bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bending of Pretwisted Beams
Authors: Zickel J. 
Published: June 2021

Abstract
The general theory of pretwisted beams and columns is applied to the bending of an initially straight and uniformly pretwisted beam of doubly symmetric thin-walled section. Pretwisting brings planes of various bending stiffness into play with a resulting stiffness which in a sense averages the stiffness of the beam in its principal directions. It is shown that compared with bending of an untwisted beam in its most flexible direction a thin strip can have its deflection in the plane of bending reduced 72 per cent by an initial twist of 0.83π. Simultaneously, however, lateral deflections of almost equal magnitude are induced. For pretwists above 2π, the lateral deflections become practically negligible and the deflections in the plane of bending are still reduced as much as 44 per cent. With increasing initial twist, however, the pretwisted beam becomes more flexible, and for an initial twist of 6.5π it is as flexible as the untwisted beam in its most flexible direction. Beams of equal flexibility in all directions simply become more flexible with initial twist, a fact which corresponds to the observations made by Den Hartog in some of his experiments.
Nutation of a Free Gyro Subjected to an Impulse
Authors: Plymale B. T. , Goodstein R. 
Published: June 2021

Abstract
It is the purpose of this paper to call attention to a particular gyro motion which has been observed and studied in our laboratories. The phenomenon is of extreme practical importance for all instruments which use a gyro as a space-stable element, and no published usable information has been found concerning it. A description and explanation of the motion will be presented. An Appendix contains the basic equations for the system and the results of approximate solutions.
Simplified Formulas for Boundary-Value Problems of the Thin-Walled Circular Cylinder
Authors: Pohle Frederick V. , Nardo S. V. 
Published: June 2021

Abstract
N. J. Hoff has presented formulas which can be used in the solution of boundary-value problems of circular cylinders. The purpose of this note is to express these results in exact simplified form; a more detailed investigation appears elsewhere. The notation will be that of Hoff, unless otherwise stated.
Combined Tension-Torsion Tests With Fixed Principal Directions
Authors: Davis E. A. 
Published: June 2021

Abstract
A series of combined tension-torsion-internal pressure tests, each with a different amount of torsion present, are discussed. The specimens were tested in such a manner that the principal directions of the increments of natural plastic strain were kept constant. These increments can be summed in various ways, the simplest of which would yield finite strains with fixed principal directions. The octahedral shearing-stress versus octahedral shearing-strain diagrams for the four specimens tested coincide quite closely. The principal directions of stress were measured at each increment of strain and found to agree well with those of the increments of strain.
Experiments Concerning the Yield Surface and the Assumption of Linearity in the Plastic Stress-Strain Relations
Authors: Naghdi P. M. , Rowley J. C. , Beadle C. W. 
Published: June 2021

Abstract
Combined tension and torsion experiments for six tubular 24S-T4 aluminum-alloy specimens with considerable initial anisotropy are reported. In all cases the results reveal the existence of corners on the yield loci of the material.
A Criterion for Minimum Scatter in Fatigue Testing
Authors: McClintock F. A. 
Published: June 2021

Abstract
When a number of fatigue tests are run on specimens with a longitudinal radius of curvature, there results a scatter in both the number of cycles to failure and the position of failure. A previous statistical analysis showed that if the variations in life are due solely to local inhomogeneities in the specimen, then there is a definite relation between the scatter in position of failure and the scatter in the number of cycles to failure. If the scatter in life significantly exceeds that corresponding to the scatter in position of failure, then there is some factor other than local inhomogeneities contributing to the scatter in life. Such other factors can be eliminated by improving the experimental technique. The usefulness of this criterion is illustrated by its application to crack detection tests on polycrystalline ingot iron.
A New Approach to the Analysis of Large Deflections of Plates
Authors: Berger H. M. 
Published: June 2021

Abstract
Simplified nonlinear equations for a flat plate with large deflections are derived by assuming that the strain energy due to the second invariant of the middle-surface strains can be neglected. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses for the circular plate and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.
Integral Methods in Natural-Convection Flow
Authors: Levy Salomon 
Published: June 2021

Abstract
This paper presents an evaluation of the range of application, accuracy, and usefulness of integral methods in natural-convection flow. The study reveals (a) that integral methods may be utilized to obtain approximate answers to free-convection problems whenever exact analytical solutions become too involved. Specific-flow examples considered here (natural convection from inclined plate, horizontal cylinder, arbitrary body, or within enclosed channels) confirm their adaptability to complicated configurations. (b) Over-all accuracy of the solutions is good. For inclined plates the derived equations reduce at high Grashof numbers to the correlation proposed and verified by Rich (1) while in the case of horizontal cylinders the results compare satisfactorily with the theoretical values of Hermann (2) and the accepted experimental relations (12). (c) The integral method of solution may be extended to apply to low Prandtl number fluids, laminar or turbulent flow, variable wall temperature, and convection within confined spaces.
Stress Distribution in Square Plates With Hydrostatically Loaded Central Circular Holes
Authors: Durelli A. J. , Barriage J. 
Published: June 2021

