• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.997-1016
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• 2015

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 ($n{\rho}$), 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.

• Journal of the Korea Concrete Institute
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• v.19 no.6
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• pp.745-754
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• 2007

This paper presents a unified modeling technique for tension stiffening effect in structural concrete members. The model is mathematically derived from the bond stress-slip relationships which account for splitting crack. The relationships in CEB-FIP Model Code 1990 and Eurocode 2 are employed together with the assumptions of a linear slip distribution along the interface and the uniform condition of concrete tensile contribution for the mid section of cracked member at the stabilized cracking stage. With these assumptions, a model of tension stiffening effect is proposed by accounting for the force equilibrium and strain compatibility condition associated to the steel strain and concrete contribution by bond stress. The model is applied to the test results available in literatures, and the predicted values are shown to be in good agreement with the experimentally measured behavior.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10b
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• pp.873-878
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• 2000

Tension stiffening effects of reinforced concrete member with large diameter bar, mainly used at reactor building of nuclear power plant, are studied by uniaxial structural tests. Bond length and stress of steel bar, size of steel bar, and compressive strength of concrete are evaluated to tension stiffening by uniaxial tests. Problems and solution during the uniaxial test are suggested. The prevent splitting cracks, concrete cover-to-bar diameter ratio $c/d_{b}$ is kept 2.6~2.8. Because the bond length is increased as the size of steel bar, the specimen length of the D35 steel bar is required at least 2.0 m. The specimen length must be decided with bond length as well as concrete cover-to-bar diameter ratio to prevent splitting crack.

• Steel and Composite Structures
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• v.33 no.2
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• pp.225-243
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• 2019

Cold-formed steel (CFS) sections when used as primary load carrying members often require additional strengthening for retrofitting purposes. In some cases, it is also necessary to reduce deflections in order to satisfy serviceability requirements. The introduction of angle sections, screwed to the webs so as to act as external stiffeners, has the potential to both increase flexural strength as well as reduce deflections. This paper presents the results of ten four-point bending tests, on built-up CFS sections, both open and closed, with different stiffening arrangements. In the laboratory tests, the stiffening arrangements increased the moment capacity and stiffness of the CFS beams by up to 85% and 100% respectively. The increase in moment capacity was more evident for the open sections, while that reduction in deflection was largest for the closed sections.

• Journal of the Korea Concrete Institute
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• v.22 no.6
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• pp.859-866
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• 2010

To overcome weak and brittle tensile characteristics of concrete, many studies have been conducted on fiber reinforced concrete (FRC). Recently, high performance fiber reinforced cementitious composites (HPFRCC), which shows strain hardening behavior, has been actively investigated. However, most of the studies focused on the material behavior of HPFRCC itself. Only a few studies have been conducted on the tensile behavior of HPFRCC with steel reinforcement. Therefore, a tension stiffening test for HPFRCC members has been conducted in this study in order to investigate the effect of a reinforcing bar on the tensile behavior of HPFRCC. Tensile stress-strain relationship of HPFRCC has been derived from the tests. The HPFRCC resisted tensile stress continuously from the first cracking to the yield of reinforcing bar. Through the comparison with the tensile behavior of HPFRCC members without a reinforcement, it was shown the tensile strength and capacity of HPFRCC were reduced due to the combined effect of the high shrinkage of HPFRCC, restraining effect of steel reinforcement, and the strain hardening behavior of HPFRCC. It is expected that the tension stiffening test results can be useful for an application of HPFRCC with steel reinforcement as structural members.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.107-108
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• 2010

This paper provides test results on the tension stiffening behavior of high strength concrete (HSC) members used silica fume free binder (SFFB) instead of silica fume. The objective of this study is to evaluate the capability of replacing expensive silica fume to SFFB in HSCs with compressive strength of 60 and 80MPa. Test results indicated that for two mixes of 60 and 80 MPa HSC, cracking and strength behavior of tension members, which are replaced silica fume to SFFB, showed equivalent performance to those of tension members used silica fume.

• Journal of Industrial Technology
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• v.18
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• pp.87-95
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• 1998

Cracking is considered to be one of the important factors in determining the durability of reinforced concrete structures. When the bending stress exceeds the modulus of rupture of the concrete, cracking form along the length of members. The total load is transferred across these cracks by the reinforcement, but the concrete between cracks is still capable of carrying stresses due to the bond between steel and concrete. This phenomenon is called the tension stiffening effect. The tension stiffening effect is affected by many variables, such as the bond stress, strength of concrete, interrocking of aggregate, type of steel, and dowel action of steel. Also, this tension stiffening effect is usually quite significant in beams under service loading, and must be taken into account in the calculation of deflection and crack widths. In this study, the experiment was carried out on types of specimen, strength of concrete, and steel ratio and finite element analysis were compared in terms of load-deflection relationship, crack pattern.

• Journal of the Korea Concrete Institute
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• v.22 no.6
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• pp.761-768
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• 2010

When cracks occur in reinforced concrete structures, a steel carries all tensile force at crack section, while the concrete between cracks carries a part of the tensile force due to bond, so that the steel is less elongated. This is called the tension-stiffening effect, that plays an important role in verification of a serviceability limit state. But it is a complicated work to use a complex strain distribution between cracks, therefore an average strain is used to calculate deflection and crack width. In Eurocode 2, tension-stiffening effect expressed in the first order form or the second order form is used in calculating an average curvature for deflection. In this study for a flexural member deflection and crack width are calculated using various models for the tension-stiffening effect and the results are compared with the values of Eurocode 2 and KCI provisions. As results, the predicted values using the second order form are appeared to be well agreed with the experimental values and it could secure more analytical consistency.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1A
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• pp.35-41
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• 2011

In concrete structural design provisons, two methods are normally provided to control deflection; direct method and indirect method. It is more efficient to use the indirect deflection control by which the span/depth ratio is limited not to exceed an allowable deflection limit. Because actual deflections are affected by many causes, it is complicated to evaluate actual deflections. In this study, limit span/depth ratios are derived from the deflection calculated directly at the serviceability limit state in RC members. The deflection is obtained from using average curvature, which depends on materials model used. The main variables examined are tension stiffening effect, concrete strength, cross section size and compressive steel ratio. It could be appeared that more analytical consistency is secured to use the 2nd order form of tension stiffening effect. And the limit span/depth ratio is dependent on material strength, tensile and compressive steel ratio but it is independent on cross-section size.

• Steel and Composite Structures
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• v.42 no.4
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• pp.447-458
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• 2022

Cold-formed steel (CFS) sections are thin-walled, therefore, more susceptible to different types of geometric imperfections. Global type of geometric imperfections has a significant impact on the load-carrying capacity of flexural members. This paper reports an experimental study that discusses the influence of global imperfections on the flexural response of CFS built-up I-beams composed of two lipped channels, with simply supported ends, under four-point loading. Global imperfections of magnitude over eight times the maximum permissible ones were induced in the specimens, leading to their distress. Using various simple stiffening schemes, the capacity and stiffness of the distressed specimens were improvised. The performance comparisons were made based on the maximum loads resisted, flexural stiffnesses offered, and failure modes experienced by the specimens. As experimental data on such distressed specimens are currently lacking in the literature, the test results of the present study will provide the necessary data needed by future researchers to numerically extend this study further, which will help in the development of necessary design guidelines for the same. The stiffening schemes significantly improved the structural efficiency of distressed specimens in terms of strength and stiffness, by over 60%. As a result, an effective and time-saving solution to such realistic structural engineering problems is given.