Local Imperfections Research Articles

Post-fire local buckling behaviour of cold-formed S700 high strength steel circular hollow sections under axial compression: Experiments, modelling and design

This paper presents experimental and numerical studies of the local buckling behaviour and compression resistances of cold-formed S700 high strength steel circular hollow sections (CHS) after exposure to elevated temperatures. The testing programme included post-fire material tests, initial local geometric imperfection measurements and stub column tests on ten specimens. Then, finite element models were developed to simulate the test structural responses and employed to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions. Given that there are no existing design standards for high strength steel structures after exposure to elevated temperatures, the relevant ambient temperature design rules were evaluated, using post-fire material properties, for their applicability to cold-formed S700 high strength steel CHS after exposure to elevated temperatures, based on the test and numerical data. The evaluation results revealed that (i) the codified slenderness limits were generally accurate when used for cross-section classification of post-fire cold-formed S700 high strength steel CHS and (ii) although the codified design rules resulted in overall relatively accurate cross-section compression resistance predictions, the predicted resistances were conservative for cold-formed S700 high strength steel non-slender CHS after exposure to elevated temperatures of 900 °C and 1100 °C (owing to the high levels of material strain hardening) and those slender CHS (owing to the conservatism of the codified effective width methods).

Cold-formed steel elliptical hollow section stub columns under combined compression and biaxial bending

The paper presents a numerical study on the cross-section behavior of cold-formed (CF) steel elliptical hollow sections (EHS) under combined compression and biaxial bending. In the present study, a finite element (FE) model for CF steel tubular stub columns under combined compression and biaxial bending was first developed, in which the local geometric imperfections, residual stresses and enhanced material behavior were predicted by a rigorous numerical simulation of roll forming. The developed FE model for CF steel tubular stub columns under combined compression and biaxial bending was validated against test results of various tubular sections (including EHS). Then, the validated FE model was employed to carry out a parametric study for CF steel EHS with a large range of steel grades (including both high strength and normal grade steels), section sizes, loading eccentricities and angles. Based on the generated FE data, the traditional design specifications for doubly symmetric cross-sections under combined loading in EN 1993-1-1: 2005 (CEN, 2005) and ANSI/AISC 360-16 (AISC, 2016), as well as the current design equations for hot-finished (HF) normal grade steel EHS suggested by Gardner et al. (2011) under combined loading were evaluated for the design of CF steel EHS under combined loading. New slenderness limits of Class 2 and Class 3 sections, as well as new design equations of cross-section resistances, for CF steel EHS stub columns under combined compression and biaxial bending are proposed.

Equivalent geometrical imperfections for local and global interaction buckling of welded square box section columns

The demand for welded box-sections is increasing in the construction industry due to their easy fabrication and limited stability issues compared to other open sections. The instabilities of welded box-section can be mainly categorized into three types: global buckling, local buckling, and interaction buckling. Nowadays, more attention is paid to interaction buckling, as designers tend to use lighter sections to save on weight and cost. Nevertheless, there is no suitable method to consider the nonlinear effect of interaction between the global and the local buckling, which can be directly incorporated using FEM-based design. Moreover, the currently adopted equivalent geometrical imperfections for flexural buckling in the Eurocode were developed based on geometric nonlinear imperfect analysis (GNIA), and it is inappropriate to be used in geometrically and materially nonlinear analysis (GMNIA). Therefore, the current research investigates the accurate application of the imperfections and imperfection combinations for welded box-sections using the GMNIA technique to determine the accurate buckling resistance by the FEM-based design approach. The investigation starts with developing a numerical model and validating it against test results available in the literature. The validated numerical model is used to conduct a parametric study to find the accurate buckling resistance using previously developed combinations of geometrical imperfections and residual stresses. Then, additional parametric studies are executed to back-calculate the necessary equivalent global and local imperfections and find a suitable rule for combining the global and local imperfections based on the accurate buckling resistance. The proposed equivalent geometric imperfection magnitudes can be applied in the numerical model to aid in the FEM-based design approach.