Abstract
The stress distribution in square plates with hydrostatically loaded central circular holes was determined using photoelasticity and brittle coatings. Photoelasticity was used to determine the maximum shear lines (isochromatics) and a brittle coating was used to determine the directions of the principal stresses (isostatics). The investigation was conducted for plates with holes producing seven ratios of the diameter to the square side (D/a). Curves are presented which show the distribution of the maximum shear stress along the axis and along the diagonal of the square plate, as a function of D/a, Figs. 3 and 4. The maximum principal stress along the exterior and interior boundaries as a function of D/a, Figs. 5 and 6, has also been given. A comparison is made of the stress ratios (σ1/P) at a point on the axis of the square at the interior boundary with that calculated for a thick-wall cylinder using Lamé’s equation, Fig. 1. Stress ratios (σ1/P) also are determined for a point on the diagonal of the square plate at the interior boundary, Fig. 8. A diffused-light polariscope was used. The loading jig consisted of rubber tubing in a grooved block. The photoelastic material (CR39) was calibrated automatically. No new methods are developed in the paper but it is felt that the use of the presently available methods has been simplified appreciably.
Free Vibrations of Thin Cylindrical Shells Having Finite Lengths With Freely Supported and Clamped Edges
Authors: Yu Yi-Yuan 
Published: June 2021

Abstract
Free vibrations of thin cylindrical shells having finite lengths are investigated on the basis of a set of three differential equations which are derived in a similar manner as Donnell obtained his equations for the bending and buckling problems. The equations can be solved readily after a simplifying assumption is introduced. In this manner the frequency equations are obtained for cylindrical shells with both edges freely supported, with both edges clamped, and with one edge freely supported and the other edge clamped. It is found that the lowest frequency given by the frequency equation is the smallest in the first case, larger in the third, and the largest in the second. The other two frequencies yielded by the frequency equation are approximately the same in all cases. As a result of the approximations, the characteristic equations for the three cases are found to be similar to the frequency equations for the lateral vibration of beams with similar end conditions. For the case of freely supported edges the normal functions obtained are identical in form with those assumed by Flügge and by Arnold and Warburton. For the same case, natural frequencies of one numerical example are computed by means of the present method, and the results are in good agreement with those obtained by these previous authors.
Some Solutions of the Timoshenko Beam Equations
Authors: Boley B. A. , Chao C. C. 
Published: June 2021

Abstract
Solutions are obtained by the method of Laplace transformation for four types of loadings applied to a semi-infinite beam. Numerical results are presented for two of these, both for suddenly applied and gradually varying loads. The effects of shear deformations and rotatory inertia are taken into account according to Timoshenko’s beam model. A comparison with the corresponding results of the Bernoulli-Euler theory are briefly presented.
Asymmetrical Bending of a Cylindrically Aeolotropic Tapered Disk
Authors: Baclig E. S. , Conway H. D. 
Published: June 2021

Abstract
Variations of thickness, anisotropy, and asymmetry of loading usually tend to increase the mathematical difficulty of obtaining solutions to the small-deflection problems of plate bending. However, for the bending of a cylindrically aeolotropic disk twisted about its diameter and having a certain thickness variation, it is possible to obtain a relatively simple solution in closed form. This solution is presented here, numerical results being given for oak and for isotropic material.
Analysis of Short Thin Axisymmetrical Shells Under Axisymmetrical Edge Loading
Authors: Horvay G. , Linkous C. , Born J. S. 
Published: June 2021

Abstract
On the basis of recent work by Hildebrand, formulas are established for the effects of axisymmetrical edge moments and edge shears on short shells of variable wall thickness and variable meridional curvature. While the formulas are inferior in accuracy to those developed for bolted flange assemblies by Waters, Rossheim, Wesstrom, and Williams, in simplicity of use and speed of calculations, they are on a par with the well-known Geckeler formulas, without being subject to many of the limitations of the latter. The formulas are particularly suited for the analysis of the tapered hub portion of a flanged shell. Other uses are also obvious. Particular applications to redundant shell (torus-type) problems will be given in a separate paper.
The Effect of the Earth’s Rotation on Laminar Flow in Pipes
Authors: Benton G. S. 
Published: June 2021

Abstract
The theory of laminar pipe flow has been developed, retaining the effect of the earth’s rotation. A secondary flow is set up in the pipe cross section which results in distortion of the usual parabolic profile. The distortion may be significant in pipes of moderate diameter. Laboratory studies tend to substantiate these conclusions.
Comparison of Slip-Line Solutions With Experiment
Authors: Thomsen E. G. 
Published: June 2021

