Publications of Boyan Mihaylov
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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 (2017, September 07)

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

Conference (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 detailTwo-Parameter Kinematic Approach for Shear Strength of Deep Concrete Beams with Internal FRP Reinforcement
Mihaylov, Boyan ULiege

in Journal of Composites for Construction (2017), DOI: 10.1061/(ASCE)CC.1943-5614 .0000747

Tests of deep concrete beams with internal fiber-reinforced polymer (FRP) reinforcement have shown that such members can exhibit lower shear strength than members with conventional steel reinforcement. To ... [more ▼]

Tests of deep concrete beams with internal fiber-reinforced polymer (FRP) reinforcement have shown that such members can exhibit lower shear strength than members with conventional steel reinforcement. To model this effect, the current paper proposes an approach based on a two-parameter kinematic theory (2PKT) for conventional deep beams. The 2PKT is built on a kinematic model with two degrees of freedom that describes the deformation patterns of cracked beams. Using this theory shows that large strains in FRP longitudinal reinforcement result in reduced shear resistance of the critical loading zones (CLZ) of deep beams. The original 2PKT is therefore modified by introducing a reduction factor for the shear carried by the CLZ. The extended 2PKT approach is then applied to a database of 39 tests of FRP-reinforced deep beams from the literature, resulting in an average shear strength experimental-to-predicted ratio of 1.06 and a coefficient of variation of 18.3%. The results show that the 2PKT adequately captures the effects of the stiffness of the reinforcement, section depth, concrete strength, and shear-span-to-depth ratio on the shear strength of FRP-reinforced deep beams. [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 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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See detailModelling the ultimate shear behaviour of deep beams with internal FRP reinforcement
Mihaylov, Boyan ULiege

in Performance-based approaches for concrete structures, fib Symposium Proceedings, Cape Town 21 to 23 November 2016 (2016, November 22)

Fiber reinforced polymer (FRP) reinforcement in deep beams has been proposed as an alternative to steel reinforcement to increase the durability of members in corrosive environments. Since FRP ... [more ▼]

Fiber reinforced polymer (FRP) reinforcement in deep beams has been proposed as an alternative to steel reinforcement to increase the durability of members in corrosive environments. Since FRP reinforcement has lower stiffness than steel reinforcement and typically exhibits higher tensile strength, there is a need for new models capable of capturing the effect of these properties on the shear strength of deep beams. This paper proposes such an approach for members without shear reinforcement, which is an extension of a two-parameter kinematic theory (2PKT) for steel-reinforced deep beams. The original approach is modified to account for the effect of large flexural strains on the shear capacity of the critical loading zones in deep beams where the concrete crushes at failure. It is shown that a simple modification based on test data can result in adequate shear strength predictions. It is also shown that the extended 2PKT captures well the effect of reinforcement stiffness, shear-span-to-depth ratio, and section depth on the shear capacity of deep beams with FRP reinforcement. [less ▲]

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See detailA MACRO-ELEMENT FOR THE NONLINEAR ANALYSIS OF DEEP BEAMS BASED ON A THREE-PARAMETER KINEMATIC MODEL
Liu, Jian ULiege; Mihaylov, Boyan ULiege

Conference (2016, November 22)

This paper presents a computationally-effective macro element for predicting the complete shear response of RC deep beams. The element stems from a three-parameter kinematic theory (3PKT) for the shear ... [more ▼]

This paper presents a computationally-effective macro element for predicting the complete shear response of RC deep beams. The element stems from a three-parameter kinematic theory (3PKT) for the shear strength and deformation capacity of deep beams under double curvature. The macro element consists of two rotational springs and one transverse spring to simulate the nonlinear flexural and shear behaviour of deep shear spans. The element is applied to two deep beams tested to shear failure under three-point bending. The results are used to study the effect of unsymmetrical shear failures on the pre- and post-peak behaviour of nominally symmetrical members. It is found that the post-peak response is sensitive to the unloading path of the shear resisting mechanisms as well as to the global roughness of the critical diagonal cracks. Based on these analyses, modifications to the constitutive relationships of the shear mechanisms are proposed, and the macro element is applied to a continuous deep beam. It is shown that the model adequately captures the complete behaviour of the beam, including the redistribution of forces following the shear failure in the critical shear span. [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

in fib bulletin (in preparation) (2016, September 06)

