven numerical modeling approach is still missing. As an effort to contribute to bridging this gap, a numerical modeling approach is established in this research for UHPFRC members. The approach is based on the Diverse Embedment Model within the global framework of the Disturbed Stress Field Model, a smeared rotating-crack formulation for 2D modeling of concrete structures. This study aims to capture the behavior of UHPFRC by using only a few input parameters. The established model is validated with large-scale tests of UHPFRC beams from the literature. The beams considered incorporate various cross-section and reinforcement details, and exhibit a range of failure modes including flexure and shear. The validation studies, based on comparisons with the experimental results, demonstrate that the proposed modeling approach provides accurate response simulations through simple models with short analysis times. [less ▲]

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See detailA study on the numerical modelling of UHPFRC-strengthened members
Franssen, Renaud ULiege; Guner, Serhan; Courard, Luc ULiege et al

in Alexander, M. G.; Beushausen, Hans; Dehn, F (Eds.) et al International Conference on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR 2018) (2018)

The maintenance of large aging infrastructure across the world creates serious technical, environmental, and economic challenges. Ultra-high performance fibre-reinforced concretes (UHPFRC) are a new ... [more ▼]

The maintenance of large aging infrastructure across the world creates serious technical, environmental, and economic challenges. Ultra-high performance fibre-reinforced concretes (UHPFRC) are a new generation of materials with outstanding mechanical properties as well as very high durability due to their extremely low permeability. These properties open new horizons for the sustainable rehabilitation of aging concrete structures. Since UHPFRC is a young and evolving material, codes are still either lacking or incomplete, with recent design provisions proposed in France, Switzerland, Japan, and Australia. However, engineers and public agencies around the world need resources to study, model, and rehabilitate structures using UHPFRC. As an effort to contribute to the efficient use of this promising material, this paper presents a new numerical modelling approach for UHPFRC-strengthened concrete members. The approach is based on the Diverse Embedment Model within the global framework of the Disturbed Stress Field Model, a smeared rotating-crack formulation for 2D modelling of reinforced concrete structures. This study presents an adapted version of the DEM in order to capture the behaviour of UHPFRC by using a small number of input parameters. The model is validated with tension tests from the literature and is then used to model UHPFRC-strengthened elements. The paper will discuss the formulation of the model and will provide validation studies with various tests of beams, columns and walls from the literature. These studies will demonstrate the effectiveness of the proposed modelling approach. [less ▲]

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See detailEffect of upgrading concrete strength class on fire performance of reinforced concrete columns
Gernay, Thomas ULiege; Peric, Vlado; Mihaylov, Boyan ULiege et al

in Gillie, Martin; Wang, Yong (Eds.) Proceedings of ASFE 2017 Conference (2018)

High strength concrete (HSC) provides several advantages over normal strength concrete (NSC) and is being used in multi-story buildings for reducing the dimensions of the columns sections and increasing ... [more ▼]

High strength concrete (HSC) provides several advantages over normal strength concrete (NSC) and is being used in multi-story buildings for reducing the dimensions of the columns sections and increasing the net marketable area. However, upgrading of concrete strength class in a building may affect the fire performance, due to higher rates of strength loss with temperature and higher susceptibility to spalling of HSC compared with NSC. Reduction of columns sections also leads to increased member slenderness and faster temperature increase in the section core. These detrimental effects are well known, but their impact on fire performance of structures has not been established in terms of comparative advantage between NSC and HSC. In other words, it is not clear whether the consideration of fire resistance limits the opportunities for use of HSC for reducing the dimensions of columns sections in multi-story buildings. This research aims to address this question by comparing the fire behaviour of reinforced concrete columns made of NSC and HSC using nonlinear finite element modelling. The evolution of load bearing capacity of the columns is established as a function of the fire exposure duration. A 15-story car park structure is adopted as a case study with alternative designs for the columns based on strength classes ranging from C30 to C90. Results show that, although the replacement of NSC by HSC accelerates the reduction rate of columns capacity under fire, the columns generally have significant reserves in resistance leading to sufficient fire resistance. This study gives an insight into the impact of replacing stocky sections in NSC by more slender sections in HSC on fire resistance rating for multi-story structures. [less ▲]

