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- Instituto Politécnico de Bragança
- Universidade de Coimbra
- PERGAMON-ELSEVIER SCIENCE LTD
- Biblioteca Digitais de Teses e Dissertações da USP
- Elsevier
- Conselho Brasileiro de Oftalmologia
- Sociedade Brasileira de Oftalmologia
- The Brazilian Society of Mechanical Sciences
- Associação Brasileira de Ciências Mecânicas
- Universidade Federal do Rio Grande
- Journal of the South African Institution of Civil Engineering
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## A simple model for lateral torsional buckling resistance of steel I beams under fire condition – comparison with experimental results

Fonte: Instituto Politécnico de Bragança
Publicador: Instituto Politécnico de Bragança

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

37.24%

When a beam is bent about its axis of greatest flexural rigidity it may twist before it reaches its strength
limit state. This flexural stability limit state is most commonly referred to as lateral torsional buckling of a beam.
The twisting of the beam occurs when the compression flange becomes unstable as a result of its being subjected to
flexural induced axial stresses. Lateral torsional buckling is of importance when the compression flange is laterally
unsupported as is often the case in continuous beams, cantilever beams, frame beams and frame columns.
The aim of this work is to develop a simple model, i. e., an analytical method to be used by designers for the
calculation of the resistance moment of steel I-beams failing by lateral torsional buckling when submitted to the fire.
A particular attention has been paid to the possibility to use the same model as the one proposed in
Eurocode 3 – Part 1-1, simply modifying material properties according to the temperature. This is the procedure
currently proposed in Eurocode 3 – Part 1-2, although its accuracy has never been demonstrated and can indeed be
questioned. Due to the fact that higher temperatures usually develop at the end of the flanges than in the rest of the
section...

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## Lateral-torsional buckling of singly symmetric web-tapered thin-walled I-beams: 1D model vs. shell FEA

Fonte: Universidade de Coimbra
Publicador: Universidade de Coimbra

Tipo: Artigo de Revista Científica
Formato: aplication/PDF

ENG

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37.3%

#Lateral-torsional buckling#Web-tapered I-beams#One-dimensional model#Rayleigh-Ritz method#Shell finite element analysis#Pre-buckling deflections

This paper assesses the global performance and the underlying assumptions of a recently developed one-dimensional model characterising the elastic lateral-torsional buckling behaviour of singly symmetric tapered thin-walled open beams, which is able to account for the influence of the pre-buckling deflections. A comparative study involving the critical load factors and buckling modes yielded by (i) the one-dimensional model and (ii) two-dimensional shell finite element analyses (reference results) is presented and discussed. The results concern I-section cantilevers and simply supported beams (i) with uniform or linearly tapered webs, (ii) equal or unequal uniform flanges and (iii) acted by point loads applied at the free end or mid-span sections, respectively. In general, the one-dimensional predictions are found to agree well with the shell finite element results. Some significant discrepancies are also recorded (for the shorter beams), which are due to the occurrence of relevant cross-section distortion or localised buckling phenomena.; http://www.sciencedirect.com/science/article/B6V28-4MSR8K0-2/1/f7ad3ba3b8d3321ce16a83e7babb4007

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## Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

Fonte: PERGAMON-ELSEVIER SCIENCE LTD
Publicador: PERGAMON-ELSEVIER SCIENCE LTD

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

37.34%

#Buckling#Extensible rod#Elastic instability#Post-buckling#Method of multiple scales#BEHAVIOR#ELASTICA#Mechanics

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive...

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## Flambagem por distorção da seção transversal em perfis de aço formados a frio submetidos à compressão centrada e à flexão" ; Distortional buckling of cold-formed steel members under compression and bending.

