Tension Stiffening Effect Research Articles

The Tension-Stiffening Contribution of NSM CFRP to the Behavior of Strengthened RC Beams.

Tension stiffening is a characteristic behavior of reinforced concrete (RC) beams which is directly affected by the bond-slip property of steel bar and concrete interfaces. A beam strengthened with a near-surface mounted (NSM) technique would be even more affected by tension stiffening, as the NSM reinforcement also possess a bond-slip property. Yet assessing how much the tension stiffening of NSM contributes to the behavior of RC beams is difficult due to the fact that bond-slip effects cannot be directly incorporated into a strain-based moment-curvature analysis. As such, the tension stiffening is typically incorporated through various empirical formulations, which can require a great deal of testing and calibrations to be done. In this paper a relatively new method, which can be called the mechanics-based segmental approach, is used to directly simulate the tension stiffening effect of NSM reinforcements on RC beams, without the need for empirical formulations to indirectly simulate the tension stiffening. Analysis shows that the tension stiffening of NSM fiber reinforced polymer (FRP) contributes a significant portion to the stiffness and strength of the strengthened RC beam not only during serviceability, but at all load levels.

Maximum Crack Width Prediction in Deck Slab Concrete Structure

Inspection of crack width prediction procedures proposed by various researchers indicates that each formula contains a different set of variables. A literature review also suggests that there is no general agreement among various researchers on the relative significance of different variables affecting the crack width, despite the large number of experimental work carried out during the past few decades. An analytical method is developed to determine the concrete stress distribution near flexural cracks in reinforced concrete one-way slabs and used to investigate the effects of various variables on the spacing and width of cracks. The formula is developed using a large number of curvature values calculated from the concrete and steel strains at various sections between adjacent cracks for a number of composite precast deck slabs. The present method of incorporating the tension stiffening effect is verified by comparing calculated fracture mechanic and those measured by other investigators. The curvature values at sections between adjacent cracks are calculated using an empirical formula. Development of this formula is based on the curvature values calculated using the concrete and steel strains at various sections between successive cracks, for a number of composite precast deck slabs. Using the curvature values evaluated by the proposed formula, short-term deflections were determined for a large number of flexural members and the results were compared with those measured by other investigators. This comparison indicated that the present method of incorporating the tension stiffening effect in fracture mechanic calculations is acceptable.

Effect of tension stiffening on the behaviour of square RC column under torsion

Presence of torsional loadings can significantly affect the flow of internal forces and deformation capacity of reinforced concrete (RC) columns. It increases the possibility of brittle shear failure leading to catastrophic collapse of structural members. This necessitates accurate prediction of the torsional behaviour of RC members for their safe design. However, a review of previously published studies indicates that the torsional behaviour of RC members has not been studied in as much depth as the behaviour under flexure and shear in spite of its frequent occurrence in bridge columns. Very few analytical models are available to predict the response of RC members under torsional loads. Softened truss model (STM) developed in the University of Houston is one of them, which is widely used for this purpose. The present study shows that STM prediction is not sufficiently accurate particularly in the post cracking region when compared to test results. An improved analytical model for RC square columns subjected to torsion with and without axial compression is developed. Since concrete is weak in tension, its contribution to torsional capacity of RC members was neglected in the original STM. The present investigation revealed that, disregard to tensile strength of concrete is the main reason behind the discrepancies in the STM predictions. The existing STM is extended in this paper to include the effect of tension stiffening for better prediction of behaviour of square RC columns under torsion. Three different tension stiffening models comprising a linear, a quadratic and an exponential relationship have been considered in this study. The predictions of these models are validated through comparison with test data on local and global behaviour. It was observed that tension stiffening has significant influence on torsional behaviour of square RC members. The exponential and parabolic tension stiffening models were found to yield the most accurate predictions.

