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By H. M. Chance

In the early part of 1893, I had occasion to make for the owners a professional examination of the Rich Patch tract; and, with their permission, I present in this paper, omitting the commercial portions of my report, those portions which may be valuable to future students of that region. Location, Topography And Geology. The Rich Patch tract comprises about 9000 acres, located about 3 miles west of Low Moor, on the Chesapeake and Ohio Railway, in Alleghany county, Va., and immediately adjoining the Low Moor property. In shape the tract is roughly quadrangular, being about 3 miles broad in a northerly and southerly direction, by about 6 miles long from east to West. Potts creek and Jackson river run along its northern boundary. It is drained by Hayes Gap run, Mill branch and Laurel creek, which flour north into Potts creek, and by Karnes creek, which flows northeasterly through the Low Moor property into Jackson river. The topography of the tract is shown by the accompanying map (Fig. I), and need not be described here. The valleys are cut down from 1000 to 1500 feet below the mountain summits, which generally reach an altitude of about 3000 feet above tide. The geological structure of the district is indicated by the geological cross-sections shown in Figs. 2 and 3. These sections show that the formations underlying the property extend from the Lower Silurian lin~estones up to the Devonian slates, including the numbers of the Paleozoic system of rocks as defined by the geological surveys of Virginia, Pennsylvania and New York, from No. 11. to No. VIII. • No. IX. Old Red Sandstone, No. VIII. Slates and Shales, Devoman-

Jan 1, 1900

By Serge L. Delinois

President Kennedy said that before 1970 this country will send a man to the Moon and get him back on Earth safely. Today, no one doubts that his promise will become reality. He who asks "What, then, is next for us in space?" is no longer considered a dreamer. And one of the very first things he discovers in trying to answer this question is that in whatever does come next, geologists and mining engineers will play a prominent role. This will be true not only in the conquest of the Moon, but also in that of the whole solar system. After 1970, it is very likely that a permanent lunar camp will be established. This beachhead, supplied entirely from Earth, in the beginning, will gradually develop into a research complex where virtually all scientific disciplines are investigated.

Jan 1, 1966

By George A. Hill

WE of the oil industry, devoted to freedom of initiative, free competitive enter- prise, and free American institutions, applaud, with one voice, affirmation by the President of the national will and purpose to preserve and to protect, against all aggressors, "our American way of life with our individual and national freedom." We subscribe utterly and completely to this guiding declaration and seek its further definition as applied to the oil industry. Fortunately for all, the policy of the Government, after adequate study and deliberation, has been given precise definition. The National Defense Advisory Commission, with its patriotic, highly qualified, and distinguished personnel, has unanimously agreed to and adopted twelve general principles governing national defense contracts and also fair labor standard requirements. The President of the

Jan 1, 1940

By Robert Goodrich

EXPERIMENTS ON A PORPHYRY COPPER ORE FROM BISBEE, ARIZ. THIS research was done partly in the non-ferrous laboratory of the Department of Metallurgy of Columbia University, under the direction of Dr. Edward F. Kern, and completed elsewhere. Acknowledgment is due to Prof. Arthur L. Walker, Dr. Edward F. Kern and Dr. William Campbell of the Department of Metallurgy, for their kind advice and for the inspiration derived from their instruction. This report is given under the following heads: Petrographic Description (Microscopic Study); Sampling and Preparing Ore for Treatment; Chemical Analysis; Treatment of Ore. PETROGRAPHIC DESCRIPTION Texture: Variable. Fine to medium mixed aggregate. Original structure: Obscure. Secondary structure: Fractured; healed.

