The influence of shear span ratio on load capacity of fibre reinforced concrete elements with various steel fibre volumes

This paper analyses the influence of steel fibre volume and shear span ratio on the strength of fibre reinforced concrete elements in various states of stress. 36 beams with three different shear spans (a/h = 1, 1,5, and 2 %) and three different fibre volumes (1, 1,5, and 2 %) were tested to examine how these factors influence the behaviour of such elements. Test results suggest that steel fibre volume and shear span can increase load capacity, plasticity and cracking. Experimental research showed that steel fibre volume has different influence at different shear span ratios. Regression analysis of experimental data was carried out and empirical approach showing different effect of these factors was proposed. Furthermore, test results were compared with different theoretical and empirical approaches of other authors. Jėgos peties ir aukščio santykio įtaka betoninių elementų laikomajai galiai, esant įvairiems dispersinio armavimo kiekiams Santrauka Straipsnyje analizuojama plieninių fibrų kiekio įtaka dispersiškai armuotam betonui, esant įvairiems įtempimų būviams. 36 sijos su trimis skirtingomis lenkimo momento ir skersinės jėgos santykio reikšmėmis (arba a/h = 1, 1,5, 2 santykiais) bei su trimis plieninių fibrų armavimo procentais (1 %, 1,5 %, 2 %) buvo išbandytos, siekiant nustatyti, kaip šie veiksniai daro įtaką dispersiškai armuoto betono elgsenai. Eksperimentiniai tyrimai parodė, kad šie veiksniai turi didelę įtaką dispersiškai armuotų betoninių bandinių įlinkiams, pleišėtumui, plastiškumui bei laikomajai galiai, be to, plieninių fibrų kiekis esant skirtingoms jėgos peties ir aukščio santykio reikšmėms, turi skirtingą įtaką. Atlikus eksperimentinių tyrimų regresinę analizę, straipsnyje pateikta išraiška, parodanti skirtingą šių veiksnių įtaką. Gauti eksperimentiniai rezultatai taip pat palyginti su įvairių autorių teoriniais skaičiavimo metodais. First Published Online: 14 Oct 2010 Reikšminiai žodžiai: dispersiškai armuotas betonas, laikomoji galia, plastiškumas, pleišėtumas

Probability based design of punching shear resistance of column to slab connections

The paper analyzes the dependence of punching shear strength reliability index β, calculated according to EN 1992-1-1:2004 (2004) and STR 2.05.05:2005 (2005) in reinforced concrete floor slab-to-column joint on the values of random factors. The paper deals with theoretical research of the influence of independent random variables, such us the value of the characteristic compressive strength fck of concrete, the area As of the longitudinal reinforcement, effective cross-section depth d and the ratio of the self-weight and the effective load on the value of the reliability index β. The paper presents experimental results of reinforced concrete slabs with different longitudinal reinforcement ratio ρ subjected to a concentrated load. I t was determined that when the effective load makes around 50% of the construction self-weight load, i.e. Gk /Qk = 2 and when minimal variation coefficient estimates are taken (for concrete strength δfc = 0.1, for effective depth δd = 0,1 and for the area of longitudinal reinforcement cross-section δAs = 0.05 or δAs = 0.075 and when Gk = Qk i.e. Gk /Qk = 1 where δfc = 0.1, δd = 0.1 and δAs = 0.05) the reliability index β of the analyzed slabs calculated according to EN 1992-1-1:2004 (2004) as well as β calculated according to STR 2.05.05:2005 (2005), is bigger than EN 1990:2002 (2002) recommendation for the minimum value of reliability index – 3.8 for RC2 construction reliability class ultimate. In other cases the reliability index β is close to 3.8 or much smaller than 3.8

