Small Slenderness Ratio Research Articles

Buckling behavior of thin-walled cold-formed steel latticed column with lacings under axial compression

Extensive research has been undertaken on built-up cold-formed steel (CFS) column with I-shaped or box-shaped section. However, there has been little attention given to lattice CFS columns, particularly regarding their buckling performance and the design methods for determining buckling capacity. This paper proposes a latticed CFS column, formed by combining two G-shaped (complex edge stiffener) channels using lacings (LCCFS). Eighteen LCCFS columns were tested under axial compression, divided into two groups with web widths of 75 mm and 200 mm. The experimental results demonstrated that no distortional buckling failure occurred in the G-shaped channels of all specimens, mainly due to the constraint provided by lacings on the flanges. A general consistency in the ultimate bearing capacities and failure modes was observed among duplicate specimens. Specimens with a small slenderness ratio predominantly experienced local buckling failure, leading to a more abrupt failure. In contrast, specimens characterized by a large slenderness ratio primarily demonstrated failure due to global buckling. The specimens with larger web width-to-thickness ratios exhibited earlier and more pronounced local buckling, resulting in a reduction in axial compressive stiffness. Furthermore, FE models have been developed to analyze the effects of different parameters on the axial compressive buckling performance of LCCFS columns. The existing direct strength method exhibited notable deviations in predicting axial compressive buckling capacity of LCCFS column, which are deemed unsatisfactory. Based on direct strength method, a method was proposed for determining the axial compressive buckling capacity of LCCFS column.

Experimental Study and Design Method of Cold-Formed Thin-Walled Steel Unequal-Leg Angles under Axial Compression

An experimental study of cold-formed thin-walled steel unequal-leg angles (CFTWS-ULAs) under axially oriented pressure is presented in this paper. Firstly, the initial imperfections and material properties of the angle specimens were measured in detail. The angle specimens were tested under fixed-ended conditions. The results of the experiments showed that the angle specimens with small slenderness ratios were susceptible to local buckling, the angle specimens whose legs had high slenderness ratios and low width–thickness ratios were found to easily suffer from the occurrence of flexural buckling, and the angle specimens whose legs had high width–thickness ratios were found to easily suffer from the occurrence of interactive buckling between local buckling and flexural buckling. The finite element analysis of the ULAs was conducted using ABAQUS6.14 finite element software by creating a model. The buckling modes and ultimate bearing capacities of the test specimens were compared, and the finite element analysis verified that the established model built using the finite element is credible and subsequent parametric analysis was performed. The slenderness ratio had the most significant impact on the ultimate bearing capacities of the unequal-leg angles, as indicated by the analysis results. When the width–thickness ratio and the width ratio of the legs fell within a specific range, the ultimate bearing capacities of the unequal-leg angles increased as the width–thickness ratio and the width ratio of the legs increased. Finally, the comparison results showed that the design strengths predicted by the specifications were very conservative, because the local buckling and torsional buckling were calculated at the same time. Therefore, a recommendation was proposed that the calculation of the load-carrying capacity of an unequal-leg angle should ignore torsional buckling.

Examination of Beam Theories for Buckling and Free Vibration of Functionally Graded Porous Beams.

This paper examines the accuracy and effectiveness of various beam theories in predicting the critical buckling loads and fundamental frequencies of functionally graded porous (FGP) beams whose material properties change continuously across the thickness. The beam theories considered are classical beam theory (CBT), first-order shear deformation beam theory (FSDBT), third-order shear deformation beam theory (TSDBT), and the broken-line hypothesis-based shear deformation beam theory (BSDBT). Governing equations for those beam theories are formulated by using the Hamilton's principle and are then solved by means of the generalised differential quadrature method. Finite element simulation solutions are provided as reference results to assess the predictions of those beam theories. Comprehensive numerical results are presented to evaluate the influences of the porosity distribution and coefficient, slenderness ratio, and boundary condition on the difference between theoretical predictions and simulation results. It is found that the differences significantly increase as the porosity coefficient rises, and this effect becomes more noticeable for the rigid beam with a smaller slenderness ratio. Nonetheless, the results produced by the BSDBT are always the closest to simulation ones. The findings in this paper will contribute to the establishment of more refined theories for the mechanical analysis of FGP structures.

