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![1.: Selection of buckling curve for a cross-section according to [1]](profile/Nicole-Schillo/publication/321331892/figure/fig7/AS:747564156612608@1555244592660/Selection-of-buckling-curve-for-a-cross-section-according-to-1.png)
![Figure 2.1.: Development of high strength steel [5]](profile/Nicole-Schillo/publication/321331892/figure/fig2/AS:747564156604416@1555244592431/Development-of-high-strength-steel-5_Q320.jpg)
![Figure 2.2.: Classification of imperfection sensitivity, taken from [8][9]](profile/Nicole-Schillo/publication/321331892/figure/fig3/AS:747564156588034@1555244592496/Classification-of-imperfection-sensitivity-taken-from-89_Q320.jpg)
![Figure 2.5.: Derivation of C-factor by Winter [17]](profile/Nicole-Schillo/publication/321331892/figure/fig5/AS:747564156588035@1555244592568/Derivation-of-C-factor-by-Winter-17_Q320.jpg)
Contexts in source publication
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... according to their sensitivity towards these imperfections. E.g for weak-axis bending of an I-section, the corresponding buckling curve is always worse than the curve for strong axis bending. Higher strength steel is generally better classified due to lower residual stress. The allocation of cross-section to imperfection factor α is shown in Fig. 3.1 and the corresponding values in geometrical imperfections of the real structural member, which is applied on the perfect column to achieve the realistic ultimate ...
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... the imperfection factor and analysis method, the corresponding initial curvature and initial imperfection e 0 can be read. These imperfection factors are depending on the buckling curve and analysis method, elastic or plastic. In this thesis, the definition for e 0 was used under the assumption of buckling curve b for welded box sections, see Fig. 3.1 and elastic analysis, resulting in e 0 = 1/250 · Length, see Table 3.1. The value was used in the numerical parametric studies in section 7.8. Table 3.2.: Design value of initial local bow imperfection e 0 /L for members [1] elastic analysis plastic analysis buckling ...
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... resulting widths can be taken from Fig. 3.2. Figure 3.2.: Effective width of internal compressed elements [2] Under uniform stress, [2] assumes for each plate hinged boundary conditions and thus a buckling factor k σ = 4. The slenderness is characterised by: ...
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... critical load of a given structure [67], see section 3.4.3. With the input of Young's modulus (210,000 MPa), the cross-section geometry and the load pattern ψ, a load amplification factor is given as output, defining the critical load but also the buckling factor k. Thereby, k can be described in dependance of the load pattern ψ, as depicted in Fig. 3.3. The figure was derived in this study for squared box sections, evaluating several cases at specific points and interpolating with a polynomial ...
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... graphical interpretation of the safety concept is illustrated in Fig. 3.4. On the left hand side one can see that for a distance of 2 standard deviations (= 1.64σ) to the mean value µ, the 5%-fractile is reached and thus applicable for characteristic values. To reach the design value, equaling the 0.1%-fractile, 3 standard deviations (= 3.09σ, 0.8 · 3.8 · σ, respectively) are ...
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... is assumed that the basic variables on which the failure mode depends in the case investigated are following a normal or log-normal distribution, as indicated in Fig. 3.5 and that they are independent of each other. This is a rather simplified assumption, as e.g. the strength of steel material is known to be thickness dependent. Certain quantities are usually neglected, e.g. the Young's Modulus E which is usually not determined in the material certificates and thus not available for evaluation ...
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... developments led to the inclusion of a "constrained" FSM. By applying smartly constraints, it is possible to separate the failure modes and study them in detail. An example for an open section is shown in Fig. 3.6. The "constrained" solution is not in the pre-settings and has thus to be chosen separately. More details on the FSM and CUFSM can be found e.g. in [63] and [67]. Several other programmes are available, e.g. THIN-WALL [74], which is provided by the Centre for Advanced Structural Engineering, University of ...
