• Steel and Composite Structures
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• v.9 no.2
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• pp.89-101
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• 2009

This paper presents a simplified model to study post-buckling behaviours of the axially restrained steel column at elevated temperatures in fire. The contribution of axial deformation to the curvature of column section is included in theoretical equations. The possible unloading at the convex side of the column when buckling occurs is considered in the stress-strain relationship of steel at elevated temperatures. Parameters that affect structural behaviours of the axial restrained column in fire are studied. The axial restraint cause an increase in the axial force before the column buckles; the buckling temperature of restrained columns will be lower than non-restrained steel columns. However, the axial force of a restrained column decreases after the column buckles with the elevation of temperatures, so make use of the post-buckling behaviour can increase the critical temperature of restrained columns. Columns with temperature gradient across the section will produce lower axial force at elevated temperatures.

• Advances in nano research
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• v.9 no.2
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• pp.69-82
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• 2020

In this paper, a new explicit analytical formula is derived for the critical buckling load of Double Walled Carbon Nanotubes (DWCNTs) embedded in Winkler elastic medium without taking into account the effects of the nonlocal parameter, which indicates the effects of the surrounding elastic matrix combined with the intertube Van der Waals (VdW) forces. Furthermore, we present a model which predicts that the critical axial buckling load embedded in Winkler, Pasternak or Kerr elastic medium under axial compression using the nonlocal Donnell shell theory, this model takes into account the effects of internal small length scale and the VdW interactions between the inner and outer nanotubes. The present model predicts that the critical axial buckling load of embedded DWCNTs is greater than that without medium under identical conditions and parameters. We can conclude that the embedded DWCNTs are less susceptible to axial buckling than those without medium.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.347-354
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• 2006

In this paper, we work with steel circular tubes and propose analysis model which can consider local buckling that it has an effect on failure of steel structures and induce the relation between loading and deformation. First of all, in respect to axial symmetry local buckling, which is simplest case, elasto-plastic behavior acting only axial loads is object Therefore, it suggests analysis model for axial symmetry local buckling. And that is explainable the process from increasing internal force to decreasing passing maximum internal force. Besides, we induce the relation between the axial force and axial deformation.

• Proceeding of KASS Symposium
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• 2006.05a
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• pp.73-80
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• 2006

In this paper, we work with steel circular tubes and propose analysis model which can consider local buckling that it has an effect on failure of steel structures and induce the relation between loading and deformation. First of all, in respect to axial symmetry local buckling, which is simplest case, elasto-plastic behavior acting only axial loads is object. Therefore, it suggests analysis model for axial symmetry local buckling. And that is explainable the process from increasing internal force to decreasing passing maximum internal force. Besides, we induce the relation between the axial force and axial deformation.

• Steel and Composite Structures
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• v.51 no.5
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• pp.543-562
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• 2024

While the external axial compressive load is applied to only the shell edge of stringer-stiffened shell in the most of numerical and analytical previous studies (entitled as conventional approach), a part of external load is applied to the stringers in real conditions. It leads to decrease the accuracy of the axial buckling load calculated by the conventional eigenvalue analysis approach performed in the most of previous studies. In this study, the distribution of stress in the pre-buckling analysis was enhanced by applying the axial external compressive load to both shell and stringers to perform an accurate eigenvalue analysis of the stringer-stiffened composite shell. In this regard, a model was developed in FORTRAN environment to simulate the laminated stringer-stiffened shell under axial compressive load using finite strip method. The axial buckling load of the shell was obtained through eigenvalue analysis. A comparison was made between the results obtained from the model and those available in the previous studies to evaluate the validity of the results obtained from the model. Through a parametric study, the effects of different parameters such as stringer properties and composite layup on the buckling load of the shell under different loading patterns were investigated. The results indicated that in some cases, the axial buckling load obtained for the conventional approach used in the most of previous studies is significantly overestimated or underestimated due to neglecting the stringer in distribution of external load applied to the stringer-stiffened shell. According to the results obtained from the parametric study, some graphs were derived to show the accuracy of the axial buckling load obtained from the conventional approach utilized in the literature.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.87-103
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• 2015