Effect of tension stiffening on the behaviour of reinforced concrete circular columns under torsion

Combination of torsion and axial compressive loading frequently occurs in bridge columns during earthquake vibrations. However, very few investigations in the past have explored the behaviour of Reinforced Concrete (RC) members under such load combinations. Softened Truss Model (STM) can be used to predict the torsional response of RC members such as beams and columns. In the present study, STM is used to predict the behaviour of RC circular columns under combined action of torsion and axial compression and the analytical prediction has been compared with experimental observation. It has been found that the overall torque–twist curve and in particular the post-peak behaviour of the tested columns is not accurately predicted by the original STM. The present study focuses on development of an improved analytical model for RC circular columns under torsional load conditions. The tensile strength of concrete being very small, its contribution to torsional strength of RC members was considered insignificant and was neglected in the original STM. The present investigation revealed that neglecting tension stiffening is the main reason behind the less accurate predictions of STM in the past compared to test data. The original STM has been extended in this study to include the effect of tension stiffening (TS) to get an improved prediction. Three different tension stiffening models have been considered for this purpose. The efficiency of each model in predicting the overall torsional response of RC columns under combined torsion and axial compression has been validated by comparing the analytical predictions of TS-STM with experimentally observed values. It is observed that exponential tension stiffening model can best represent the torsional behaviour of circular RC columns.

Modelling of tension-stiffening in bending RC elements based on equivalent stiffness of the rebar

The contribution of tensioned concrete between cracks (tension-stiffening) cannot be ignored when analysing deformation of reinforced concrete elements. The tension-stiffening effect is crucial when it comes to adequately estimating the load-deformation response of steel reinforced concrete and the more recently appeared fibre reinforced polymer (FRP) reinforced concrete. This paper presents a unified methodology for numerical modelling of the tension-stiffening effect in steel as well as FRP reinforced flexural members using the concept of equivalent deformation modulus and the smeared crack approach to obtain a modified stress-strain relation of the reinforcement. A closed-form solution for the equivalent secant modulus of deformation of the tensioned reinforcement is proposed for rectangular sections taking the Eurocode 2 curvature prediction technique as the reference. Using equations based on general principles of structural mechanics, the main influencing parameters are obtained. It is found that the ratio between the equivalent stiffness and the initial stiffness basically depends on the product of the modular ratio and reinforcement ratio (<TEX>$n{\rho}$</TEX>), the effective-to-total depth ratio (d/h), and the level of loading. The proposed methodology is adequate for numerical modelling of tension-stiffening for different FRP and steel reinforcement, under both service and ultimate conditions. Comparison of the predicted and experimental data obtained by the authors indicates that the proposed methodology is capable to adequately model the tension-stiffening effect in beams reinforced with FRP or steel bars within wide range of loading.

Quality assessment of material models for reinforced concrete flexural members

AbstractNon‐linear constitutive models for concrete in compression are frequently defined in design codes. The engineer generally uses either the linear (in SLS) or non‐linear (in ULS) compression model. However, a large variety of different approaches exists for describing the behaviour of the cracked concrete tension zone, and the selection of a corresponding model is usually based on qualitative engineering judgement. The aim of this paper is to assess the prediction quality of several concrete material models in order to provide a quantitative model selection. Therefore, uncertainty analysis is applied in order to investigate the model and parameter uncertainty in the bending stiffness prognosis for flexural members. The total uncertainty is converted into a prognosis model quality that allows a quantitative comparison between the material models considered. The consideration of the reinforced concrete in tension is based on the characterization of the tension stiffening effect, which describes the cracking in an average sense. In the interest of the practical applicability of the models considered, even for large structures, no discrete crack simulations based on fracture mechanics are considered. Finally, the assessment identifies that the prediction quality depends on the loading level and, furthermore, the quality across the models can be quantitatively similar as well as diverse.

Structural behavior of a continuous composite truss with a composite bottom chord

A continuous composite truss bridge combining steel box girders and composite truss girders was suggested to increase the span length of steel-concrete composite bridges. A bridge model with total length of 30m was fabricated, and static tests were performed. Composite bottom chord members, comprising a concrete filled steel box section, increase the flexural stiffness of the composite truss section in the negative moment region, while cracking of the slab reduces the flexural stiffness of the composite truss section in the negative moment region. Before cracking at concrete slab, the longitudinal stress of top chord members was remarkably reduced due to the contribution of the concrete slab. After cracking, the effective stiffness of the concrete slab considering tension stiffening effects corresponded well with the measured deflection. Cracking and the crack width of the concrete slab were observed and measured. Crack width control by longitudinal reinforcing bars can be used for the serviceability design of concrete slab in tension.