Experimental investigation of austenitic stainless steel I-section stub columns at elevated temperatures

Due to the absence of fundamental fire test data on the cross-section behaviour of stainless steel columns, an experimental investigation of stainless steel stub columns has been conducted at elevated temperatures to fill this gap. A total of six austenitic stainless steel welded I-section stub columns were isothermally tested at three different elevated temperature levels. Two stub columns were tested at room temperature as the reference group. Complementary material tests and local geometric imperfection measurements were conducted and presented herein. On the basis of the obtained experimental results, the accuracy and reliability of the design methods of the existing European fire design standard (EN 1993-1-2) and the design method of Xing et al. for cross-sectional behaviour of stainless steel columns in fire, which has been incorporated into the upcoming version of EN 1993-1-2, are evaluated. It is concluded that, compared to the existing design rules of EN 1993-1-2, the design method of Xing et al. can provide safe and reliable cross-sectional resistance predictions for the tested austenitic stainless steel I-section stub columns.

Consistency of Imperfections in Steel Eurocodes

The second-order theory was used to analyze the flexural buckling of an individual member simply supported on both member ends, with a uniform double symmetric cross-section under a uniform axial force in an elastic state. The purpose was to show the influence of four different amplitudes of initial imperfections on the shape of the elastic buckling mode ηcrx used in the current EN 1993-1-1 and its new draft, prEN 1993-1-1. Three methods were followed for the analysis: the equivalent member (EM) method, the unique global and local initial (UGLI) imperfection method, and second-order theory with the initial imperfection having an initial local bow imperfection e0. For the relevant quantities, simple formulae were derived and their distribution was drawn on diagrams to represent their graphical interpretations for the first time ever. The formulae and diagrams were valid for the ultimate limit state, which means NEd=Nb,Rd. The influence of four different amplitude values was evaluated: (a) e0,k, proposed for the UGLI imperfection method in the draft EN 1993-1-1; (b) the initial local bow imperfection e0, utilized in the current EN 1993-1-1; (c) the other one employed in its draft; and (d) e0,d, used in the UGLI imperfection method in the current EN 1993-1-1, the current EN 1999-1-1, and the draft prEN 1999-1-1. The main conclusion was that e0,k must not be used in the draft EN 1993-1-1. The UGLI imperfection method was also applied to the column fixed at one end and simply supported at the other end. This example showed the geometrical interpretation of relevant amplitudes. The historical development of the UGLI imperfection method is also presented. All the relations are illustrated in two numerical examples, and the geometrical interpretations of formulae were used in the diagrams. The partial results were verified by the independent computer programs FE-STAB and IQ 100.

Investigations into the local buckling and post-buckling behaviour of fixed-ended hybrid I-section stub columns with slender web

It has been known that thin plate can carry loads considerably more than the buckling loads. This phenomenon is defined as the post-buckling behaviour, which is affected by material properties, geometric dimensions and boundary conditions of the plate. Hybrid I-section is a design concept where flanges are made of high strength steel and web is made of lower steel grade. In order to investigate the effect of slender web on the local buckling and post buckling of hybrid I-section under pure compression, experimental studies of twelve fixed-ended I-section stub columns with slender web were conducted. Tensile coupon tests and initial local geometric imperfection measurement were carried out before stub column tests. Experimental and theoretical methods for determining the critical local buckling load of plate elements were discussed, followed by a post-test finite element analysis to investigate the effects of stub column length and sectional steel combination on the buckling behaviour. Based on the experimental and numerical results, it was observed that for specimens which web plate failed by elastic local buckling, the ultimate test loads are affected by the web strength grade, indicating that the unbuckled portion of slender web plate still provides the post-buckling strength for I-section stub columns even after yielding. By comparing the existing design methods with the numerical ultimate loads, it was found that the Eurocode 3 gives the less scattered predictions than the North American code, Australian code and Chinese code, as well as the existing direct strength method and continuous strength method.

