Showing papers in "Thin-walled Structures in 1998"
TL;DR: In this article, a research program was carried out in co-operation with the aluminium industry in Norway to assess the crashworthiness of aluminium extrusions under axial loading conditions and to give experimental data for validation of a numerical model in the computer code LS-DYNA.
Abstract: In order to assess the crashworthiness of aluminium extrusions, a research programme was carried out in co-operation with the aluminium industry in Norway. The main objective was to study the behaviour of aluminium extrusions under axial loading conditions and to give experimental data for validation of a numerical model in the computer code LS-DYNA. In order to increase the energy absorbing capabilities of thin-walled aluminium members under axial loading, an experimental investigation was performed to study the combined behaviour of extrusions and aluminium foam.
171 citations
TL;DR: An analytical model to determine the behavior of thin steel plate shear walls was developed and is given in this article, where the model is capable of depicting the behaviour of walls with plates welded or bolted to the surrounding beams and columns of the building frame.
Abstract: Steel plate shear walls have been used in buildings in North America and Japan. Until recently, the design practice has been to limit the strength of the wall to the buckling strength of the plate. The post-buckling strength of thin plates subjected to shear has been recognized for more than 60 years, since it was outlined by Wagner in the early 1930s. Tests of a quarter and one third scale specimens of thin steel plate shear walls under cyclic loading were performed; the tests are described and the results are summarized. An analytical model to determine the behavior of thin steel plate shear walls was developed and is given. The model is capable of depicting the behavior of walls with plates welded or bolted to the surrounding beams and columns of the building frame. Comparisons between the analytical and experimental results are made.
115 citations
TL;DR: In this article, results of a numerical study on cyclic behavior of thin-walled steel structures are presented, and a series of proposed formulas are given to obtain the strength and ductility of various types of structures.
Abstract: In the present paper, results of a numerical study on cyclic behavior of thin-walled steel structures are presented. Analyses are conducted on steel plates with or without stiffeners, steel stub columns of pipe-sections, and steel cantilever columns of box or pipe sections. To trace with good accuracy the inelastic cyclic behavior of steel, a modified two-surface model developed at Nagoya University is employed for material nonlinearity. Discussions of the results are concerned with the cyclic behavior, strength and ductility of the structures. Especially, a series of proposed formulas are given to obtain the strength and ductility of various types of structures, and it is expected that the formulas are useful to researchers and practical engineers.
69 citations
TL;DR: In this paper, the authors describe the treatment of terrestrial shell structures in Eurocode 3: steel structures, and the axially compressed cylindrical shell is used as an example illustrating the range of real problems which need to be addressed and the paucity of current data on many aspects of these problems.
Abstract: Shell structures are widely used in a great variety of applications from space rockets to domestic food and drink containers. Civil engineers are principally concerned with steel shell structures such as silos, tanks, pipelines, chimneys, towers and masts, though other examples may be found in offshore structures and stadium roofs. This paper describes the treatment of terrestrial shell structures in Eurocode 3: Steel structures. It outlines the principles which are guiding the development of the standard, the range of applications covered, and some details of the current proposals. The axially compressed cylindrical shell is then chosen as an example illustrating the range of real problems which need to be addressed, and the paucity of current data on many aspects of these problems. This example is also used to outline the complexity involved even in this one area, recent progress and current needs.
68 citations
TL;DR: In this paper, the critical load is sensitive to the opening angle or circumferential size of the hole and the effect of the location and the number of holes on the stability of cylindrical shells with cut-outs.
Abstract: Experimental and numerical methods are used to study the stability problem of cylindrical shells with cut-outs. The paper presents parametric research of the shape (square, rectangular, circular), the dimensions (axial and circumferential sizes, diameter) of the hole. The effect of the location and the number of the holes are also studied. The analysis indicates that the critical load is sensitive to the opening angle or circumferential size of the hole. The function (critical load-opening angle) is linear for large openings and independent of the geometrical imperfections of the shell. However for small openings, it is necessary to take into account the coupling between the initial geometrical imperfections and the openings. The linear approach does not fit because of the importance of the evolution of the displacements near the openings. These results will be used for the development of European rules.
