Current Eurocode Research Articles

Shear capacity of flexurally strengthened old low-performance concrete elements

This paper describes an experimental study to evaluate the shear capacity of small to medium height old buildings constructed in Israel more than 50 years ago with poor materials and construction practices resulting in low performance concrete (LPC), also known as plum concrete. Such LPC is characterized by its low compressive strength and in many cases – by the inclusion of large stones (up to ~300 mm) among its coarse aggregates. The tests conducted in this study were aimed at providing assessment of the shear capacity of existing slender LPC walls. The experimental program comprised beams sawed out of authentic samples, which were extracted from old buildings prior to their demolition, as well as larger specimens cast in the laboratory from concrete mixes designed to represent the main characteristics of authentic LPC. Control specimens, made of the lowest standard concrete class, were also tested. The 14 beam specimens failed in shear and their measured load capacities were compared with the shear capacity of beams without shear reinforcement, on the basis of their measured concrete compressive strength as prescribed by Eurocode 2 and ACI 318 provisions. This comparison indicates that the current Eurocode 2 formula, as well as that of ACI 318, provide reasonably conservative estimates for the shear capacity of LPC walls without shear reinforcement. Hence, engineers who lacked any information on how to assess the shear capacity of such low-performance concrete walls can now refer to this study. • Low Performance Concrete (LPC) in structural elements was studied. • Experiments were performed to evaluate the shear capacity of flexurally strengthened LPC elements. • Authentic sample beams, sawed out from old buildings, were tested. • Larger laboratory made specimens were tested as well. • Shear capacity of flexurally strengthened LPC walls can be evaluated based on the research findings.

Comparative analysis of code-based approaches for seismic assessment of existing steel moment resisting frames

Nowadays, there is a lack of adequate code provisions for the seismic performance and risk assessment of steel structures to be used within European countries. At the same time, in several occasions, existing steel moment resisting frames (MRFs) have demonstrated to be very fragile with respect to seismic actions due to their inadequate ductility capacity. This combination highlights the urgent need for an update of the current Eurocode 8 – Part 3 (EC8‐3), thus promoting a reliable assessment of existing steel structures. To this aim, the present study provides a comprehensive and quantitative comparison of the EC8‐3 with the three versions of the American ASCE 41 (i.e., ASCE 41‐06, ‐13 and ‐17), which are here assumed as a reference, as they reflect the evolution of ‘similar’ assessment procedures during the last two decades. The comparison of the capacity values provided by the codes for different engineering demand parameters (EDPs) highlights significant differences pointing out drawbacks of the EC8‐3. In addition, the comparison is made by assessing the seismic performance of two existing steel MRFs, by performing Incremental Dynamic Analyses and deriving fragility curves in a probabilistic approach which considers local EDPs which are compliant with the codes, and that are conventionally used in deterministic studies, e.g., chord rotations in beams and columns, shear strain in panel zones. The comparison of the codes, and the probabilistic assessment of the case studies by using code-based (i.e., local) EDPs, provide significant insights and directions for revision of the EC8‐3.

Proposal of modification of Eurocode 2 in terms of calculation of the punching shear capacity of RC column footings

The paper first presents the calculation of the punching shear capacity of concentrically loaded reinforced concrete column footings according to the current Eurocode 2, which can be carried out in two ways: by conducting an iterative procedure and by a simplified procedure applying the diagrams. By using these procedures, the punching shear capacity calculation was performed for the footings examined within the experimental research of the authors of this study, as well as for the footings that were considered by experiments conducted by other authors. Based on the conducted analysis of the calculation results and experimentally recorded results, a modification of the expression of the current Eurocode 2 with regard to the calculation of the punching shear capacity of concentrically loaded RC column footings is proposed. The proposed modification more realistically takes into account the influence of compressive strength of concrete and the reinforcement ratio in the footing, so that its application provides the results of punching failure forces that are closer to the results recorded by experimental tests.