Laboratory tests, numerical simulations and design of press-braked S690 high strength steel channel sections under major-axis combined loading

Testing and numerical modelling have been conducted to investigate the cross-sectional behaviour and resistances of press-braked S690 high strength steel channel sections under combined compression and major-axis bending. The testing programme included initial local geometric imperfection measurements and twenty major-axis eccentric compression (combined loading) tests. The numerical modelling programme included a validation study, where finite element models were developed and validated against test results, and a series of parametric studies, where the developed finite element models were adopted to generate further numerical data over a wide range of cross-section dimensions and loading combinations. The obtained test and numerical data were used to evaluate the existing design interaction curves for press-braked S690 high strength steel channel sections under combined compression and major-axis bending, as specified in the European code, North American specification, and Australian/New Zealand standard. The evaluation results revealed that the codified design interaction curves led to conservative resistance predictions, owing to the linear shapes and inaccurate end points. Improved design interaction curves featuring more efficient shapes and anchored to more accurate end points were then proposed. The proposed design interaction curves were shown to result in more accurate resistance predictions for press-braked S690 high strength steel channel sections under combined compression and major-axis bending than their codified counterparts. The reliability of the proposed design interaction curves was confirmed by means of statistical analyses.

Press-braked ferritic stainless steel slender channel section beam–columns: Tests, simulations and design

This paper reports an experimental and numerical investigation into the buckling behaviour and resistance of press-braked ferritic stainless steel slender channel section beam–columns under combined compression and minor-axis bending moment. An experimental programme was firstly performed, including material coupon tests, initial global and local geometric imperfection measurements and ten beam–column tests. The experimental programme was followed by a numerical modelling programme, where finite element models were developed and validated against the experimental results and then adopted to conduct parametric studies to generate additional numerical data. Based on the obtained test and numerical data, the existing design interaction curves, as set out in the European code, American specification and Australian/New Zealand standard, were evaluated and found to result in conservative and scattered resistance predictions. An improved design interaction curve, anchored to more accurate end points and featuring more appropriate shape, was then developed and shown to offer more accurate and consistent resistance predictions for press-braked ferritic stainless steel slender channel section beam–columns over the codified design interaction curves. Statistical analyses were also performed to confirm the reliability of the new proposal.

Atomic‐Scale Observation of the Local Structure and 1D Quantum Effects in vdW Stacking Mo6Te6 Nanowires

AbstractThe sub‐nanometer‐diameter transitional‐metal chalcogenides (M6X6) molecular wires are ideal 1D quantum systems. The electronic properties of such system are very sensitive to the interface interaction and local imperfection. Here, the atomic structure and local electronic structure of van der Waals (vdW) stacking Mo6Te6 nanowires fabricated by using molecular beam epitaxy are reported. Atomic‐resolution scanning tunneling microscopy measurement shows that the vdW interface distance varies from 0.71 to 1.05 nm when Mo6Te6 wires stacked on graphite, MoTe2, and Mo6Te6 surfaces. Scanning tunneling spectroscopy confirmed the 1D quantum effect of van Hove singularity and Tomonaga–Luttinger liquid behavior at 77.8 K. Single Te vacancies and their effect to the local structure distortion are observed as well. These observations shed light on the local structure and quantum effects of the M6X6 nanowire materials, which may find applications in future electronic devices.

Experimental and numerical investigations into S960 ultra-high strength steel welded I-section stub columns after exposure to elevated temperatures

This paper reports experimental and numerical investigations into S960 ultra-high strength steel welded I-section stub columns after exposure to elevated temperatures. A testing programme was firstly conducted and included heating, soaking and cooling of specimens as well as post-fire tensile coupon tests, initial local geometric imperfection measurements and stub column tests. Following the testing programme, a numerical modelling programme was conducted, where finite element models were developed and validated against the test results and then employed to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions. Given that there are currently no available design standards for high strength steel structures after exposure to elevated temperatures, the relevant ambient temperature design rules, as set out in the European code, American specification and Australian standard, were assessed, using post-fire material properties, for their applicability to S960 ultra-high strength steel welded I-section stub columns after exposure to elevated temperatures. The assessment results revealed that the codified slenderness limits for plate elements in compression were generally accurate when used for cross-section classification of S960 ultra-high strength steel welded I-section stub columns after exposure to elevated temperatures up to 700 °C but conservative for higher temperatures beyond 700 °C. Moreover, the codified design rules were shown to provide accurate and consistent post-fire cross-section compression resistance predictions for S960 ultra-high strength steel welded I-section stub columns after exposure to elevated temperatures up to 700 °C but resulted in conservative predictions for higher temperatures beyond 700 °C.

