Design of SFRC structural elements: post-cracking tensile strength measurement

Utilisation of steel fibre reinforced concrete (SFRC) for designing structural members requires knowledge of the post-cracking tensile response. This paper reviews the experimental characterisation tests and subsequent analysis commonly used for determining the post-cracking tensile properties of SFRC. The experimental program supporting this investigation comprised five different SFRC mixes with fibre volumes ranging from 0.75 to 1.25% used to fabricate a set of characterisation specimens for uniaxial tension tests, notched beam tests and round panel tests carried out in parallel with an extensive experimental program on large scale beams. Characterisation test results allowed a comparison between direct stress–crack opening measurements and the stress–crack openings retrieved from the inverse analysis of bending tests. Discrepancies in post-cracking tensile results obtained with the three types of tests are analyzed and related mainly to test configurations, the presence of a predefined crack, support conditions, fibre orientation, and cracked surface size. Results obtained using material characterisations are then applied to the reproduction of the structural behaviour of large scale beams, documented in a companion paper.     

Implications of test methodology on post-cracking and fracture behaviour of Steel Fibre Reinforced Concrete

It is now universally recognized that the mechanical, cracking and fracture, properties of Steel Fibre Reinforced Concrete (SFRC) are far superior to those of plain concrete. The use of SFRC contributes effectively to preserve the structural stability and structural integrity of concrete elements and improve their ductile behaviour.To optimize the performance of SFRC in structural members it is necessary to establish the mechanical properties very precisely. The best test methodology to evaluate the post-cracking and toughness properties of SFRC is the beam bending test. Design codes recommend one of two bending test configurations: the three-point or the four-point bending test. The results obtained from these two test configurations are not identical.The overall focus of this paper is to evaluate the contributions of fibres to the post-cracking and fracture behaviour of concrete as determined by the two different standard test procedures. To achieve these aims plain and fibre concrete specimens were tested. All the test specimens were extensively instrumented to establish the strength properties, crack tip and crack mouth opening displacement, post-cracking and fracture behaviour. The results of the two types of bending tests were then critically analysed and evaluated to identify the differing effects of the bending load configurations on material and structural behaviour.SFRC specimens subjected to four-point bending test showed higher stress values compared to those obtained from the three-point bending tests. The first crack strength values evaluated following the two standards are close with an improvement of 10% for the European standard.     

Mechanical properties of steel fibre reinforced concrete exposed at high temperatures

Steel fibre reinforced concrete (SFRC) is an advanced cementitious composite where fibres can act as a profitable replacement for diffused reinforcement, like welded steel mesh, especially for thin cross sections. In this case fire becomes a very important condition in the design. Previous experimental research has shown the benefits in fire resistance of steel fibres, when structural elements are bent. A careful mechanical characterization of a SFRC used for prefabrication after thermal cycles at high temperature is here presented. Three different tests are considered: four point bending, uniaxial compression and fixed-end uniaxial tension. In the paper the decay of peak and post-cracking strengths versus temperature increase for uniaxial compression, uniaxial tension and bending are discussed.     

Prediction of steel fibre reinforced concrete under flexure from an inferred fibre pull-out response

Steel fibre-reinforced concrete (SFRC) is being used in a variety of structural applications, yet there is still considerable debate how to express and evaluate flexural toughness for design purposes. This is holding back the material's development as a permanent structural material. Existing beam and slab test methods have problems with variability or their application in structural design. Furthermore, existing models of SFRC flexural behaviour do not fully capture what happens at the cracked section in terms of the fibre-matrix interactions. Typical of these approaches is the modelling of the tension zone from single fibre pull-out tests, which is problematic in measurement of the load-displacement relationship, the interaction of groups of fibres and the extensive testing required to cover all permutations of fibre geometry. An alternative approach is proposed where the average pull-out response of the fibres bridging the cracked zone is inferred from flexural beam tests. The characteristic load versus crack-mouth opening displacement behaviour for a particular fibre concrete then forms part of the stress and strain/displacement profile in a flexural analysis to predict moment capacity in a design calculation. The model is explained together with its validation by comparing the predicted load-displacement response for a range of fibre volumes in sprayed and cast SFRC. It is concluded that the analysis of beam load/deflection curves to infer the fibre pull-out response is a viable approach. It offers a promising solution to the need for a flexural design model combined with a practical method of characterizing the tensile contribution of steel fibres.     

