Elastic Buckling Resistance Research Articles

Seismic design and analysis of truss‐confined buckling‐restrained braces

AbstractThe truss‐confined buckling‐restrained brace (TC‐BRB) with a varying or constant section truss confining system was proposed for applications of long span and large force capacities. Their feasibility and hysteresis behavior were examined through experimental investigations. This paper presents an original formulation of the elastic buckling resistance of the novel restraining system, considering the shear reduction effect. The findings indicate that the chord predominantly contributes to the flexural rigidity in the restraining system, while the post primarily contributes to the overall shear rigidity. Subsequently, the ultimate compressive strength of a TC‐BRB is evaluated, incorporating the effects of chord residual stress, length differences between the restrainer and entire brace, and initial in‐plane flexural deformation, based on available experimental data. A numerical procedure employing finite element model (FEM) analysis is introduced to simulate the mechanical characteristics of TC‐BRBs. The critical loads are verified through FEM analyses and test results. The failure mode observed in the numerical models is the instability of the chords near the midspan, as expected. A simplified approach for determining the ultimate compressive strength and design recommendations for TC‐BRBs are provided for engineering practice.

Elastic buckling analysis and optimization of thin-walled bamboo-like pipe beam subjected to pure bending

In this paper, a stiffening design imitating the bamboo node is proposed for weight reduction of the long composite pipe beam subjected to bending load. The distribution of bamboo nodes can efficiently suppress the ovalization of the section, thus significantly improving the bending resistance of the bamboo. Based on this principle, ring stiffeners are proposed to be fixed to the pipe beam, making the long beam equivalent to the combination of a series of short pipes that suffered less section ovalization. A database of the optimal laminate orientations for different normalized lengths is obtained through optimizations, where the discreteness of the ply count is considered. Based on this database, weight optimizations are conducted, and the optimal designs of beams with and without stiffeners are obtained and compared. The comparison results show that the proposed bamboo-like stiffened beam not only regains a near-linear load–displacement relationship, but also reduces the weight by up to 16% under the same buckling load. In addition, it is found that for the pipe beams with radius-to-thickness ratios of more than 18, increasing the radius leads to a decrease in elastic buckling resistance when the weight remains a constant, which is opposite to the design for strength and stiffness. The model and database developed in this paper can provide a reference for weight reduction design and weight estimation for composite pipe beams.

Effect of simplified wind girder modelling on MNA-LBA analysis of open steel tanks

The MNA/LBA design methodology for metal shells, including open-top tank steel shells, plays an important role in the European Standard on Strength and Stability of Shell Structures. However, when using this design format, particular doubts as to the correctness of the obtained results may arise when simplifications are used in modelling of key elements of tank structures in order to improve modelling and numerical calculation processes. This paper presents the results of numerical studies that address the question of how the simplifications in the modelling of the primary wind girder affect the values of the elastic buckling resistance and the plastic reference resistance determined from linear bifurcation analysis (LBA) and materially nonlinear analysis (MNA), respectively. Forty-two computational models of wind-loaded open storage tanks with three height-to-diameter ratios and with variable or constant wall thickness of a cylindrical shell, equipped with six different representations of the wind girder, were investigated in order to provide guidelines in the above-mentioned scope. It has been proven that the applied simplifications in the modelling of the primary wind girder allows for relatively faithful representation of the reference models, i.e. models in which the stiffening ring was modelled using shell finite elements, in the LBA analysis. In turn, a varied influence of the applied simplifications in modelling on the results of the MNA analysis was observed. The obtained results indicated a limited range of applicability of the results of the materially nonlinear analysis for the formal assessment of the relative overall slenderness of the considered shells. Finally the obtained results allowed for the formulation of practical conclusions for the purposes of design of open-top steel tanks using the MNA/LBA methodology.

Elastic compressive buckling resistance for back-to-back double angle assemblies

The present study investigates the elastic buckling resistance of compression members consisting of non-slender hot-rolled double angles connected back-to-back with discrete interconnectors. Towards this goal, the study (a) formulates a thin-walled beam finite element buckling solution that treats both angles as independent members away from the intermediate connector locations while constraining the displacements for both angles at interconnector locations, and (b) develops an extension of the Vlasov thin-walled beam theory, originally intended for monolithic members, to determine the effective torsional/warping sectional properties for back-to-back double angle members. The validity of the thin-walled beam finite element model is then verified against experimental results and shell finite element models and its predictions are shown to asymptotically converge to the Vlasov theory extension developed in the present study as the number of interconnectors is increased. A systematic parametric study consisting of 1250 finite element runs is then conducted and the database of results generated is used to propose a simple equation to predict the elastic compressive buckling resistance of double angle compression members.

