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IC 
 
 8992 
 
 Bureau of Mines Information Circular/1984 
 
 Use of Steel Sets in Underground Coal 
 
 By J. H. Steers, M. O. Serbousek, and K. E. Hay 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 
Information Circular 8992 ^-r- 
 
 Use of Steel Sets in Underground Coal 
 
 By J. H. Stears. M. O. Serbousek, and K. E. Hay 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 William P. Clark, Secretary 
 
 BUREAU OF MINES 
 Robert C. Horton, Director 
 
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 Library of Congress Cataloging in Publication Data: 
 
 Stears, J. H. (Juel H.) 
 
 Use of steel sets in underground coal. 
 
 (Information circular / United States Department of the Interior, 
 Bureau of Mines ; 8992) 
 
 Bibliography: p. 15. 
 
 Supt. of Docs, no.: I 28.27:8992. 
 
 1. Mine timbering. 2. Ground control (Mining). I. Serbousek, M. 
 O. (Maynard O.). II. Hay, K. E. (Kenneth E.). III. Series: Informa- 
 tion circular (United States. Bureau of Mines) ; 8992. 
 
 '¥m^%^iA [TN289] 622s [622'.334] 84-600202 
 
CONTENTS 
 
 Page 
 
 Abstract. 
 
 Introduction 
 
 Steel support accidents 
 
 Survey of current practices 
 
 Steel support systems 
 
 Steel crossbars 
 
 Rigid steel arches 
 
 Yielding steel arches 
 
 Background information for design of steel supports 
 
 Types of roof strata 
 
 Overburden pressure 
 
 Seam thickness 
 
 Immediate roof type 
 
 Floor type 
 
 Ent ry vd.d th 
 
 Entry shape 
 
 Rock properties 
 
 Rock mechanics data 
 
 Steel type : 
 
 Backpacking 
 
 Expeditious support installation 
 
 Example of steel support selection for U.S. mines 
 
 Load determination 
 
 Support selection 
 
 Checks for support adequacy 
 
 Shear capacity 
 
 Lateral stability 
 
 Deflection 
 
 Localized flange or web buckling 
 
 Support length (web crippling) 
 
 Summa ry 
 
 References 
 
 Appendix. — Explanation of symbols 
 
 ILLUSTRATIONS 
 
 1. Steel arch configurations 3 
 
 2. Arch-member cross sections 4 
 
 3. Types of bolted joints 4 
 
 4. Butt plate joint 4 
 
 5. Typical yielding arch shapes 6 
 
 6. Yield box construction 7 
 
 7. Typical arch with U-shaped cross section 7 
 
 8. Examples of poor and good backpacking practices 9 
 
 9. Possible roof support envelopes for entry width 10 
 
 10. Nomogram for determining support loads 11 
 
 11. Types of beam loading conditions 12 
 
 12. Pertinent properties for selected beam 13 
 
 TABLE 
 1. Summary of accidents involving steel support members 2 
 
 1 
 
 1 
 
 2 
 
 2 
 
 3 
 
 3 
 
 3 
 
 5 
 
 6 
 
 7 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 9 
 
 9 
 
 9 
 
 10 
 
 10 
 
 11 
 
 12 
 
 12 
 
 13 
 
 13 
 
 13 
 
 14 
 
 14 
 
 15 
 
 16 
 

 UNIT OF MEASURE 
 
 ABBREVIATIONS USED 
 
 IN THIS REPORT 
 
 ft 
 
 foot 
 
 lb 
 
 pound 
 
 ft-lb 
 
 foot pound 
 
 lb/ft 
 
 pound per foot 
 
 h 
 
 hour 
 
 lb/ft3 
 
 pound per cubic foot 
 
 in 
 
 inch 
 
 pet 
 
 percent 
 
 in3 
 
 cubic inch 
 
 psi 
 
 pound per square inch 
 
 kips 
 
 thousand pound 
 
 yr 
 
 year 
 
USE OF STEEL SETS IN UNDERGROUND COAL 
 
 By J. H. Stears, ^ M. 0. Serbousek,^ and K. E. Hay^ 
 
 ABSTRACT 
 
 This Bureau of Mines report presents information on the use of steel 
 supports in U.S. coal mines, including accident statistics for a 3-yr 
 period and a survey of present applications and problems. It also con- 
 tains a summary of available steel arch configurations and a descrip- 
 tion of steel support design criteria for ground control applications. 
 
 INTRODUCTION 
 
 A primary goal of Bureau of Mines research is to provide better roof 
 control and thus reduce the exposure of miners to falls of roof rock. 
 Much of the coal lying under easily supported roof has already been 
 mined. As mining progresses into deeper coal seams and poorer roof 
 areas, ground control will become more difficult, and accidents result- 
 ing from roof falls can be expected to increase. Steel beams and rails 
 are widely used in the mining industry to support difficult ground. 
 Steel arches, which are slowly gaining acceptance in U.S. mines, are 
 the most successful devices for ground control in poor conditions. 
 
 Numerous accidents occur while handling and installing steel sup- 
 ports. It is likely that accidents will increase with expected in- 
 creased use of steel for support. Some of the safety problems appear 
 to involve failure to use adequate design criteria already available. 
 
 This report presents information on the use and application of steel 
 supports in U.S. coal mines. It includes accident statistics associ- 
 ated with the use of steel supports for a 3-yr period, a survey of coal 
 mining companies for applications and problems associated with the use 
 of steel supports, a description of the various arch configurations 
 available, and a presentation of steel support design criteria. 
 
