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IC 8992Bureau 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 INTERIORWilliam P. Clark, Secretary

BUREAU OF MINESRobert C. Horton, Director

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CONTENTSPage

Abstract.IntroductionSteel support accidentsSurvey of current practicesSteel support systems

Steel crossbarsRigid steel archesYielding steel arches

Background information for design of steel supportsTypes of roof strataOverburden pressureSeam thicknessImmediate roof typeFloor typeEnt ry vd.d thEntry shapeRock propertiesRock mechanics dataSteel type :BackpackingExpeditious support installation

Example of steel support selection for U.S. minesLoad determinationSupport selectionChecks for support adequacy

Shear capacityLateral stabilityDeflectionLocalized flange or web bucklingSupport length (web crippling)

Summa ryReferencesAppendix.Explanation of symbols

ILLUSTRATIONS

1. Steel arch configurations 32. Arch-member cross sections 43. Types of bolted joints 44. Butt plate joint 45. Typical yielding arch shapes 66. Yield box construction 77. Typical arch with U-shaped cross section 78. Examples of poor and good backpacking practices 99. Possible roof support envelopes for entry width 1010. Nomogram for determining support loads 1111. Types of beam loading conditions 1212. Pertinent properties for selected beam 13

TABLE

1. Summary of accidents involving steel support members 2

1

1

2

2

3

3

3

5

67

88888

8

889

9

9101011121213131314141516

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 steelsupports in U.S. coal mines, including accident statistics for a 3-yrperiod 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 roofcontrol and thus reduce the exposure of miners to falls of roof rock.Much of the coal lying under easily supported roof has already beenmined. As mining progresses into deeper coal seams and poorer roofareas, ground control will become more difficult, and accidents result-ing from roof falls can be expected to increase. Steel beams and railsare widely used in the mining industry to support difficult ground.Steel arches, which are slowly gaining acceptance in U.S. mines, arethe 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 appearto involve failure to use adequate design criteria already available.

This report presents information on the use and application of steelsupports 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 coalmining companies for applications and problems associated with the useof steel supports, a description of the various arch configurationsavailable, 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 summarizedin table 1 for 1978-80. These data wereobtained by searching through the acci-dent files for the period covered; someaccidents may have been missed owing toclassification and filing procedures.

TABLE 1, - Summary of accidents involvingsteel support members

Category 1978 19 79 1980 TotalTransportation.

.

28 34 17 79Installing:Handling 7 18 8 33Beam slippedand fell 1 2 2 5

Recovering 1 1 2Total 36 55 28 119

The first category listed is the trans-porting of steel members. This includesloading, unloading, moving, lifting, orcarrying supports. The injuries includesuch items as mashed and cut fingers andtoes , mashed hands , bruises to various

parts of the body, and sprained musclesin the neck, shoulder, back, abdomen, andlegs. Generally, the weight and awkward-ness of the beams create difficulties inhandling in tight quarters.

The second category is installing sup-ports. Most of the accidents occurredwhile handling the beams during installa-tion. They include mashed, cut, bruised,or sprained muscles that occurred whilemoving the beams into position. Some ofthe beams were being manually lifted intoposition against the roof, while otherswere being placed on machine booms forsubsequent lifting into position. A fewaccidents occurred when beams slipped andfell off the jacks or machine booms whilebeing lifted into position.

In the third category of recoveringmembers , only one accident occurred in19 79 and one in 1980. They involved asprained shoulder muscle and a mashedhand.

SURVEY OF CURRENT PRACTICES

A limited survey of selected coal min-ing companies using steel supports wasmade to obtain information on pertinentpractices and problems. Five companiesoperating 17 mines were contacted. Thecompanies were located in central andsoutheastern Pennsylvania, northern WestVirginia, and western Virginia.

Steel supports were used in supportinghaulageways , ventilation overcasts, androof-fall areas. They were also used inlongwall entries and faces and as airwaysupports. Steel beams ranging in sizefrom 4 to 8 in and steel rails ranging insize 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 withcorrugated 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 timberbooms were used to lift the supportsagainst the roof. Equipment for holdingthe supports in position until legs areinstalled include beam jacks, hydraulicjacks, and roof-bolted saddles. None ofthe companies presently recover any steelsupports. Care is taken to install thehorizontal beams level and the supportposts plumb. The support posts werefirmly wedged under the beams, and anyvoids above the beam were blocked to pro-vide support against the roof.

