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By W. M. Albrecht, W. D. Klopp, R. I. Jaffee, B. G. Koehl

Kinetic studies were made of the reactions of tantalum with oxygen, nitrogen, and air at 400o to 1500°C. The tantalum-oxygen reaction is linear from 500° to 1250°C. The tantalum-nitrogen reaction follows a cubic rate law at 400° to 700°C and a parabolic rate law at 800" to 1475°C. The reaction behavior in air is initially parabolic followed by a transition to linear behavior. In the search for high-temperature materials, considerable interest is being shown in the refractory metal, tantalum. It is the third highest melting metal with a melting point of 2996°C. Also, tantalum has excellent ductility, making it one of the most workable refractory metals. In considering high-temperature applications of tantalum, the oxidation kinetics of the metal must be known. Such information also serves as a basis for the development of corrosion resistant tantalum-base alloys. Therefore, this study was made to investigate the reaction of tantalum with air, nitrogen, and oxygen. LITERATURE Several oxides of tantalum have been reported. The pentoxide, Taz05, is the only oxide of tantalum whose identity has been established. A high-temperature modification, aTa2Os, has been reported by several investigators.1-4 A low-temperature phase, ßTa2O5, undergoes an allotropic transformation at 1320o to 1350oC. 5-8 Four other oxides of tantalum have been reported. The oxides TaO2, TaO, and Ta4O have been reported by schonberg.9 A suboxide Ta2O, was observed by Wasilewski 6. However, the presence of oxides lower than Ta2O5 is questioned by Lagergren and Magneli.7 In oxidation studies, vermilyeal0 and Peterson, et al.,12 reported one possible phase intermediate between Ta and Ta2O5. Only Ta2O5 was formed in the tantalum air reaction, as reported by Michae1.l3 Several studies have been made on the kinetics of the tantalum-oxygen reaction. vermilyeal4 investigated the range 50° to 300°C and found that the rate of growth of a thin adherent oxide film could be described by the Cabrera-Mott theory. Gulbransen and Andrew15,18 studied the reaction kinetics of tantalum in oxygen pressure of 1/10 atm at 250° to 450°C. At all temperatures the reaction followed the parabolic rate law for periods up to two hours. The oxidation behavior in the range 500" to 1000°C was found to be linear at oxygen pressures of 0.2 to 600 psi according to Peterson. et al.l1 At very low pressures (1 x 10-3 to 2 X lo-' mm of Hg) Gebhardt and seghezzi17 reported linear oxidation at 800° to 1500°C. The reaction of tantalum with air is similar to the reaction with oxygen. Studies have been made by Waber, et a1.,12 and Michae1.l3 Two nitrides of tantalum, TaN and Ta2N are known. Their structures have been determined by Brauer and Zapp 18,19 The tantalum-nitrogen reaction kinetics have been investigated by Gulbransen and Andrews. 15, 16 The reaction follows the parabolic rate law at 500° to 850°C at a nitrogen pressure of 1/10 ,atm. At the same temperature, the tantalum-nitrogen reaction is much slower than the tantalum-oxygen reaction. EXPERIMENTAL TECHNIQUES Material— The material used in this study was high-purity, electron-beam-melted tantalum obtained from the Temescal Metallurgical Corp. The hardness of the as received ingot was 76 Vhn. The analysis of the material is given in Table I. Methods—Cylindrical specimens of tantalum approximately 0.9 cm in diam and 0.5 cm in length