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See detailThree-parameter kinematic approach for shear behaviour of short coupling beams with conventional reinforcement
Mihaylov, Boyan ULiege; Franssen, Renaud ULiege

in fib Bulletins (2018), 85

This paper presents a three-parameter kinematic theory (3PKT) for predicting the shear strength and deformation patterns of short coupling beams. The 3PKT approach is situated between simple and ... [more ▼]

This paper presents a three-parameter kinematic theory (3PKT) for predicting the shear strength and deformation patterns of short coupling beams. The 3PKT approach is situated between simple and conservative strut-and-tie models and complex nonlinear finite element (FE) models. It is aimed at improving the strength predictions of strut-and-tie models while maintaining relative simplicity and clear physical basis. In addition, it is aimed at providing estimates of the ultimate deformations in coupling beams which are typically calculated with FE models. While FE models use a large number of degrees of freedom (DOFs) to describe the deformation patterns in coupling beams, the 3PKT is based on a kinematic model with only three DOFs. In addition to kinematic conditions, the 3PKT also includes equilibrium equations and constitutive relationships for the mechanisms of shear resistance in short coupling beams. The paper presents the formulation of the 3PKT and compares its shear strength predictions to results from tests, FE simulations, and strut-and-tie models based on the fib Model Code 2010. It is shown that the 3PKT approximates well the predictions of the FE models while the strut-and-tie model produces significantly lower strengths. [less ▲]

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See detailMacro-Kinematic Approach for Shear Behaviour of Short Coupling Beams with Conventional Reinforcement
Mihaylov, Boyan ULiege; Franssen, Renaud ULiege

in High Tech Concrete: Where Technology and Engineering Meet - Proceedings of the 2017 fib Symposium (2017, June 13)

Short coupling beams in wall structures work predominantly in shear and develop complex deformation patterns. For this reason they cannot be modelled based on the classical plane-sections-remain-plane ... [more ▼]

Short coupling beams in wall structures work predominantly in shear and develop complex deformation patterns. For this reason they cannot be modelled based on the classical plane-sections-remain-plane hypothesis, and are typically designed with strut-and-tie models. However, because strut-and-tie models are inherently conservative, they can result in very large amounts of shear reinforcement (stirrups), and therefore significant construction difficulties. In addition, strut-and-tie models do not provide information about the deformation capacity of coupling beams, which is important for performance-based seismic design. To address these challenges, this paper discusses a three-parameter kinematic theory (3PKT) for the shear strength and deformation patterns of short coupling beams. The 3PKT approach is situated between simple and conservative strut-and-tie models and complex non-linear finite element (FE) models. While FE models use a large number of degrees of freedom (DOFs) to describe the deformation patterns in coupling beams, the 3PKT method is based on a kinematic model with only three DOFs. The paper presents the formulation of the model and its validation with tests. [less ▲]

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See detailTowards Mixed-Type Modelling of Structures with Slender and Deep Beam Elements
Liu, Jian ULiege; Mihaylov, Boyan ULiege

Conference (2017, June 12)

Concrete frame structures often include both slender and deep beams. Deep beams possess a large shear capacity, and thus are typically used as transfer girders to carry heavy loads over large spans. The ... [more ▼]

