Distortional buckling of I-beams by finite element method

Distortional buckling, unlike the usual lateral-torsional buckling in which the cross-section remains rigid in its own plane, involves distortion of web in the cross-section. This type of buckling typically occurs in beams with slender web and stocky flanges. Most of the published studies assume the web to deform with a cubic shape function. As this assumption may limit the accuracy of the results, a fifth order polynomial is chosen here for the web displacements. The general line-type finite element model used here has two nodes and a maximum of twelve degrees of freedom per node. The model not only can predict the correct coupled mode but also is capable of handling the local buckling of the web.

vertex effect in polycrystalline materials : simulation, a macroscopic model, and structural application

Polycrystal Plasticity, Yield-Vertex, Corner, Vertex-Effect, Microscale, Macroscale, Multiaxial, Torsional Buckling, Cruciform Column

Capacity of an I-beam made of S960 QC based on Eurocode 3

The capacity of beams is a very important factor in the study of durability of structures and structural members. The capacity of a high-strength steel I-beam made of S960 QC was investigated in this study. The investigation included assessment of the service limits and ultimate limits of the steel beam. The thesis was done according to European standards for steel structures, Eurocode 3. An analytical method was used to determine the throat thickness, deformation, elastic and plastic moment capacities as well as the fatigue life of the beam. The results of the analytical method were compared with those obtained by Finite Element Analysis (FEA). Elastic moment capacity obtained by the analytical method was 172 kNm. FEA and the analytical method predicted the maximum lateral-torsional buckling (LTB) capacity in the range of 90-93 kNm and the probability of failure as a result of LTB is estimated to be 50%. The lateral buckling capacity meant that the I-beam can carry a safe load of 300 kN instead of the initial load of 600 kN. The beam is liable to fail shortly after exceeding the elastic moment capacity. Based on results in of the different approaches, it was noted that FEA predicted higher deformation values on the load-deformation curve than the analytical results. However, both FEA and the analytical methods predicted identical results for nominal stress range and moment capacities. Fatigue life was estimated to be in the range of 53000-64000 cycles for bending stress range using crack propagation equation and strength-life approach. As Eurocode 3 is limited to steel grades up to S690, results for S960 must be verified with experimental data and appropriate design rules.

Response of Grilage-Like Structures by the Mobility Approach

This work presents an application of the Mobility Approach to the analysis of the power flow through grillage-like structures. Such structures are usually found in offshore platforms, supporting large and heavy machines. Different wave kinds (longitudinal, flexural and torsional) were initially considered in the power flow analysis between two beams joined in L. Beams excited by an in-plane point force showed strong coupling between longitudinal-flexural waves, while that for out-of-plane point force excitation, flexural-torsional waves coupling represents the most important mechanism of energy transmission. The response determination of grillages by the mobility approach requires the structure to be separated into simple beam-like structural components. Equations for rotations and displacements at the joints of all beams are written for as mobility functions, and moments and forces acting at the joints. A system of equations relating all such internal forces and moments is obtained. This approach was applied to simple grillages. Response results showed good agreement when compared to those provided by Finite Elements.

Kylmälaitekoneikon runkorakenteen kehittäminen

Kylmälaitekoneikot ovat kylmäkomponentteja sisältäviä rakenteita, joiden avulla toteutetaan suurten tilojen, kuten elintarvikemyymälöiden sisäilman jäähdytys. Lisäksi koneikkojen avulla jäähdytetään matalampiin lämpötiloihin pienempiä kylmähuoneita. Osa koneikoista ottaa talteen kylmäprosessissa syntyvän lämmön, jota hyödynnetään tilojen lämmityksessä. Tämän diplomityön tavoitteena oli suunnitella ja mitoittaa kahdeksalle eri kylmälaitekoneikolle entistä kustannustehokkaammat runkorakenteet, jotka ovat niin kestäviä, että koneikkoja on mahdollista pinota tilan säästämiseksi kolme päällekkäin. Lisäksi runkorakenteilta vaadittiin helppoa kuljetettavuutta, hyviä kiinnitysominaisuuksia ja korroosionkestävyyttä. Aluksi työssä selvitettiin runkorakenteisiin kohdistuvat vaatimukset, jonka jälkeen materiaalin valinta tehtiin materiaaliin kohdistuvien vaatimusten perusteella. Rakenteiden palkit mitoitettiin tarvittavan taivutusvastuksen ja kiepahduksen mukaan. Pilarit puolestaan mitoitettiin nurjahduksen ja kaksiaksiaalisen taivutustilan perusteella. Tämän jälkeen mitoitettiin eri sauvojen väliset hitsi- ja ruuviliitokset siten, että rakenne hajoaa ylikuormitustilanteessa mahdollisimman turvallisesti. Työssä tehdyt laskelmat varmennettiin elementtimenetelmän avulla ja lopullisille rakenteille tehtiin elementtimenetelmällä vielä ominaistaajuusanalyysejä. Lopuksi työssä suunniteltiin runkorakenteille sopiva korroosionsuojaus.

MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.

Global optimisation of cold-formed steel sections

In this thesis, standard algorithms are used to carry out the optimisation of cold-formed steel purlins such as zed, channel and sigma sections, which are assumed to be simply supported and subjected to a gravity load. For zed, channel and sigma section, the local buckling, distortional buckling and lateral-torsional buckling are considered respectively herein. Currently, the local buckling is based on the BS 5950-5:1998 and EN 1993-1-3:2006. The distortional buckling is calculated by the direct strength method employing the elastic distortional buckling which is calculated by three available approaches such as Hancock (1995), Schafer and Pekoz (1998), Yu (2005). In the optimisation program, the lateral-torsional buckling based on BS 5950-5:1998, AISI and analytical model of Li (2004) are investigated. For the optimisation program, the programming codes are written for optimisation of channel, zed and sigma beam. The full study has been coded into a computer-based analysis program (MATLAB).

