Tension Stiffening Analysis for Cyclically Loaded RC Beams

Ductility is an important aspect of cyclically loaded reinforced concrete (RC) structures. One of the method that can be used to measure the ductility of an RC structure is the moment-curvature approach. However, due to it being a strain-based approach it cannot be used to directly simulate behaviour associated with interface displacement that occur when an RC member is cracked. This leads to dependency on empirical values, which imposes limitations on how the moment-curvature approach can be used. In recent years a new displacement based method for measuring ductility has been developed, and can simulate the interface displacement behaviours through the use of partial-interaction theory and shear friction theory. This paper aims to extend the general tension stiffening analysis of the displacement-based approach to allow for cyclic loading. The tension-stiffening analysis was then validated against experimental results and the results were found to agree fairly.

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MODELLING DEFORMATION BEHAVIOUR OF RC BEAMS ATTRIBUTING TENSION-STIFFENING TO TENSILE REINFORCEMENT

Engineering Structures and Technologies ◽

10.3846/skt.2009.17 ◽

2009 ◽

Vol 1 (3) ◽

pp. 141-147 ◽

Cited By ~ 2

Author(s):

Donatas Salys ◽

Gintaris Kaklauskas ◽

Viktor Gribniak

Keyword(s):

Deformation Behaviour ◽

Tensile Force ◽

Material Model ◽

Rc Beams ◽

Tension Stiffening ◽

Load Carrying ◽

Reinforced Steel ◽

Internal Forces ◽

The Moment ◽

Stiffening Effect

After cracking, the stiffness of the member along its length varies, which makes the calculation of deformations complicated. In a cracked member, stiffness is largest in the section within the uncracked region while remains smallest in the cracked section. This is because in the cracked section, tensile concrete does not contribute to the load carrying mechanism. However, at intermediate sections between adjacent cracks, concrete around reinforcement retains some tensile force due to the bond-action that effectively stiffens member response and reduces deflections. This effect is known as tension-stiffening. This paper discusses the tension-stiffening effect in reinforced concrete (RC) beams. Numerical modelling uses the approach based on tension-stiffening attributed to tensile reinforcement. A material model of reinforced steel has been developed by inverse analysis using the moment-curvature diagrams of RC beams. Total stresses in tensile reinforcement consist of actual stresses corresponding to the average strain of the steel and additional stresses due to tension-stiffening. The carried out analysis employed experimental data on RC beams tested by the authors. The beams had a constant cross section but a different amount of tensile reinforcement. It has been shown that additional (tension-stiffening) stresses in the steel depend on the area of reinforcement. However, the resulting internal forces are less dependent on the amount of reinforcement.

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Partial-interaction tension-stiffening properties for numerical simulations

Advances in Structural Engineering ◽

10.1177/1369433216660654 ◽

2016 ◽

Vol 20 (5) ◽

pp. 812-821 ◽

Cited By ~ 10

Author(s):

Tao Zhang ◽

Phillip Visintin ◽

Deric J Oehlers

Keyword(s):

Reinforced Concrete ◽

Equivalent Stress ◽

Major Effect ◽

Concrete Member ◽

Tension Stiffening ◽

Closed Form Solutions ◽

Reinforced Concrete Member ◽

Partial Interaction ◽

Displacement Based ◽

Crack Widths

The partial-interaction behaviour of tension-stiffening affects or controls virtually all aspects of reinforced concrete member behaviour as it controls the formation and widening of cracks as well as the load developed within the reinforcement crossing a crack. In this article, simple closed-form solutions for the tension-stiffening behaviour of reinforced concrete prisms are derived through mechanics and are presented in a form that can be easily used in both displacement-based and strain-based numerical modelling. This research quantifies not only the pseudo material properties of tension-stiffening such as equivalent stress–strain relationships or equivalent moduli that simulate the increase in reinforcement stiffness associated with tension-stiffening but also the crack spacings and crack widths. It is shown that the bond properties have little, if any, effect on tension-stiffening but a major effect on crack spacings and widths.