Flexural-torsional buckling of high-strength steel beams

High-strength steel (HSS) is gaining widespread acceptance in contemporary engineering structures, with grades of up to 690MPa being included in many design standards. However, although strength grades well in excess of 690MPa are possible with modern metallurgical processes, these are not compliant with most design codes of practice. HSS is advantageous when strength, rather than stiffness, predominates the structural response. When this is the case, HSS is very useful in reducing the self-weight of the structure, as many be needed in structural modification, or in contriving a design that minimises the carbon footprint of the structure.Research on the flexural-torsional buckling of steel structures is extremely abundant in the literature, and guidance in codes is very comprehensive. It is known that the resistance to flexural-torsional buckling depends on the interaction of (i) elastic buckling; (ii) yielding and post-yielding and (iii) residual stresses. Current design curves are based on the elastic buckling resistance, which is modified to account for the yield and post-yield response of structural steel and the residual stresses in the cross-section. However, HSS with yield stresses exceeding 690MPa have somewhat different yield and post-yield characteristics and significantly different patterns of residual stresses when compared with structural steel.This paper uses ABAQUS software to investigate the flexural-torsional buckling strength of HSS I-section beams, by incorporating the stress-strain curves and residual stresses measured experimentally and reported in the literature. With a similar methodology to structural steel members, the interaction of elastic buckling at the member level with the material characteristics at the cross-sectional level is investigated and a strength design formulation is proposed.

EQUIVALENT MOMENT APPROACH FOR ELASTIC LATERAL-TORSIONAL BUCKLING OF TAPERED BEAMS

The assessment of the design buckling resistance of single members is usually based either directly on the elastic buckling resistance of the member or indirectly on its non-dimensional slenderness computed from the elastic buckling resistance. Specifically, Eurocode 3 buckling curves define the buckling reduction factors as a function of non-dimensional slenderness and, according to EC3 "General Method", these curves may also be used for non-uniform members. In this context, a new procedure will be presented for the computation of the elastic critical moment of tapered members. As is well known, the elastic critical moment strongly depends on both the bending moment diagram and end support restrictions. For uniform members, elastic critical moments may be computed using a relatively simple formula in which the bending moment distribution is taken into account by an equivalent uniform moment factor, and the end support restrictions are introduced through the buckling length. Unfortunately, this formula has not been extended to tapered members and, as a consequence, the elastic critical moment for tapered beams must be obtained using numerical methods such as the finite element methods. Based on a comprehensive parametric study for the elastic critical moment of tapered beams with different moment diagrams, this paper offers a new procedure, called the Equivalent Moment Approach, for the substitution of a tapered beam with any moment diagram by an equivalent uniform beam. One advantage of the present procedure is that closed form expressions valid for uniform beam can be generalized and used for tapered beams.

Distortional buckling of overhanging monorails

Abstract This paper is concerned with the elastic lateral-distortional (LD) buckling of overhanging steel monorail I-beams and its influence on their design strengths. Distortion of a slender web reduces the elastic buckling resistance of an intermediate length beam below its flexural-torsional (FT) resistance. A finite element computer program was used to study the elastic LD buckling of overhanging monorails with bottom flange loads at the free ends. The ratio M L D / M F T of the elastic LD to FT buckling moments decreased significantly as the flange width-to-thickness ratio b f / t f decreased, but varied only slightly with the web depth-to-thickness ratio b w / t w . The value of M L D varied almost linearly with the ratio of the supported span to the overhang length, and the effect of top flange torsional restraint at the exterior support on M L D was similar to that on M F T . Distortion effects were very small when there was no torsional restraint, but they increased significantly with the torsional restraint stiffness. The full plastic moment was often reached before M L D , especially for low values of b f / t f and high values of the torsion parameter K . Conservative approximations were developed for predicting the elastic LD buckling moments for ranges of sections, slendernesses, span ratios, and torsional restraint stiffnesses. A method of designing overhanging steel monorails against LD buckling was proposed and its use demonstrated by a worked example.

Lateral–distortional buckling of monorails

This paper is concerned with the elastic lateral–distortional (LD) buckling of single span steel monorail I-beams and its influence on their design strengths. The distortion of a slender web reduces the elastic buckling resistance of an intermediate length beam below its flexural–torsional (FT) resistance. A finite element computer program was used to study the elastic LD buckling of single span beams. The LD to FT buckling moment ratios were generally higher for simply supported beams with bottom flange central concentrated loads than for uniform bending, and lower for shear centre concentrated loads. For beams with bottom flange loading and unrestrained bottom flanges, there were very significant reductions in these ratios, but they increased when rigid web stiffeners or top flange torsional restraints were provided at the supports. For beams with bottom flange loading and unrestrained bottom flanges, the reductions in the elastic buckling resistance were greater for beams with stocky flanges than for slender flanges. Approximations were found for estimating the reduced resistances which were generally of high accuracy or conservative, and for estimating the increased resistances caused by elastic and rigid top flange end torsional restraints. A method of designing steel beams against LD buckling was proposed and its use demonstrated by a worked example.

