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By R. Dawson Hall

THE stresses in the e simplest structures are often those we find most difficult to analyze. The most complex condition in mine stresses is found in simple tunnels where the roof, the sides, and the floor are a monolith. The functions of the parts are like the parts themselves not distinct and specialized, and the problems to be solved are like those in a metal structure with riveted joints or a redundancy of bars. This difficulty explains perhaps why the condition has not been treated. But just because it cannot be discussed in its entirety is no reason why it should be treated as an action of parts with specialized functions as a roof 'beans with supports and a foundation. The problem cannot be ignored on the ground that it is not of sufficient importance to warrant careful consideration, because conditions of complete monolithism, of which the tunnel is the type, are found materially unchanged) in room-and-pillar and in longwall work. This unity between roof, sides, and floor, which to the coal miner is a difficult conception, really deserves a scientific appellation, and perhaps holoid (from holos, whole, and eidos, form) will serve the purpose as well as any other. In a simple tunnel the roof, the sides, and the floor form integral parts of one and the same structure; and the distortion of one cannot be conceived without a consequent strain in the others. Thus when the roof of the tunnel droops by reason of its weight, the upper parts of the sides are drawn in because they are integrally-connected with the roof and must approach each other whenever, by the sagging of the roof, the distance between any two points in it is diminished. (See Fig. 1.)

Jan 9, 1915

By David L. Holt, Walter A. Backofen, Anwar-ul Karirn

ANNEALING the binary alloy, Mg-0.5 wt pct Zr in a hydrogen atmosphere results in extensive precipitation of zirconium hydride. The morphology of these precipitates has already been investigated.lm3 Squires, Weiner, and phillips4 found, following creep testing of the hydrided alloy at 450" and 500°C, that hydride denuded zones formed along grain boundaries that were aligned approximately normal to the tensile axis. Zone formation was attributed to diffusional creep by magnesium transport down the prevailing stress gradients.4'5 Recently, electron microprobe analysis by Karim, Holt, and Backofen6 showed the zones indeed to be zirconium-free and furthermore it was shown that in compression, zones formed along boundaries approximately parallel to the stress axis. Thus it was confirmed that the zones are formed by diffusional creep. Typical zone-formation is shown in Fig. 1. Karim, Holt, and Backofen also measured the con- tribution to the total strain, from diffusional flow, slip creep, and grain boundary shear: results showed that diffusional strain tends to saturate with increasing imposed strain, while grain boundary shear eventually becomes the dominant deformation mode. It was suggested in explanation that the precipitate-denuded zones are soft and easily sheared, such deformation contributing to the grain boundary shear measurement. A point to be emphasized is that the Mg-0.5 Zr alloy was not superplastic for the index of strain rate sensitivity of flow stress, m = a log log 6 was only 0.25. It was recognized that diffusional creep in a poly crystalline aggregate must be accompanied by boundary shearing.' The suggestion was that the non Newtonian-viscous character of diffusional creep in the Mg-0.5 wt pct Zr alloy is due to resistance to sliding of boundaries lying approximately parallel to the tensile axis.= The work described in the present note should be seen against the above background for it represents initial efforts to observe in a similar way diffusional creep in a superplastic alloy. Previous work with the ternary-alloy Mg-6 Zn-0.5 Zr, pellet extruded, showed it to be superplastic however it does not contain resolvable precipitates to act as internal markers for diffusional creep. Also the fine grain size of the alloy (0.5 p) made conventional metallography rather difficult. Solubility relationships in the Mg-Zn-Zr system are not well known, however making reasonable guesses about the probable phase diagram of the ternary, Mg-Zn-Zr, various heat treatments were attempted to produce hydride precipitation. Finally a 16-hr anneal at 495' in hydrogen was found to pro-

Jan 1, 1970

Masjid-i-Su1aiman.—There have been no new developments in the Masjid-i-Sulaiman field during the year. Drilling, deepcning and acidizing operations for maintenance of production havc continued normally. Reservoir conditions have been unchanged, the rate of fall of dome prcssure remaining very low—at about 0.4 lb. per sq. in. per million tons net production. Drilling on the Lali structure northwest of Masjid-i-Sulaiman has continued but oil has not been encountered in commercial quantities. Haft Kel.—The progressive drilling program extending the production capacity of the Haft Kel field was completed carly in the year and the field is now on a routine maintenance basis. Drilling has continued on the white-oil springs structurc northwest of Haft Kel. Naft-i-Shah.—No developments of interest have occurred in Naft-i-Shah field. Offtake is for local markets only. A further large produeer was completed during the year. Gach Saran.—By the end of 1939, work on plant and pipe lines to put, the field on a production basis was approaching completion. Two substantial producers were also drilled in the initial production area. Pazanun and Agha Jari.—No further drilling was carried out on the Pazanun structure during the year, gas only having been obtained to depths exceeding 8000 ft. On the adjacent Agha Jari structure, however, a second satisfactory oil producer was completed.

