Search Documents

By Victor E. Kral

"SUMMARYFollowing a magnetometer survey on the McCoy iron deposit, a trenching and drilling program was carried out by the Bureau of Mines in August 1944.This deposit is 32.3 miles southwest of Battle Mountain in the McCoy Mining District, Lander County, Nevada, and lies on the east flank of the Fish Creek Mountains at an altitude of 5,400 feet, about 1 1/2 miles south of the gold camp of McCoy.Total production from the deposit has been 400 tons of magnetite, mined by hand and shipped to the west coast for ship's ballast.Bureau drilled two holes to a total depth of 92 feet and excavated 12 feet of trenches. Both holes were drilled in the same ore body and engineered magnetite ore 14 and 11 feet thick. Trenching was used successfully to show the lateral limits of the ore.Magnetite ore bodies were found to occur as replacements of a limestone bed in quartzite. They outcrop near and parallel to the exposure of a diorite entrusting that forms a long westward-trending ridge. Although magnetic outcrops can be traced for 5,000 feet trenching definitely proved the ore bodies to be disconnected to have little or no lateral extent beyond their outcrops. Only two ore bodies more than 10 feet thick were found; one of these is the inaccessible to and the other was drilled by the Bureau."

Jan 1, 1947

By D. T. White

Pressure acid leaching of nickel laterite ores typically involves the production of an intermediate product that is releached and refined to pure nickel and cobalt products. BHP Billiton is developing the Ravensthorpe Nickel Project to produce up to 50,000 t/y of nickel via a mixed hydroxide intermediate, which will be refined at its Queensland Nickel (QNI) Yabulu Refinery near Townsville, Queensland. The hydroxide precipitation flowsheet has been adapted to process high magnesium ores through an atmospheric leach stage, eliminate iron(III) as jarosite and oxidise iron(II) during neutralisation. The neutralisation conditions are controlled to precipitate aluminium, chromium and silicon, and to ensure good solid-liquid separation. Soluble impurities such as magnesium are purged with the tailings stream and will be managed over the long term by crystallisation in evaporation ponds.

Jan 1, 2006

Jan 1, 1961

Although not immune from the problems affecting the U.S. economy generally, the mineral industry in 1991 contributed nearly $300 billion in the value of processed materials of mineral origin. Supporting this contribution, the Bureau of Mines continued the research and analytical programs highlighted in this annual review. Featured in 1991 were such relatively new programs as minewide monitoring applications in ground control and advances in processing of ceramics and composites, along with more traditional research into health, safety, and mining technology, minerals and materials science, and environmental technology. Under Bureau sponsorship, a National Minerals Policy Forum brought together some 200 executives from industry and Government concerned with minerals policy to begin a dialogue on developipng a policy statement on current minerals issues. A major feature of the forum was the keynote address by Secretary of the Interior Manuel Lujan, Jr.

Jan 1, 1992

By Russell C. Frith

This paper examines the design of longwall shields, focusing on those aspects that are critical to either their successful application or contribution to failure during longwall extraction. In many instances, longwall shields are assessed and designed along lines similar to that of roadway ground support systems, namely according to typical or normal geotechnical conditions. However it will be contended that for longwall shields, this is inappropriate because unlike roadway ground support systems, longwall shields cannot be supplemented with additional or secondary support in localised areas of adverse geotechnical conditions. In other words, the longwall shield needs to be designed according to what are judged to be worst case or adverse geotechnical conditions?the outcome being that a well-designed shield will be significantly over-rated for the majority of its working life. Therefore, it will be argued that the additional capital cost of such shield design can be readily justified as a prudent riskbased outcome that is essential to minimising future business risks due to strata instability on the longwall face. Shield geometry will be discussed, including such relevant factors as leg angle, inclination of the top caving shield, canopy ratio, operating height range, and tip to face distance. These are all well-established longwall shield design considerations and, most importantly, areas whereby inadequate design can render a longwall shield as highly ineffective. The issue of tip to face distance will be considered in detail, in particular, the extent by which it is an important geotechnical design consideration, the conclusion being reached that, in fact, it is not. The critical importance of maximising set to yield ratio within practical operating limits will be justified, the wisdom of this having been subject to questioning in more recent technical literature. Overall, the aim is to provide the industry with a set of suggested guidelines for future use when designing longwall shields and, hopefully, to initiate discussion on a subject that, unlike roadway ground support design, is not well covered in its entirety in the published technical literature.