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 09/04/2003
PT

Relevância na Pesquisa

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#cold-formed members#distortional buckling#estruturas de aço#flambagem distorcional#flambagem por distorção#perfis formados a frio#steel structures

Os perfis de aço formados a frio apresentam, em geral, elevada relação largura/espessura, tornando-os suscetíveis à flambagem local, caracterizada por uma flambagem de chapa, mas que também pode ocasionar um outro modo de flambagem, denominado flambagem por distorção, desconsiderado no dimensionamento de perfis laminados, mas que pode resultar crítico principalmente nos perfis com enrijecedores de borda e constituídos por aço de elevada resistência mecânica. Tal fenômeno é caracterizado pela perda de estabilidade do conjunto formado pelo elemento comprimido e seu enrijecedor de borda, alterando a forma inicial da seção transversal. Portanto, as normas mais atuais têm apresentado procedimentos para avaliar a resistência de barras com base na flambagem por distorção, como o procedimento simplificado da norma australiana AS/NZS 4600:1996, proposto por HANCOCK e que foi também adotado pela recente norma brasileira NBR 14762:2001, o método direto de resistência, recentemente proposto para incorporação à especificação do AISI (American Iron and Steel Institute) e a GBT (Generalized Beam Theory).Nesse trabalho é feita uma abordagem dos procedimentos propostos para a avaliação da flambagem por distorção em barras submetidas à compressão centrada e à flexão...

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## Lateral-torsional buckling of unrestrained steel beams under fire conditions: improvement of EC3 proposal

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

37.17%

The final draft of the EN version of part 1.1 of Eurocode 3 has introduced significant changes in the evaluation of
the lateral-torsional buckling resistance of unrestrained beams at room temperature that reduce the over-conservative
approach of ENV 1993-1-1 in the case of non-uniform bending.
Numerical modelling of the lateral-torsional buckling of steel beams at elevated temperature has shown that the
beam design curve from prEN 1993-1-2 is over-conservative for loadings other than uniform bending.
In line with the safety format of the lateral-torsional buckling code provisions for cold design, an alternative proposal
for rolled sections or equivalent welded sections subjected to fire is presented in this paper, that addresses the issue
of the influence of the loading type on the resistance of the beam, achieving better agreement with the real behaviour
while maintaining safety.

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## Refractive changes after scleral buckling surgery

Fonte: Conselho Brasileiro de Oftalmologia
Publicador: Conselho Brasileiro de Oftalmologia

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/10/2003
EN

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37.3%

PURPOSE: A prospective study was conducted to compare the refractive changes after three different types of scleral buckling surgery. METHODS: A total of 100 eyes of 100 patients were divided into three groups according to the type of performed buckling procedure: Group 1, encircling scleral buckling (42 patients); Group 2, encircling with vitrectomy (30 patients); Group 3, encircling with additional segmental buckling (28 patients). Refractive examinations were performed before and at 1, 3 and 6 months after surgery. RESULTS: Changes in spherical equivalent and axial length were significant in all 3 groups. The amount of induced astigmatism was more significant in Group 3. No statistically significant difference was found in the amount of surgically induced changes between Groups 1 and 2, at any postoperative period. CONCLUSIONS: All three types of scleral buckling surgery were found to produce refractive changes. A correlation exists between additional segments and extent of refractive changes.

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## Corneal topographic changes after 20-gauge pars plana vitrectomy associated with scleral buckling for the treatment of rhegmatogenous retinal detachment

Fonte: Sociedade Brasileira de Oftalmologia
Publicador: Sociedade Brasileira de Oftalmologia

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/04/2013
EN

Relevância na Pesquisa

37.17%

PURPOSE: To evaluate the changes in corneal topography after 20-gauge pars plana vitrectomy associated with scleral buckling for the repair of rhegmatogenous retinal detachment. METHODS: Twenty-five eyes of 25 patients with rhegmatogenous retinal detachment were included in this study. 20-gauge pars plana vitrectomy associated with scleral buckling was performed in all patients. The corneal topography of each was measured before surgery and one week, one month, and three months after surgery by computer-assisted videokeratoscopy. RESULTS: A statistically significant central corneal steepening (average, 0,9 D , p<0,001) was noted one week after surgery. The total corneal astigmatism had a significant increase in the first postoperative month (p=0,007). All these topographic changes persisted for the first month but returned to preoperative values three months after the surgery. CONCLUSION: Pars plana vitrectomy with scleral buckling was found to induce transient changes in corneal topography.