64 citations
TL;DR: In this article, the authors performed quasi-static and impact tests on round tubes of different sizes and made of aluminium and mild steel, both in as received and annealed conditions, and found that the presence of holes alters the mode of collapse of the tubes and as a consequence, affords the possibility of avoiding Euler buckling even when relatively much longer tubes are employed.
Abstract: Quasi-static and impact tests were performed on round tubes of different sizes and made of aluminium and mild steel, both in as received and annealed conditions. Length, diameter and thickness of these tubes were varied in different tests, and cut-outs in the form of circular holes varying in diameter were laterally drilled in them. Typical histories of deformation of these tubes and their load-compression curves are presented, and influence thereon of the annealing process, the tube size or the discontinuity present is discussed. It is seen that the presence of holes alters the mode of collapse of the tubes and as a consequence, affords the possibility of avoiding Euler buckling even when relatively much longer tubes are employed. Relations are presented for the computation of the peak load and the mean collapse loads in terms of the Vickers hardness number and the other parameters.
53 citations
TL;DR: In this paper, the importance of the slotted stud for the Light Steel Framing System is lighten up by a description of building components as exterior walls, interior walls and light weight floor structures.
Abstract: The development of the slotted steel stud made it possible to use steel in external walls in countries with cold climate, like Sweden. By slotting the web the thermal bridges are significantly reduced. Several fabricators of lightweight constructions in Scandinavia now have slotted studs in their range, intended for load-bearing external walls in single family houses and for infill walls in blocks of flats. The development of the slotted stud has also led to the development of the building system for residential called Light Steel Framing. This paper mainly considers design methods for slotted steel studs for external walls. The importance of the slotted stud for the Light Steel Framing System is lighten up by a description of building components as exterior walls, interior walls and light weight floor structures. The thermal properties, sound insulation, springiness and vibrations, fire proof are described as well as building services, architecture, planning and production.
52 citations
TL;DR: In this paper, a finite element analysis model for the post-local buckling behavior of cold-formed steel (CFS) members subjected to axial compression has been developed, which consists of a Total Lagrangian nonlinear 9-node finite element, and experimental-based material properties models to represent the body of the CFS sections.
Abstract: A finite element analysis model for the post-local buckling behaviour of cold-formed steel (CFS) members subjected to axial compression has been developed. The finite element model consists of a Total Lagrangian nonlinear 9-node “assumed strain” shell finite element, and experimental-based material properties models to represent the body of the CFS sections. Experimentally derived residual stress variations, and initial geometric imperfections have also been incorporated. A special loading technique and a displacement solution algorithm were employed to obtain a uniform displacement condition at the loading edges. Details of a test program involving 20 non-perforated, and perforated cold-formed stub-column steel sections have been presented in the second part of the paper. The comparison between the test results, and the finite element results was performed for axial and lateral displacement behaviour, buckling loads, ultimate loads, and axial stress distribution. The comparison forms the basis for the evaluation of the efficiency, and the accuracy of the finite element model, and it indicated that the finite element analysis model constructed herein gives accurate and consistent results for the behaviour of the cold-formed steel members subjected to axial compression.
44 citations
TL;DR: In this article, the authors used finite element analysis to quantify critical elastic response and imperfection sensitivity through numerical models, whose adequacy has been quantified through comparisons with test data, and developed a design approach for stringer-stiffened cones under compression, with a philosophy and format compatible with the European Shell Buckling Recommendations.