비정질 강섬유로 보강된 철근콘크리트 인장부재의 인장강화효과

이 논문은 비정질 강섬유 및 일반 강섬유로 보강된 철근콘크리트 인장 부재의 인장강화효과에 대해서 직접인장 실험을 통하여 비교ㆍ분석한 것이다. 이를 위하여 피복두께를 변수로 하는 직사각형 단면의 비정질 강섬유 및 일반 강섬유로 보강된 직접인장실험체를 각 6개씩 제작하여 실험을 실시하였다. 실험결과에 따르면 강섬유로 보강된 철근콘크리트 인장부재는 피복두께가 두꺼워질수록 인장강화효과가 증가하였으며, 비정질 강섬유가 일반 강섬유보다 인장강화효과가 더 우수하였다. 강섬유 보강에 따른 쪼갬균열의 발생 및 진행이 크게 감소하였으며, 비정질 강섬유로 보강된 경우는 철근 직경의 2배 이상 피복두께가 확보되면 쪼갬균열이 억제되고 그에 따라서 인장강화효과가 크게 증가하였다. 특히 일반 강섬유와 비교하여 비정질 강섬유로 보강된 철근콘크리트 부재의 경우는 현행 설계기준의 인장강화효과 규정과는 다르게 작용하중에 따라서 인장강화효과가 증가하였는데, 이 결과는 인장강화효과의 크기를 결정하는 인장강성 계수의 분석을 통하여 확인하였다.

Serviceability uncertainties in flat slabs

AbstractService load tests on the 6th floor of the full‐scale reinforced concrete building at BRE Cardington are described. Both deflections and reinforcement strains were measured. Finite element analyses of the floor slab were then undertaken using the measured material properties and four different models for the behaviour of the concrete in tension, the tension stiffening effect being known to influence slab behaviour significantly. Calculated deflections and reinforcement strains from the four analyses were compared with values measured in the load tests. As a consequence, comments, reservations and recommendations are made concerning the use of FE analyses for predicting deflections and reinforcement strains. Finally, the need to appreciate and accommodate the indeterminate nature of many of the parameters involved is emphasized.

Experimental study of tension stiffening in GFRP RC tensile members under sustained load

Sustained load effects on steel reinforced concrete structures due to creep and shrinkage in the concrete have been widely studied. However, knowledge of behaviour under sustained loads needs extending to the more recently developed fibre reinforced polymer (FRP) reinforced concrete structures. In this experimental study, the effect of tension stiffening on tensile glass fibre reinforced polymer (GFRP) reinforced concrete elements under sustained load is investigated. A total of six specimens with three different concrete strengths were tested for a period of between 35 and 40days, when it was seen that deformations stabilized. Some of the specimens included internal instrumentation of the reinforcing bar to capture the reinforcement strain profile and analyse long-term effects. Results confirm bond deterioration due to sustained load, with a reduction in the mean bond stress and concrete tensile stress, and showed how deterioration stabilized at approximately 28days. The influence of concrete strength on the loss of tension stiffening is also confirmed, with higher concrete compressive strength showing the smallest loss of concrete tensile stresses. The results are compared to predictions using Eurocode 2 approach, in which the effects of sustained load are incorporated by applying the effective modulus method (EMM). Predictions using this methodology compare well with experimental results.

Experimental Investigation of the Deformation Behavior of SFRC Beams with an Ordinary Reinforcement

The paper reports test results for steel-fiber-reinforced concrete beams. Four-point bending tests on 12 full-scale beams (with longitudinal reinforcement ratios of 0.3 and 0.6%) were carried out to investigate the postcracking behavior of the members. The content of fibers, spaced at equal intervals, ranged from 0 to 120 kg/m3, resulting in the amount of 0, 0.5, 1.0, and 1.5% by volume. A simple deflection analysis technique based on a linear interpolation between the cracking and yielding points is discussed. It is shown that this technique adequately assesses the bending moment at yielding, but significantly overestimates the corresponding deflections. It is concluded that the model discussed should be improved by taking into account the tension stiffening effect.

