Flexure of a Circular Plate With a Ring of Holes

1962 ◽  
Vol 29 (3) ◽  
pp. 489-496 ◽  
Author(s):  
H. Kraus
Keyword(s):  
Circular Plate ◽  
Shear Force ◽  
General Boundary Condition ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Moment Distribution ◽  
Theory Of Plates ◽  
Circular Holes ◽  
The Moment ◽  
Kirchhoff Theory

The problem of the moment distribution resulting from a uniform pressure load acting over the surface of a circular plate containing a ring of equally spaced circular holes with, and without, a central circular hole is solved within the framework of the Poisson-Kirchhoff theory of plates. A general boundary condition is applied at the outer rim of the plate to make the solution valid for a range of conditions from the simply supported case to the clamped case. The edges of the perforations are allowed to be either free or to have a net shear force acting. Numerical results in the form of curves are given for typical cases, and the results of a photoelastic test are also presented.

Numerical Simulations for Bending Moment Distribution on Linings of Tunnel Excavated by Shield

2015 ◽  
Vol 744-746 ◽  
pp. 1033-1036
Author(s):  
Zi Chang Shangguan ◽  
Shou Ju Li ◽  
Li Juan Cao ◽  
Hao Li
Keyword(s):  
Numerical Simulations ◽  
Axial Force ◽  
Shear Force ◽  
Bending Moment ◽  
Geological Data ◽  
Fem Model ◽  
Maximum Moment ◽  
Moment Distribution ◽  
Negative Moment ◽  
The Moment

In order to simulate moment distribution on linings of tunnel excavated by shield, FEM-based procedure is proposed. According to geological data of tunnel excavated by shield, FEM model is performed, and the moment, axial force and shear force distributions on linings are computed. The maximum moment on segments decreases while Poisson’s ratio of soil materials touching to segments increases. The moment value and distribution vary with Young’s modulus of soil materials. The maximum positive moment on linings is approximately equal to the maximum negative moment.

Bending stresses in thin circular plates with single eccentric circular holes

1976 ◽  
Vol 11 (4) ◽  
pp. 202-224 ◽  
Author(s):  
E Ollerton
Keyword(s):  
Circular Hole ◽  
Uniform Pressure ◽  
Plate Surface ◽  
Circular Plates ◽  
Concentrated Force ◽  
Simply Supported ◽  
Bending Stresses ◽  
Circular Holes

The bending stresses in thin circular plates having a single eccentric circular hole and small deflections are reported. The plates can have any mixture of clamped and simply supported boundaries, and can be subjected to a concentrated force uniformly distributed round the inner boundary, moments about two perpendicular axes, or uniform pressure on the plate surface. A previous paper (1)∗ has described the method of analysis using bipolar co-ordinates, and has given values for deflection and slope coefficients for varying diameter ratios and eccentricities under the loads described above. The present paper discusses the stresses found in the plates under the same conditions.

Bending of an Elastically Restrained Circular Plate Under Normal Loading Over a Sector

1958 ◽  
Vol 25 (1) ◽  
pp. 37-46
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Variable Method ◽  
General Boundary Condition ◽  
Single Treatment ◽  
Normal Loading ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Elastically Restrained

Abstract The complex variable method is used to find the deflection, bending and twisting moments, and shearing forces at any point of a thin circular plate normally loaded over a sector and supported at its edge under a general boundary condition including the usual clamped and simply supported boundaries. In this way separate treatments for these two cases are avoided and a single treatment is available.

Bending and Buckling of an Elastically Restrained Circular Plate

1952 ◽  
Vol 19 (2) ◽  
pp. 167-172
Author(s):  
H. Reismann
Keyword(s):  
Circular Plate ◽  
Classical Theory ◽  
Physical Significance ◽  
Buckling Loads ◽  
Simply Supported ◽  
Elastic Boundary ◽  
Theory Of Plates ◽  
Degree Of Restraint ◽  
Elastically Restrained ◽  
Clamped Edge

Abstract This paper considers the effect of an elastic boundary restraint upon the deflection, moments, and critical (buckling) loads of a circular plate. The solutions given are based on the classical theory of plates and are exact within the assumptions underlying this theory. They include, as particular limiting cases, the known solutions for the simply supported and rigidly clamped edge. The physical significance of the results obtained is discussed in detail with particular emphasis upon the degree of restraint along the clamped edge.