Abstract: In most shell buckling codes, guidance on the design of conical shells is restricted to unstiffened cones and even in this case the clauses are based on the procedures for cylindrical shells. Virtually no guidance is offered on stiffened cones and the particular characteristics of conical shells are not treated in detail. In this paper, use is made of finite element analysis to quantify critical elastic response and imperfection sensitivity through numerical models, whose adequacy has been quantified through comparisons with test data. The finite element results obtained were aimed at validating existing design recommendations for unstiffened cones and at developing a design approach for stringer-stiffened cones under compression, with a philosophy and format compatible with the European Shell Buckling Recommendations (ECCS).
41 citations
Journal Article•
TL;DR: In this article, a versatile spline finite strip method for analyzing the geometrically non-linear response of rectangular, composite laminated plates of arbitrary lay-up to progressive end shortening in their plane is presented.
Abstract: Description is given of a versatile spline finite strip method for analysing the geometrically non-linear response of rectangular, composite laminated plates of arbitrary lay-up to progressive end shortening in their plane. The plates are assumed to be thin, thus allowing the analysis to be based on the use of classical plate theory, and the non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumption. A number of finite strip models have been developed but attention is concentrated on a particular model whose displacement field uses cubic B-splines longitudinally and quadratic crosswise interpolation of the in-plane displacements. Description is given of the use of this model in applications involving plates which have simply supported ends and which either are made of homogeneous, isotropic material or of anistropic material or are laminates with unbalanced cross-ply or angle-ply lamination.
41 citations
TL;DR: In this article, an experimental investigation of the elastic-plastic degradation and collapse of steel tubes with square cross-section under cyclic pure bending in a curvature symmetric fashion is presented.
Abstract: This paper presents the results of an experimental investigation of the elastic–plastic degradation and collapse of steel tubes with square cross-section under cyclic pure bending in a curvature symmetric fashion. The results indicate that the structural performance of the tubes degrades due to the growth of periodic, transverse deflections in their flanges. The wavelength of these deflections is equal to the wavelength of the buckling mode of the tubes under monotonic pure bending. Persistent cycling induces localization of the amplitude of these deflections and leads to the formation of a kink in one of the flanges. This causes collapse of the tube.
TL;DR: In this article, the theoretical external pressure carrying behavior of edge-stiffened thin-walled cantilever shells is discussed with regard to both bifurcation and postbuckling phenomena.
Abstract: Open cylindrical steel tanks for the storage of liquids tend to be rather thin-walled because they are primarily designed for the circumferential tensile stresses from hydrostatic internal pressure. It is desirable to take advantage of the postbuckling strength of the thin cylindrical wall when designing the empty tank against wind load. The theoretical external pressure carrying behaviour of edge-stiffened thin-walled cantilever shells is discussed with regard to both bifurcation and postbuckling phenomena. For experimental verification, a series of postbuckling tests on cylindrical PVC and steel specimens with large radius/thickness ratio (r/t=2500) under internal underpressure and under a “wind-like” load arrangement has been carried out. Based on the numerical and experimental results, recommendations are put forward for an economic postbuckling strength design strategy. They are compared with existing design rules in tank codes.
TL;DR: In this paper, a new nonlinear strain-displacement theory for thin shells of general form was proposed, based on the nonlinear theory of three-dimensional solids.
Abstract: A basic building block in any numerical (geometrically) nonlinear and buckling analysis is a set of nonlinear strain–displacement relations. A number of such relations have been developed in the past for thin shells. Most of these theories were developed in the pre-computer era for analytical studies when simplicity was emphasized and terms judged to be small relative to other terms were omitted. With the availability of greatly increased computing power in recent years, accuracy rather than simplicity is given more emphasis. Additional complexity in the strain–displacement relations leads to only a small increase in computational effort, but the omission of a term which may be important in only a few complex problems is a major flaw. It is therefore necessary to re-examine classical shell theories in the context of numerical nonlinear and buckling analysis. This paper first describes a set of nonlinear strain–displacement relations for thin shells of general form developed directly from the nonlinear theory of three-dimensional solids. In this new theory, all nonlinear terms, large and small, are retained. When specialized for thin shells of revolution, this theory reduces to that previously derived by Rotter and Jumikis and others. Analytical and numerical comparisons are carried out for thin shells of revolution between Rotter and Jumikis' theory as a special case of the present theory and other commonly used nonlinear theories. The paper concludes with comments on the suitability of the various nonlinear shell theories discussed here for use in numerical buckling analysis of complex branched shells.
