Experimental and Analytical Investigation of Deformations and Stress Distribution in Steel Bands of a Two-Span Stress-Ribbon Pedestrian Bridge

The article is dedicated to the analysis of problems related to design of pedestrian bridges with flexible ribbon bands made of steel. The study is based on test results of a bridge model that has two spans (each with a length of five meters). A simplified analytical technique has been proposed for predicting vertical deformations of the bridge structure subjected to symmetrical or asymmetrical loading patterns. The technique also allows assessing the tension forces in the ribbons, which are very important for design of such structures. The analysis reveals the importance of the flexural rigidity of the ribbons that might cause significant redistribution of stresses within the steel bands

Generalised tension-stiffening relationship conforming to Chinese Design Code GB 50010-2010

A generalised stress-strain tension-stiffening relationship conforming to the Chinese Code for Design of Concrete Structures GB 50010-2010 is proposed. Based on the provisions in GB 50010-2010 for rigidity and curvature calculations of reinforced concrete flexural members, tension-stiffening relationships were derived from moment-curvature relations by means of the inverse technique for deformation analysis. A parameterized stress block for tension-stiffening was suggested. The proposed tension-stiffening model was applied to nonlinear finite element analysis of reinforced concrete beams. Good agreement between the analysis results based on the proposed model and those based on the codified formulas in GB 50010-2010 was achieved. The proposed model will be able to serve as a design aid for serviceability evaluation of concrete beams in general

Tension-stiffening behaviour of reinforced concrete ties of various strength classes

A new law of tension-stiffening for reinforced concrete (RC) ties is proposed in the present study. It is based on the test data of 11 experimental programs of RC elements of various strength classes reported in the literature. The experimental programs covered a wide range of characteristics of mechanical and geometrical parameters of specimens such as compressive strength of concrete, reinforcement ratio and diameter of reinforcement bars. By eliminating the effect of shrinkage from the test load-strain diagrams of the ties, a simple model with no dependence on reinforcement ratio could be derived. The proposed tension-stiffening law is compared with the formulation in Eurocode 2. Statistical analysis of strain predictions of RC ties based on Eurocode 2 was conducted. It is found that the Eurocode 2 significantly underestimated strains in the RC ties with the errors reaching 50% for the lightly reinforced members. Nevertheless, when shrinkage effect was accounted for in the test load-strain diagrams, the predictive capability of the Eurocode 2 formulation could be significantly improved

A new method for formulating crack spacing models of RC ties

Cracking of concrete is one of the most complicated phenomena in reinforced concrete analysis and is one of the key aspects governing serviceability analysis of RC structures. Current methods for investigating cracking rely on empirical approaches that give unreliable results with errors of multiple times the real value. A new non-empirical method based on the combination of the stress-transfer and the smeared approaches is proposed for deriving crack spacing models. The stress-transfer approach governs the strain distribution of the reinforcement between the consecutive cracks whereas the smeared approach allows for the estimation of the mean strain of the element. The suggested method introduces the concept of damage zones: the bond in the area adjacent to the normal cracks is considered to be fully damaged, thus bond behaviour is non-uniform in the segment between cracks. Crack spacing models were derived using the load-strain analysis method presented in the Eurocode 2 and were shown to give results that are in good agreement with the crack spacing values taken from available experimental data

Experimental and Numerical Analysis of Strain Gradient in Tensile Concrete Prisms Reinforced with Multiple Bars

This work is a continuation of the ongoing research on deformation behavior of reinforced concrete elements under tension. The previous studies have revealed that deformation behaviors of elements reinforced with multiple bars and the traditional prismatic members reinforced with a center bar are essentially different. The latter layout, though typical of laboratory specimens, could not represent the norm of structures in real-life. Thus, a new test methodology to investigate the strain distribution in concrete prismatic members reinforced with multiple bars subjected to axial tension is devised. Prismatic concrete specimens with different reinforcement configurations were fabricated and tested using the proposed setup. Deformation behavior of the specimens is modeled with a tailor-designed bond modeling approach for rigorous finite element analysis. It is revealed that the average deformations of the concrete could be different from the prevailing approach of average deformations of the steel, and are dependent on the reinforcement configurations. Therefore, the efficiency of concrete in tension should be carefully taken into account for rational design of structural elements. The study endorses promising abilities of finite element technique as a versatile analysis tool whose full potential is to be revealed with the advent of computer hardware