This paper focuses on an analytical research on the critical buckling load of cylindrical shells with stepwise variable wall thickness under axial compression. An arctan function is established to describe the thickness variation along the axial direction of this kind of cylindrical shells accurately. By using the methods of separation of variables, small parameter perturbation and Fourier series expansion, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under axial compression are derived. The analysis is based on the thin shell theory. Analytic results show that the critical buckling load of the uniform shell with constant thickness obtained from this paper is identical with the classical solution. Two important cases of thickness variation pattern are also investigated with these analytical formulas and the results coincide well with those obtained from other authors. The cylindrical shells with stepwise variable wall thickness, which are widely used in actual engineering, are studied by this method and the analytical formulas of critical buckling load under axial compression are obtained. Furthermore, an example is presented to illustrate the effects of each strake's length and thickness on the critical buckling load.

• Nuclear Engineering and Technology
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• v.25 no.1
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• pp.148-153
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• 1993

A fifth-order Fourier series technique is applied in Core Operating Limit Supervisory System (COLSS) to construct the on-line core average axial power shape from in-core detector signals because of its simplicity and fast computation. Such a synthesizing accuracy depends on number of Fourier series modes and axial boundary conditions. COLSS currently uses the five-mode Fourier series technique which utilizes the five axially located fixed in-core detector signals and a constant axial boundary condition. Therefore, the constant axial boundary condition should be appropriately chosen based on the evaluation of its effect on the accuracy of the on-line calculations. The four cases of axial buckling (0.75, 0.8, 0.9 and 1.0) were examined for Yonggwang Nuclear Units 3&4 as the axial boundary conditions in this paper. The core average axial power shapes and the operating margins were compared for each case to determine the optimal constant axial buckling. The axial buckling of 0.9 was found to be the optimal value.

• Steel and Composite Structures
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• v.13 no.3
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• pp.295-308
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• 2012

This paper experimentally investigated the buckling capacity of built-up steel columns mainly, Cruciform Columns (CC) and Side-to-Side (SS) columns fabricated from two Universal Beam (UB) sections. A series of nine experimental tests comprised of three UB sections, three CC sections and three SS sections with different lengths were tested to failure to measure the ultimate axial capacity of each column section. The lengths used for each category of columns were 1.8, 2.0, and 2.2 m with slenderness ratios ranging from 39-105. The measured buckling loads of the tested specimens were compared with the predicted ultimate axial capacity using Eurocode 3, AISC LRFD, and BS 5959-1. It was observed that the failure modes of the specimens included flexural buckling, local buckling and flexural-torsional buckling. The results showed that the ultimate axial capacity of the tested cruciform and side-by-side columns were higher than the code predicted design values by up to 20%, with AISC LRFD design values being the least conservative and the Eurocode 3 design values being the most conservative. This study has concluded that cruciform column and side-to-side welded flange columns using universal beam sections are efficient built-up sections that have larger ultimate axial load capacity, larger stiffness with saving in the weight of steel used compared to its equivalent universal beam counterpart.

• Steel and Composite Structures
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• v.12 no.1
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• pp.31-51
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• 2012

Local buckling can be ignored for hot-rolled ordinary strength steel equal angle compression members, because the width-to-thickness ratios of the leg don't exceed the limit value. With the development of steel structures, Q420 high strength steel angles with the nominal yield strength of 420 MPa have begun to be widely used in China. Because of the high strength, the limit value of the width-to-thickness ratio becomes smaller than that of ordinary steel strength, which causes that the width-to-thickness ratios of some hot-rolled steel angle sections exceed the limit value. Consequently, local buckling must be considered for 420 MPa steel equal angles under axial compression. The existing research on the local buckling of high strength steel members under axial compression is briefly summarized, and it shows that there is lack of study on the local buckling of high strength steel equal angles under axial compression. Aiming at the local buckling of high strength steel angles, this paper conducts an axial compression experiment of 420MPa high strength steel equal angles, including 15 stub columns. The test results are compared with the corresponding design methods in ANSI/AISC 360-05 and Eurocode 3. Then a finite element model is developed to analyze the local buckling behavior of high strength steel equal angles under axial compression, and validated by the test results. Following the validation, a finite element parametric study is conducted to study the influences of a range of parameters, and the analysis results are compared with the design strengths by ANSI/AISC 360-05 and Eurocode 3.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.