Current Eurocode Research Articles

The use of a general method for calculating the resistance of strengthened concrete columns

Columns are one of the basic types of vertical load-bearing elements. In buildings, they are used where there is a requirement to create free spaces. This results in an effort to minimize the cross-section dimensions of the column and to maximize the use of its resistance. The need of the increase in resistance is the reason for columns strengthening. The choice of a suitable strengthening method must take into account the way the column is loaded. Some methods are universal, the others are more effective in the case of predominant compressive, or predominant bending loading. In presented research, the attention is focused on strengthening slender reinforced concrete columns by progressive methods - FRP (fibre reinforced polymer) and FRC (fibre reinforced concrete) applications. For slender columns, second-order effects must be taken into account. The current Eurocode lists three methods of analysing these effects. The simplified methods proposed for the analysis of a reinforced concrete column cannot be applied directly to the calculation of the resistance of a column strengthened by any of the progressive methods. The article is devoted to the calculation of column resistance using a general method that allows the contribution to column resistance from strengthening to be considered.

Behavior of high-strength stainless steel S600E welded I-section beams

S600E is a new type of high-strength stainless steel with sorbite microstructure. Its yield strength is as high as 600 MPa, and its cost is lower than the commonly used stainless steel due to its low content of precious metallic elements Ni and Cr. This paper studied the bending capacity of high-strength stainless steel S600E welded I-section beams with lateral-torsional buckling. Tests on seven I-section beams were performed using an innovative four-point bending test rig. Thereafter, comparisons between the bending capacities and the values predicted using the current Eurocode, American code, and Chinese specification were conducted. The results showed that the predictions of the three existing codes were all conservative. Finite element models for the beams were established and verified, meanwhile, parametric analyses based on the simplified models were carried out on the influence of key parameters. Subsequently, through the results of the test and finite element analysis, the design formula for the lateral-torsional buckling was modified and the design formula for the local buckling in the companion study was verified. The complete design procedure of high-strength stainless steel S600E I-section beams was developed by the combination of the two formulae. Finally, to prove the accuracy of the design method proposed in this paper, comparisons between the predictions of the proposed method with the test data and four hundred finite element models were conducted.

Assessment of Eurocode shear design provisions for cold-formed steel sections

Cold-formed steel (CFS) sections are widely used in structural systems and are particularly prone to shear failure in short span applications. Therefore, accurate shear strength estimation is essential for the design. However, while there exists an abundance of research studies investigating the shear behaviour of CFS sections, there is a clear need for the assessment of Eurocode 3 shear design provisions. Towards meeting this need, the design of CFS sections subjected to shear is studied herein. Existing experimental data on CFS lipped channels and hollow flange sections were assembled from the literature. The collected experimental data was then used to assess the accuracy of the current Eurocode 3 shear design provisions. The current Eurocode 3 design provisions are shown to provide overly conservative shear strength predictions against the experimental data. Modifications, including the slenderness of the cross-section to reflect the shear buckling coefficient were proposed. The proposed modifications to the current design provisions offer substantially improved accuracy in shear strength predictions.

Reliability‐based calibration of design code formulas: Application to shear resistance formulas for reinforced concrete members without shear reinforcement

AbstractThis paper presents a reliability‐based calibration method for design code formulas. The method is demonstrated on the shear design formulas in Eurocode 2 and fib Model Code 2010 (MC2010). We found that the partial factor in the current Eurocode 2 is about 20% lower than the optimal value and, thus, provides an insufficient safety margin. The obtained optimal partial factor in the (modified) Eurocode 2 and MC2010 formulas is 1.53 and 1.36, respectively. The difference stems from higher accuracy and, hence, lower uncertainty of the MC2010 model in predicting experimental results. Hence, on average, the MC2010 formula leads to about 13% larger design resistances compared to Eurocode 2 given that the target reliability for both design formulas is the same. To stimulate and facilitate future structural code development and derivation of partial factors, we make the used computer code freely available.

