Determination of Stresses in Cemented Lap Joints

1953 ◽  
Vol 20 (3) ◽  
pp. 355-364
Author(s):  
R. W. Cornell

Abstract A variation and extension of Goland and Reissner’s (1) method of approach is presented for determining the stresses in cemented lap joints by assuming that the two lap-joint plates act like simple beams and the more elastic cement layer is an infinite number of shear and tension springs. Differential equations are set up which describe the transfer of the load in one beam through the springs to the other beam. From the solution of these differential equations a fairly complete analysis of the stresses in the lap joint is obtained. The spring-beam analogy method is applied to a particular type of lap joint, and an analysis of the stresses at the discontinuity, stress distributions, and the effects of variables on these stresses are presented. In order to check the analytical results, they are compared to photoelastic and brittle lacquer experimental results. The spring-beam analogy solution was found to give a fairly accurate presentation of the stresses in the lap joint investigated and should be useful in analyzing other cemented lap-joint structures.

Author(s):  
Mohammed F. Abdul Azeez ◽  
Alexander F. Vakakis

Abstract This work is aimed at obtaining the transient response of an overhung rotor when there are impacts occurring in the system. An overhung rotor clamped on one end, with a flywheel on the other and impacts occurring in between, due to a bearing with clearance, is considered. The system is modeled as a continuous rotor system and the governing partial differential equations are set up and solved. The method of assumed modes is used to discretize the system in order to solve the partial differential equations. Using this method numerical experiments are run and a few of the results are presented. The different numerical issues involved are also discussed. An experimental setup was built to run experiments and validate the results. Preliminary experimental observations are presented to show qualitative comparison of theory and experiments.


1988 ◽  
Vol 53 (5) ◽  
pp. 929-938
Author(s):  
František Skopal

The time dependence of the volume of solution of one reaction component injected continuously to the solution of the other reaction component is derived for the case that the injection is controlled by feedback to hold the absorbance of the reaction mixture constant. An experimental apparatus based on this principle has been set up and its function tested on two 2nd order reactions, whereby the theoretical relations derived for the determination of the rate constants have also been verified.


Seeing that hitherto our knowledge of the flame speeds involved in the “inflammation” and “detonation” of carbonic oxide-oxygen mixtures has been mainly confined to those of the theoretical 2CO+O 2 mixture, and that complete data over the whole “explosion range” are needed for the determination of questions relating to the combustion of carbonic oxide, we have lately carried out experiments with a view to suppyling the deficiency; and this paper embodies the results thereof. Experimental. A.-Flame Speeds in the Initial Phase of "Inflammation." It may be recalled that when a quiescent explosive mixture is ignited at the open end of a horizontal tube, the other end being closed, a slow and usually uniform flame movement is initially set up. Except in mixtures very near to one or other of the explosion limits, this initial phase is soon succeeded by an oscillatory movement during which the flame swings backwards and forwards, usually with increasing amplitude, until it is either extinguished, by swinging too far backwards into its own products of combustion, or gives rise to a must accelerated movement, may be ending up in "detonation" if sufficiently accelerated during a forward swing.


1884 ◽  
Vol 12 ◽  
pp. 234-235
Author(s):  
Matthew Hay ◽  
Orme Masson ◽  
Crum Brown

Investigations have been made by Railton, Williamson, Hess and Schwab, Beckerhinn, and Sduer and Ador for the purpose of ascertaining the elementary composition and the constitution of nitroglycerine. They all agree in regarding it as a nitrate of glyceryl; but, whilst some consider that it is a tri-nitrate, others hold that it is a variable mixture of the tri-nitrate with di-nitrate and mononitrate. Their analyses are quite insufficient to establish either the one or the other conclusion, and have mainly been confined to estimations of the nitrogen. If we except a comparative estimation of the carbon with the nitrogen, there exist absolutely no determinations of the carbon or of the hydrogen. And, as the decomposition of nitroglycerine with potash has been shown to occur in a manner considerably different from that suggested by Railton and Williamson, the main reason in support of the constitution of nitroglycerine as a tri-nitrate has been removed. The authors of the present communication therefore believed that they were amply justified in making a fresh and more careful and complete analysis of the composition of nitroglycerine. Absolute determinations were made, not only of the nitrogen, but also of the carbon and hydrogen; and, in order to ascertain the uniformity in composition of nitroglycerine, the nitrogen of samples prepared by various methods was estimated. The nitroglycerine was both pure and thoroughly dried. For the determination of the nitrogen, modifications of Dumas's method and of Schloesing's method were employed. The carbon and hydrogen were estimated by a modification of Liebig's method. Every precaution was taken to insure that the results obtained should be correct. The average of the determinations gave 15 · 91 per cent, of carbon, 2 · 49 per cent, of hydrogen, and 18 · 05 per cent. (Dumas) or 18 · 14 per cent. (Schloesing) of nitrogen. Theoretically nitroglycerine, regarded as the tri-nitrate of glyceryl, contains 15 · 86 per cent, of carbon, 2 · 20 per cent, of hydrogen, and 18 · 50 per cent, of nitrogen. The quantities obtained by experiment agree so closely with the theoretical quantities that they may be regarded as affording proof that nitroglycerine is, in reality, the tri-nitrate of glyceryl. The authors also conclude, from the unvarying amount of nitrogen obtainable from variously prepared specimens of nitroglycerine, including one from Nobel's dynamite, that nitroglycerine is constant in composition and does not contain any of the lower nitrates of glyceryl, unless very imperfectly washed.