Jan 1, 2013

By F. Guo

"The leaching kinetics of zinc sulphide concentrate was studied under total pressures ranging from 0.3 MPa to 0.5 MPa and leaching temperatures ranging from 358 K to 378 K. The apparent activation energy of leaching reaction under different total pressures was calculated. The results show that for the extraction of zinc at low-temperature pressure leaching is controlled by an interfacial chemical reaction. This was supported mineralogical analysis of the leaching residue. The kinetic equation for low-temperature pressure leaching of zinc sulphide concentrate was further established by quadratic regression on the basis of shrinking core model.INTRODUCTIONThe Roast-Leach-Electrowinning Process (RLE) is the primary route for zinc production and responsible for more than 85% of the total zinc production (Souza et al., 2007). During the roasting of zinc concentrates, fugitive SO2 causes pollution. The prevention of SO2 emissions from the RLE process can be one of the challenges to this technology (Deller, 2005). In the 1980s, the Zinc Pressure Leach (ZPL) process changed the concept of zinc hydrometallurgy, in which zinc sulphide concentrate is directly leached at approximately 423 K and approximately 0.7 MPa oxygen overpressure and the sulphidic sulphur is oxidized into elemental sulphur so that the pollution by SO2 is completely avoided. Since 1981, five zinc plants have adopted the ZPL process either for expansion by integration with existing roasting facilities, or for the production of zinc without any roasting at all (Collins et al. 1994; Barth et al. 1998). The innovation of the ZPL process has made the zinc industries more competitive although it needs an autoclave. The direct leaching technology of zinc is still in development."

Jan 1, 2012

It is almost eight years to the day when we launched the original SAMREC Code in March 2000. Since that date I think the SA minerals industry has matured beyond recognition in its approach to reserve and resource reporting, and I believe we can be justifiably proud of that progress. Many of those companies that have led the way in reporting standards are listed on our sponsors list. We thank them for their sponsorship but even more for their considerable support in all aspects of the SAMCODE organization. Matt Mullins, my co-speaker here today, has been instrumental in the revision of the SAMREC Code over a long period of time and also took up the reigns with the SAMVAL Code after the retirement of Rob Croll. I would like to formally thank Matt for his immense contribution in producing the two Codes; he can take great pride in the final product and fully deserves the many accolades that we have already received from our international counterparts. He has done all this whilst still maintaining a very demanding day job at BHPBilliton. Matt will be the first to admit that he has received tremendous support from more than 100 people who participated in the various working groups, many of whom are employed by our sponsors. There are obviously too many to mention by name but they deserve a big vote of thanks for their personal contributions. In addition to launching the two Codes we are also launching our ?branding? initiative with our own SAMCODE logo and the SAMCODE website: www.samcode.co.za. All the slides used in the presentation today will be on the website later today as will a newsletter which will serve as a media release.

Jan 1, 2008

By Brianna M. Eiter, Jennica L. Bellanca

Mineworkers face a challenging and dynamic work environment every workday. To maintain a safe workplace, mineworkers must be able to recognize worksite hazards while they perform their jobs. Though hazard recognition is a critical skill, recent research from the National Institute for Occupational Safety and Health (NIOSH) indicates that mineworkers fail to identify a significant number of hazards. To further the understanding of mineworkers’ hazard recognition ability and to begin to address hazard recognition performance, NIOSH researchers analyzed data collected during a laboratory research study to determine the effect of individual mineworker factors including risk attitude, work experience, and safety training on hazard recognition accuracy. The results of this study show that mineworker risk attitude and safety-specific work experience affect hazard recognition performance while hazard-specific safety training does not. These results suggest that some of these individual factors can be overcome through experience and training. Potential strategies that can be used to address these factors are also discussed.