Jan 1, 1962

By AIME AIME

HOWARD H. PRESTON, professor of economics and business at the University of Washington, presented a paper before the North Pacific Section, A.I.M.E., on Jan. 23, on the "Economic Aspects of Gold and Silver." He carefully reviewed recent governmental actions that have affected those metals and gave an interpretation of their effects. A brief excerpt from his address; follows: Including the proclamation of March 6, 1933, the principal steps of the present Administration which have carried the United States off the gold standard and led up to the present program have been: (1) The Presidential proclamation of March 6 controlling gold. (2) The monetary sections of the Emergency Banking Act of March 9. (3) Mobilization of gold under Executive orders issued March 10 and April 5. (4) The gold embargo by Executive order, April 20. (5) The controlled inflation bill, May 12. (6) The joint resolution abrogating the gold clauses, June 5. (7) The Executive orders on newly mined gold, Aug. 28. (8) The President's radio address of Oct. 22 and the R.F.C. gold-buying program. (9) New anti-hoarding order calling in small holdings of gold, Dec. 28, 1933 and Jan. 15, 1934. (10) Nationalization and revaluation of gold' (Message to Congress, Jan. 15).

Jan 1, 1934

By Ivan B. Cutler, Milton E. Wadsworth

Coprecipitation of anionic and cationic polyelectrolytes has been applied to floccula-tion of several mineral systems. Results obtained in a study of the flocculation of kaolinite and hematite suspensions of polycationic and polyanionic electrolytes are presented. Greatly increased settling rates were observed following precipitation of positive and negative polyelectrolytes on the surface of finely divided minerals in aqueous suspension. The ratios of polycationic to polyanionic electrolytes required to produce maximum sedimentation have been shown to correspond closely with the equivalence points obtained by light scattering studies of systems containing the positive and negative polyelectrolytes by themselves. DISPERSION of colloids has been of interest to surface chemists for many years. Flocculation studies have been employed to evaluate the limits of colloid stability. In water suspensions, colloids become unstable and flocculate when the 5 potential, the potential of the kinetic solvation sheath, falls to a value at which van der Waals forces may act to draw the particles together. This may happen through an adjustment of the pH of the suspension or by addition of a salt. Optimum conditions for rapid formation of large flocs are found in the region of minimum < potential. In addition to these well known considerations, colloids in water suspensions are known to be flocculated by certain large organic macromolecules. These polyelectrolytes in some cases minimize the 5 potential and in other instances increase the attractive forces by supplying sites for hydrogen bonding.&apos; Use of organic polyelectrolytes in flocculation of mineral colloids has increased rapidly in recent years. These materials are now recognized as indispensable aids to fluid-solid separations in many extractive metallurgical operations. They have been found to increase both the settling rate in thickeners and the filtration rate of filters. In the elucidation of the characteristics of these organic reagents as floc-culants in this laboratory, it was discovered that interaction of certain polyelectrolytes had a surprisingly good effect on flocculation of mineral colloids. Experimental Procedure: The anionic flocculants used in this study were Lytron 886 and 887, produced by Monsanto Chemical Co. Both reagents are copolymers of vinyl acetate and maleic anhydride. Lime is added to Lytron 886, whereas Lytron 887 is all organic. These reagents possess two carboxyl groups for each acetate group and are therefore anionic in character. The cationic reagents used were the Peter Cooper Co. 1-X and 2-X glues. The structures are not definitely known, but the re- agents are amines and are cationic in character. The glues were prepared in the chrome-alum form. Both types of reagents may be classified as polyelectrolytes in that they are high molecular weight polymers and ionize in water. All data presented are in terms of sedimentation rate, measured in 250-ml glass-stoppered graduated cylinders. With suitable precautions such measurements are fairly reproducible and provide a sensitive means for selecting important parameters such as PH, reagent concentration, and floc size and density. Agitation was standardized with five complete end over end cycles of the suspensions in the stoppered graduated cylinders.