Investigating deformations of RC beams: experimental and analytical study

In this paper, a theoretical and experimental study of the sectional behaviour of reinforced concrete beams subjected to short-term loads is carried out. The pure bending behaviour is analysed with moment-curvature diagrams. Thus, the experimental results obtained from 24 beams tested by the authors and reported in literature are compared with theoretical results obtained from a layered model, which combines the material parameters defined in Model Code 2010 with some of the most recognized tension- stiffening models. Although the tests were carried out for short-term loads, the analysis demonstrates that rheological effects can be important and must be accounted to understand the experimental results. Another important conclusion for the beams tested in this work is that the method proposed by EC-2 tends to underestimate the tension-stiffening effects, leading to inaccuracies in the estimations of deflections. Thus, the actual formulation is analysed and a simple modification is proposed. The idea is the separation of the deflection prediction in two parts: one for short-term loads and other for rheological effects (shrinkage). The results obtained are in fairly good agreement with the experimental results, showing the feasibility of the proposed modification.

Thermal-pressure loading effect on containment structure

Because the elevated temperature degrades the mechanical properties of materials used in containments, the global behavior of containments subjected to the internal pressure under high temperature is remarkably different from that subjected to the internal pressure only. This paper concentrates on the nonlinear finite element analyses of the nuclear power plant containment structures, and the importance for the consideration of the elevated temperature effect has been emphasized because severe accident usually accompanies internal high pressure together with a high temperature increase. In addition to the consideration of nonlinear effects in the containment structure such as the tension stiffening and bond-slip effects, the change in material properties under elevated temperature is also taken into account. This paper, accordingly, focuses on the three-dimensional nonlinear analyses with thermal effects. Upon the comparison of experiment data with numerical results for the SNL 1/4 PCCV tested by internal pressure only, three-dimensional analyses for the same structure have been performed by considering internal pressure and temperature loadings designed for two kinds of severe accidents of Saturated Station Condition (SSC) and Station Black-out Scenario (SBO). Through the difference in the structural behavior of containment structures according to the addition of temperature loading, the importance of elevated temperature effect on the ultimate resisting capacity of PCCV has been emphasized.

Experimental Investigation of Bond Stress and Deformations in LWAC Ties Reinforced with GFRP Bars

ABSTRACTThe structures' durability is an engineering concern for a long time but has been increased in the last years. Lightweight aggregate concrete (LWAC) combined with glass fibre reinforced polymer bars allows to create structures with high performance in terms of durability. The glass fibre reinforced polymer (GFRP) bars have different ribs from those of steel bars, and consequently, its bond to concrete is affected. Moreover, the Young's modulus of GFRP is much below compared with that of steel, and this influences significantly the behaviour of structural elements reinforced with this material. This paper presents an experimental study focused on bond between LWAC and reinforcing bars of GFRP. Thirty‐six pull‐out tests were carried out using steel and GFRP bars. These reinforcements were combined with three types of concrete, all with the same design density 1900 kg m−3 but with different values of compressive strength: 35, 55 and 70 MPa. Furthermore, 12 reinforced ties were tested, combining different types of bars (steel and GFRP), two different diameters (12 and 16 mm) and the three types of LWAC. Based on experimental results, several relations were established to understand the behaviour of LWAC structures reinforced with GFRP bars, mainly in the serviceability conditions. These results point out that ties deformation and crack width are very affected by the reduced Young's modulus of GFRP: deformations and crack width of ties reinforced with GFRP are significantly higher, approximately three times greater, compared with those of ties reinforced with steel. The tension stiffening effect was also analysed in detail, and it was found that it is slightly influenced by the concrete compressive strength but is highly dependent of the Young's modulus of the reinforcing material.

Effect of longitudinal reinforcement and prestressing on stiffness of composite beams under hogging moments

To investigate the stiffness of steel–concrete composite beams subjected to hogging bending moments and their enhancement through prestressing using external tendons, laboratory experiments were conducted on five steel–concrete composite beams. Three of the beams were two-span continuous composite beams with box steel girders and the others were simply supported. The parameters investigated included the amount of longitudinal reinforcement and the arrangement of prestressing. From the experimental results, it was found that prestressing significantly improved the cracking moment of composite beams, and crack spacing was dominated by the transverse reinforcement spacing. The stiffness enhancement and crack control suggest the advantages to the mechanical performance of composite beams prestressed by external tendons. A theoretical model is proposed to estimate the effective stiffness of a composite beam subjected to hogging bending moments, taking into account the tension stiffening effect of concrete cracking.

