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By Georgc E. Collins

SEVERAL years ago, I estimated the total stock of gold in the world to be about a thousand million ounces, of which rather over one-third was available for monetary uses. Robert H. Ridgway has estimated the world's production from 1493 to 1927 as slightly over this amount. Of this total, 1.5 per cent was produced between 1493 and 1850 (before the Californian and Australian goldfields began to flood the world with gold), 331/2 per cent from 1851 to 1900, and 511/2 per cent from 1900 to 1927. Allowing for loss by attrition and permanent consumption in the arts, and for loss of buried treas¬ure, my first-mentioned estimate is perhaps not far from the truth; but my estimate of the monetary stock was certainly too low. Of the total production stated by Rid-way. 28 per cent came from North America. 26.9 per cent from Africa, 1.6.8 per cent from Australasia, 12.4 per cent from South America, and 11.2 per cent from Asia. Excepting that from the African conglomerate beds, the ultimate origin of which is still the subject of controversy, by far the greater part of the total production was derived from alluvials. Weighing all contingencies, it is improbable that any such production as has been made during the last forty years will be repeated in any similar period, if the present price level is maintained. The gold standard today seems firmly established except for temporary digressions. Nevertheless, no well-informed mining engineer will venture to assert the probability that the material for its maintenance throughout future generations can be furnished.

Jan 1, 1932

By G. W. Thomas

Jan 1, 1967

By A. Moskowitz, L. S. Redmerski

The corrosion resistance of stainless steels can be strongly affected by surface treatments. Changes in corrosion resistance can relate to surface composition, integrity and stability of the passive film, and to surface profile (roughness). Operations producing oxidation at the surface, such as annealing, heat treating, and welding, can result in a chromium-rich scale and a chromium-depleted metal surface. In order to restore full corrosion resistance, chemical or mechanical clean-up techniques must remove not only the oxide, but also a very thin layer of metal. Laboratory and field test studies show that these factors are particularly significant in less highly alloyed steels. Annealing stainless in a reducing atmosphere (bright annealing) avoids chromium depletion, but as-bright-annealed material does not display optimum corrosion resistance in certain environments. Electro passiva-tion can be applied to improve pitting resistance without significantly changing bright surface appearance. Potentiometric studies show that electropassivated material also displays significantly greater resistance to breakdown of passivity in acid solutions. The application of special surface finishes for appearance purposes can affect corrosion resistance. Roughness is a key factor. Samples of related appearance but with different surface profiles can show significant differences in corrosion resistance. Thus nonreflec-tive stainless with a relatively smooth surface produced by a special rolling process is much superior to material chemically etched to a similar low reflectivity. THE corrosion resistance of a stainless steel is affected by other factors in addition to its bulk composition and metallurgical structure. These other factors include those relating to the specific chemical and physical condition of the steel's surface. This paper will consider certain aspects of surface condition in relation to corrosion resistance. In particular, studies will be described on the effects of oxidation encountered in heat treating or welding operations, of passivation after bright annealing, and of different surface finishes. EFFECTS DUE TO OXIDATION When stainless steels are exposed to high temperature in an oxidizing environment, as in annealing or welding, the oxides formed are relatively rich in chromium. As a consequence of oxidation, the metallic layer directly beneath the scale may be low in chromium to some very thin but finite depth.1"8 Such a change in chromium content could lower the corrosion resistance at the surface, whether or not the oxide layer is removed. Studies were performed relating to the effect of oxidation and chromium depletion produced during annealing and welding on the corrosion resistance of stainless steels. The nominal compositions of steels used in this study and others are given in Table I. A) Annealing Studies on 17 pet Cr Steels. 1) Effects of Pickling Treatments. Studies were performed to investigate the corrosion resistance of air annealed type 430 stainless as a function of the amount of electrolytic pickling after annealing. The material used in this study had been air annealed and electrolytically pickled in the mill. All scale had been removed, and yet the material showed unusually poor corrosion resistance. Laboratory electrolytic pickling studies were performed to determine whether additional metal removal from the surface would improve corrosion resistance. Electrolytic pickling was performed in a sulfuric acid bath using various conditions of bath acidity, temperature, time, and current density. The samples were then rated for corrosion resistance in a ferric chloride spot test. For this spot test, a solution was prepared by dissolving 10 g of FeCl3 . 6H2O, 5 g of NaCl, and 2.5 ml of concentrated HC1 in 200 ml of water. An area on a specimen was cleaned and a drop of test solution was placed on the prepared area. After 5 min, the drop was rinsed off and the area wiped dry. The spot was then rated between 1 and 5 by visual comparison with standard spots. The numerical rating of the standard spots can be described as follows: 1—No clouding of surface; 2—very slight clouding of surface; 3—slight clouding of surface; 4—moderate clouding of surface; 5—strong clouding of surface. A rating of 1 or 2 was considered to have passed the test, a rating of 4 or 5 represented failure, and a rating of 3 was considered borderline. The severity of etching in this test has been related to the actual chromium content at the surface.4 Etching (clouding) occurs on type 430 stainless (rating of 4 to 5) when the surface chromium content is 14 pct or less. The effects of current density and retention time when electrolytically repickling this material in 6 pct sulfuric acid are shown in Fig. 1. Increasing the cur-rent density or retention time improved corrosion resistance as measured by the spot test. Similarly, increasing acid concentration of the bath or bath tem-perature was found to improve corrosion resistance. The conditions making for improved spot ratings resulted in increased metal removal, regardless of specific pickling conditions used, Fig. 2.