TL;DR: In this article, the effect of manufacturing variabilities, such as initial geometric imperfections and residual stresses, on elasto-plastic buckling response is investigated through parametric reliability studies of plate panels and cylinders under axial compression.
Abstract: For many years, a significant amount of research has been directed towards experimental modelling of thin-walled plates and shells, as well as towards the development of analytical and numerical methods to improve their design against buckling. This paper presents methodologies for probabilistic buckling analysis and reliability assessment of such structural components and examines the link between probabilistic and deterministic studies. In particular, the effect of manufacturing variabilities, such as initial geometric imperfections and residual stresses, on elasto-plastic buckling response is investigated through parametric reliability studies of plate panels and cylinders under axial compression.
TL;DR: In this article, an initial investigation of the collapse behaviour of thin-walled beams under concentrated loads applied through one or both flanges is carried out, and the analysis methods given in some current design specifications with respect to web crushing are outlined and compared.
Abstract: An initial investigation of the collapse behaviour of webs of thin-walled beams under concentrated loads applied through one or both flanges is carried out. The analysis methods given in some current design specifications with respect to web crushing are outlined and compared. Theoretical examinations of the behaviour of channel sections under single or two flange loading are derived and compared with the predictions of different design specifications. The theoretical investigations make use of simple Energy Analysis as well as finite strip and finite element examinations. A design approach which incorporates the European column curves is set out.
TL;DR: In this paper, a response surface design approach is used to approximate the failure response of curved composite C-section frames subjected to an axial tensile loading using a minimum number of finite element analyses.
Abstract: Curved frame structures are often used as part of the internal skeletal structure in aircraft. Laminated composite materials offer potential weight savings for such structures, but composite frames have different and more complex failure mechanisms than metallic frames. In particular, failure mechanisms involving interlaminar stresses are important in composite structures. Interlaminar stresses can be directly computed from three-dimensional finite element models, but the computational expense of these models is prohibitive. In this work, two- and three-dimensional (2D and 3D) finite element models are combined to reduce the computational expense associated with designing composite frames. A response surface design approach is used to approximate the failure response of curved composite C-section frames subjected to an axial tensile loading using a minimum number of finite element analyses. Results are presented for two examples with two and five design variables, respectively.
TL;DR: In this paper, the effect of axially loaded cylindrical shells on the load-carrying capacity of steel containments was investigated on the basis of numerical investigations, which were verified by experimental results of steel models.
Abstract: Cylindrical steel containments, like silos and tanks, frequently rest on column-supports, which induce high local axial forces into the shell. This causes pronounced stress concentrations, which might impair the shell by local yielding or buckling failure above the support. The load-carrying behaviour of such axially loaded cylindrical shells has been investigated in recent years resulting in proposals for design rules. However, in many practical cases the axial loading acts in combination with internal pressure caused by the filling medium of the containment, which induces circumferential (hoop) stresses in the shell. The effect of these stresses on the load-carrying capacity is the objective of this paper. The study was carried out on the basis of numerical investigations, which were verified by experimental results of steel models. The calculations, based on geometrically nonlinear analyses, include the effects of geometrical imperfections as well as material plasticity. The scope of the paper covers unstiffened cylinders with a radius/thickness ratio of 500 and the steel grade Fe 360 resting on four local supports.
TL;DR: In this paper, two independent shell buckling programs (BOSOR and INCA) were employed to calculate the internal buckling pressures for some test cases and the agreement between the results of the two programs is very good, with both programs predicting that buckling occurs.