Enhancement of the punching shear verification of slabs with openings

AbstractOpenings in flat slabs near to columns are often needed to supply the building with utilities. The presence of these openings can lead to a decrease of the punching resistance which is related to (i) the reduction of the control perimeter, (ii) the stress concentrations at the edges of the openings, (iii) the reduction of the unitary shear resistance caused by increased flexural deformations, and (iv) the moment transfer in the slab connection in case of unsymmetrical openings. The effect of the openings on the punching shear resistance is strongly related to the geometry, the location, the number, and the size of the openings. To quantify the strength reduction due to the openings, current code approaches account for a reduction of the control perimeter defined by radial lines from the centroid of the column to the edges of the opening. Even though slabs with opening have been investigated since the 1960s, available experimental evidence on the behavior of slabs with openings without shear reinforcement is scarce and some effects are neglected in current design codes. Eurocode 2 and fib Model Code do not consider the effect of unsymmetrical openings leading to moment transfer in the slab‐column connection. ACI 318:2019 recommends considering these cases as free edges; however, additional information is necessary to perform the analysis. The present paper analyses a database of 68 flat slab specimens with openings according to ACI 318:2019, current Eurocode 2 (EN 1992‐1‐1:2004), the draft for the second generation (prEN 1992‐1‐1:2021), fib MC 2010:2013, and the Critical Shear Crack Theory. This paper proposes a new approach and a new definition of the control perimeter to improve the prediction of the punching shear resistance of slabs with openings based on the results of the database, the previous studies, and the linear‐elastic analyses of the shear force distribution along the control perimeter.

Behaviour and design of high strength steel homogeneous and hybrid welded I-section beams

The behaviour and design of high strength steel (HSS) beams are addressed in the present study. Six in-plane three-point bending tests on three different welded I-sections − two homogeneous S690 steel welded I-sections and one hybrid welded I-section with S690 steel flanges and an S355 steel web, were first conducted. The beam tests were carried out in major axis bending and a bespoke restraint system was designed and employed in the test programme to prevent lateral-torsional buckling. Following the experimental investigation, a thorough finite element (FE) modelling programme was performed, which included a validation study confirming the accuracy of the developed FE models in replicating the flexural behaviour of HSS welded I-section beams, and a parametric study generating additional FE data on HSS welded I-section beams over a broader range of cross-sectional slendernesses, steel grades and loading configurations. The test results obtained in the present study and collected from the literature, together with the generated FE data from the parametric study, were used to evaluate the suitability of the current Eurocode 3 cross-section slenderness limits for HSS homogeneous and hybrid welded I-sections in bending. It is shown that the current Eurocode Class 2 and Class 3 slenderness limits are suitable for the classification of the outstand flange (in compression) and internal web (in bending) elements of both HSS homogeneous and hybrid welded I-sections subjected to major axis bending, while stricter Class 1 slenderness limits are considered necessary to achieve sufficient rotation capacity for plastic design. The findings from the present study indicate that plastic design can be used for HSS structures, provided the proposed stricter Class 1 slenderness limits are employed.

Stainless steel I-section columns fire design considering the influence of loading history

The flexural buckling resistance of welded I-section stainless steel columns in fire considering the influence of the loading history is investigated in this paper. Finite element procedure used to replicate the response of stainless steel columns in fire has been developed and validated against existing experimental tests. Developed finite element procedure replicates real fire situation where column is firstly loaded and then heated until failure. Poor accuracy of the flexural buckling resistance according to the current Eurocode 3 design rules and recently proposed design rules was observed through an extensive parametric analysis, thus indicating that new contributing parameters need to be included in the design expressions. Two main contributing parameters were analyzed, ratio of the flange and web area Af/Aw and ratio of the flange and web thickness tf/tw. New flexural buckling rules were proposed and calibrated using the results from 3000 numerical simulations, according to the developed finite element procedure, considering a range of elevated temperature levels of practical importance, stainless steel grades, cross-sectional proportions and column slendernesses. The accuracy and reliability of new proposal were assessed against the results obtained through finite element procedure. Compared to the current Eurocode 3 design rules and recently proposed design rules, new proposal provides significantly more accurate prediction of flexural buckling resistance of stainless steel columns in fire.

Seismic performance of Eurocode‐compliant ductile steel MRFs

AbstractSteel moment resisting frames (MRFs) are drift‐sensitive structures and their design is largely influenced by code requirements to limit the lateral displacements and to control the second order effects. Current and next generation of Eurocode 8 recommend different rules to verify the lateral rigidity and resistance of steel MRFs that lead to structures that are substantially different in terms of size of members and overall performance. In order to investigate the influence of the design rules on the seismic behaviour of ductile steel MRFs a parametric numerical study was carried out on 48 structures designed according to Eurocodes as well as US codes, the latter analysed as benchmark, varying the number of storeys, moment resisting spans and seismic intensity. The results of non‐linear static and dynamic analyses show that the structures complaint with current Eurocode 8 are the most expensive and characterised by the greater lateral rigidity and resistance, while MRFs designed in accordance with ASCE7 rules have the smaller profiles and the lower overstrength. The frames designed with rules of the latest version of next generation of Eurocode 8 have an intermediate behaviour even if closer to ASCE7‐compliant structures. These results are also confirmed by the probability of collapse that is smaller than the minimum value specified by EN1990 for the considered consequence class of the examined buildings.