New method for metal beams sensitive to lateral torsional buckling with an equivalent geometrical UGLI imperfection

The Eurocodes EN 1993-1-1:2005, prEN 1993-1-1:2020, and EN 1999-1-1:2007, prEN 1999-1-1:2020 propose the same method. They take into account the geometrical equivalent Unique Global and Local Initial (UGLI) imperfections. According to the Eurocodes, the assumed shape of UGLI imperfections may be derived from the elastic buckling mode and provide a method that enables computing the amplitude of a UGLI imperfection in slender metal structures. The authors method presented enables computing the amplitude of the initial imperfection for the lateral torsional buckling of beams with a doubly symmetric section. This is a generalization of Eurocode rules that is valid only for members in compression. Numerical examples are presented in order to understand the authors method. The buckling resistance is verified with the test of Wieschollek et al. and compared with the results of four other authors, the results of a Geometrically and Materially Non-linear Analysis (GMNIA) with imperfections and the results of other methods used in the current Eurocode 3 and a draft of its new generation.

Buckling resistance of longitudinally stiffened plates: Eurocode-based design for column-like and interactive behavior of plates with closed-section stiffeners

Buckling resistance of longitudinally stiffened plates subjected to compression is a crucial issue in the design of many steel bridges. The design methodology of the current Eurocode describes the behavior as a combination of column-like and plate-like behavior. Previous studies well explored the plate-like behavior of compressed stiffened plates with closed longitudinal stiffeners, leading to the conclusions that the critical stress calculation is sensitive to the details of the numerical model, and that in certain situations the Winter-curve is unconservative to calculate the reduction factor for plate-like buckling of stiffened plates. One of the goals of the research presented in this paper is to study the pure column-like behavior similarly. Recent results also suggest that the handling of the interactive behavior in the current Eurocode is sometimes too conservative, and could be improved. The systematic analysis of the interactive behavior is another main goal of the reported research program, focusing on the compression resistance of stiffened plates with closed-section longitudinal stiffeners. To achieve the goals, numerical studies have been conducted by using the shell finite element method. A large number of cases have been investigated, by performing linear buckling analyses to calculate critical stresses, as well as geometrically and materially nonlinear analyses with imperfections, to calculate the resistances. The systematic evaluation of the results finally has yielded an enhanced interpolation between the column-like and plate-like behavior modes, leading to more accurate design resistances.

Shear strength model for RC joints, consistent with the shear design rules for prismatic members in the second-generation Eurocodes

The CEB/FIP 1985 seismic model code, the 1994 ENV and the 2004 EN versions of Eurocode 8, as well as the 2019 draft of the future Eurocode 8, have adopted different models for the shear strength of RC joints, without paying much attention neither to the shear design rules applying at the time to RC structures designed to non-seismic actions, nor to the large volume of available test results. In the light of current experimental knowledge, these provisions have moved from a high average safety margin in the past to a safety deficit in recent proposals for future. Moreover, the scatter of their predictions renders some of them meaningless. A new rational model is proposed for the cyclic shear strength of RC joints, fully consistent with the shear design rules in the new-generation Eurocodes 2 and 8 for RC members. As such, it has been adopted in the 2020 draft of the second-generation Eurocode 8. It considers the stress fields in the concrete and the reinforcement as continuous and uniform within the joint’s volume, uses first principles of mechanics (principal stresses and strains, constitutive relations, equilibrium) and searches for the inclination of the compression field direction and of the principal compressive strain in the joint which maximizes its shear resistance. The model gives unbiased, low-scatter predictions of the shear strength for over 650 shear-critical joint specimens. Taking the average of the beam and column widths as effective width of the joint gives overall better agreement with test results than the approach in the current Eurocode 8 and its predecessors. The shear force at cracking of the uncracked joint should be considered as lower limit to its ultimate shear strength. If applied with design values of material strengths, the model gives values of the joint’s shear strength which exceed the actual, experimental strength in 2% of the cyclic tests of interior joints and in 5% of those of exterior ones.

