Critical Slenderness Research Articles

Axial compressive mechanical behavior of a CFRP-confined composite member composed of bamboo strips and a thin-walled steel tube

To utilize fully the excellent mechanical properties of bamboo, thin-walled steel, and carbon fiber-reinforced polymer (CFRP), a CFRP-confined composite member composed of bamboo strips and a thin-walled steel tube (CBSC) was proposed to design a bamboo member with high-bearing capacity and ductility. The axial compressive tests were conducted on 26 CBSC members. Based on the validated finite-element (FE) model, a parametric analysis was performed to investigate the effects of different parameters on the axial compressive mechanical behaviors of CBSC members. Finally, the predictions of the ultimate axial compressive bearing capacity derived from the unified theory of concrete-filled steel tube columns agreed well with the test and FE results. The results showed that the failure mode of short CBSC members was strength failure, including material damage in the middle of the member, and end-crushing failure. However, the slender CBSC members exhibited typical global buckling failure. CBSC members can fully utilize the mechanical characteristics of the three materials to exert their combined effects. In terms of improving the bearing capacity, the recommended number of CFRP layers for all CBSC members is one except for the short CFRP-confined bamboo strip, thin-walled, circular steel-tube composite members, which is equal to two. The critical slenderness ratios of the CBCSC specimens and CBSSC specimens for distinguishing strength failure and global buckling are 19 and 36, respectively. The proposed predicted equations can accurately estimate the ultimate bearing capacity of CBSC members under axial compression.

Determination of natural frequencies of non‐uniform aluminum beams coated with functionally graded material

AbstractThe present study comprises a numerical analysis used to find the dimensionless natural frequencies of non‐uniform aluminum beams coated with functionally graded material. The beams have variable width, and their variation is described by exponential and linear functions. While the coating material properties vary with a polynomial function, the lamination theory is used to calculate the overall properties of the functionally graded material coating. The beam is modeled as a modified Timoshenko beam and the gradual transition of the coating material properties as 25 layers of homogeneous isotropic material. In order to find the natural frequencies of the beam, finite element analysis was used, and the numerical results were processed with MATLAB, which were in good agreement with literature values. A parametric study is performed to study the effects of slenderness (L/H), coating thickness (h/H), skewness rate (S) and taper ratio (w2/w1) on the dimensionless natural frequencies. The study showed that tapering and skewing had a limited effect on the natural frequencies in general, however there exists a critical slenderness for every taper ratio and skewness rate where shape variation has a significant effect on the natural frequencies and should be considered.

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.

Measuring and Rigidity Moduli of GFRP Experimentally

Although GFRP poles are widely accepted today due to their low cost and weight and high electrical and corrosion resistance, they suffer large deformations due to the low elastic and rigidity moduli (E & G) values of the GFRP. Accordingly, it is essential to accurately measure these values to estimate the actual deformation of the pole. This study presented a procedure to measure (E & G) values using three different tests on three sample sizes: full, scale pole, conic sample, and ad coupon sample, instead of using the manufacturer values as usual. This study is also concerned with the shear modulus value and when it can be neglected as usual in other traditional materials. The GRG optimization technique was used to analyze the results and determine the optimum values for (E & G) considering the results of the three tests. The results showed that the values of (E & G) are greatly affected by the sample’s size and shape, the slenderness ratio of the sample (L/r), and the shear deformation contribution. The critical slenderness ratio (L/r), corresponding to a shear deformation contribution of 10%, was determined for each test. This value is recommended as the upper boundary for any test that measures the (E & G) values. Testing several samples with different (L/r) values is also recommended to enhance accuracy. This study was concerned with determining the optimum values of elastic and rigidity moduli for GRFP poles compared to the manufacturer’s conservative values. The results indicated that the shear modulus can be neglected and the importance of the scale effect on the results of flexure and shear modulus. Doi: 10.28991/CEJ-2023-09-08-07 Full Text: PDF

Buckling in columns. Solution of the indeterminations of Euler's theory and derivation of an equation for inelastic buckling