Aug 31, 2020

The goal of this presentation is to firstly, review mine effluent permits in a number of regulatory jurisdictions; and secondly, to develop a strategy for incorporating the regulatory requirements into the environmental assessment (EA) process for new mine proposals. The focus was on the province of British Columbia (BC) and their recent initiative on the One Project, One Process initiative. This task was approached by reviewing mine effluent permits for various regulatory jurisdictions and comparing them to BC mine effluent permits. This comparison revealed a variety of approaches for designing mine effluent permits, but there is a common scientific approach, which supports the conclusion that the permitting of mine site discharges can be designed based on a scientific approach. This approach is expected to: (a) achieve sound environmental protection, (b) demonstrate the application of Best Achievable Technology, (c) incorporate sound sustainability approaches, (d) incorporate regulatory objectives, and (e) create efficiencies for the regulator and mining industry. There is an essential precursor to developing a sciencebased effluent permit for which the proponent must provide: (1) the necessary technical assessment information to demonstrate the mine effluent permit application will result in an environmentally protective effluent discharge, to the satisfaction of the permitting agency; (2) the necessary level of detail for essential mitigation pollution control works to demonstrate how they will be operated to achieve the necessary treatment goals; (3) the necessary level of detail for non-treatment mitigation (passive treatment, or passive pollution control); and (4) the necessary level of detail to demonstrate how pollutants will be prevented from being mobilized (or being generated) from ore and waste materials, or, if the pollutant originates from an added milling reagent, how the reagent will be reduced. While (active) mitigation pollution control equipment is more definable in an effluent permit, non-treatment mitigation is more nebulous in terms of defining in a mine effluent permit; it is therefore recommended that appropriate management plans be developed for essential mitigation pollution control and non-treatment mitigation (passive treatment) and submitted with the proponent?s EA/effluent permit application packages. Major deficits in adequate active and passive pollution control will inevitably lead to regulatory impediments to developing a permit and allowing a mine to be developed, although EA processes strive to preclude major permit information gaps; the onus is on the proponent to provide complete information in this area. Hence the importance of EA processes ensuring that the major technical information requirements for effluent permit development are included in the EA phase. Recently, this aspect of the mine EA process has taken on a new role under the political efforts of One Project, One Review Process (Canadian) and One Project, One Process (in BC). These initiatives translate, in part, to ?synchronous permitting? (in BC): effluent permitting, for example, may be initiated shortly after the proponent submits the EA application to Ministry of Environment.

Aug 1, 2013

By Oliver Bowles

From remote antiquity stone has been employed for structural, ornamental, and memorial purposes. It was, and still is, so used because of its availability in innumerable localities and its architectural adaptability, dignity, substantiality, and durability. The principal varieties of stone used are granite, marble, limestone, sandstone, and slate. This report deals with granite. OCCURRENCE AND CHARACTER OF GRANITE Granites usually have been classed as igneous rocks derived from molten masses or magmas, but there is wide evidence that the origin of some granites may be attributed to regional metamorphism of preexisting rocks, rearrangement and recrystallization taking place without a liquid or molten stage. In any event granitization is a slow, deep-seated process.