Abstract: It was predicted recently that some complete toroidal shells of elliptical cross-section would buckle when subjected to internal pressure. As yet there is no experimental evidence for this, so two independent shell buckling programs (BOSOR and INCA) were employed to calculate the internal buckling pressures for some test cases. The agreement between the results of the two programs is very good, with both programs predicting that buckling occurs. Calculations were also carried out by using BOSOR on complete toroids having cross-sections in the form of prolate (k = a/b > 1.0) ellipses. The ranges of the parameters were: R/b = 4 and 10, b/t = 50, 100 and 200, and 1.3 < k < 2.5. The shells were assumed to be perfect, made from steel and to behave elastically. The buckling pressures and circumferential wavenumbers are given in tabular form and some are plotted graphically. The deformed shapes of some typical cross-sections prior to buckling are also illustrated, along with the buckling modes.
TL;DR: In this article, the spline finite strip method and the incremental time-space finite element procedure are used to analyse large amplitude vibration of plates with initial stresses, and two improvements for the procedure are presented.
Abstract: The spline finite strip method and the incremental time–space finite element procedure are used to analyse large amplitude vibration of plates with initial stresses. Two improvements for the procedure are presented. The free vibration and the internal resonance of plates with initial stress as well as the forced vibration of plates with damping and initial stress are computed. The results compared favourably with those available in other publications.
TL;DR: In this paper, the effect of knuckle size and length of the cylindrical flange on the buckling strength of externally pressurised torispheres with a sharp knuckle is examined numerically.
Abstract: The effect of knuckle size and length of the cylindrical flange on the buckling strength of externally pressurised torispheres with a sharp knuckle is examined numerically. Both elastic and elastic–perfectly plastic modelling is used. It is illustrated how sensitivity of the load-carrying capacity to the boundary conditions can be removed by the adoption of a large enough knuckle or a cylindrical flange of appropriate length. Experimental results available for the sharp knuckle domes are collected and 10 new tests are carried out on machined steel domes. Two tests on spun torispheres are also included. The tests demonstrate that the safety margin as used for externally pressurised hemispheres and deep torispheres is inadequate for sharp knuckle torispheres with a 6% knuckle.
TL;DR: In this article, the statistical characteristics (mean and variance) of cold-formed steel plates in uniform compression and pure bending are calculated and compared to deterministic approximations, based on existing experimental data, appropriate probability distributions are determined for the three random variables.
Abstract: The statistical characteristics (mean and variance) of the ultimate strength of cold-formed steel plates in uniform compression and pure bending are calculated and compared to deterministic approximations. Three quantities: plate thickness, longitudinal flexural residual stress magnitude and first mode imperfection magnitude, are treated as random variables. Based on existing experimental data, appropriate probability distributions are determined for the three random variables. The ultimate strength calculations are performed numerically using the finite element method (FEM). The statistical characteristics are calculated using two methods: Monte Carlo simulation and Taylor series approximation. The results are compared to the deterministic design approach of the American Iron and Steel Institute (AISI) Specification for the design of cold-formed structural members.
TL;DR: In this article, the effects of peripheral differential settlement on the shell are evaluated for the practical case of a tapering wall thickness in floating roof tanks which have a relatively flexible response to warping displacements.
Abstract: For economic reasons, foundations of large tanks for fluid storage tend to be shallow and may consequently suffer differential settlement under load. But these tanks are ductile and are able to tolerate limited settlement without distress. For an economic limitation of settlement, the structure should be analyzed rationally. In this paper, the effects of peripheral differential settlement on the shell are evaluated for the practical case of a tapering wall thickness in floating roof tanks which have a relatively flexible response to warping displacements. Previous research has centred on walls of uniform thickness, and is therefore of more limited relevance. Settlement of harmonic form is imposed at the base, and shell deformations and stresses determined in accurate finite element analysis. The significance of stresses in the primary wind girder, adjoining shell and at the bottom is assessed in relation to radial displacement at the top arising from the warping displacement. Results of recent laboratory tests particularly relevant to stress distribution are reported.
