Design of SFRC structural elements: flexural behaviour prediction

Practical steel fibre reinforced concrete (SFRC) applications in load-carrying structural members have yet to gain wide acceptance in design codes. This is partly explained by the lack of a unified design philosophy adapted to this material. A model based on simple and widely accepted assumptions is proposed for the analysis and the design of SFRC members subjected to bending moments. In order to evaluate the accuracy of the analytical model predictions, an extensive experimental program was conducted on 21 rectangular and T-beams of various sizes produced with five different types of SFRC. The contribution of fibres at different loading phases in bending is described in detail. The analytical model accuracy to predict maximum crack opening applicable in service conditions and at the ultimate flexural strength are compared to experimental measurements. Discrepancies observed are related to the dispersion of the material properties and the difference of fibre orientation in beams and characterization specimens. Finally, the proposed design approach is applied to the design of a realistic T-beam subjected to positive and negative bending moments.     

Statistical theory for the tensile strength of solids with structural defects

More accurate consideration of the probability of local concentration of defects leads to a logarithmic relationship for the dimensional effect. The probability is determined of the fracture at a prescribed stress and also the strength limit in tension depending on the average concentration of defects p. Estimates are given for the application limits for the theory developed. Results for differential (with respect to p) strength limits agree with the possibility considered previously of determining the relative strength by linear acoustics methods.Translated from Problemy Prochnosti, No. 2, pp. 40–43, February, 1994.     

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.     

Designing cutouts for optimum residual strength in plane structural elements

The paper presents a new approach for shape optimisation of structures with residual strength as the design objective. It must be emphasized that flaws are inevitably present in most structures, and hence the influence of cracks on optimised shapes needs to be investigated. Numerical simulation of cracks using the finite element method requires a very fine mesh to model the singularity at crack tip. This makes fracture calculations computationally intensive. Furthermore, for a damage tolerance based optimisation numerous cracks are to be considered along the structural boundary, and fracture analysis needs to be repeated for each crack at every iteration, thus making the whole process extremely computationally expensive for practical purpose. Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult. As a result, little attention has been paid to date to consider fracture parameters in the optimisation objective. To address this, the paper presents a methodology for the shape optimisation of structures with strength and durability as the design objectives. In particular, the damage tolerance optimisation is illustrated via the problem of optimal design of a ‘cutout in a rectangular block under biaxial loading’. A parametric shape representation has been used to describe the problem geometry. Damage tolerance based optimisation was performed using nonlinear programming algorithms, and NE-NASTRAN was used for finite element analysis. The first order mathematical programming algorithms, viz: the Broydon–Fletcher–Goldfarb–Shanno (BFGS) and the Fletcher–Reeves (Conjugate Direction) Methods were evaluated as the potential algorithms for optimising the residual strength in the presence of flaws. Another recently developed Sequential Unconstrained Minimisation Technique (SUMT), based on an exterior penalty function method and especially suited for large problems, was also investigated for fracture based optimisation. The effects of the orientation and the number of boundary cracks on the optimal solutions were also studied. It has been shown that the residual strength optimised shapes can be different from the corresponding and commonly adopted stress optimised solution. This emphasises the need to explicitly consider residual strength as the design objective. In all cases a significant reduction in the maximum stress intensity factor was achieved with the generation of a ‘near’ uniform fracture critical surface. The design space near the optimal region was found to be relatively flat. This is beneficial as a significant structural performance enhancement is important rather than precise identification of the local/global optimum solution. The optimal solutions obtained using the nonlinear programming algorithms were compared against those obtained in the literature using a heuristic optimisation method (Biological algorithm). The results obtained using the two methods, employing inherently different (gradient-based and gradient-less) algorithms, were found to agree very well.     

Electrical resistivity measurement to predict uniaxial compressive and tensile strength of igneous rocks

Electrical resistivity values of 12 different igneous rocks were measured on core samples using a resistivity meter in the laboratory. The resistivity tests were conducted on the samples fully saturated with brine (NaCl solution) and the uniaxial compressive strength (UCS), Brazilian tensile strength, density and porosity values of the samples were determined in the laboratory. The test results were evaluated using simple and multiple regression analysis. It was seen that the UCS and tensile strength values were linearly correlated with the electrical resistivity. The correlation coefficients are generally higher for the multiple regression models than that of the simple regression models. It was concluded that the UCS and tensile strength of igneous rocks can be estimated from electrical resistivity. However, the derived relations are purely empirical and they should be checked for other igneous rocks. The effect of rock types such as sedimentary and metamorphic rocks on the derived equations also needs to be investigated.     

