Slenderness Values Research Articles

Effect of web holes on web crippling capacity of rectangular hollow steel sections under two flange loadings

This paper presents experimental and numerical investigations on web crippling behavior of hot rolled rectangular hollow section (RHS) with web holes. A total of 20 rectangular hollow sections, subjected to interior-two-flange (ITF) and end-two-flange (ETF) loading conditions undergoing web crippling, were experimentally tested. The experimental program was designed to obtain web crippling of specimen having slenderness (h/t) value of 21.32, by varying size and offset distance of web holes under two flange loading conditions. Finite element models of experimentally tested beams were developed, and results of finite element analysis showed good agreement with experimental results. A parametric study was then conducted using finite element analysis on different cross section sizes, to demonstrate the effect of size and position of web holes on web crippling capacity of rectangular hollow sections. It was demonstrated that ratio of diameter of web hole to the depth of flat portion of web (a/h) and ratio of offset distance of web hole to the flat portion of web (x/h) are the primary parameters affecting the web crippling strength. Design recommendations in the form of reduction factors for both loading conditions are proposed, that are conservative to both experimental and finite element results. To assess the reliability level of design recommendations, reliability analyses were undertaken.

Behaviour, finite element modelling and design of flanged cruciform section steel columns

A study into the mechanical behaviour and design of flanged cruciform section steel members subjected to axial compression is presented herein. The mechanical behaviour of flanged cruciform section columns is first described, with particular emphasis on the newly developed approach for determining the elastic local buckling load for full flanged cruciform cross-sections. Existing experimental data on flanged cruciform section steel columns collected from the literature are then employed to validate numerical models developed within the finite element package ABAQUS. A comprehensive parametric study is subsequently conducted that encompasses a broad spectrum of cross-sectional geometries and global slenderness values. The mechanical behaviour and ultimate resistance of flanged cruciform section columns are shown to be dependent on not only the global slenderness, but also on the ratio of the elastic torsional to flexural buckling loads. The existing experimental data alongside the numerical parametric study results are employed to evaluate the resistance predictions provided in the current Eurocode 3 design codes, revealing a high degree of conservatism. Finally, a new design approach for flanged cruciform section columns, suitable for incorporation into future revisions of Eurocode 3, is proposed which provides significantly improved accuracy and consistency in resistance predictions compared with the current provisions. A reliability analysis of the proposed design approach is conducted in accordance with the EN 1990 procedure, resulting in a recommended partial safety factor γM1=1.0.

Vertical spanning wall elastically restrained at the top: validation and parametric dynamic analysis

In unreinforced masonry structures, among the most dangerous events that can occur during earthquakes are the out-of-plane mechanisms. This type of response significantly changes if the wall is restrained by a horizontal element. The collapse, in this case, could take place for slipping/failure of the diaphragm connection or for overturning of the wall, following the formation of a crack at an intermediate height between the base and the top. A specific analytical model is used to capture the complex dynamic behavior of the wall, formed by two stacked rigid bodies (free to rock) with the top one connected to a flexible diaphragm. The model is calibrated using experimental data available in the literature and it is then used to carry out a dynamic parametric analysis. The variation range of relevant parameters refers to the building features surveyed in Emilia-Romagna region, Italy, and their effect on the global response of the system is investigated. Further, the influence of ground motion is considered, using different ground accelerations. The results of the analysis highlight that, for the considered area and return period, the maximum rotations of the system are significant only for large slenderness values. Further, the investigation shows that the diaphragm plays a crucial role in the dynamic response of the system. The stiffness of the diaphragm can significantly reduce the rotations and consequently the risk of overturning. Additionally, the study on the effect of the wall size pointed out how a top spring causes a reverse scale effect.

Fabrication and characterization of flexible natural cellulosic fiber composites through collaborative modification strategy of sodium hydroxide and γ-Aminopropyl triethoxysilane

The primary purpose of this work is to study the fabrication of a flexible natural cellulosic fiber composite. In this respect, natural cellulosic fiber was obtained by modified poplar wood fiber through sodium hydroxide (NaOH) and γ-Aminopropyl Triethoxysilan. Then, the composites were fabricated by hot-pressing the modified wood fibers and polyurethane following characterization. Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), and scanning electron microscope (SEM) observation results confirmed that some of the hemicellulose and lignin were removed from wood fibers after NaOH modification and successfully grafted with alkoxy structures after KH550 modification. NaOH&KH550 modification improved the interfacial compatibility between poplar wood fibers and polyurethane. The flexibility of the composites was improved (the slenderness value was reduced by 113 %), allowing flexible deformations such as bending, twisting, and knotting. In addition, thermal stability, tensile strength (increased by 105 %), elongation at the break (increased by 125 %), and water resistance were increased. This flexible natural cellulosic fiber composite is expected to be applied in the veneering of curved materials and special-shaped structure furniture, providing a theoretical basis for improving the added value of wood-based composites.