Influence of Fiber Shape on the Strength of Steel Fiber Reinforced Concrete

The paper presents analysis and comparison of theoretical models, evaluating the shape of steel fiber for anchoring properties in concrete. The analysis shows that all models evaluate this effect differently. Either way all discussed modes leads to different calculation results of strength of steel fiber reinforced concrete. According to this analysis, the test results of steel fiber pull-out tests is made and discussed in paper. The theoretical-empirical coefficient of evaluation of fiber shape, based on analysis of mentioned models and the test results, is suggested. This coefficient is verified with tests results of steel fiber reinforced concrete elements, subjected to bending and compression

Probability-based design of an optimal elastic–plastic truss / Optimalios tampriai plastinės santvaros projektavimas tikimybiniu statistiniu metodu

According to Eurocode EN 1990 and Lithuanian Technical Regulation of Construction STR 2.05.03:2003, structures should be designed to satisfy reliability requirements. The reliability of a structure can be achieved using one of 3 methods: partial factor (PF), PF assisted by testing and direct probability-based method. When PF methods are used, the determined reliability of a structure is often greater than required; therefore the direct probability methods allow a more cost-efficient design. The reviewed literature suggests that even greater economical effect can be achieved by combining probability-based design methods with optimization. Unfortunately, the literature presents very few such methodologies. This article focuses on an optimal design of a truss under variable repeated loading at shakedown. The authors propose a model of a truss volume minimization problem with direct probabilistic evaluation of safety margin. The developed technique allows finding minimum volume of desirable reliability structure when loading, provided stochastic parameters are known in advance. The finite element method is applied for the discretisation of a structure. Mathematical programming is used to resolve the optimization problem. Santrauka Europos projektavimo normos EN 1990 ir Lietuvoje galiojantys statybos techniniai reglamentai STR 2.05.03:2003 reglamentuoja konstrukcijų projektavimą užtikrinant normuotąjį patikimumą. Konstrukcijos patikimumas gali būti užtikrintas trimis metodais: dalinių koeficientų (DK), DK su bandymais ir tikimybiniu informaciniu statistiniu (TIS) metodu. Taikant DK ar DK su bandymais metodus suprojektuotos konstrukcijos patikimumas dažnai viršija normuotojo patikimumo reikšmę, o tiesioginis tikimybinis projektavimas sudaro prielaidas projektuoti ekonomiškiau. Kaip rodo literatūros šaltinių analizė, pasiekti dar didesnį konstrukcijos ekonomiškumą galima jungiant TIS metodą su konstrukcijos optimizavimu. Straipsnyje pademonstruota, kad, pasitelkus nesudėtingus matematinius skaičiavimus ir pritaikius optimalaus sprendinio paieškos algoritmą, galima efektyviai projektuoti statybines konstrukcijas užtikrinant reikiamą normuotąjį patikimumą. Straipsnyje nagrinėjama kintamosios kartotinės apkrovos veikiama prisitaikanti santvara. Sudarytas tūrio minimizavimo uždavinio modelis, tiesiogiai tikimybiškai įvertinant konstrukcijos atsparumo atsargą. Iš pateikto skaitinio pavyzdžio rezultatų nustatyta, kad didžiausią įtaką optimaliam santvaros tūriui iš visų atsitiktinių dydžių turi plieno takumo įtempių kvadratinė nuokrypa. Todėl jos mažinimas yra efektyviausias būdas siekiant didesnio konstrukcijos ekonomiškumo. Konstrukcijos diskretizacijai taikomas baigtinių elementų metodas. Skaitiniam optimizavimo uždavinio sprendimui pasitelktas matematinis programavimas. Reikšminiai žodžiai: tiesioginis informacinis statistinis projektavimas, santvara, optimizacija, matematinis programavima