Abstract
Plane-strain and axially symmetric approximate solutions for a perfect plastic are compared with experimental results obtained from the extrusion of a billet of commercially pure aluminum. The extrusion process was carried out at room temperature under essentially negligible external wall friction with a reduction of area of 87.8 per cent. It is found that the plane-strain solution is in good agreement with the experimental results, if a constant k = σ̄/2 = 20,000 psi (maximum shear stress for Tresca’s criterion) is substituted in the plane-strain solution. The flow stress (σ̄ ≅ 40,000 psi) was determined from a property test for the aluminum billet, at a strain equivalent to the uniform deformation in the extrusion (i.e., same area reduction without shear deformation). It is found that the Haar and von Karman yield condition is not valid for the present case, and further that the axially symmetric solution demonstrates no real advantage over the simpler plane-strain solution in predicting the stress distribution in an axially symmetric extrusion problem.
On the Ideally Plastic Indentation of Inset Rectangular Bands
Authors: Ross E. W. 
Published: June 2021

Abstract
One of the limit design theorems of ideal plasticity is applied to find an upper bound on the initial indentation pressure for the case where a flat, smooth die is pushed into an inset band of rectangular cross section. The dependence of the upper bound on the clearance and width of the band is given, and a possible extension to asymmetrically inset bands is suggested.
Stiffness of Curved Circular Tubes With Internal Pressure
Authors: Kafka P. G. , Dunn M. B. 
Published: June 2021

Abstract
A method is presented for computing the flexibility factor for plane pipe lines with internal-pressure effects considered. Formulas for the first and second approximation to both the flexibility and the stress-intensification factors are given. Comparisons of the second approximations with experimental results are also made.
Bending of a Uniformly Loaded Semicircular Plate Simply Supported Around the Curved Edge and Free Along the Diameter
Authors: Muster D. F. , Sadowsky M. A. 
Published: June 2021

Abstract
Within the limits of classical plate theory, a solution is obtained in series form for the problem of a uniformly loaded, semicircular plate, simply supported around the curved edge and free along the diameter. The solution, although singular at the corners, is otherwise analytic and amenable to numerical evaluation by electronic calculators. The solution results are compared to those obtained experimentally by Robinson and Huggenberger. The agreement is reasonable, when account is taken of the manner in which their empirical results were obtained.
On the Theory of the Acceleration Damper
Authors: Grubin Carl 
Published: June 2021

Abstract
The acceleration damper reduces the vibration of a mechanical system through momentum transfer by collision and conversion of mechanical energy into heat. A typical unit consists of a mass particle moving in a container fixed to the primary vibrating system. The direct problem is to determine the motion of a single-degree-of-freedom system with a damper, when the driving force is simple harmonic. The inverse is to determine the characteristics of a damper for reducing the vibration of the same system to a prescribed value. Numerical results indicate that the damper is most effective at resonance.
Time-Dependent Tangent Modulus Applied to Column Creep Buckling
Authors: Carlson R. L. 
Published: June 2021

Abstract
The relation of the time-dependent tangent-modulus load—as conceived by Shanley—to actual column capacity is clarified. It may be interpreted as a limiting case of the “allowable-load capacity” which has been shown to be a conservative estimate. The time-dependent tangent-modulus load is, therefore, an approximation to a conservative estimate. The approximation, however, may be either conservative or nonconservative when applied to imperfect or real columns. Typical cases are discussed and experimental results for two alloys are cited.
An Elastoplastic Thermal-Stress Analysis of a Free Plate
Authors: Weiner Jerome 
Published: June 2021

Abstract
The thermal stresses in a free plate of elastoplastic material subjected to a varying heat input over one face are determined. A heuristic solution is first found by suitable modifications of the known elastic solution. It is then verified that the solution satisfies all the conditions of the appropriate uniqueness theorem and represents therefore the unique solution to the problem. Residual stresses are determined and found to depend markedly on the peak magnitude of the heat input.
Impact With Finite Acceleration Time of Elastic and Elastic-Plastic Beams
Authors: Alverson R. C. 
Published: June 2021

Abstract
The purpose of the work described in this paper was to provide information on the elastic and plastic deformation of steel beams subjected to transverse impact. The particular impact problem treated was chosen to correspond to conditions in tests in which a beam initially at rest is struck by a massive hammer, so that a specified change of velocity is imposed at a certain cross section in a small time interval. In the present analysis the initial elastic and subsequent elastic-plastic motions were obtained by methods similar to those used by Bleich and Salvadori (3). As in (3), it is assumed that plastic deformation occurs only at a single stationary plastic hinge (in this case at the struck cross section). Results obtained are compared with those of a “rigid-plastic” solution of the same problem, in which plasticity conditions are correctly taken into account but elastic vibrations are not included.
Flexural Vibrations of Rectangular Plates
Authors: Mindlin R. D. , Schacknow A. , Deresiewicz H. 
Published: June 2021