 Mining engineer. 
 ^Structural engineer. 
 -^Supervisory civil engineer. 
 
 Spokane Research Center, Bureau of Mines, Spokane, WA. 
 
STEEL SUPPORT ACCIDENTS 
 
 Steel support accidents are summarized 
 in table 1 for 1978-80. These data were 
 obtained by searching through the acci- 
 dent files for the period covered; some 
 accidents may have been missed owing to 
 classification and filing procedures. 
 
 TABLE 1, - Summary of accidents involving 
 steel support members 
 
 Category 
 
 1978 
 
 19 79 
 
 1980 
 
 Total 
 
 Transportation. . 
 
 28 
 
 34 
 
 17 
 
 79 
 
 Installing: 
 
 
 
 
 
 Handling 
 
 7 
 
 18 
 
 8 
 
 33 
 
 Beam slipped 
 
 
 
 
 
 and fell 
 
 1 
 
 2 
 
 2 
 
 5 
 
 Recovering 
 
 
 
 1 
 
 1 
 
 2 
 
 Total 
 
 36 
 
 55 
 
 28 
 
 119 
 
 The first category listed is the trans- 
 porting of steel members. This includes 
 loading, unloading, moving, lifting, or 
 carrying supports. The injuries include 
 such items as mashed and cut fingers and 
 toes , mashed hands , bruises to various 
 
 parts of the body, and sprained muscles 
 in the neck, shoulder, back, abdomen, and 
 legs. Generally, the weight and awkward- 
 ness of the beams create difficulties in 
 handling in tight quarters. 
 
 The second category is installing sup- 
 ports. Most of the accidents occurred 
 while handling the beams during installa- 
 tion. They include mashed, cut, bruised, 
 or sprained muscles that occurred while 
 moving the beams into position. Some of 
 the beams were being manually lifted into 
 position against the roof, while others 
 were being placed on machine booms for 
 subsequent lifting into position. A few 
 accidents occurred when beams slipped and 
 fell off the jacks or machine booms while 
 being lifted into position. 
 
 In the third category of recovering 
 members , only one accident occurred in 
 19 79 and one in 1980. They involved a 
 sprained shoulder muscle and a mashed 
 hand. 
 
 SURVEY OF CURRENT PRACTICES 
 
 A limited survey of selected coal min- 
 ing companies using steel supports was 
 made to obtain information on pertinent 
 practices and problems. Five companies 
 operating 17 mines were contacted. The 
 companies were located in central and 
 southeastern Pennsylvania, northern West 
 Virginia, and western Virginia. 
 
 Steel supports were used in supporting 
 haulageways , ventilation overcasts, and 
 roof -fall areas. They were also used in 
 longwall entries and faces and as airway 
 supports. Steel beams ranging in size 
 from 4 to 8 in and steel rails ranging in 
 size from 60 to 120 lb were employed. 
 Both yielding and rigid arches were used, 
 with 4 in being the predominant size. 
 One company covered its 4-in arches with 
 corrugated steel tunnel liner. 
 
 Steel supports were installed both man- 
 ually and with equipment. Manual instal- 
 lation involves jacking the supports 
 
 against the roof with a beam jack. Roof- 
 bolting machines equipped with timber 
 booms were used to lift the supports 
 against the roof. Equipment for holding 
 the supports in position until legs are 
 installed include beam jacks, hydraulic 
 jacks, and roof -bolted saddles. None of 
 the companies presently recover any steel 
 supports. Care is taken to install the 
 horizontal beams level and the support 
 posts plumb. The support posts were 
 firmly wedged under the beams, and any 
 voids above the beam were blocked to pro- 
 vide support against the roof. 
 
 Handling of steel supports was a ma- 
 jor problem. This operation is difficult 
 and hazardous due to the size, weight, 
 and bulkiness of the supports. All com- 
 panies indicated that most of their in- 
 juries occurred while handling supports. 
 Strains to various muscles occurred when 
 lifting and moving the heavy beams and 
 rails. Mashed fingers and hands that 
 
were caught between the support being 
 handled and another object were especial- 
 ly prevalent. Foot injuries from fall- 
 ing supports were also quite conunon. 
 Another major problem was the excessive 
 time required for the installation of 
 steel supports. 
 
 Various modes of support failure were 
 reported. These include bending failure 
 of beams, shearing and twisting failure 
 of steel rails, and compression failure 
 
 of the supporting legs. Footing failures 
 in fire clay bottom were also reported. 
 
 Two companies commented on possible re- 
 search needs. One company mentioned that 
 safe and timely installation of the heavy 
 steel supports in the confining mine en- 
 vironment remains the greatest obstacle. 
 Another company suggested further inves- 
 tigation of resupporting roof-fall cavi- 
 ties with arch supports and corrugated 
 steel tunnel liner. 
 
 STEEL SUPPORT SYSTEMS 
 
 Much of the following information on 
 steel support systems is based on litera- 
 ture from Bethlehem Steel,'* Commercial 
 Shearing, Inc., and the Dosco Corp. 
 
 STEEL CROSSBARS 
 
 Steel crossbars are the most common 
 steel support. They are usually adequate 
 for fairly heavy loads. However, they 
 are inadequate in extreme situations such 
 as massive fall areas or excessively 
 squeezing ground conditions. Heavy loads 
 will create excessive bending and even- 
 tual failure of the beams. Wide-flange 
 or H-sections are preferred because of 
 their greater resistance to bending. 
 Steel rails are also used as crossbars. 
 However, old rails may have lost ductil- 
 ity and, consequently, may be susceptible 
 to catastrophic failure. 
 