Buckling in columns under central load has always been a complex problem and until now remains unclear. This work consists of two parts. In the first, a theory is presented to solve the indeterminations of Euler's theory, such as: Moment, slope, deflection, moment and shear reactions. In this sense, the column is analyzed as if it were a prismatic member under pure bending, due to the application of a bending moment and consequently the elastic curve of the column is calculated by the traditional method. Using a second hypothesis, it is established that elastic buckling occurs when the compressive and bending energies become equal; and solving it the Euler's Formula for the critical load is obtained exactly. In the second part, and with the indeterminations already resolved, the maximum-strain-energy failure criterion is raised, in the critic section, where the maximum moment occurs, due to the compressive load and subsequent bending. This allows us to obtain an extraordinary equation for inelastic flexural buckling that predicts highly accurate results consistent with laboratory tests. In the stress diagram versus slenderness, we can see the flat zone of the short columns, and the critical slenderness ratio, that in the case of ASTM-A36 structural steel, points directly to one hundred and twenty (120). And, of course, we can calculate the critical stress according to the type of cross-section and buckling axis and direction. An ideal column is considered, i.e., without initial deflection, with the application point of load on the centroid, and without residual stresses. A lineal stress-strain diagram is used until the yield point.

Computational methodology for the optimal design of steel truss frames integrating MATLAB and FEA platforms

Seeking to define more robust and executable structures, this article presents a computational framework for the optimal design of steel truss frames, which integrates two software of great prominence in structural engineering, MATLAB and ANSYS. Computational interfaces were created to enable the automation of the iterative optimization process. The optimization algorithm and computational interfaces were developed on the MATLAB platform, while structural analyses were performed with the ANSYS Mechanical APDL platform. Some details of the computational implementation are presented herein. The objective is to minimize the cost of structures by determining the optimal positioning of nodal coordinates and the optimal choice of commercially available structural profiles - shape and size optimization, respectively. For shape optimization, a computational model was defined to automatically generate the geometry of the structure, maintaining some intrinsic relations of symmetry and collinearity between elements. The design constraints are critical nodal displacements, stresses, and slenderness of elements, following the requirements of ABNT NBR 8800:2008. To exemplify the application of the proposed methodology, this article presents the optimal design of trusses for roofs of industrial sheds, considering its non-linear geometric behavior, typical of this type of structure.

Investigation on behavior of anchored sheet pile quay wall improved by cement-soil: Centrifuge and numerical modelling

By using the centrifuge test and three-dimensional (3-D) finite element (FE) simulation with an advanced soil constitutive model, this study investigated the suitability and reinforcement effect of cement deep mixing (CDM) for stabilizing the anchored sheet pile quay (ASPQ) in soft clay. Besides, a parametric study was designed to analyse the influence of three factors, including the excavation depth ratio, the slenderness ratio and the strength of the CDM block, on the responses of quay wall and quay-surface settlement. The results showed that the effectiveness of CDM was closely related to its strength, slenderness ratio, and excavation depth ratio. There existed a critical slenderness ratio of the CDM block to minimize the lateral deflection of the quay wall. The influence of CDM block strength on the response of the quay wall was significant only when it had low rigidity. As a result of material improvement, the reduction in maximum wall displacement became more significant as the excavation depth ratio increased. A CDM block-to-excavation-strength shape factor was proposed to characterise the lateral response of quay walls in cement-improved soil.

Fragmentation of inviscid liquid and destination of satellite droplets

The breakup process of the inviscid liquid bridge sandwiched between two coaxial and equal-sized rods is investigated by tracking its profile. Here, the focus is on the quasi-static profile of the liquid bridge close to rupture and its influence on the subsequent dynamic breakup behaviors. With the increasing distance between the two rods, the profile of the liquid bridge close to rupture undergoes a transition from symmetry to asymmetry. We found there exists a critical slenderness above which the liquid bridge will be asymmetric and present a profile that can be well fitted by one cycle of the sine wave. It is demonstrated both experimentally and theoretically that the ratio of the length of the bridge to its equivalent radius, defined as geometric mean of the radii at the peak and trough of the bridge, is always 2π for the asymmetric bridge close to rupture. Different with the symmetric evolution of the short bridge, the long asymmetric bridge pinches off first from the side near the bigger sessile drop and then from the other side, which endows the satellite droplet with a lateral momentum, resulting in the satellite re-collected by the sessile drop. The influence of the slenderness on the time interval among the asymmetric pinch-off, velocity, destination, and size of the satellite was investigated. A scaling law was proposed to describe the relationship between the lateral momentum of the satellite and the time interval between two pinch-off. This work is expected to benefit the utilizing or suppressing the satellite in practice.