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... is characterised by a snap through and/ or snap back and possibly large deflections, see also section 2.3. The snap shown in the respective load-displacement course depends on the ratio of local and global slenderness as well as the absolute slenderness values. Numerically, this phenomenon needs special treatment, as the solution is not distinct. Fig. 3.7 illustrates the issue, where a load-displacement curve is shown exemplified for a complex structure. Applying the Newton-Raphson method, the solution would be not robust as for a load controlled path, the solution would not converge after reaching the ultimate load where the declining branch cannot be depicted. A displacement ...
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... convergence, e.g. the search orthogonal to the last secant or to the first tangent [9]. The modified method implemented in ANSYS was developed by Crisfield [79] who suggested to search on a circle with the centre in the last converged solution, see Fig. 7.4. However, for snapping problems there might be two solutions on the track as indicated in Fig. 3.9 for snap through (left) and snap back (right) courses. In practice, only the forward solution is wanted. Moreover, if the backwards solution does not follow on the same path, e.g. in case of plasticity, the solution is not distinct and might end in not usable results. More details on the arc-length method can be found e.g. in ...
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... can thus be used to determine the point of plastic instability (or ultimate load/strength) occurrence. This implies that with invariable hardening a reduction of uniform elongation with increasing yield strength occurs, see Figure 3.10 [82]. ...
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... presentation of Eq. 3.45 in dependence of the slenderness can be seen in Fig. 3.11. Here, the slenderness is shown versus a It shows that columns around a slenderness of ¯ λ c = 0.81 are more sensitive to imperfections than e.g. very slender ones. Applying similar global imperfections will thus lead to greater impact in this ...
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... an extra imperfection e at the load introduction as shown in Fig. 3.12 will lead in case of short columns to a constant moment (M 0 ) along the column. For slender columns, however, the exact solution would lead to an increase of transversal displacement in the middle of the column and also to an increase of moment at the same place. Evaluating the increase in transversal displacement, the gross ...
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... In case of elastic calculation and buckling curve b, according to [1] l/250 is assumed. The second term includes the intentional load eccentricity e multiplied by a load depending factor using the secant formula to achieve an exact solution. The loss in stiffness in the column due to an additional eccentricity is shown exemplified in Fig. 3.13. The curves show the load-displacement course for different ratios of the eccentricity e to the radius of the core s. For a ratio of e/s = 0, the second term remains naught, and the displacement depends only on the initial bow imperfection and the second order effect. With increasing ratio, up to 1, which means that one face is ...
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... i denotes the radius of gyration. In Fig. 3.14, the impact of eccentricity in terms of bending stress in proportion to the gross stress was evaluated in dependency of the local and global slenderness. For compact cross-section, i.e. ¯ λ p = 0.75, it can be seen that the bending proportion increases exponentially with decreasing ψ. For concentrically loaded columns, the combined ...
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... CS effect. CS already present and could thus be amplified, for the limit case of concentrically loaded columns no loss in stiffness could be achieved, see Fig. 3.14 and 3.15 for ψ = 1. Additionally, due to the secant proportion, the eccentricity applied at the end of the column would also lead to an additional bow imperfection in the middle of the column, which might lead to an extra conservative ...
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... on the other hand an initial bow imperfection e p as presented in Fig. 3.16, no uncontrolled additional terms have to be considered. The increase in moment is for this case directly proportional to the applied bow imperfection. As this approach is simpler to control in its impact on the structural behaviour and is also in compliance with the in EC3 used equivalent imperfections, the method was favoured ...
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... to derive a scaled shape of the intended imperfection figure. This shape can be used in further plastic analysis by displacing the nodes of the structure accordingly. The amplitude of the node displacement can be taken from the informative Annex C of [2], where recommendations are given how to apply equivalent imperfections. The shape is shown in Fig. 3.17, the amplitudes are summarised in Table 3 For global imperfection, a modal analysis can be used to derive the desired half-wave bow of the pinned column. However, the result of a modal analysis is its frequency. For practical use, the frequency has to be scaled first to 1 and multiplied subsequently with e 0 (or another target ...
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... to find the quadratic pattern. The usage in long columns of either the first mode or the mode containing the quadratic pattern for the local imperfection shape showed to be of influence and is discussed in detail in section 7.8.5. The result of the Eigenbuckling-analyis is a scaled, deformed shape. An example for the 1 st mode is shown in Fig. 3.18 for a column with ¯ λ p = 1.0 and ¯ λ c = 0.8. Thus, the shape can be implemented for further analysis simply with a multiplier equalizing the local imperfection ...