Scour Effect on the Lateral Bearing Behaviour of Monopiles Considering Different Slenderness Ratios

Scour leads to the loss of soil around monopile foundations for offshore wind turbines, which affects their structural safety. In this paper, the effect of scour on the lateral behaviour of monopiles was extensively investigated using finite element analysis, and calibration and comparison were undertaken using centrifuge tests. Piles with three slenderness ratios, i.e., 3, 5 and 8, were studied by keeping the diameter constant and varying the embedment length. Three scour types (local narrow, local wide and global) and four scour depths (0.5D, 1D, 1.5D and 2D; D signifies the pile diameter) were considered in this investigation. The results indicate that the lateral resistance of the pile is the greatest in the case of local narrow scour, followed by that in the cases of local wide scour and global scour. When the scour depth is larger than 1D, the influence of the scour type on the pile lateral bearing behaviour is insignificant. The influence of the scour type and scour depth on the pile lateral bearing behaviour is broadly similar for piles with slenderness ratios of 3, 5 and 8. However, the piles featured with smaller embedment lengths show a larger decrease rate in their lateral capacity, which means the effect of scour should cause more concern on small slenderness ratio monopiles.

Dynamic response of a large-diameter end-bearing pile in permafrost

Vertically dynamic model of a large-diameter pile in frozen soil is established, in which the frozen soil is described to a saturated frozen porous media, and the large diameter end-bearing pile is simplified to a one-dimensional rod considering the influence of the transverse inertia effect. Analytical solutions of the longitudinal coupling vibration between the end-bearing pile and the frozen soil are obtained using Helmholtz decomposition and variable separation methods in the frequency domain. By comparing the dynamic responses of the longitudinal vibration of the large diameter end-bearing pile with the traditionally one-dimensional pile, as well as the impedance factor of the frozen soil layer induced by the pile vibration, these demonstrate the influence of the transverse inertia effect on the high frequency vibration of large diameter pile is significant, and the influence on the pile with a smaller slenderness ratio is larger. The temperature and the Poisson’s ratio also have significant effects on the vertical vibration of large diameter piles in frozen soil, which cannot be ignored in the analysis.

Tests, numerical simulations and design of G550 high strength cold-formed steel lipped channel section columns failing by interactive buckling

This paper presents the experimental and numerical investigations into the structural performance and strengths of G550 high strength cold-formed steel (CFS) lipped channel section columns failing by interactive buckling. A testing program was first conducted, comprising material testing, measurements of initial local, distortional and global geometric imperfections and ten pin-ended column tests. The interaction between different buckling modes was observed and discussed for all the examined specimens upon testing. A numerical modeling program was subsequently performed, where numerical models were created and verified with reference to the test results and afterwards utilized to conduct parametric analysis to produce more numerical data over an extensive spectrum of cross-section geometries and effective member lengths. The effective width method (EWM) codified in the European code and direct strength method (DSM) specified in American and Australian standards were evaluated, based on the combined set of numerical and test data, for their suitability to G550 high strength CFS lipped channel section columns susceptible to interactive buckling. The evaluation results indicated that (i) the EWM yielded scattered and conservative ultimate strengths for columns with small and intermediate slenderness ratios, but relatively accurate results for those of large slenderness ratios and (ii) the DSM led to more consistent and accurate strength predictions for G550 high strength CFS lipped channel section columns failing by interactive buckling, though a number of strength predictions were on the unsafe side.

Influence of slenderness ratio on the lateral force of a slender body at high angle of attack

