DEFLECTIONS OF AN INFINITE PLATE

1950 ◽  
Vol 28a (3) ◽  
pp. 293-302 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Elastic Foundation ◽  
Maximum Stress ◽  
Infinite Plate ◽  
Ice Sheets ◽  
Uniform Load ◽  
Circular Area ◽  
Concentrated Load ◽  
Loaded Plate ◽  
Simplifying Assumptions ◽  
Domain Of Validity

Problems associated with the thickness of ice sheets on Canadian lakes led the author to investigate mathematically the deflection of a loaded plate resting upon an elastic foundation. Certain simplifying assumptions, which appear to be not unreasonable, permit the solutions obtained to be applied to the strength of a floating ice sheet. Relations for maximum stress and maximum deflections in terms of known functions are derived, both for a concentrated load and a uniform load distributed over a circular area. The resulting expressions should be tested experimentally to determine their domain of validity. Owing to similarity of conditions, these results may also be applied to the design of concrete roadways and airport runways.

Bearing Capacity of a Coulomb Plate on Elastic Foundation

1975 ◽  
Vol 42 (1) ◽  
pp. 121-126 ◽  
Author(s):  
M. M. Mohaghegh ◽  
M. D. Coon
Keyword(s):  
Bearing Capacity ◽  
Elastic Foundation ◽  
Yield Criterion ◽  
Infinite Plate ◽  
Ice Sheets ◽  
Plate Material ◽  
Rigid Plastic ◽  
Plastic Bending ◽  
Coulomb Criterion ◽  
Plate On Elastic Foundation

The bearing capacity of an infinite plate resting on elastic foundation is determined assuming that the plate material is rigid-plastic satisfying the Coulomb yield criterion. The sandwich idealization of the plate is utilized and the Coulomb criterion is developed for this plate. The bearing capacity is determined using the method of limit analysis. The analysis shows that the plastic bending of the Coulomb plate is associated with the development of compressive forces which increase the limit moment and therefore the bearing capacity. An example of applying the analysis results is given by determining the bearing capacity of floating ice sheets.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

1954 ◽  
Vol 21 (1) ◽  
pp. 45-51
Author(s):  
Herbert Reismann
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Series Solution ◽  
Circular Disk ◽  
Symmetric Problem ◽  
Concentrated Load ◽  
Transverse Loads ◽  
Infinite Extent ◽  
Theory Of Plates ◽  
Pure Moment

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

Studies in collapse analysis of rigid-plastic plates with a square yield diagram

1957 ◽  
Vol 241 (1226) ◽  
pp. 311-338 ◽  
Keyword(s):  
Reinforced Concrete ◽  
Boundary Conditions ◽  
Upper Bound ◽  
Plastic Plate ◽  
Rigid Plastic ◽  
Concentrated Load ◽  
Arbitrary Boundary ◽  
Loaded Plate ◽  
Concrete Plate ◽  
Collapse Analysis

The collapse loads and mechanisms of a rigid-plastic plate with a square yield diagram, such as continuously reinforced concrete plate, are considered. Particular attention is paid to the case of a single concentrated load applied to a plate of arbitrary plan and with arbitrary boundary conditions. Upper-bound solutions are also given for a uniformly loaded plate of regular polygonal plan.

Loading Analysis and Mathematical Calculation for Arc Axis of the Exponential Function

2013 ◽  
Vol 834-836 ◽  
pp. 1382-1385
Author(s):  
Li Xiang ◽  
Zhu Feng ◽  
Zhai Qiu ◽  
Ruo Yin Zhang
Keyword(s):  
Exponential Function ◽  
Internal Force ◽  
Force Distribution ◽  
Shipping Industry ◽  
Uniform Load ◽  
Concentrated Load ◽  
Long Span ◽  
Mathematical Calculation ◽  
Dangerous Section ◽  
Loading Analysis

The concept of arch longitudinal beam wharf was brought out in the contemporary shipping industry of China as a result of the conflict between traditional high-piled wharfs and the increasing size of freights. Different alignments of arch axis will lead to different internal force distributions and the most dangerous section. A series of equations for the arch axis are derived through the transformation of the exponential function under a 40-meter-long span. Based on the analysis of equations affected by the combined force of uniform load and concentrated load, it is providing reference for engineers and analysts with the internal force distribution under some commonly used axis and the location of the most dangerous section for the archs.

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