Discrete Supports Research Articles

Elasto-plastic failure of locally supported silos with U-shaped longitudinal Stiffeners

Ranging from agriculture to food processing, from mining to industrial processing, all these sectors have a need for the temporary storage of (dry) powdered, granular, and bulk materials between different stages of all kinds of manufacturing processes and between manufacturing process and transportation, or vice versa. Silos are therefore the perfect solution to meet this need, because they can easily store large volumes on a relatively limited floor space. Frequently, silos have a circular platform and are placed in elevated position. The latter can be achieved by a limited number of discrete equidistant supports around the barrel circumference. However, in such cases, large loads have to be transferred to the limited number of supports, causing locally high axial compressive stress concentrations, and consequently premature failure due to plastic yielding and/or elastic buckling (depending on the thickness of the silo wall). A possible answer to avoid these problems is to provide a partial-height U-shaped longitudinal stiffener above each support. Such stiffeners allow for a more gradual load transfer to the supports, increasing the maximum failure load. This paper aims to map the influence of the dimensions of such longitudinal stiffeners (i.e. the parameters of the cross-section and the height) on the failure behaviour of thick-walled silos. All results and findings are based on geometrically and materially non-linear analyses or GMNA performed with finite element software. The simulations indicate that correctly, for thick-walled silos, failure will always occur by (elasto-)plastic yielding. Depending on the longitudinal stiffener cross-section, the location of failure will occur in the stiffened zone of the silo just above the supports for silos with stiffeners with a small cross-section, whereas for stiffeners with larger cross-sections, failure occurs in the unstiffened zone just above the terminations of the stiffeners. In addition, the stiffener width in circumferential and radial direction have respectively an advantageous and a disadvantageous influence on the failure load. Finally, the stiffener height only has a positive impact on the failure load when failure occurs in the unstiffened silo wall. This can be addressed to the distribution of the supporting force over the entire circumference with higher stiffeners.

Hanging tie study using the “moving deflection spectrum”

A hanging tie is a form of railroad track distress that occurs when voids have developed beneath the ties due to uneven ballast settlement and improper maintenance practices. It will lead to an increase in dynamic impact loading on the top of the ballast thereby further deteriorating the track structure. This paper proposes a fast, nondestructive screening method to identify the hanging tie problem. The method utilizes a dynamic track model to characterize the track’s “moving deflection spectrum” under different tie-supporting scenarios. The model includes a moving dynamic load and ties with discrete supports. The moving deflection spectrum shows dynamic responses of the “track moving deflection” in the frequency domain. The modeling results indicate that a significant discrepancy exists in the moving deflection spectrum depending on whether or not there is a hanging tie condition. To validate this method, preliminary field tests were carried out on both Boston Metro and St. Louis Metro lines. Then the moving deflection spectrum generated by the model is compared with the moving deflection spectrum in the field tests as measured by the accelerometers installed on a high-rail vehicle. Results show that the method is effective in identifying the hanging tie problem and has great potential to be employed by the rail industry in the future.

Evaluating the potential of a rolling deflection measurement system to estimate track modulus

Over the past two decades, a rolling deflection measurement system aiming to continuously measure the track modulus has been under development at the University of Nebraska – Lincoln under the sponsorship of the Federal Railroad Administration. This system measures the relative vertical distance (referred to as Yrel) between the rail surface and the rail/wheel contact plane at a distance of 1.22 m from the nearest wheel to the sensor system. The aim of this study was to investigate the potential of using the Yrel measurement as an indicator of the track modulus for various rail foundation conditions. To meet this objective, a detailed finite element model capable of simulating moving loads and track modulus variation was developed. One of the unique contributions of this study is that it presents a comprehensive study of the Yrel–track modulus relationship by defining more realistic support conditions using discrete spring supports and by simulating the stochastic nature of the track modulus along a 160-m track length. The numerical model was employed to examine the accuracy of estimating the track modulus using the Yrel measurements when foundation stiffness is variable. Furthermore, the correlation between the statistical properties of the track modulus and Yrel was studied over different track segment lengths.

CONSIDERATION ON TRUSS AND SPLICE JOINT DESIGN MODELS IN EXTREMAL LOADING

In this study the behavior of elements and joints in hard loaded Warren trusses is analyzed theoretically with the purpose of disclosing the sections and elements which possibly can become extremely stressed under the design load proposed being real before the ultimate limit state. The significance of truss topology selected has been brought forth, since unfavorable loading of a tensioned chord connection is discussed in this paper. Three types of tensioned splice joints have been examined considering expected elongations of bolts in order to determine additional stresses induced due to the redistribution of tensile forces. An assumption of a continuous beam model on elastically deformed discrete supports has been adopted as a design model for the examination of stresses possibly caused in the sections of bolts. It has been proved that a joint with extended end-plates over both flanges of chord I profile may be accepted as the one which is safe and robust enough for use in tensile chords of bearing structures. The joint type with end-plates extended over a more tensioned flange only and the one with connecting bolts all hidden between flanges has been subjected to sharp criticism due to the extremely nonuniform behavior and the overloading of bolts. The results of this numerical case study promote a deeper understanding and help assessing the endplate joint behavior since they lack the uniqueness of the solution recommended by the building codes, which is particularly significant when hard-loaded structures have been designed for covering the spans of public building areas.