Assessment of crack width estimation models for RC tension members

The objective of this study is to assess the crack width estimation equation suggested in CEB-FIP Model Code 1990 (1991) in terms of concrete strength. To evaluate the crack width estimation equation, a numerical model for a crack element is introduced by adopting detailed bond stress slip models. A remarkable advantage of the use of the model is that all significant internal variables within a crack element can be analysed, including average bond stress and tension stiffening effect, which are the vital parameters for the equation in CEB-FIP Model Code. Experimental results from literature were compared with those obtained by the estimation model equation in CEB-FIP Model Code and by the numerical analysis using the crack element model. The average bond stress and tension stiffening effect given in CEB-FIP Model seem to be overestimated and thus need to be reduced to properly reflect the effect of concrete strength.

RC Beams Strengthened with Mechanically Fastened Composites: Experimental Results and Numerical Modeling

The use of mechanically-fastened fiber-reinforced polymer (MF-FRP) systems has recently emerged as a competitive solution for the flexural strengthening of reinforced concrete (RC) beams and slabs. An overview of the experimental research has proven the effectiveness and the potentiality of the MF-FRP technique which is particularly suitable for emergency repairs or when the speed of installation and immediacy of use are imperative. A finite-element (FE) model has been recently developed by the authors with the aim to simulate the behavior of RC beams strengthened in bending by MF-FRP laminates; such a model has also been validated by using a wide experimental database collected from the literature. By following the previous study, the FE model and the assembled database are considered herein with the aim of better exploring the influence of some specific aspects on the structural response of MF-FRP strengthened members, such as the bearing stress-slip relationship assumed for the FRP-concrete interface, the stress-strain law considered for reinforcing steel rebars and the cracking process in RC members resulting in the well-known tension stiffening effect. The considerations drawn from this study will be useful to researchers for the calibration of criteria and design rules for strengthening RC beams through MF-FRP laminates.

Tension stiffening approach in concrete of tensioned members

This paper presents an analytical model to calibrate the tension stiffening effect of tensile reinforced concrete members. The tension stiffening behaviour is a primordial task in reinforced concrete mechanic field. In this model, the stress–strain relationship of the tension stiffening effect described in the cracking range is proposed. The application of the analytical expression for tensile reinforced concrete member aims principally to quantify the tension stiffening phenomenon in the cracking range. In this concern, a parametrical study is established, which concerns the influence on the tension stiffening behaviour of concrete strength, reinforcement ratio, bar diameter and instantaneous properties of concrete. Obtained results relative to the influence of different parameters of the analysis are shown and commented.

Influence of steel fibres on tension stiffening and cracking of reinforced geopolymer concrete

An experimental investigation was conducted to study the influence of steel fibres on the tension stiffening effect and cracking behaviour of geopolymer concrete (GPC). A total of ten concentrically reinforced concrete prisms (60 × 60 × 600 mm) were cast and tested under uniaxial tension. Out of these, two were made of GPC and the remainder were of steel-fibre-reinforced GPC. The grade of concrete was M40. Different volume fractions of 0·25% (16·62 kg/m3), 0·50% (39·25 kg/m3), 0·75% (58·87 kg/m3) and 1% (78·50 kg/m3) of crimped steel fibres of aspect ratio 66 were used. The test results indicate that the incorporation of steel fibres improves the tension stiffening effect and reduces the spacing and width of cracks. A method was also proposed to predict the width of cracks.

Experimental Study and Evaluation of Tension Stiffening Model in High Strength Concrete Beams

Abstract In strength limit states design, it is assumed that after cracking, reinforcement carries all tension in the tension zone of reinforced concrete members. However, it can be seen the concrete between cracks will contribute to carrying a part of the tension stress in actual concrete members particularly at service load levels, this effect is referred as tension stiffening effect.In this study, tension stiffening models and high strength concrete beam flexural test results were verified through comparison. The relationship between moment-curvature and load-deflection was evaluated by result of tension stiffening model and test result values. The analysis results showed that ACI 318 and Owen & Damjanic generally shows good agreement. Keywords :Tension stiffening effect, tension stiffening model, moment-curvature, high strength concrete † Corresponding author: Tel: +82-31-201-3815; E-mail: leeyh@khu.ac.krReceived February 1 2014; Revised February 10 2014;Accepted February 11 2014Ⓒ2014 by Computational Structural Engineering Institute of KoreaThis is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons. org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.