Inelastic buckling and strengths of steel I-section arches with central torsional restraints

The elastic flexural–torsional buckling behaviour of arches with a central elastic torsional restraint has been reported elsewhere by the authors, and it was found that a central elastic torsional restraint restricts the buckling shape of an elastic arch and increases its elastic buckling resistance. However, both the inelastic buckling and strength of arches with a central elastic torsional restraint have hitherto not been investigated. It is not known whether the threshold stiffness for elastic buckling can be applied to arches which buckle inelastically, nor is it known how to determine the strength of steel arches with a central elastic torsional restraint. This paper modifies a finite element model for the nonlinear inelastic flexural–torsional analysis of steel I-section arches by including the effects of elastic restraints, and uses it to investigate the influence of central elastic torsional restraints on the inelastic flexural–torsional buckling and strength of steel I-section arches. It is found that a central elastic torsional restraint increases the strength of steel arches, but that the increase in strength decreases as the modified slenderness of the arches decreases. The threshold value of the stiffness of a central elastic torsional restraint at which the inelastic strength of an arch is equal to that of the corresponding arch with a rigid restraint is related to both the modified slenderness and included angle of the arch. For an arch with a low modified slenderness and with a small included angle which buckles inelastically, the threshold restraint stiffness is much smaller than that for an arch which buckles elastically. Design formulae for the strengths of steel I-section arches in uniform bending and in uniform compression with a central elastic torsional restraint are proposed. Comparisons with finite element results show that the proposed formulae provide good predictions for the strength of thin-walled steel I-section arches with a central elastic torsional restraint.

Elastic Flexural-Torsional Buckling of Discretely Restrained Arches

This paper presents a study of the effects of elastic discrete restraints on the elastic flexural-torsional buckling of arches in uniform bending and compression. It was found that established results for the elastic flexural-torsional buckling of restrained beams in uniform bending cannot be used directly for restrained arches in uniform bending, nor can those for elastic flexural or torsional buckling of restrained columns in uniform compression be used directly for restrained arches in uniform compression. Because of the curved profile of an arch, restraints are more effective in increasing the elastic buckling resistance of an arch than that of the corresponding straight member. Approximate formulas for the threshold values of the stiffness of the central torsional and lateral-translational restraints for a restrained arch in uniform bending and for the threshold value of stiffness of the lateral-translational restraints for a restrained arch in uniform compression at which the flexural-torsional buckling mode changes from being symmetric to antisymmetric are proposed. Approximate formulas for elastic flexural-torsional buckling resistance of centrally or end restrained arches in uniform bending and in uniform compression are also proposed. Finite element results show that these proposed formulas are accurate.

Distortion and Warping at Beam Supports

When a doubly symmetric I-beam buckles elastically in a lateral-distortional mode, its web distorts, so that the two flanges have increased relative lateral displacements and may have different twist rotations. The centroid, shear center, and principal axes of the distorted cross section are all different from those of the undistorted cross section. The end connections to adjacent members may induce flange restraining moments that oppose warping deformations and modify the elastic buckling resistance. This paper investigates the effects on the lateral-distortional buckling of beams of web distortion and of the warping restraints induced by end-support conditions. It is found that a doubly symmetric I-section becomes unsymmetric during lateral-distortional buckling and that web distortion reduces the effective torsional and warping rigidities. The proposed approximations for the elastic lateral-distortional buckling resistances of beams without and with end warping restraints provide good predictions. Equations for the warping restraint stiffness induced by some commonly used end conditions are established. Comparisons with ABAQUS shell element results show that they provide good approximations.

Optimisation of columns and frames against buckling

A simple method using the finite element analysis is presented for the optimum design of columns and frames to enhance the elastic buckling resistance of structures. From the results of finite element analysis, the effect on the fundamental buckling load due to the local modification of each element is assessed. Based on this assessment, an iterative procedure is set up for gradually shifting the material from the strongest part of the structure to the weakest part while keeping the structural weight constant. A simple procedure for bimodal and multimodal optimisation is also introduced. Numerical examples are included to demonstrate the efficiency and effectiveness of the proposed method for the optimum design of columns and frames with single modal, bimodal and trimodal buckling failures.

Pseudo-Cylindrical Shells: A New Concept for Undersea Structures

A new structural concept is proposed which offers promising new alternatives to the design of undersea pressure-resisting structures. This novel geometrical configuration consists of a concave polyhedral cylinder which exhibits stress distributions similar to those in “true” cylinders, but exhibits markedly higher elastic buckling resistance. Several undersea applications of this concept are suggested. Geometrical, stress, and stability properties have been examined by experimental and finite-element analysis.