Optimal stiffening configuration for locally supported cylindrical silos: Engaged columns

Cylindrical steel silos are often supported by discrete supports or columns to be able to provide a hopper and to facilitate emptying operations beneath the cylindrical barrel. The simplest mean of support for a light silo is by the use of engaged columns, without the use of unnecessarily expensive ring stiffeners. Such engaged columns gradually introduce the support load into the silo wall by shear, spreading the stresses in circumferential direction. In general, the highest axial compressive stress concentrations can be found in the shell wall in the vicinity of the top of the engaged column, resulting in failure due to excessive yielding and/or local instability.The study aims to identify the optimal combination of dimensions of an engaged column (i.e. the height, the widths in circumferential and radial direction and the thickness) to obtain a failure load as high as possible with as little material in the column as possible. An important condition is the requirement that the columns must withstand a higher load than the silo wall itself. In other words, failure should occur in the vicinity of the terminations of the columns (and not in the column itself). All results and conclusions are based on numerical finite element analyses.

Investigation of the effects of sleeper-passing impacts on the high-speed train

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.

Strength and stiffness requirements for intermediate ring stiffeners on discretely supported cylindrical shells

Silos in the form of a cylindrical metal shell are often supported on a ring beam which rests on discrete column supports. This support condition produces a circumferential non-uniformity in the axial membrane stresses in the silo shell. One way of reducing the non-uniformity of these stresses is to use a very stiff ring beam which partially or fully redistributes the stresses from the local support into uniform stresses in the shell. A better alternative is to use a combination of a flexible ring beam and an intermediate ring stiffener. Recent research by the authors has identified the ideal location of the intermediate ring stiffener to provide circumferentially uniform axial membrane stresses above the stiffener. To be fully effective, this intermediate ring should locally prevent both radial and circumferential displacements in the shell. This paper explores the strength and stiffness requirements for this intermediate ring stiffener. Pursuant to this goal, the cylindrical shell below the intermediate ring stiffener is analysed using the membrane theory of shells and the reactions produced by the stiffener on the shell are identified. These reactions are then applied to the intermediate ring stiffener. Vlasov's curved beam theory is used to derive closed form expressions for the variation of the stress resultants around the circumference to obtain a strength design criterion for the stiffener. A stiffness criterion is then developed by considering the ratio of the circumferential stiffness of the cylindrical shell to that of the intermediate ring stiffener. The circumferential displacements of the ring and the shell are found for the loading condition previously obtained to determine the required strength. A simple algebraic expression is developed for this intermediate ring stiffness criterion. These analytical studies are then compared with complementary finite element analyses that are used to identify a suitable value for the intermediate ring stiffness ratio for practical design.

RESEARCH OF STABILITY NONCENTRAL COMPRESSED OF COMPOSITE BAR

In a publication the decision of task of stability of the compressed bar is resulted with the use of model as the stratified system. The bars of the stratified beam are connected by resilient discrete supports (by slats) or resilient layer

ESTIMATES FOR SOLUTIONS TO DISCRETE CONVOLUTION EQUATIONS

We study solvability of convolution equations for functions with discrete support in , a special case being functions with support in the integer points. The more general case is of interest for several grids in Euclidean space, like the body-centred and face-centred tessellations of 3-space, as well as for the non-periodic grids that appear in the study of quasicrystals. The theorem of existence of fundamental solutions by de Boor et al is generalized to general discrete supports, using only elementary methods. We also study the asymptotic growth of sequences and arrays using the Fenchel transformation.

Buckling of cylindrical metal shells on discretely supported ring beams

Silos in the form of cylindrical metal shells are usually supported on evenly spaced columns in applications where an access space is needed for the discharge of contained solids. In large silos a ring beam is used to distribute the column forces into the shell. The presence of discrete supports results in a circumferential non-uniformity of axial stresses in the shell. This non-uniformity leads to high local stresses that must be considered in assessing the possibility of shell buckling. Design standards provide recommendations for the buckling of shells under uniform axial compression, but are largely silent concerning stress peaks that may vary in width. Designers must resort either to onerous finite element analyses that include both geometric and material nonlinearities with imperfections (GMNIA) or trust to their own judgment. This paper presents a parametric study to develop resistance or capacity curves which can be used directly in design without the need for complicated analysis. The proposed design method uses only hand calculations apart from a simple linear finite element analysis to determine the degree of non-uniformity in the axial stresses.