Jan 1, 1957

Born, March 28, 1853 Died July 23, 1916 On July 25, 1916, the Board of Directors adopted the following minute and directed that it be entered upon the records of the Board & published in the Bulletin of the Institute, and thereof be sent to the family of Mr. Kirchhoff: Charles Kirchhoff was one of the oldest, most widely known and most highly esteerned members of the American Institute of Mining Engineers. On his return in 1875 from a European course of study, to begin a highly successful professional career, he joined the Institute, then just commencing to acquire both national and international recognition. He became at once, and-for more than 40 years continued to be, its earnest , and active supporter, serving it as Manager, Councilor or Director for terms aggregating 9 years,-as Vice-President for 2 years, and twice as President for a year. During the critical period of the erection of the United Engineering Society&apos;s building, and the transfer of the Institute to permanent head-quarters therein, Mr. Kirchhoff was its efficient representative in the United Engineering Society, and on the Building Committee. In 1910, amid the congratulations of colleagues, employees, and innumerable friends, Mr. Kirchhoff retired from active business as Vice- President and General Manager of a great technical publishing company. Yet he sacrificed of his well-earned leisure yet one more year, to serve the Institute as President through 1911.

Jan 9, 1916

Jan 7, 1976

By W. A. Hockings, D. W. Fuerstenau, A. L. Mular

This paper briefly describes a simple air pycno-meter and its use for rapid determination of the composition of mixtures of solid particles. Research on such problems as the pelletizing of solids, the mixing of solid particles, and the comminution of mixtures can be simplified by means of this analytical tool. THEORY OF OPERATION Liquid pycnometers1 are commonly employed to measure volumes. These devices are time consuming and sometimes give inconsistent results. The liquid used in the pycnometer may have an undesired influence on the material to be measured; moreover, complete displacement of air by the liquid is seldom

Jan 1, 1963

By Ivan E. Goodner, Charles H. Fulton

THE subject of the constitution of copper-iron mattes has received considerable attention in recent years by Keller,1 Bolles,2 Hofman,3 and Gibb and Philp.4 Still more recently Friedrich, Röntgen, Wiedmann, Heyn and Bauer, and Leroux have published, in some instances, elaborate researches on the various systems of the sulphides, and the sulphides and their respective metals, which enter into the constitution of mattes, and have added very greatly to the knowledge of the subject. The work of Friedrich has been especially fruitful. But to date no effort has been made to correlate the data obtained in the latter researches and apply then to the study of the product called " matte," which is made in such large quantities by copper and lead-smelters. In this paper we propose to determine, by metallographic and chemical means, the constitution of copper-iron and copper-lead mattes in the light of the recent data above mentioned. We do not discuss copper-nickel mattes or speisses (artificial arsenides). The paper is divided into three sections I. A review and discussion of the various binary systems of the metallic, sulphides, and the binary systems of various metals and their respective sulphides entering into the constitution of mattes; also a discussion of the physical and chemical properties of these sulphides. II. A description of the results obtained from the chemical and metallographic examinations of the samples of copper-iron and copper-lead-iron matte obtained from various plants.

Nov 1, 1908

By C. Dinis da Gama

Because of the growing importance of back analysis for the interpretation of rock slope failures, particularly in open pit mines, it is suggested a methodologic sequence of activities for dealing with those problems. The principal mathematical tools for the interpretation of the most common mechanisms of slope failures are reviewed, including methods of stress and strain analysis, which seem to be more powerful for parametrization studies, and for developing more realistic explanations of slope behaviour, such as the measurement of displacements. An application of those methods is described, using slope failures detected in a Brazilian uranium mine (Cercado), thus providing reliable shearing strength parameters for the rock mass discontinuites, which were used in the final pit design. The concept of using backanalysis results to supply input data for pit design was implemented by means of the excavation of an experimental trench within mine limits, where specific instruments were installed, and several slope failures were monitored and backanalysed, in order to yield information about sliding mechanisms in the future open pit.