Load-Settlement Analysis of Axially Loaded Piles in Unsaturated Soils

Unsaturated soil covers a significant part of the world, and studying the behavior of deep foundations in this medium is an important step in increasing accuracy and economic efficiency in geotechnical studies. This paper presents an analytical solution to investigate the load-carrying characteristics of single piles embedded in unsaturated soils, accounting for the effect of groundwater level on the pile’s response. For this purpose, relationships for shear modulus and Poisson’s ratio for unsaturated soils were collected from the literature to consider their effects as key parameters on pile performance. A parametric study was conducted to evaluate the effect of soil moisture content on the behavior of the pile-soil system for different soil types, and the effect of pile slenderness on its load-settlement behavior was studied for varying soil moisture contents. The results indicate that the pile stiffness increases as the soil suction increases while below a critical slenderness value, hence increasing the pile load capacity. However, this improvement occurs within a limited range of soil suction that is narrower for coarse-grained soils. The pile settlement corresponding to soil failure was also evaluated by modifying the existing solutions for unsaturated soils. The developed solutions were verified against the predictions of published solutions as well as the results of finite element analysis and pile load tests. It was found that the system stiffness decreases by 50% when the water table rises from the pile toe level to the ground surface in the studied soil.

Lateral‐torsional buckling experiments of built‐up section CFS beams

AbstractThis paper investigates the lateral‐torsional buckling of built‐up cold‐formed steel beams featuring two or three component C‐ or sigma‐sections arranged to have a closed loop. Several thicknesses of each cross‐section with nominal yield stress values of 450 MPa and 550 MPa were tested to obtain lateral buckling strength data for a range of cross‐section slenderness values. Complementary reference tests were conducted on the same built‐up sections braced laterally to obtain the in‐plane section capacities, precluding the effect of lateral‐torsional buckling. Coupon tests were also conducted to determine the mechanical properties of the steel material. The test rig featured a dual‐actuator set‐up, with one actuator (applying vertical load) mounted on a trolley that was moved horizontally by the second actuator in response to the signal from a transducer measuring the lateral buckling displacement at the mid‐length of the beam, thus ensuring vertical loading throughout the experiments. The rig also featured specialized end bearings allowing free flexural rotations and warping, while restraining lateral displacements and twist rotations. The paper describes the test rig and the results of the in‐plane and lateral‐torsional buckling experiments. Particular attention is paid to the use of closed parts to enhance the torsional rigidity of the built‐up sections and thereby their lateral‐torsional buckling capacity.

Strain‐hardening dependent cross‐sectional slenderness limits for the elastic resistance of steel beams

AbstractIt is important that cross‐sections are correctly classified, as this determines their utilisation. The focus of this paper lies on the analysis of the transition point between cross‐sectional classes 3 and 4 for I‐shaped and hollow cross‐sections. In particular, it studies how various degrees of strain hardening and ratios between ultimate and yield strength influence this transition point, which defines whether the elastic moment resistance of a section can be exploited. Numerical simulations with geometrically and materially nonlinear analysis with imperfections (GMNIA) were carried out. The results of the numerical simulations were analysed and consequently, limit slenderness values could be determined and correlations to the hardening behaviour could be found and integrated into corresponding formulas.

Strength enhancement and stub-column behavior of cold-formed stainless steel elliptical hollow sections

This paper aims to investigate the strength enhancement, local geometric imperfections, and stub-column behavior of cold-formed (CF) stainless steel elliptical hollow sections (EHS) by using finite element methods. In the present study, an advanced numerical approach was used to conduct a comprehensive parametric study for CF stainless steel EHS with a wide range of cross-section dimensions and slenderness values as well as different stainless steel alloys. By analyzing the generated numerical data from the parametric study, the effects of cold-forming and material parameters on the strength enhancement were examined. Predictive models of the strength enhancement as well as the local geometric imperfections for CF stainless steel EHS are proposed. The slenderness limits for CF stainless steel circular hollow sections (CHS) and CF steel EHS in the existing design methods were assessed for CF stainless steel EHS. New slenderness limits are proposed for CF stainless steel EHS. In addition, the existing equivalent diameter method, the Continuous Strength Method (CSM) and the Direct Strength Method (DSM) were evaluated for the design of CF stainless steel EHS. Modifications on these existing design methods are proposed for CF stainless steel EHS, which can improve their accuracy.