The slenderness ratio is an important feature of the slender body, but the effect of slenderness ratio on the lateral force of the slender body at high Angle of attack have not clearly. In this paper, the Detached eddy simulation (DES) method is verified and adopted to simulate the flow of five models with slenderness ratio SR=10, 12.5, 15, 17.5 and 20. The simulation is carried out under the conditions of 15.3m/s incoming flow and 55° Angle of attack. Based on the simulation results, the vorticity magnitude and surface pressure coefficient of the five models are compared. It is concluded that the increase of slenderness ratio will increase the fluctuation cycle of pressure along the axial direction. To further analysed the relationship between pressure distribution and lateral force in different models, the pressure values of multiple sections were extracted and integrated to draw the change curve of unit lateral force coefficient along the X direction. From the analysis of unit lateral force coefficient, the difference of pressure between the two sides induced by asymmetric vortex at the head is the main source of lateral force. The unit lateral force coefficient (Cfzpm ) of the model with small slenderness ratio oscillated more dramatically and attenuated more slowly than that of the model with large slenderness ratio, due to the interaction between the head vortex and the high-pressure region at the bottom of body with a small slenderness ratio at a large Angle of attack. The interaction between the head vortex and the bottom high-pressure region makes the lateral force coefficient of the model with small slenderness ratio not necessarily significantly smaller than that of the model with large slenderness ratio. With the increase of slenderness ratio, the influence of head vortex on the pressure distribution of rear surface decreases, and the asymmetry of rear surface pressure distribution decreases. The conclusion of this paper can help to solve the problem of lateral force coefficient variation that may occur in multistage rocket engineering.

Static Design for Laterally Loaded Rigid Monopiles in Cohesive Soil

Rigid monopiles with small slenderness ratios (i.e., ratio of monopile embedded length to outer diameter) are widely used as foundations to resist lateral load and moment transferred from superstructures, e.g., large diameter steel pipes used by offshore wind turbines and piers in electric utility industry or sound barriers. A design model for laterally loaded rigid monopiles in cohesive soil is presented in this paper. The proposed design model assumes a constant depth of rotation point as well as a trilinear distribution model of soil lateral reaction along the embedded length of the monopile, and introduces a mobilization coefficient of soil reaction to quantify the magnitude of soil reaction mobilized under a certain load applied at the monopile head. The relationship between the mobilization coefficient and monopile head rotation is established by back-analyzing test results measured from series of laterally loaded pile tests, and then a general design procedure for a laterally loaded rigid monopile in cohesive soil is recommended. The feasibility and reliability of the proposed design model is validated against three cases of numerical simulations on laterally loaded piles in cohesive soils. It shows that this study’s proposed design model produces a relatively satisfactory prediction of the nonlinear load-deformation response, and can be used for laterally loaded monopile design in the sites with undrained shear strength being uniform or increasing linearly with depth.

Parametric study on nonlinear vibration of FG-GNPRC dielectric beam with Kelvin–Voigt damping

Internal damping plays an essential role in the structural behaviors of composites. This paper adopts Kelvin–Voigt model to investigate the effects of the internal damping on nonlinear vibration of functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) beam with dielectric properties. Within the framework of Timoshenko beam theory, governing equations for the vibration of the damped beam are developed by incorporating the internal damping in terms of energy. The governing equations are discretized by differential quadrature (DQ) method after state–space​ transformation and then solved numerically by direct iteration. The validated results demonstrate that the nonlinear natural frequency of the structure is highly dependent on the shear proportionality constant of the Kelvin–Voigt internal damping. It is found when the beam is subjected to higher voltage, the functionally graded distribution of the reinforcing filler enables the composite structure to be more stable compared to uniform distribution. Moreover, the nonlinearity of the structure is more sensitive to DC voltage for composite beams with smaller slenderness ratio and thickness.

EXPERIMENTAL REPORT ON GLASS PANELS AGAINST STATIC AND REPEATED IN-PLANE COMPRESSION LOADING

Primary load-bearing members used in glass structures, such as columns consisting of glass panels, are frequently subjected to in-plane loading. Its allowable stress for safety design appears to be a significant subject. By analyzing the results of static (without repeated loading) and cycling compression loading tests, the authors explore the mechanical features and failure mechanism of the tempered glass panels subjective to in-plane compression loading, including its ultimate stress and buckling load. In addition, a statistical method based on the experimental results is adopted to evaluate the allowable compressive stress. The experimental results show that the ultimate loads of specimens with high slenderness ratios satisfy Euler's critical load formula. In contrast, the ultimate loads of specimens with low thickness ratios distribute in a certain variance range. For the cycling loading test, after 30 times of repeated loading with maximum stress equivalent to 2/3 of the ultimate static stress, the average strength is almost the same or bigger than that of static loading tests. No fatigue fracture due to repeated loading was found for the tempered glass panels. Consequently, the allowable stress for in-plane compressive loading can be formulated based on Euler's critical load formula for a glass panel with a bigger slenderness ratio. The formulation for the allowable compressive stress of a glass panel with a smaller slenderness ratio is promoted using statistical analysis with a 95 percent confidence level for the safety design.