Buckling behavior and design of concentrically loaded T-section aluminum alloy columns

Tees are utilized as chord members in a number of arrangements of aluminum alloy trusses. The purpose of this study is to investigate the buckling behavior and design methods of concentrically loaded T-section aluminum alloy columns. Using column tests and finite element analysis, this study analyzed the buckling modes and ultimate strengths of high-strength aluminum alloy T-columns under axial compression and validated the numerical model against the experimental results. Comparisons with the current Eurocode 9 and Direct Strength Method (DSM) design rules were also conducted. Fixed- and pin-ended columns exhibit a quite different buckling behavior. The failure modes of flexural buckling about the two principal axes could be treated with sufficient safety and accuracy using the column design rules in Eurocode 9 and DSM. The effects of the effective centroid shift due to the local buckling of slender parts could be ignored. The Eurocode 9 and DSM leads to inaccurate and conservative results for fixed-ended columns failing by local-torsional buckling and flexural–torsional buckling. The paper recommends suggestions based on the DSM approach that improve the design strength predictions for aluminum alloy T-section columns.

A closed‐form shear resistance model for regions of prestressed beams without flexural cracks

AbstractWhen the shear resistance of prestressed beams with stirrups is determined with the current Eurocode, no distinction is made between regions with and without flexural cracks. This while it may be expected that a region without flexural cracks will have a higher shear resistance. This is due to the lower longitudinal strains and the narrow crack widths, resulting in a higher contribution of aggregate interlock. Also, the Eurocode does not take into account that in regions without flexural cracks, a significant part of the shear force is transferred through the uncracked flanges. This article proposes therefore a shear resistance model, based on Modified Compression Field Theory (MCFT), that does consider the low longitudinal strains and shear transfer through the uncracked flanges. From a comparison it was found that the proposed model can determine shear resistance as accurately as the most comprehensive level III approach of the Model Code 2010. However, the proposed model was found to be much easier to use in engineering practice as no iterations are necessary.

Compression tests on large angle columns in high‐strength steel

AbstractNominated for Eurosteel 2021 Best Paper AwardThe paper addresses the instability of large angle columns in high‐strength steel subjected to compression loads. It presents a number of compression tests on such columns with different eccentricities and slenderness and the resulting different buckling failure modes observed. The experimental campaign is intended to widen our understanding of the behaviour of high‐strength steel columns with large angle sections in compression and bending and so to complement previous experimental studies. The tests were accompanied by numerical analyses and calculations of the load carrying capacities based on current Eurocode 3 design recommendations. The numerical simulations were conducted using the FEM software FINELG, which takes into account the influence of geometrical and material non‐linearities. The numerical and analytical results are compared with the corresponding experimental ones. The experimental campaign and the numerical simulations were conducted as part of the ANGELHY project funded by the European Commission's Research Fund for Coal and Steel (RFCS).

Local/global coupled instabilities of slender I-sections under compression

Current standards usually deal with local/global interactive buckling behaviour rather roughly through combining the traditional Effective Width Method (E.W.M.) with member buckling curves; this leads to long and tedious design calculation processes, sometimes also providing inaccurate resistance predictions. A more economic and simple design method following the actual local/global interactive behaviour is proposed here, based on the Overall Interaction Concept (O.I.C.), through decomposing interactive buckling through local/global interaction factors. The accuracy of this O.I.C.-based design proposal is evaluated against numerical results from validated shell F.E. models, which evidences that the O.I.C. predicts more accurate member resistance than the current Eurocode 3 and American Standards recommendations, for both hot-rolled and welded slender I-section members under axial compression. The reliability of the proposed O.I.C. approach is also found excellent, following statistical analysis guidelines from EN 1990.