Jan 1, 1983

By Y. Oka, H. Majima

When a rock particle is subjected to an external force, internal stresses and deformations are experienced by the particle. Assuming that the breakage of a rock is mainly due to tensile stresses generated by the action of a pair of concentrated loads, F, directed in compression towards the loading points at the shortest distance, as illustrated in Fig. 1, the stress and deformation experienced by a particle of irregular shape can be determined with the aid of the theory of elasticity. According to the photoelastic experiments made by one of the present authors,&apos; the stress states in a rock particle of irregular shape are quite similar to that of an inscribed sphere of diameter x, as indicated in Fig. 1, but accompanied by the faint stresses, in the vicinity of the particle outside of the inscribed sphere. Therefore, the stress components in an irregularly shaped particle can be estimated by referring to stress components in a sphere. Applying polar spherical coordinates to an elastic spherical body, as shown in Fig. 1, the stress components are all expressed as multiples of F /x2 and more or less influenced by the loading angle and Poisson&apos;s number m. In general, the energy w, acting on a rock particle is defined as the product of loading compression F

Jan 1, 1970

By GERALD H. HUTTON

SINCE the inception of dredge mining, the attention of engineers and operators has been directed primarily toward mechanical improvements and refinements calculated to, reduce operating costs and to increase recoveries. The result has been to develop an efficient excavating and value-saving machine, which, in some instances, has an actual capacity of 15,000 cu yd. per day. Steel hulls and superstructures minimize the risk of destruction by fire and lengthen the life of the plant. Dredges now restore, to some extent, agricultural possibilities to mined ground. Large buckets, with correspondingly heavy parts, are able to handle heavy wash and massive boulders. Mechanical weaknesses have been strengthened. The use of manganese steel in bucket lines and tumblers permits the application too the bank of a digging force that can be withstood only by solid material, such as rock, cement or frozen ground. Various alloys of steel have been applied to certain duties and experiments in their heat treatment are still progressing. Haulage by tractor or truck is in common use. Discarded and worn steel parts are repaired or rebuilt by the use of the oxy-acetylene flame and the arc-welding machine. Gold and platinum saving is more efficient, although still subject to improvement. Dredging for tin ore is in successful operation. Crews are now highly specialized and experience has developed improved methods of work; particularly in the manipulation of dredges to build levees of tailings and to leave open waterways where desired. To sum up by the distribution of overhead expense over several units, ground under favorable conditions can now be dredge-mined for 5)2 c. per cu: yd., in spite of the increase in cost of supplies, power, and labor during, the past few years. Improvements in prospecting methods, however, have not kept pace with mechanical developments. Standard practices of ; testing ground today produce only wide approximations of values; although they obtain information concerning the character of the deposit and bedrock. It is interesting to note that few important changes in the methods of ten years ago are .to be recorded; the latest comparisons between pros¬pecting results and mined recoveries-have been at such variance as to cause confusion to the operator, and, in a degree, the sacrifice of the confidence of the capitalist. On this account, and because the growing scarcity of dredging ground. demands closer calculations on the part of the engineer, this appeal for collaboration and