Sinusoidal buckling behaviour of surface casing with negative friction in thawing permafrost

During the development of oil fields in permafrost regions, once the surface casing buckling occurs under the formation thawing and subsidence, it will cause great economic losses. In this paper, sinusoidal buckling of surface casing under negative friction is studied and preliminarily discussed. Based on the Winkler foundation theory and considering the different distribution forms of negative friction and soil resistance, the elastic stability model of casing is established. Combining dimensionless and Rayleigh-Ritz method, the critical slenderness ratio of sinusoidal buckling is obtained. The influence of boundary conditions, soil resistance and negative friction distribution on casing stability is quantitatively analysed on the basis of sufficient data calculation. It is found that the product of the critical slenderness ratio and the square root of the strain at the lower boundary is a fixed value which only depends on the boundary conditions and the value of soil resistance parameter, and the negative friction of different distribution forms can be superimposed according to the principle of ‘inverse square’ of the critical slenderness ratio. On this basis, the approximate calculation formula of the critical slenderness ratio is obtained by fitting, and the average error is less than 0.4%. The numerical example shows that the increase of soil resistance will weaken the influence of negative friction distribution on the critical slenderness ratio significantly. The ability to resist sinusoidal buckling can be improved by increasing the constraint of the lower casing section and increasing the casing thickness.

Bearing capacity of single stone column in clay using finite element limit analysis

Stone columns are used as an efficient ground improvement technique, which could increase the bearing capacity of native soft soil, reduce settlement, increase rate of consolidation and mitigate liquefaction potential. In this study, the finite element limit analysis (FELA) with the adaptive mesh, including both upper bound and lower bound approaches, was applied for prediction of ultimate bearing capacity of single stone column. It was observed that a critical slenderness ratio exists in which the failure mechanism changes from punching to bulging. An equation was derived for prediction of the critical slenderness ratio as a function of cohesion of the native clayey soil and friction angle of the stone column. A two-criteria equation is also presented to predict the ultimate bearing capacity of single stone column under both punching and bulging mechanisms. Moreover, the effect of footing roughness on the ultimate bearing capacity of the stone column was investigated. It was observed that the influence of footing roughness is more significant for bulging-type failure. The results of this study are also compared with some of the previously published analyses in the literature.

Mechanical behavior of Beishan granite samples with different slenderness ratios at high temperature

This paper aims at the temperature and slenderness ratio effects on physical and mechanical properties of Beishan granite. A series of uniaxial compression tests with various slenderness ratios and temperatures were carried out, and the acoustic emission signal was also collected. As the temperature increases, the fracture aperture of intercrystalline cracks gradually increases, and obvious transcrystalline cracks occurs when T > 600°C. The failure patterns change from tensile failure mode to ductile failure mode with the increasing temperature. The elastic modulus decreases with the temperature and increases with slenderness ratio, then tends to be a constant value when T = 1000°C. However, the peak strain has the opposite evolution as the elastic modulus under the effects of temperature and slenderness ratio. The uniaxial compression strength (UCS) changes a little for the low-temperature specimens of T < 400°C, but a significant decrease happens when T = 400°C and 800°C due to phase transitions of mineral. The evolution denotes that the critical brittle-ductile transition temperature increases with slenderness ratio, and the critical slenderness ratio corresponding to the characteristic mechanical behavior tends to be smaller with the increasing temperature. Additionally, the AE quantity also increases with temperature in an exponential function.

Experimental determination of the limiting flexibility of eucalyptus wood for axially compressed elements

Relevance. Wood is one of the most widely used building materials throughout history, and because of its physical-mechanical properties it mainly has been used in flexed and compressed elements. Eucalyptus was introduced to Latin America in the mid-19th century and nowadays is one of the most used woods for construction in the Andean region of Ecuador. To designing slender structural elements under axial loading engineers usually use the Euler formula, but it is applicable only if the compression stress does not exceed the proportional limit. One way to determine if the compression stress will be below the proportional limit is by comparing of the slenderness of the element with the limiting flexibility of its material which allows knowing if the buckling will occur in the elastic zone where Euler formula applies. The aim of the work - determine the magnitude of the limiting flexibility of eucalyptus, since this wood has been the subject of some investigations, however, no information about the limiting flexibility magnitude for the calculation of axially compressed elements. Methods. The laboratory tests to determine the magnitudes of the modulus of elasticity, proportional limit, admissible compression stress and limiting flexibility was carried out. Results. This experimental investigation shows that the magnitude of the limiting flexibility or so-called critical slenderness ratio for eucalyptus globulus is 59.