Elastic failure of locally supported silos with U-shaped longitudinal stiffeners

For practical considerations, thin-walled steel silos are often supported by a limited number of discrete equidistant supports around their circumference. In such cases, large loads are transferred to the limited number of supports, causing locally high axial compressive stress concentrations. A possible solution is to add a partial-height U-shaped longitudinal stiffener above each support. Such stiffeners create a more gradual transmission of vertical loads to the supports, increasing the maximum failure load. This paper aims to map the influence of the dimensions of such longitudinal stiffeners on the failure behaviour of a thin-walled silo. Both the parameters of the cross-section and the height of the stiffeners are discussed. All the results and the findings are based on geometrically and material nonlinear analyses — GMNA — performed with finite element software. The simulations indicate that, in general, thin-walled silos will fail by pure elastic buckling in the unstiffened silo wall above the terminations of the longitudinal stiffeners. However, this is only true if the cross-section of the stiffeners, and to a lesser degree the moment of inertia, is sufficiently large in order that the longitudinal stiffeners can absorb the supporting loads. In contrast, for longitudinal stiffeners with a small cross-section, the silo structure will fail by premature elasto-plastic collapse of the stiffeners itself at significantly lower load levels. Furthermore, the height of the stiffeners and the degree of support - the circumferential width of the supports and the stiffeners is equal to each other — are the most important geometrical parameters which are beneficial to reach a maximum load level for a specific silo. Finally, the buckling behaviour and the failure load are hardly influenced by radial width and the thickness of the longitudinal stiffeners.

Dynamic response of continuous beams with discrete viscoelastic supports under sinusoidal loading

Analysis of vibrations of continuous beams with discrete viscoelastic supports has been established through theoretical modeling and a finite element analysis. The theoretical model is based on the Euler–Bernoulli theory, and the Ritz approach was employed to obtain numerical results from which the attenuation of the beam׳s vibration was obtained. In parallel, a finite element analysis was carried out in ABAQUS using 3D beam elements. It is shown that the results of theoretical calculation agree well with those of the finite element analysis.Both models were applied to explore geometric and design variations, and then to a full model of a bridge expansion unit as an application example. The vibration of the beams in the design, the influence of the stiffness and the viscous damping coefficient of the supports were discussed, demonstrating the models׳ usefulness in helping with design optimization.

On Representing Information: A Characterization of the Analog/Digital Distinction

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported by examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice.

Ideal Location of Intermediate Ring Stiffeners on Discretely Supported Cylindrical Shells

Silos in the form of a cylindrical metal shell are commonly elevated to provide access to the space beneath, permitting the contained materials to be directly discharged. A few discrete column supports at evenly spaced intervals are commonly used. However, the structural design of discretely supported cylindrical shells presents a variety of challenges. The presence of discrete supports results in circumferential nonuniformity in the axial compressive stress as well as a progressive vertical decay above the support. Several approaches can be adopted in design depending on the severity of the nonuniformity of the stresses. Relevant research to date has focused mostly on the behavior of cylinders supported on brackets, local forces at the base, or stiff ring beams. The use of intermediate ring stiffeners to provide circumferential uniformity in the axial membrane stresses has long been recognized, but few studies have given a clear view of the practical requirements for such rings. In this paper, a combination of base and intermediate ring stiffeners is explored to develop a practical and cost-effective solution that leads to more uniformity in the axial membrane stresses above the intermediate ring stiffener. For the purposes of obtaining a simple analytical solution, the cylindrical shell is subjected to the fundamental harmonic of the column support and analyzed using membrane theory. It is shown that an ideal location exists for an intermediate ring stiffener such that the axial membrane stress above this ring is circumferentially completely uniform. The ideal location of this ring is determined analytically and is expressed in terms of the basic geometric variables. This ideal ring location is then independently verified using many linear finite-element analyses. A further study explores the effect of placing the intermediate ring stiffener below the ideal location. The results are presented in a manner that makes them suitable for direct adoption into traditional design specifications.

Transition wave in a supported heavy beam

We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models are examined and compared: (a) a uniform elastic beam on a distributed elastic foundation, (b) an elastic beam in which the mass is concentrated at a discrete set of points corresponding to the discrete set of the elastic supports and (c) a uniform elastic beam on a set of discrete elastic supports. Stiffness of the support is assumed to drop when the stress reaches a critical value. In the formulation, it is also assumed that, at the moment of the support damage, the value of the ‘added mass’, which reflects the dynamic response of the support, is dropped too. Strong similarities in the behavior of the continuous and discrete-continuous models are detected. Three speed regimes, subsonic, intersonic and supersonic, where the failure wave is or is not accompanied by elastic waves excited by the moving jump in the support stiffness, are considered and related characteristic speeds are determined. With respect to these continuous and discrete-continuous models, the conditions are found for the failure wave to exist, to propagate uniformly or to accelerate. It is also found that such beam-related transition wave can propagate steadily only at the intersonic speeds. It is remarkable that the steady-state speed appears to decrease as the jump of the stiffness increases.