Jan 1, 1956

By Richard A. Hawkins

O the American coal man, Australian coal mining most appear to have little, if any, influence on American coal-mining practice and to bear little relation to it. Actually, the relationship has been close, for Australian operators have carefully studied American practice by reading American technical publications, by consulting American engineers, and by visits to Ameriean operations. They have leaned heavily on America for their supply of mechanization equipment and many American mining-machinery manufacturers are active in that country, supplying its needs and furnishing technical assistance. Australia's influence on American coal mining has been obscure and probably negligible. However, it seems reasonable to assume that this influence will increase. The wartime development of air transportation will inevitably bring these two countries into much more intimate contact than existed in recent years. American servicemen. many of them former miners and coal-mining technicians, have visited Australian operation, while stationed in that country, have talked with operators and men over there, and undoubt-

Jan 1, 1945

By Peter L. Swanson

This investigation, which began 90 minutes after the February 3, 1995, seismic event, has benefitted from the assistance of a large number of individuals. These individuals provided information, data, analysis, brainstorming opportunities, field equipment, assistance with communication, conducted rock mechanics tests, and provided insight into mining in the southwestern Wyoming trona district. They include Rich Hodgson, Ron Hughes, Larry Refsdal. Mike Weller, John Kolesar, Joe Vendetti, and Rick Casey (Solvay Minerals), Dave Delling (Solvay consultant - former Solvay President), Karl Zipf (formerly with USBM, now with MSHA), Bob Friend, Bob Ferriter, Dave Ropchan, Jerry Davidson (MSHA Tech Support), Don Stauffenberg, Ben Hohler (Wyoming State Mine Inspector's office), Bruce Presgrave (USGS/NEIC), Chris Wood, Dan O'Connell (Bureau of Reclamation), Sue Nava, Jim Pechmann (University of Utah), John Norgord and members of FMC's mine rescue team (FMC Corp.), Bill Walter (Lawrence Livermore National Laboratory), Ron Gerlick, Kevin Wood, and Mike Harmel (USBM rock mechanics lab), Jim Case (Wyoming State Geological Survey), and Solvay consultants. In addition, many individuals helped us gather information on other recent large mining-related seismic events in Germany, Russia, and Australia. and other parts of the United States. These individuals include Wolfgang Minkley (IfG Institut fur Gebirgsmechanik, Leipzig), Arnfinn Prugger (Potash Corp. of Saskatchewan), Hartmut Spetzler (University of Colorado/ University of Bayreuth), Sergei Stanchits (Ioffe Poly-technical Institute, St. Petersburg), Rocky Thompson (Cyprus-Amax) and numerous seismologists throughout the Internet.

Jan 1, 2011

By H. Huang, R. N. Gow

"EH-pH diagrams are useful tools in understanding how mineral surfaces react in solution and particularly how aqueous conditions can be changed to enhance mineral leaching processes. Successful application of these diagrams, however, requires that several considerations be kept in mind to prevent what had been termed as “gross errors” in their calculation and use. In this paper, the aqueous Cu-S system is used as the basis for explaining the mass-balanced method of calculating EH-pH diagrams with the STABCAL thermodynamic equilibrium software. A breakdown of the Gibbs’ Phase Rule and how it is used in STABCAL to modify the diagrams is included. The methodology was applied to the aqueous Cu-As-S system, and resulting diagrams were compared against examples of those generated using the predominant-ion method. The complexity of such diagrams increases with every additional component, and competition between species becomes more apparent, as can be seen by curvature in the resulting mass-balanced diagrams. The complete diagram for enargite (Cu3AsS4) is shown. It compares well with spectroelectrochemical measurements from Raman spectroscopy and cyclic voltammetry studies.IntroductionInnovation in the field of processing arsenicbearing copper ores has been of particular interest. Copper arsenic sulfosalt minerals such as enargite (Cu3AsS4) and tennanite (Cu12As4S13) are now frequently prevalent in ore bodies as the oxide and easily leachable sulfides become harder to find. These minerals, unless pretreated somehow, concentrate in copper sulfide flotation processes, in turn concentrating the arsenic levels. Increasing environmental restrictions on arsenic content for smelters makes the hydrometallurgical processing of these concentrates more favorable. While enargite is considered one of the more refractory copper sulfides, more so than chalcopyrite (CuFeS2), there are still several methods, both industrially proven and in development, that are capable of processing these ore types. Alkaline sulfide leaching can be used as a pretreatment method to solubilize arsenic selectively (Delfini et al., 2003; Anderson and Twidwell, 2008; Tongamp, Takasaki and Shibayama, 2010a, 2010b), or the entire metal content can be leached using acid-type leaches such as acidified ferric sulfate (Dutrizac, 1981; Hackl et al., 1995; Klauber, 2008), or the chloride assisted, CESL (McDonald and Muir, 2007) or nitrogen species catalyzed (Anderson, 2003) processes can be used.As development of these leaching technologies proceed, it is also important to develop an understanding of the mineral thermodynamics. To date, there are numerous studies on the Cu-Fe-S-H2O system, particularly as it relates to chalcopyrite leaching, yet few studies have done on the Cu-As-S-H2O system. Computer-generated EH-pH diagrams have been employed to illustrate the importance of thermodynamic calculations in providing insight into such a system."