 RIGID STEEL ARCHES 
 
 Rigid arches are designed to support 
 without yielding. The arch is more effi- 
 cient than the flat crossbar. Depending 
 on the shape and loading conditions of 
 the arch, the imposed load in the arch is 
 transmitted as compression rather than 
 bending forces. 
 
 A variety of configurations can be sup- 
 plied by the different companies. Some 
 of the standard ones are shown in figure 
 
 '^Reference to specific products or man- 
 ufacturers does not imply endorsement by 
 the Bureau of Mines. 
 
 1. These include the two- and three- 
 piece continuous arch and the two-piece 
 rib-and-post. Flat-top arches with ei- 
 ther straight or curved sides are also 
 available. In mines with a swelling bot- 
 tom, invert-strut arches are recommended. 
 Almost any desired conf igiiration for dif- 
 fering ground conditions can be supplied 
 on special order. 
 
 Arch members with wide-flange beam 
 cross sections are available, as shown in 
 figure 2A, However, this cross section 
 
 2-piece continuous arch 
 
 3-piece continuous arch 
 
 2-piece rib andpost Flat lop with straight sides 
 
 Flat top wrih curved sides 
 
 Invert strut 
 
 FIGURE 1. - Steel arch configurations. 
 
is relat 
 forces 
 twisted 
 steel jo 
 section) 
 able (f 
 similar 
 and , in 
 
 ively weak in resisting oblique 
 
 and is susceptible to being 
 
 out of shape by them. Rolled 
 
 ist (American standard beam or S 
 
 cross sections are also avail- 
 
 ig. 2S), These offer properties 
 
 to those of the wide-flange beams 
 
 addition, are two to three times 
 
 V////J 
 
 / 
 / 
 / 
 ' 
 
 / 
 I 
 / 
 
 -rrm 
 
 I 
 
 r 1 
 
 / V 
 
 arTihrm. (rm/nrTY^^^^^^'::^ 
 
 A B C 
 
 FIGURE 2. « Arch-member cross sections. A, 
 Wide-flange beam; B, rolled steel joist; C, box 
 sections. 
 
 stronger under oblique loadings. Box- 
 section beams (fig. 2C) are two shapes 
 continually seam-welded. They give bet- 
 ter all-round performance under heavy 
 loading than the rolled-joist sections. 
 
 Connectors are necessary in most arches 
 since effective one-piece units cannot be 
 transported underground. Joining of the 
 arch sections is done in a variety of 
 ways. One type of joint is shown in fig- 
 ure 3j4 . A single bolt holds the two 
 forged lugs tightly together to form a 
 rigid joint and transmit shear forces and 
 bending moment from one member to the 
 other. 
 
 A flexible joint is shown in figure 3B. 
 A single bolt holds two rounded forged 
 lugs together which roll on themselves 
 under weight, thus enabling the joint to 
 rotate under load without fracturing. 
 
 Another vender uses butt plates welded 
 to the beam ends (fig. 4). The beam ends 
 are butted together and connected with 
 bolts through holes provided in the 
 plates. 
 
 Arches are usually installed on 3- to 
 6-f t centers , and they are connected to- 
 gether with tie rods for lateral sta- 
 bility. Normally, the periphery of the 
 arches is lagged with 2- to 3-in treated 
 wooden boards. 
 
 B 
 
 FIGURE 3. - Types of bolted joints. A, 
 Rigid joint; B, flexible joint. 
 
 For maximum efficiency, the void space 
 between the outside of the arches and the 
 strata must be backfilled or solidly 
 blocked. This provides uniform loading 
 of the arch structure and avoids point 
 loading that would locally overstress the 
 arches and destroy the overall support 
 capacity of the total arch. Rigid arches 
 
 FIGURE 4. - Butt plate joint. 
 
are usually installed on main haul- 
 ageways, slopes, and shaft stations that 
 require permanent support where large 
 ground movements are not expected. 
 
 YIELDING STEEL ARCHES 
 
 Yielding mine arches consist of arch 
 or ring sets that incorporate a sliding 
 friction assembly to accommodate heavy 
 ground pressure and thus prevent distor- 
 tion of the support. 
 
 The yielding arch is designed to relax 
 before it becomes excessively bent or 
 distorted. The joint acts as a safety 
 valve to keep the steel set from being 
 destroyed; it is designed to yield at a 
 load below the yield point of the steel. 
 
 Yielding arches serve the same function 
 as rigid arches but are much more ef- 
 fective in areas of severe pressures or 
 squeezing ground conditions, which pro- 
 duce large deformation that would destroy 
 a rigid arch. They are an economical 
 support method under severe conditions 
 where extensive movements occur because 
 of faulted ground, overstressed strata, 
 longwall operations, or strata with vari- 
 able properties. 
 
 Yielding arches are fabricated in vari- 
 ous shapes such as circular and horseshoe 
 and consist of three or more segments of 
 high-strength steel with a yield point 
 above 50,000 psi. Three typical arch 
 shapes are shown in figure 5. The three- 
 segment symmetrical arch with leg seg- 
 ments toed in (fig. 5A) is used where the 
 ground pressure is predominantly verti- 
 cal, the three-segment symmetrical arch 
 with leg segments toed out (fig. 5B) re- 
 sists lateral as well as vertical ground 
 pressures, and the symmetrical ring (fig. 
 5C) resists ground pressures from all 
 directions. 
 