Generalisation of the effective notch stress concept for the fatigue assessment of arbitrary steel structures

The paper addresses current implementations and potentials for the future in the field of fatigue assessment using local stress concepts. The background of the effective notch stress concept and its numerical application are described in detail. Common codes and regulations containing local stress approaches have been analysed and compared. A useful approach to apply the notch stress concept not only for welded, but also for unwelded steel components and machined or ground welded joints is presented. It has been shown that this approach coincides with fatigue regulations in EN 1993-1-9. Moreover, typical and innovative application areas for the effective stress concept are summarised. These comprise local weld imperfections and even for additive manufactured steel components the concept can be applied. Finally, an approach using the effective notch stress concept with random radii is presented. The relation between fatigue class and applied radius at the weld toe can be expressed by an exponential relationship.

Local stability of laser-welded stainless steel slender I-sections under combined loading

This paper presents a comprehensive experimental and numerical investigation into the local buckling behaviour of laser-welded stainless steel slender I-sections under combined compression and bending moment. A testing programme was firstly carried out, including initial local geometric imperfection measurements and eccentric compression tests on ten laser-welded stainless steel slender I-section stub column specimens. Following the testing programme, a numerical modelling programme was conducted. Finite element models were developed and validated against the test results, and then adopted to perform parametric studies to generate additional numerical data. The obtained test and numerical data were used to evaluate the applicability of the interaction curves in the European and American codes and the continuous strength method to laser-welded stainless steel slender I-sections under combined loading. The evaluation results generally show that the three sets of considered interaction curves offer adequate design accuracy for laser-welded stainless steel slender I-sections under combined compression and major-axis bending moment, but they yield unduly conservative and scattered resistance predictions for laser-welded stainless steel slender I-sections under minor-axis combined loading, owing principally to the conservative minor-axis bending end points. Finally, an improved design interaction curve for the minor-axis combined loading case was developed and shown to yield substantially more accurate and consistent resistance predictions for laser-welded stainless steel slender I-sections under minor-axis combined loading than the three considered design methods. The reliability of the new design interaction curve was confirmed based on a reliability study.

Post-fire behaviour and residual resistance of hot-rolled stainless steel channel sections under major-axis combined loading

This paper presents experimental and numerical investigations into the post-fire local buckling behaviour and residual resistance of hot-rolled stainless steel channel sections under combined compression and major-axis bending. The experimental investigation included heating and cooling of specimens as well as post-fire material testing, initial local geometric imperfection measurements and fourteen eccentric compression tests. A subsequent numerical investigation was performed, where finite element models were developed to simulate the test results and then used to conduct parametric studies to generate additional numerical data over a wide range of cross-section dimensions and loading combinations. Due to the lack of specific design standards for stainless steel structures after exposure to elevated temperatures, the relevant ambient temperature design interaction curves, as set out in the European code and American specification, were evaluated, using post-fire material properties, for their applicability to hot-rolled stainless steel channel sections under major-axis combined loading after exposure to elevated temperatures. The evaluation results revealed that the codified design interaction curves result in conservative post-fire residual resistance predictions, due to the conservative end points and inefficient shapes. Finally, new design interaction curves, with more accurate end points and efficient shapes, were proposed and shown to provide improved design accuracy than the codified design interaction curves for hot-rolled stainless steel channel sections under major-axis combined loading after exposure to elevated temperatures.