Jan 1, 1940

Masjid-i-Su1aiman.—There have been no new developments in the Masjid-i-Sulaiman field during the year. Drilling, deepcning and acidizing operations for maintenance of production havc continued normally. Reservoir conditions have been unchanged, the rate of fall of dome prcssure remaining very low—at about 0.4 lb. per sq. in. per million tons net production. Drilling on the Lali structure northwest of Masjid-i-Sulaiman has continued but oil has not been encountered in commercial quantities. Haft Kel.—The progressive drilling program extending the production capacity of the Haft Kel field was completed carly in the year and the field is now on a routine maintenance basis. Drilling has continued on the white-oil springs structurc northwest of Haft Kel. Naft-i-Shah.—No developments of interest have occurred in Naft-i-Shah field. Offtake is for local markets only. A further large produeer was completed during the year. Gach Saran.—By the end of 1939, work on plant and pipe lines to put, the field on a production basis was approaching completion. Two substantial producers were also drilled in the initial production area. Pazanun and Agha Jari.—No further drilling was carried out on the Pazanun structure during the year, gas only having been obtained to depths exceeding 8000 ft. On the adjacent Agha Jari structure, however, a second satisfactory oil producer was completed.

Jan 1, 1940

The following tables showing the output of coal during the year 1913 have been secured y R. H. Morris, of Pocahontas, Alberta, Canada, for the use of the Committee through the kindness of John T. Stirling, Chief Mine-Inspector of Alberta. The principal mining districts are, Crow's Nest Pass, Calgary, Lethbridge, and Edmonton, the outputs from which were as follows: Tons Crow's Nest Pass 1,849,435 Calgary...: 627,461 Lethbridge ; 966,020 Edmonton 863,430 Total 4,306,346 Of this quantity there was exported to the United States, principally from the Crow's Nest Pass district, 138,201 tons of 2,000 lb., that being the ton used throughout the Province. This production consisted of lignite, bituminous coal, anthracite, coking coal and coal used in making. briquettes, as follows: Tons "Lignite coal" (lignitic?) 1,763,225 Bituminous coal 2,374,401 Anthracite coal 168,720 Coking coal 104,012 Coke produced 65,167 Briquettes produced 130,861 The only district in which coke was made is the Crow's Nest Pass district, and the entire product was consumed in Canada. The total number of persons employed is as follows: Above ground 2,231 Underground 5,837 Total 8,068 The per capita production was as follows: Tons of coal mined per employee 533 Tons of coal mined per underground employee 737

Jan 7, 1914

There have been no major field developments during 1935. Operations have proceeded normally on the company's three producing fields, Masjid-i-Sulaiman, Haft Kel and Naft-i-Shah. The refinery at Kermanshah was commissioned in September, 1935, with a rated throughput capacity of 75,000 tons a year of topped crude to meet local requirements. Crude production from the Masjid-i-Sulaiman and Haft Kel fields is tabulated below: Masjid-i-Sulaiman Field.—The flowing lives of wells have been extended by (I) a process of acid treatment, thereby reducing the bottom-hole pressure differentials, and (2) by reducing the back-pressure. Optimum producing conditions for individual wells have been determined as a result of an experimental study of the amount of available energy in the reservoir crude and of energy losses in flowing wells. The return of surplus products to the reservoir has continued to be a satisfactory economic operation and the crude throughput capacity of the topping plant has been increased. The viscosity of residue returned to the reservoir is reduced before injection by regassing at 35 lb. per sq. in. absorption pressure with surplus gas. The pressure in the gas dome is falling at the low rate of one pound per annum. Haft Kel Field.—The delimitation of the main structure has proceeded; the oil-bearing area so far proved being about 50 square miles.