Concrete frame structures often include both slender and deep beams. Deep beams possess a large shear capacity, and thus are typically used as transfer girders to carry heavy loads over large spans. The overloading of such members due to extreme events such as earthquakes may result in the collapse of the entire structure. To evaluate the resilience of large frame structures under extreme loading, it is necessary to model the interaction between the deep girders and the rest of the structure in an accurate and computationally effective manner. To address this issue, this paper proposes a mixed-type modelling framework by formulating an innovative 1D macro deep-beam element and coupling it with 1D slender elements. The new macro element aims to combine the accuracy of 2D micro finite elements with the simplicity of 1D macro elements. The paper summarizes the formulations of this element, based on the three-parameter kinematic theory, and integrates it into an existing global nonlinear analysis procedure to create a mixed-type modeling framework. The verification study, including a frame structure with a deep transfer girder, has shown that this approach captures the response of the frame with an accuracy similar to that of 2D micro finite elements, while requiring approx. 20% of the analysis time. [less ▲]

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See detailDecoding the disciplines – A pilot study at the University of Liège (Belgium)
Verpoorten, Dominique ULiege; Devyver, Julie ULiege; Duchâteau, Dominique ULiege et al

in Andersson, Roy; Martensson, Katarina; Roxa, Torgny (Eds.) Proceedings of the 2nd EuroSoTL Conference - Transforming patterns through the scholarship of teaching and learning (2017, June)

This paper reports on a first attempt to apply the two first stages of the “Decoding the disciplines” framework (Pace, 2017) at the University of Liège (Belgium). In this context, 7 professors volunteered ... [more ▼]

This paper reports on a first attempt to apply the two first stages of the “Decoding the disciplines” framework (Pace, 2017) at the University of Liège (Belgium). In this context, 7 professors volunteered to reflect, through a structured process, upon “bottlenecks” in their courses, with the help of IFRES’ (Institute for Training and Research in Higher Education) pedagogical advisers. This pilot delivered contrasted observations: while participants granted value to their exposure to this approach, especially in terms of enhanced awareness of possible discrepancies between what experts and newcomers in the field might consider as obvious, none of them activated the possibility offered to tackle the identified bottlenecks, according to the systematic approach (stages 3-7) suggested by the framework. The paper presents the pedagogical setting, analyses the interviews of participants and the outcomes of the project, outlines explanations for its results, and shares some lessons learnt. [less ▲]

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See detailDisplacement Capacity of Shear-Dominated Reinforced Concrete Walls
Tatar, Nikola ULiege; Mihaylov, Boyan ULiege

Conference (2017, January 12)

In this paper the load-displacement response and displacement capacity of shear-dominated reinforced concrete walls is studied with the help of a three-parameter kinematic theory (3PKT). The 3PKT is a ... [more ▼]

In this paper the load-displacement response and displacement capacity of shear-dominated reinforced concrete walls is studied with the help of a three-parameter kinematic theory (3PKT). The 3PKT is a rational and efficient approach based on a three-degree-of-freedom kinematic description of the deformation patterns in cantilever walls with aspect ratios ≤3.0. In addition to kinematics, the 3PKT also includes equations for equilibrium and constitutive relationships for the load-bearing mechanisms in walls. The paper summarizes this approach and applies it to nine wall tests from the literature featuring a wide range of test variables. It is shown that the model captures adequately the response of both moderately short walls (aspect ratios 2.2-3.0) and squat walls (ratios 0.33-0.54). With the help of the load-bearing mechanisms predicted by the 3PKT, it is shown that shear failures in squat walls develop due to the complex interaction between concrete crushing in the toes of the walls and aggregate interlocking along flat critical cracks. A modification to the 3PKT is proposed to capture the effect of loading conditions on squat shear walls. With this modification, it is shown that the 3PKT can also capture the effect of concrete stiffness, concrete compressive strength, and reinforcement ratios on the shear response of squat members. For all tests considered in this study, the 3PKT produced an average shear strength experimental-to-predicted ratio of 1.05 and a coefficient of variation COV=10.5%. Similarly accurate predictions were obtained for the displacement capacity of the walls: an average of 0.90 and COV=15.69%. [less ▲]

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See detailDeformation Patterns and Behavior of Reinforced Concrete Walls with Low Aspect Ratios
Tatar, Nikola ULiege; Mihaylov, Boyan ULiege

Conference (2017)