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... (local, global, distortional). Using different settings, it can be distinguished between the calculation of global and local failure modes. The so-called signature curve depicts the critical stress in dependence of the length of the structural member, assuming one sinus half-wave as shape of the failing column, as commonly assumed, see also Fig. 3.16. The slenderness referred to is here the non-dimensional slenderness of the gross cross-section ¯ λ c . For a box-column with varying b/t-ratio, and thus including local effects, the resulting curves are depicted in Fig. 3.19. The figure shows in the very stocky With increasing global slenderness the local effects yield to the ...
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... of the structural member, assuming one sinus half-wave as shape of the failing column, as commonly assumed, see also Fig. 3.16. The slenderness referred to is here the non-dimensional slenderness of the gross cross-section ¯ λ c . For a box-column with varying b/t-ratio, and thus including local effects, the resulting curves are depicted in Fig. 3.19. The figure shows in the very stocky With increasing global slenderness the local effects yield to the global ones, merging finally to one curve. This curve represents the Euler-curve and the corresponding flexural failure mode, indicating that global buckling becomes dominant and local effects negligible. The distortional mode for ...
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... The CUFSM-programme allows here for a setting considering general boundary conditions and prescribing the number of half-waves for the failure mode. Evaluated for two different squared hollow sections, SHS120 -which equals ¯ λ p = 0.64 -and SHS250 -equals ¯ λ p = 1.41, the signature curve and the local curves for up to 10 half-waves are shown in Fig. 3.20. As it was pointed out by Taras in [84], the elastic bifurcation critical load is governed by the axial force and is thus independent of bending moments. This is correct for slender columns, where the Euler-curve is reached. In Fig. 3.20, the influence of a load eccentricity was evaluated for a ψ varying between 1 (no eccentricity) ...
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... SHS250 -equals ¯ λ p = 1.41, the signature curve and the local curves for up to 10 half-waves are shown in Fig. 3.20. As it was pointed out by Taras in [84], the elastic bifurcation critical load is governed by the axial force and is thus independent of bending moments. This is correct for slender columns, where the Euler-curve is reached. In Fig. 3.20, the influence of a load eccentricity was evaluated for a ψ varying between 1 (no eccentricity) and 0 (one face not loaded, opposite face fully loaded). The resulting load factor on the y-axis has to be multiplied here with the integral of the applied stress (100 N/mm 2 ) and the stress pattern (ψ) to assess the critical load N crit ...
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... Fig. 3.21 the graphical interpretation of Eq. 3.53 can be seen. Assuming that the local mode would be characterised by one half-wave deflection shape along the column (m = 1), in short columns the local mode is dominant and global of no significance. The sector between 500 and 1800 would be the interaction area, where both critical stress (σ ...
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... columns the local mode is dominant and global of no significance. The sector between 500 and 1800 would be the interaction area, where both critical stress (σ p and σ c ) are of influence until the global mode governs the resulting σ crit , see left hand side of the figure. But following the chain of thought derived earlier and shown already in Fig. 3.20, Fig. 3.21 shows on the right hand side the resulting σ crit when more local half-waves are taken into account. The solution according to Eq. 3.53 is accurate for clearly distinguishable failure modes (global, distortional). However, as the real number of half-waves for the local failure mode cannot be known and is usually assumed ...
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... local mode is dominant and global of no significance. The sector between 500 and 1800 would be the interaction area, where both critical stress (σ p and σ c ) are of influence until the global mode governs the resulting σ crit , see left hand side of the figure. But following the chain of thought derived earlier and shown already in Fig. 3.20, Fig. 3.21 shows on the right hand side the resulting σ crit when more local half-waves are taken into account. The solution according to Eq. 3.53 is accurate for clearly distinguishable failure modes (global, distortional). However, as the real number of half-waves for the local failure mode cannot be known and is usually assumed to be ...