Determination and modelling of bond properties of synthetic macro-fibres in concrete

Bond behaviour of a synthetic macro-fibre in concrete is the object of this research. The bond strength and stiffness are the parameters characterising the bonding mechanism that determines the efficiency of the reinforcing material. However, there is no general methodology developed to evaluate fibre efficiency. There also exists neither a straightforward procedure to estimate the bond quality of a synthetic macro-fibre nor a reliable numerical model to simulate the bond behaviour of such fibres. In this work, the bond mechanisms of 40 mm long synthetic macro-fibres are investigated using pull-out tests: 16 concrete cubes were made for that purpose. One type of synthetic macro-fibre available at the market is considered. In each test sample, three fibres were inserted perpendicular to the top and two side surfaces; two bonding lengths (10 mm and 20 mm) were used. A gripping system was developed to protect the fibres from local damage. A physically non-linear finite element model of the pull-out sample was developed. A bond model was proposed to simulate deformation behaviour of the fibres. Article in English. Betono ir sintetinio makroplaušo sukibties savybių nustatymas ir modeliavimas Santrauka Šio tyrimo objektas – sintetinio makroplaušo sukibties elgsena betone. Sukibties stiprumas ir standumas yra parametrai, apibūdinantys sukibties mechanizmą, kuris lemia armatūrinės medžiagos efektyvumą. Tačiau nėra bendros metodikos, kuria būtų galima įvertinti plaušo efektyvumą. Taip pat nėra nei paprasčiausios sintetinio makroplaušo sukibties kokybės įvertinimo procedūros, nei patikimo skaitmeninio modelio, kuris imituotų tokių plaušų sukibties elgesį. Šiame darbe 40 mm ilgio sintetinių makroplaušų sukibties mechanizmai tiriami atliekant ištraukimo bandymus. Tam buvo pagaminta 16 betono kubelių. Išbandoma viena iš rinkoje esančių sintetinių makroplaušų rūšių. Kiekviename bandinyje trys plaušai buvo įgilinami statmenai viršutiniam ir dviem šoniniams paviršiams. Buvo naudojami du įgilinimo ilgiai (10 mm ir 20 mm). Sukurta įtvirtinimo sistema, apsauganti plaušus nuo vietinių pažeidimų. Buvo sukurtas fiziškai netiesinis iš betono ištraukiamų plaušų baigtinių elementų modelis, pasiūlytas sukibties modelis, siekiant imituoti plaušų elgseną deformuojantis. Reikšminiai žodžiai: sintetiniai plaušai, ištraukimas, bandymas, sukibties elgsena, skaitmeninis modeliavimas

Discussion: Tension stiffening in concrete beams. Part I: Fe analysis

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Mechanical behavior of concrete prisms reinforced with steel and GFRP bar systems

Being immune to corrosion, and having a tensile strength up to three times higher than structural steel, glass fiber reinforced polymer (GFRP) bars are suitable for reinforcing concrete structures exposed to aggressive environmental conditions. However, a relatively low elasticity modulus of GFRP bars (in respect to the steel) favors the occurrence of relatively large deformability of cracked reinforced concrete. Lack of ductility and degradation of properties under high temperature can be also identified as debilities of GFRP bars over steel ones. Combining GFRP and steel bars can be a suitable solution to overcoming these concerns. Nevertheless, the application of such hybrid reinforcement systems requires reliable material models. The influence of the relative area of GFRP and steel bars on the tensile capacity of cracked concrete (generally known as tension-stiffening effect), was never investigated from the experimental point of view, mainly crossing results from different tools on the assessment of the cracking process. This paper experimentally investigates deformations and cracking behavior of concrete prisms reinforced with steel bars and GFRP bars in different combinations. The test results of 11 elements are reported. A tensile stress-strain diagram is conceptually proposed for modelling the tension-stiffening effect in elements with such hybrid combination of the reinforcement. The cracking process in terms of crack width and crack spacing is analyzed considering the hybrid reinforcement particularities and a preliminary approach is proposed for the prediction of the crack width for this type of reinforced concrete elementsResearch Council of Lithuania (Research Project S-MIP-17-62). The second author also 590 wish to acknowledge the support provided by FCT through the PTDC/ECM591 EST/1882/2014 projec