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Fragility Curves and Probabilistic Seismic Demand Models on the Seismic Assessment of RC Frames Subjected to Structural Pounding

Applied Sciences ◽

10.3390/app11178253 ◽

2021 ◽

Vol 11 (17) ◽

pp. 8253

Author(s):

Maria G. Flenga ◽

Maria J. Favvata

Keyword(s):

Fragility Curves ◽

Seismic Demand ◽

Rc Structures ◽

Structural Pounding ◽

Rc Frames ◽

Rc Structure ◽

Demand Models ◽

Probabilistic Seismic Demand ◽

Displacement Based ◽

The Impact

This study aims to evaluate five different methodologies reported in the literature for developing fragility curves to assess the seismic performance of RC structures subjected to structural pounding. In this context, displacement-based and curvature-based fragility curves are developed. The use of probabilistic seismic demand models (PSDMs) on the fragility assessment of the pounding risk is further estimated. Linear and bilinear PSDMs are developed, while the validity of the assumptions commonly used to produce a PSDM is examined. Finally, the influence of the PSDMs’ assumptions on the derivation of fragilities for the structural pounding effect is identified. The examined pounding cases involve the interaction between adjacent RC structures that have equal story heights (floor-to-floor interaction). Results indicate that the fragility assessment of the RC structure that suffers the pounding effect is not affected by the examined methodologies when the performance level that controls the seismic behavior is exceeded at low levels of IM. Thus, the more vulnerable the structure is due to the pounding effect, the more likely that disparities among the fragility curves of the examined methods are eliminated. The use of a linear PSDM fails to properly describe the local inelastic demands of the structural RC member that suffers the impact effect. The PSDM’s assumptions are not always satisfied for the examined engineering demand parameters of this study, and thus may induce errors when fragility curves are developed. Nevertheless, errors induced due to the power law model and the homoscedasticity assumptions of the PSDM can be reduced by using the bilinear regression model.

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Short-term deflection of RC beams using a discrete rotation approach

International Journal of Advanced Structural Engineering ◽

10.1007/s40091-019-00247-5 ◽

2019 ◽

Vol 11 (4) ◽

pp. 473-490 ◽

Cited By ~ 3

Author(s):

Mohamed El-Zeadani ◽

Raizal Saifulnaz Muhammad Rashid ◽

Mugahed Yahya Hussein Amran ◽

Farzad Hejazi ◽

Mohd Saleh Jaafar

Keyword(s):

Concrete Surface ◽

Rc Beams ◽

Shear Cracks ◽

Limit States ◽

Rc Structures ◽

Linear Behavior ◽

Partial Interaction ◽

Current Design ◽

Full Interaction ◽

Experimental Findings

Abstract Quantifying the deflection of RC beams has been performed traditionally using full-interaction moment–curvature methods without considering the slip that takes place between the reinforcement and the surrounding concrete. This was commonly carried out by deriving empirically based flexural rigidities and using elastic deflection equations to predict the deformation of RC structures. However, as flexural and flexural/shear cracks form in RC beams with increase in applied load, the reinforcement steel begins to slip against the surrounding concrete surface causing the cracks to widen and ultimately increasing the deflection at mid-span. Current design rules cannot cope directly with the deformation induced by the widening of cracks. Because of that, this study focused on predicting the non-time dependent deflection of RC beams at both service and ultimate limit states using a mechanics-based discrete rotation approach. The mechanics-based solution was compared with experimental test results and well-established code methods to which a good agreement between the results was observed. The method presented accounts for the non-linear behavior of the concrete in compression, the partial-interaction behavior of the reinforcement, and the deflection was computed while considering the rotation of discrete cracks. Due to its generic nature, the method presented does not require any calibration with experimental findings on the member level, which makes it appropriate to quantify the deflection or RC structures with different types of concrete and novel reinforcement material.

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Flexural strength of FRP plated RC beams using a partial-interaction displacement-based approach

Structures ◽

10.1016/j.istruc.2019.09.008 ◽

2019 ◽

Vol 22 ◽

pp. 405-420 ◽

Cited By ~ 5

Author(s):

Mohamed El-Zeadani ◽

M.R. Raizal Saifulnaz ◽

Y.H. Mugahed Amran ◽

F. Hejazi ◽

M.S. Jaafar ◽

...