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## Buckling analysis of PVC sheets with RIB

Fonte: The Brazilian Society of Mechanical Sciences
Publicador: The Brazilian Society of Mechanical Sciences

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/01/2000
EN

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37.17%

This study has a technical and applied character. A PVC structured wall pipe can be produced by spirally winding a ribbed sheet having a male-female lock, chemically welded by an adhesive. These pipes are "flexible" and are used mainly in underground installations, to convey fluids in free duct regime. Initial studies have indicated that the buckling resistance of the ribs from the sheet coiling to the tube manufacturing is the critical design parameter. This study presents the theoretical analytical development in order to obtain the critical buckling moment of these sheets. This analysis uses concepts initially developed to calculate buckling resistance in monosymmetrical profiles that are very used in the metallic structure industry. Since the material used was PVC, that has different mechanical properties than steel and aluminum, it was necessary to consider the differences in the analytical treatment. It is important to emphasize that the results obtained are product of the co-operative work of engineers from industry and university.

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## A numerical investigation into the effects of parabolic curvature on the buckling strength and behaviour of stiffened plates under in-plane compression

Fonte: Associação Brasileira de Ciências Mecânicas
Publicador: Associação Brasileira de Ciências Mecânicas

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/09/2010
EN

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37.24%

#curved stiffened plate#parabolic curvature#eigenvalue buckling#Finite Element Method (FEM)#heavy and light stiffening

The main targets of this research are mainly divided in to two parts: (1) identifying the effects of parabolic curvature on the buckling strength and behaviour of stiffened plates under in-plane compression, (2) generating practical graphs for extracting eigenvalue buckling stress of parabolic curved stiffened plate to dimensionless parameters. A parametric model for study of the problem is created. The model includes different parameters related to plate, stiffeners and also parabolic curvature. Three distinct sensitivity cases are assumed. In each sensitivity case, many different models are analysed and their buckling strengths are obtained using a finite element commercial program (ANSYS). Buckling strength and behaviour of all models with different ratios of parabolic curvature are compared to each other.

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## Thermomechanical buckling oftemperature-dependent FGM beams

Fonte: Associação Brasileira de Ciências Mecânicas
Publicador: Associação Brasileira de Ciências Mecânicas

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/03/2013
EN

Relevância na Pesquisa

37.17%

Buckling of beams made of functionally graded materials (FGM) under thermomechanical loading is analyzed herein. Properties of the constituents are considered to be functions of temperature and thickness coordinate. The derivation of the equations is based on the Timoshenko beam theory, where the effect of shear is included. It is assumed that the mechanical and thermal nonhomogeneous properties of beam vary smoothly by distribution of the power law index across the thickness of the beam. The equilibrium and stability equations for an FGM beam are derived and the existence of bifurcation buckling is examined. The beam is assumed under three types of thermal loadings; namely, the uniform temperature rise, heat conduction across the thickness, and linear distribution across the thickness. Various types of boundary conditions are assumed for the beam with combination of roller, clamped, and simply-supported edges. In each case of boundary conditions and loading, closed form solutions for the critical buckling temperature of the beam is presented. The results are compared with the isotropic homogeneous beams, that are reported in the literature, by reducing the results of the functionally graded beam to the isotropic homogeneous beam.

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## Local/Distortional/Global buckling mode interaction on thin walled lipped channel columns

Fonte: Associação Brasileira de Ciências Mecânicas
Publicador: Associação Brasileira de Ciências Mecânicas

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/12/2014
EN

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37.34%

#Direct Strength Method#Distortional buckling#Global buckling#Lipped channel column#Local buckling#Local#Distortional#Global Interaction