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... a slightly different representation, Fig. 3.22 shows the critical load normalised by the plastic resistance of the gross cross-section. The values are plotted against the non-dimensional global slenderness of the gross cross-section. With increasing global slenderness, the decisive curve for each local slenderness case merges with the Euler-curve, see Eq. 3.52, thus showing the ...
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... graphical interpretation is shown in Fig. 4.3, with the absolute values of imperfections on the left hand side and the ratio to the limits given in [7] on the right hand side. The values are plotted against the local slenderness of the specimens. A moderate scatter and rather constant values independent of the width of the specimens can be observed. Due to larger tolerances for ...
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... the experimental results are compared with the resistance prediction of [2] and including the data available from other researchers, see database summarised in Annex Tables A.2 to A.5, Fig. 5.2 is obtained. The actual slenderness ¯ λ p,act is calculated with the k-value in dependence of the occurring ψ-ratio as shown in Fig. 3.3. It can be seen that the deviation of the experimental results from the theoretical resistance increases with slenderness, while the tendency directs to more and more optimistic results. Another outcome are the generally better performance of the own RWTH experiments. This is traced back to the more precise evaluation possibilities, as ...
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... the sensitivity of the scatter of the basic variables (thickness, width and yield strength) on the resulting coefficient of variation for the model, V rt , was studied, using Eq. 3.29. In Fig. 6.3 the resulting V i -values in dependence of the nominal slenderness ¯ λ p,nom is shown and it can be observed ...
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... all four edges of the plate. However, evaluating the k σ -factor for the decisive plate of a box column in bending using CUFSM, a general formulation to capture the clamping effect of the adjacent faces can be derived. The formula is only depending on the stress distribution in the column, and yields for concentrically loaded cases to 4, see also Fig. ...
Similar publications
The aim of the article is to present the application of finite element method (FEM) programs ABAQUS/Standard [1] and ABAQUS/Explicit [2] and the constitutive models of incompressible isotropic hyperelastic materials [3] in the analysis of local and global buckling of axially compressed shell elements made of elastomers. Three FEM models of tubes wi...
Citations
... Schillo [3] conducted recent research on welded box-section columns to study the interaction buckling behavior of high-strength steel (HSS) columns. A new design formula was proposed that utilizes an equivalent geometrical imperfection to account for the effect of local buckling. ...
... Among these tests, twenty-four were subjected to concentric loading conditions, while the remaining three were subjected to eccentric loading configurations. Schillo [3] conducted a comprehensive investigation involving thirteen buckling tests performed on welded box-sections fabricated from S500 and S960 high-strength steels. The authors proposed a new method based on the EN 1993-1-1 [1] approach to estimate the buckling capacity of welded box-sections. ...
... The method introduced a new modification factor ( f mod ) that depends on the local and global slenderness ratios, as shown in Eq. (1). The modification factor ( f mod ) is determined according to Eqs. (2), (3). The global and local interaction effects were separated, and the design calculations followed the rules of Eurocode. ...
The present study focuses on investigating the interaction behavior of local and global buckling resistance of welded box-section columns by using stochastic analysis. Previous studies mainly investigated this failure mode using experimental or numerical investigations but using deterministic approaches. The current research employs Monte Carlo simulations as a robust numerical tool to estimate the interaction buckling resistance. Stochastic variables are defined, encompassing variabilities in geometrical and material properties, as well as local and global imperfections. To facilitate these simulations, a rigorously validated numerical model is employed, utilizing geometrical and materially nonlinear analysis with imperfections (GMNIA). This advanced modeling approach accounts for the complex nonlinearities inherent in the behavior of welded box-section columns. The characteristic resistance derived from the Monte Carlo simulation is compared to 1. test results, 2. analytical buckling resistance according to the Eurocode design approach, and 3. previously proposed deterministic approaches. Within the research program, an improved generalized design formula is developed to estimate the buckling resistance for pure local, global, and interaction buckling modes. The new design equation is compatible with the design rules of the Eurocode and enhances the ease of use of the standard regulations.