Transversally loaded stainless steel beams under fire: Local/global behaviour, strength and design

This paper presents and discusses the results of a numerical investigation concerning the post-buckling behaviour, strength and design of stainless steel I-section beams prone to local or global (lateral-torsional) buckling under elevated temperatures. Non-linear shell finite element models are employed to assess the structural response and failure loads of I-beams (i) subjected to distinct loading conditions, namely uniform bending, uniform transverse loading, 3 and 4-point bending (the transverse loadings are applied along either the shear centre, top flange-web or bottom flange-web longitudinal axes), (ii) made from three common stainless steel grades (ferritic 1.4003, austenitic 1.4301 and duplex 1.4462), (iii) subjected to eight temperatures (θ = 100 to 800 °C), and (iv) covering wide local and global slenderness ranges. Special attention is paid to the influence of the transverse loading location (load height effect), a topic lacking research in the context of local buckling, by means of (i) Generalised Beam Theory (GBT) buckling and (ii) ABAQUS shell finite element post-buckling analyses. The last part of the paper is devoted to design considerations, based on the numerical failure loads obtained and involving the assessment of the current Eurocode 3 design rules for stainless steel beams failing in local and global modes.

Seismic design of non-structural components mounted on irregular reinforced concrete buildings

The seismic response of non-structural components (NSCs) attached to irregular reinforced concrete (RC) multi-storey buildings is underestimated by current European design provisions. This paper presents a new design model for NSCs, accounting for the effect of torsion and seismic capacity of an irregular RC primary structure (P-structure). The proposed model is a modification of the current Eurocode 8 (EC8) model for the acceleration amplification factor of NSCs. It is based on the results of some 5000 nonlinear dynamic finite element analyses conducted on thirty-three building cases. The finite element analyses covered a wide range of parameters including plan layout, seismic capacity, fundamental vibration period, total height, floor rotation, ground type and eccentricity ratio. The proposed model has been demonstrated to be an improvement over EC8 model, especially for NSCs mounted on the flexible side and in tune with the fundamental vibration period of a P-structure.

Flexural buckling of normal and high strength steel CHS columns

This paper presents an experimental and numerical investigation into the stability of normal and high strength steel circular hollow section (CHS) columns. Two cold-formed S700 CHS profiles – 139.7×4 and 139.7×5 (in mm), were studied in the experimental programme, and twelve column tests (six on each profile), together with accompanying material tests, were performed. The load-deformation histories and key results from the tests are reported. Following the physical testing, a numerical simulation campaign was conducted. The developed finite element (FE) models for CHS columns were initially validated against the test results. Parametric studies were then carried out, where 2000 additional buckling resistance data were numerically generated for hot-finished and cold-formed CHS columns, covering steel grades from S355 to S900. The obtained test and FE results, together with existing experimental data from the literature, were used to assess the current Eurocode 3 stability design rules. It was shown that the normalised performance of CHS columns is influenced by the yield strength, which is not fully captured by the EC3 design approach. The somewhat conservative Class 3 slenderness limit for compression further worsen the accuracy for those with slender cross-sections. Improvements to the EC3 design rules were proposed to address these shortcomings, including (a) modified Ayrton-Perry formulae enabling a continuous transition of buckling curves across the yield strength spectrum and (b) a new Class 3 limit for CHS in compression. The modified EC3 approach was assessed and shown to improve the accuracy and consistency of resistance predictions over the current EC3 approach, while meeting the Eurocode structural reliability requirements.

Influence of mixing tropical timber species and material heterogeneities on the long-term stability of slender glulam beam columns

ABSTRACT Slender glulam beams are high value products that may be used differently concerning large span structures. They can be manufactured in developing countries without significant industrial resources by using two tropical timber species, while preserving emblematic species and promoting lesser known ones. The current Eurocode 5 design rules, based on the effective length method, are not adapted for designing such products, subjected to axial compression. An approach, based on a work-energy method, is investigated in this work. The goal of the paper is to provide a refined modeling of the long-term buckling strength of mixed and slender tropical glulam beam column, based on the finite element method. The variability of the rheological properties of the materials is considered, as well as the geometrical imperfection of the product, characterized by initial deflection. Variations of the glulam composition are also considered. Monte-Carlo simulations of the beam behavior over time are performed. Results provide for each glulam composition a set of analytic and decreasing evolution of the long-term buckling strength with time. The relative gap between the initial and final critical load can reach up to 18%. The possibility of optimizing the parameters that drive the long-term stability of beams is discussed. Moreover, the study may unlock a new standard design approach for the designers and engineers, aiming at guaranteeing the long-term safety of the slender and mixed glulam products.