The buckling behaviour of pin ended cold-formed steel lipped channel columns affected by local / distortional / global buckling mode interaction under axial loading is simulated by using finite element software ABAQUS, and the results are compared with the test results available in the literature. The comparisons show that the proper analysis model can simulate the buckling behaviour and ultimate capacity of cold-formed steel columns. Then a parametric analysis is carried out for 15 column geometries of 3 yield stress values of different dimension, thickness and lengths. The cross sectional dimensions and length of the specimen have been chosen such that to have almost equal local, distortional and global critical buckling stresses by using the CUFSM software. The selected sections also satisfied the limitations given for pre-qualified sections in Direct Strength Method (DSM). After comparing the FEM column ultimate loads with the estimates predicted by the current Direct Strength Method (DSM) design curves against local, distortional and global failures, which clearly shows that they lead to inaccurate and often very unsafe ultimate load estimates. At the end, a design recommendation is made for current design practice of evaluating the ultimate strength of the lipped channel columns.

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## Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/01/2014
EN

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#Analytical solutions#buckling analysis#Euler-Bernoulli beam theory#pseudo-dynamic analysis#von Kármán nonlinearity

Exact solutions of buckling configurations and vibration response of post-buckled configurations of beams with non-classical boundary conditions (e.g., elastically supported) are presented using the Euler-Bernoulli theory. The geometric nonlinearity arising from mid-plane stretching (i.e., the von Kármán nonlinear strain) is considered in the formulation. The nonlinear equations are reduced to a single linear equation in terms of the transverse deflection by eliminating the axial displacement and incorporating the nonlinearity and the applied load into a constant. The resulting critical buckling loads and their associated mode shapes are obtained by solving the linearized buckling problem analytically. The buckling configurations are determined in terms of the applied axial load and the transverse deflection. The first buckled shape is the only stable equilibrium position for all boundary conditions considered. Then the pseudo-dynamic response of buckled beams is also determined analytically. Natural frequency versus buckling load and natural frequency versus amplitudes of buckling configurations are plotted for various non-classical boundary conditions.

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## Geometric optimization based on the constructal design of perforated thin plates subject to buckling

Fonte: Universidade Federal do Rio Grande
Publicador: Universidade Federal do Rio Grande

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

37.3%

Elastic buckling is an instability phenomenon that can occur if a slender and thin-walled plate is subjected to axial compressive load. It is well known that the presence of holes in structural plate elements is almost inevitable in inspection, maintenance, and service purposes, or to reduce the structural weight. In this paper constructal design was employed to optimize the geometry of thin perforated plates submitted to elastic buckling. Simply supported rectangular perforated plates were analyzed with three different shapes of centered holes: elliptical, rectangular, and diamond. The purpose was to obtain the optimal geometry that maximizes the critical buckling load. The ratio between the height and length of the plate was kept constant, while the ratio between the characteristic dimensions of the holes was optimized for several hole volume fractions (φ). A finite-element model was used to assess the plate buckling load, and the Lanczos method was applied to the solution of the corresponding eigenvalue problem. When φ ≤ 0.20 the optimum geometry is the diamond hole, reaching maximum buckling loads around 80.0,21.5, and 17.4% higher than a plate without perforation and plates with elliptical and rectangular holes, respectively. For intermediate and higher values of φ...

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## Constructal design applied to the elastic buckling of thin plates with holes

Fonte: Universidade Federal do Rio Grande
Publicador: Universidade Federal do Rio Grande

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

37.24%

Elastic buckling is an instability phenomenon that can occur if a slender and thin plate is subjected to axial compression. An important characteristic of the buckling is that the instability may occur at a stress level that is substantially lower than the material yield strength. Besides, the presence of holes in structural plate elements is common. However these perforations cause a redistribution in plate membrane stresses, significantly altering their stability. In this paper the Bejan’s Constructal Design was employed to optimize the geometry of simply supported, rectangular, thin perforated plates subjected to the elastic buckling. Three different centered hole shapes were considered: elliptical, rectangular and diamond. The objective function was to maximize the critical buckling
load. The degree of freedom H/L (ratio between width and length of the plate) was kept constant, while H0/L0 (ratio between the characteristic dimensions of the holes) was optimized for several hole volume fractions (φ). A numerical model employing the Lanczos method and based on the finite element method was used. The results showed that, for lower values of φ the optimum geometry is the diamond hole. For intermediate and higher values of φ, the elliptical and rectangular hole...