Handling of steel supports was a ma-jor problem. This operation is difficultand 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 whenlifting and moving the heavy beams andrails. Mashed fingers and hands that

were caught between the support beinghandled and another object were especial-ly prevalent. Foot injuries from fall-ing supports were also quite conunon.Another major problem was the excessivetime required for the installation ofsteel supports.

Various modes of support failure werereported. These include bending failureof beams, shearing and twisting failureof steel rails, and compression failure

of the supporting legs. Footing failuresin fire clay bottom were also reported.

Two companies commented on possible re-search needs. One company mentioned thatsafe and timely installation of the heavysteel 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 corrugatedsteel tunnel liner.

STEEL SUPPORT SYSTEMS

Much of the following information onsteel support systems is based on litera-ture from Bethlehem Steel,'* CommercialShearing, Inc., and the Dosco Corp.

STEEL CROSSBARS

Steel crossbars are the most commonsteel support. They are usually adequatefor fairly heavy loads. However, theyare inadequate in extreme situations suchas massive fall areas or excessivelysqueezing ground conditions. Heavy loadswill create excessive bending and even-tual failure of the beams. Wide-flangeor H-sections are preferred because oftheir greater resistance to bending.Steel rails are also used as crossbars.However, old rails may have lost ductil-ity and, consequently, may be susceptibleto catastrophic failure.

RIGID STEEL ARCHES

Rigid arches are designed to supportwithout yielding. The arch is more effi-cient than the flat crossbar. Dependingon the shape and loading conditions ofthe arch, the imposed load in the arch istransmitted as compression rather thanbending forces.

A variety of configurations can be sup-plied by the different companies. Someof the standard ones are shown in figure

'^Reference to specific products or man-ufacturers does not imply endorsement bythe Bureau of Mines.

1. These include the two- and three-piece continuous arch and the two-piecerib-and-post. Flat-top arches with ei-ther straight or curved sides are alsoavailable. In mines with a swelling bot-tom, invert-strut arches are recommended.Almost any desired conf igiiration for dif-fering ground conditions can be suppliedon special order.

Arch members with wide-flange beamcross sections are available, as shown infigure 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 relatforcestwistedsteel josection)able (fsimilarand , in

ively weak in resisting obliqueand is susceptible to beingout of shape by them. Rolled

ist (American standard beam or Scross sections are also avail-

ig. 2S), These offer propertiesto those of the wide-flange beamsaddition, 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 shapescontinually seam-welded. They give bet-ter all-round performance under heavyloading than the rolled-joist sections.

Connectors are necessary in most archessince effective one-piece units cannot betransported underground. Joining of thearch sections is done in a variety ofways. One type of joint is shown in fig-ure 3j4 . A single bolt holds the twoforged lugs tightly together to form arigid joint and transmit shear forces andbending moment from one member to theother.

A flexible joint is shown in figure 3B.A single bolt holds two rounded forgedlugs together which roll on themselvesunder weight, thus enabling the joint torotate under load without fracturing.

Another vender uses butt plates weldedto the beam ends (fig. 4). The beam endsare butted together and connected withbolts through holes provided in theplates.

Arches are usually installed on 3- to6-f t centers , and they are connected to-gether with tie rods for lateral sta-bility. Normally, the periphery of thearches is lagged with 2- to 3-in treatedwooden boards.

B

FIGURE 3. - Types of bolted joints. A,Rigid joint; B, flexible joint.

For maximum efficiency, the void spacebetween the outside of the arches and thestrata must be backfilled or solidlyblocked. This provides uniform loadingof the arch structure and avoids pointloading that would locally overstress thearches and destroy the overall supportcapacity of the total arch. Rigid arches

FIGURE 4. - Butt plate joint.

are usually installed on main haul-ageways, slopes, and shaft stations thatrequire permanent support where largeground movements are not expected.

