Buckling of Thin-Walled Long Steel Cylinders Subjected to Bending

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Sotiria Houliara ◽  
Spyros A. Karamanos
Keyword(s):  
Structural Response ◽  
Cylinder Wall ◽  
Imperfection Sensitivity ◽  
Bifurcation Instability ◽  
Buckling Mode ◽  
Cross Sectional ◽  
Moment Capacity ◽  
Thin Walled ◽  
Cylindrical Steel ◽  
Element Technique

The present paper investigates structural response and buckling of long unstiffened thin-walled cylindrical steel shells, subjected to bending moments, with particular emphasis on stability design. The cylinder response is characterized by cross-sectional ovalization, followed by buckling (bifurcation instability), which occurs on the compression side of the cylinder wall. Using a nonlinear finite element technique, the bifurcation moment is calculated, the post-buckling response is determined, and the imperfection sensitivity with respect to the governing buckling mode is examined. The results show that the buckling moment capacity is affected by cross-sectional ovalization. It is also shown that buckling of bent elastic long cylinders can be described quite accurately through a simple analytical model that considers the ovalized prebuckling configuration and results in very useful closed-form expressions. Using this analytical solution, the incorporation of the ovalization effects in the design of thin-walled cylinders under bending is thoroughly examined and discussed, considering the framework of the provisions of the new European Standard EN1993-1-6.

Buckling of Thin-Walled Long Steel Cylinders Under Bending

2009 ◽  
Author(s):  
Sotiria Houliara ◽  
Spyros A. Karamanos
Keyword(s):  
Structural Response ◽  
Cylinder Wall ◽  
Imperfection Sensitivity ◽  
Bifurcation Instability ◽  
Buckling Mode ◽  
Cross Sectional ◽  
Moment Capacity ◽  
Thin Walled ◽  
Cylindrical Steel ◽  
Element Technique

The present paper investigates structural response and buckling of long unstiffened thin-walled cylindrical steel shells, subjected to bending moments, with particular emphasis on their stability design. The cylinder response is characterized by cross-sectional ovalization, followed by buckling (bifurcation instability), which occurs on the compression side of the cylinder wall. Using a nonlinear finite element technique the bifurcation moment is calculated, the post-buckling response is determined, and imperfection sensitivity with respect to the governing buckling mode is examined. The results show that the buckling moment capacity is affected by cross-sectional ovalization. It is also shown that buckling of bent elastic long cylinders can be described quite accurately through a simple analytical model, which considers the ovalized pre-buckling configuration and results in closed-form expressions. Using this analytical solution, the incorporation of the ovalization effects in the design of thin-walled cylinders under bending is discussed, in the framework of the provisions of the new European Standard EN1993-1-6.

Coupled Deflection Analysis of SMA Fiber Hybrid Composite Active Blade

2009 ◽  
Vol 79-82 ◽  
pp. 1455-1458 ◽  
Author(s):  
Yong Sheng Ren ◽  
Shu Lian Yang ◽  
Ting Riu Liu ◽  
Xiao Hui Wang
Keyword(s):  
Phase Transformation ◽  
Volume Fraction ◽  
Structural Response ◽  
Laminated Beams ◽  
Cross Sectional ◽  
Variational Asymptotic ◽  
Deflection Analysis ◽  
Variational Asymptotic Method ◽  
Thin Walled ◽  
Work Done

The constitutive equations relating cross-sectional loads(forces and moments)to cross-sectional displacements(stretching, bending, twisting) of thin-walled laminated beams with integral shape memory alloy (SMA)active fibers was presented. The variational asymptotic method was used to formulate the force- deformation relationships equations, accounting for the presence of active SMA fibers distributed along the cross-section of the beam. The constitutive relationships for evaluation of the properties of a hybrid SMA composite ply were obtained following the rule of mixtures. The analytical expressions of the actuation components for the active beam were derived based on Tanaka’s constitutive equation and Lin’s linear phase transformation kinetics for SMA fiber. The general form of constitutive relation was applied to the case of stretching-twist coupling, corresponding to Circumferentially Uniform Stiffness (CUS). The present analysis extended the previous work done for modeling generic passive thin-walled laminated beams. Numerical results shown that significant stretching and twisting deflection occur during the phase transformation due to SMA actuation. The effects of temperature on structural response behavior during phase transformation from martensite to austenite are significant. The effects of the volume fraction of the SMA fiber, the martensitic residual strain and ply angle were also addressed