The assessment of wall structures featuring low aspect ratios remains a challenging problem due to their complex deformation patterns and susceptibility to sudden shear failures under seismic actions. To ... [more ▼]

The assessment of wall structures featuring low aspect ratios remains a challenging problem due to their complex deformation patterns and susceptibility to sudden shear failures under seismic actions. To address this issue, a three-parameter kinematic theory (3PKT) for shear-dominated walls has been recently proposed by Mihaylov et al. (2016). This rational approach uses only three degrees of freedom to predict the complete load-displacement response of a member, and captures shear failures occurring prior to or after the yielding of longitudinal reinforcement. Due to its relative simplicity and computational effectiveness, the 3PKT can be used for the performance-based evaluation of existing structures. To further validate and extend the kinematic approach, an experimental program was performed at the University of Liege, and is the focus of this paper. The test campaign consisted of testing to failure of three cantilever walls with an aspect ratio of 1.7, which featured uniformly distributed longitudinal and transverse reinforcement. The main test variable was the level of axial load which has a significant impact on the failure mechanism and lateral displacement capacity. In addition to more conventional measurements using displacement transducers, the experiments involved the measuring of the complete deformation patterns of the walls using an optical LED system. This paper presents the main test results in terms of load-displacement responses, crack patterns and failure modes. The walls developed major diagonal cracks but failed in flexure-dominated modes. The measured deformation patterns are compared to the patterns predicted by the kinematic model for shear-dominated walls. Even though the failure of the test specimens was governed by flexure, their deformations were predicted well by the model. [less ▲]

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See detailLoad-Displacement Envelopes of Shear-Dominated Concrete Walls based on a Three-Parameter Kinematic Theory
Tatar, Nikola ULiege; Mihaylov, Boyan ULiege

in Journal of Earthquake Engineering (2017)

In this paper the complete load-displacement response of shear-dominated reinforced concrete walls is studied with a three-parameter kinematic theory (3PKT). The 3PKT is a rational and efficient approach ... [more ▼]

In this paper the complete load-displacement response of shear-dominated reinforced concrete walls is studied with a three-parameter kinematic theory (3PKT). The 3PKT is a rational and efficient approach based on a three-degree-of-freedom description of the deformation patterns in walls with aspect ratios ≤3.0. In addition to kinematics, the 3PKT also includes equations for equilibrium and constitutive relationships for the load-bearing mechanisms in walls. The paper summarizes this approach and applies it to tests from the literature featuring a wide range of variables. It is shown that the 3PKT captures adequately the local and global response of both rectangular walls and walls with barbells. [less ▲]

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See detailShear-flexure interaction in the critical sections of short coupling beams
Mihaylov, Boyan ULiege; Franssen, Renaud ULiege

in Engineering Structures (2017)

Heavily-loaded short coupling beams with large amounts of transverse reinforcement fail in sliding shear or diagonal compression under the complex interaction between shear and flexure. These failure ... [more ▼]

Heavily-loaded short coupling beams with large amounts of transverse reinforcement fail in sliding shear or diagonal compression under the complex interaction between shear and flexure. These failure modes often occur after yielding of the flexural reinforcement and limit the displacement capacity of the member. To study such failures, this paper compares experimental results with predictions of models with various levels of complexity. It is shown that complex nonlinear finite element models (FEM) can capture adequately the entire behaviour of short coupling beams, while the classical flexural model produces unconservative strength predictions. It is also shown that strut-and-tie models are reasonably conservative provided that their geometry is selected to maximize the strength predictions. To produce similarly adequate strength predictions as those of the FEM – while at the same time maintaining the simplicity of the flexural model – the paper proposes a mechanical model based on strain compatibility. The main assumption of the model links the principal compressive strains in the critical section to the longitudinal strains in the tension zone. It is shown that the model captures well the effect of different test variables on the shear strength. When applied to a database of 24 tests, the model produced an average shear strength experimental-to-predicted ratio of 1.12 with a coefficient of variation of 8.4%. [less ▲]

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