Dynamics of size-dependent multilayered shear deformable microbeams with axially functionally graded core and non-uniform mass supported by an intermediate elastic support

The current study investigates the coupled dynamics of a size-dependent third-order shear deformable multilayered microbeam with an axially functionally graded core, a non-uniform mass distribution (mass imperfection) and an intermediate elastic support. A power-law function is used to model the material properties in the longitudinal direction of the core. The equations of motion are obtained by formulating the energies of the system while employing the modified couple stress theory to include miniature size effects within the multilayered microbeam structure. Hamilton's principle and the modal decomposition method are utilised to derive and solve the coupled motion equations. The equations of motion are first verified against a former work on a simplified microbeam system, while the numerical results are validated by comparison to those of a simplified functionally graded in axial direction obtained by finite element macrobeam simulation. It was concluded that increasing either the power term constant of the material grading or the value of the localized mass imperfection (when xm*=0.3) causes the first and second transverse and axial natural frequencies of the three-layered microbeam to decrease, whereas increasing the length-scale parameter causes the natural frequencies of transverse modes to increase, demonstrating the size-dependent effects of the three-layered microbeam.

Effective Stiffness of Thin-Walled Beams with Local Imperfections.

Thin-walled beams are increasingly used in light engineering structures. They are economical, easy to manufacture and to install, and their load capacity-to-weight ratio is very favorable. However, their walls are prone to local buckling, which leads to a reduction of compressive, as well as flexural and torsional, stiffness. Such imperfections can be included in such components in various ways, e.g., by reducing the cross-sectional area. This article presents a method based on the numerical homogenization of a thin-walled beam model that includes geometric imperfections. The homogenization procedure uses a numerical 3D model of a selected piece of a thin-walled beam section, the so-called representative volume element (RVE). Although the model is based on the finite element method (FEM), no formal analysis is performed. The FE model is only used to build the full stiffness matrix of the model with geometric imperfections. The stiffness matrix is then condensed to the outer nodes of the RVE, and the effective stiffness of the cross-section is calculated by using the principle of the elastic equilibrium of the strain energy. It is clear from the conducted analyses that the introduced imperfections cause the decreases in the calculated stiffnesses in comparison to the model without imperfections.

Equivalent local imperfections for FEM-based design of welded box sections

Nowadays, significant research activities are running parallel and focusing on the development of equivalent geometric imperfections applicable for GMNI analysis which provides safe-sided and reliable buckling resistance using FEM-based design. The currently available local buckling-type imperfection given in EN1993-1-5, which is widely used by researchers and designers, has been developed based on the Winter-type buckling curve. Many researchers criticized this buckling curve in the past for overestimating the local buckling resistances of square welded box section columns. Therefore, an improved buckling curve has been developed and calibrated in the past, fitting the experimental and numerical results with adequate safety. To this new buckling curve, the magnitude of the equivalent geometric imperfection has been adjusted by the authors. The current research aim is to validate this new imperfection magnitude and to check if it accurately represents the improved local buckling curve and satisfies the safety requirement of EN1990. Furthermore, the current study aims to provide a constant value imperfection representing the improved buckling curve, which satisfies the mentioned safety requirements for welded square box section columns made of normal strength steel (S235, S355, and S460). The proposed imperfection factor can be used as an alternative to the currently adopted imperfection factor given in the EN 1993-1-5 for GMNI analysis.

Hybrid welded T-section stub columns with Q690 flange and Q355 web: Testing, modelling and design

Comprehensive experimental and numerical investigations on hybrid T-section stub columns under compressive load were performed and are presented in this paper. The hybrid welded T-section stub columns comprise high strength steel Q690 flange and normal strength steel Q355 web. Material property studies were implemented through tensile coupon tests. Residual stress in membrane type was measured and recorded and its impact on structural performance was also assessed. Initial local geometric imperfection measurements were conducted for all the specimens. In conjunction with experimental studies, numerical investigation was performed to generate more test specimens extending the range of cross-section dimensions by which test data pool can be supplemented. The Eurocode of EN 1993-1-1, EN 1993-1-5 and EN 1993-1-12, the North American code of ANSI/AISC 360-16 and the Australian code of AS 4100 together with design approaches of Direct Strength Method and Continuous Strength Method were examined for its applicability for cross-section classification and compression resistance predictions of hybrid T-sections. Overall, the current specified limits were applicable for hybrid welded T-section and strength predictions from design codes were comparatively consistent and reliable. Strength predictions from Direct Strength Method and Continuous Strength Method were relatively appropriate though overly conservative predictions were provided for cross-section with large slenderness. In this study, modifications on the Direct Strength Method and Continuous Strength Method are proposed, which is shown to provide accurate predictions at cross-sectional level in a reliable manner.