Jan 1, 1936

There have been no major field developments during 1935. Operations have proceeded normally on the company's three producing fields, Masjid-i-Sulaiman, Haft Kel and Naft-i-Shah. The refinery at Kermanshah was commissioned in September, 1935, with a rated throughput capacity of 75,000 tons a year of topped crude to meet local requirements. Crude production from the Masjid-i-Sulaiman and Haft Kel fields is tabulated below: Masjid-i-Sulaiman Field.—The flowing lives of wells have been extended by (I) a process of acid treatment, thereby reducing the bottom-hole pressure differentials, and (2) by reducing the back-pressure. Optimum producing conditions for individual wells have been determined as a result of an experimental study of the amount of available energy in the reservoir crude and of energy losses in flowing wells. The return of surplus products to the reservoir has continued to be a satisfactory economic operation and the crude throughput capacity of the topping plant has been increased. The viscosity of residue returned to the reservoir is reduced before injection by regassing at 35 lb. per sq. in. absorption pressure with surplus gas. The pressure in the gas dome is falling at the low rate of one pound per annum. Haft Kel Field.—The delimitation of the main structure has proceeded; the oil-bearing area so far proved being about 50 square miles.

Jan 1, 1936

By Henry N. Toler

Oil and gas development in Mississippi during 1936 was about the same as during the past three or four years, with less drilling activity in the proven fields; although at the end of the year there was a decided increase in interest and activity. Jackson Gas Field Six wells were drilled in the Jackson gas field, three of which were producers and three dry holes. The gas production for 1936 was 12,968,-000,000 cu. ft., which is 2,500,000,000 cu. ft. more than for any previous year. The total gas production from the field to the end of 1936 has been 58,092,000,000 cubic feet. Thirteen producing gas wells were abandoned during the year because of encroachment of salt water. At present there are 99 producing gas wells in the field. The three oil wells on the edge of the field, which had been producing, were not produccd during 1936, although they are still capable of making some oil with much salt water. The rock pressure at the end of the year was 930 lb., which is a decline of 80 Ib. since the discovery of the field. In March of 1936, the State Legislature appropriated $115,000 to be used by the State Mineral Lease Commission in drilling some gas wells

Jan 1, 1937

By G. H. Clevenger

Discussion of the paper of ALLAN J. CLARK presented at the San Francisco meeting, September 1915, and printed in Bulletin No. 103, July, 1905, pp. 1381 to 1398. G. H. CLEVENGER, Palo Alto, Cal.-Since the precipitation of extremely dilute solutions as regards cyanide presents one of the greatest problems of zinc-dust precipitation, I should like to ask Mr. Clark the minimum concentration in cyanide of the solution from which it is possible to precipitate satisfactorily the gold with zinc dust in Homestake practice. A. J. CLARK.-For a day's work about 0.015 per cent. That is precipitating a very low-grade solution, very low in alkalinity. It requires probably 0.2 lb. of zinc dust to the ton. JOHN A. FULTON, Melones, Cal.-At the Melones mine, we have been working very low-grade rock for a number of years, the process being amalgamation and concentration up to the last year. The value of the ore increased so that we had to supplement the concentration with a sand and slime plant. Classification was a problem, since to install classifiers would mean tearing the mill all to pieces. We are therefore making use of a Wilfley table for this purpose. The amount of wash water is increased and a stream of fresh water is also run into the feed box at the

Jan 12, 1915

Uranium, discovered in 1949 at Rum Jungle, 40 miles south of Darwin, N. T., was mined and processed to U3O8 from 1954 to 1963 by the Territory Enterprises Pty. Ltd. TEP is a Government company managed by Conzinc RioTinto of Australia Ltd. During this period, the uranium oxide was sold under contract to the Combined Development Agency, a joint Anglo-American uranium procurement agency. When the contract terminated in 1963, more than 31/4 million pounds of uranium oxide had been delivered which had been mined from three open pits. Copper ores, found with the uranium, necessitated the addition of a copper circuit to the concentrator. Copper concentrates containing 12,981 pounds of copper were also produced. Rum Jungle was the largest single industrial enterprise in the Northern Territories and, as such, was an important economic and social factor in this sparsely settled tropical region. To stretch out the life of this enterprise for the above reasons, and with the added possibility that the uranium market might improve, the Commonwealth mined out and stockpiled 650,000 tons of ore containing 9.6 lb of U,O, per ton, which is sufficient to sustain the treatment plant at 200 tpd until about 1971. In the plant, uranium is recovered from solution by solvent ex- traction. Current output is being stockpiled pending suitable market conditions.

