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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 (in press)

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 and Materials Journals (in press)

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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 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 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 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 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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