Abstract
The influence of rotatory inertia and shear deformation on the flexural vibrations of isotropic, rectangular plates is investigated. Three independent families of modes are possible when the edges are simply supported. Coupling of the modes is studied for the case of one pair of parallel edges free and the other pair simply supported. The development of the coupling is traced by means of a solution for elastically supported edges. Special attention is given to the higher modes and frequencies of vibration which are beyond the range of applicability of the classical theory of thin plates.
Three “Neutral” Loading Tests
Authors: Gill S. S. 
Published: June 2021

Abstract
Three tests have been carried out using hollow tubes of alpha brass subjected to combined torsion and internal pressure. An initial torque was applied sufficient to cause plastic deformation, and then the torque was decreased and the internal pressure increased to keep the octahedral shear stress constant in two tests and the maximum shear stress constant in the third test. These loading paths were chosen because they would be neutral loading if the material obeyed the von Mises-Hencky or Guest yield criterion, respectively. Shear strain, axial, and circumferential strain were measured. All three tests gave some plastic strain during the “neutral” loading, but the constant maximum shear-stress loading gave much larger plastic strains than the constant octahedral stress loading. The plastic-strain increment vectors have been plotted to illustrate their direction relative to the loading path.
A Method for Determining the Flexural Effects of Statically Loaded Beams on Multiple Elastic Supports
Authors: Di Taranto R. A. 
Published: June 2021

Abstract
Herein is presented a means for calculating the static deflections, slopes, moments, and shears of a nonuniform beam on two supports for any end conditions and on three simple supports when subjected to concentrated loads and/or concentrated moments. The method is an extension of a simple tabular procedure as used by Myklestad (1) for use on a desk calculator or electronic digital computer. The procedure is such that it may be easily carried out by one who need not have any knowledge of beam theory. Influence coefficients may be easily and directly calculated for nonuniform beams on two and three elastic supports. The two-support beam is formulated for simply supported one overhang, two supports with linear and torsional springs, and fixed-fixed end conditions. Extensions of this method to any other boundary conditions are indicated.
Influence of Large Amplitudes on Free Flexural Vibrations of Rectangular Elastic Plates
Authors: Chu Hu-Nan , Herrmann George 
Published: June 2021

Abstract
In a recent paper (1) a set of plate equations was derived, which governs motions with small elongations and shears, but moderately large rotations, valid for an isotropic material obeying Hooke’s law. The resulting theory, which may be considered the dynamic analog of the von Karman plate theory, is applied presently to the study of free vibrations of a rectangular, elastic plate with hinged, immovable edges. The nonlinear equations are solved approximately by employing a perturbation procedure and also the principle of conservation of energy directly. The influence of large amplitudes on the period of free vibration and on the maximum normal stress is established. The free vibrations of a beam are studied as a special case and the resulting period compared with a previous investigation.
Kinematic Phenomena Observed During the Oblique Impact of a Sphere on a Beam
Authors: Goldsmith Werner , Cunningham D. M. 
Published: June 2021

Abstract
Experimental data relating to the kinetics of oblique impact of 1/2-in-diam steel sphere upon steel beams at initial velocities ranging from 30 to 150 fps are presented. The variation of beam deflection, contact duration, trajectory of the sphere, and contour topography with angle of incidence, beam size, and initial velocity have been determined, and the velocity of propagation of several waves has been ascertained.
Electronic Analog Computer Solutions of Nonlinear Vibratory Systems of Two Degrees of Freedom
Authors: Atkinson C. P. 
Published: June 2021

Abstract
The main contribution of this paper is its account of the use of an electronic differential analyzer for solving the exact differential equations of certain two-degree-of-freedom nonlinear vibrating systems, and the comparison of the differential-analyzer solutions with the approximate analytical solutions obtained from a single-term harmonic approximation (Ritz approximation). The results of these two methods for solving nonlinear differential equations compare favorably over much of the ranges of variables. Where discrepancies arise between the results of the two methods the value of the differential-analyzer approach can be practically appreciated. For example, in the region where superharmonics might be expected, the single-term harmonic approximation ignores them, while the analyzer solutions contain the superharmonic components of the exact solution. A secondary contribution of the paper is the account of the use of the differential analyzer for verification of suspected stability criteria for two-degree-of-freedom nonlinear vibrating systems. Analytical solutions that were reproducible on the analyzer were considered stable; those that were not reproducible were considered unstable. This paper also can be considered as a call for further application of modern computer techniques to the problems of nonlinear mechanics. Since the computer solves the exact or complete differential equations, the results are the complete solutions including transient phenomena, steady state, subharmonics, super-harmonics, and so on. These exact solutions are produced as functions of time which are analogous to the actual vibrations of the physical system studied.