A Short-Gage-Length Extensometer and Its Application to the Study of Crankshaft Stresses

1942 ◽  
Vol 9 (1) ◽  
pp. A15-A20
Author(s):  
C. W. Gadd ◽  
T. C. Van Degrift
Keyword(s):  
Experimental Methods ◽  
Gage Length ◽  
Mathematical Treatment ◽  
Mathematical Methods ◽  
Elastic Stresses ◽  
Machine Elements

Abstract The mathematical methods of determining elastic stresses in machine elements, particularly those of irregular contour, may be excessively complex, so resort is frequently made to approximate calculations, which tend to lose accuracy while achieving simplicity. As a result a constant effort is made to supplement the mathematical treatment with experimental methods of studying stress. In this paper, the authors describe a short-gage-length extensometer and explain its application in the determination of crankshaft stresses. This instrument meets the requirement of convenience in operation, which is so essential in assuring that it will be used for the study of localized stresses.

scholarly journals Investigation of hydraulic fitting losses

2018 ◽  
Vol 168 ◽  
pp. 02011 ◽  
Author(s):  
Marian Bojko ◽  
Milada Kozubková
Keyword(s):  
Flow Direction ◽  
Experimental Methods ◽  
Numerical Approach ◽  
Model Verification ◽  
Hydraulic Systems ◽  
Mathematical Methods ◽  
Standards And Regulations ◽  
Definition Of ◽  
Resistance Coefficients

Fluid flow in hydraulic systems, fittings, and piping causes hydraulic losses due to the change of flow direction and friction in the fluid. The main consequence of the resulting losses is the increase in the overall pressure gradient of the circuit. The paper is focused on the investigation of valve losses and the determination of resistance coefficients, the definition of which depends on the valve type. Methods of determination are of two types, i.e. experimental methods and mathematical methods. In the case of experimental methods, the procedures prescribed by the standards and regulations must be respected. Mathematical methods are related to defining an appropriate mathematical model and numerical approach. Both methods are applied to the ball valve and model verification is performed at the same time. The output of the thesis is the methodology for determination of resistance coefficients of valves with other diameters and other flowing media based on verified mathematical modeling.

scholarly journals The diamagnetic susceptibilities of salts forming ions with inert gas configurations II-The alkaline halides

1935 ◽  
Vol 152 (876) ◽  
pp. 342-353 ◽  
Author(s):  
G. W. Brindley ◽  
F. E. Hoare ◽  
Richard Whiddington
Keyword(s):  
Crystalline State ◽  
Experimental Methods ◽  
Inert Gas ◽  
Complete Set ◽  
Sodium And Potassium ◽  
Potassium Halides

The data so far published on the diamagnetic susceptibilities of the alkaline halides, measured for the salts in the crystalline state, are very discordant and incomplete, as reference to Table I will show. The aim in carrying out these experiments has been twofold: firstly, to obtain a complete set of values for these salts and secondly to examine more closely than has hitherto been possible how rigorously the susceptibilities of simple crystalline salts are additive. It has already been established that the susceptibilities are approximately additive, but it has not been possible to test this with exactitude because of ( a ) the large discrepancies between the results obtained by previous observers, and ( b ) the lack of data for many crystals. The discrepancies may have arisen to some extent from the different experimental methods, some of which are more accurate than others and some of which may introduce errors peculiar to themselves. We have therefore made a complete re-determination of the susceptibilities of all the alkaline halides, using the same apparatus and method under the same conditions. Since any systematic experi-mental errors will affect all our results to approximately the same extent, we shall be in a stronger position for testing the additivity of the susceptibilities than if we rely partly on our own and partly on other observers’ results. Previous investigators have measured the susceptibilities of some compounds in the crystalline state and others in solution; the latter are of no help in connexion with our problem, for an examination of the available data suggests that solutions have susceptibilities higher by several per cent, than the corresponding crystals. We cannot, therefore, arrive at any certain conclusion by using results obtained partly for crystals and partly for solutions. 2—Method The method previously described has been used to obtain a complete set of values for the susceptibilities of the alkaline halides. Although slight modifications have been made from time to time, the apparatus has remained, in essentials, the same as when used for the measurement of the susceptibilities of the sodium and potassium halides.