Testing, FE modelling and design of pin-ended stainless steel equal-leg angle section columns and beam–columns

The behaviour and design of pin-ended stainless steel equal-leg angle section members under compression and compression plus minor-axis bending are investigated herein. The studied members are cylindrically pinned about the minor axis. An experimental investigation, including material testing, initial geometric imperfection measurements and physical tests on hot-rolled stainless steel equal-leg angle section members is first presented. Numerical models are developed and validated against the new experimental data. A numerical parametric study is then presented considering both hot-rolled and cold-formed stainless steel angle section columns alongside beam–columns with a wide range of slenderness values. Finally, new design proposals for pin-ended stainless steel equal-leg angle section members under compression and combined compression and minor-axis bending are developed and verified against the results of existing physical experiments, as well as the newly-generated test and numerical results. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the EN 1990 procedure.

Strain-hardening dependent cross-sectional slenderness limits for the plastic resistance of steel beams

Cross-sectional classification forms a relevant preliminary condition for the selection of the appropriate resistance models in the design of structural steel elements. It is thus important that cross-sections are correctly classified, as this determines their utilisation. The focus of this paper lies on the analysis of the transition point between cross-sectional classes 2 (compact) and 3 (elastic sections) for typical steel cross-section shapes. In particular, it studies how various degrees of strain hardening and ratios between ultimate and yield strength influence this transition point, which defines whether the plastic moment resistance of a section can be exploited. Based on numerical simulations on short beams, calibrated against full-scale tests, three independent cases were investigated i) outstand flanges and similar elements supported along one longitudinal edge loaded in pure compression, ii) webs and other internal elements supported along two edges, loaded in pure bending and iii) elements supported along two edges, loaded in pure compression. The first eigenform retrieved from the lateral buckling analysis (LBA) was used as initial imperfection for the geometric and material non-linear analysis (GMNIA). The results of the numerical simulations were analysed: in particular, the maximum achieved moment was compared with the theoretical plastic moment resistance. From these analyses, generalised observations could be made on whether the plastic moment resistance could be reached or not and consequently whether the cross-section should be assigned to class 2 or 3. Consequently, limit slenderness values could be determined and correlations to the hardening behaviour could be found and integrated into corresponding formulas.

Experimental and numerical investigation of pultruded GFRP circular hollow tubular columns under concentric and eccentric loading

This paper presents an experimental investigation of pultruded glass fibre reinforced polymer (GFRP) circular hollow section (CHS) columns under concentric and eccentric compression. The member slenderness of the selected columns was in the short, intermediate, and long range, and two different eccentricities were chosen within the column's cross section. Predominant failure modes observed in the experiment include longitudinal splitting and localized delamination buckling. The load-carrying capacities of the concentric column under different slenderness values were quantified and compared with existing design rules. Under eccentric loading, the ultimate loads of the columns decrease with increasing eccentricity and slenderness, and the load–strain behaviour displayed non–linear characteristics due to geometric non-linearity. Failure modes of all the tested columns were well predicted by the FE models, and it was found that splitting material failure was due to hoop matrix tensile rupture.

Versatile hysteretic model of reinforcing steel bars with buckling

The buckling of reinforcing steel should be considered in the design of reinforced concrete elements subjected to compression since it can influence the load-carrying capacity and energy dissipation under cyclic loading detrimentally. To capture the influence of buckling in the stress–strain behavior of steel, some models have incorporated geometric and material nonlinearities in the formulation. Others have provided phenomenological curves calibrated with experimental data. Using a lumped plasticity model and sectional analysis based on a fiber model, nonlinearities can be incorporated into the problem. However, solving the equilibrium and compatibility in the nonlinear problem involves complex and inefficient computational methods. In this work, iterations to reach moment equilibrium are avoided by utilizing an expression that relates the average axial strain to the curvature. Cyclic experimental tests collected from the literature, using slenderness values from 6 to 15 and strain range up to 10%, verify the model’s accuracy, resulting in prediction errors of the energy enclosed by the hysteretic curves of less than 4% in all cases compared to the iterative model. The results were also consistent with the experimental test results.