Jan 1, 1970

By J. B. Clark

In multiphase ternary diffusion studies, plots of the variation bf the composition on the isotherm constitutes one of the most effective methods of presenting experimental results, especially if such plots are made in a manner which relates the composition path on the isotherm with the diffusion layer structure in the couple. Unfortunately, if different conventions for plotting are used serious misinterpretations occur readily, causing apparent disagreement between investigators who actually share the same viewpoint. A common convention for mapping these diffusion paths is needed at this time because with the increasing use of the electron-probe X-ray microanalyzer, a much greater number of ternary diffusion studies can be expected in the near future. In an effort to prevent unnecessary confusion in the future litera- ture, a convention for these plots is proposed, as outlined below. A hypothetical example of the use of these conventions is given in Fig. 1 where the path of composition through the diffusion structure of the 100 pct A/50 pct B, 50 pct C couple is plotted on the appropriate isotherm of the ABC system. The lower case letters relate the region in the diffusion layer structure to the appropriate composition on the ternary isotherm. 1) The diffusion path is plotted on the isothermal section corresponding to the diffusion temperature of the couple. 2) The terminal compositions of the plotted diffusion path are the initial compositions of the couple halves—provided infinite boundary conditions are maintained. If, in either couple half, infinite conditions are not maintained, then the path terminates at the composition of the exterior surface of the couple. If, at this surface, the composition varies with time or if the plotted path is time dependent, then the diffusion time should be noted beside the plotted path. 3) A solid line crossing a single phase field (e.g., line a-b in Fig. 1) denotes an existing layer of that phase in the diffused couple. 4) A dashed line crossing a two-phase field parallel to the tie lines (e.g., line g-h) represents an interface between the two phases with interfacial compositions designated by the ends of the tie-line. The line represents no spatial extent. 5) A solid line crossing a two-phase field so as to cut tie lines (e.g., line b-c or line j-k) represents a locally equilibrated columnar two-phase layer. The solid line should cut those tie lines which correspond to the lateral interfacial equilibria along the columnar