Effects of rocking coefficient and critical contact area ratio on the performance of rocking foundations from centrifuge and shake table experimental results

The major objective of this study is to correlate rocking foundation performance parameters with their capacity parameters and earthquake demand parameters using results obtained from 142 centrifuge and shaking table experiments, which include a variety of soil conditions, foundation geometries, structural models, and types of ground motions. The analysis presented in this paper considers all experimental results together, collectively as big data, through nondimensional parameters to identify hidden relationships among different parameters in a capacity-demand-performance framework. Rocking system performance parameters such as seismic energy dissipation in soil, permanent settlement, peak and permanent rotation, tipping-over stability ratio, self-centering ratio, rocking moment capacity, and acceleration amplification ratio are correlated with rocking system capacity parameters such as critical contact area ratio, rocking coefficient, and slenderness ratio of rocking systems and the earthquake demand parameters such as Arias intensity and peak ground acceleration of earthquake. It is found that energy dissipation and settlement correlate reasonably well with rocking coefficient and Arias intensity of earthquake, while peak rotation and acceleration amplification ratio correlate reasonably well with slenderness ratio, rocking coefficient, and peak ground acceleration of earthquake. Rocking foundations in clayey soils show superior performance in terms of seismic energy dissipation and permanent settlement compared to those in sandy soils, especially for relatively small to medium intensity shakings, and the ability of rocking foundations to de-amplify the earthquake motion increases as the magnitude of shaking increases.

Analysis of the Behaviour of Very Slender Piles: Focus on the Ultimate Load

The paper aims to analyse the influence of slenderness on the ultimate behaviour of piles with a very small diameter (less than 10 cm) that are often employed in soil reinforcement and for which the slenderness can significatively influence the failure behaviour, reducing the ultimate load. The aim is reached by means of numerical analyses on small-diameter piles of different geometries, embedded in clayey soil. The critical load is evaluated numerically in undrained conditions and then compared to the bearing capacity estimated by the classical approaches based on limit equilibrium method. The numerical model is first calibrated on the basis of the results of experimental laboratory tests on bored piles of a small diameter in a cohesive soft soil (average undrained shear strength cu = 15 kPa). The comparison between the critical load and the bearing capacity shows that their ratio becomes less than 1 for critical slenderness LCR that decreases, nonlinearly, with the decreasing of the pile diameter. The results of the analysis show that varying the diameter of the pile from 0.06 to 0.18 m, LCR varies from 65 to 200. The aforementioned evidence suggests that the evaluation of the ultimate load of piles of very small diameter has to follow the considerations on the critical load of the pile, especially if it is embedded in soft soil; on the contrary for piles of greater diameters (bigger than 20 cm) the buckling is not meaningful because LCR is so big that the common slenderness does not exceed it.

Glulam columns made of European beech timber: compressive strength and stiffness parallel to the grain, buckling resistance and adaptation of the effective-length method according to Eurocode 5

This article presents experimental and numerical investigations on the buckling behaviour of glulam columns made of European beech (Fagus sylvatica L.) timber and a design proposal. First, the compressive strength parallel to the grain (textit{f}_{mathrm{c,0}}) and the modulus of elasticity parallel to the grain (textit{E}_{mathrm{c,0}}) were experimentally determined in tests on stocky columns (slenderness ratio lambda = 12.5) of strength classes GL 40h, GL 48h, and GL 55h. Subsequent experimental buckling tests on slender columns with buckling lengths of 2.40 m (lambda = 41.5) and 3.60 m (lambda = 62.3) allowed investigating the buckling behaviour and quantifying the influence of the buckling length on the buckling resistance. Applicability of the effective-length method, which is the design method for columns in Eurocode 5 (EN 1995-1-1: Design of timber structures - Part 1-1: General - Common rules and rules for buildings. European Committee for Standardization, Brussels, 2010), was evaluated and a proposal for input parameters valid for columns made of European beech glulam is made. Numerical simulations revealed buckling resistances very close to the experimental results, confirming the proposed critical relative slenderness ratio lambda _{mathrm{rel,0}} = 0.25 and the fitted straightness factor beta _{mathrm{c}} = 0.25. In addition, the numerical simulations allowed for an extension of the scope of the investigations.

Failure mode transformation of ZnO nanowires under uniaxial compression: from phase transition to buckling

The failure modes of ZnO nanowires (NWs) with hexagonal cross section subjected to a uniaxial load are systematically investigated by using molecular dynamics (MD) simulations and two theoretical models considering the surface effect. Our results show that two different failure modes of the phase transition and buckling are triggered when the NWs are under uniaxial compression along the [0001] direction, in which the transformation between the two modes is related to the slenderness ratios of the NWs. Such slenderness-ratio-dependent mode transformation is mainly attributed to the competition between the critical stresses of phase transition and buckling. The Euler and Timoshenko models considering surface effect are further proposed to derive the critical slenderness for such mode transformation. The obtained analytical threshold values agree well with those of present MD simulations. Our results should be of great help for shedding some light on the design and application of functional devices based on ZnO NWs.