Critical view on the level of maximum punching strength of flat slabs and column bases using database evaluations

AbstractThe level of maximum punching strength is of major importance to design highly stressed slab‐column connections and to choose the type of punching shear reinforcement. Since a couple of years, there is consensus that the maximum punching strength of shear‐reinforced concrete slabs can be defined as a multiple of the reference punching strength without shear reinforcement. The upper bound of this load‐increasing effect depends mainly on the anchorage and arrangement of shear reinforcement elements. Despite numerous research studies and database evaluations, there are ongoing discussions regarding the final effectiveness of stirrups and double headed studs installed in flat slabs and column bases.In this paper, a strictly filtered punching database is used to highlight the significant impact of underlying reference strength comparing the maximum load increase according to current Eurocode 2 and the draft for the next generation of Eurocode 2 (prEC2). Based on this unifying database, the origin of current discrepancies is discussed and a combination of constant lower bound coefficients with a refined formula as specified in prEC2 is proposed. Additionally, the effect of adapting current European Technical Approvals for double‐headed studs and punching shear optimized lattice girders to prEC2 is shortly analyzed. A further database evaluation also allows for setting the basis for optimized detailing provisions regarding the maximum permissible diameter of shear reinforcement.

Numerical investigation for the design of rectangular concrete encased steel composite columns

AbstractAdvanced design methods are becoming more important for the structural analysis. However, their results depend strongly on the quality of the numerical model and its underlying assumptions. Current Eurocode 4 does not provide clear guidance for this analysis type.A literature review on the compression tests conducted on concrete encased steel composite columns is presented. It was found out that there is a lack in the literature when it comes to the testing of slender composite columns as opposed to numerous tests done on stub columns. A selection of existing specimen tests are then simulated using finite element analysis software ABAQUS. Nonlinearity in the model was defined through materials and geometry. The interface modelling between steel and concrete as well as the modelling of load introduction are discussed. The finite element model was intended to be as generic as possible so that it can be taken as a basis for future parameter studies. Moreover, the column resistance check using interaction curves was discussed. Different approaches to form interaction curves namely strain limitation and plastic section capacity were compared.

Probabilistic risk assessment of the effects of fire service intervention on structural fire resistance design of unsprinklered buildings

This paper presents a probabilistic analysis method to explicitly include the influences of fire service intervention (FSI) in structural reliability analysis of unsprinklered buildings exposed to fire. The method considers different scenarios of fire behaviour following FSI, based on probabilistic analysis of the current UK fire data to estimate different components of intervention time, size of the fire on arrival of the fire service and extent of damage of the fire at the end of intervention. These statistical data are then used to generate random fire temperature-time curves to calculate the probability of structural failure of intumescent coating protected steel members using the Monte Carlo Simulation method. To aid deterministic design, a simplified method is developed to derive fire load modification factors (δn,FSI) to account for the effects of FSI so that when the fire load modification factor is applied, the deterministic design method gives the same probability of structural failure as that from explicit probabilistic calculation. An extensive parametric study covering a wide range of practical design factors has been carried out and an Analysis of Variance (ANOVA) is performed on the results to examine whether any design factor has significant effect on the fire load modification factor. The results show that fire growth rate and compartment floor area are the most influential. The effects of fire load, steel critical temperature and fire protection thickness have moderate effects. Based on the results of this study, it is suggested that the design fire load should not be reduced if the fire floor area does not exceed 250 m2, or the fire growth rate is ultrafast. If the fire growth rate is fast, the design fire load should not be reduced for fire floor areas less than 1000 m2. For other situations, a fire load modification factor of δn,FSI = 0.78, as in the current Eurocode, may be applied.

Evaluation of current Eurocode 8 provisions on R/C ductile wall design

In this study, the applicability and conservativeness of current Eurocode 8 (2004) provisions for the design of ductile reinforced concrete (R/C) shear walls are evaluated. Apart from adequate strength supply, a successful design also requires that the provided section curvature ductility should satisfy the respective demand. The Code, striving to maintain a balance between ease of application and accuracy, provides practical directives to facilitate the required ductility supply. However, at the end of the design there is no tangible verification whether the provided ductility satisfies the requirement. To provide insight regarding the applicability of these Code provisions, an extensive series of rectangular wall cases is analyzed, and various design approaches adopted by engineering practice are evaluated. Moment-curvature analysis including confinement effects is performed on all wall configurations for verification purposes. It is found that simplified Code approaches cannot always guarantee an acceptable design; in this regard, a few alternatives are presented, favoring conservativeness and accelerating the design workflow. The paper concludes with an evaluation of the current design practice, under the light of the upcoming Code revision.