Jan 1, 1963

Abbey, Robert Graham, District Mgr. The W W. Sly Mfg. Co,. 50 Church St, New York, N. Y. '21 Abbott, A. N., Mines Supt., Mazapil Copper Co., Ltd ..Concepcion del Oro, Zac., Mexico. '23 Abbott, Argyle Campbell, Dev. Dept, E I du Pont de Nemours & Co, Wilmington, Del. '29 Abbott, Clarence E., V.P, Charge of Raw Materials, Tenn. Coal, Iron & R. R. Co, 1242 Brown-Marx Bldg, Birmingham, Ala. '04 Abbott, Louis Benjamin, Chief Engr., Elkhorn Div., Consolidation Coal Co, Jenkins, Ky. '15 Abeel, George H., Jr., Cons. Min. Engr Box 427, Santa Monica, Cal. '18 Abel, Albert E., Asst. to Pres, Valley Mould & Iron Corp Hubbard, Ohio. '19 Abel, Raymond L., Asst. Prof., Dept. of Pet Refin., Univ. of Pittsburgh Pittsburgh, Pa. '28 Abell, Leo M., Research Engr, Sullivan Concentrator Chapman Camp, B. C., Canada. '31 Abernathy, George Elmer, Prof. of Geol. & Min . Kansas State Teachers College, Pittsburg, Kans. '20 Aborn, Robert H., Research Lab, U. S. Steel Corp. Lincoln Highway, Kearny, N. J. '19 Abozeid, Mahmood, Dept. of Mines & Quarries Cairo, Egypt. '26 Abraham, Arthur W. Box 1466, Bakersfield, Cal. '20

Jan 1, 1923

Jan 1, 1970

By H. F. Silliman, Daniel R. Hull, Earl W. Palmer

THE brass-rolling industry has not had a great deal of experience with antimony in its product. There have been some recent excursions with antimony as a corrosion inhibitor in tubes, but in sheet brass it has been regarded with apprehension and generally avoided. This is not to say that [ ] contaminations have never occurred, and probably a great many brass mill men have had their own ideas on the effect of such contamination. Our own views were based upon certain experiences some years ago with strip castings that split lengthwise in the early stages of rolling. The nature of this splitting is shown in Fig. I, from a photograph taken in 1922 as a record of 20 bars of 65-35 common brass made with an antimonial brand of copper. These bars were cast 6 ¾ in. wide by 1 in. thick by 45 in. long. In the first pass through the rolls, 19 of the 20 split lengthwise throughout their length, while each half curved outward in a wide arc as it emerged from the rolls. [ ] In those days, if splitting was not a frequent occurrence, it was not unfamiliar. One can recall periods of short duration when large amounts of common brass would behave in this way. There was nothing imaginary about these spells. The affected metal would split lengthwise in the breaking rolls, and no maneuvering of mill practice made any difference. The condition would descend like a plague, demoralize the mill for several days, and disappear. It is doubtful if anyone knew the cause-however many explanations may have been current. In 1921 a quantity of split brass was traced to the use of fired small-arms

Jan 1, 1943

By R. L. Fullman, J. W. Cahn

A method is derived for obtaining the distribution of sphere diameters and plate thicknesses (or pearlite spacings) from size distribution functions obtained along randomly oriented lines. The method described offers several advantages over existing methods. IT is often of interest to measure not only the average particle size but also the distribution in sizes of particles dispersed in an opaque material, such as an alloy. Particles of a single size will exhibit a range of apparent sizes on the plane of polish. If the sample contains a distribution of particle sizes, the distribution of observed sizes on the plane of polish is related to the distribution of actual particle sizes by an integral equation, For example, a distribution of sphere sizes, N(r),