Experimental and Numerical Investigations of Vibrations at a Railgun with Discrete Supports

Within the French-German Research Institute of Saint-Louis (ISL) railgun design, discrete supports in the form of steel bolts uniformly distributed along the length of the railgun counteract the repelling magnetic forces acting on the rails. In the past, numerical simulations on the structural mechanics of these setups have been performed. However, the establishment of the displacement amplitude during an experiment is the final goal. The first task to manage in this respect is the application of a sensor capable of sensing vertical rail displacements. Experimental investigations started at the ISL at a short-circuited railgun employing an optical (noncontact) method. However, this sensor turned out to be nonsuitable for the job due to its lack of a preferred axis. This became clear when comparative measurements with an accelerometer (a single-axis measurement device) were carried out. Consequently, in further experimental investigations, accelerometers were used, and the first experimental results were reported. Finally, the validity of the experimental results was proven by comparing with numerical calculations based on the 1-D and the 3-D models.

Analysis of the dominant vibration frequencies of rail bridges for structure-borne noise using a power flow method

The use of concrete bridges in urban rail transit systems has raised many concerns regarding low-frequency (20–200Hz) structure-borne noise due to the vibration of bridges when subjected to moving trains. Understanding the mechanism that determines the dominant frequencies of bridge vibrations is essential for both vibration and noise reduction. This paper presents a general procedure based on the force method to obtain the power flows within a coupled vehicle–track–bridge system, the point mobility of the system and the dynamic interaction forces connecting various components. The general coupling system consists of multi-rigid-bodies for the vehicles, infinite Euler beams representing the rails, two-dimensional or three-dimensional elements of the concrete bridges, and spring-dashpot pairs to model the wheel–rail contacts, the vehicle suspensions, the rail pads and the bridge bearings. The dynamic interaction of the coupled system is solved in the frequency domain by assuming the combined wheel–rail roughness moves forward relative to the stationary vehicles. The proposed procedure is first applied to a rail on discrete supports and then to a real urban rail transit U-shaped concrete bridge. The computed results show that the wheel–rail contact forces, the power flows to the rail/bridge subsystem and the accelerations of the bridge are primarily dominated by the contents around the natural frequency of a single wheel adhered to the elastically supported rail.

Numerical estimation of stresses in railway axles using a train–track interaction model

The fatigue design of railway axles requires that the stresses arising in the axle in real service are accurately quantified. This paper describes a method to compute the dynamic stresses arising in railway axles as the effect of train–track interaction, based on the numerical simulation of the dynamic interaction between a flexible wheelset and a flexible track. The wheelset is modelled as a flexible rotating body using an Eulerian approach, whereas track is regarded as an infinite periodic system with the rail modelled as a Timoshenko beam resting on discrete elastic supports, considering the inertia associated with the sleepers.The paper presents an application of the proposed procedure to the calculation of the dynamic stresses caused in the axle by different types of geometric imperfection occurring on the wheel and rail surfaces, considering the cases of a single harmonic rail corrugation, random rail roughness and a wheelflat.

Influence of the cylinder height on the elasto-plastic failure of locally supported cylinders

Frequently, steel silos are supported by discrete supports or columns to permit easy access beneath the barrel. In such cases, large loads are transferred to the limited number of supports, causing locally high axial compressive stress concentrations in the shell wall above the supports. If not dealt with properly, these increased stresses will lead to premature failure of the silo due to local instability in the regions above the supports. Local stiffening near the supports is a way to improve the buckling resistance, as material is added in the region of elevated stresses, levelling these out to values found in uniformly supported silos. The aim of a study on the properties of local stiffening will then be to increase the failure load, governed by an interaction of plastic collapse and elastic instability, to that of a discrete supported silo. However, during the course of such a study it was found that, although the failure remains local, the cylinder height is also a parameter that influences the failure mechanism, a fact that is not properly taken into account in current design practice and codes. This paper describes the mechanism behind the effect of the cylinder height on the failure load, which is related to pre-buckling deformations of the shell structure. All results and conclusions are based on geometrically and materially non-linear finite element analyses.

Numerical Analysis of Submerged Pipelines for Deep Water S-Lay

A mixed method to solve deep water S-Lay is presented. A singular perturbation technique is first used to determine the configuration of pipeline in the sagbend. The moment distribution of pipeline in the overbend is then determined by the nonlinear finite element method. The stinger is modeled as discrete supports in this study. Finally, an extensive parametric study is carried out to identify the optimal spaces of roller boxes for achieving minimum moment distribution of pipeline in the overbend.