Jan 1, 2016

By P. Conrad, S. Rosenthal

"Engineers remain in demand. Job opportunities in the United States still exceed the number of students graduating from college with degrees in Mining Engineering. Although enrollment is up for freshman studying Mining Engineering, many of those students will either change majors or not complete their degree, maintaining that deficit of available Mining Engineers. What can be done to ensure that enough Mining Engineers will graduate to fill the needs of the mining industry over the next ten to 20 years? The authors believe that this need can be met by recruiting students to Mining Engineering programs who are genuinely interested in working in the mining industry. With this in mind, Montana Tech conducted its first Mining Engineering camp in July 2014 to get junior and senior high school students interested in careers in the mining industry by showing them that Mining Engineering is both an exciting and rewarding career. This paper discusses What a Blast! The 2014 Montana Tech Mining Camp. INTRODUCTION The concept of summer camps for high school students is not new. For example, Missouri University of Science and Technology has offered their “Explosives Camp” for several years. A large percentage of attendees to these camps discover or confirm an interest in Mining Engineering and enroll in the school’s program. The Dean of the Montana Tech School of Mines and Engineering challenged department heads to develop and offer summer camps for prospective high school students to get a taste of engineering with the goal being to improve recruitment for each discipline. Mining Engineering embarked on the concept of a summer camp in 2013 with a concept to provide a week’s experience in Mining Engineering during the summer of 2014. What it takes to progress from concept to reality, with some of the learnings to be shared, follows."

Jan 1, 2015

By F. A. Rutledge, H. Marstraander, J. H. Hulbert, G. A. Apell

"INTRODUCTION The inability of Alaska coal mines to supply the quantity of coal required by public and private consumers and by the armed forces in Alaska caused the Coal Procurement Section of the Alaska Department, U. S. Army, to be established. It proposed to investigate the coal deposits and to expedite production of coal. The Bureau of Mines has closely cooperated in this program and was in direct charge of exploration. As to develop and equip an underground coal mine would have taken time and the need for coal was acute, a deposit that could be prepared for mining quickly was desirable. Several such deposits of stripping coal were known to occur in the Nenana field and were examined by the Bureau. One of these, the Diamond strip mine 4 miles west of Healy, was brought into production late in the fall of 1943. This mine was operated for the Army Coal Procurement Section by the C. F. Lytle Co. and the Green Construction Co.The Roth property, or Leasing Block No. 28, in the Healy Creek Valley offered the largest available tonnage of both stripping coal and total reserves. A program of exploration by the Bureau of Mines was inaugurated in 1943 and completed in 1944. Field parties of the Federal Geological Survey mapped the area had correlated the coal beds during the 1944 and 1945 summer seasons."

Nov 1, 1946

By G. Mark Aylmore

Various processes have been developed using a combination of elevated temperature and chemical treatment processing to recover Li from silicate minerals. To facilitate further process development, a comprehensive understanding of the deportment of Li and associated minerals in ore bodies is essential to allow the industry to predict the response of ore reserves to metallurgical treatment options. This paper describes results from the integrated use of the John de Laeter Centre’s state of the art analytical and mass spectrometry techniques to characterise a selection of Li bearing ore bodies and determine their amenability to potential processing options for the extraction of Li. The mineralogy, mineral associations, and liberation characteristics of ore-bearing and gangue minerals were characterised using a combination of the TIMA and XRPD studies. The Li content and distribution within minerals were defined using LA-ICPMS and field emission scanning electron microscopy techniques (EBSD, ToF-SIMS) and atomic probe microscopy.