Jan 1, 1957

By L. E. Lynd

Ilmenite concentrates prepared from beach and dune sands of Florida, India, Australia, and other localities deviate to varying degrees from the theoretical composition of pure ilmenite, and generally contain more TiO2 than the formula FeTi03 would indicate, and some Fe2O3. This variation in composition is due to different amounts of altered ilmenite in the concentrates. (') The alteration has been shown to take place by oxidation and leaching of the iron in ilmenite, to yield residual products consisting of amaphous or very finely crystalline titanium dioxide and ferric oxide. Other studies(2) have stressed that ilmenite may alter first to an amorphous titanium-iron oxide, or to an amorphous mixture of titanium and iron oxides, with later alteration to crystalline titanium dioxide. There has been some speculation as to whether alteration of ilmenite is usually caused by weathering or by hydrothermal pr0cesses.(3,4,5 Three main methods of approach were used to study the mechanism and rate of ilmenite weathering. (1) Etch tests were used to learn the relationship between crystallographic orientation and the rate of chemical attack on ilmenite. (2) Altered ilmenites in New Jersey sands were compared with ilmenite in rocks of the area from which the sands were probably derived. (3) Experiments were carried out to determine at what rate, and by what agents, originally fresh ilmenite could be altered in the laboratory under simulated weathering conditions. ETCH FIGURES ON ILMENITE CRYSTAL PLANES A rather large ilmenite crystal from Sannidal, Norway, about 11/2 x 11/2 x 2 inches, bearing a few natural faces with imperfect surfaces, was prepared for etching by grinding and polishing crystal planes whose Bravais-Miller indices (referred to hexagonal axes) had been determined by X-ray methods to be 00.1, 10.0, and 10.2. Metallographic examination showed that the crystal was homogeneous, and uniform in orientation, except for the presence of twin lamellae which were oriented with their broadest surfaces parallel to the 00.1 planes of the large crystal. Since ilmenite is rather inert to standard etch reagents, strong solutions of hot sulfuric acid and cold hydrofluoric acid were used. Preliminary tests established that better etch figures were obtained using HF than with H2So4 solutions. The etch figures produced on 00.1 and 01.0 planes of ilmenite by etching 3 to 5 minutes in cold concentrated HF solution are shown in Figures 1, 2, and 3. The figures on 00.1 are "etch hillocks", rather than pits, and according to Honess(6), this phenomenon

Jan 1, 1961

By JO. E. SHERID

THE Dawson coal-mines are owned and operated by the Stag Canon Fuel Co., of which Dr. James Douglas is President and E. L. Carpenter general manager. The property is situated in Colfax county, N. M., and the openings now in operation are in townships 28 and 29 N. R. 20 E., and township 28 N. R. 21 E., shown in Fig. 1. The mines are part of the southern end of the Raton coal-field, which extends north into Colorado and embraces many coal-camps of the Trinidad section. II. GEOLOGY. Geologically, the coal-measures, commonly known as the Laranmie series of the Cretaceous system, have a thickness of about 800 ft. in the vicinity of Dawson. The coal makes an excellent coke, and, according to some authorities, its coking properties are clue to the action of intruded sheets and sills of igneous rock, the sheets occasionally thickening into masses resembling laccoliths, at such places making nearer approach to the coal and sometimes producing small areas of natural coke. There are but few dikes through¬out the entire southern portion of the field and little or no faulting along the dikes. In some parts of this great coal-field the intrusive sheets are far removed in the green shales below the coal-measures, and are so much altered as to be difficult of identification. There is but little disturbance of the strata through¬out the Raton coal-field in as far as it extends into New Mexico. There are two workable seams in the coal-measures, and two or three smaller coal-seams, ranging from 1 to 2.5 ft. in thick-