Jan 8, 1915

By W. A. Backofen, A. T. English

The kinetics of re crystallization were determined metallographically for a 3-1/4 pcl Si-Fe rapidly compressed at temperatures of 710° to 911°C, and held for various times at the working temperature. As in re crystallization following cold wwk, the time for re crystallization was reduced by increased temperature and strain. Nucleation occurred chiefly at grain edges, although other pre-existing interfaces, notably inclusions, also served as nucleation sites. The importance of intragranular nucleation to grain refinement in hot working is pointed out, together with some possible techniques by which nucleation might be induced within the grains. The observed isothermal growth rates are quite accurately described by the equation G = 4 x 10-'/t (cm per sec), independent of temperature and strain at all but the shortest times. Changes in G during recrystalliza-tion can exceed two orders of magnitude. It is argued that release of stored energy associated with lattice defects cannot adequately explain the time dependence. A suggested alternative involves processes of solute segregation and desegregation in the unrecrystallized matrix and at the moving boundary, respectively. EFFORTS to improve hot-working practice are hampered by an incomplete understanding of the fundamental metallurgy involved. Research directed at establishing the required basic foundation falls into two categories, the first concerned with measurement of mechanical properties under the conditions of high temperature and strain rate which characterize such processing, the second focused on structure and its relation to the deformation conditions. Rossard,' Rossard and Blain,2 and Hardwick and Tegart have conducted many high-speed, high-temperature torsion tests on various metals. One of their objectives was interpretation of stress-strain curves in terms of the structures of specimens rapidly quenched following interruption of twisting. They showed that appreciable hardening occurred in the early part of the test, and that this hardening reflected the concurrent development of an increasingly dense substructure within the grains. The detailed nature of this substructure was observed to depend on the ease of polygonization which, at least in fcc metals, varies with the stacking-fault energy.= By holding specimens after interruption but before quenching, the nucleation and growth of new grains could also be studied. Some success has been realized in relating the microstructure of hot-rolled steel to its temperature:strain rate:strain history with such testing.' The same general observations have been made by others investigating rolling4f5 and drop-hammer forging.~-~ Incident to these experiments, some efforts were made to determine the kinetics of re-crystallization as well as the velocity of the migrating boundaries. The results have been largely qualitative, owing to difficulties of interpreting hardness measurements5 and microstructures. The work described here was undertaken to obtain more quantitative information from tests on a material having suitable metallographic properties, and, in this way, to provide further insight into the fundamentals of this practically most important kind of deformation processing. I) MATERIALS AND EXPERIMENTAL TECHNIQUES Materials. Electrolytic etching of a Si-Fe alloy reveals dislocations and substructure in unrecrystallized grains.8'9 This unique characteristic makes possible a precise determination of the extent of recrystallization. For that reason, it was the material selected for all experiments in the present work. The two particular alloys that were used are identified in Table I. A major difference between "A" and "B" is the number of inclusions, as noted in the table. Most of the experiments were made with material "A". It was received as hot-rolled plate 1 in. thick, sawed to 2-in. widths, hot-forged at 1200°C to 5/8-in. rounds, and finally annealed in a mechanical vacuum at 1000°C for 24 hr. The result was substructure-free grains of mean diameter 0.05 cm.*

Jan 1, 1964

By I. R. Taylor

Union Carbide has recently developed two open- pit vanadium mines in the Wilson Srpings area of central Arkansas about five miles southeast of Hot Springs. The ores from these mines, together with those from a larger vanadium deposit at nearby Magnet Cove, are processed at a new 1600- tpd plant built by the company in the immediate vicinity (Fig. 1). The Wilson Springs vanadium deposits are associated with the Potash Sulfur Springs intrusive, a circular igneous complex which is exposed over an area that is somewhat less than a mile in diameter.1 The complex has a crude ring structure similar to that of the larger Magnet Cove instrusive six miles to the east.2