... However, the normative rules of composite columns according to Eurocode 4 [1] are a central problem, as they only consider steels up to S460, which represents the state of the art from the 1980s to the 1990s. Investigations of high-strength members have only recently been undertaken, but they are limited to either the examination of pure steel columns [2] [3] or stubby high-strength composite columns without stability problems [4] [5]. Round hollow sections with embedded solid core section have only been examined for steel grades up to S460 [6] [7]. ...
Due to price developments, steel composite columns have lost significant market shares to prefabricated reinforced concrete columns in recent years. Using high‐strength steel (HSS) in composite columns may offer a way of reviving the market for these kinds of columns. There are different ways of using HSS for composite columns, however, many are associated with the use of welds. Welding of HSS can lead to cold and hot cracks, while also causing high residual stresses which can lead to a decrease of the load bearing capacity. Hollow section composite columns with embedded solid core cross‐sections and using HSS may offer a way to solve this problem.
Round hollow sections with embedded solid core as a composite column have so far only been investigated for steel grades up to S460. Within the scope of German FOSTA research project P1501, a concept for a test setup is derived to investigate hollow sections with embedded solid core as a composite column made of HSS. The experimental results will be used as the basis for further numerical studies, which will be discussed within the scope of this paper. Based on these models, parametric studies will be conducted in the future to validate design concepts.
... In addition to column tests under ambient and fire conditions, small scale tests are necessary to investigate various influencing factors and to create the basis for new and easy to use design and construction principles that allow efficient applica tion. [6,7] oder gedrungener höchstfester Verbundstützen ohne Stabilitätsgefährdung [8][9][10]. Ausbetonierte Rundhohlprofil-Verbundstützen mit massivem Kern wurden bisher nur für Stahlgüten bis S460 in [11,12] untersucht. ...
In den letzten Jahren werden Stahlverbundstützen aus normalfesten Stählen in der Baupraxis immer seltener eingesetzt. Grund für den Marktverlust ist u. a. die Preis‐ und Technologieentwicklung der konkurrierenden Stahlbeton‐Fertigteilbauweise. So wird erst durch den Einsatz hochfester Baustähle die Stahlbauweise für den Stützenmarkt im Hochbau wieder relevant. In Deutschland allerdings stehen der Verwendung höchstfester Baustähle derzeit große Hindernisse in Form von normativen Regelungen entgegen, die die Anwendung in Stahlverbundstützen praktisch ausschließen. Allerdings haben Hohlprofil‐Verbundstützen mit eingestellten Vollkernquerschnitten unter Verwendung von höchstfesten Stählen ohne Schweißverbindungen das Potenzial, Marktanteile im Hochbau zurückzugewinnen. Im Rahmen eines von der AiF (Arbeitsgemeinschaft industrieller Forschungsvereinigungen) geförderten Forschungsprojekts wird diese Thematik experimentell und theoretisch untersucht. Der vorliegende Aufsatz soll das Konzept solcher neuartigen Verbundstützen mit hochfesten Stählen aufzeigen und erste Einsichten in die experimentellen Forschungsergebnisse geben. Neben Stützenversuchen im Kalt‐ und Heißfall werden Kleinteilversuche durchgeführt, um verschiedene Einflussfaktoren zu untersuchen und die Grundlagen für neue und zugleich einfache Entwurfs‐ und Konstruktionsprinzipien zu schaffen.
... Schillo et al. [8] performed thirteen tests on square welded box section columns with a high b/t ratio of S500 and S960 steel grades having different global slenderness. The validated numerical model was used to perform a parametric study to determine the reduction factors to design box section columns undergoing interaction of both global and local buckling. ...