YIELDING STEEL ARCHES

Yielding mine arches consist of archor ring sets that incorporate a slidingfriction assembly to accommodate heavyground pressure and thus prevent distor-tion of the support.

The yielding arch is designed to relaxbefore it becomes excessively bent ordistorted. The joint acts as a safetyvalve to keep the steel set from beingdestroyed; it is designed to yield at aload below the yield point of the steel.

Yielding arches serve the same functionas rigid arches but are much more ef-fective in areas of severe pressures orsqueezing ground conditions, which pro-duce large deformation that would destroya rigid arch. They are an economicalsupport method under severe conditionswhere extensive movements occur becauseof faulted ground, overstressed strata,longwall operations, or strata with vari-able properties.

Yielding arches are fabricated in vari-ous shapes such as circular and horseshoeand consist of three or more segments ofhigh-strength steel with a yield pointabove 50,000 psi. Three typical archshapes are shown in figure 5. The three-segment symmetrical arch with leg seg-ments toed in (fig. 5A) is used where theground pressure is predominantly verti-cal, the three-segment symmetrical archwith leg segments toed out (fig. 5B) re-sists lateral as well as vertical groundpressures, and the symmetrical ring (fig.5C) resists ground pressures from alldirections.

The two most common yielding mechanismsare the yield box and the overlap joint.The yield box was developed for usewith standard-type beam sections such as

the wide-flange, joist, and box-sectionbeams. The yield box is placed on thefloor, and the lower end of the arch legis inserted into its top. Constructionof a yield box is shown in figure 6.When the support is set, frictional re-sistance is established between the archleg, the wooden wedge, the brake shoe,and the rear side of the box.

Several companies furnish arches madeof U-shaped cross sections that nest to-gether at the ends to form an overlappingjoint. Heavy U-bolt clamps are installedover the joints to provide the yieldingfeature. The joints are tightened enoughto hold under normal loads, but when ex-cessive pressures develop, they permitthe nested segments to slide or yield be-fore the yield strength of the steel isreached. This relieves the load andmaintains the structural integrity of thearch while the ground is permitted torelax gradually until equilibrium isreached. As the successful functioningof a yielding set depends on its abilityto yield when required, it is criticalthat 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 theU-shaped cross section are shown infigure 7. The most commonly used sec-tions weigh from 10 to 25 lb/ft and haveoutside dimensions of 3 to 7 in. Moduliof sections on "XX" and "YY" axes arepractically equal, thereby offering uni-form resistance to eccentric loading.Ordinary H-beams give poor support whenloads are applied at an angle to themajor axis of inertia, causing torsionalmoment on the section. The high torsion-al resistance of the U-shaped sectionsallows them to be twisted out of the ver-tical plane and still provide adequatestrength.

^Underlined numbers in parentheses re-fer to items in the list of referencespreceding the appendix.

Arches are spaced at 2- to 5-ft inter-vals

,depending on expected ground pres-

sure. Adjoining sets are connected withhorizontal struts made of steel channels,pipes , or rods to maintain spacing andprovide lateral stability. Treated tim-ber lagging is installed around the

outside of the arches, and blocking orbackfilling is used to provide uniformloading. Footers of steel plate, channelsteel, or wood blocks are placed betweenthe bottom of the legs and the floor toreduce penetration if the floor is soft.

BACKGROUND INFORMATION FOR DESIGN OF STEEL SUPPORTS

This section was extracted from "SteelSupports Design Criteria: A Summary ofEuropean Data" (2^) . This Bureau contractreport presents information pertaining tothe relationship between steel support

selection and the physical and geologicalparameters that make up the support envi-ronment. The following parameters wereexamined to determine their contributionto support design.

B

FIGURE 5. - Typical yielding arch shapes. A, Three-segment symmetrical with legs toedin; B, three-segment symmetrical with legs toed out; C, symmetrical ring.

Arch leg

Wooden'wedge

U-bolt

Brake shoe

Rear sideof box

FIGURE 6. - Yield box construction.

