Interactive buckling curves for thin-walled sections

The present paper continues to compare and analyse the most recent design codes formulae for interactive buckling of thin-walled members. A first analysis was performed using a statistical comparison between theoretical and experimental results and was presented at the SSRC Annual Technical Session, held in Pittsburgh. An analytic comparison between ECCS 1987, EUROCODE 3, AISI and the author's formula is performed. A proposal for a cross-sections classification from the point of view of an ‘erosion factor’ is also presented.     

Aesthetics of thin-walled structures

Thin-walled structures are assumed to include all ‘surface-acting’ structures. This is a brief review of the factors generally considered to influence our emotional and intellectual response to built forms. General problems arising from the strong forms and large plain surfaces of thin-walled structures are considered. A number of specific types are then treated under the headings of ‘bridges’, ‘shells’, ‘silos’, ‘tents’ and ‘air-supported structures’.     

Understanding imperfection-sensitivity in the buckling of thin-walled shells

The buckling of thin-walled shell structures under load is still imperfectly understood, in spite of much research over the past 50 years. In this paper the author traces the history of the ideas which have been deployed in order to shed light on what is often referred to as ‘imperfection-sensitive’ buckling behaviour of shells. The ideas, which recur in various combinations, involve interaction of competing buckling modes, nonlinear behaviour, the growth of initial geometric imperfections under load and the alteration of the distribution of membrane stress as imperfections grow. The author claims that there are strong grounds for supposing that ‘locked in’ initial stresses on account of imperfect initial geometry and the static indeterminacy of boundary conditions of real shells have a pronounced effect on the buckling performance. This effect has been ignored in the past, and is the subject of a current experimental study.     

Long-term performance of geocomposites used as highway edge drains

Prefabricated highway edge drains have been widely used in the USA since 1985. Laboratory testing and initial on-site evaluations have been generally positive, however long-term performance is an unknown. The major areas of concern are ‘blinding’ of the filter fabric that would prevent water from entering into the geocomposite and the ‘clogging’ of the core with fines. This paper presents the results of 72 randomly selected sites that were excavated in 3 states representing a total of 900 000 m (3 000 000 ft) of installed geocomposite edge drain.     

Minimum weight of cold-formed steel sections under compression

This paper presents a combined theoretical and experimental study on the minimum weight and the associated optimal geometric dimensions of an open-channel steel section with given length subjected to a prescribed axial compressive load. Sections both with and without lips are analyzed. The results obtained using a nonlinearly constrained optimization method are compared with those estimated from a simple-minded optimization procedure that assumes the simultaneous occurrence of all failure modes in a minimum weight structure. The types of failure mode considered include yielding, flexural buckling, torsional–flexural buckling, and local buckling. The failure criterion is based purely on compressive strength, with other possible design constraints (e.g. bending stiffness, minimum gauge and cost) ignored. The effects of end support conditions and restraint on torsional buckling are examined. The load capacity of a C-section calculated according to the 1998 British Standard Institution’s specifications on Structural Use of Steelwork in Building is used to check the validity of theoretical predictions. Finally, two new C-sections with lips were designed and manufactured based on the optimal results, and tested. Test results confirm the analytical predictions, with the optimal C-sections performing much better than the existing ones.     

Load-capacity estimation and collapse analysis of thin-walled beams and columns—recent advances

The present paper is devoted to the recent results of research in the area of load-capacity and post-failure behaviour of thin-walled beams and columns (among them thin-walled cold-formed profiles). It deals with ultimate load and collapse of box-section girders (tubes) of different cross-sections under bending, as well as of lipped and plain channel-section beam-columns. The paper contains the presentation of theoretical analysis and experimental investigation of plastic mechanisms of failure and collapse behaviour of these thin-walled sections. The short review of results obtained in recent years in general precedes those obtained by the Department of Strength of Materials and Structures, TUL. The problem of post-failure behaviour is solved using the rigid-plastic theory adopted and modified for the purposes of the solution taking into consideration strain-hardening of the member’s material. On the basis of experimental investigations theoretical models of plastic mechanisms of failure are produced for different sections. Theoretical analysis is based on the principle of virtual velocities. The problem is solved in an analytical–numerical way. The particular attention has been paid to the influence of the strain-hardening of the material after yielding upon the collapse structural behaviour and also to the influence of cross-section shape and dimensions on the character of collapse. The upper-bound estimation of the load-carrying capacity of analysed thin-walled sections by combining results of non-linear, elastic post-buckling analysis with the results of plastic mechanism analysis is carried out. Results are presented in diagrams showing post-failure curves as well as curves representing structural behaviour in the whole range of loading up to and beyond the ultimate load. Some results are compared with experimental results and those obtained from FE analysis. A comparison of lower- and upper-bound estimation of the load-carrying capacity is discussed and illustrated in diagrams. Conclusions dealing with the influence of strain-hardening phenomenon displayed by the material upon the load-carrying capacity and collapse behaviour of examined sections are derived. Also conclusions concerning different upper- and lower-bound estimations of the load-carrying capacity of analysed sections are presented.     