Experiment and Design Method of Cold-Formed Thin-Walled Steel Double-Lipped Equal-Leg Angle under Axial Compression

The cold-formed steel (CFS) double-lipped equal-leg angle is widely used in modular container houses and cold-formed steel buildings. To study the buckling behavior and bearing capacity design method of the cold-formed steel (CFS) double-lipped equal-leg angle under axial compression, 24 CFS double-lipped equal-leg angles with different sections and slenderness ratios the axial compression were conducted. The test results showed that the distortional buckling occurs for specimens with a small width-to-thickness ratio and small slenderness ratio. The buckling interactive with distortional and global flexural buckling was observed for the specimens with small width-to-thickness ratios and large slenderness ratios. The specimens with large width-to-thickness ratios and small slenderness ratios showed interactive buckling with local and distortion buckling. The specimens with large width-to-thickness ratios and large slenderness ratio developed interactive buckling with local, distortional, and global flexural buckling. The finite element model established by ABAQUS software was used to simulate and analyze the test. The buckling modes and the load-carrying capacities analyzed by the finite element model agreed with the test results, which showed that the developed finite element model was feasible to analyze the buckling and bearing capacity of the CFS double-lipped equal-leg angles. The experimental results were compared with those calculated by the direct strength method in the North American standard and the effective width method in the Chinese standard. The comparisons indicated that the calculated results are very conservative with maximum value 36% and 51% for direct strength method and effective width method, respectively. The coefficient of variation was 0.276 and 0.397, respectively. Finally, the modified direct strength method and the modified effective width method were proposed based on the experimental results. The comparison on the ultimate strength between test results and calculated results by using the modified method showed a good agreement. The modified method can be as a proposed desigh method for the ultimate strength of the CFS double-lipped equal-leg angles under axial compression.

Influence of the aspect ratio on seismic performance of adobe buildings

Adobe buildings usually are characterized by having walls with small and uniform slenderness ratios; nevertheless, there are some historical adobe buildings with existing large walls, where the influence of the aspect ratio becomes quite important in the seismic behavior. This article analyzes the seismic behavior of adobe buildings with larger walls in one axis than the other orthogonal axis. Also, the influence of the aspect ratio of the wall height respects on the wall length is analyzed by varying the wall length. Finite element models were elaborated using the concrete damaged plasticity model to study the influence of the aspect ratio on the seismic behavior of adobe buildings. Four models of buildings having different aspect ratios, varying in length from eight meters to fifty-two meters have been considered. Nonlinear time history analyses with three Peruvian seismic records are conducted. Regarding material, information was collected on the parameters necessary for finite element modeling for adobe masonry. From the non-linear simulations, the cracking patterns of the four buildings were identified. The influence of the aspect ratio in the seismic capacity of these kind of adobe buildings is analyzed. Finally, the results obtained in the numerical models are compared with the evidence of damage caused by past earthquakes.

Restoring force model of square tubular columns filled with extra‐high‐performance reactive powder concrete

SummarySquare tubular column filled with extra‐high‐performance reactive powder concrete (RPC) is a novel composite structure that takes advantage of strong bending resistance of steel tubes and high compressive strength and toughness of RPC. To study the seismic performance of square tubular columns filled with RPC, a series of low‐cycle lateral loading tests were performed on four square tubular columns filled with RPC. The steel content and steel fiber content were selected as test parameters. Experimental results show that a higher steel content and 1% steel fiber result in good energy dissipation and deformation performance of specimens. To establish the restoring force model of square tubular columns filled with RPC, 18 column models with different steel content, axial compression ratio, and slenderness ratio were simulated and analyzed using ABAQUS. The simulation results show that a larger steel content and smaller slenderness ratio can improve the column bearing capacity, but the influence of axial compression ratio is negligible. A restoring force model considering stiffness degradation is proposed using a regression analysis method, which is in good agreement with the experimental results.