局部高密度钢纤维混凝土弯曲疲劳损伤演变规律

在混凝土弯曲构件底部用高密度钢纤维局部增强称为局部高密度钢纤维混凝土(PHPFRC)与同样纤维掺量的传统钢纤维混凝土(SFRC)比较它可以用相近的价格获得高得多的刚度﹑承载力和抗疲劳断裂性能为了能够预测PHPFRC在循环荷载作用下的疲劳寿命需要确定其疲劳损伤演变规律本文通过试验发现局部高密度钢纤维混凝土的弯曲疲劳损伤表现出韧性材料所具有的性质基本上接近韧性损伤这与素混凝土及传统钢纤维混凝土有本质的不同根据其疲劳特性的实验结果探讨了PHPFRC弯曲疲劳损伤阈值结合损伤理论建立了适合于纤维体积掺量为1.2%的局部高密度钢纤维混凝土试件的弯曲疲劳损伤演变方程     

Modelling of SFRC using inverse finite element analysis

A method of inverse finite element analysis is used to determine the constitutive relationship of SFRC in tension, using primary experimental data. Based on beam bending test results and results from pull-out tests, an attempt is made to explain the physical processes taking place during the cracking stage. Basic models predicting the behaviour of SFRC in tension are proposed.     

Shear behavior model for steel fiber-reinforced concrete members without transverse reinforcements

Due to the complex shear mechanism of steel fiber-reinforced concrete (SFRC) members, there is lack of comprehensive shear behavior models for SFRC members. The shear behavior model, based on a smeared crack model, requires the tensile stress–strain constitutive equation of SFRC membrane subjected to biaxial stresses. After SFRC panel tests under biaxial stresses were recently conducted, it has been possible to create a more complete smeared crack model for estimating the shear behavior of SFRC members. It is, however, very difficult to conduct such experiments for different types of steel fibers, various amount of steel fibers, different ranges of concrete strengths, etc. Thus, in this study, steel fibers are modeled as average direct tensile contribution elements in a modified smeared crack truss model, considering directionality and distribution of fibers. In this way, only simple bond tests are required to reflect the effects of different characteristics of SFRC. In addition, the shear contribution of steel fibers can be obtained considering the bond failure of steel fibers. The proposed model was compared to the test results of 8 SFRC panels and 80 SFRC beams, and the shear behavior of the SFRC members was well estimated.     

On the fracture behaviour of thin-walled SFRC roof elements

The paper presents an experimental and a numerical investigation on precast, prestressed reinforced concrete (RC) and steel fibre reinforced concrete (SFRC) roof elements. The element investigated has a complex geometry, because it is characterized by a thin-walled open cross-section and a long span. In order to reduce the total weight of the traditional RC element and favour an industrialized production process, the structure can be made of fibre reinforced concrete. This composite presents a significant toughness after cracking that can substitute the diffused reinforcement made of common steel-welded meshes, conserving the longitudinal prestressed reinforcement. The mechanical characterization of SFRC material has found recently a shared design approach that starts with the identification of the uniaxial tension constitutive law obtained from a standardized bent notched specimen. Nevertheless, for defined casting procedures of the structure, like in prefabrication, the identification of the uniaxial tension constitutive law can be performed by a four point bending tests on suitable unnotched specimens, able to take into account the effective fibre orientation in the structure and the real nominal thickness of the critical portion of the element. The latter two different experimental test procedures (on notched or unnotched specimens) lead to significant differences in the tension softening response. For this reason SFRC tension softening relations, coming from the previously mentioned experimental tests, are analyzed in this paper in order to evaluate their effects on the structural response of this large-scale roof element. The results of the experimental tests on the roof element presented in this paper show that second-order effects drastically anticipated the achievement of the longitudinal bending moment resistance calculated following the beam theory and neglecting transverse equilibrium and in-plane cross section deformation. Two numerical models are proposed in this paper to evaluate second-order effects in the resistance assessment of the precast structure. The first one is based on a plane section approach (PSA), while the second one is based on a non-linear finite element analysis (NLFEA). Both second-order effect and uniaxial tension constitutive relationship roles are examined in relation to the global response of the structure up to failure. The final remarks, coming from a careful comparison between experimental and numerical results, highlight that the failure is mainly led by a structural behaviour, because second-order effects prevail on non-linear response of SFRC materials adopted.     