Experimental investigation of concrete edge failure for single stud anchors and anchor groups after fire exposure

In the present study headed stud anchors with single stud, two- and four-stud anchor groups are exposed to various duration of fire and after cooling (cold state) loaded in shear perpendicular to and towards the free edge of concrete member up to failure. The standard ISO 834 fire curve with fire durations of 15 min and 60 min are employed in the experiment. The influence of the number of studs and the duration of fire on the load-bearing behaviour of anchors is experimentally investigated. As expected, the results show that the anchor behaviour is significantly influenced by the fire exposure. Due to the thermally induced damage of concrete the failure pattern is changing from the typical concrete edge failure to a combination of concrete edge failure and pryout failure. For fire duration of only 15 min, the reduction of resistance can be more than 50% of the reference resistance. After 60 min of fire, the reduction factor is approximately corresponding to the reduction factor for 90 min of fire exposure according to current Eurocode 2. Considering concrete capacity method (CC-method), it is demonstrated that simply replacing the compressive strength of concrete at ambient temperature with the reduced compressive strength after fire is not appropriate for predicting the resistance of single stud anchors and anchor groups. However, the projected area ratio of the fracture seems to be valid for predicting the resistance of anchor group based on the reduced resistance of corresponding single stud anchor after fire exposure.

Stress–strain–temperature relationship for concrete

When concrete structures are subjected to load and temperature simultaneously, it is essential to take into account the coupled effects between stress and expansion. However, due to incomplete understanding, such coupled effects have only been incorporated into current Eurocode 2 (EC2) stress–strain curves by means of empirical correlations. These empirical correlations at different target temperatures are presented in tables that do not allow to clearly identify the correlation chosen to obtain the specific values. A further limitation of these tables is that the relationships cannot be used to evaluate the performance of concrete structures during the cooling phase. In this paper, a physically-based model of the coupled effects between stress and expansion is used to define the strain corresponding to the compressive strength, and thus to develop a simple formulation for stress–strain–temperature relationship of concrete. The results are then compared with the EC2 stress–strain–temperature table. The expression of stress–strain–temperature relationship developed in this paper successfully agrees with the stress–strain curves of concrete in EC2 used for the heating phase. More importantly, the proposed stress–strain–temperature relationship can also be applicable for design purposes of concrete structures during the cooling phase.

Elasto-plastic behaviour and design of semi-compact circular hollow sections

Previous research has revealed shortcomings in the current Eurocode 3 (EC3) provisions for the design of semi-compact (Class 3) cross-sections. These shortcomings arise primarily from the lack of utilisation of partial plastification in bending, leading to a step in the design resistance function at the boundary between Class 2 and 3 cross-sections and an underestimation of the available capacity. This affects the accuracy of resistance predictions in bending and under combined loading, and applies at both cross-sectional and member level. To address this issue, the use of an elasto-plastic section modulus, which lies between the plastic and elastic section moduli, has been proposed and employed in the design of semi-compact I- and box sections. The aim of the present study is to develop new cross-section and member buckling design rules incorporating the elasto-plastic section modulus for semi-compact circular hollow sections (CHS), and to assess their accuracy against existing experimental and freshly generated numerical data. Firstly, an experimental database, consisting of previous cross-section and member buckling test results on steel CHS, was established. A comprehensive numerical simulation programme was subsequently carried out; in this programme, finite element (FE) models were developed, validated and used for parametric studies, where over 600 numerical structural performance data on semi-compact CHS were generated. New sets of cross-section and member buckling design expressions featuring elasto-plastic section properties were then proposed and assessed against the test and numerical data. The proposals were shown to offer improved accuracy and design efficiency over the elastic EC3 methods. The reliability of the proposed elasto-plastic design rules was then confirmed through statistical analyses in accordance with EN 1990, demonstrating their suitability for inclusion into the next revision of EN 1993-1-1. • Existing cross-section and member buckling test data on CHS were collected. • Numerical simulation was conducted to generate further data on CHS. • New design rules were developed to capture the elasto-plastic behaviour of semi-compact CHS. • Accuracy of the current Eurocode 3 and proposed methods were assessed and compared. • Reliability of the proposed design rules was confirmed through statistical analyses.