Interrupted interface on the cybernetics of digital design process

From the viewpoint of Batesonian cybernetics, ‘conscious purpose’ and ‘artistic process’ are distinct ends of a spectrum of the functioning of ‘self’. The conceptual stage of the design process is essentially an artistic activity unencumbered with accuracy, dimensionality, scale, program or even tectonics, albeit all of these maybe tacitly present at the ‘back of a designer's mind’. Artistic activities involve broad mental processes that are beneath the stratum of consciousness. By definition, consciousness is selective awareness; it is linear in execution and limited in its capability to synthesize complex parameters. One of the central questions of this paper is “if artistic process requires one to abandon, or relinquish conscious purpose at the time of the generation of the work of art, and if the early stages of artistic process is a result of a vast number of ‘unconscious’ forces and impulses, then how can the computer, which demands (and thus propagates) geometric precision, focused operation and rational execution, be part of that process?” This paper will explore how, cybernetically, the computer can be ‘coupled’ with ‘self’ (via a visual interface) and the artistic process. Three specially devised conceptual design exercises—namely BlurrDesign, BlinDesign and BlitzDesign—and three corresponding “interruptive” computer interface modifications were deployed in an introduction to digital media course. The results of this study are now under consideration for their effectiveness in promoting conceptual design using the computer, and how the ‘self’ might form a cybernetic whole with the machine. The findings could have implications in design pedagogy, informatics and interface design.     

Prestressed membrane structures — The ultimate thin-walled structure

Whilst for normal thin-gauge materials such as steel and aluminium, buckling is a problem when the ratio of unsupported width to thickness is perhaps in the order of 200 or so, membrane roof structures may behave satisfactorily with ratios of up to 50 000 and thus might be termed the ‘ultimate thin-walled structure’. All modern architectural membrane structures are prestressed to maintain a tensile state and to reduce deflections under applied loadings such as from wind. These forms of ‘soft shells’ are in two broad categories — the air-supported type and the tension type. This paper discusses the general design principles which are used to achieve exciting, visual and technologically intriguing forms with such high slenderness ratios.     

Numerical investigation of channel columns with complex stiffeners—part I: test verification

A numerical investigation on fixed-ended cold-formed steel channel columns with complex stiffeners subjected to axial load is described in this paper. The complex stiffeners of the channel sections consist of simple lips with return lips. The specimens were brake-pressed from high strength zinc-coated structural steel sheets having a nominal yield stress of 450 MPa. A non-linear finite element model is developed and verified against experimental results of fixed-ended channel columns with complex stiffeners. Initial geometric imperfections and material non-linearity are included in the model. The calibrated model is shown to provide accurate predictions of the experimental ultimate loads and failure modes of the tested columns.     

Compression tests on cold-formed steel columns with monosymmetrical section

This paper presents the results of an experimental study on cold-formed steel columns made at the Building Research Institute of Timisoara. The specimens were press-braked and their thickness ranged from 2 to 4 mm. Channel sections and lipped channel sections were tested, including columns and stub columns tests.

Theoretical ultimate capacities were determined by bdAISI, ECCS and Eurocode 3—Annex A specifications. Differences between designed and experimental values for these three methods are insignificant, and theoretical results are confirmed by experimental tests for stub columns. For columns, good agreement with theoretical predictions is obtained by applying the reduction coefficients for ultimate loads given in specifications. Both for columns and stub columns, the results are more conservative for channel than for lipped channel sections.     