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## Elastic and elasto-plastic buckling analysis of perforated steel plates

Fonte: Universidade Federal do Rio Grande
Publicador: Universidade Federal do Rio Grande

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

37.45%

Many steel structures such as ships and offshore structures are composed by welded stiffened or unstiffened plate elements. Cutouts are often provided in these plate elements for inspection, maintenance, and service purposes, and the size of these holes could be significant. In many situations, these plates are subjected to axial compressive forces which make them prone to instability or buckling. If the plate is slender, the buckling is elastic. However, if the plate is sturdy, it buckles in the plastic range causing the so-called inelastic (or elasto-plastic) buckling. Furthermore, the presence of these holes redistributes the membrane stresses in the plate and may cause significant reduction in its strength in addition to changing its buckling characteristics. So, the objective of this paper is to investigate the changes that the presence of circular holes
produces in the elastic and inelastic buckling of steel rectangular plates. The finite element method (FEM) has been used to evaluate the elastic and elastoplastic buckling load of uniaxially loaded rectangular plates with circular cutouts. By varying the hole diameter, the plate aspect ratio and the plate thickness during the analyses, the changes in the plate buckling behavior can be determined. The results show that while the circular hole can in some cases even increase the elastic buckling load...

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## Constructal design of perforated steel plates subject to linear elastic and nonlinear elastoplastic buckling

Fonte: Universidade Federal do Rio Grande
Publicador: Universidade Federal do Rio Grande

Tipo: Conferência ou Objeto de Conferência

ENG

Relevância na Pesquisa

37.37%

#Constructal design#Perforated steel plates#Linear elastic buckling#Nonlinear elasto-plastic buckling#Numerical simulation

Steel plates are used in a great variety of engineering applications, such as deck
and bottom of ship structures, and platforms of offshore structures. Cutouts are often
provided in plate elements for inspection, maintenance, and service purposes. So, the design
of shape and size of these holes is significant. Usually these plates are subjected to axial
compressive forces which make them prone to instability or buckling. If the plate is slender,
the buckling is elastic. However, if the plate is sturdy, it buckles in the plastic range causing
the so-called inelastic (or elasto-plastic) buckling.Therefore, the goal of this work is to obtain
the optimal geometry which maximizes the buckling load for steel plates with a centered
elliptical perforation when subjected to linear and nonlinear buckling phenomenon by means
of Constructal Design. To do so, numerical models were developed in ANSYS software to
evaluate the elastic and elasto-plastic buckling loads of simply supported and uniaxially
loaded rectangular plates with elliptical cutouts. The results indicated that the optimal shapes
were obtained in accordance with the Constructal Principle of "Optimal Distribution of
Imperfections", showing that the Constructal Design method can be satisfactorily employed in
mechanic of materials problems.

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## Medida do buckling e da probabilidade de fuga de nêutrons do núcleo do reator IPEN/MB-01; Determination of buckling and probability of leakage of neutron in the IPEN/MB-01 reactor in cylindrical configuration

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 24/09/2014
PT

Relevância na Pesquisa

37.46%

#buckling#curvatura do fluxo de nêutrons#fluxo de nêutrons#fuga de nêutrons#nêutron flux#neutron leakage#núcleo do reator#probabilidade de fuga de nêutrons#probability no leakage#reactor core

Um dos parâmetros fundamentais da física de reatores é a curvatura do fluxo de nêutrons (Buckling) do núcleo do reator. Ele está relacionado com outros parâmetros importantes, tais como as taxas de reação, potencia de operação, queima de combustível, entre outros. Num reator crítico, o Buckling depende das características geométricas e de material do núcleo do reator. Este trabalho apresenta os resultados do Buckling experimental para o reator nuclear IPEN/MB-01 em sua configuração cilíndrica com 28 barras de combustível ao longo de seu diâmetro. O IPEN/MB-01 é um reator de potência zero projetado para operar em uma potência máxima nominal de 100 watts. É uma instalação nuclear versátil que permite a simulação de todas as características de um grande reator nuclear e ideal para este tipo de medição. Foi realizado um mapeamento do fluxo de nêutrons no interior do reator e, assim, determinado o Buckling total da configuração cilíndrica. O reator foi operado durante uma hora para cada experimento. Em seguida, a taxa de reação nuclear das varetas de combustível foram medidas por espectrometria gama em um detector de germânio hiper-puro (HPGe) que escaneou as varetas axial e radialmente. Foram analisados os fótons gama do 239Np ( 276...