TYPES OF ROOF STRATA

The roof strata in underground coalmines are normally divided into threeclasses: immediate roof, main roof, andtotal remaining overburden. The immedi-ate roof is that portion of the strataimmediately above the mined opening thatwill fall if left unsupported for a rela-tively short period (usually a few days).The behavior of the immediate roof ishighly dependent on opening width, insitu stresses, induced mining stresses.

Arch profile

Cross section

FIGURE 7. - Typical arch with U-shaped crosssection.

structure, and environmental factors suchas temperature and moisture. The immedi-ate roof is of the most direct concernfor safety in the mined opening and,therefore, is the stratum toward whichthe most control efforts have been di-rected. The two basic methods of controlthat can be applied to the immediate roofare internal, such as rock bolts, and ex-ternal, such as steel supports.

The second class of roof strata is themain roof. This is the stratum that liesabove the immediate roof and spans theopening if the immediate roof falls. Itis generally agreed in the mining indus-try that the main roof cannot be sup-ported by artificial means. This meansthat roof bolts, cribs, steel supports,etc. , will not be effective in supportingthe main roof.

The third strata classification is thetotal remaining overburden. This over-burden will settle, but normally thissettlement can be postponed long enoughto permit mining; its stability dependsupon the action of the main roof.

In multiple-seam mining, pillar rem-nants in overlying seams may causelarge stress concentrations. The entriesshould be aligned, as much as possi-ble, to provide more uniform stressconditions,

OVERBURDEN PRESSURE

Overburden pressure does not have a di-rect effect on the selection of a steelsupport design. However, the overburdenpressure does have an indirect effect inthe following ways:

1, The overburden pressure is one ofthe factors that determine the amount ofconvergence that can be expected in anopening and, hence, the amount of defor-mation that the support can be expectedto receive,

2, The overburden pressure also af-fects the stress in the immediate roofthat will comprise the support load. Theoverburden pressure is one of the factorsthat determine the height of the expectedsupport envelope.

SEAM THICKNESS

The seam thickness enters into supportselection both directly and indirectly.Directly, the seam thickness determinesthe height of the openings and supportsand, therefore, the resistance of thesupports to column failure. Indirectly,the seam thickness is one of the factorsin determining of convergence and, there-fore, in determining the amount of ex-pected deformation,

IMMEDIATE ROOF TYPE

The immediate roof type is the singlemost important factor in determining

steel support design. The immediateroof's weight, thickness, stress, andcompetence all influence the design ofthe support. The immediate roof is thestrata that are actually being supportedby the steel supports and, therefore, itsproperties 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, thefloor type also determines the need forfootpads or other load-spreading devices.

ENTRY WIDTH

Support design is directly dependent onentry width in two ways. First, sup-ported load is directly proportionalto width. Second, support design andstrength are directly proportional tospan.

ENTRY SHAPE

Entry shape (rectangular, arched, fullcircle, etc.) has a significant effect onthe stability of the opening. It alsoaffects the amount of artificial suupportrequired,

ROCK PROPERTIES

Strength parameters for the strataaround the opening should be determined.Although the strength of coal does notdirectly enter into any of the design in-formation, it does affect convergence andexpected deformation. Convergence is in-fluenced by the mechanical strength ofthe materials in the main roof , immediateroof, coal seam, and floor,

ROCK MECHANICS DATA

The height and shape of the supportenvelope that the structure must be de-signed for are determined by the heightand integrity of the pressure arch thatwill form (assuming laminated strata)when the entry material is removed.

STEEL TYPE

Mild steel (grade 40 to 60) with goodductility is desirable for undergrounduse. The ductility of the steel de-termines its ability to accept localizedyielding without catastrophic failureof the support. Surface hardness is im-portant for yielding arches to ensurethat sliding movement can still takeplace under load without gouging of thesliding surfaces. Detailed discussionsof steel for use in underground sup-ports can be found in chapter 5 of FritzSpruth's book, "Steel Roadway Supports"(_3) , and in chapter 2 of Proctor andWhite's book, Rock Tunneling With SteelSupports" (^) . Available standard U.S.steel sections are listed in the manualof steel construction (_5) by the Amer-ican Institute of Steel Construction(AISC). This manual also includes designand fabrication procedures for severalgrades of steel. The allowable stresseslisted in the manual can be increasedto the yield point of the steel forunderground temporary support. Severalgood textbooks covering elastic and plas-tic steel design procedures are avail-able (^~8^) They cover the principlesof good steel design which account forbending, axial, torsion, and shearstresses, safety factors, axial and lat-eral buckling, shear stiffness, end bear-ing, etc.