MOLECULAR MASS MANIPULATION ENABLED BY GRAPHENE BASED NANOSTRUCTURES

The surge of interest in graphene, as epitomized by the Nobel Prize in Physics in 2010, is attributed to its extraordinary properties. Graphene is ultrathin, mechanically tough, and has amendable surface chemistry. These features make graphene and graphene based nanostructure an ideal candidate for the use of molecular mass manipulation. The controllable and programmable molecular mass manipulation is crucial in enabling future graphene based applications, however is challenging to achieve. This dissertation studies several aspects in molecular mass manipulation including mass transportation, patterning and storage. For molecular mass transportation, two methods based on carbon nanoscroll are demonstrated to be effective. They are torsional buckling instability assisted transportation and surface energy induced radial shrinkage. To achieve a more controllable transportation, a fundamental law of direction transport of molecular mass by straining basal graphene is studied. For molecular mass patterning, we reveal a barrier effect of line defects in graphene, which can enable molecular confining and patterning in a domain of desirable geometry. Such a strategy makes controllable patterning feasible for various types of molecules. For molecular mass storage, we propose a novel partially hydrogenated bilayer graphene structure which has large capacity for mass uptake. Also the mass release can be achieved by simply stretching the structure. Therefore the mass uptake and release is reversible. This kind of structure is crucial in enabling hydrogen fuel based technology. Lastly, spontaneous nanofluidic channel formation enabled by patterned hydrogenation is studied. This novel strategy enables programmable channel formation with pre-defined complex geometry.

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic-perfectly plastic. Condition of slip at the interfaces are determined by a Mohr-Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87-104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright (C) 2001 John Wiley & Sons, Ltd.

Effective Length K-Factors For Flexural Buckling Strengths Of Web Members In Open Web Steel Joists

Open web steel joists are designed in the United States following the governing specification published by the Steel Joist Institute. For compression members in joists, this specification employs an effective length factor, or K-factor, in confirming their adequacy. In most cases, these K-factors have been conservatively assumed equal to 1.0 for compression web members, regardless of the fact that intuition and limited experimental work indicate that smaller values could be justified. Given that smaller K-factors could result in more economical designs without a loss in safety, the research presented in this thesis aims to suggest procedures for obtaining more rational values. Three different methods for computing in-plane and out-of-plane K-factors are investigated, including (1) a hand calculation method based on the use of alignment charts, (2) computational critical load (eigenvalue) analyses using uniformly distributed loads, and (3) computational analyses using a compressive strain approach. The latter method is novel and allows for computing the individual buckling load of a specific member within a system, such as a joist. Four different joist configurations are investigated, including an 18K3, 28K10, and two variations of a 32LH06. Based on these methods and the very limited number of joists studied, it appears promising that in-plane and out-of-plane K-factors of 0.75 and 0.85, respectively, could be used in computing the flexural buckling strength of web members in routine steel joist design. Recommendations for future work, which include systematically investigating a wider range of joist configurations and connection restraint, are provided.

Torsional creep buckling of open tubes having arbitrary cross-section.

Mode of access: Internet.

Theoretical and experimental studies of unbraced tubular trusses allowing for torsional stiffness

This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.

Influence of nonlinear stiffness on the dynamics of a slender elastic beam under torsional oscillations

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams.

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.

Structural behaviour of glass reinforced plastics

The aim of this research is to promote the use of G.R.P. as a structural material. In the past, the use of G.R.P. has been confined to non-load carrying applications. Such uses are still rapidly increasing but in addition significant changes have been made during the last decade in the development of semi-structural and now even fully structural applications. Glass-reinforced plastic is characterized by a high strength but a relatively low modulus of elasticity. For this reasona G.R.P. structure can expect to show large deformations as a result of which the individual structural members will fail under load due to a loss of stability rather than approaching the ultimate strength of the material. For this reason the selection of the geometrical shapes of G.R.P. structural elements is considered to be an important factor in designing G.R.P. structures. The first chapter of this thesis deals with a general review of the theoretical and experimental methods used to describe the structural properties of G.R.P. The research programme includes five stages dealing with the structural behaviour of G.R.P. The first stage (Chapter 2) begins with selecting and designing an optimum box beam cross-section which gives the maximum flexural and torsional rigidity. The second stage of investigation (Chapter 3) deals with beam to beam connections. A joint was designed and manufactured with different types of fasteners used to connect two beam units. A suitable fastener was selected and the research extended to cover the behaviour of long span beams using multiple joints. The third part of the investigation includes a study of the behaviour of box beams subjected to combined bending, shear and torsion. A special torque rig was developed to perform the tests. Creep deformation of 6 m span G.R.P. was investigated as the fourth stage under a range of loading conditions. As a result of the phenomenon of post buckling behaviour exhibited in the compression flange during testing of box beams during earlier stages of the investigation it was decided to consider this phenomenon in more detail in the final stage of the investigation. G.R.P. plates with different fibre orientation were subjected to uniaxial compression and tested up to failure. In all stages of the investigation theoretical predictions and experimental results were compared and generally good correlation between theory and experimental data was observed.