Jan 4, 1969

By D. Harker, M. J. Murphy

The mechanism by which age-hardening takes .place is still not completely understood. The principal theories range from the extreme of "precipitaiion-hardening" to that of "order-hardening," with many intermediate gradations. In the hope of obtaining new data on which to base a choice among the many theories, the authors have made electron micrographs of formvar replicas taken from metallic specimens at various stages of age-hardening. The results so obtained on an alloy of 2 per cent beryllium in copper and one of 20 per cent molybdenum in iron will be described in the following pages, as well as the technique used in preparing the replicas. Preparation of Formvae. Replicas of Metallic Specimens This section is concerned with the techniques that have roved successful in preparing formvar replicas for studying the microstructure of metals with the electron microscope. Because of its simplicity and accuracy, the formvar replica1 method developed in the General Electric Research Laboratory has been used exclusively, since it is much simpler than the silica replica method of Heidenreich and Peck2 and produces as good results. The formvar method to be described requires a technique acquired only by practice, and no foolproof set of rules can be given. it is a rapid method and a replica can be obtained in less than five minutes under favorable conditions. This does not mean that perfect replicas can be produced every five minutes, but rather that one can well afford to take several strippings* in order to produce a replica of high quality. The metallographic technique required for replica work—very fine polishing and etching with very dilute solutions—is described here. It can be said, in general, that almost any surface that has been carefully prepared for a photomicrograph at 1000 or more diameters can be used to obtain a replica for the electron microscope. Preparation of Metallographic Specimens The preparation of the metallographic specimens is somewhat more exacting than that usually given to samples to be used for inspection under the light microscope. After much experimentation, it was concluded that the best method consists in polishing the metal through to the coarse cloth, then etching and repolishing on final cloth until the layer of distorted metal is removed. After this procedure has been completed, a dilute etch—to approximately the depth necessary for a micrograph at 1000 diameters—usually produces a sur-

Jan 1, 1945

By Guy N. Bjorge, A. J. M. Ross, S. J. Staple, J. D. Johnson, J. F. Wiggert

In recent years the Homestake mine has been served by three shafts, the B. &. M., the B. & M. No. 2 and the Ellison, supplemented by an inside shaft, the Milliken, extending from the 2000-ft. level to the 3200-ft. level. In 1932, when a new operating shaft was under consideration, the bottom of the mine was at the 3200-ft. level. The B. & M. and the B. & M. No. 2 shafts were down to the 1550-ft. level and the Ellison was being deepened from the 2600 to the 3200-ft. level. All ore was hoisted at the B. & M. and Ellison shafts. Levels below the 2600 level, which were under development only, were served by the Milliken shaft. Below the 1550-ft. level, the mine was served only by the Ellison shaft from the surface. Within a few years, when ore reserves above the 1550-ft. level would be depleted, operation would be limited to the Ellison shaft and the auxiliary underground shaft. The Ellison shaft alone was not adequate for hoisting the entire output from the deeper levels and also handling all men and supplies. Furthermore, assurance of safety and uninterrupted operation required two fully equipped shafts to the deeper levels. Therefore a new operating shaft was authorized in November, 1932, and was named for A. J. M. Ross, the mine superintendent. Plans for New Shaft The B. & M. shaft, begun in 1878 before much was known of the form and extent of the orebodies, was too near the ore and was endangered by ground movement. In 1924 this shaft was seriously threatened and sinking of the B. & M. No. 2 shaft, to supplant it, was begun. The latter was completed to the 1550-ft. level in 1928. In the meantime ground movement at the B. & M. shaft had practically stopped and, though loss of the shaft constantly threatened, ore hoisting was con-

Jan 1, 1937

By R. S. Shoemaker, F. W. McQuiston

BENGUET EXPLORATION, Inc. Tuba, Benguet, Philippines 1970 Operating Data ORE DESCRIPTION: Complex ore mostly sulfides and composed mainly of sphalerite and pyrite with minor amounts of chalcopyrite, galena, arsenopyrite, hematite, magnetite, chlorite, calcite, garnet and quartz. TYPE OF MINE: Underground, cut and fill method ORE HAULAGE TO MILL: Mine rail cars with electric locomotives. CAPACITY in TONS/24 HRS: 130 ASSAYS: Mill Heads Mill Tails Au = 0.65 oz per ton Au = 0.096 oz per ton Cu = 0.75% CU = 0.27 % Zn = 10.50 % Zn = 0.64 % Ag = 3.20 oz per ton Ag = 0.33 oz per ton Cd = 0.01 % PRODUCT: Au, Ag, Cu, Zn and Cd RECOVERIES: = 90% ~g = 89% Cu = 60% Zn = 94% SCREEN ANALYSIS OF MILL FEED: 90% -200 mesh POWER: Grinding 25.4 Kwh/T Copper Flotation 14.5 Zinc Flotation 13.3 Cyanidation 20.4 Others 25.0 TOTAL POWER: 98.6 KwH/T WATER: Pumped from riverside and underground 50 to 100 meters distance. Consumption of about 700 gallons per ton of new water.