By H. Kinilakodi

In 2008, the authors developed a methodology for assessing underground coal mines for high risk for major-hazard events. It focused on major hazard-related violations of safety standards associated with high-risk conditions. Later using a sample of 103 mines with 2008 and 2009 data, injury measures and MSHA citation data were combined into a Safe Performance Index (SPI). The SPI was used to assess the relative safety-related risk of mines, including by mine-size category. In this paper, comparisons are made of SPI-associated, normalized safety performance measures across mine-size categories, with emphasis on small-mine safety performances as compared to large and medium-sized mines.

Jan 1, 2011

By H. Westengen

The AE alloy family exhibits remarkable combinations of properties when utilized as high pressure die castings. This performance relies on the fact that the rapid cooling rate resulting from the direct contact between the molten alloy and the steel die walls effectively refines the structure through rapid solidification. Furthermore, the rare earth additions modify the solidification pattern, dramatically reducing the solidification interval. A solid shell forms at temperatures exceeding 500C, reducing the tendency for die sticking and inverse segregation. As a result, the die castability is excellent, giving parts with a smooth and shiny surface. Unlike other magnesium die casting alloys developed to improve elevated temperature creep properties, AE alloys do not suffer from the commonly observed tendency to introduce brittleness. This feature is attributed to the fact that the massive magnesium- aluminium intermetallic phase is substituted by a finely dispersed lamellar structure of Al-RE intermetallics. The resulting combination of excellent elevated temperature properties and good ductility, as well as excellent corrosion resistance, means superiority of these alloys for demanding automotive engine and chassis applications.

Jan 1, 2006

By Peter Hayes, Evgueni Jak, Taufiq Hidayat, Gary O’Connell, Denis Shishin, Jeff Chen, Francis Letarte

"Knowledge of slag properties is required for the optimisation of smelting operations. The phase equilibria and viscosities of the Al2O3-CaO-FeO-Fe2O3-MgO-MnO-NiO-Cr2O3-SiO2 slags at conditions of interest to Koniambo Ni-laterite smelting operations have been investigated. High-temperature re-equilibration phase equilibrium experiments of industrial slags followed by rapid quenching and direct measurement of phase compositions using electron probe X-ray microanalysis (EPMA) have been undertaken in the olivine and pyroxene primary phase fields at temperatures between 1475 and 1600°C and SiO2/MgO weight ratios between 1.57 and 2.09. Phase equilibria predictions were performed using FactSage thermodynamic software. A slag viscosity model available in the FactSage thermodynamic package has been used to calculate the viscosities of the liquid slags. The Einstein-Roscoe equation combined with the predicted phase equilibria data have been used to estimate the viscosities of the slag slurries (slag + solids). The information provided can be used to assist in the evaluation of the furnace performance, to assess further optimisation of slag composition and to explore possibilities of targeted feed changes.INTRODUCTION One of the key steps in the production of ferronickel from nickel laterite ore at Koniambo Nickel SAS involves reduction and smelting of pre-dried nickel-bearing saprolitic ore (high Mg and Si) in an electric furnace at temperatures up to 1650°C. The characterisation of the slag properties as functions of key operational parameters, such as, temperature and composition, including liquidus, the proportions of solids and viscosity, is essential for improving control and optimisation of the operations. The slag produced in the smelting process is a complex oxide system with the major chemical components including Al2O3, CaO, Cr2O3, “FeO”, MgO, “MnO”, “NiO” and SiO2. Characterisation of these multi-component systems using a solely experimental approach becomes increasingly complex as the number of components is increased."

Jan 1, 2017

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960