Variable strut inclination model for shear design of FRP reinforced concrete members with shear reinforcement

To avoid brittle shear failures, the shear strength of reinforced concrete beams has to be verified at ultimate limit state. For this purpose, simple but accurate shear design provisions or shear resistance models are required. In this paper, the derivation of a simple shear design model for beams with FRP shear reinforcement is presented. At first, the suitability of existing code provisions and shear resistance models is evaluated using a large databank on shear tests on members with FRP shear reinforcement. Based on the results, a shear resistance model is developed based on a truss model with variable strut inclination, which is also the basis of the shear design of members with steel shear reinforcement according to current Eurocode 2. An important aspect regarding the derivation of the model is the definition of an appropriate method to determine the angle of the compression strut. For this purpose, a compression field model originally developed for steel reinforced concrete beams is adopted. The proposed resistance model is validated by means of a databank evaluation. Moreover, an equation to determine the minimum shear reinforcement ratio of FRP reinforced concrete members is derived based on the shear design provisions according to Eurocode 2.

Testing of hot-finished high strength steel SHS and RHS under combined compression and bending

Abstract An experimental investigation into the cross-sectional behaviour of hot-finished high strength steel tubular sections, to support the assessment and development of structural design guidance, is presented. Two grades of quenched and tempered high strength steel – S690 and S770 and eight cross-sections – seven square hollow sections (SHS) and one rectangular hollow section (RHS), covering a wide range of local slenderness, were examined. This test programme consisted of twelve tensile coupon tests, five stub column tests and 30 short beam-column tests, with various initial loading eccentricities employed to achieve a spectrum of compression and bending combinations. Local geometric imperfection measurements were carried out on each test specimen using 3D laser-scanning, and a rational approach to analysing the local imperfection distributions using the scanned data was subsequently proposed. Following the experimental study, the current Eurocode 3 cross-section design provisions were evaluated through comparisons with the results from the present research and additional results from the literature. The experimental results and findings from the present study provide a basis for the development of numerical models and the enhancement of existing design methods in the future.

Uncertainty of shear resistance models: Influence of recycled concrete aggregate on beams with and without shear reinforcement

The model uncertainty of the shear resistance equations of three design codes {the current Eurocode 2 (2004), Model Code (2010), and the final draft of the Eurocode 2 (2020)} was investigated for coarse natural and recycled aggregate concrete beams. Databases of beams with and without shear reinforcement were made with clearly defined criteria. The statistics of the model uncertainty of natural and recycled concrete beams were compared and it was found that recycled aggregate incorporation has detrimental effects on the model uncertainty of shear design. Surprisingly, recycled concrete aggregate beams designed following the current version of Eurocode 2 (2004) are safer than those designed using the other codes. This is due to the shear resistance equations of the latter overestimating the aggregate interlock of recycled aggregate. A preliminary partial factor was proposed, offsetting the influence of recycled aggregate on the safety of beam designs. The database of beams with shear reinforcement lacks representativeness but hinted that recycled aggregate incorporation also reduces the safety of this type of shear design. The paper finishes presenting suggestions of experiments that would complement the current knowledge on this topic.

ANALYSIS OF THE GLOBAL AND LOCAL IMPERFECTION OF STRUCTURAL MEMBERS AND FRAMES

Stresses of a structure are determined with a first or a second order analysis. The choice of the method is guided by the potential influence of the structure’s deformation. In general, considering their low rigidity with regard to those of buildings, scaffolding and shoring structures quickly reach buckling failure. Imperfections, such as structural defects or residual stresses, generate significant second order effects which have to be taken into account. The main challenge is to define these imperfections and to include them appropriately in the calculations. The present study suggests a new approach to define all the structure’s imperfections as a unique imperfection, based on the shape of elastic critical buckling mode of the structure. This study proposes a method allowing to determine the equation of the elastic critical buckling mode from the eigenvectors of the second order analysis of the structure. Subsequently, a comparative study of bending moments of different structures calculated according to current Eurocode 3 or 9 methods or according to the new method is performed. The obtained results prove the performance of the proposed method.