Jan 1, 1975

By J. O. Lewis

Oil wells usually reach their maximum daily output shortly after they are completed. From that time they decline in-production, the rapidity of decline depending on the output of the wells and on other' factors governing their productivity. The production curve of a well shows the mount of oil produced per unit of time for several consecutive periods; if the conditions affecting the rate of production are not changed by outside influences, the curve will be fairly regular, and, if projected, mill furnish useful knowledge as to the future production of the well. By the aid of this knowledge the value of a property may he judged, and proper depletion and depreciation charges may be made on the books of the

Jan 2, 1918

The following petition for amendment of the constitutional provisions relating to qualifications for membership in the Institute, signed by 75 members, of whom 27 are members of the Committee on Increase of Membership, was received by the Board of Directors, was printed on the program of the New York Meeting sent to all members early in January, and is now being voted upon by the membership: In accordance with the terms f Article X, we hereby propose the following amendment to the Constitution, Article II, Section 2: Members shall comprise all those persons who on the third Monday of February, 1918, were members of the Institute, and in addition thereto, all those thereafter, elected or transferred into the, class of Members. A person to he eligible for election or transfer into the class of Members must he at least 27 years of age and must have had at least six years' employment in the practice of engineering, mining, geology, metallurgy or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. Graduation from the scientific course of a college, approved by the Committee on Membership, shall be considered equivalent to two years' employment, as required in the previous sentence.

Jan 2, 1918

[United Engineering Trustees, Inc. ALBERT ROBERTS. '47 R. M. ROOSEVELT, '49 RALPH B. WILLIAMS, '48 The Engineering Foundation F. F. COLCORD. '46 M. A. PRENTIS. Jn.. '48 It. >I. ROOSEVELT. '49]

Jan 1, 1946

By R. V. Ramani, C. J. Bise

The potential of deep-mineable coal reserves in the western United States for meeting future energy needs has been recognized for quite some time. However, two of the major constraints tending to limit the development of these underground reserves are the great thicknesses of the coal seams encountered and their high pitch. Although new mining methods may need to be developed to recover these reserves, at least in the short-term the industry has to incorporate presently available equipment not originally designed for thick-seam mining. The purpose of this paper is to present an analysis of the various equipment in use today and their possible application to thick-seam mining. The paper also addresses various ground control and safety considerations unique to thick-seam extraction.

Jan 1, 1984

By Zay Jeffries

It has been known for centuries that iron and steel could be hardened by cold hammering and that the metal could be restored to the normal condition by heating to a red heat arid cooling, either rapidly or slowly with nearly pure iron, but slowly with steels containing considerable carbon. The art of tempering steels is also very old. When a medium- or high-carbon steel is quenched from a cherry-red heat, the hardness is increased; this hardness can be reduced by heating to various temperatures below the lower thermal critical point,, which is near 700" C. The present paper will not consider these old and well known changes in iron and steel below the thermal critical range but will confine itself to the more unusual changes, some of which have been studied recently. Stromeyer,1 for example, In 1886, reports that both working steel and heat treatment of steel in the blue-heat range arc highly injurious. Recently, however, some metallurgists believe that the straiglltening of warped steel forgings at a blue heat produces a beneficial effect on the metal2 The Engineering Division of the National Research Council has constituted a committee on Physical Changes in Iron and Steel below the Thermal Critical Range, which has the following personnel: K. R. -Abbott, H. C. Boynton, William Campbell, J. V. Emmons, F. B. Foley, H. J. French, H. M. Howe, Zay Jeffries (chairman), F. C. Langenberg, J. A. Mathews, P. D. Merica, A. H. Miller, J. H. Nelson, G. A. Reinhardt, W. E. Ruder, H. F. Wood. This committee is studying several aspects of the physical changes in iron and steel. The results, reported in the literature and obtained by recent experimentation, will be given; this will be followed by a general theoretical discussion of the more important