Jan 10, 1964

By E. J. Bruderlin

A METALLURGICAL process to be economically successful must be carried on under proper conditions of control and equipment. The question of equipment is always of primary importance. In the dis-tillation process for the recovery of zinc by retorting, the retort is the all-important piece of equipment. Each retort in a working block must function as a separate unit. Over-all block efficiency is the result of the ability of the individual retort -to withstand the severe conditions of operation for a maximum period of time. Therefore retort manufacture has been an ever present problem with the operator of a zinc-retort-ing plant. During recent years the zinc-plant operator has been faced with rapid changes in the character of the ores and concentrates. Operating costs have increased as a result of the- introduction of the flotation process and the amount of flotation concentrates to be handled. To counteract increasing costs, the operator has found it necessary continually to attempt heavier loading of retorts, until a 45 to 50-lb. charge per cubic foot of retort space has become common practice. Heavy loading has brought about severe firing conditions, which, in turn, have emphasized the necessity for further improving the quality of the retort. Increasing percentages of detrimental impurities in the retort charges have also added to the operator's difficulties.

Jan 1, 1936

By Edgar S. Cook

The Warwick furnace at Pottstown, Pa., constructed for anthracite fuel, is, as may be remembered, 554 feet high, with 15; feet bosh. The actual working height from stock-line to bottom is only 474 feet, the bell-and-hopper taking up 8 feet. During the year 1886 we used mixed fuel, in the proportion of three-fourths anthracite and one-fourth coke. The total product of iron was 30,6299 tons of 2280 lbs., being a weekly average of 589 tons, including all ordinary and extraordinary stoppages. Deducting the latter, the weekly average would be about 600 tons. The fuel-consumption for the year was 1.2 tons per ton of iron, while the ore-mixture yielded 52 per cent. of iron. For about two months during the summer of 1887 we were obliged to run on anthracite exclusively, owing to the Connellsville coke strike. In the fall of 1885, in relining the furnace, the crucible had been built 8 feet 9 inches in diameter, with the view of using regularly one-quarter of coke (the largest previous diameter having been 7 feet 5 inches), and we felt somewhat apprehensive of the results when compelled to use anthracite only. The average of seven weeks' run on coal, as compared with the average of the seven corresponding weeks of 1886 (using one-quarter coke), was as follows:

Jan 1, 1889

By J. Walter Scott

IT is usual practice in the copper industry to use open horizontal molds for casting tough-pitch copper wire bars.1 A wire bar cast in this manner is partly characterized, by heavy wrinkles and a comparatively deep skin of oxide on the top of the bar, corresponding to the open side of the mold. On the theory that the rough, high-oxide surface might have an adverse effect on the rolling and drawing properties of a wire bar and might account for some of the irregularities of mill behavior, several bars which had been planed to remove the wrinkled surface were processed into wire. These bars responded to mill treatment more satisfactorily than did the regular wire bars. Realizing that machining the surface of one face of each bar would not be commercially feasible, it was decided that casting the metal into a vertical mold and cropping off the pouring end would accomplish. approximately the same result. Several wire bars of commercial size (250 lb.) were so cast and processed into wire for comparative test with bars cast in the usual horizontal molds. It is the purpose of this paper to present the results obtained from this investigation, in which commercial bar sizes and processing technique were used throughout. The results show that in general copper wire bars cast vertically are superior to those cast horizontally.

Jan 1, 1930

By H. D. Peterson, G. E. Butts, J. F. Spisak

In 1978, Anschutz Mining Corp. began efforts to develop the Madison Cobalt Project in southeast Missouri. Preliminary metallurgical studies indicated that intermediate grade cobalt products, suitable for shipment to existing refineries, could be recovered from the sulfide mineralization of the ore body. However, tolling and freight charges were significant, as the refineries were located outside the US. These refineries would not satisfy the goal of strategically insulated production of superalloy-grade cobalt. The acquisition of proven, readily available refinery technologies was then evaluated. However, licensing costs were substantial and the "proven" technologies were not directly applicable to the unique chemistry of Madison materials. Faced with these challenges, Anschutz, in conjunction with the Colorado School of Mines Research Institute, embarked on an effort to develop a sulfate-based separation and refining process. CSMRI performed bench-scale and continuous pilot experiments on solutions generated through other pilot campaigns conducted by Lurgi, Hazen Research, and Sherritt Gordon. The results indicated that cobalt could be selectively extracted from sulfate media using a new generation of organophosphates. The solvent extraction system produced a solution suitable for electrolysis of high-purity cobalt. Preliminary cost studies indicated the novel process was competitive with other refinery systems. Plans to develop the detailed engineering-design information required to commercialize the process were abandoned when the price of cobalt collapsed to less than $17.64/kg ($8.00 per lb).