Some comments on the numerical analysis of plates and thin-walled structures

The paper briefly reviews the theoretical analysis of plates structures that might exhibit multiple ‘loading paths’ and highlights the need for engineers using non-linear numerical modelling to be aware of the multi-mode phenomenon and to ensure that the modelling is set up in such a manner that the various ‘loading paths’ and possible changes of path would be incorporated in the modelling response. The paper presents a simple example of numerical analysis of thin-plate buckling that involves ‘coupled buckling modes’ and provides comments on suitable methods for defining in a simple and straightforward way the numerical modelling that could ensure that results from computer analysis describe the physically correct relationship between applied loadings and deformations of thin-walled structural components.     

On the upward movement of smoke and related shopping mall problems

The data of Morgan and his co-workers for the movement of smoke in 1/10 scale shopping malls are re-examined. This has been done to see how far a simple theoretical treatment based on plume theory and virtual sources (a basis for many calculation methods) can be exploited instead of the more complicated theory of sources of finite sizes. The work follows and extends the work of Law.

A number of theoretical relationships are used to correlate data and, in particular, they confirm Law's view that the data can be used to give plausible values for the positions of the virtual sources. Some of the complexities of the theory for finite strip sources may be bypassed if experiments are used for estimating the position of effective virtual sources. Experiments to locate the effective virtual source and the limiting asymptotic form of the theory (appropriate to line sources) can correlate and scale data to an accuracy satisfactory for fire engineering purposes. Various aspects of theory are discussed including the method of allowing for the ‘ends’ of finite strip sources, and the use of the theory of weak plumes for strong plumes.

There remains however a problem in reconciling the ‘near’ field of the plume rising around the balcony edge to the ‘far field’, but it is shown that the introduction of an exceptionally high local entrainment could — for these data — be avoided if: (a) the mass at any level in the plume is about 45% larger than expected from other laboratory experiments on plumes; or (b) there is extra entrainment due to the deflection and consequent disturbance as the plume strikes the ceiling; or (c) there is extra upward flow owing to radiation heating up the lower walls and floor as suggested by recent investigations. These matters await further investigation.     

An engineering approach to crashworthiness of thin-walled beams and joints in vehicle structures

The paper summarises the main points of the long-term engineering experience at Cranfield Impact Centre Ltd in the field of crashworthiness of thin-walled beams and joints in vehicle structures. Subjects covered are: the ‘hybrid’ approach to crashworthiness design/analysis (where beams and joints are treated separately from complete structures), the deep bending collapse of beams and joints from the points of view of static and dynamic testing and analytical prediction (models of hinge mechanisms, regression analysis, finite element analysis and from experimental databases). Use of the component properties in the simplified finite element analysis of complete structures is also presented. Illustrations are shown during the oral presentation.     

Interaction of breathing with the cumulation of damage in the webs of steel plate girders

The contribution describes the main results of two Prague experimental investigations into the ‘breathing’ of slender steel webs, the first of them focusing on web breathing under repeated partial edge loading and the other upon that under repeated shear. The effect of the initiation and propagation of cracks in breathing webs on the failure mechanisms and the ultimate load behaviour of steel plate girders is studied.     

Effect of pre- and postbuckling behaviour on load capacity of continuous beams

The nonlinear moment-curvature relationship of thin-walled beams, due to a combination of non-Hookean material behaviour and local buckling, inevitably leads to a ‘strain-softening’ component after a peak has been reached. Representation of this relationship in continuum mechanics leads to fallacious estimates of the static or incremental collapse load capacity of continuous beams. More realistic results are obtained when it is recognised that the moment-curvature relationship can only develop over a finite length associated with the half-wavelength of the final plastic buckle. It cannot develop over an infinitesimal length.     

Plastic strength of thin-walled plated members—Alternative solutions review

The paper presents results of the comparative theoretical study into plastic strength of thin-walled plated structures (plates and columns) using two different approaches: energy method and equilibrium strip method. Two types of members, a thin plate and a channel section column subjected to compression, were under investigation. Numerical results obtained using both methods, together with FE simulation are presented in load-deformation diagrams. Experimental verification of theoretical analysis (using two methods under investigation together with standards strength predictions) focused on stub columns (lipped channel sections) is presented.     