Jan 1, 1922

By Zay Jeffries

It has been known for centuries that iron and steel could be hardened by cold hammering and that the metal could be restored to the normal condition by heating to a red heat arid cooling, either rapidly or slowly with nearly pure iron, but slowly with steels containing considerable carbon. The art of tempering steels is also very old. When a medium- or high-carbon steel is quenched from a cherry-red heat, the hardness is increased; this hardness can be reduced by heating to various temperatures below the lower thermal critical point,, which is near 700" C. The present paper will not consider these old and well known changes in iron and steel below the thermal critical range but will confine itself to the more unusual changes, some of which have been studied recently. Stromeyer,1 for example, In 1886, reports that both working steel and heat treatment of steel in the blue-heat range arc highly injurious. Recently, however, some metallurgists believe that the straiglltening of warped steel forgings at a blue heat produces a beneficial effect on the metal2 The Engineering Division of the National Research Council has constituted a committee on Physical Changes in Iron and Steel below the Thermal Critical Range, which has the following personnel: K. R. -Abbott, H. C. Boynton, William Campbell, J. V. Emmons, F. B. Foley, H. J. French, H. M. Howe, Zay Jeffries (chairman), F. C. Langenberg, J. A. Mathews, P. D. Merica, A. H. Miller, J. H. Nelson, G. A. Reinhardt, W. E. Ruder, H. F. Wood. This committee is studying several aspects of the physical changes in iron and steel. The results, reported in the literature and obtained by recent experimentation, will be given; this will be followed by a general theoretical discussion of the more important

Jan 1, 1922

By F. H. Gilpin

SINCE Noah pitched his ark within and without with pitch, the use of asphalt in human endeavor has been increasing-for Noah's pitch was asphalt. Asphalt is a bituminous material found in nature, either pure or admixed with smaller or greater quanti-ties of mineral and non-mineral materials, or obtained by the refining of crude asphaltic-base petroleum under proper methods of control. Native or "natural" asphalts are scattered through-out the world, though the commercial value of the various deposits varies greatly, depending upon both their accessibility and magnitude and the quality of the material found. It is an acknowledged fact that such asphalts have been produced through natural causes by practically the same application of tempera-ture and pressure as are used in the modern refining of crude asphaltic-base petroleum. The best known of all the native asphalt deposits are those of Trinidad Lake in the Island of Trinidad, British West Indies, and of Bermudez Lake in Vene-zuela. Asphalt from Trinidad Lake, after refining to remove organic and some inorganic diluents, contains approximately 35 per cent, of inorganic residue, and the asphalt thus produced must be fluxed with lighter asphaltic or semi-asphaltic base oil to make it com-mercially utilizable. The refined asphalt obtained from the Bermudez Lake deposit contains from 4 to 6 per cent. of inorganic material which cannot be removed. This asphalt, also, must be fluxed to produce com-mercial products. Small quantities of similar materials are available in other locations. The best pure native asphalt' is known as. gilsonite and is mined in com-mercial quantities in the State of Utah. In numerous places in the United States, particularly Oklahoma and Kentucky, there are deposits of sand¬stone and limestone impregnated with bitumen, which are known as rock asphalts. These rock asphalts may be used, particularly in the paving industry, either as found or by slight fluxing; from some deposits the asphalt is extracted and marketed commercially.