 The two most common yielding mechanisms 
 are the yield box and the overlap joint. 
 The yield box was developed for use 
 with standard-type beam sections such as 
 
 the wide-flange, joist, and box-section 
 beams. The yield box is placed on the 
 floor, and the lower end of the arch leg 
 is inserted into its top. Construction 
 of a yield box is shown in figure 6. 
 When the support is set, frictional re- 
 sistance is established between the arch 
 leg, the wooden wedge, the brake shoe, 
 and the rear side of the box. 
 
 Several companies furnish arches made 
 of U-shaped cross sections that nest to- 
 gether at the ends to form an overlapping 
 joint. Heavy U-bolt clamps are installed 
 over the joints to provide the yielding 
 feature. The joints are tightened enough 
 to hold under normal loads, but when ex- 
 cessive pressures develop, they permit 
 the nested segments to slide or yield be- 
 fore the yield strength of the steel is 
 reached. This relieves the load and 
 maintains the structural integrity of the 
 arch while the ground is permitted to 
 relax gradually until equilibrium is 
 reached. As the successful functioning 
 of a yielding set depends on its ability 
 to yield when required, it is critical 
 that the U-bolts at the joints be proper- 
 ly tightened. The U-bolt nuts are usu- 
 ally torqued to between 150 and 180 ft-lb 
 (J,, p. 406). 5 
 
 Views of a typical arch and the 
 U-shaped cross section are shown in 
 figure 7. The most commonly used sec- 
 tions weigh from 10 to 25 lb/ft and have 
 outside dimensions of 3 to 7 in. Moduli 
 of sections on "XX" and "YY" axes are 
 practically equal, thereby offering uni- 
 form resistance to eccentric loading. 
 Ordinary H-beams give poor support when 
 loads are applied at an angle to the 
 major axis of inertia, causing torsional 
 moment on the section. The high torsion- 
 al resistance of the U-shaped sections 
 allows them to be twisted out of the ver- 
 tical plane and still provide adequate 
 strength. 
 
 ^Underlined numbers in parentheses re- 
 fer to items in the list of references 
 preceding the appendix. 
 
Arches are spaced at 2- to 5-ft inter- 
 vals , depending on expected ground pres- 
 sure. Adjoining sets are connected with 
 horizontal struts made of steel channels, 
 pipes , or rods to maintain spacing and 
 provide lateral stability. Treated tim- 
 ber lagging is installed around the 
 
 outside of the arches, and blocking or 
 backfilling is used to provide uniform 
 loading. Footers of steel plate, channel 
 steel, or wood blocks are placed between 
 the bottom of the legs and the floor to 
 reduce penetration if the floor is soft. 
 
 BACKGROUND INFORMATION FOR DESIGN OF STEEL SUPPORTS 
 
 This section was extracted from "Steel 
 Supports Design Criteria: A Summary of 
 European Data" (2^) . This Bureau contract 
 report presents information pertaining to 
 the relationship between steel support 
 
 selection and the physical and geological 
 parameters that make up the support envi- 
 ronment. The following parameters were 
 examined to determine their contribution 
 to support design. 
 
 B 
 
 FIGURE 5. - Typical yielding arch shapes. A, Three-segment symmetrical with legs toed 
 in; B, three-segment symmetrical with legs toed out; C, symmetrical ring. 
 
Arch leg 
 
 Wooden' 
 wedge 
 
 U-bolt 
 
 Brake shoe 
 
 Rear side 
 of box 
 
 FIGURE 6. - Yield box construction. 
 
 TYPES OF ROOF STRATA 
 
 The roof strata in underground coal 
 mines are normally divided into three 
 classes: immediate roof, main roof, and 
 total remaining overburden. The immedi- 
 ate roof is that portion of the strata 
 immediately above the mined opening that 
 will fall if left unsupported for a rela- 
 tively short period (usually a few days). 
 The behavior of the immediate roof is 
 highly dependent on opening width, in 
 situ stresses, induced mining stresses. 
 
 Arch profile 
 
 Cross section 
 
 FIGURE 7. - Typical arch with U-shaped cross 
 section. 
 
 structure, and environmental factors such 
 as temperature and moisture. The immedi- 
 ate roof is of the most direct concern 
 for safety in the mined opening and, 
 therefore, is the stratum toward which 
 the most control efforts have been di- 
 rected. The two basic methods of control 
 that can be applied to the immediate roof 
 are internal, such as rock bolts, and ex- 
 ternal, such as steel supports. 
 
 The second class of roof strata is the 
 main roof. This is the stratum that lies 
 above the immediate roof and spans the 
 opening if the immediate roof falls. It 
 is generally agreed in the mining indus- 
 try that the main roof cannot be sup- 
 ported by artificial means. This means 
 that roof bolts, cribs, steel supports, 
 etc. , will not be effective in supporting 
 the main roof. 
 
The third strata classification is the 
 total remaining overburden. This over- 
 burden will settle, but normally this 
 settlement can be postponed long enough 
 to permit mining; its stability depends 
 upon the action of the main roof. 
 
 In multiple-seam mining, pillar rem- 
 nants in overlying seams may cause 
 large stress concentrations. The entries 
 should be aligned, as much as possi- 
 ble, to provide more uniform stress 
 conditions, 
 
 OVERBURDEN PRESSURE 
 
 Overburden pressure does not have a di- 
 rect effect on the selection of a steel 
 support design. However, the overburden 
 pressure does have an indirect effect in 
 the following ways: 
 
 1, The overburden pressure is one of 
 the factors that determine the amount of 
 convergence that can be expected in an 
 opening and, hence, the amount of defor- 
 mation that the support can be expected 
 to receive, 
 
 2, The overburden pressure also af- 
 fects the stress in the immediate roof 
 that will comprise the support load. The 
 overburden pressure is one of the factors 
 that determine the height of the expected 
 support envelope. 
 