TL;DR: In this article, a new finite strip method for the analysis of deep beams and shear walls is presented, which adopts displacement functions possessing the right amount of continuity at the ends as well as at locations of abrupt changes of thickness.
Abstract: This paper presents a new finite strip method for the analysis of deep beams and shear walls The essence of the method lies in the adoption of displacement functions possessing the right amount of continuity at the ends as well as at locations of abrupt changes of thickness The concept of periodic extension in Fourier series is utilized to improve the accuracy of the stresses at the strip ends The equilibrium conditions at locations of abrupt changes of thickness are taken into account by the incorporation of piecewise linear correction functions As these displacement functions are built up from harmonic functions with appropriate corrections, they possess both the advantages of fast convergence of harmonic functions as well as appropriate order of continuity Numerical results also show that the method is versatile, efficient and accurate
TL;DR: In this article, the authors tried to simulate the buckling processes of shells computationally using path-following and stability criteria, which are necessary in order to carry out the two major tasks needed to be carried out in such a simulation, namely (1) tracing of the time history of structural response, and (2) application of appropriate perturbation in initial condition when a deformed state has become unstable, are first clarified.
Abstract: In this paper, we have tried to simulate the buckling processes of shells computationally. The two major tasks needed to be carried out in such a simulation, namely (1) tracing of the time history of structural response, and (2) application of appropriate perturbation in initial condition when a deformed state has become unstable in order to trigger the buckling process, are first clarified. We then proceed to the explanation about the tools, namely (1) path-following scheme, and (2) stability criteria, which are necessary in order to carry out the above two tasks. We have omitted the exposition about the path-following scheme and touched only on the stability criteria based on Liapunov's concept of stability. Finally, we show the results of simulation carried out on three examples of shell structures. From the results, it could be concluded that numerical simulation of buckling processes of shells is possible.
TL;DR: In this paper, the authors studied the effect of different imperfection shapes on the inelastic stability of liquid-filled conical tanks and determined the critical imperfection shape that would lead to the minimum limit load.
Abstract: The aim of this investigation is to study the effect of different imperfection shapes on the inelastic stability of liquid-filled conical tanks and to determine the critical imperfection shape that would lead to the minimum inelastic limit load. The study is carried out numerically using a self-developed shell element used to simulate a number of conical tanks having an imperfection shape in the form of Fourier series of equal coefficients. The Fourier analysis of the buckling modes indicates that the existence of axisymmetric imperfection will lead to the critical inelastic limit load for conical tanks.
TL;DR: A major research program on the interaction buckling behavior of thin-walled beam-columns has been performed over several years at the University of Sydney as discussed by the authors, which involved testing of slender cross-section square hollow sections (SHS) and thin-wall I-sections.
Abstract: A major research program on the interaction buckling behaviour of thin-walled beam-columns has been performed over several years at the University of Sydney. The program involved testing of slender cross-section square hollow sections (SHS) and thin-walled I-sections bent about both the major and minor principal axes. All sections tested experienced local buckling before overall buckling which involved flexural deformation for the SHS and I-sections bent about the minor principal axis, and flexural–torsional deformation for the I-sections bent about the major principal axis. The paper compares all of the test results with the design rules in the Australian Steel Structures Standard, AS4100:1998, Eurocode3, and the American Institute of Steel Construction Load and Resistance Factor Design Specification.
TL;DR: In this article, a method to reduce dynamic effects and suppress resonance effects in mass flow during silo emptying was proposed, which was verified with experiments and FE-calculations.