Jan 2, 1923

By Lawrence K. Jetter, Robert F. Mehl

SOME advances have been made recently in the theory of the kinetics of precipitation from metallic solid solution despite the complexities of the problem, but there is surprisingly little quantitative information available on rates of precipitation with which to test present theory or upon which to build new theory.? Attempts to measure rates of precipitation have been beset with difficulties which originate both in the anomalies that attend the changes in the properties selected for measurement, as, for example, in electrical conductivity or mechanical properties, and also in the complexities in the structural changes in some systems, as in the aluminum-copper system. If the functional relationship between the quantity of precipitate and the value of the selected property is uncertain, measurements of that property are obviously of uncertain utility in determining absolute rates of precipitation. If the precipitating system passes through one or more transition stages, the interpretation of measured rates lacks definiteness; in such cases, it is necessary to measure the rate of reaction in each separate stage, if the rate measurements are to have any significance from the kinetic point of view.* These difficulties cannot be wholly avoided, for at least in some measure they are characteristic of the process of precipitation from solid solution, but they can be minimized both by the selection of a simple system and by the use of a method of measurement relatively free from anomalous behavior. The present paper reports dilatometric measurements on the rate of precipitation of silicon from the aluminum-rich solid solution in the aluminum-silicon system-a study that approaches the desiderata of simplicity. The aluminum-silicon system offers advantages from these points of view: there are no known anomalies in the property changes accompanying precipitation ;2,3,4 there are no known transition stages; the precipitate is an element, not a compound, and both matrix and precipitate are cubic, and while the structures are not identical (the solid solution is face-centered cubic and the precipitate is diamond cubic), the system at least approaches the ideal case of a crystal precipitating from a matrix of the same crystal type-the ideal case which Becker5 assumed in treating the precipitation process theoretically. The dilatometric method, while not free from disturbing effects, as the subsequent dis-

Jan 1, 1942

By A. W. Schillinger

Drilling was not entirely satisfactory in the search for native copper in the Osceola amygdaloid footwall, for oreshoots mined were more continuous than drilling indicated. The Geophysics Dept of Michigan Technological University developed a portable induced polarization drill hole probe with a 3-electrode configuration and a sampling radius of 5 ft ±. A 20 ma current of alternately reversed polarity is pulsed at 3.5 sec intervals and readings are taken every 2 ft. Potential is read during the "on" cycle for resistivity determinations. During the "off" cycle, after 10 ms delay, the 1P potential is sampled for 10 ms and recorded. Resistivity (ohm-ft) and "S" values (mv/v) are plotted on semi-log paper. A lithologic log is plotted based on resistivity and anomalous S values noted. The low resistivity amygdaloid contains sills of high resistivity basalt. Verified by core logs, contacts between amygdaloid and basalt could be picked to ± 0.5 ft from resistivity alone. Lithologic logs of long-steel holes, based on resistivity, then replaced sludge logging. An S value of 30 mv/v was established as the lower limit of diagnostic 1P effects in mineralized amygdaloid and 50 mv/v as a threshold value for ore. Of 914 footwall zones drilled, 315 were probed yielding 203 anomalies. Success increased from 34% for drilling to 72% for drilling and probing. As checked by mining, 46 probe results were 78% correct. Failures were due to the instrument not detecting copper or to the misinterpretation of an anomaly. No false anomalies were found. During the past ten years, the Calumet Div. of Calumet &Hecla, Inc has conducted extensive exploration and mining in the footwall of the Osceola amygdaloid lode in the native copper district in Michigan's Upper Peninsula. In an attempt to delineate more clearly the extent and nature of high-grade footwall copper mineralization, 876 diamond drill and long steel holes aggregating slightly more than 47,000 ft have thus far been drilled from the accessible hanging-wall workings in the Osceola No. 6, 13, 14 and 15 shafts. Early in this program it became obvious, through inspection of footwall workings in progress, that due to the erratic and bunchy occurrence of the native copper in the footwall zone, the exploration drilling was failing to outline completely the extent of the oreshoots. Early drilling re-