Experimental study on stainless steel tubular members under cyclic loading

Stainless steel is an excellent construction material due to its high ductility, strain hardening, durability and aesthetic characteristics. To date, most studies on stainless steel have been devoted to understanding its mechanical properties and the behaviour of individual structural members and simple structures under monotonic loading. As a result, next versions of stainless steel codes, traditionally based on carbon steel codes, will enable efficient structural designs under static forces. However, advances related to the performance of stainless steel structural members under cyclic forces are still scarce, and there are no specific rules for the seismic design of stainless steel structures in Eurocode 8 in spite of the notable differences between this material and other steels. On this basis, an experimental programme on austenitic stainless steel hollow section elements subjected to cyclic loading has been recently conducted. A total of nine specimens with different local and member slenderness values were tested under cyclic bending around their major axis following a cantilever loading scheme. This paper describes the experimental set-up adopted for the tests, including the loading scheme and instrumentation, and discusses the load–displacement, moment–rotation, degradation of stiffness and energy dissipation values obtained in detail. In addition to providing fundamental information on the response of stainless steel members under cyclic loading, the description of the set-up reported in this paper will assist researchers in planning similar experimental programmes, while the results will serve as a reference to validate numerical analyses of stainless steel members and frames subjected to cyclic loading.

Slenderness‐dependent Equivalent Imperfections in Plate Buckling

AbstractIn this study, various approaches to and combinations of imperfections are investigated using geometrically and materially non‐linear analysis with imperfections (GMNIA) of unstiffened buckling plates. These imperfections have a decisive influence on load‐bearing behaviour during stability failure (plate buckling). When applying GMNIA, the user can opt for either equivalent geometric imperfections or a combination of geometrical and structural imperfections as given in EN 1993‐1‐5 Annex C. Here, the exact influence of the individual imperfections and their combinations on the load‐bearing behaviour is not conclusively clarified. Furthermore, EN 1993‐1‐5 Annex C does not contain a recommendation for a suitable residual stress model. The aim of this investigation is to compare the ultimate load due to compressive stress using different approaches to imperfections. Six different combinations are analysed using GMNIA. The results make it clear that a variety of ultimate loads lie above the Winter curve for larger related slenderness values, ̄λp, and thus lead to non‐conservative ultimate loads. In addition, initial recommendations for the required size of the imperfection are given for the application of equivalent geometric imperfections depending upon the related slenderness, ̄λp. Applying adjusted equivalent geometric imperfections to square plates under compressive stress achieves very good agreement with the Winter curve in the range relevant to the construction industry.

Elastic–plastic buckling behaviour of beetle elytron plate with simple, fixed and flexible core supports

Beetle elytron plate (BEP) is a new type of sandwich structure inspired by the internal architecture of beetle elytra and characterised by trabeculae in the core to achieve higher load bearing capacity compared to the basic conventional honeycomb sandwich plate. This paper investigates elastic–plastic buckling behaviour of the compressive skin of BEP with flexible core. The development is based on adapting existing solutions for relevant structures through the following three transformation steps: (1) obtaining the elastic–plastic buckling stresses of BEP with simple and fixed supports by extending respective solutions for conventional sandwich plate; (2) modifying the elastic buckling stress solution for conventional sandwich plate with flexible core to BEP with flexible core through replacement of deformation shape functions; (3) assuming that the interpolation function between simple and fixed supports for BEP with flexible core for elastic buckling stresses is applicable to elastic–plastic buckling stresses. Despite complexity of the problem and simplification in the above mentioned transformation steps, the proposed analytical method is shown to be quite accurate by comparison against numerical simulation results using a validated ABAQUS model for a variety of BEP geometries (such as trabecular diameter, slenderness values of the compressive skin and the core layer) and different material properties as represented by Ramberg–Osgood model covering the entire spectrum of elastic buckling to plastic behaviour, with the maximum difference between the proposed analytical model and numerical simulation results being 7%.

Experimental investigations on material properties and stub column behaviour of high strength steel irregular hexagonal hollow sections

Comprehensive experimental investigations into the material properties and stub column behaviour of cold-formed high strength steel (HSS) irregular hexagonal hollow sections (IHexHS) are presented in this paper. Apart from the tensile coupons taken from the parent plates, tensile coupons extracted from the flat and corner portions from the cross-sections were also tested in order to measure the effect of the fabrication process on material properties. The strength enhancement predictive models proposed by previous studies were compared with the obtained test results from corner coupons with increased strength due to the cold-forming effect. A total of 20 HSS IHexHS stub column specimens were tested under axial compression and the cross-section classification from the existing structural steel design codes of EN 1993-1-12, ANSI/AISC 360–16, AS 4100, AISI S100–16 and design approaches of DSM and CSM were compared and assessed against the obtained results. It was found that the design provisions of cross-section classification in current design codes cannot be extended to the HSS IHexHS stub columns. Based on current codified yield slenderness limits, the strength predictions from design codes exhibit conservatism without the consideration of strain hardening and beneficial effect of element interaction whereas cross-sections with intermediate slenderness values were over-predicted.