Girder moments in simply supported skew composite bridges

1996 ◽  
Vol 23 (4) ◽  
pp. 904-916 ◽  
Author(s):  
Tarek Ebeido ◽  
John B. Kennedy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Study ◽  
Distribution Factor ◽  
The Finite Element Method ◽  
Simply Supported ◽  
Moment Distribution ◽  
Composite Bridges ◽  
The Moment ◽  
Element Method

The evaluation of girder moments in composite bridges becomes more urgent with the trend to increasing truck loads. The method specified by the American Association of State Highway and Transportation Officials for such an evaluation depends only on the centre-to-centre girder spacing. This method does not account for skew and therefore is extremely conservative for skew composite bridges, since the presence of skew reduces the longitudinal moments in the girders. The method proposed by the Ontario Highway Bridge Design Code (OHBDC) depends on the longitudinal and transverse rigidities of the bridge in addition to the girder spacing. However, this method is limited to bridges with skew parameters less than a certain value specified in the code. In this paper, the influence of skew on the moment distribution factor is investigated. Furthermore, the influences of other factors such as girder spacing, bridge aspect ratio, number of lanes, number of girders, and intermediate transverse diaphragms on the moment distribution factor are examined. An experimental program was conducted on six simply supported skew composite steel–concrete bridge models. The finite element method was used for the theoretical analysis. Good agreement is shown between the experimental results and the theoretical results. In addition, the finite element method was employed to conduct an extensive parametric study on more than 300 prototype composite bridge cases. The data generated from the parametric study were used to deduce expressions for the moment distribution factor for OHBDC truck loading and for dead load. An illustrative example is presented. Key words: bridges, codes of practice, composite, distribution, moment, reinforced concrete, skew, structural engineering, tests.

scholarly journals Green's function of the clamped punctured disk

1977 ◽  
Vol 20 (2) ◽  
pp. 175-181 ◽  
Author(s):  
Mitsuru Nakai ◽  
Leo Sario
Keyword(s):  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
American Mathematical Society ◽  
Point Load ◽  
Thin Elastic Plate ◽  
Constant Sign ◽  
Boundary Circle ◽  
Simply Supported ◽  
Image Position

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.

The Method of Finite Differences in Solutions Concerning Circular Plate

2011 ◽  
Vol 490 ◽  
pp. 305-311
Author(s):  
Henryk G. Sabiniak
Keyword(s):  
Circular Plate ◽  
Finite Differences ◽  
Machine Building ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Technical Problems ◽  
Theory Of Plates ◽  
Worm Gearing ◽  
Mixed Derivatives ◽  
Plate Deflection

Finite difference method in solving classic problems in theory of plates is considered a standard one [1], [2], [3], [4]. The above refers mainly to solutions in right-angle coordinates. For circular plates, for which the use of polar coordinates is the best option, the question of classic plate deflection gets complicated. In accordance with mathematical rules the passage from partial differentials to final differences seems firm. Still final formulas both for the equation (1), as well as for border conditions of circular plate obtained in this study and in the study [3] differ considerably. The paper describes in detail necessary mathematical calculations. The final results are presented in identical form as in the study [3]. Difference of results as well as the length of arm in passage from partial differentials to finite differences for mixed derivatives are discussed. Generalizations resulting from these discussions are presented. This preliminary proceeding has the purpose of searching for solutions to technical problems in machine building and construction, in particular finding a solution to the question of distribution of load along contact line in worm gearing.

scholarly journals Impact Coefficient Analysis of Curved Box Girder Bridge Based on Vehicle-Bridge Coupling

2022 ◽  
Vol 2022 ◽  
pp. 1-11
Author(s):  
Fei Guo ◽  
Heng Cai ◽  
Huifang Li
Keyword(s):  
Shear Force ◽  
Primary Beam ◽  
Dynamic Loads ◽  
Box Girder ◽  
Impact Coefficient ◽  
Force Impact ◽  
Girder Bridge ◽  
The Moment ◽  
The Impact ◽  
Load Weight

In the current vehicle-bridge dynamics research studies, displacement impact coefficients are often used to replace the moment and shear force impact coefficients, and the vehicle model is also simplified as a moving-load model without considering the contribution of vehicle stiffness and damping to the system in some concerned research studies, which cannot really reflect the mechanical behavior of the structures under vehicle dynamic loads. This paper presents a vehicle-bridge coupling model for the prediction of dynamic responses and impact coefficient of the long-span curved bending beam bridge. The element stiffness matrix and mass matrix of a curved box girder bridge with 9 freedom degrees are directly deduced based on the principle of virtual work and dynamic finite element theory. The vibration equations of vehicle-bridge coupling are established by introducing vehicle mode with 7 freedom degrees. The Newmark-β method is adopted to solve vibration response of the system under vehicle dynamic loads, and the influences of flatness of bridge surface, vehicle speed, load weight, and primary beam stiffness on the impact coefficient are comprehensively discussed. The results indicate that the impact coefficient presents a nonlinear increment as the flatness of bridge surface changes from good to terrible. The vehicle-bridge coupling system resonates when the vehicle speeds reach 60 km/h and 100 km/h. The moment design value will maximally increase by 2.89%, and the shear force design value will maximally decrease by 34.9% when replacing moment and shear force impact coefficients with the displacement impact coefficient for the section internal force design. The load weight has a little influence on the impact coefficient; the displacement and moment impact coefficients are decreased with an increase in primary beam stiffness, while the shear force impact coefficient is increased with an increase in primary beam stiffness. The theoretical results presented in this paper agree well with the ANSYS results.

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