Jan 1, 1964

By PAUL DYER MERICA

PAUL DYER MERICA, who has been awarded the James Douglas Gold Medal for his achievements in non-ferrous metallurgy, is a Hoosier, having been born at Warsaw, Ind., in 1889. His father, a clergyman and educator, was president of the University of Wyoming from 1908 to 1913. After graduating from the University of Wisconsin in 1908, young Merica (not yet twenty years of age) went to China, where he was professor of chemistry in Chekiang Provincial College, Hangchow, until 1911. He then went to Germany to s t u d y and was fortunate enough to receive his Ph.D. from the University of Berlin just a few months before the outbreak of the World War in 1914. Returning to America, his first position was as special investigator at the En¬gineering Experiment Station of the University of Illinois, but before the year was out he joined the staff of the U. S. Bureau of Standards as associate physicist. Since 1918, he has been superintendent of research for the International Nickel Co. His work during those years is excellently summarized in the following quotation from the statement of Zay Jeffries recommending him for the award.

Jan 1, 1929

By H. Matlock

Beam-columns with continuous or discontinuous transverse and angular loads and elastic restraints are represented mathematically in a manner corresponding to finite-element mechanical models. Solutions for linearly elastic cases are accomplished by direct recursion-equation elimination of unknowns, and for cases involving nonlinear loads and supports, by repeated trial-and-adjustment of complete elastic-type solutions. Five practical applications are presented by which various capabilities of the general method are illustrated. The examples include simulation of a pipeline launching and the bending and collapse of a conductor pipe in deep-water drilling operations. INTRODUCTION The diversified and complex operations being conducted in support of the production of offshore oil have produced a wide variety of new problems in structural mechanics. Many of these problems cannot be solved by conventional analytical or experimental approaches and have therefore stimulated inquiry into new methods of solution. It is the purpose of this paper to give a brief description of an analytical method for solving nonlinear beam-column problems and to illustrate the generality of the method by applying it to several problems related to offshore operations. Although the data for all of the examples are artificial, the cases discussed will be recognized as being based on actual situations. DESCRIPTION OF METHOD The analytical approach which is to be described stems from research on offshore foundations, in particular, the study of lateral-load behavior of foundation piles. The method represents a generalization of a technique which was suggested by Gleser' and extended by Focht and McClelland2 and Reese and Matlock." To maintain generality and therefore versatility in the method, a considerable variety of input data is considered. Fig. 1 illustrates the various types of loads and restraints which might be applied to a short segment of a beam. Each of the terms illustrated in the figure is shown acting in a positive sense. Capital letters are used to designate concentrated quantities whereas the corresponding lower-case symbols indicate effects which are distributed in some way along the length of the beam. The transverse loads and the elastic restraints may be divided into two classes: (1) loads Q and q and springs S and s, which act normal to the axis of the beam, and (2) couples T and t and rotational springs R and r, which act in an angular sense. In addition, there is an axial force P which may be constant or may vary along the length of the beam. The bending stiffness of the beam (the product EI of the modulus of elasticity and the moment of inertia) is designated by the symbol F. The assumptions of conventional elementary beam theory provide the basis for the present method. Among these are the neglect of shearing and axial deformations and the limiting of consideration to straight beams of symmetrical cross-section. Lateral deflections are considered to be small compared to original dimensions. A deformed element of such a beam is shown in Fig. 2a. The curvature of the beam is approximated by the second derivative of the deflection y with respect to distance x along the beam. It is assumed that the material of the beam is linearly elastic and therefore the relation of Eq. 1 between curvature and bending moment M is the ordinary expression from elementary beam theory. A generalized beam element is shown in Fig. 2b. The element has been deflected in a positive direction by an amount y and tilted through a small positive angle dy/dx. The various loads and elastic restraint reactions are detailed in the figure. Temporarily, only distributed effects are considered; provision for concentrated loads and restraints will be made subsequently. Eq. 2 in Fig. 2b is obtained by summing the forces and moments acting on