Seismic Behaviour of EC8-Compliant Moment Resisting and Concentrically Braced Frames

The design procedure codified within current Eurocode 8 for dissipative moment resisting and concentrically braced frames have led to the design of massive systems characterized in the most of cases by poor energy dissipation capacity. The research activity presented in the current paper addresses the identification of the main criticisms and fallacies in the current EN 1998-1 for those seismic-resistant typologies. In this regard, the design provisions and codified rules for both moment resisting frames (MRFs) and chevron concentrically braced frames (CCBFs) are critically discussed and numerically investigated. Static and incremental dynamic analyses were performed on a set of 3 and 6-story frames designed compliant to EN 1998-1. The results from the numerical analyses are reported and discussed.

Honing safety and reliability aspects for the second generation of Eurocode 7

ABSTRACTTen years after their publication, the Eurocodes, including Eurocode 7 for Geotechnical design, are being revised taking into account experiences with their use and developments in design concepts and practices since their publication to produce a second generation of the Eurocodes. The objectives for this second generation of Eurocode 7 are to improve its ease of use, harmonise its structure with the other Eurocodes, reduce the number of nationally determined parameters, include measures for robustness and include sections on topics not covered in the current Eurocode 7, such as numerical methods, reinforced soil and ground improvement. The evolution of Eurocode 7 aims to hone its safety and risk assessment aspects by developing the concept of Geotechnical Categories, expanding the supervision, monitoring and maintenance requirements, and explicitly allowing for reliability differentiation.

An assessment of the lateral-torsional buckling and post-buckling behaviour of steel I-section beams using a geometrically exact beam finite element

The goal of this paper is twofold. The first goal is to show that geometrically exact beam finite elements can be successfully employed to determine, accurately, the behaviour of steel I-section beams undergoing large displacements and finite rotations. For this purpose, a two-node geometrically exact beam element is presented and validated, which can handle arbitrary initial configurations (e.g. curved configurations), plasticity, geometric imperfections and residual stresses. The second goal is to employ the proposed element to assess the behaviour of I-section beams undergoing lateral-torsional buckling. In particular, the element is used to determine (i) elastic non-linear bifurcation loads (i.e., bifurcation loads accounting for pre-buckling deflections), (ii) large displacement elastic post-buckling paths including geometric imperfection effects and (iii) large displacement elastoplastic equilibrium paths accounting for geometric imperfections and residual stresses. Three support/loading cases are examined, namely: (i) simply supported beams under uniform moment, (ii) simply supported beams subjected to a mid-span vertical force and (iii) cantilevers subjected to a free end vertical force. Besides I-sections with standard height-to-width ratios, wider flange sections are also considered and it is demonstrated that, for the latter, the post-buckling behaviour is quite different from that of standard sections and an increase in the load carrying capacity is observed, which is not predicted by the current Eurocode 3 [1] provisions. Based on the results obtained, a set of relevant conclusions are drawn.

Numerical evaluation of the plastic hinges developed in headed stud shear connectors in composite beams with profiled steel sheeting

For composite beams using novel steel sheeting, the current Eurocode 4 rules sometimes overestimate the load-bearing capacity of headed stud shear connectors. This is due to the larger rib heights and the smaller rib widths in comparison with the old studies, which have been carried out to calibrate the current design equations. The RFCS Project “DISCCO” investigated this phenomena and the working group under mandate M515, CEN/TC250/SC4/SC4.T3 is enhancing this equation and working on a proposal to be taken over in the new version of Eurocode 4.The proposed new equation covers the failure behaviour of the shear connection more in detail. The test results show, that the failure consists in a combined concrete cone and stud in bending. Due to the geometry of novel steel sheeting, the load bearing capacity of the headed stud shear connector is no more limited by its shear capacity, but by its bending capacity.A 3D non-linear finite element model is developed and validated through the support of the DISCCO push-out tests. A good agreement between numerical and experimental results in terms of force-slip behaviour is achieved. Special attention of this work lies on the numerical evaluation of the number of plastic hinges ny: a stress-based procedure is presented and the results are compared to the equations presented for new Eurocode 4.The numerical simulations show that the upper plastic hinge moves up as the slip increases due to the progressive crushing of the concrete in the rib. From the parametric study, it turns out that ny is linearly proportional to the embedment depth. Compared to pre-punched hole decking, through-deck welding specimen activates less plastic hinges in the studs because of the higher stiffness provided at the base of the stud.