Numerical evaluation on collapse-resistant performance of steel-braced concentric frames

Steel-braced concentric frames (SBCFs) are a popular form of structure and has been widely employed in seismic regions owing to their high strength and elastic stiffness; however, the effects of key parameters on the collapse behavior of SBCFs are unclear due to insufficient investigations, which should be further explored in column removal scenarios. To this end, numerical models were employed to explore the key parameters affecting the collapse behavior of SBCFs in this study. The numerical models of steel frames with or without braces were validated based on previous experimental results. According to the refined model, the effects of brace members of various types and with different slenderness ratios on the collapse behavior were illustrated. The results showed that an X brace type with smaller slenderness ratio is the most appropriate for enhancing robustness against progressive collapse. Thereafter, full-scale numerical models were established to investigate the effect of the column removal position, and the results showed that the frame relied purely on flexural action in a side column loss. Moreover, the effect of the position of horizontal brace layers on the collapse behavior was investigated in the middle and side column removal scenarios. To gain deeper insight into the load-resisting mechanisms, the specific contributions to the total resistance of different mechanisms in different stories, bare steel frames and braces, and tensile and compressive braces were separated. Finally, a strategy for the robustness enhancement of high-rise steel frames was empirically proposed, and it was suggested that the provision of a brace layer for approximately every 10 stories would be effective for the anti-collapse design of high-rise buildings.

Experimental investigation of steel built-up beam-columns composed of tracks and channels cold-formed sections

In this paper, a built-up column of novel cold-formed cross-section that composed of four elements is investigated. The proposed built-up column is suitable for carrying axial, uni-axial, and bi-axial loading. The web of the new cross-section is composed of back-to-back track sections while the flanges of the cross-section are two lipped channels connected to the web using interconnectors. Elements comprising the cross-section are assembled and connected by enough interconnector bolts depending on the column built-up configurations. The interconnector spacing is varied among specimen cross-section and column length. In the present study, series of axially, uni-axially, and bi-axially compression columns were tested experimentally. Eleven specimens with various cross-section aspect ratios as well as different overall slenderness ratios were tested. Numerical finite element model that accounts for both material and geometrical nonlinearities was developed using ‘ABAQUS’ software to analyze the tested columns. A good agreement was achieved between the experimental test and the finite element model results. Experimental test results revealed that for axially loaded columns with small, medium, and high slenderness ratios, the failure modes were local buckling, local-flexural buckling, and flexural-distortional buckling; respectively. On the other hand, for uni-axially loaded columns having small, medium, and high slenderness ratios, the failure modes were local buckling, interaction between local and lateral-torsional buckling as well as lateral-torsional buckling; respectively. Furthermore, for bi-axially loaded columns, the failure mode was lateral-torsional buckling.

Hoop and axial plastic buckling modes of submerged cylindrical shells subjected to side-on underwater explosion shock wave

Cylindrical shells are widely used in marine structures from small-sized pipes to various immersed containers and large submarines. Dynamic plastic buckling of the shells could be caused by underwater explosion (UNEX) loads in industrial accidents or hostile attacks. Influential factors including non-dimensional hull shock factor reflecting the resilience of the material to shock intensity, slenderness ratio, localised ring stiffener and endcap are identified. Their impacts on the dynamic buckling modes are discussed relied on the finite element investigations. The results show that the global hoop and axial buckling modes are mainly determined by the hull shock factor and slenderness ratio, respectively. With the increase of hull shock factor, i) back-side buckling, ii) back- and front-side buckling with dominant buckles at the back-side, iii) back- and front-side buckling with dominant buckles at the front side, and iv) overall buckling with very large buckles at the front-side originating from the priority buckling modes can be observed in the circumferential direction. The competition between the front- and back-sides buckling is attributed to their different buckling mechanisms. The former one is caused by shock transmitted from the explosion source through the fluid, whereas the later one is due to striking of the structural hoop stress waves propagated from the front-side via the shell itself. Axial buckling modes consisted of primary and potential buckles alternating in the axial direction could be triggered for a large slenderness ratio, but be concealed by localised buckling modes for small slenderness ratio. The localised buckling modes are controlled by the ring-stiffener and endcap, because they alter the continuity of compression potential of shells.