Analysis of research and design models for the punchning shear of flat RC slabs

The paper presents the review and analysis of the existing methods and models for calculating punching shear strength. The analysis of the existing design methods has showed that there is no unified theory about calculating punching shear strength. The models are similar in the way that fictitious shear stresses act in the fictitious shear area and are mainly obtained from the test results that may differ in their values. Therefore, the difference between the results obtained employing various calculation methods can be as high as 1,37 times, whereas the difference between the results of theoretical calculations and test research may vary up to 1,8 times. These facts clearly demonstrate that punching shear phenomena are not completely analyzed and require additional researches. The paper also proposes an in-deep analysis of famous analytical punching shear calculation models suggested within the last 50 years like Kinnunen and Nylander (1960), Moe (1961), Breastrup et al. (1976), Georgopoulos (1989), Broms (1990), Hallgren (1998), Menetrey (2002) and Theodorakopoulos (2002). The development of the above mentioned design models, the main assumptions and an algorithm for calculating punching shear strength are discussed in the article. The review of the existing models for calculating punching shear strength has also revealed that two main model types can be distinguished: type 1 – failure occurs when the compression zone is cut by shear and compression stress; type 2 – failure occurs when tensile stresses in concrete punching cone exceeds its tensile strength. A comparison between theoretical models and test results performed by different authors demonstrate that more accurate results can be obtained by calculating punching shear strength using the first types of models. The analysis has revealed it is purposeful to search for more effective reinforcing methods that can change the character of failure from brittle to plastic. A more effective replacement of reinforcement and the behaviour of concrete taking into account complex stress state in the failure zone should be applied. Gelžbetoninių besijų perdangos plokščių praspaudimo tyrimo ir skaičiavimo modelių analizė Santrauka Straipsnyje analizuojamas suirimas nuo praspaudimo bei įvairus jo interpretavimas šiuolaikinėse projektavimo normose bei per paskutinius 50 metų sukurtuose analitiniuose skaičiavimo modeliuose. Straipsnyje aptariamas daugumos projektavimo normų bendrumas, aptariama, kodėl gaunami skaičiavimo rezultatų skirtumai. Detaliai analizuojami žymiausi analitiniai praspaudimo skaičiavimo modeliai, aptariama modelių kilmė, juose taikytos prielaidos, skaičiavimo algoritmas, pateikiamas daugumos praspaudimo skaičiavimo modelių palyginimas su eksperimentiniais duomenimis, aptariama, kodėl gaunami skaičiavimo rezultatų skirtumai. Remiantis analize išskiriamos dvi modelių grupės, pateikiama, kurie modeliai yra tiksliausi. First Published Online: 16 May 2013 Reikšminiai žodžiai: besijės perdangos plokštės, praspaudimas, gelžbetonis, stipris, laikomoji gali

Anchoring Issues of CFRP Laminates to Concrete Members

In recent years, carbon fibre reinforced polymer (CFRP) laminates have conquered the structural rehabilitation market due to their ease and quick installation, high strength, anticorrosion properties, and other properties often repeated in the literature. The full potential of these high-strength elements can only be exploited by prestressing. However, the glued laminate joint is partially rigid, resulting in slippage that leads to premature debonding and failure. Therefore, anchoring of the laminate ends is required to stop or delay premature failure and/or perform prestressing. This article discusses the anchoring issues of CFRP laminates and guidelines for the development of anchoring systems. To achieve this goal, the laminate strip was bent, the required clamping forces were determined, possible cases of damage were identified, and individual stress concentrations were modelled. The methodology for calculating the anchor length and the pull-off force is also presented

Analytical Method and Analysis of Cold-Joint Interface

The behaviour of the interface between two concrete layers, subjected to shear, is a complex process that is influenced by many different parameters. Knowledge of concrete interface performance is insufficient to this day. Most of the existing analytical methods are only suitable for determining the highest interface shear resistance and do not consider the interface behaviour at other stages. This article focuses on smooth concrete interfaces, which have their layers cast at different times (cold-joint interface). By analysing the results of different experimental push-off tests, presented in the literature, a novel analytical method was developed for the previously described concrete interface. Furthermore, numerical models of push-off tests were developed. A parametric numerical analysis was employed to determine the influence of various physical parameters that might affect interface shear behaviour. Most importantly, the results acquired using the proposed analytical method were compared with the findings of numerical analysis and experimental results acquired by other authors. The values of shear stress and slippage were found to be relatively close. Therefore, the proposed analytical method is suitable for the analysis of smooth concrete interfaces cast at different times