The methods hitherto employed by mathematicians for determining the variations which the elements of the orbit of a planet undergo in consequence of perturbation, and for expressing these variations analytically in the manner best adapted for computation, are found to depend upon a theory in mechanics, of considerable intricacy, known by the name of the Variation of the Arbitrary Constants . In seeking the means for abridging the severe labour of the calculations, we must separate the general principles on which they are founded from the analytical processes by which they are carried into effect; and in some important problems great advantage is obtained by adapting the investigation to the particular circumstance of the case, and attending solely to the principles of the method in deducing the solution. The author suggests the possibility of simplifying physical astronomy by calling in the aid of only the usual principles of Dynamics, and by setting aside every formula or equation not absolutely necessary for arriving at the final results. The present paper contains a complete determination of the variable elements of the elliptic orbit of a disturbed planet, deduced from three differential equations, that follow readily from the mechanical conditions of the problem. In applying these equations the author observes, the procedure is the same whether a planet is urged by the sole action of the constant force of the sun, or is besides disturbed by the attraction of other bodies revolving round the luminary; the only difference being that, in the first case, the elements of the orbit are all constant, whereas in the other case they are all variable. The success of the method followed by the author is derived from a new differential equation between the time and the area described by the planet in its momentary plane, which greatly shortens the investigation by rendering it unnecessary to consider the projection of the orbit. But the solution given in the present paper, although it makes no reference to the analytical formulæ of the theory of the Variations of the Arbitrary Constants , is no less an application of that method and an example of its utility, and of the necessity of employing it in very complicated problems.


2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. C. Ndogmo

The comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. A result on the determination of the finite transformations of the infinitesimal generator of the larger group, which is useful for the determination of the invariant functions of the differential equation, is also given. In addition, the Levidecomposition of the Lie algebra associated with the larger group is found; the Levi factor of which is shown to be equal, up to a constant factor, to the Lie algebra associated with the smaller group.


2013 ◽  
Vol 67 (3-4) ◽  
pp. 259-268
Author(s):  
Ljubica Spasojevic-Kosic ◽  
Sara Savic

There are two basic aspects of hunting dog?s health care: infectious diseases of hunting dogs and dog?s hunting performance. Concerning infectious diseases of hunting dogs, special attention is paid to public health, preventing possible dangers that could possibly arise. On the other hand, hunting performance of dogs depends on their nutrition. A complete analysis of hunting dogs? health care in our country requires an assessment of awareness level in hunters about dangers which both humans and hunting dogs are exposed to, evaluation of preventive measures implementation in dogs by hunters, the prevalence of certain infections in dogs and determination of health risk for dogs and people related to hunting. This paper shows the results of a survey conducted among hunters with the objective to perceive their awareness of medical risks that hunters and hunting dogs could possibly be exposed to during hunting.


1986 ◽  
Vol 109 ◽  
pp. 463-464
Author(s):  
A.S. Kharin ◽  
L.A. Kukharskij ◽  
P.F. Lazorenko ◽  
N.F. Minyajlo ◽  
M.L. Tsesis

The Wanschaff vertical circle, set up at Goloseevo in 1949 was built in 1914. The instrument was originally equiped with four visual microscopes for reading the circle, with a visual eyepiece micrometer, and with two levels for the determination of the inclination of the vertical axis. After the instrument had been installed in a new pavilion in 1972, the visual microscopes were replaced by photographic devices, and a semi-automatic machine for measuring the circle readings with output on punched tape was developed. In 1973,the eyepiece micrometer was equiped with a precision potentiometer of the type which together with an automatic voltmeter of the type the digitizer micrometer readings punches them on tape. The other information is punched on cards by the operator at the data desk.


1939 ◽  
Vol 6 (1) ◽  
pp. A21-A24
Author(s):  
Harold W. Semar

Abstract The paper describes apparatus for testing models of piping installations to determine the forces set up in the full-size installation due to expansion. The method consists in fixing one end of the model in a slide which can be moved a measured amount, and measuring the forces at the other end by means of a fixture which holds that end rigidly in place and permits measurement of six forces in three coordinate planes, which are the equivalent of forces in coordinate directions plus moments in coordinate planes. The slide of the movable end is placed so that its direction of motion coincides with the direction of the pipe expansion. A complete example is given showing the steps in determining the end reactions of an inlet pipe for a steam turbine.


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