Risk based structural safety methods in context

Structural reliability calculations are now recognised by many as only one part of the assessment of structural safety. They provide partial evidence about the total problem which has to be integrated with other evidence to support decision making. It is proposed that a ‘holistic’ systems view based on a clear understanding of process is required. The model consists of interacting processes arranged in a hierarchy of differing levels of precision of definition and scope. The various attributes of each process are outlined under the generic headings of ‘who, what, why, where, when and how’. The ‘how’ attributes of a process which are important in the control of a process are hazard and risk. It is suggested that Interval Probability Theory is a suitable measure of the evidence that a process is being and will be managed to a successful conclusion. This can be combined with structural reliability predictions to give bounds on the evidence about the success of the total process which covers all foreseeable aspects of the uncertainty.     

Short vs. long column behavior of pultruded glass-fiber reinforced polymer composites

Analytical and experimental studies were conducted for the purpose of establishing a distinguishing criterion between short and long FRP composite column behaviors. The results of investigating 24 full-scale GFRP composite columns are presented. The experimental studies utilized specimens with commonly used ‘Universal’ and ‘Box’ cross-sections which were manufactured by the pultrusion process using E-glass fibers in various forms as reinforcement and polyester and vinylester as binding matrices. The effective slenderness ratios (L/r) of the investigated columns were 3.79, 32.7, 47.9, 63.1 and 75.4 for the ‘Universal’ section and 9.38, 53.9 and 78.9 for the ‘Box’ section. The specimen lengths were 18 inches (0.46 m), 8 foot (2.44 m), 12 foot (3.66 m), 16 foot (4.88 m) and 19.25 foot (5.87 m). All columns were tested in a vertical position and under compressive axial static loading and the fundamental pinned–pinned end-conditions. The columns’ compressive strains, buckling and crippling loads, lateral displacements, initial curvatures, and modes of failure were documented during the course of this investigation. Orthotropic mechanical properties of the composites were experimentally obtained utilizing 44 coupons cut from the column specimens. Analytically, Euler's formula was employed to obtain critical loads for the slender columns. For short columns, the classical plate theory was used to predict columns’ buckling loads. Based on experimental evaluations and analytical results, a slenderness ratio based criterion was established for distinguishing between short and long composite column behaviors. Further conclusions and design recommendations were made.     

Thin-walled cold-formed sections subjected to compressive loading

The weakening effects of local buckling on the compressive load carrying capability of thin-walled cold-formed sections is examined and discussed. Theoretical results are presented for the pin-ended support condition and a study is made of the local buckling and overall bending interaction behaviour of compression members with different cross-sectional shapes. It is shown that singly symmetric plain channel sections exhibit considerably different interactive equilibrium characteristics to those of I-sections for which the shear centre and section centroid are coincident.

The theoretical results given have been obtained through the solution of a differential equation which governs, approximately, the overall bending behaviour of a locally buckled compression member. Both local and overall imperfections are considered in the theoretical approach and it is shown that the effect of these is to reduce the ultimate compressive carrying capacity of cold-formed sections.

An experimental investigation of the behaviour of concentrically loaded pin-ended I-section struts and columns is reported and the findings from this are compared with theoretical predictions. The theoretical predictions of load-deflection equilibrium behaviour and stress variations with load are shown to be in good agreement with those obtained from test.

The provisions made in the UK Code of Practice and the American Specification pertaining to the design of cold-formed compression members are briefly outlined and compared. It is shown that with regard to I-section struts and columns the American design procedure gives, in general, more conservative estimates of collapse.     

Loading arrangement and structures, as one system—temporary instability of elements and structure

The paper deals with some special questions of experimental research being important when frames are tested and the load carrying capacity of the structure is lost because of any instability phenomena. Computer simulation results are presented:

• -to illustrat the difference between the real and ‘virtual’ structural behaviour, which is dependent on the character of loading, and

• -to show that in certain conditions a structure, which became unstable because of the instability of one of its elements, is able to turn to a stable state and to carry increasing loads before complete loss of its load carrying capacity.

This paper is a modified (slightly extended) version of that which was presented during the ‘First International Conference on Coupled Instabilities in Metal Structures’. Reflections of participants initiated some modification.