 SEAM THICKNESS 
 
 The seam thickness enters into support 
 selection both directly and indirectly. 
 Directly, the seam thickness determines 
 the height of the openings and supports 
 and, therefore, the resistance of the 
 supports to column failure. Indirectly, 
 the seam thickness is one of the factors 
 in determining of convergence and, there- 
 fore, in determining the amount of ex- 
 pected deformation, 
 
 IMMEDIATE ROOF TYPE 
 
 The immediate roof type is the single 
 most important factor in determining 
 
 steel support design. The immediate 
 roof's weight, thickness, stress, and 
 competence all influence the design of 
 the support. The immediate roof is the 
 strata that are actually being supported 
 by the steel supports and, therefore, its 
 properties are vital, 
 
 FLOOR TYPE 
 
 The type of floor is one of the con- 
 tributors of the convergence and, hence, 
 the expected deformation. Since the sup- 
 port normally rests on the floor, the 
 floor type also determines the need for 
 footpads or other load-spreading devices. 
 
 ENTRY WIDTH 
 
 Support design is directly dependent on 
 entry width in two ways. First, sup- 
 ported load is directly proportional 
 to width. Second, support design and 
 strength are directly proportional to 
 span. 
 
 ENTRY SHAPE 
 
 Entry shape (rectangular, arched, full 
 circle, etc.) has a significant effect on 
 the stability of the opening. It also 
 affects the amount of artificial suupport 
 required, 
 
 ROCK PROPERTIES 
 
 Strength parameters for the strata 
 around the opening should be determined. 
 Although the strength of coal does not 
 directly enter into any of the design in- 
 formation, it does affect convergence and 
 expected deformation. Convergence is in- 
 fluenced by the mechanical strength of 
 the materials in the main roof , immediate 
 roof, coal seam, and floor, 
 
 ROCK MECHANICS DATA 
 
 The height and shape of the support 
 envelope that the structure must be de- 
 signed for are determined by the height 
 and integrity of the pressure arch that 
 will form (assuming laminated strata) 
 when the entry material is removed. 
 
STEEL TYPE 
 
 Mild steel (grade 40 to 60) with good 
 ductility is desirable for underground 
 use. The ductility of the steel de- 
 termines its ability to accept localized 
 yielding without catastrophic failure 
 of the support. Surface hardness is im- 
 portant for yielding arches to ensure 
 that sliding movement can still take 
 place under load without gouging of the 
 sliding surfaces. Detailed discussions 
 of steel for use in underground sup- 
 ports can be found in chapter 5 of Fritz 
 Spruth's book, "Steel Roadway Supports" 
 (_3) , and in chapter 2 of Proctor and 
 White's book, Rock Tunneling With Steel 
 Supports" (^) . Available standard U.S. 
 steel sections are listed in the manual 
 of steel construction (_5) by the Amer- 
 ican Institute of Steel Construction 
 (AISC). This manual also includes design 
 and fabrication procedures for several 
 grades of steel. The allowable stresses 
 listed in the manual can be increased 
 to the yield point of the steel for 
 underground temporary support. Several 
 good textbooks covering elastic and plas- 
 tic steel design procedures are avail- 
 able (^~8^) • They cover the principles 
 of good steel design which account for 
 bending, axial, torsion, and shear 
 stresses, safety factors, axial and lat- 
 eral buckling, shear stiffness, end bear- 
 ing, etc. 
 
 BACKPACKING 
 
 Most steel support failures occur from 
 point loads that overstress the support 
 locally. Failure in this context means 
 failure of the steel support to maintain 
 entry shape because of local deformation. 
 To prevent this type of failure, attempts 
 are made to provide a continuous struc- 
 tural interconnection between the support 
 and the surrounding rock. In practice, 
 this is accomplished in two steps. 
 
 First, considerable care is taken to 
 cut the entry to the approximate shape 
 of the support. This avoids the need 
 to fill large openings, which is costly. 
 Also, large openings are difficult to 
 fill with a material that will evenly 
 
 distribute the load from the surrounding 
 strata. Figure 8 shows examples of poor 
 and good practices. 
 
 Second, when the support is set, the 
 space between the support and the sur- 
 rounding rock is packed with a material 
 that is deforraable and yet has the struc- 
 tural integrity necessary to transfer the 
 load from the surrounding strata. A com- 
 mon material used is waste rock. In 
 British mines, the waste rock is placed 
 in paper bags, and the bags are then 
 packed into the space. The small size 
 of the rock and the use of bags make 
 the material handleable and yet give 
 it the needed properties of deformation 
 and integrity. The most common material 
 used in U.S. mines is wood because of its 
 availability. 
 
 EXPEDITIOUS SUPPORT INSTALLATION 
 
 Steel supports should be installed 
 closely behind the face to minimize the 
 span of unsupported roof and the time 
 that a section of roof remains unsup- 
 ported. European practice is to install 
 steel arches within about 6 ft of the 
 face and within 8 h after roof exposure. 
 
 D hu n n II n nnn 
 
 nnnnnunniin armr 
 
 n n I 1 u u g y u a_Q.jafl_XL 
 
 Poor practice Overcutting requires 
 excessive timbering 
 
 Good practice Close cutting requires 
 minimal amount of blocking 
 
 FIGURE 8. - Examples of poor and good back- 
 packing practices. 
 
10 
 
 EXAMPLE OF STEEL SUPPORT SELECTION FOR U.S. MINES 
 
 The following example describes a two- 
 step process for the design of steel sup- 
 ports using available U.S. steel sec- 
 tions. The two steps involved are load 
 determination and support selection. 
 