High-temperature creep and long-term strength of structural elements under cyclic loading

We present a method for solving problems of high-temperature cyclic creep and damage accumulation in structural elements. The asymptotic expansion and averaging techniques both over the period of forced vibrations of a body and that of slowly varying loads are used for the set of equations describing the creep and damage processes in thin-walled structural elements. __________ Translated from Problemy Prochnosti, No. 5, pp. 45–53, September–October, 2008.     

Influence of concrete strength on crack development in SFRC members

Tension stiffening is still a matter of discussion into the scientific community; the study of this phenomenon is even more relevant in structural members where the total reinforcement consists of a proper combination of traditional rebars and steel fibers. In fact, fiber reinforced concrete is now a worldwide-used material characterized by an enhanced behavior at ultimate limit states as well as at serviceability limit states, thanks to its ability in providing a better crack control.This paper aims at investigating tension stiffening by discussing pure-tension tests on reinforced concrete prisms having different sizes, reinforcement ratios, amount of steel fibers and concrete strength. The latter two parameters are deeply studied in order to determine the influence of fibers on crack patterns as well as the significant effect of the concrete strength; both parameters determine narrower cracks characterized by a smaller crack width.     

The tensile strength of hardmetals

In conventional bend tests on hardmetal specimens with a rectangular cross-section the strength values exhibit a wide scatter as a result of fracture being initiated from pores and inclusions. A new bend test-piece geometry has been devised which subjects a relatively small volume of material to a high tensile stress and so reduces the probability of fracture starting from defects. The test gives reproducible results with low scatter, and, by suppressing defect initiated failures, it enables a more accurate assessment to be made of the effect of metallurgical variables, such as grain-size and composition, on strength.     

Fatigue strength of tubular structural elements under bending oscillations. Report 1. Evaluation of the stress state of tubular structural elements and fatigue strength under regular loading

A method and experimental facility for examining the fatigue strength of tubular structural elements are described. The results of fatigue tests are presented and the stress state of tubular structural elements, subjected to the effect of cyclic bending loading, is analyzed in detail.Translated from Problemy Prochnosti, No. 3, pp. 82–86, March, 1994.     

Modulus of elasticity and tensile strength of self-compacting concrete: Survey of experimental data and structural design codes

To enable an overall view on the mechanical performance of Self-Compacting Concrete (SCC), a database was constructed. Included within this database are informations with regard to: mix-design, fresh and hardened properties. This dataset contains results of more than 250 papers, of researches conducted worldwide on SCC during the last two decades.In this paper, an in depth analyses is provided on the modulus of elasticity and the tensile strength of SCC. The SCC results collected within the database are compared with those predicted from the formulations and existing models developed and validated for vibrated concrete (e.g. Eurocode 2 and the Model Code (MC 90 and/or MC 2010)). The influences of different mix-design parameters (aggregate type, paste volume, etc.) on the E-modulus and the tensile strength are analysed, and a more detailed view on the performance of SCC, and the different models, is obtained.     

Fatigue strength of tubular structural elements under bending oscillations. Report 2. Fatigue strength of tubular structural members under programmed loading

Programs are presented for block loading with determined and random alternation of stress amplitude simulating the service loading spectrum. The results of fatigue tests of straight and bent tubular structural members are presented. It is concluded that low fatigue strength of bent tubular structural members is caused by the unfavorable technological effects of bending these pipes and by warping of the cross section during testing.Translated from Problemy Prochnosti, No. 4, pp. 89–93, April, 1994.     

Compressive strength and diametral tensile strength of some calcium-orthophosphate cements: a pilot study

More than 100 different formulations of calcium-orthophosphate cements were subjected to determinations of the compressive strength and the diametral tensile strength after storage at room temperature for 24 h under 100% relative humidity (RH). It was found that setting occurred on more than 15 combinations of reactants. Further, it was shown that the mechanical properties of the cements which were obtained were also dependent on the water/powder ratio, the content of seed material and the storage conditions. Other factors which are thought to be of importance are the particle form and the particle size of the powder constituents as well as the addition of modifiers.     

Design strength of ceramics for use in elements of gas-turbine engines

Strength of Materials -