Introduction to the theory of plates stanford university. An orthotropic bridge or orthotropic deck is one whose deck typically comprises a structural steel deck plate stiffened either longitudinally or transversely, or in both directions. Mechanics of laminated composite plates and shells theory and analysis j. In particular, two typical structural configurations have been examined and results are discussed aiming at obtaining a simple procedure for primary supporting. Correlation between some stability problems for orthotropic and isotropic plates under biaxial and uniaxial direct stress volume 4 issue 1 w. A semianalytical threedimensional 3d elasticity solution for the vibration of the orthotropic plate is presented under arbitrary boundary conditions. Whilst an appropriate anisotropic plate theory has been available for some years very few studies of the shear buckling of other than special orthotropic plates appear to have been published. We will develop a twodimensional plate theory which employs the inplane.
Idealization of a planar structure, such as a plate, reduces the number of peridynamic interactions to be solved. It should be noted that proposed bimoment theory of plates presents a twodimensional theory of elastic orthotropic layer, which is. The second edition of the book includes details of developments in the design and construction of orthotropictype bridges. A rectangular orthotropic plate, with all edges simply supported, subjected to compression on its ends and a known compression or tension on its sides. Patel 9 introduces two variable refined plate theory for orthotropic plate analysis. The displacement model contains exponential terms in addition to classical plate theory terms. A nonclassical model for an orthotropic kirchhoff plate embedded in a viscoelastic medium is developed by using an extended version of the modified couple stress theory and a threeparameter foundation model. Steel plate deck bridges publisher cleveland, james f. Threedimensional 3d elasticity theory provides the theoretical support for the energy function of orthotropic plates. Orthotropic deck bridges theory and design of bridges. The methods were found to give very similar results.
This allows the deck both to directly bear vehicular loads and to contribute to the bridge structures overall loadbearing behaviour. Stress and strain, plane stress for specially orthotropic plates the previous section dealt with an extremely simple type of stress state, uniaxial. Contrary to this, it is possible to obtain plastic collapse load by applying rigid plastic mechanism analysis. Buckling analysis of orthotropic plates stiffened plate and steel sandwich plates. Aisc orthotropic plate design manual american institute. Aisc orthotropic plate design manual american institute of. Much attention is also given to orthotropic and stiffened plates and shells, as well as to multishell structures. The orthotropic deck may be integral with or supported on a grid of deck. A numerical solution for the clamped orthotropic plate equation is obtained. Intent and scope this report is intended only to be used as a quick reference guide on the mechanics of continuous fiberreinforced laminates.
The application of plate theory that is influence surfaces of plates has been taking more and more important roles in the design of bridge floor slabs. Applications to limited examples show that the methods have merit especially if means of handling very large systems of equations are utilized. Pdf as usage of plates, especially thick plates, are increased in. Orthotropic definition of orthotropic by merriamwebster. Aisc orthotropic plate design manual, engineering journal, american institute of steel construction, vol. An orthotropic deck is thin because the ribs nest between the. When modeling an orthotropic deck, a rough model could be built up with a plate element, considering different bending stiffness into the two principal directions. If the applied load acts either parallel or perpendicular to the fibers, then the plate is considered specially orehohropic.
Buckling of eccentrically stiffened orthotropic cylinders by david l. On the shear buckling of clamped narrow rectangular. On the peridynamic formulation for an orthotropic mindlin. Generalized integral transform solution for free vibration. So it is necessary to analyze this kind of problem using elasticity theory based rayleigh ritz method to evaluate for the most accurate behavior of frequencies of the plate. Mar 20, 2020 free vibration of orthotropic rectangular thin plates of constant thickness with two opposite edges clamped and one or two edges free is analyzed by generalized integral transform technique. Bernoulli beam theory, which exploits the slender shape of a beam. A nite element formulation for bending analysis of isotropic and. The erasmus bridge has an orthotropic deck for both its cablestayed bridge and bascule span. Orthotropic plates an overview sciencedirect topics. It includes a discussion of some the various applications of orthotropic bridge construction to provide background with case study examples. In the buckling analysis of the stiffened plate, five different methods where compared. In this dissertation the extension of the theory of influence surfaces to orthotropic plates are made the approach being based on the mathematical concept of greenvs function for the.
Consequently, solving equations have been inferred girkman, 1959. Balch division of mechanics and computation department of mecanical engineering stanford university stretching and bending of plates fundamentals introduction a plate is a structural element which is thin and. The purpose of this paper is to present a new theory for orthotropic plate analysis. Abstract in this paper, a modified couple stress model containing only one material length. In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat. Jul 25, 2017 a nonclassical model for an orthotropic kirchhoff plate embedded in a viscoelastic medium is developed by using an extended version of the modified couple stress theory and a threeparameter foundation model. Journal of the mechanics and physics of solids, vol. It includes a discussion of some the various applications of orthotropic bridge.
Pdf the thick orthotropic plates analysis methods, part i. The key component in obtaining the thinnest superstructure is the deck thickness. The structural system with which we are concerned is orthogonal anisotropic plate popularly termed orthotropic. The equations of motion and the boundary conditions are simultaneously obtained through a variational formulation based on hamiltons principle. For the orthotropic system, the direction must be specified. However, it is only the elastic behavior that an orthotropic plate model can simulate.
