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# Applied Mechanics

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APPLIED MECHANICS. Applied me chanics, based on the same laws and principles as theoretical or rational mechanics, neverthe less differs from it in methods of solving problems as well as in the problems themselves. It is the aim in applied mechanics to obtain a faithful representation of the circumstances which condition the state of rest and motion of real, actual systems. It deals therefore with the rational and economic design and con struction of structures (bridges,. buildings, waterways, etc.) and machines (engines, motors and machinery in general). We no longer meet with the (perfect° fluids, the "perfectly° elastic, rigid, or smooth bodies of theoretical mechanics. Friction, viscosity, plasticity, deviations from the laws of Hooke, Boyle, and Charles are brought into every problem so far as mathe matical difficulties and experimental deficiencies will permit. No problem is considered solved until a result is obtained which is verified by experiment and which can be used in making numerical computations. Consider for instance the behavior of a steam engine. The actual steam pressure on the piston varies every in stant according to a law compared with which Newton's law of attraction is a model of sim plicity; added to that the yielding of the parts, the rubbing of interacting surfaces, the exact role of lubricants, the vibrations of the sup ports, the escape of heat through the cylinder walls, the friction of the steam in passing through the slide valve, and the almost erratic variation of the resistance offered by the ma chine actuated by the steam engine make what the mathematician terms a (complete solution' hopeless of attainment. Applied mechanics does not attempt the impossible, yet some solution of such problems as this must most urgently be found. But the solution need not be more reliable than the measured experimental data. The precision of engineering data is hardly ever better than 1 per cent and sometimes does not exceed even 10 per cent. Therefore bold approximations and graphical processes will usually give results as precise and correct as, and decidedly more rapid than, those found by analytical methods. Sometimes the conditions which make an analytical solution too difficult to be attempted are neglected; the formulas or results obtained by this simplification — they might be called qualitative as opposed to quan titative solutions —are then compared with ex periment and properly modified by means of empirical constants. Thus, the volume of water discharged from an orifice in a tank is calcu lated on the assumption of steam line flow (see HYDRODYNAMICS) ; when multiplied by an empirical coefficient it gives the precise dis charge and applies also to flow under many different circumstances. Here is the keynote of the •science of applied mechanics: Correct and precise results deduced as far as possible from first principles and co-ordinated with experiment. Correctness and precision differ from exactness; a yardstick may be correctly and precisely measured as being one yard long but its exact length may never be known. In physics and engineering means ac cording to fundamental laws, means according to measurement. °Exact( implies a finality and absoluteness which science regards as unattainable.

Theoretical mechanics was fully developed early in the 19th century before applied me chanics existed at all. Pioneers like Euler, the Bernoullis, Cauchy, Lagrange, Laplace, Gauss, Poisson, Fourier and Hamilton were primarily mathematicians. They were indeed men capable of building a utilitarian science, but it seems the element of' interest was lacking. It is difficult to explain by other reasons why the perturbations in the solar system were worked out before the simple problem of finding the forces in a truss had been solved graphically, or why the analytical theory of heat conduction should have been finished almost a quarter century before thermodynamics was really be gun. But it was nevertheless a mathematician

who wrote the first systematic treatise on ap plied mechanics. Isolated problems had of course been studied long before. Galileo had experimented, although unsuccessfully, with cantilever beams, and Euler, Bernoulli, Coriolis Napier, Smeaton and others had made import ant contributions to hydraulics and the strength of materials. Poncelet, professor of geometry in Metz, was commissioned by the French Min istry of War in 1824 to found a course in the `science of machines° at the Ecole d'Applica tion. His 'Cows de micanique appliquee aux machines> appeared in 1826. The mathema tician Dupin saw at once that applied mechanics was in itself a science and not merely a collec tion of isolated applications of theoretical me chanics. He reported to the Academy in 1827: "It is a production remarkable for the rigor of the mind that developed it (qui en a trace la marche] and for the simplifications made to render less difficult of application to practice those calculations reserved for the most part to transcendental speeulations.° Poncelet's work was soon followed by that of others. In 1858 Rankine published the 'Manual of Applied Mechanics' containing his celebrated preface on the (Harmony of Theory and Practice in Mechanics.> The inclusion of this essay in a textbook is significant in show ing that the ancient scholastic contempt for experiment had been completely transformed in the minds of engineers into contempt for what they called °pure theory.° To-day, fortu nately, the fictitious clash between theory and practice has vanished and to its disappearance must be attributed some of the most valuable contributions, from a utilitarian standpoint,' that have been made to engineering science by such mathematician-engineers as St. Venant, Bous sinesq and Grashof. Rankine's Movers' shortly followed the treatise on mechanics and contained for the first time in an English book the new science of thermodynamics which he and Clausius had developed independently. Willis and Reuleux had meanwhile laid the foundations of the kinematics of mechanism. Applied mechanics thus reached maturity soon after the middle of the 19th century. Still one field, however, remained to be developed: the dynamics of machinery. The necessity of this arose in connection with the balancing and stabilizing of high-speed engines which were now beginning to be introduced. Although in vestigations along these lines were made from about 1850, by Lechatelier, Villarceau, %Seal and Redtenbacher, to the important contribution by Radinger in 1870 mit hoher KolbengeschwindigIceit'), it was left to Yarrow (1892) and Schlick (1893) to make complete application of the new methods. Since then the whole subject of balancing, governing and gyroscopic effect has been exhaustively examined with the aid of the most powerful mathematical analysis. But in spite of its value it has not yet succeeded in displacing in most textbooks a host of academic problems on falling bodies, friction, centroids and moments of inertia.

Applied mechanics is subdivided on peda gogical grounds into KINEMATICS OF MECH ANISM ; GRAPHICAL STATICS, DYNAMICS OF MACHINERY; STRENGTH OF MATERIALS ; HY DRAULICS ; THERMODYNAMICS ; AERODYNAMICS. These are treated in this Encyclopedia under their respective titles.