Abstract: Silo-quake can be observed in granular bodies during silo emptying in the form of dynamic effects as pulsations or shocks. Measurements were carried out in full-scale aluminium silos containing potato powder and polymer granulates, and in a model perspex silo containing different fills to investigate this phenomenon. Theoretically, dynamic effects in silos were analysed with a finite element method developed in the frame of a polar (Cosserat) continuum using an elastoplastic and a hypoplastic approach. The onset of a dynamic silo flow with controlled and free outlet velocity in a plane strain model silo was simulated. A reliable, practical method to significantly reduce dynamic effects and to suppress resonance effects in mass flow during silo emptying was proposed. It was verified with experiments and FE-calculations.
TL;DR: In this article, the authors present a method for inferring the complete pressure distribution from a large body of strain observations on the silo wall, and a simple practical example involving unsymmetrical loads is used to explore the effect of observation errors on the inferred pressures.
Abstract: A thin cylindrical shell structure which is subjected to local or unsymmetrical loading often displays a very complex pattern of response, involving multiple alternative potential failure conditions in different parts of the structure. The loading may therefore need to be defined with great precision. In the field of silo structures, it is widely recognised that such local loads often exist, but experimental observations of the patterns of load are very difficult to obtain because of the expense of instrumentation and the need to use full-scale testing to avoid granular solid scale errors. This paper presents a newly developed technique which permits these local unsymmetrical load patterns to be determined in a much more cost-effective way. In addition, because the loading is deduced from the structural response, the method has an inherent robustness in that when the deduced loadings are generalised and used to predict a structural response, it is more likely to be close to the real response. The same cannot be said for loading patterns deduced from single discrete observations of loading with imaginative interpolations between them, which form the basis of most current design rules. The paper describes a rigorous procedure for inferring the complete pressure distribution from a large body of strain observations on the silo wall. The method is outlined and a simple practical example, involving unsymmetrical loads, is used to explore the effect of observation errors on the inferred pressures. A sample set of pressures in a specially built full-scale test silo under eccentric solids discharge is also derived.
TL;DR: In this article, the UMR studies at the University of Missouri-Rolla (UMR) have focused on developing a better understanding of the behavior of cold-formed steel members and truss assemblies.
Abstract: Recent research studies at the University of Missouri-Rolla (UMR) have focused on developing a better understanding of the behavior of cold-formed steel members and truss assemblies. This research was initiated by the more widespread use of cold-formed steel in the residential construction market, and the need to provide structurally reliable, as well as highly economical design solutions. Steel trusses are commonly assembled using C-shaped sections and self-drilling screws. Based on UMR findings, appropriate design recommendations have been proposed for the web and chord members of a truss. Also of concern is the introduction of large holes in the webs of floor joists. To assess the effect of the web opening, a multi-phased research effort has recently been concluded. This paper summarizes the UMR studies, and the suggested design recommendations.
TL;DR: In this paper, the authors examined the buckling behavior of end supported cylindrical vessels when they were supported by two saddles and found that the stresses that cause buckling behaviour are the longitudinal and circumferential membrane stresses.
Abstract: Previous experimental work, by one of the authors, examined the behaviour of end supported cylindrical vessels loaded centrally. It was found that the vessels failed by buckling when the radius to thickness ratio (R/t) was greater than 150. These results provided the motivation for examining the buckling behaviour of such vessels when they are supported, in a more conventional way, by using two saddles. In the cases examined it was noted that the stresses that cause buckling behaviour are the longitudinal and circumferential membrane stresses. These occur at four vessel locations, i.e. the zenith and nadir (top and bottom) of both the vessel mid-span and the saddle centre profiles. Known buckling formulae based on simple loading patterns, such as an axially loaded cylinder and a cylinder under pure bending, will be utilized in determining the allowable buckling stress. Present British Code rules and European recommendations will also be discussed. The allowable buckling load will be compared with theoretical stresses obtained from a small displacement linear elastic analysis, using a Fourier series method. From these results a design method will be presented.