Jun 1, 1909

By Fulton Flick

THE micrography and macrography of aluminum and its alloys present certain difficulties. Many of the difficulties attendant on the micrography have been removed by methods developed during the past few years, notably those of E. H. Dix, Jr.1 The development of grain size in aluminum and its alloys may be equally troublesome, yet comparatively little detailed attention appears to have been given to it. Satisfactory reagents. are available for the development of such structures in ferrous and most non-ferrous metals, but those applied to aluminum and its alloys, i. e., alcoholic or aqueous solutions of sodium hydroxide or hydrofluoric acid are not entirely satisfactory. Hanson and Archbutt,2 in speaking of these two reagents, state that "These two reagents give fairly satisfactory results, but they sometimes produce badly tarnished surfaces from which the surface deposit is difficult to remove." It has been our experience that neither of these reagents is to be entirely relied on for developing structures suitable for study or photography. This means that when the etch fails to produce satisfactory results the, specimen must be repolished, through the 000-paper at least, and then etched with another reagent. This procedure entails a con¬siderable loss of time, and the final results may not be all that might be desired. However, the reagent to be described, although not a panacea for all etching troubles, has improved results so markedly that it is felt that it is worth offering as a grain-size etch generally applicable to aluminum and aluminum alloys. Czochralski3 in 1915 mentioned the application of a solution of 10 to 20 c. c. concentrated hydrofluoric acid in 100 c.c. absolute alcohol, etching in this reagent being followed by dipping in concentrated hydrochloric-acid solution.

Jan 2, 1925

By L. A. Cranson

WHEN I came out of Stanford University in 1922, the out-look for men trained in geology, petroleum engineering, and mining was indeed dismal; in fact, so much so that most of us looked upon our future in those fields as pretty hopeless. Neither our professors nor those men in industry with whom we came in contact gave us any enthusiastic encouragement as to the future of ourselves or the fields we had chosen for our labors. I believe that the attitude of pessimism which saturates everyone about graduation time is lament able and short-sighted, and may often start a young man on his way with an attitude of defeatism. Instead, he should be starting out knowing that he can expect hard work and keen competition, but that the fields of his labours are expanding at an accelerated rate, and that strong, energetic efforts will as always accomplish highly satisfactory results.

Jan 1, 1941

'T. C. MERRIMAN, New Haven, Conn. (written discussion *).-This most interesting paper gives much carefully obtained and valuable data. However, there are two points in connection with the commercial application of such data that might possibly be a source of trouble and mis-understanding. In the first place, the examination of thin sections of annealed brass, subjected to standard Brinell test.(500 kg. on a 10-mm. diameter ball) at thicknesses from 0.075 to 0.150 in. (1.9 to 3.8 mm.) indicates that cold work has been performed on the specimen during the application of the load sufficient to extend way through the section, and have the hardness of the metal affected by the backing. If the usual steel support is used, this effect is very evident. If a piece of soft brass is used as a support, there is an indentation in the surface of the support accompanied by a bulge on the under side of the tested specimen opposite the impression made by the 10-mm. ball. The result is that Brinell specifications (governmental or otherwise) on stock for a certain purpose may not be fair in all cases, since manufacturers, owing to differences in equipment, etc., may not all use precisely the thickness and conditions of stock on which the Brinell specifications were based. This would mean that the government Brinell specification might not give them the temper of stock best suited for their manufacturing methods. The concluding paragraph of this paper, stating that "the hardness of cartridge brass may be determined with greater accuracy by the Brinell hardness measurement than by attempting to judge it from the grain size" appears to be in line with the movement of the last year or so among brass manufacturers toward substitution of the Brinell test for microscopic examination as an acceptance test on cartridge brass. The statement may he strictly true that the Brinell test is the best test for hardness, but it is not, as the statement might readily be construed, a sufficient test of suitable condition. For instance, some cartridge brass might accidentally have been overheated to a point where it would be distinctly unsafe to use for the manufacture of small arms cases and then be so rolled (reduction 3 to 5 per cent.) as to pass perfectly proper Brinell specifications. Under such conditions the microscope would reveal its unsuitability where the Brinell test had failed so to do.