The construction industry is witnessing an increased utilization of steel elements due to their effectiveness and durability, with the ability to fabricate lightweight sections having high bearing capacity. Welded box‐section is one of those elements that gain more attention as it is easy to fabricate and has limited stability issues. Buckling is considered one of the major issues that hinder the ability of the steel box‐section to attain its full capacity. The buckling problem for this type of column can be classified into three major types: overall buckling, local buckling, and interacting buckling. Different research activities studied the overall and the local buckling stabilities of box‐section columns, while only a limited number of researchers studied the interaction stability that compromises both types of buckling. Additionally, the available design standards do not account for the nonlinear nature of combining these two buckling types and only use a simple approach to account for their combined effect, leading to a considerably conservative estimation of the buckling capacity. The current research utilizes a FEM‐based design approach to account for the combined nonlinear effect through the utilization of geometrical and material nonlinear analysis (GMNIA) by the creation of a numerical model of square welded box‐section columns, applying a nonlinear material model, an improved combination of local and global imperfections developed by the authors during previous research as well as the residual stresses. The numerical model is validated against experimental tests available in the literature. Then, it is used to carry out a numerical parametric study with a significant number of tests to build a numerical database that can be used to develop an enhanced design approach for the interactive buckling resistance of box‐sections columns under pure compression. The new approach is based on a reliable and accurate numerical model considering an improved combination of the local and global geometric imperfections and residual stresses, which gives more accurate results than the previous model published in international literature. The paper also describes the way of the imperfection combinations to be applied. The new design approach also considers the interaction of the global and local reduction factors depending on the global and local slenderness ratio leading to accurate buckling resistance.
... The samples were taken from two different research programs. The first set consists of five samples from Bridge's research program [9], and the remaining samples were taken from Schillo's experimental program [21]. The first set is 282 MPa steel with plate slenderness ranging from 0.68 to 2.12. ...
Determining the plate or the local buckling resistance is highly important in designing steel buildings and bridges. The EN 1993-1-5Annex C provides a FEM-based design approach to calculate the buckling resistance based on numerical design calculations (geometrical and material nonlinear analysis - GMNIA). Within the GMNIA analysis-based stability design, the application of the imperfections has a special role. Thus, the applicability of the EN 1993-1-5 based buckling curve (Winter curve) has been questioned for pure compression, and previous investigations showed the buckling curve of EN 1993-1-5 Annex B is more appropriate for the design of slender box-section columns subjected to pure compression, the magnitude of the equivalent geometric imperfection to be applied in numerical models for local buckling is also questioned and investigated by the authors within the current paper. The aim of the current research program is to investigate the necessary equivalent geometric imperfections to be applied in FEM-based design calculations using GMNIA calculations. A numerical parametric study is executed to investigate the imperfection sensitivity of box-section columns having different local slenderness. The necessary imperfection magnitudes are determined to each analyzed geometry leading to the buckling resistance predicted by the standardized buckling curves. Based on the numerical parametric study, a proposal for the applicable equivalent geometric imperfection magnitude is developed, which conforms to the plate buckling curves of the EN 1993-1-5 and giving an improvement proposal to the local buckling imperfection magnitudes of the prEN 1993-1-14, which is currently under development.
... The reliability of the EC3 and proposed design rules for S690 high strength steel slender welded I-section columns failing by local-flexural interactive buckling was evaluated in accordance with the requirements and procedures given in EN 1990 [39]. In the present reliability analysis, the material over-strength ratio for high strength steels was taken as 1.1, with the COV of 0.033 [40], and the COV of the geometric dimensions of high strength steel members was taken as 0.050 [40]. The key statistical parameters calculated according to EN 1990 [39] are summarised in Table 7, where kd,n is the design (ultimate limit state) fractile factor, b is the mean ratio of test (or numerical) to design model resistances, Vδ is the COV of the test (or numerical) resistances relative to the resistance model, Vr is the combined COV incorporating all the variable uncertainties and γM1 is the (required) partial safety factor. ...
... The reliability of the EC3 and proposed design rules for S690 high strength steel slender welded I-section columns failing by local-flexural interactive buckling was evaluated in accordance with the requirements and procedures given in EN 1990 [39]. In the present reliability analysis, the material over-strength ratio for high strength steels was taken as 1.1, with the COV of 0.033 [40], and the COV of the geometric dimensions of high strength steel members was taken as 0.050 [40]. The key statistical parameters calculated according to EN 1990 [39] are summarised in Table 7, where kd,n is the design (ultimate limit state) fractile factor, b is the mean ratio of test (or numerical) to design model resistances, Vδ is the COV of the test (or numerical) resistances relative to the resistance model, Vr is the combined COV incorporating all the variable uncertainties and γM1 is the (required) partial safety factor. ...