Experimental Determination of KI for Short Internal Cracks

2001 ◽  
Vol 68 (6) ◽  
pp. 937-943 ◽  
Author(s):  
K. Bearden ◽  
J. W. Dally ◽  
R. J. Sanford
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Edge Crack ◽  
Series Solution ◽  
Experimental Studies ◽  
Experimental Methods ◽  
Internal Crack ◽  
Intensity Factors ◽  
Mode Stress

Since the pioneering discussion by Irwin, a significant effort has been devoted to determining stress intensity factors (K) using experimental methods. Techniques have been developed to determine stress intensity factors from photoelastic, strain gage, caustics, and moire´ data. All of these methods apply to a relatively long single-ended-edge crack. To date, the determination of K for internal cracks that are double-ended by experimental methods has not been addressed. This paper describes a photoelastic study of tension panels with both central and eccentric internal cracks. The data recorded in the experiments was analyzed using a new series solution for the opening-mode stress intensity factor for an internal crack. The data was also analyzed using the edge-crack series solution, which is currently employed in experimental studies. Results indicated that the experimental methods usually provided results accurate to within three to five percent if the series solution for the internal crack was employed in an overdeterministic numerical analysis of the data. Comparison of experimental results using the new series for the internal crack and the series for an edge crack showed the superiority of the new series.

scholarly journals Determination of the number of radicals in the initial chain reactions by mathematical methods

2009 ◽  
Vol 63 (2) ◽  
pp. 121-127
Author(s):  
Branko Pejovic ◽  
Milovan Jotanovic ◽  
Vladan Micic ◽  
Milorad Tomic ◽  
Goran Tadic
Keyword(s):  
General Chemistry ◽  
Difference Equation ◽  
Analytical Form ◽  
Mathematical Methods ◽  
Linear Difference Equations ◽  
Efficient Procedure ◽  
Chain Reactions ◽  
Chemical Equation ◽  
The Difference

Starting from the fact that the real mechanism in a chemical equation takes places through a certain number of radicals which participate in simultaneous reactions and initiate chain reactions according to a particular pattern, the aim of this study is to determine their number in the first couple of steps of the reaction. Based on this, the numbers of radicals were determined in the general case, in the form of linear difference equations, which, by certain mathematical transformations, were reduced to one equation that satisfies a particular numeric series, entirely defined if its first members are known. The equation obtained was solved by a common method developed in the theory of numeric series, in which its solutions represent the number of radicals in an arbitrary step of the reaction observed, in the analytical form. In the final part of the study, the method was tested and verified using two characteristic examples from general chemistry. The study also gives a suggestion of a more efficient procedure by reducing the difference equation to a lower order.

scholarly journals DETERMINING THE FORCES OF INTERACTION OF MAIN GEOKHODS SYSTEMS WITH GEO-ENVIRONMENT AND WITH EACH OTHER

2018 ◽  
pp. 23-30
Author(s):  
V. Yu. Beglyakov ◽  
V. V. Aksenov ◽  
I. K. Kostinets ◽  
A. A. Khoreshok
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Interaction Process ◽  
Generalized Model ◽  
Machine Elements ◽  
General Mathematical Model ◽  
Mine Workings ◽  
Modular Principles ◽  
Sufficient Strength

The processes occurring during the geodetic excavation of underground excavations are characterized by the interaction of the elements of the geokhod with each other and with the geo-environment. The interaction process can be investigated in mathematical modeling, solving the problems of justifying the parameters of the drives and interacting forces, ensuring sufficient strength of the machine elements and the bearing capacity of the contour array. The proposed block-modular principles of constructing a mathematical model allow solving particular problems of the system and its individual elements. From the solution of particular problems, it is now necessary to proceed to the solution of the generalized model, using equivalent loads and reduced total moments (forces). The construction of a generalized model requires a number of assumptions, but its solution will reveal the interaction between the elements of the geokhod and the geo-environment, which is very relevant.As an example, the solution of a particular problem is given-the determination of the value of the forces arising from the interaction of the blade of an external engine with the medium.A list of assumptions is formulated that allow us to describe a general mathematical model of the interaction between the geo-environment and the geokhod, as well as the processes occurring during geodetic excavation of mine workings.

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