Experimental investigation of steel fiber reinforced concrete box beams under bending

Reduction of dead weight of a reinforced-concrete (RC) structure without too much concession in its load carrying capacity has always been an attractive study subject because it engenders (1) a decrease in dimensions of the members, (2) a decrease in the reinforcement steel, and (3) a decrease in lateral inertia forces during severe earthquakes. In this study, nine RC beams of outer dimensions of 300 × 300 × 2000 mm, six of which are box beams, designed and produced using a C20 class steel fiber concrete, (SFRC) with the commonly used steel fiber type of Dramix-RC-80/0.60-BN at a dosage of 30 kg/m³, are tested under bending. The mechanical behaviours of all these nine beams under bending are recorded from the beginning of the test till the ultimate failure of the tensile reinforcement in a two-point beam-loading setup. The proportions of (1) loss in ultimate load versus reduction in dead weight and (2) (ultimate experimental load)/(ultimate theoretical load) of the SFRC box beams are determined for two different box thicknesses. Dimensionless behaviour relationships of all the SFRC beams are determined, and the experimentally obtained relationship between the ratio of (actual ultimate load)/(theoretical ultimate load) and the ratio of (wall thickness)/(beam height) for the SFRC box beams is expressed diagrammatically.     

Effect of steel fibres on mechanical properties of high-strength concrete

Steel fibre reinforced concrete (SFRC) became in the recent decades a very popular and attractive material in structural engineering because of its good mechanical performance. The most important advantages are hindrance of macrocracks’ development, delay in microcracks’ propagation to macroscopic level and the improved ductility after microcracks’ formation. SFRC is also tough and demonstrates high residual strengths after appearing of the first crack. This paper deals with a role of steel fibres having different configuration in combination with steel bar reinforcement. It reports on results of an experimental research program that was focused on the influence of steel fibre types and amounts on flexural tensile strength, fracture behaviour and workability of steel bar reinforced high-strength concrete beams. In the frame of the research different bar reinforcements (2∅6 mm and 2∅12 mm) and three types of fibres’ configurations (two straight with end hooks with different ultimate tensile strength and one corrugated) were used. Three different fibre contents were applied. Experiments show that for all selected fibre contents a more ductile behaviour and higher load levels in the post-cracking range were obtained. The study forms a basis for selection of suitable fibre types and contents for their most efficient combination with regular steel bar reinforcement.     

Efficient technique for constitutive analysis of reinforced concrete flexural members

One of the most difficult issues in the theory of reinforced concrete (RC) is an adequate modelling of deformation behaviour, cracking and, particularly, post-cracking behaviour, as one of the major sources of non-linearity. Applying the concept of average cracking and average strains, deformation behaviour of RC can be modelled by stress–strain tension–stiffening relationships. The authors proposed an innovative inverse technique for constitutive modelling of flexural RC elements. The technique is based on the smeared crack approach and layer model of RC section. The inverse technique aims at deriving tension–stiffening constitutive models from experimental moment–curvature diagrams. The present analysis takes into account the shrinkage effect that is often neglected in other studies. Based on the inverse technique, free-of-shrinkage tension–stiffening relationships are derived using test data of shrunk RC beams. Examples of the application for the analysis of the experimental data obtained by the authors are presented to illustrate the calculation efficiency of the proposed technique.     