ELASTIC BUCKLING OF THIN-WALLED CIRCULAR TUBES CONTAINING AN ELASTIC INFILL

2006 ◽  
Vol 06 (04) ◽  
pp. 457-474 ◽  
Author(s):  
M. A. BRADFORD ◽  
A. ROUFEGARINEJAD ◽  
Z. VRCELJ
Keyword(s):  
Axial Compression ◽  
A Priori ◽  
Local Buckling ◽  
Steel Tube ◽  
Transcendental Equation ◽  
Buckling Mode ◽  
Buckling Stress ◽  
Elastic Tubes ◽  
Thin Walled ◽  
Energy Formulation

Circular thin-walled elastic tubes under concentric axial loading usually fail by shell buckling, and in practical design procedures the buckling load can be determined by modifying the local buckling stress to account empirically for the imperfection sensitive response that is typical in Donnell shell theory. While the local buckling stress of a hollow thin-walled tube under concentric axial compression has a solution in closed form, that of a thin-walled circular tube with an elastic infill, which restrains the local buckling mode, has received far less attention. This paper addresses the local buckling of a tubular member subjected to axial compression, and formulates an energy-based technique for determining the local buckling stress as a function of the stiffness of the elastic infill by recourse to a transcendental equation. This simple energy formulation, with one degree of buckling freedom, shows that the elastic local buckling stress increases from 1 to [Formula: see text] times that of a hollow tube as the stiffness of the elastic infill increases from zero to infinity; the latter case being typical of that of a concrete-filled steel tube. The energy formulation is then recast into a multi-degree of freedom matrix stiffness format, in which the function for the buckling mode is a Fourier representation satisfying, a priori, the necessary kinematic condition that the buckling deformation vanishes at the point where it enters the elastic medium. The solution is shown to converge rapidly, and demonstrates that the simple transcendental formulation provides a sufficiently accurate representation of the buckling problem.

The Influence of Stochastic Imperfection Field on the Bearing Capacity of Hyperbolic Cooling Towers

2011 ◽  
Vol 374-377 ◽  
pp. 2297-2300
Author(s):  
Hai Zhao ◽  
Ya Zhou Xu ◽  
Guo Liang Bai
Keyword(s):  
Bearing Capacity ◽  
Large Scale ◽  
Initial Imperfection ◽  
Orthogonal Basis ◽  
Imperfection Sensitivity ◽  
Stochastic Field ◽  
Buckling Mode ◽  
Material Inhomogeneity ◽  
Initial Imperfections ◽  
Distribution Form

The uncontrollable factors such as construction errors, material inhomogeneity, etc. will inevitably lead to a certain initial imperfections. It is generally known that the stochastic initial imperfection of the structure is an important factor for affecting structural stability and bearing capacity. Since these imperfections are random in nature, this paper proposes the method mainly based on the standard orthogonal basis to expand the stochastic field, taking into account the decomposition of the stochastic initial imperfections related to structures, which is projected in the buckling mode orthogonal basis. In the end, the article by the stability analysis example shows that this method can use less random variables effectively describing the original stochastic imperfection field, and efficiently search for the most unfavorable initial imperfection distribution form in order to ensure the imperfection sensitivity structures have a higher reliability, so it can be applied to large-scale engineering structure stochastic imperfection analysis.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Torsional Stiffness of a Thin-Walled Beam Braced by Pinned or Rigidly Fixed Transverse Diaphragms

1973 ◽  
Vol 15 (5) ◽  
pp. 351-356
Author(s):  
T. Harrison ◽  
J. M. Siddall
Keyword(s):  
Experimental Evidence ◽  
Theoretical Work ◽  
Torsional Stiffness ◽  
Cross Sectional ◽  
Cross Sectional Profile ◽  
Thin Walled ◽  
Sectional Profile ◽  
Good Agreement

The torsional stiffness of a thin-walled beam of open cross-sectional profile braced by evenly spaced transverse diaphragms is studied. Diaphragms rigidly fixed or attached by frictionless pins are treated and it is seen that, in either case, the only effect is to modify the St Venant torsional constant for the thin-walled beam. The theoretical work is supported by experimental evidence from two braced perspex channels which simulate the two assumed methods of attaching the diaphragms. Good agreement is demonstrated.

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