Generalized integral transform solution for free vibration of. The thick orthotropic plates analysis methods, part i. Appendix a orthotropic plate theory the orthotropic plate approach has two simplifying assumptions viz. An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core. Twodimensional orthotropic plate analysis for an integral. The governing equation of an orthotropic kirchhoff plate loaded transversely by a. A microstructuredependent orthotropic plate model based on a modified couple stress theory g. The results obtained by present theory are in excellent agreement with those of exact results and other higher order theories. After discussing the theory, the existing models and theories where compared including. A general theory of elastic and inelastic plate failureii. Semantic scholar extracted view of a mathematical theory of elastic orthotropic plates in plane strain and axisymmetric deformations by yi han lin. Theory 1, 0 can be used only for approximate calculation of force and deflections. In this study, a peridynamic plate formulation of an orthotropic plate with transverse shear deformation is proposed. In general, exact solutions for cantilever plates using plate theory are quite involved and few exact solutions can be found in the literature.
Bending theory for multilayer orthotropic sandwich plates. On solution of the problem of bending of orthotropic plates. The twovariable re ned plate theory can be used for thin and thick plates and predicts parabolic variation of transverse shear stresses. Zhu and law 6 analyzed the dynamic behavior of an orthotropic plate under moving load using lagrange equation. The danziger bridge of new orleans is a very large vertical lift bridge. Orthotropic definition is having the longer axis more or less vertical. It is assumed that a midsurface plane can be used to represent the threedimensional plate in twodimensional form. Theoretical formulations to obtain the free vibration information of orthotropic mindlin plate structures under general boundary conditions, the combination of the artificial spring technique together with rayleighritz method is feasible. For such plates the principal elastic axes are orthogonal to the plate geometric axes. An orthotropic deck may be the most expensive deck system per square meter in a shortspan bridge. Cheng introduction the solution of the planestress or planestrain problem for an infinite strip of orthotropic material was studied by green 7. In the present work, an exponential shear deformation theory is presented for orthotropic plate analysis. Offered bimoment theory of plates 8is described by two unrelated problems, each of which is form 5 ulated on the basis of nine twodimensional equations with corresponding boundary conditions.
A semianalytical threedimensional elasticity solution for. A nonclassical model for an orthotropic kirchhoff plate. A microstructuredependent orthotropic plate model based on a. Free vibration analysis of orthotropic rectangular mindlin.
For brevity, the derivation of the sandwich theory. Bhavani sankar, and raphael haftka university of florida, gainesville, florida 32611. Flexure of thick orthotropic plates by exponential shear. Pdf the thick orthotropic plates analysis methods, part. Keywords shear deformation, thick orthotropic plate, transverse normal strain, free vibration, frequencies. Orthotropic design meets cold weather challenges an overview of orthotropic steel deck bridges in cold regions. This paper focuses on the application of orthotropic plate bending theory to stiffened plating. Classical plate theory is based on its use of conventional isotropic thin. Reissner and stein provide a simplified theory for cantilever plates that is an improvement over older theories such as saintvenant plate theory. The theory was developed in 1888 by love using assumptions proposed by kirchhoff. The paper presents an unconventional generalized twodimensional theory of layered orthotropic plates. The numbers of unknown variables are same as that of first order shear deformation theory.
In the present work, the analysis of vibrational behavior of nonhomogeneous orthotropic rectangular plates with linearly varying thickness along one direction resting on winkler foundation on the basis of the classical plate theory have been investigated. The behavior of double bottom structure can be simulated by analytically modeling the double bottom as an orthotropic plate 8. The orthotropic deck consists of the deck plate, with a thickness of 12 mm. So why would the most expensive deck be a standard for the german railroads. On solution of the problem of bending of orthotropic. It is possible to refit a bridge originally designed with a concrete or nonstructural deck to use an orthotropic deck, which was first utilized in vancouvers lions gate bridge. Correlation between some stability problems for orthotropic. Unlike any other theory, the theory presented gives rise to only two governing equations, which are completely uncoupled for static analysis, and are only inertially coupled i. This manual covers the relevant issues related to orthotropic steel deck bridge engineering, including analysis, design, detailing, fabrication, testing, inspection, evaluation, and repair. Twodimensional orthotropic plate analysis for an integral thermal protection system oscar martinez. Numerically stable eigenfunctions in exponential function forms of eulerbernoulli beams with appropriate boundary conditions are adopted for each direction of the plate. A microstructuredependent orthotropic plate model based. Study the effect of thermal gradient on transverse.
The orthotropic plates which have the arbitrary boundary condition are realized by the way of arranging three sets of. In section 4 the analysis of the stiffened plate can be found and seen how well they. Application of the orthotropic plate theory to garage. This paper develops finite element techniques for applicability to plane stress problems and plate problems involving orthotropic materials such as wood and plywood. Applications to limited examples show that the methods have merit especially if means of handling very large systems of. Study the effect of thermal gradient on transverse vibration. Hence 4 is the amplitude of the total normal load applied to the plate per unit area and directed along y. Consider a clamped narrow rectangular orthotropic plate of length, width, and thickness, subjected to a uniformly distributed shear load per length figure 1. A new theory, which involves only two unknown functions and yet takes into account shear deformations, is presented for orthotropic plate analysis.
Schades design charts for rectangular plates are extended to the case where the boundary contour is clamped, which is almost totally incomplete in the afore mentioned charts. Manual for design, construction, and maintenance of. The second edition of the book includes details of developments in the design and construction of orthotropic type bridges. By continuous fiberreinforced laminates, the following is assumed. Langley research center langley station, hampton, va. Free vibration of orthotropic rectangular thin plates of constant thickness with two opposite edges clamped and one or two edges free is analyzed by generalized integral transform technique. Allowing for shear deformation in orthotropic plate theory proceedings of the institution of civil engineers, 483, pp.