Jan 1, 1921

By G. S. Baker, S. H. Carpenter

Langenecker has reported significant reduction in strength of high-strength metals during ultrasonic t&apos;ibration. Decreases in static yield stress an order of magnitude greater than the calculated stress amplitude of vibrations were reported by him for a stainless steel and for tungsten. in the present work, attempts were nzadc to verify such large reductions in yield and flats stresses using resonant librations of measured amplitudes. The results show that both the soft metals (copper and aluminum) and the high-strength metals (sleels) hare reductions in yield and .flow stresses no larger than the stress amplitude of libration. BLAHA and Langenecker,&apos; investigating the effect of vibratory stresses on the deformation of zinc and aluminum, found a decrease in the static yield and flow stresses approximately equal to the vibratory stress imposed. Langenecker later extending this work to high-strength metals such as stainless steels and tungsten2 found a much larger effect. In these metals the static yield and flow stresses decreased by an amount more than an order of magnitude greater than the calculated vibratory stresses. It was suggested that this phenomenon could be a serious hazard to high-strength structures in an acoustic environment, such as a large rocket at launch, or could be used advantageously in the working of hard-to-work materials such as the refractory metals. Langenecker and others3 have investigated the effect of high-amplitude vibrations on many metal-forming operations. The results have been quite favorable with usually a large decrease in the energy necessary for the forming operation. The processes, however, involve large frictional forces and it is not clear whether the decreases in forming forces are to be ascribed to decreased friction or to decreased flow stresses. The present paper reports an attempt to determine the effect of accurately known vibratory stresses on the static yield and flow stresses. I) EXPERIMENTAL TECHNIQUE The standard multicomponent resonator technique for measuring internal friction has been adapted to allow simultaneous high-amplitude vibration, internal-friction measurement, and tensile deformation. This has been described in detail elsewhere.4 Longitudinal oscillations of approximately 50 kc frequency are excited in a multicomponent resonator by a quartz transducer. A second transducer measures the amplitude of vibrations. Fig. 1 shows a schematic drawing of the resonator and grip arrangement and the displacement pattern produced. Since the centers of the dummy bars are at displacement nodes, they represent points where attachments will not materially affect the vibrations. The force is applied by a standard Instron tester. The sample may be deformed while simultaneously vibrating at up to 104 strain amplitude. 11) EXPERIMENTAL RESULTS The effect of high-amplitude vibrations on the yield and flow stresses of copper. aluminum, tantalum. a soft iron, and a stainless steel has been measured. In addition samples of tungsten vibrating at stress levels up to 10&apos; dynes per sq cm have been subjected to static stresses near the static yield stress with no indication of macroscopic deformation. Fig. 2 gives typical results for 99.999 pct polycrys-talline copper. A vibratory stress of 7 x 107 dynes per sq cm is applied at points "a" and removed at points "h". The behavior of aluminum is identical. In agree-

Jan 1, 1967

By H. B. Menardi

THE history, geology, ore deposits and current mining operations of the Huitzuco district have been described by C. W. Vaupell1 and the current mill operations by David Segura.2 This paper completes the story of Huitzuco with a description of the reduction of the flotation concentrates. The predominant ore mineral in the Huitzuco deposit is livingstonite, a rare, mercury-antimony sulphide (HgS.2Sb2S3). Other associated minerals include cinnabar, stibnite and elemental sulphur. The gangue is largely limestone and gypsum. Former operators mined a selected grade of ore, from which the mercury was recovered by an expensive, inefficient operation. A consid-erable tonnage of rejects and fills, carrying mercury and antimony, was left in the mine. In order to recover both mercury and antimony from these fills and also from newly developed ore, a combination method has been developed, by means of which the livingstonite is concentrated by flotation and the flotation concentrates subsequently reduced to metallic mercury and antimony. An essential part of the flotation treatment, as developed by Segura, is the use of copper sulphate as an activating agent. A typical analysis of concentrates now being produced at the property is as follows: Hg, 7.73 per cent; Sb, 26.40; Fe, 1.20; S, 29.68; CaO, 11.50; MgO, 7.25; Si02, 1.63; A1203, 0.65.

Jan 1, 1939

By Harry C. Wiess

PETROLEUM has come to be one of the most important and essential of the mineral re- sources of the nation. It is the most advantageous source of mineral fuels and of lubricants, and as such it has provided in large measure for the phenomenal development in our modern means of travel and in the facilities for transportation by land, sea, and air. Without it the remark- ably rapid industrial and social progress in our country during the past thirty years could not have occurred. In view of its important place and the fact that petroleum is irreplaceable and existent in limited quantities in nature, its conservation is essential.

Jan 1, 1939

By A. T. Yu

The energy crisis and the resurgence of mining activities highlighted 1972-73. Added to the impetus for more effective materials handling systems has been the continued upward trend of inflation and labor costs. The need for addressing the fundamentals has led to the trend toward an overall systems approach to materials handling problems.1 The decision to move forward with large mining ventures such as the $150 million Hibbing taconite comple2 and the immense Carajas iron project must base themselves on indepth studies of a host of factors viewed in the context of an integral mine-transport-market system. What&apos;s important is that each ton of pellet or ore must be an economical commodity at the end users&apos; furnace. The project can still be viaable even if certain components in the entire network appear to be individually costly.

