Uniform Lateral Load Research Articles

Stresses in Short Noncircular Cylindrical Shells Under Lateral Pressure

This paper presents an analysis of the deflections of and stresses in a short noncircular cylindrical shell of uniform wall thickness whose median-surface cross section is described analytically by a simple expression corresponding to a family of doubly symmetric ovals. The cylinder is under a uniform lateral load and is simply supported at its edges. The small deflection analysis considered is based upon a series solution of appropriate differential equations of shell theory which leads ultimately to infinite sets of algebraic equations, truncated forms of which are considered. Numerical values of the significant stresses and displacements for points of the oval cylinder, which are 5 percent of the axial length and 2.5 percent of the circumferential length a part, have been calculated for an oval cross section with a major-minor axis ratio of 1.10.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Heat-Flux Distribution Over Hemispherical-Nosed Bodies in Hypersonic Flight

a simple and rapid matter. I t should be noted that the end moments MA and MB are given explicitly, and do not require the solution of a set of simultaneous equations as in reference 1. Curves, similar to Figs. 2 and 3, may be plotted for distributed uniform and triangular lateral loads and, by superposition, a limited number of plots may thus be used for a great variety of lateral load distributions. For the random, single, concentrated load W, the lateral load function JA(W) is given by

Creep Deflections and Stresses of Beam-Columns

Abstract A method of calculating the creep deflections and stresses of a beam-column is shown. The differential equation of equilibrium in terms of creep strain is solved by the method of integrating factors with Green’s function. For restrained and built-in ends, the end moments are found from the end conditions. An illustrative example is given for a beam-column of an ideal H-section with built-in ends and subjected to uniform lateral load. The deflection-time curve and flange stresses at different instants are shown.

A Note on Limiting Laminar Nusselt Number in Ducts With Constant Temperature Gradient by Analogy to Thin-Plate Theory

Abstract In this paper it is pointed out that the existing solutions for the deflections of thin plates under uniform lateral load and simply supported along all edges can be applied to the determination of the limiting temperature distributions in a fluid flowing in laminar motion in ducts of the same cross sections as those of the plates. The direct application of this solution is permissible only when (a) the axial temperature gradient is constant, with respect to both flow length and cross-section position. This implies uniform heating or cooling. (b) The cross section is a polygon. When the cross-section boundary contains curves, the constants of integration must be adjusted so that the boundary condition of nonslip flow is satisfied. Since the temperature and velocity distributions obtained by this analogy are expressed analytically, values of local heat transfer at any point in the cross-section boundary can be calculated. Examples are given for four cross sections, namely, rectangular, equilateral triangular, right-angled isosceles triangular, and semicircular. The heat-transfer distributions on the boundaries are calculated for square and equilateral triangular cross sections.

Bending of a thin elliptic plate of an orthotropic material under uniform lateral load

Der Verfasser lost das Biegeproblem fur eine dunne elliptische Platte aus orthotropem Material unter einer gleichmassigen Querlast. Er gibt Losungen fur zwei Hauptfalle an, namlich fur eingespannten und aufgelegten Rand, und zwar unter der Voraussetzung, dass die Symmetrieachsen des Materials nicht mit den Ellipsenachsen zusammenfallen. Als Beispiel wird eine Eichenplatte numerisch durchgerechnet, die parallel zu den Fasern geschnitten ist und das Achsenverhaltnis 3∶1 besitzt; die Ergebnisse werden mit denjenigen der isotropen Platte verglichen. *** DIRECT SUPPORT *** A1325009 00002

Study on Bending of Thin Aeolotropic Plates (2nd Report)

In the preceding paper, we obtained solutions for a circular plate of an aeolotropic material, subjected to uniform lateral load. In this paper, we introduce the general solution for a rectangular plate with clamped edges where the load is distributed over the surface of the plate in any way. Numerical solution for a simple example is also given.

Bending of a Thin Circular Plate of an Aeolotropic Material under Uniform Lateral Load (Supported Edge)

The bending problem is solved mathematically for a thin circular plate subjected to a uniform load. The material of the plate is assumed to have three symmetrical planes with respect to its elastic properties. The solution is carried out in the case when the edge is simply supported, and it involves some numerical calculations. An empirical formula for the deflection is also given in a simpler form.

Bending of Rectangular Plates Subjected to a Uniformly Distributed Lateral Load and to Tensile or Compressive Forces in the Plane of the Plate

Abstract This paper presents a method of determining the distribution of deflection and stress in simply supported rectangular plates subjected simultaneously to a uniform lateral load and to uniform tensile or compressive forces in the plane of the plate. The problems are of particular importance in the design of a ship’s bottom plating and, for this reason, graphs are given whereby the maximum stress and deflection may easily be calculated. Illustrative examples are included to demonstrate the use of these graphs. An example is also given to illustrate how the method may be extended to include the case of hydrostatic pressure.

The Orthogonally Stiffened Plate Under Uniform Lateral Load

Abstract The problem of designing structures with orthogonally stiffened plates under lateral loading has been solved approximately by the infinite-strip method and has been applied, for example, to the double-bottom structure of a ship. Under certain conditions where the side ratio, that is, the ratio of the longitudinal dimension to the transverse dimension, is small, the approximate solution is inadequate. The author gives herein an exact solution applicable to all side ratios.