Testing and modeling of Nomex™ honeycomb sandwich Panels with bolt insert

Nomex™ honeycomb core sandwich panels with a bolt insert were load tested and modeled. The objective was to predict the honeycomb local buckling load and to identify a Nomex™ honeycomb constituent material model. Sandwich specimens were subjected to bolt pull-out load tests. The same sandwich structure was also tested in flat-wise tension with strain gages installed on the honeycomb walls. Finite element models of the flat-wise tension and bolt pull-out tests were built. The honeycomb geometry and strain gages were modeled with shell elements. An orthotropic honeycomb material model was identified by comparing the two test models to the experimental data. The material parameters identified are in the mid-range of previously published values. The pull-out test model was used to predict honeycomb wall buckling with a nodal rotation vector sum criterion. The buckling loads predictions closely corresponded to the start of the experimental load/displacement slope transition zone.     

Generalization of the Barcelona test for the toughness control of FRC

Through different researches and application in works, the Barcelona test has proven to be adequate for toughness control of fiber reinforced concrete (FRC) and has recently been standardized in Spain (UNE 83515-2010). However, to determine FRC toughness an extensometer is required for measuring the circumferential displacement of the specimen in the post-cracking regime. In order to generalize the use of this test, this paper shows the results of an extensive experimental campaign in which circumferential and axial displacements of specimens were measured during tests. Results show a linear correlation between these displacements in a wide range of post-cracking regime, with a scatter lower than bending tests, commonly used to quantify FRC toughness. These results allow to use axial displacement measurement in place of the circumferential displacement. Additionally, the axial displacement it related with the piston stroke reaching highly successful results.     

Strain rate dependent properties of ultra high performance fiber reinforced concrete (UHP-FRC) under tension

The results of an experimental investigation of UHP-FRC tensile response under a range of low strain rates are presented. The strain rate dependent tests are conducted on dogbone specimens using a hydraulic servo-controlled testing machine. The experimental variables are strain rate, which ranges from 0.0001 1/s to 0.1 1/s, fiber type, and fiber volume fraction. Five different types of fibers are considered including straight and twisted fibers with different geometric properties. The rate sensitivity of the composite material in tension is evaluated in terms of its first cracking strength, post-cracking strength, energy absorption capacity, strain capacity, elastic modulus, fiber tensile stress and number of cracks. The test results show pronounced rate effects on post-cracking strength and energy absorption capacity. Further, post cracking strength varies linearly with the fiber reinforcing index and energy absorption capacity varies linearly with the product of the fiber length and the reinforcing index, as predicted from the theory for fiber reinforced concrete.     

单向受拉状态下的钢纤维混凝土本构模型

在混凝土中添加随机分布的钢纤维能有效提高混凝土力学性能。为了更好地考虑纤维对单向受拉状态下钢纤维混凝土（SFRC）的增强作用，提出一个钢纤维混凝土的弥散开裂本构模型。在弹性阶段，纤维混凝土被视为简单复合材料，基于两相复合材料理论，对SFRC的弹性刚度矩阵进行修正；在受拉开裂后，混凝土的塑性变形量被视为纤维与混凝土界面脱粘过程中滑移量，利用粘结滑移模型计算纤维在混凝土开裂面上的桥接作用。该文通过有限元软件ABAQUS中子程序二次开发接口Umat，进行Fortran编程，在ABAQUS中实现该本构模型。通过数值模拟结果与受拉实验数据进行对比，验证了该本构模型的准确性。通过数值模拟分析，进一步探究钢纤维混凝土相关参数对抗拉性能的影响，为钢纤维混凝土在实际的工程中的应用提供建议。     

Strength and fracture properties of industrially prepared steel fibre reinforced concrete

The paper reports on a study of steel fibre reinforced concrete (SFRC) which was prepared using normal industrial mixing, compaction and curing conditions. Both strength (compressive and tensile) and fracture (toughness measurements) characteristics have been investigated with test specimens prepared from 5 m long SFRC piles. The piles contained only steel fibre reinforcement and were manufactured in exactly the same way as ordinary piles.Slight differences in the tensile strengths (determined via torsion tests) were observed due to the existence of preferential fibre orientation. Flexural tests on notched beams (to evaluate fracture characteristics) produced a much more stable, reproducible, test than that observed for un-notched beams. Hence, it is concluded that the notched beam is a better geometry in terms of test stability and reliability. The results showed that tests specimens taken from industrially prepared SFRC displayed similar characteristics compared to that observed with test specimens prepared under laboratory conditions, with regards to the strength, fracture characteristics and, in particular, the variation observed.     