Cross-Section Stability and Design of Normal Strength and High Strength Steel I-Sections in Fire

The structural response and design of normal strength and high strength steel I-sections at elevated temperatures are investigated in this paper. The shell finite element models of steel I-section elements capable of replicating their behavior in fire are developed and validated against experimental results from the literature. The validated shell finite element models are then utilized to generate extensive structural performance data for steel I-sections, considering a broad range of plate slenderness values for cross-section elements, elevated temperature levels, cross-section aspect ratios as well as different loading conditions and normal strength and high strength steel grades. The accuracy of the existing methods provided in the European structural steel fire design standard EN 1993-1-2 and its upcoming version prEN 1993-1-2 for the ultimate strength predictions of normal strength and high strength steel cross-sections in fire is assessed. Scope for improvement is observed. Considering this, a new method for the ultimate strength predictions of normal strength and high strength steel sections at elevated temperatures is put forward. It is shown that the proposed method leads to more accurate ultimate strength predictions for normal strength and high strength steel I-sections in fire with a higher level of reliability relative to the existing design methods provided in EN 1993-1-2 and prEN 1993-1-2.

Experiments on welded shells with section alteration under axial and peripheral pressure

This research elaborates the interactive response of thin steel cylindrical shells under axial and uniform peripheral pressure. The method of the research was mainly experimental, which was evaluated against theoretical analyses of other studies and design standards. The geometric variable was applied as thickness variation in a stepwise manner whilst designing the specimens; this is seen in cylindrical shells employed as storage structures such as silos. The axial loading was applied as a constant pre-loading to all specimens, which followed by applying uniform pressure that increased until the initial buckling, global buckling (hereafter called buckling in this paper), and collapse of the specimens were observed.The results underscored the significance of the slenderness on the capacity of the shells with varying thicknesses. For shells with lower slenderness values of the bottom strake(s), a more stable post-buckling response was identified. These specimens experienced somewhat symmetric formation of the buckling lobes compared to the specimens with a single strake. The capacity rise was also evaluated against the mass gain, and for some specimens, an insignificant mass gain led to a remarkable capacity gain.

Testing, numerical analysis and design of stainless steel equal-leg angle section beams

The stability and design of stainless steel equal-leg angle section members subjected to uniaxial bending are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and physical tests on hot-rolled austenitic stainless steel equal-leg angle section beams is first presented. The test results are then used to validate shell finite element models developed within ABAQUS, which are in turn used to undertake numerical parametric studies that consider both hot-rolled and cold-formed equal-leg angle section beams in austenitic, duplex and ferritic stainless steel with a wide range of slenderness values. Recent studies have shown that for angles under major-axis bending, both lateral-torsional and local buckling can arise, while under minor-axis bending, lateral-torsional buckling and Brazier-type flattening can occur. When designing for major-axis bending according to Eurocode 3, both local and lateral-torsional buckling are considered; it is shown herein that equal-leg angle sections under major-axis bending can be designed using a normalised slenderness based on the minimum of the local and lateral-torsional elastic buckling moments, while also considering their ratio. Under minor-axis bending, however, in comparison with the current provisions in Eurocode 3 that only require cross-section checks, it is shown that both safer and more accurate resistance predictions can be achieved when account is taken for lateral-torsional buckling and Brazier-type flattening. New design proposals for stainless steel equal-leg angle section beams, covering both major- and minor-axis bending, are therefore developed. The proposed design rules offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the procedure provided in EN 1990.

Aleatory uncertainties with global resistance safety factors for non-linear analyses of slender reinforced concrete columns

The present study aims to investigate and evaluate the influence of aleatory uncertainties (i.e., material and geometric uncertainties) when non-linear numerical analyses are developed to assess the global resistance of slender reinforced concrete columns. For instance, a set of 40 experimental tests on slender reinforced concrete columns with different slenderness values known from the literature is considered. The experimental tests have been reproduced by means of non-linear numerical simulations adopting specific modelling hypotheses able to minimize the model uncertainty. Successively, the calibrated non-linear numerical models of the 40 columns are used to perform a probabilistic analysis of the global structural resistance (i.e., ultimate axial load) including material uncertainties only and, then, both geometric and material uncertainties. The two groups of the probabilistic investigation are useful to characterize the influence of both material and geometric uncertainties on the global structural response of slender RC columns. Finally, global resistance safety factors are proposed as a function of the slenderness discussing also the procedure to incorporate the proposed results within the use of the global resistance safety formats.