Use of HSS and VHSS in steel structures in civil and offshore engineering

AbstractIn Memoriam of Prof. Dr. Bernt JohanssonThe use of high‐strength steels (HSS, 460 < fy ≤ 700 MPa) and particularly very high‐strength steels (VHSS, fy > 700 MPa) is limited in steel structures in civil and offshore engineering. This is due to a lack of experience in structures made of these materials and a lack of understanding of the structural performance of HSS and VHSS. The main questions that are unanswered concern the topics of static strength, fracture toughness, fatigue, material (in)homogeneity and manufacturing. With regard to the static strength, it is unclear as to whether requirements currently stated in the Eurocodes for the yield‐to‐tensile strength ratio (fy/fu) as well as the Von Mises yield criterion are applicable to structural designs in HSS and VHSS. With regard to fracture toughness, it is unclear as to whether the crack arrest capability of HSS and VHSS is currently sufficiently covered in Eurocode requirements. Furthermore, Eurocode requirements for maximum plate thickness are quite restrictive if they are extrapolated to HSS and VHSS. Other questions relate to the homogeneity of the material. Are HSS and VHSS sufficiently resistant to lamellar tearing and is material testing in different orientations necessary? This study gives an overview of the relevant questions, outlines the requirements in the current Eurocode system, presents answers to these questions where possible and provides a recommended research focus for the coming years.

Ductility reduction factor formulations for seismic design of RC wall and frame structures

Seismic design of standard structures is typically founded on a force-based design approach. Over the years this approach has proven robust and easily applicable by design engineers and – in combination with capacity design principles – it provides a good protection against premature structural failures. However, it is also known that the force-based design approach as it is implemented in the current generation of seismic design codes suffers from some shortcomings; among these is the fact that the base shear is computed using a pre-defined force reduction factor, which is constant for a given structural system. Thus, for the same design input, structures of an identical type but different geometry are subjected to varying ductility demands and may perform differently during an earthquake. The objective of this research is to present an alternative formulation for computing force reduction factors for RC wall and frame structures, using simple analytical models which only require input data already available at the beginning of the design process. Such analytical models allow to link global to local ductility demands and therefore to compute an estimate of the force ductility reduction factors that lead to equal local ductility demands and expected damage levels. A series of pushover and nonlinear time history analyses are run on simplified numerical models of a set of wall and frame structures. The results show that the proposed alternative formulation yields a more accurate ductility reduction factor than the current Eurocode 8 design approach.

Punching strength of conventional slab-column specimens

This paper presents an improved rational method for predicting the punching strength of conventional reinforced concrete slab-column specimens extending to the nominal line of contraflexure in a flat slab structure. The proposed method of analysis is for square and circular, isotropically reinforced, conventional slab-column specimens, concentrically loaded using square or circular columns. The method is based on an earlier two-phase approach, in which the punching strength was predicted as the lesser of the flexural punching strength and the shear punching strength. The earlier approach had previously been shown to be more reliable than other methods, including the major building code methods, and the proposed method represents a further significant improvement. The improvement in the proposed method is due to the incorporation of slab depth factors for both the flexural and shear modes of punching failure and refinements to the effects of concrete strength, reinforcement percentage and reinforcement yield strength, for the shear mode of punching failure. Comprehensive test data is presented for 217 tests on conventional slab-column specimens reported in the literature in the sixty year period 1956–2016. Analysis of these results by the proposed method resulted in significantly improved correlation over that of the authors’ previous two-phase approach. The method is also shown to be significantly more accurate and consistent than the current Eurocode 2 (2004) method, the ACI 318-14 (2014) method and the fib Model Code (2010) method for predicting the punching strength of conventional reinforced concrete slab-column specimens.