 LOAD DETERMINATION 
 
 First, it is necessary to determine the 
 expected loads and the support required 
 for those loads. The analysis is based 
 on the immediate roof envelope. Figure 9 
 shows three roof envelopes at heights of 
 b/2, b, and 3b/2 above the roof line. It 
 is assumed that the envelope acts as a 
 free surface (that is, the rock above the 
 envelope is self-supporting and no loads 
 are transferred from the surrounding 
 strata). The heights of the roof enve- 
 lopes shown in figure 9 are idealizations 
 that include conditions normally encoun- 
 tered in practice. The actual height of 
 the envelope in a particular mine may be 
 less or greater than those depicted. 
 
 The shape of the roof envelope is con- 
 sidered to be a parabola. Assuming a 
 
 Height to 
 
 3b/2 
 
 envelope 
 
 Height to 
 
 b 
 
 envelope 
 
 Height to 
 
 b/2 
 
 envelope 
 
 FIGURE 9. - Possible roof support envelopes 
 for entry width. 
 
 parabolic roof envelope at a height of h 
 ft in the roof above an entry b ft wide, 
 the area of the parabola between the roof 
 line and the envelope is 
 
 A = 2/3 bh. 
 
 (1) 
 
 Multiplying by a distance of 1 ft along 
 the entry gives the volume of rock be- 
 tween the roof line and the envelope. 
 
 V = 2/3 bhl. 
 
 (2) 
 
 Multiplying by y (the density of the rock 
 in pounds per cubic feet) gives the 
 weight of rock per foot of entry length 
 that must be held up by the supports: 
 
 P = 2/3 bhy. 
 
 (3) 
 
 A nomographic solution of equation 3 is 
 shown in figure 10. The nomogram is used 
 as follows: (1) Select the entry width 
 on the right side of the X axis; (2) move 
 vertically upwards to the appropriate 
 rock density curve; (3) move horizontally 
 to the left to the appropriate support 
 envelope height curve; and (4) move ver- 
 tically downwards, and read the weight of 
 rock to be supported per foot of entry 
 length on the left side of the X axis. 
 The correct routing is depicted by the 
 three arrows in the figure. Support 
 loads for special situations having pa- 
 rameters outside the range of the nomo- 
 graph can be calculated with equation 3. 
 
 Equation 3 or figure 10 permits the de- 
 termination of support loads per foot of 
 entry length for various entry widths, 
 rock densities, and envelope heights. An 
 estimate of envelope height can be ob- 
 tained from prior roof falls. Multiply- 
 ing this quantity by the spacing between 
 supports along the entry gives the total 
 weight to be supported by each support. 
 Design of the support beam can then be 
 determined by reference to the "Manual 
 of Steel Construction" (5) or a similar 
 steel design manual. 
 
11 
 
 
 
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 100 90 80 7C 6 50 403530 25 20 15 109 8 7 6 5 4 3 5 3 2.5 2 
 
 SUPPORT LOAD, kips/ft of entry length 
 
 1.5 
 
 1 10 
 
 15 20 
 
 ENTRY 
 WIDTH, ft 
 
 FIGURE 10. - Nomogram for determining support loads. 
 
 Four different types of beam loadings 
 are shovm in figure 11. They include 
 concentrated loading, uniform loading, 
 uniformly varying loading, and parabolic 
 loading. Formulas for calculating end 
 reaction, maximum shear, maximum moment, 
 and maximum deflection are presented for 
 each case. 
 
 rock to be carried by each support. The 
 maximum moment to be resisted in terms of 
 the total load and beam length is 
 
 M 
 
 5 WL 5 (164,000) (16) 
 
 ma X 
 
 32 
 
 32 
 
 = 410,000 fflb. 
 
 (4) 
 
 SUPPORT SELECTION 
 
 The design example is based on the fol- 
 lowing assumptions. A 16-ft-wide entry 
 is to be supported. The roof is composed 
 of shale rock with a density of 160 lb/ 
 ft-'. Support envelope height is esti- 
 mated as 24 ft (3b/2), indicating that 
 heavy loading is expected. The supports 
 will be spaced 4 ft apart along the en- 
 try. Parabolic loading of the supports 
 by the roof rock (case 4) is assumed. A 
 typical yield strength of structural 
 steel is 36,000 psi. It is assumed that 
 the critical load condition causes yield- 
 ing of the section. In other words, the 
 failure load is defined when one element 
 of the supporting structure has reached 
 yield strength of the steel. 
 
 The nomograph of figure 10 gives a sup- 
 port load of 41 kips per foot of entry 
 length for a 16-ft-wide entry, 160-lb/ft^ 
 rock density, and 24-ft-high support en- 
 velope. Multiplying this number by the 
 4-ft support spacing gives 164 kips or 
 164,000 lb as the total weight of roof 
 
 The required section modulus is obtained 
 by converting the maximum moment to inch 
 pounds and dividing by the yield strength 
 of 36,000 psi. 
 
 S = 
 
 M„ 
 
 (410,000) (12) 
 36,000 
 
 = 137 in^. (5) 
 
 Referring to the "W Shapes, Properties 
 for Designing" section of a steel con- 
 struction manual (_5 ) , and using the plas- 
 tic modulus (Zj<) column, choose the fol- 
 lowing beams as having at least a 137-in^ 
 section modulus: 
 
 W 14 X 82, 
 
 W 16 X 77, 
 
 W 18 X 71, 
 
 W 21 X 62. 
 