Keyword(s):

Flexural Strength ◽

Rc Beams ◽

Partial Interaction ◽

Displacement Based

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Flexural Performance of RC Beams Strengthened with Externally-Side Bonded Reinforcement (E-SBR) Technique Using CFRP Composites

Materials ◽

10.3390/ma14112809 ◽

2021 ◽

Vol 14 (11) ◽

pp. 2809

Author(s):

Md. Akter Hosen ◽

Fadi Althoey ◽

Mohd Zamin Jumaat ◽

U. Johnson Alengaram ◽

N. H. Ramli Sulong

Keyword(s):

Absorption Capacity ◽

Experimental Program ◽

Rc Beams ◽

Rc Structures ◽

Functional Changes ◽

Flexural Strengthening ◽

Cfrp Laminates ◽

Flexural Performance ◽

Design Loads ◽

Predicted Values

Reinforced concrete (RC) structures necessitate strengthening for various reasons. These include ageing, deterioration of materials due to environmental effects, trivial initial design and construction, deficiency of maintenance, the advancement of design loads, and functional changes. RC structures strengthening with the carbon fiber reinforced polymer (CFRP) has been used extensively during the last few decades due to their advantages over steel reinforcement. This paper introduces an experimental approach for flexural strengthening of RC beams with Externally-Side Bonded Reinforcement (E-SBR) using CFRP fabrics. The experimental program comprises eight full-scale RC beams tested under a four-point flexural test up to failure. The parameters investigated include the main tensile steel reinforcing ratio and the width of CFRP fabrics. The experimental outcomes show that an increase in the tensile reinforcement ratio and width of the CFRP laminates enhanced the first cracking and ultimate load-bearing capacities of the strengthened beams up to 141 and 174%, respectively, compared to the control beam. The strengthened RC beams exhibited superior energy absorption capacity, stiffness, and ductile response. The comparison of the experimental and predicted values shows that these two are in good agreement.

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A Practical Finite Element Modeling Strategy to Capture Cracking and Crushing Behavior of Reinforced Concrete Structures

Materials ◽

10.3390/ma14030506 ◽

2021 ◽

Vol 14 (3) ◽

pp. 506 ◽

Cited By ~ 1

Author(s):

Alexandre Mathern ◽

Jincheng Yang

Keyword(s):

Finite Element ◽

Reinforced Concrete ◽

Constitutive Relations ◽

Fe Analysis ◽

Rc Beams ◽

Cracking Behavior ◽

Concrete Cracking ◽

Rc Structures ◽

Nonlinear Fe Analysis ◽

Modeling Strategy

Nonlinear finite element (FE) analysis of reinforced concrete (RC) structures is characterized by numerous modeling options and input parameters. To accurately model the nonlinear RC behavior involving concrete cracking in tension and crushing in compression, practitioners make different choices regarding the critical modeling issues, e.g., defining the concrete constitutive relations, assigning the bond between the concrete and the steel reinforcement, and solving problems related to convergence difficulties and mesh sensitivities. Thus, it is imperative to review the common modeling choices critically and develop a robust modeling strategy with consistency, reliability, and comparability. This paper proposes a modeling strategy and practical recommendations for the nonlinear FE analysis of RC structures based on parametric studies of critical modeling choices. The proposed modeling strategy aims at providing reliable predictions of flexural responses of RC members with a focus on concrete cracking behavior and crushing failure, which serve as the foundation for more complex modeling cases, e.g., RC beams bonded with fiber reinforced polymer (FRP) laminates. Additionally, herein, the implementation procedure for the proposed modeling strategy is comprehensively described with a focus on the critical modeling issues for RC structures. The proposed strategy is demonstrated through FE analyses of RC beams tested in four-point bending—one RC beam as reference and one beam externally bonded with a carbon-FRP (CFRP) laminate in its soffit. The simulated results agree well with experimental measurements regarding load-deformation relationship, cracking, flexural failure due to concrete crushing, and CFRP debonding initiated by intermediate cracks. The modeling strategy and recommendations presented herein are applicable to the nonlinear FE analysis of RC structures in general.

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