... As can be seen from Table 7, the resulting (required) partial safety factors for both the EC3 and proposed design rules are slightly greater than the current limit value of 1.0 specified in EN 1993-1-12 [4]. Previous studies [40][41][42] suggested that a higher target value of γM1=1.1 be adopted for high strength steel structures, which is supported by the results of the present reliability analysis. ...
The present paper reports a thorough experimental and numerical investigation into the local–flexural interactive buckling behaviour and resistances of S690 high strength steel slender welded I-section columns. A testing programme, adopting two S690 high strength steel slender welded I-sections, was firstly conducted and included initial geometric imperfection measurements and ten pin-ended column tests. The testing programme was accompanied by a numerical modelling programme, 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 and member effective lengths. On the basis of the test and numerical results, the interaction of local and flexural buckling of S690 high strength steel slender welded I-section columns was carefully analysed. Regarding the design of S690 high strength steel slender welded I-section columns failing by local–flexural interactive buckling, the existing European code, Australian standard and American specification adopt the same design concept of using effective width method to consider local buckling and buckling curves to consider flexural buckling. Evaluation of the three existing design standards generally indicated that both the European code and Australian standard yield conservative interactive buckling resistance predictions for S690 high strength steel slender welded I-section columns, owing mainly to the adoption of conservative design flexural buckling curves, while the American specification results in an overall good level of design accuracy, but with many over-predicted resistances. An improved approach was then developed through the use of a new design flexural buckling curve combined with the effective width method given in the European code, and shown to yield accurate, consistent and safe interactive buckling resistance predictions for S690 high strength steel slender welded I-section columns.
... The results indicated that the effect of buckling on the bearing capacity cannot be ignored, and an equation for estimating the ultimate load of welded thin-walled members under axial compression was proposed. Schillo [18] conducted experiments on welded boxshaped columns made of S500 and S960 materials, and proposed a ''generalised slenderness approach'' for considering the local-overall interactive buckling. Usami [19] performed a test of 690 MPa welded-box members under axial compression and proposed an equation for predicting their bearing capacities based on the effective section method. ...
... Eurocode 3 [3] and ANSI/AISC 360-10 [45]) for estimating the ultimate load of welded H-section members fabricated from 800 MPa HSS, the experimental results obtained in this study are utilised (Table 5). Here, existing test data for HSS columns, such as that reported by Schillo [18], Su et al. [46], and Rasmusse and Hancock [47], are also employed. The value of a in Eq. (13) is 0.13, as the 0 curve in Eurocode 3 [3] is more accurate for estimating the ultimate load. ...
... The limits of the width-to-thickness ratio for flanges and webs are established based on Shen's model [50], as shown in Eqs. (18) and (19). ...
In this study, three different types of columns (i.e. columns with a low width-to-thickness ratio of the plates,
columns with a high height-to-thickness ratio of the web, and columns with a high width-to-thickness ratio
of the flange) are designed to investigate the buckling behaviour of welded H-section columns fabricated
from 800 MPa high-strength steel (HSS). Different buckling behaviours are established, including the load–
axial displacement curves, relationships between the local out-of-plane displacement and overall lateral
displacement, and ultimate loads of the columns. Current specifications, such as ANSI/AISC and Eurocode
3, are evaluated using the experimental results of this study. It is concluded that ANSI/AISC and Eurocode 3
slightly underestimate the ultimate load of 800 MPa HSS welded H-section members under axial compression.
Numerical analyses are performed to estimate the buckling behaviours of 800 MPa HSS welded H-section
members under axial compression, and the model is verified using the experimental results in this study. The
effects of several parameters (i.e. the slenderness ratio, width-to-thickness ratio of the flange, and height-tothickness
ratio of the web) on the buckling behaviour are investigated. Finite element analyses are carried
out for 94 different models, and a more accurate model for estimating the ultimate load of welded H-section
members fabricated from 800 MPa HSS is developed. Existing experimental data for HSS columns are collected,
and reliability analyses are performed for ANSI/AISC, Eurocode 3, and the proposed model.
... Refs. [8] or [22]. In the actual research, the buckling curve given in Annex B of EN 1993-1-5 is applied as an alternative to the Winter-curve. ...