 Without concern for headroom or clear- 
 ance, select the lightest weight section, 
 which is the W 21 x 62 beam. The second 
 number in the W designation is the beam 
 weight in pounds per foot. Pertinent 
 properties of the selected beam are 
 listed in figure 12. 
 
12 
 
 W 
 
 R 
 
 End reaction; R = 
 
 W 
 
 Maximum shear; V, 
 
 Maximum moment: M 
 
 W 
 
 WL 
 
 max 
 
 Maximum deflection; fS 
 
 = 0.0 208- 
 
 max 48EI ^ 
 
 Case 1 - c o nc e n t r a t e d load 
 
 Total load: W = 
 
 End reaction: R = 
 
 qL w 
 
 Maximum shear:Vmax~ 
 
 W 
 
 qL*^ WL 
 
 Maximum m o m e n t : M^ a x = T^ = "~5~ 
 Maximum d e f I e c t i o n: 6 m a x = 120EI ^ 60EI 
 Case 3-uniformly varying load 
 
 A n 
 
 -* L »► 
 
 Total load ; W = qL 
 
 End reaction; R = 
 
 qL W 
 
 Maximum shear; V, 
 
 W 
 2 
 
 Maximum moment;Mmax = 
 Maximum deflection; '^ 
 
 qJLf_^WL 
 8 8 
 
 _ 5 q L^ ^ 5 W L^ 
 f^a^' 384EI 384EI 
 
 0.0 13 
 
 WL- 
 
 Case 2-uniform load 
 
 FIGURE 11.. Types of 
 CHECKS FOR SUPPORT ADEQUACY 
 
 The selected beam will now be checked 
 for the following conditions. 
 
 1. Shear capacity. 
 
 2. Lateral stability. 
 
 3. Deflection, 
 
 4. Localized buckling. 
 
 5. Support length (web crippling). 
 
 Total load: W = 
 
 2qL 
 
 q L w 
 End r e a c t i on: R = — -- = — 
 
 q L w 
 Maximum s h e a r: V^ a x ~ ""T~~ T 
 
 5qL^ _ 5WL 
 32 
 
 Maximum moment:M 
 
 max 
 
 48 
 
 Maximum d e f le c t io n:5 , 
 
 eiqL^ 6 1WL' 
 
 f"^^ 5,760EI 3,840EI 
 Case 4-parabolic loading 
 
 beam loading conditions. 
 
 All steel design and review calcula- 
 tions are based on the specifications of 
 the American Institute of Steel Construc- 
 tion. Plastic design methods have been 
 used throughout this example. 
 
 Shear Capacity 
 
 The maximum shear on the beam is 
 
 V„,, . f . i^MOO , 82.000 lb. (6) 
 
13 
 
 ill 
 
 1,375 
 
 + 25, 
 
 (8) 
 
 'w 
 
 Y 
 
 f 
 
 ZxPlastic section m o d u I u s = 1 4 4 In-' 
 
 d:beam depth=21 in 
 
 tyy:web thick ness=«04 in 
 
 r;radlus of gyration about Y axis=1.77 in 
 
 l:tnoment of inertia about X axis»1,330 in^ 
 
 bfiflange width=8.24 in 
 
 t|:flange t tiic k ness= . 6 1 5 in 
 
 k:distance from outer face of flange to web toe 
 
 of fillet* 1 25 in 
 E: modulus of e la s 1 1 c i t y= 2 9 , , 00 psi 
 
 Fyiyield strengfti of steel»36.000 psi 
 
 FIGURE 12. • Pertinent properties for selected 
 beam. 
 
 The allowable shear for the selected beam 
 in terms of the yield strength (Fy), web 
 thickness, and beam depth (see figure 12 
 for symbols and values) is 
 
 Va = 0.55 (Fy) (tj (d) 
 
 = 0.55 (36,000) (0.4) (21.0) 
 
 = 166,300 lb. (7) 
 
 Since the allowable shear is greater than 
 the maximum shear, this size beam is ac- 
 ceptable for the shear loading. 
 
 Lateral Stability 
 
 The critical length for lateral stabil- 
 ity is calculated by the formula 
 
 where the yield strength of the steel 
 (F ) is used in kips per square inch. 
 Substituting in the formula gives 
 
 cr 
 
 = (1.77) 
 
 = HI in. 
 
 1,375 
 36 
 
 + 25 
 
 (9) 
 
 As the beam is 16 ft long, it should be 
 braced (struts from beam to beam) on the 
 compression flange at the midspan of the 
 beam. This lateral bracing will prevent 
 buckling of the compression flange. 
 
 Deflection 
 
 The deflection formula (figure 11, case 
 d) is 
 
 = 61 WL^ 
 •"^x 3^840 EI 
 
 = 61 (164,000) (16)^ (12)3 
 3,840 (29,000,000) (1,330) 
 
 = 0.478 = 0.5 in. (10) 
 
 Measurement of beam deflection permits a 
 quick check on the condition of the beam. 
 The midspan deflection can be measured 
 with a pocket tape by stretching a string 
 from one support to the other. For exam- 
 ple, if 0.25-in deflection is measured, 
 the beam still retains approximately 50 
 pet of its load capacity. 
 
 Localized Flange or Web Buckling 
 
 Beams are made with different flange 
 and web thicknesses and may be subject 
 to localized buckling, even though their 
 section modulus is adequate for the load. 
 
 Flange thickness is checked with the 
 following formula: 
 
14 
 
 2t, 
 
 < 8.5. 
 
 (11) 
 
 R 
 
 Substituting the selected beam values 
 in the formula. 
 