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 non-linear finite element (FE) models. It is aimed at improving the shear 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, finite element simulations, and strut-and-tie models. It is shown that the 3PKT approximates very well the predictions of the FE models, while the strut-and-tie model produce significantly lower strengths. [less ▲]

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See detailA Macro-Element Formulation and Solution Procedure for Shear Analysis of RC Deep Beams
Liu, Jian ULiege; Mihaylov, Boyan ULiege

in the 11th fib International PhD Symposium in Civil Engineering (2016, August 30)

This paper presents a computationally-effective macro element capable of predicting the complete shear response of RC deep beams in analogy with beam elements for slender beams. The element stems from a ... [more ▼]

This paper presents a computationally-effective macro element capable of predicting the complete shear response of RC deep beams in analogy with beam elements for slender beams. The element stems from a three-parameter kinematic theory (3PKT) for the shear strength and deformation capacity of deep beams subjected to double curvature. The macro element is composed of two rotational springs and one transverse spring to simulate the nonlinear flexural and shear behaviour of the shear span. The element has two nodes (end sections) with two DOFs per node, which enables it to be easily connected to other elements of the same or different types to model structures with deep beams. The numerical implementation of the element is based on the secant stiffness approach which provides robust convergence properties. Validation studies are performed by using thirteen tests from the literature showing excellent results for the complete shear response. The obtained peak load experimental-to-predicted ratios have an average of 1.10 with a coefficient of variation of 14.2%, while these values for the mid-span deflection are 1.16 and 17.0%. [less ▲]

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See detailMC2010 Shear Provisions and Recent Developments in Shear Research
Mihaylov, Boyan ULiege

Conference (2016, April 13)

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See detailThree-parameter kinematic theory for shear-dominated reinforced concrete walls
Mihaylov, Boyan ULiege; Hannewald, Pia; Beyer, Katrin

in Journal of Structural Engineering (2016)

This paper is aimed at addressing the need for physically accurate and computationally effective models for predicting the response of shear-dominated reinforced concrete walls. The presented theory is ... [more ▼]

This paper is aimed at addressing the need for physically accurate and computationally effective models for predicting the response of shear-dominated reinforced concrete walls. The presented theory is based on a three-degree-of-freedom kinematic model for the deformation patterns in walls with aspect ratios smaller than approximately 3. In the kinematic model, the wall is divided into two parts—a rigid block and a fan of struts—by a diagonal crack. The mechanisms of shear resistance across this crack are modeled with nonlinear springs to capture the prepeak and postpeak shear behavior of the member. The base section of the wall is also modeled to account for yielding of the reinforcement and crushing of the concrete. It is shown that this approach captures well the global and local deformations measured in a test specimen with detailed instrumentation. A more comprehensive validation of the theory is performed with 34 wall tests from the literature. The obtained peak load experimental-to-predicted ratios have an average of 1.03 with a coefficient of variation of 11.6%, while these values for the drift capacity are 0.99 and 16.4%. [less ▲]

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See detailA comparative study of models for shear strength of reinforced concrete deep beams
Liu, Jian ULiege; Mihaylov, Boyan ULiege

in Engineering Structures (2016), 112(April), 81-89

Since the 1960s, researchers have proposed different empirical formulas and analytical models for the shear strength of deep reinforced concrete beams. Some of these approaches have shown adequate ... [more ▼]

Since the 1960s, researchers have proposed different empirical formulas and analytical models for the shear strength of deep reinforced concrete beams. Some of these approaches have shown adequate accuracy when applied to small sets of beam tests, while their ability to predict the effect of a large range of test variables remains unknown. This paper presents a summary of models for deep beams from 73 publications, and focuses on a detailed evaluation of ten more recent models by using a database of 574 deep beam tests. It is found that a semi-empirical strut-and-tie model (STM) and a two-parameter kinematic theory (2PKT) for deep beams produce the least scattered predictions. The former model produced an average shear strength experimental-to-predicted ratio Vexp/Vpred of 1.00 with a coefficient of variation (COV) of 19.8%, while the latter resulted in an average of 1.08 with a COV of 15.4%. The two models are also compared by plotting the Vexp/Vpred ratios against different tests variables, and by performing parametric studies with individual test series. It is shown that the semi-empirical STM exhibits certain bias with respect to the shear-span-to-depth ratio, while the 2PKT produces uniform results across the entire range of experimental data. It is also noted that the semi-empirical STM requires somewhat less computational effort than the 2PKT approach. [less ▲]