Jan 4, 1919

Jan 1, 1923

Jan 1, 1923

Carlisle: An old friend and good friend, Alan Bateman, is the Silliman Professor of Geology Emeritus at Yale and editor of the Journal of Economic Geology. Now, Alan, let's start off by telling us something about how you became interested in copper. Bateman: Well, after I left Yale in 1913, I was appointed one of the field members of the Secondary Enrichment Investigation. We spent three years in the field studying all the copper deposits of North America, trying to find out how secondary copper enrichment took place. As part of this investigation, I went up to Kennecott, Alaska, in 1916. After the trip I was asked by the president of the company to become consulting geologist to them. I accepted his offer, and to this day I'm still consulting geologist to the Kennecott Copper Corp. Up at Kennecott, there were both Henry Krumb and my good friend Henry DeWitt Smith, who was general superintendent. He and I had been together at Yale, and I had ushered at his wedding. Interestingly enough, Henry took his bride to Alaska and I took mine there two months later. My assistant was Don McLaughlin, and I think that was his first experience in a mining camp. We published a paper on Kennecott together and cemented a friendship lasting to this day.

Jan 11, 1964

By Fred H. Perfect

The thermite process, now approximately 80 years old, has heretofore been practiced in ceramic vessels. This paper outlines the successful production of several million pounds of alloy produced in zuater-cooled copper vessels. THE high temperatures necessary to produce fluid high-alumina slags have probably discouraged earlier workers from attempting to utilize water-cooled vessels. The following is a report of the successful application of this method, together with a report of the physical and chemical problems which had to be solved to make the process practical. About 1955, when Reading Alloys was more concerned with the production of ferrotungsten than with most other types of alloys, it was found to be exceedingly difficult to predict the reaction rate that one would experience from one tungsten ore to another . This difficulty was increased for two reasons: the physical state of the ore as received was seldom uniform, and the size of the mass to be reduced is a very important factor in developing the proper mix for the final reaction rate and temperature. For example, the reduction of ferric oxide with aluminum would theoretically produce temperatures of about 2600°C, and, in spite of the losses due to radiation, the energy is quite sufficient to produce a very fluid slag and iron effecting a very clean separation. On the other hand, the reduction of ferrous oxide with aluminum, while it is not as energetic as the first reaction, nevertheless should give temperatures above 2000"C, which should cause separation of alumina and iron, but, in practice, this is not the case and good fluid slag is not obtained. The heat of reaction, calculated from the thermo-dynamic heats of formation of the constituents of the reaction, offers a convenient guide to the feasibility of a thermite reaction. Thus, the values listed in Table I can be used as an approximate guide for estimating the results which may be expected in the reduction of various oxides and combinations of oxides using aluminum as the reducing agent. As a generalization, those reactions releasing approximately 600 cal per g of total mass represent the lower limit at which to expect separation of slag and metal. On the other hand, those reactions which release 1100 to 1200 cal per g are too violent to be used successfully without the addition of considerable inert material, such as lime, fluorspar, and so forth. Reaction rate is also a very important factor. This, of course, is governed very largely by the sizing and intermingling of the oxidant and reductant and by the starting temperature of the reactants. This is why those figures shown in Table I can only be a general guide. Further, it must be understood, that by adding powerful oxidizing agents, such as nitrates, chlorates or metallic oxides, such as molybdenum trioxide or chromium trioxide, certain problems respecting low temperatures are not necessarily solved. This is true in the addition of oxidants, such as sodium chlorate. By adding too high a concentration of sodium chlorate as a booster for a particular reduction, explosions are generated. Generally, they are of an intermittent type so as to give a Roman Candle effect to the reduction itself; with each surge resulting from a minor explosion more and more material is thrown