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## Modeling of reinforcement global buckling in RC elements

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artículo de revista

EN

Relevância na Pesquisa

37.5%

Artículo de publicación ISI; Buckling of longitudinal reinforcement in reinforced concrete (RC) columns or walls is commonly seen
with a length equal to the spacing between stirrups (local buckling), but experimental observations have
shown that the length of buckling can span a larger length, deforming several stirrups within the buckling
length (global buckling).
The behavior of the longitudinal reinforcement under compression resulting in global buckling is studied
in this work, based on a concentrated plasticity fiber model that considers four (4) plastic hinges. The
model was originally validated for local buckling and here is extended to global buckling by introducing
the effect of transversal reinforcement and expansion of the core concrete in the analysis. Modeling of the
forces from the stirrups acting on the longitudinal bar assumes that part of the force is transferred
directly to the expanding concrete core and the remaining force is balanced by internal stresses in the
longitudinal bar.
The bar buckling behavior is evaluated for different buckling length values and the length is chosen
such that it delivers the lowest maximum stress. The proposed model is validated by comparison of
the predicted buckling mode with experimental test results from the literature. The average error in
the mode prediction is 0.59 (about half the space between stirrups)...

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## Buckling of short cold-formed lipped channels in compression

Fonte: Journal of the South African Institution of Civil Engineering
Publicador: Journal of the South African Institution of Civil Engineering

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/08/2014
EN

Relevância na Pesquisa

37.24%

#cold-formed lipped channels#short columns#compressive resistance#local buckling#distortional buckling

ABSTRACT This paper presents an experimental investigation of short cold-formed lipped channel columns compressed between pinned ends. The short columns are subjected to pure axial compressive loading. Twelve column specimens are tested and the columns are categorised into three groups, depending on the length and thickness. The buckling modes of failure that occurred include local buckling and distortional buckling. A comparison of the experimental results with the loads predicted by the South African standard for the design of cold-formed steelwork (SANS 10162-2) shows that the code is not conservative enough to cater for these columns.

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## A rational approach to predicting the buckling length of compression chords in prefabricated timber truss roof structures braced by means of diagonal bracing

Fonte: Journal of the South African Institution of Civil Engineering
Publicador: Journal of the South African Institution of Civil Engineering

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/04/2012
EN

Relevância na Pesquisa

37.4%

In South Africa, timber-trussed roofs supporting concrete tiles have for many years often been braced solely by means of diagonal braces. Failures have shown that the diagonal brace was inadequate for larger span roofs, and the use of diagonal bracing has subsequently been limited to spans of less or equal to 10 m. When designing the compression chords of a timber truss in a braced roof, SANS 10163:1 (2003) recommends a minimum effective length for out-of-plane buckling of not less than 15 x b, which is 540 mm for a 36 mm wide member. This effective or out-of-plane buckling length of the top chord was later assumed to be equal to the spacing of the trusses. With the availability of PC-based packages that are able to perform three-dimensional buckling analyses, it is perhaps useful to investigate the validity of using the effective length equal to the truss spacing, and then also the 10 m limit on span for roofs braced by means of diagonal braces. A common error made when analysing three-dimensional buckling problems is to assume connectivity on the centreline of the members, thereby neglecting eccentricity between the centreline of the bracing and the centreline of the member being braced (see Figure 1). In timber-trussed roofs, the diagonal brace is nailed to the underside of the top chord of a number of adjacent trusses. The brace runs at more or less 45° and triangulation appears to be complete when viewed on plan...

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