Relationship between fiber orientation/distribution and post-cracking behaviour in ultra-high-performance fiber-reinforced concrete (UHPFRC)

The relationship between fiber orientation/distribution and post-cracking behaviour in ultra-high-performance fiber-reinforced concrete (UHPFRC) was quantitatively evaluated. A circular UHPFRC panel was cast from its center and prismatic specimens were cut at angles of 0, 30, 60 and 90° between the specimen axis and the radial direction of the panel. The post-cracking behaviour was assessed with three-point bending tests, and fiber orientation/distribution throughout the panel was then evaluated using image analysis and 3D visualization of fiber orientation based on X-ray computed tomography (CT) data. The post-cracking flexural strengths of the specimens cut at angles of 60, 30 and 0° were 80, 40 and 10% of that for the specimens cut at an angle of 90°, indicating perfect linear dependence on the contribution of fibers near the fracture surfaces. Two rectangular UHPFRC panels with a 1:2 width/length ratio were cast, and similar fiber orientation characteristics were found for the circular and rectangular panels.     

钢纤维混凝土遮弹层抗弹丸侵彻效应试验研究与分析

钢纤维混凝土遮弹层抗常规武器侵彻效应问题,是防护工程界亟待解决的一个崭新课题。为研究这种新型防护材料的抗侵彻性能,利用Φ12.7mm弹道炮-测速靶系统对混凝土及钢纤维混凝土进行了弹道冲击对比试验,获得了弹丸着靶速度及对应的最大侵彻深度、弹坑直径、靶体破坏形态等试验参数,并利用高速摄影系统记录了靶体的动态破坏过程。针对现有经验公式均不能反映钢纤维混凝土材料高韧性影响的不足,引入钢纤维混凝土材料韧度R,对试验数据进行了回归分析,导出了侵彻深度工程计算公式。计算结果与试验数据对比表明,预估公式计算精度较高,公式中相关参数简单易于确定,且能反映钢纤维混凝土的高强高韧性特点,在实际工程应用中具有重要的参考价值。     

钢纤维混凝土多轴损伤比强度准则EI北大核心CSCD

以损伤比强度理论为基础,建立了钢纤维混凝土真三轴损伤比强度准则,并根据钢纤维混凝土试验资料,推荐了钢纤维混凝土损伤比变量表达式中的6个经验参数。利用钢纤维混凝土在单轴、双轴和三轴受力状态下的应力-应变曲线试验结果验证了损伤比取值合理性,对比了单轴受拉、单轴受压和双轴等压等典型受力状态下钢纤维混凝土和普通混凝土损伤比变量取值的差异。通过与国内外共104组钢纤维体积率为0.5%~2.5%的钢纤维混凝土三轴强度试验资料的比较,表明六经验参数钢纤维混凝土损伤比强度准则的三维破坏包络面接近已有认识;通过与国内外强度准则比较,表明损伤比强度准则与钢纤维混凝土三轴试验数据有较高的吻合度。对于围压三轴受力状态,提出简化的钢纤维混凝土常规三轴强度准则,并与已有常规三轴强度准则进行比较分析。此外,对于材料处于二轴受力,推荐了简化的损伤比二轴强度准则中的经验参数取值。     

顶底角钢连接半刚性钢结构抗震性能数值分析

为了研究顶底角钢连接半刚性钢结构的抗震性能,介绍相关文献中角钢的屈服荷载及初始刚度的计算,基于角钢的拉压试验结果,验证角钢的屈服荷载及初始刚度计算方法的准确性并对角钢的屈服荷载计算公式进行修正,进而提出角钢在反复拉压荷载下的恢复力模型;编制角钢连接单元,提出基于有限元软件OpenSEES的顶底角钢连接半刚性钢结构的建模方法,对顶底角钢连接半刚性钢结构低周往复试验、振动台试验进行数值模拟,所得结果与试验结果进行比较,结果表明:该文提出的建模方法具有单元少、自由度少、建模方便、计算效率高、耗时少等优点,采用该文方法进行的数值模拟与试验结果吻合较好,精度能满足工程需求。