Jan 2, 1974

By Donald H. McLaughlin

ALTHOUGH Cerro de Pasco was well known since the early sixteen hundreds as one of the major silver districts of the Andes, its development on a modern scale did not occur until the first decade of the present century when a syndicate organized by James B. Haggin initiated the enterprise that eventually grew into the complex and widespread operations of the Cerro de Pasco Copper Corporation. Options on a few claims in Cerro de Pasco that had been brought to New York in 1900 came to the attention of A. W. McCune, a mining man from Salt Lake City, who took them to Haggin and soon succeeded in interesting that creative mining financier in the possibilities of the district. James MacFarlane, an engineer well known to both Haggin and McCune, was sent to Peru early in 1901 to make the initial examinations which promptly led to acquisition of a substantial group of claims in the heart of the mineralized area. A syndicate to which Haggin turned over his rights was organized on Feb. 26, 1902 to provide the necessary funds. The original members were J. B. Haggin, who retained a 34 per cent interest, Edward H. Clark (for Mrs. Phoebe Hearst, the widow of Haggin&apos;s old associate, George Hearst), H. McK. Twombly, H. C. Frick, D. O. Mills, and J.P. Morgan.

Jan 1, 1945

Organization Place Date 1917 American Electrochemical Society Pittsburgh, Pa. Oct. 3-6 American Institute of Mining Engineers St. Louis, MO. Oct. 8-13 American Gas Institute : Washington, D. C. Oct. 16-19 American Institute of Architects Philadelphia, Pa. _ Dec.. 26-29 American Society of Mechanical Engineers New York City. Dec. 26-29 American Mining. Congress State Chapter Phoenix, Ariz. Dec. 26-29

Jan 10, 1917

By Ott F. Heizer

The mines and the mill of the Nevada-Massachusetts Co. are on the east slope of the Eugene Mountains, in Pershing County, Nevada, 8 miles northwest of Mill City, a station on the Southern Pacific R.R. and on the Victory Highway. Fig. 1. Supplies and, concentrate are transported by truck over an automobile road of easy grade. The property is at an average elevation of 5500 ft. and climatic conditions are generally favorable for continuous operation throughout the year. The ore treated is supplied by two adjoining mines, the Stank and the Humboldt. Physical and mineral characteristics of the ores produced by these two mines are substantially similar, although variations occur in hardness and mineral distribution.&apos; The economic mineral is scheelite (CaWO4), composed, when pure, of 80.6 per cent tungstic trioxide (WO3) and 19.4 per cent lime (CaO).

Jan 1, 1935

By E. Douglas, D. N. Collins, J. R. Stevens

E. Douglas (Dept. of Scientific and lndustrial Re-search, Warren Spring Laboratory, Hertfordshire, England) — The authors are to be congratulated on the considerable improvements they have made in tailoring efficiency and selectivity terms which are generally superior to the alternative forms in current use. However, I feel that their efficiency expression is limited to lower-grade feeds; its accuracy reduces as the feed grade increases. For example, its application to such processes as the beneficiation of glass sands, refractories and clays will invoIve considerable inaccuracies. The reason for this lies in the direct use of recovery, which, with high-grade feeds, biases their empirical expression, R(1 - c/h). With a 90% grade feed, the recovery weighting for the slightest degree of beneficiation, over a zero efficiency sampling operation, will be 90+%+ I disagree with their second basic requirement which states that there can be no fundamental basis for any single quantifying expression. A formula giving a comprehensive representation of concentra- tion efficiency can be derived fundamentally accord-to the procedure outlined in the literature. &apos;&apos; This formula, called the Basic Efficiency formula, is