 8.24 
 
 = 6.70 < 8.5; 
 
 2 (0.615) 
 beam is acceptable. 
 
 (12) 
 
 The equation for checking web thickness 
 assuming no axial load is 
 
 412 
 
 Where the yield strength of the steel 
 (Fy) is used in kips per square inch, 
 substituting beam values in the equation 
 
 21 
 0.4 
 
 412 
 = 52.5 < -7^ = 68.7; 
 
 7jh 
 
 beam is acceptable. (13) 
 Support Length (Web Crippling) 
 
 This test is to check for localized web 
 buckling from the concentrated loading 
 that occurs over the supporting posts. 
 The appropriate equation is 
 
 0.75 Fy (t„) 
 
 - k. 
 
 (14) 
 
 where N = the required bearing length be- 
 tween the beam and its support, in, 
 
 R = the end reaction, lb, 
 
 and t^^ and k are defined in figure 12. 
 
 Substituting beam values into the 
 equation, 
 
 82,000 
 
 N = 
 
 0.75 (36,000) (0.4) 
 - 1.25 = 6.34. 
 
 (15) 
 
 If a bearing length between the bot- 
 tom of the beam and the supporting post 
 of less than 6.3 in is used, a stiff- 
 ener should be used at the end of the 
 beam. This reinforcement can be provided 
 by welding plates to both sides of the 
 web. 
 
 The selected beam has been checked, us- 
 ing plastic theory based upon the recom- 
 mendations of the AISC specifications, 
 and has been found to satisfy the assumed 
 loading conditions. 
 
 SUMMARY 
 
 The major source of injuries appears to 
 be handling the steel supports, primarily 
 due to their weight and awkwardness. Ac- 
 ceptable mechanical methods for quicker 
 and safer installation of the heavy steel 
 supports in the confining mine environ- 
 ment are needed. 
 
 The arch is a more efficient configura- 
 tion than the flat crossbar, as the load 
 is transmitted as compression rather than 
 bending forces. Yielding arches are more 
 effective than rigid arches under se- 
 vere conditions that produce large de- 
 formations. The void space between the 
 arch and the strata must be backfilled 
 
 or blocked to provide uniform load- 
 ing. Steel supports should be installed 
 close to the face 
 exposure. 
 
 and shortly after roof 
 
 The load to be carried by steel sup- 
 ports can be calculated by assuming a 
 parabolic-shaped roof support envelope. 
 The actual height of this support enve- 
 lope in a particular mine can be esti- 
 mated by observing roof falls. A nomo- 
 gram is provided for determining support 
 loads per foot of entry length for vari- 
 ous entry widths, rock densities, and 
 support envelope heights. The support 
 beam can then be designed by referring to 
 
15 
 
 any steel construction manual. A design 
 example is provided with pertinent equa- 
 tions and calculations. Equations are 
 provided for checking the selected beam 
 
 for adequacy, with respect to shear ca- 
 pacity, lateral stability, deflection, 
 localized buckling, and web crippling. 
 
 REFERENCES 
 
 1. Peng, S. S, Coal Mine Ground Con- 
 trol. Wiley, 1978, 405 pp. 
 
 2. Hawkins, S. A. Health and Safe- 
 ty Analysis on Support Walls. Volume 2: 
 Steel Supports Design Criteria: A Sum- 
 mary of European Data (contract JO295036, 
 Management Eng. , Inc.). BuMines OFR 
 121(2)-82, 1980, 61 pp.; NTIS PB 82- 
 251968. 
 
 3. Spruth, F. Steel Roadway Supports: 
 A Practical Handbook. Collier Guardian 
 Co., Ltd., London, v. 2, 1960, 750 pp. 
 
 4. Proctor, R. V., and T. L. White. 
 Rock Tunneling With Steel Supports, Com- 
 mercial Shearing, Inc., Youngs town, OH, 
 1946, 278 pp. 
 
 5. American Institute of Steel Con- 
 struction, Inc. Manual of Steel Con- 
 struction. 7th ed., 1973, 1200 pp. 
 
 6. Salmon, C. G. , and J. F, Johnson. 
 Steel Structures. Harper & Row, 2d ed., 
 1980, 945 pp. 
 
 7. McCormac, J. C. Structural Steel 
 Design. Harper & Row, 3d ed., 1982, 662 
 pp. 
 
 8. Kuzraanovic, B. 0., and N. Willems, 
 Steel Design Structures. Prentice-Hall, 
 2d ed. , 19 78, 600 pp. 
 
16 . 
 
 APPENDIX. —EXPLANATION OF SYMBOLS 
 
 A Area 
 
 b Entry width 
 
 bf Flange width 
 
 d Beam depth 
 
 E Modulus of elasticity 
 
 Fy Yield strength of steel 
 
 Y Density of rock 
 
 h Height of roof envelope 
 
 I Moment of inertia about Y axis 
 
 k Distance from outer face of flange to web toe of fillet 
 
 L Beam length 
 
 l(,p Critical length for lateral stability 
 
 Mn,ax Maximum moment 
 
 N Required length between beam and support 
 
 P Weight of rock that must be supported 
 
 q Magnitude of distributed load on beam 
 
 R End reaction 
 
 r Radius of gyration about Y axis 
 
 S Section modulus 
 
 tf Flange thickness 
 
 ty, Web thickness 
 
 V Volume 
 
 Vg Allowable shear 
 
 V^ax Maximum shear 
 
 W Total load 
 
 Zx Plastic section modulus 
 
 6n,ax Maximum deflection 
 
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