Calculation Model for Steel Fibre Reinforced Concrete Punching Zones of Bridge Superstructure and Foundation Slabs

The usage of steel fibre reinforced concrete in monolithic joins is well known as a good alternative of additional reinforcement because of chaotic distribution of steel fibres in complex stress ant strain state. Unfortunately, the analysis of well known design codes and different models even in punching case without steel fibres shows that there is no common theory in calculating punching shear strength. Existing models of punching shear strength with steel fibres are mainly based on empirical coefficients, or require direct tests, what makes the design of such structures more complicated. Besides, the analysis of elastic and plastic characteristics of steel fibre reinforced concrete is incomplete, because there is no unified, well-grounded theory to evaluate them. The aim of this paper is to present steel fibre reinforced concrete punching shear strength model. Suggested steel fibres reinforced concrete punching shear strength model estimates the main factors, such as concrete strength, longitudinal reinforcement, steel fibres volume, type, geometric and anchoring characteristics, and also plastic strains of steel fibre reinforced concrete. The comparison of suggested model with tests results demonstrates good accuracy of the suggested model for steel fibre reinforced concrete slabs (mean value – 1.12, standard deviation – 0.08 coefficient of variation – 7%)

A model for strength and strain analysis of steel fiber reinforced concrete / Betono, armuoto plienine dispersine armatura, stiprio ir deformaciju apskaiciavimo modelis

The article proposes a model for strength and stain analysis of steel fiber reinforced concrete (SFRC). The model is based on general principles for creating and modelling structural composites and on reinforced concrete code. Differently from other examples, the elastic and plastic properties of the components (concrete and steel) of the introduced model are directly taken into account. The model gives an opportunity to determine tension and compression strength, the elasticity modulus of fiber concrete and the main parameters of its elasticity and plasticity. A good agreement between the obtained results and those of experiments performed by other investigators was confirmed. Differences between the ratios of theoretical and experimental values are insignificant and vary within the limits of 1.06–1.10. This model may be used for the analysis of reinforced concrete members reinforced by steel fibers (SFRC) in a dispersible way assuming stress distribution diagrams. Santrauka Straipsnyje pasiulytas betono, armuoto plienine dispersine armatura, stiprio ir deformaciju skaiciavimo modelis, pagristas bendraisiais statybiniu kompozitu kurimo ir modeliavimo principais bei gelžbetonio normomis. Šiame modelyje skirtingai nuo daugelio kitu yra tiesiogiai ivertinamos tampriosios ir plastinės kompozito komponentu (betono ir plieninės dispersinės armaturos) savybės. Modelis leidžia apskaiciuoti betono, armuoto plienine dispersine armatura, tempiamaji ir gniuždomaji stiprius, tamprumo moduli ir pagrindinius jo deformatyvumo parametrus—tamprumo ir plastiškumo koeficientus. Siulomo modelio palyginimas su šio straipsnio ir kitu autoriu atliktais eksperimentu duomenimis parodė, kad rezultatai sutampa. Teoriniu ir eksperimentiniu reikšmiu santykiai skiriasi nedaug ir kinta nuo 1,06 iki 1,10. Šis modelis gali buti taikomas priimant itempiu pasiskirstymo diagramas apskaiciuojant lenkiamuosius, plienine dispersine armatura armuotus betoninius elementus. Reikšminiai žodžiai: kompozitas, betonas, plieninė dispersinė armatura, betonas, armuotas plienine dispersine armatura, deformaciju modulis, tampriosios ir plastinės deformacijo