Jan 1, 1968

By Gregory M. Dexter

Recent litigation in Pennsylvania between three coal-mining companies and a private water company resulted in the payment by the coal companies of the equivalent of about $500,000 to buy a new water supply to replace that which had been damaged by acid drainage from strip mining. An investigation of the relevant facts indicates that the water could have been treated by spending about $40,000 on equipment and $15,000 yearly for chemicals, labor, and power until the contamination could be reduced about 80 pct. The water company's supply, furthermore, had deteriorated largely by reason of dry weather before stripping was begun by the coal companies. Payment to the water company should not have exceeded $300,000 and could have been as low as $100,000. Strip mining of coal is common in Pennsylvania. The most important objection to it in Pennsylvania is generally acid pollution of runoff water. An outline of the methods, therefore, that could be used to reduce such pollution, to compare acid-contaminated waters, and to treat such waters to make them satisfactory for public and industrial use is worth-while. The watershed of the West P~M Water Co. covers about 4.5 square miles, 20 miles west of Pittsburgh, and has two 90,000,000 gal reservoirs sup- plying about 1,300,000 gal daily for public and industrial use of which 450,000 gal daily are for two railroads. The pollution arises from weathered derivatives of typical "Coal Measures"

Jan 1, 1949

By J. F. KENP

THE White Knob copper-deposits are situated about three miles south of Mackay, on the Salmon River .branch of the Oregon Short Line Railroad, in Custer county, Idaho. An outline-map of this district is given in Fig. 1. The deposits have been known and spasmodically worked for many years, and a total of over 3.5 miles of tunnels, shafts and other workings has been driven with a view to their development. These extensive excavations have exposed the deposits sufficiently to permit a careful geological examination. The peculiar features which give special interest to this paper are the branching, free-like form of the ore-bodies; the absence of zones of secondary enrichment in the partly oxidized pyritic deposits, and the fact that while the deposits are associated in a general way with the contact of an eruptive rock with limestone, which it penetrates, the garnetization has taken place not in the limestone, as is the usual case, but in the igneous

Mar 1, 1907

By L. Adler

Two basic cases involved in the design of an opening in bedded rock are: 1) where the beds deflect from each other so as to be separated; and 2) where the beds deflect onto their lower neighbor, loading the latter while reducing their own load. Analysis of case 1 is relatively simple, while the interference of the original deflection curves in case 2 complicates analysis of the latter. Figures and formulae are presented for determination of interference loading in this situation. The design of an opening in bedded rock involves two basic alternatives.1'2 In one case the beds deflect away from each other, so as to be separated from their neighbors; in the other case the beds deflect onto their lower neighbor, loading it, while reducing their own load. This is shown in Fig. 1. The first case lends itself to a simple analysis, since the upper and lower boundaries of each beam remain a free surface. In the latter case, however, due to the interference of original deflection curves, the analysis is more complex. Earlier investigators of this interference problem solved it by making the tacit assumption that this type of loading was uniformly distributed along the beam's length. While there is no intuitive justification for this assumption, its use does lead to an approximate solution. Still, a more exact solution does not require this apparently unrealistic restriction. To achieve initial simplicity, the analysis will at first be limited to a two-bedded sequence, as in Fig. 2. Since both beams have identical end conditions and spans, the original deflections of their center lines are members of the same family of curves, as shown in Fig. 3. Therefore, if interference occurs at one point along their center lines, it will occur at every point. For convenience, the midspan point is that usually examined. Deflection at midspan for a uniformly loaded beam regardless of end conditions is: where c is a constant depending on end conditions; w is the body load and equals yh, lb per ft; y is the specific weight of rock, lb per ft'; L is the span, ft; E is Young's Modulus, lb per ft2; I is moment of inertia (for a rectangular section), I = bh3/12 = h3/12, (ft4); b is the width of beam and equals one; and h is the thickness of beam, ft; or 3U > yB an Substituting the appropriate values into Eq. lb, interference between the two beds can be predicted. Should it occur, the additional loads along the lower boundary of the upper bed and the upper boundary of the lower bed must be determined. From the principle of action and reaction, these added loads are known to be equal and opposite, as indicated in Fig. 4. Since the final deflection curves for both beds are identical (Fig. 3), their successive derivatives of y with respect tox must also be identical. That is:

Jan 1, 1961