Three-dimensional scour hole model and scour effects on the ultimate capacity of lateral loaded rigid piles

The rigid pile with a large diameter and a small slenderness ratio is the most widely used foundation for offshore wind turbines. Scour around piles seriously threatens the safe operation of offshore wind turbines, so its effects on rigid piles need to be studied urgently. In this paper, scour tests under steady current and static lateral load tests after scour are conducted. According to the results of scour tests, a three-dimensional scour hole model suitable for engineering reality and its analytical expression are proposed. Then, the results of load tests indicate that scour reduces the ultimate lateral capacity of foundations, and the percentage of reduction is related to the current direction, whereas does not change with load eccentricity. Finally, a preliminary formula for evaluating the ultimate lateral capacity of rigid piles after scour is presented, which can easily and quickly determine the upper and lower limits of scour effects.

Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model

Abstract Free vibration of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium is studied on the basis of the nonlocal Timoshenko beam model. Influences of the slenderness ratios, the boundary conditions, the atomic structures and the stiffness of the embedded medium on the natural frequencies and mode shapes of SWCNT are examined. The nonlocal effect is significant for the higher modes of SWCNT with a small slenderness ratio embedded in a soft elastic medium, and it softens the SWCNT except for the fundamental frequency of the clamped–free SWCNT.

An improved analytical model that considers lateral effects of a phononic crystal with a piezoelectric defect for elastic wave energy harvesting

This paper aims to improve the existing electromechanically coupled analytical model that was developed for defect-induced phononic crystals (PnCs) designed for piezoelectric energy harvesting (PEH). The work outlined in this paper improves the model by considering lateral movements, which are not negligible when the slenderness ratio of the rods is small. Based on the Rayleigh-Love rod theory, the proposed method uses the generalized Hamilton's principle to derive two governing equations in the mechanical and electrical domains. An explicit form of the solutions to the governing equation is then used to derive an improved electromechanically coupled transfer matrix. Based on the transfer matrix method and the S-parameter method, the proposed electromechanically coupled analytical model enables the prediction of defect bands and PEH performance. To evaluate the predictive capabilities under a small slenderness ratio of the rods, the results from the proposed Rayleigh-Love rod-theory-based analytical model are compared with those found by the existing analytical model based on classical rod theory and by a finite element model. The novelties of the research outlined in this paper are as follows: 1) the proposed method considers, for the first time, lateral inertia in analytical modeling of defect-induced PnCs for PEH purposes and 2) three coefficients are newly presented to quantify the effects of lateral motions on the electromechanically coupled transfer matrix.

Dynamic modeling and analysis of an axially moving and spinning Rayleigh beam based on a time-varying element

An axially moving and spinning beam, i.e., a beam having simultaneous axial movement and spin rotation, has been widely used in some engineering fields. In general, the force status of an axially moving and spinning beam is quite complex, with the beam simultaneously producing deformations of tension and compression and bending and torsion. Presently, the main method employed in studies concerning the dynamics of axially moving and spinning beams is structural dynamics, which focuses on the vibration and stability of the beam. Nevertheless, to describe the global motion and deformation motion of an axially moving and spinning beam more efficiently and accurately, scholars have proposed an Euler element model that is suitable for a slender beam. In the Euler element, because the moment of inertia of the cross section is ignored, large errors may occur when the element is used in the dynamic modeling and analysis of an axially moving and spinning beam with a small slenderness ratio. To solve this problem, a new element model based on the Rayleigh beam theory, in which the moments of inertia of the cross section around the beam's neutral as well as center axis are naturally considered by integrating the virtual work of the inertial force at each point in the element [herein referred to as the time-varying Rayleigh beam-shaft element (TVRBSE)], is presented in this paper. Dynamic analysis was performed for the axially moving and spinning cantilever Rayleigh beam, and the kinematics results were compared with those of the structural dynamics method reported in the literature. Both results were consistent with each other, which verifies the correctness of TVRBSE. The dynamic analysis based on TVRBSE can also simultaneously obtain the internal forces (axial force, bending moment, and torque) at each section of the beam and the stresses they cause. Moreover, the solution process for the proposed TVRBSE was easier to program and demonstrated good adaptability to changes in the loading and constraint conditions of the beam, a very advantageous feature. Essentially, the results of this study show that TVRBSE can accurately and effectively solve the dynamic problem of the axially moving and spinning beam.