Comparative analysis of flexural stiffness of concrete elements with different types of composite reinforcement systems

Various materials and reinforcement technologies have been created for concrete structures. However, there is no uniform methodology to compare the mechanical characteristics of different reinforcement systems. In structural systems, residual stiffness can estimate the efficiency of the reinforcement. This study introduces a simplified approach for the flexural stiffness analysis. It employs a new testing layout designed with the purpose to form multiple cracks in a small laboratory specimen. The achieved solution requires neither iterative calculations nor a description of the loading history. Several composite reinforcement schemes, including internal glass fibre reinforced polymer (GFRP) bars, carbon fibre reinforced polymer (CFRP) sheets and near-surface mounted (NSM) strips are considered. The analysis of the test results reveals a substantial efficiency of the external CFRP reinforcement systems. Article in English. Skirtingomis kompozitinėmis sistemomis armuotų betoninių elementų lenkiamojo standumo lyginamoji analizė Santrauka Betono konstrukcijoms armuoti naudojamos įvairios medžiagos ir technologijos, tačiau unifikuotos metodikos, kuria būtų galima palyginti skirtingų armavimo sistemų mechanines savybes, nėra. Konstrukcinės sistemos armavimo efektyvumas gali būti vertinamas atsižvelgiant į elementų liekamąjį standumą. Šiame straipsnyje pateikiamas supaprastintas lenkiamojo standumo analizės metodas. Jis apima naują bandymų schemą, kuria siekiama gauti tolygų plyšių pasiskirstymą mažame laboratoriniame bandinyje. Siūlomas analitinis sprendimas nereikalauja nei iteracinio skaičiavimo, nei detalaus apkrovos istorijos aprašymo. Nagrinėjamos kelios kompozitinio armavimo sistemos: taikant stiklo pluoštu armuotus polimerinius (GFRP) strypus, išdėstytus elemento viduje, anglies pluoštu armuotus polimerinius (CFRP) lakštus, priklijuotus elemento išorėje, ir sijų paviršiuje tvirtinamas anglies pluoštu armuotas polimerines (NSM) juostas. Tyrimo rezultatai rodo anglies pluoštu armuotų polimerų (CFRP) sistemų, išdėstytų elementų išorėje, efektyvumą. Reikšminiai žodžiai: betono kompozitas, armavimas, liekamasis standumas, analitinis modelis, lenkimo bandymai

Simplified technique for constitutive analysis of SFRC

Steel fibre reinforced concrete (SFRC) has become widespread material in areas such as underground shotcrete structures and industrial floors. However, due to the absence of material models of SFRC reliable for numerical analysis, application fields of this material are still limited. Due to interaction of concrete with fibres, a cracked section is able to carry a significant portion of tensile stresses, called the residual stresses. In present practices, residual stresses used for strength, deflection and crack width analysis are quantified by means of standard tests. However, interpretation of these test results is based on approximation using empirically deduced relationships, adequacy of which might be insufficient for an advanced numerical analysis. Based on general principles of material mechanics, this paper proposes a methodology for determination of residual stress-crack opening relationships using experimental data of three-point bending tests. To verify the constitutive analysis results, a numerical modelling is utilised employing a nonlinear finite element analysis program ATENA. Simulated load-crack width relationships and moment-curvature diagrams were compared with the experimental data by validating adequacy of the derived constitutive models