Jan 1, 1985

By T. J. Hudson, P. B. Queneau, J. D. Prater

The process parameters for effective utilization of nitric acid as an oxidant for copper-iron sulfides have been developed. Leaching variables found to be important were acid concentration, temperature, time, atmosphere, pressure, mineral type, particle size, and percent solids. Particular attention was devoted to analysis and control of fumes evolving during the oxidation. Data were recorded on metal extraction, elemental sulfur formation and oxidation, product gas composition and evolution rate, reagent consumption, and residue flotation response. The study was concluded by laboratory testing a flowsheet based on the foregoing observations. Ninety-eight percent of the copper contained in a chalcopyrite-bornite concentrate was recovered, requiring 1.6 lb of nitric acid to be regenerated externally per pound of copper extracted. Iron remained in the leach residue as hydrogen jarosite and was ultimately rejected from the system by froth flotation. Sixty percent of the sulfur contained in the copper concentrate reported in the elemental form; the remainder was oxidized to sulfate and eliminated with the hydrogen jarosite in the flotation tails or by neutralization of the solvent extraction raffinate with lime. Nitrogen was evolved primarily as NO and NOD; up to 3% N2O also was present. Gases containing sulfur were absent except when pyrrhotite was solubilized in the absence of soluble copper. In this case, HAS was evolved.

Jan 1, 1974

By R. F. Marande, R. S. Busk

THE magnesium-aluminum-zinc system contains most of the magnesium-base alloys used commercially, although in practice the ternary, alloys are usually modified by the addition of a small amount [ ] of manganese. Table I contains the magnesium-base commercial sand-casting alloys most widely used throughout the world, together with their typical tensile properties. These alloys may be regarded as a single family of varying aluminum and zinc content, disregarding manganese. A concise means of presenting data for them is by means of iso-property lines plotted on triangular coordinate paper. Constitutional, casting, and mechanical properties are presented in this manner. The data are given with the object of providing reference material, and to aid in the choice of a commercial alloy to serve a particular purpose. Detailed, critical analysis of the commercial alloys has been covered in a previous paper.1 [ ] All alloys reported were made in 15-lb. melts, superheated to 1700°F. for 15 min., cooled to 1400°F. and poured in sand molds. The test bars produced had a ½ in. reduced section and were about 6 in. long. Except for the data represented in Figs. I and 3 the alloys used were of commercial purity and contained 0.1 to 0.2 per cent Mn in addition to the aluminum and zinc. CONSTITUTIONAL DATA Under the heading of Constitutional Data are included all known data on con-

Jan 1, 1946

By Bernard York, John J. Reed

Mine opening stability was investigated by loading model openings to failure. Eight-inch plaster blocks were cast with small uniform section openings passing through the centers. After curing, the models were jacketed and loaded hydrostatically in a closed vessel. Opening size, shape, and orientation were varied to determine how these factors influence opening stability. THE investigation described in this paper is a continuation of a project begun in 1946 by Bernard York and W. E. Bush. .The experimental method used in the investigation involves the hydrostatic loading of a model mine opening to failure. Most investigators agree that this loading closely approaches actual conditions in very deep mines. The conditions are further idealized by using an essentially isotropic model material. The experiments consist of casting 8-in. plaster cubes, or 8-in. diam cylinders 8-in. long, having a relatively small uniform section hole passing through their centers. After thorough drying, the models are jacketed in a flexible plastic bag and loaded hydrostatically with water in a closed vessel. At about 300 to 500 lb per sq in. pressure the central opening fails. The fracture pattern resulting from opening failure is studied in a plane normal to the longitudinal axis of the opening. The model block is sawed through its center after loading to expose this plane and to eliminate the possibility of end effect. By changing

Jan 1, 1954

By C. W. Lawr

THE ores mined by the Santa Gertrudis Co. at Pachuca, Mexico, are mainly silver-bearing; they also yield some gold and carry a little copper. Strong cyanide solutions are used to dissolve the silver and gold, and the mechanical loss of cyanide at the tailings filter has been considerable. Prior to the year 1923, the pulp, after agitation, was given a 35 to 37-min. wash with barren solution in a Butters-type leaf filter; the discharged slime cake was repulped and pumped into eight Merrill self-sluicing slime presses in which the slime was given a further wash with barren solution for 25 to 35 min., followed by a 10-min. water wash. At that time the barren solution titrated around 0.350 per cent. free KCN and 0.500 per cent. total KCN. (Aero brand cyanide is used.) It can readily be seen that a 10-min. water wash would leave considerable cyanide in the filter cake, which of course was a total loss. This averaged 0.522 kg. (1.15 lb.) KCN per ton of solution. As the daily discharge to. the dam was 1600 tons1 of slime of a 2: 1 ratio of liquid to solid, the value of this mechanical loss of cyanide was an important item and its recovery held alluring possibilities.

Jan 1, 1929

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946