Jan 1, 1963

Preheating Feature of Leyner Oil Furnace for Heating Drill Steel The No. 3 Leyner oil-burning furnace, used for heating drill steel, is now made with a preheating chamber. By this addition it is claimed that the heating capacity and, effeciency of the furnace are increased about 50 per cent. This preheater is a section which fits between the body and cover of the furnace of the old design. It may be attached to an old furnace by simply changing a few bolts. Referring to the illustration, it will be seen that the lower chamber is used for the final heating and the upper one for preheating. The type of burner now furnished with this furnace is suitable for either high- or low-pressure air. It hats merely to be throttled for high pressures and when this is done, it, is as efficient as burners designed especially for high pressures and eliminates the noise common to such burners. This furnace burns petroleum or any of its oils, such a, gasoline, kerosene, distillate, etc. Oil heating has many advantages. The steel cannot be injured by absorbing injurious elements such as sulphur, phosphorus or other impurities which :ire present in nearly all coals, nor from unequal heating since the flame imparts a uniform temperature; further, o lie steel is in full view of the operator at all times.

Jan 3, 1916

By L. Adler

The proper transfer of roof loads from props and bolts to ribs and pillars can result in appreciable savings. The author shows how to plan such load reduction in underground mines. For openings in bedded rocks, analyzed by simple beam theory, it has been shown that roof loads can be shifted from one support to another.&apos; This transfer is effected by controlling the relative deflection of adjacent supports. If this action is used to reduce loads in the props or bolts and increase them in the ribs or pillars, it could be productive of economies averaging 30 pct. Such savings can be realized by: 1) using smaller artifical supports such as props and bolts, and 2) increasing loads in the rib to induce eventual failure for longwall caving. Since the rib is relatively load-insensitive, it provides a natural load sink. However, caution must be used in applying such permissive deflections, for while the supports are being handled properly, the stresses in the roof itself are very sensitive to such manipulations.1 An underground opening overlain by a relatively thin immediate roof, and a thick main roof, is usually laid out as shown in Fig. 1. The total open span (T) between pillars or ribs is calculated on the basis of the main roof, and the secondary spans (L) on the basis of the immediate roof, so that a complete accounting of the existing loads is made. For this purpose the immediate roof is treated as a uniformly loaded continous beam, which is an indeterminate structure as shown in Fig. 2(A). The term systematic supports places the following two restrictions on the continuous beam: 1) Spans between all supports are equal: uniformity of spans. 2) Loads on all supports (excepting ribs) are equal: uniformity of supports. The usual mode of analysis of such a structure by beam theory is to divide it up into a series of simply supported beams with end moments as shown in Fig. 2(B)2 The problem now is to transfer a maximum roof load to the rib from the span immediately adjacent to it by permitting its support to deflect, and yet not fail the roof. Once this has been done, the load can be equalized on all other supports by permitting further degrees of relative deflection. It is necessary, therefore, to determine an expression for the constant load on each support, and the required deflections, in terms of properties of the roof. From Fig. 1: T/L0 = No and T/L = N [1] Where: T = allowable span of main roof, ft. (Calculated from S = Mc/l) S is allowable modulus of rupture, psi. M is maximum moment, lb-ft (in this case wT2/12). c is distance from neutral axis to extreme fiber, ft. I is moment of inertia with respect to the neutral axis, ft4. L,, = allowable span of immediate roof, ft (calculated as was T). L = actual span of immediate roof, ft. N0 and N are pure numbers where No < N and N is the integer just higher than Nu. For example: If T =100 ft and L0 - 15 ft 100 N0 =100/15= 6.667 . . .N= 7 L = T/N = 100/7 = 14.28 ft Consequently N = No + n where n is a positive fraction i.e.: 0< n < 1 Since from Eq. 1, T = NL = N0L0 Lo /L = N/No = N/N-n

Jan 1, 1961