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See detailShear Response of Prestressed Thin-Webbed Continuous Girders
Collins, Michael; Xie, Liping; Mihaylov, Boyan ULiege et al

in ACI Structural Journal (2016)

While different design codes provide similar guidance for the flexural design of prestressed thin: webbed continuous girders, the shear design provisions differ greatly. This paper investigates these ... [more ▼]

While different design codes provide similar guidance for the flexural design of prestressed thin: webbed continuous girders, the shear design provisions differ greatly. This paper investigates these discrepancies with the help of eleven experiments and a number of analytical studies. Together these provide the basis for recommendations for engineers conducting the shear design for new girders or evaluating the shear capacity of existing girders. It is shown that the traditional ACI approach of taking Vc as the smaller of Vci, flexural:shear cracking load, and Vcw, web:shear cracking load, can significantly overestimate the shear strength of such girders particularly if they are highly prestressed and contain relatively small quantities of shear reinforcement. The other codes evaluated provided more conservative predictions. It is shown that the ACI predictions can be improved significantly by taking into account the effect of flexural stresses on web shear cracking. While the ACI code uses different shear strength equations for members subjected to external axial loads versus members subjected to internal prestressing forces, the studies summarized in this paper support the idea that unification of these ACI shear provisions is possible. [less ▲]

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See detailThree-Parameter Kinematic Theory for Shear-Dominated Reinforced Concrete Walls: Implementation
Mihaylov, Boyan ULiege; Hannewald, Pia; Beyer, Katrin

Software (2015)

The tree-parameter kinematic theory (3PKT) is aimed at addressing the need for physically accurate and computationally effective models for predicting the response of shear-dominated reinforced concrete ... [more ▼]

The tree-parameter kinematic theory (3PKT) is aimed at addressing the need for physically accurate and computationally effective models for predicting the response of shear-dominated reinforced concrete walls. The theory is based on a three-degree-of-freedom kinematic model for the deformation patterns in walls with aspect ratios smaller than approximately 3. In the kinematic model the wall is divided into two parts - a rigid block and a fan of struts - by a diagonal crack. The mechanisms of shear resistance across this crack are modelled with non-linear springs to capture the pre- and post- peak shear behavior of the member. The base section of the wall is also modelled to account for yielding of the reinforcement and crushing of the concrete. The complete formulation of the 3PKT is presented in an ASCE Journal of Structural Engineering paper by Mihaylov, Hannewald and Beyer. The attached Matlab code represents an implementation of the 3PKT for time-efficient computation of the response of shear-dominated walls. The limits of applicability of the 3PKT and the code are defined in the ASCE paper. [less ▲]

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See detailA Comparative Study of Models for Shear Strength of Reinforced Concrete Deep Beams
Liu, Jian ULiege; Mihaylov, Boyan ULiege

in Civil-Comp Proceedings (2015, September 03)

The shear behaviour of deep reinforced concrete beams has been a focus of experimental and analytical studies since the early 1950s, resulting in different approaches for predicting the shear strength of ... [more ▼]

The shear behaviour of deep reinforced concrete beams has been a focus of experimental and analytical studies since the early 1950s, resulting in different approaches for predicting the shear strength of deep beams. This paper compares the main modelling assumptions of these approaches and summarizes the results from validation studies available in the literature. Based on these comparisons, a two-parameter kinematic theory (2PKT) and a mechanical model by Zararis are selected for further evaluation with the help of test series with different experimental variables. It is shown that both approaches predict the trends in beam series with varying shear-span-to-depth ratios, even though the mechanical model overestimates the shear strength of beams without web reinforcement. It is also shown that the two models differ significantly in capturing the effect of transverse reinforcement and the size effect in shear. While the 2PKT accounts for sliding shear failures which limit the effectiveness of transverse reinforcement beyond a certain reinforcement ratio, the mechanical model predicts a monotonic increase of shear strength with the ratio. The 2PKT is also shown to capture the size effect in shear observed in two series of tests well, while the mechanical model neglects this effect. [less ▲]