Crashworthiness analysis of double-arrowed auxetic structure under axial impact loading

Structures with negative Poisson's ratios have been widely applied in existing engineering, especially in the field of energy absorption. To design double-arrowed auxetic structures to better absorb energy, it is essential to conduct parametric analysis on their crashworthiness. In this paper, the effect of the geometric parameters on the crashworthiness performance is analyzed thoroughly on both macro- and micro-sized scales. At the macro scale, the effect of the slenderness ratio and size of the unit cell are analyzed. Additionally, the critical slenderness ratio is derived to distinguish the deformation modes under axial impact loading. At the micro scale, analysis of the effect of the angles and thickness of beams on the crashworthiness performance is conducted. It is found that the crashworthiness performance of double-arrowed auxetic structure is more sensitive to the parameters of the long-inclined beam than those of the short one. The discussion in this paper can help engineers to better design and optimize the double-arrowed crash box.

Experimental assessment and theoretical evaluation of axial behavior of short and slender CFFT columns reinforced with steel and CFRP bars

This paper presents the test results of an experimental program to investigate the structural performance of short and slender concrete-filled fiber-reinforced polymer (FRP)-tubes (CFFTs) columns under pure axial compression load. The test parameters include: transverse reinforcement type (steel spirals versus glass-FRP (GFRP-tube), type of longitudinal reinforcement (steel and carbon-FRP (CFRP) bars), GFRP tube thickness, and slenderness ratio.Comparisons between the experimental test results and the theoretical design equations are performed in terms of ultimate load carrying capacity. The design equation is modified to accurately predict the ultimate load capacities of CFFT columns reinforced with FRP bars. Furthermore, the experimental results showed that the axial compressive strength of CFRP-reinforced CFFT columns was reduced by 22% with increasing the slenderness ratio from 8 to 20. In general, the use of the FRP tube induces a confinement effect for concrete columns which enhances the strength and ductility of such column’s section. This enhancement resulted in a slender section which increased the possibility of buckling instability of the CFFT columns. Thus, a theoretical model was conducted to develop a simplified formula for critical slenderness limit of FRP-reinforced CFFT columns to control the buckling instability mode of failure. Results indicated that the slenderness limit of 14 was suggested as a safe value for the design purposes. A parametric study was conducted which showed the significant effect of the concrete compressive strength and hoop stiffness of FRP tube on the critical slenderness ratio of FRP-reinforced CFFT columns.

Linear Elastic Behavior of Circular Holed Steel Box Sections Under Compression

The aim of this work is to provide insights into the linear elastic behavior of steel box sections with centered and eccentric holes, placed at various points on the sides and at the corners of sections, and subjected to uniform compression. The influence of the following parameters was observed on stability, mainly through critical deformed shapes: (a) ratio of section aspects, (b) length-to-width ratio, (c) slenderness of sides, (d) diameter of holes, (e) coordinates x and y of the position of the hole on one side of the box section. Indications regarding important design aspects are given: (a) the best location for a single hole, or several holes, in cross-section; (b) the effects of circular holes with small, medium and large diameters on the linear buckling factor; (c) the effect of symmetric and eccentric holes for purposes of stability; (d) the best performing transversal section for square to rectangular holed box sections, in terms of stability; (e) critical slenderness values at which transition occurs from ultimate strength collapse of stocky box sections and critical elastic stress of slender ones.

Modified Monti-Nuti Model for Different Types of Reinforcing Bars Including Inelastic Buckling

The material model for reinforcing bar takes a very important role in the seismic analysis of reinforced concrete structures. The seismic performance of the structural elements such as column will be overestimated if the inelastic buckling is not incorporated in the material model. The Monti-Nuti Model could consider the buckling effect properly. The critical slenderness and anisotropy were discussed which has an important effect on the seismic behaviors of the reinforcement. Then this paper proposed a modified Monti-Nuti Model for different types of reinforcing bars, such as carbon steel reinforcement and stainless steel reinforcement including inelastic buckling. Subsequently, the implementation of the modified Mont-Nuti Model in OpenSees was introduced. Through validating with the experimental curves, the numerical curves generated by the modified model verified its capability.