... This curve, given by Eqs. (10)(11), is similar to the alternative curves of [8] or [22], but with two advantages. One advantage is that it is already included in EN 1993-1-5. ...
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.
... First, in 2014, Shi et al. [16] concluded that results given by available design methods (including the design method given by EN1993- [1][2][3][4][5] overestimated the ultimate stress of local buckling. In 2017, Schillo [17] collected several experimental test results on welded box-sections made from mild and high strength steel ( [20][21][22][23][24][25][26], cited in [17][18][19]) and found that the local buckling resistance provided by EN1993-1-5 [13] for this type of cross-section shape was too optimistic. At the same time, based on her own experimental campaign (reported in [27][28][29]) consisting of class 4 welded box-sections, she recommended higher values for the partial factor or, alternatively, a new exponential type expression obtained from curve-fitting to compute the reduction factor due to local buckling. ...
... First, in 2014, Shi et al. [16] concluded that results given by available design methods (including the design method given by EN1993- [1][2][3][4][5] overestimated the ultimate stress of local buckling. In 2017, Schillo [17] collected several experimental test results on welded box-sections made from mild and high strength steel ( [20][21][22][23][24][25][26], cited in [17][18][19]) and found that the local buckling resistance provided by EN1993-1-5 [13] for this type of cross-section shape was too optimistic. At the same time, based on her own experimental campaign (reported in [27][28][29]) consisting of class 4 welded box-sections, she recommended higher values for the partial factor or, alternatively, a new exponential type expression obtained from curve-fitting to compute the reduction factor due to local buckling. ...
... Concerning the amplitude, 3 possibilities were taken into account: (i) the amplitude is taken as a deterministic variable with a value of h w /200 (local panel amplitude as recommended by Annex C of EN1993-1-5), (ii) the amplitude is taken as a deterministic variable with a value of h w /500 where h w is the inner depth between flanges (see Fig. 3), and (iii) the amplitude is taken as a random variable following a Weibull distribution fitted to measurements which are documented in the literature [17,[40][41][42][43][44][45][46][47]. In total, 2024 values of amplitudes were collected (normalized to the width of the plate, w 0, max /b; Fig. 1 is the corresponding bar chart). ...
Although the stochastic nature of several parameters, the application of the methodology given in EN1993-1-5:2006 for the determination of the resistance of class 4 cross-sections under direct stresses leads to the use of the effective area where each plate is individually assessed by a semi-empirical approach proposed by Winter in 1947. Once the level of reliability of this approach is not adequate in light of the rules given in EN1990, this paper aims at finding the actual safety level of the methodology given in EN1993-1-5. In order to achieved this, Monte Carlo simulations with a Latin Hypercube sampling strategy is performed in selected cross-sections under pure compression and pure bending with varying slenderness and aspect ratio of the web plate. All parameters are stochastically modelled, and each generated element (I- and H-section stubs) is numerically computed using a general-purpose finite element software. The final results are actual partial factors values and width reduction factors for each cross-section.
... However, as far as the authors are aware, all these works are based on a deterministic approach. The considerable amount of existing experimental results, as well as the statistical data of the material and geometric properties [29], make it possible to evaluate the current design methods with a probabilistic approach. ...
... However, the current resistance function, based on Eqs. (5)-(7), Table 3: Coefficient of variation (COV) for geometric and material property parameters based on the data presented in [29]. ...
The second part of the study on the local-global mode interaction in thin-walled inelastic rectangular hollow section struts focuses on design guidance. Based on the validated finite element (FE) model from the companion paper, a framework for fully automating FE model generation, submission and post-processing for geometric and material nonlinear analysis with imperfections is first presented. The ultimate load data for specimens with different cross-section aspect ratios, cross-sectional slenderness, global slenderness and welding options are generated. The current design rules for thin-walled welded RHS struts are assessed using the numerical results and existing experimental results from the literature by means of structural reliability analysis in accordance with the methodology presented in Annex D of Eurocode EN1990. A modified Direct Strength Method (DSM) relationship is then proposed and it is demonstrated to provide superior ultimate load predictions than the current guidelines.