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See detailPredicting the non-linear shear behaviour of deep beams based on a two-parameter kinematic model
Mihaylov, Boyan ULiege

in Concrete - Innovation and Design, fib Symposium Proceedings, Copenhagen 18 to 20 May 2015 (2015, May 20)

Deep beams are often used as transfer girders in high rise buildings to support heavy loads from discontinuous columns or shear walls. Several buildings with such transfer girders were affected by the ... [more ▼]

Deep beams are often used as transfer girders in high rise buildings to support heavy loads from discontinuous columns or shear walls. Several buildings with such transfer girders were affected by the February 2011 earthquake in Christchurch, New Zealand, which produced very large vertical accelerations and overloaded the transfer girders. One of the buildings had to be stabilized urgently in the hours after the earthquake while others sustained significant damage. The structures which remained standing were those capable of redistributing the forces from the damaged transfer girders to less damaged structural members. The extent of such force redistribution, and therefore the ability of the structure to survive extreme events, depends in part on the displacement capacity and post-peak behaviour of the transfer girders. For this reason, the evaluation of structures with deep transfer girders under extreme loading requires accurate models for predicting the complete non-linear response of the girders. As deep beams usually fail in a brittle manner due to shear, predicting their non-linear behaviour represents a challenging problem even when sophisticated non-linear finite element models are used. This paper will discuss a simpler alternative approach based on a kinematic model for deep beams. The kinematic model describes the deformation patterns of the beam with the help of two degrees of freedom: the average strain along the flexural reinforcement from support to support, and the transverse displacement in the critical zones in the vicinity of the applied loads (critical loading zones). The model assumes that much of the deformations concentrate along a critical diagonal crack which widens and slips as the deflections of the member increase. The equations of the kinematic model are combined with equilibrium equations and constitutive relationships for the load-resisting mechanisms across the critical crack. These mechanisms include diagonal compression in the critical loading zones, aggregate interlock, tension in the stirrups crossing the crack, and dowel action of the longitudinal reinforcement. The complete set of equations is solved iteratively in order to compute the pre- and post- peak response of deep beams. This approach is validated with the help of tests of deep beams. The model will be used to draw conclusions on the effect of the properties of deep beams on their non-linear behaviour. [less ▲]

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See detailThree-Parameter Kinematic Theory for Shear Strength and Displacement Capacity of Deep Beams
Mihaylov, Boyan ULiege

Scientific conference (2015, February 06)

Deep reinforced concrete beams are often used as transfer girders in high rise buildings to support heavy loads from discontinuous columns or shear walls. They are typically designed with strut-and-tie ... [more ▼]

Deep reinforced concrete beams are often used as transfer girders in high rise buildings to support heavy loads from discontinuous columns or shear walls. They are typically designed with strut-and-tie models which are based on a clear visualization of the flow of forces in the member. Strut-and-tie models usually provide conservative shear strength predictions but do not provide accurate assessments of deformation patterns close to failure. Information on ultimate deformations can be critical in, for example, designing members for support settlements or evaluation of structural robustness. To address these issues, this presentation will discuss an alternative approach based on a kinematic model which describes the deformation patterns of deep beams. Within each shear span this model uses just three parameters: the average tensile strain in the top longitudinal reinforcement, the average tensile strain in the bottom reinforcement, and the vertical deformation of the critical loading zone. The equations of the kinematic model are combined with equilibrium equations and constitutive relationships for the load-bearing mechanisms across a critical shear crack. These equations can be solved with a relatively small number of hand calculations. The three-parameter kinematic theory (3PKT) will be compared to strut-and-tie models with the help of a large test database. Design examples will be used to demonstrate the advantages of the 3PKT. [less ▲]

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