Experimental study on additive manufactured 304L stainless steel tubular sections: Material properties and cross-sectional behavior

This paper presents an experimental investigation on the material properties and cross-sectional behavior of 304L stainless steel tubular sections additively manufactured using selective laser melting (SLM). A total of 76 tensile coupons, 76 hardness test specimens, and 25 stub columns were fabricated from 304L stainless steel powders by the SLM technique. Tension coupon tests and hardness tests were conducted to determine the mechanical properties. Residual stresses and local geometric imperfections of the stub columns were measured. The effects of coupon specimen orientations, thicknesses, and annealing conditions on the measured material properties were explored. In addition, the failure modes, ultimate load-carrying capacities and structural responses of the stub columns with four different cross-sections under axial compression were obtained and analyzed to evaluate the cross-sectional behavior. The test results of ultimate strengths were compared with the predictions calculated from the current design methods. The test results showed that the tensile strength of the coupon perpendicular to the building direction was higher than that of the coupon parallel to the building direction. Moreover, the tensile strength of the coupon increased with the increase of the coupon thickness. Considering the cross-sectional behavior, the square hollow section (SHS) and circular hollow section (CHS) had greater cross-sectional axial capacities than the rectangular hollow section (RHS) and elliptical hollow section (EHS), respectively. The introduction of a single stiffener in SHS and CHS reduced the load-carrying capacities to a certain extent.

Stochastic Buckling of Geometrically Imperfect Beams on Elastic Foundation

Abstract Geometrical imperfections are ubiquitous in load-bearing structures, including beams, columns, and shells. Fabrication processes of structural members most often create geometrical imperfections of random size and shape, which lead to non-deterministic load-carrying capacity. This study investigates the statistics of the buckling load of a beam with a random initial imperfection profile that rests on a nonlinear elastic foundation. The geometrical imperfection is represented by a zero-mean Gaussian random field, generated using the Karhunen–Loève expansion. The spatial distribution of the random imperfection is characterized by the probability distribution of the local imperfection magnitude and a spatial autocorrelation function. A finite-difference scheme is used to solve the governing equilibrium equation for a given initial imperfection profile, from which the buckling load is determined. Through a set of Monte Carlo simulations, the mean and variance of the buckling load are determined. The simulations reveal the influence of different length scales on the statistics of the buckling load, including the beam length and the autocorrelation length of the geometrical imperfection. The size effects predicted with the simplified model have implications for reliability-based structural design.

Cross-sectional behaviour of wire arc additively manufactured tubular beams

Wire arc additive manufacturing (WAAM) is a promising metal 3D printing technique in the construction industry for its ability to produce large and complex-shaped elements, with reasonable printing accuracy, time and costs. There is currently, however, a lack of fundamental test data on the structural performance of WAAM elements. To address this, an experimental study into the cross-sectional behaviour of WAAM tubular beams has been conducted and is presented herein. A total of 14 stainless steel square, rectangular and irregular hollow sections, spanning over all cross-section classes of EN 1993-1-4 and AISC 370, were tested in four-point bending. 3D laser scanning, silicone casting and Archimedes’ measurements were employed to collectively determine the as-built geometry and local geometric imperfections of the test specimens, while digital image correlation (DIC) was used to monitor the deformation responses of the specimens during testing. The full moment–curvature histories and key experimental results are presented and discussed. Similar cross-sectional behaviour to that of equivalent, conventionally manufactured sections was observed, with the more slender cross-sections showing increased susceptibility to local buckling. However, owing to the inherent geometric variability of WAAM, the tested 3D printed beams exhibited more variable flexural capacities between the repeat specimens than is generally displayed by conventionally produced stainless steel sections. Finally, the test results were used to assess the applicability of current cross-section design provisions in the European (EN 1993-1-4) and American (AISC 370) structural design specifications, as well as the continuous strength method (CSM), to WAAM stainless steel tubular beams.