BACKPACKING

Most steel support failures occur frompoint loads that overstress the supportlocally. Failure in this context meansfailure of the steel support to maintainentry shape because of local deformation.To prevent this type of failure, attemptsare made to provide a continuous struc-tural interconnection between the supportand the surrounding rock. In practice,this is accomplished in two steps.

First, considerable care is taken tocut the entry to the approximate shapeof the support. This avoids the needto fill large openings, which is costly.Also, large openings are difficult tofill with a material that will evenly

distribute the load from the surroundingstrata. Figure 8 shows examples of poorand good practices.

Second, when the support is set, thespace between the support and the sur-rounding rock is packed with a materialthat is deforraable and yet has the struc-tural integrity necessary to transfer theload from the surrounding strata. A com-mon material used is waste rock. InBritish mines, the waste rock is placedin paper bags, and the bags are thenpacked into the space. The small sizeof the rock and the use of bags makethe material handleable and yet giveit the needed properties of deformationand integrity. The most common materialused in U.S. mines is wood because of itsavailability.

EXPEDITIOUS SUPPORT INSTALLATION

Steel supports should be installedclosely behind the face to minimize thespan of unsupported roof and the timethat a section of roof remains unsup-ported. European practice is to installsteel arches within about 6 ft of theface and within 8 h after roof exposure.

D hu n n II n nnnnnnnnunniin armrn n I 1 u u g y u a_Q.jafl_XL

Poor practice Overcutting requiresexcessive timbering

Good practice Close cutting requiresminimal 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 loaddetermination and support selection.

LOAD DETERMINATION

First, it is necessary to determine theexpected loads and the support requiredfor those loads. The analysis is basedon the immediate roof envelope. Figure 9shows three roof envelopes at heights ofb/2, b, and 3b/2 above the roof line. Itis assumed that the envelope acts as afree surface (that is, the rock above theenvelope is self-supporting and no loadsare transferred from the surroundingstrata). The heights of the roof enve-lopes shown in figure 9 are idealizationsthat include conditions normally encoun-tered in practice. The actual height ofthe envelope in a particular mine may beless or greater than those depicted.

The shape of the roof envelope is con-sidered to be a parabola. Assuming a

Height to3b/2envelope

Height tobenvelope

Height tob/2envelope

FIGURE 9. - Possible roof support envelopesfor entry width.

parabolic roof envelope at a height of hft in the roof above an entry b ft wide,the area of the parabola between the roofline and the envelope is

A = 2/3 bh. (1)

Multiplying by a distance of 1 ft alongthe 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 rockin pounds per cubic feet) gives theweight of rock per foot of entry lengththat must be held up by the supports:

P = 2/3 bhy. (3)

A nomographic solution of equation 3 isshown in figure 10. The nomogram is usedas follows: (1) Select the entry widthon the right side of the X axis; (2) movevertically upwards to the appropriaterock density curve; (3) move horizontallyto the left to the appropriate supportenvelope height curve; and (4) move ver-tically downwards, and read the weight ofrock to be supported per foot of entrylength on the left side of the X axis.The correct routing is depicted by thethree arrows in the figure. Supportloads 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 ofentry length for various entry widths,rock densities, and envelope heights. Anestimate of envelope height can be ob-tained from prior roof falls. Multiply-ing this quantity by the spacing betweensupports along the entry gives the totalweight to be supported by each support.Design of the support beam can then bedetermined by reference to the "Manualof Steel Construction" (5) or a similarsteel design manual.

11

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>

V r \%nX\\h^^^\ \\ 1 \

h\\\vX-N^ s. N\, h^\\\N\\ \ \ s. >\ w \%\iN\ \\\ \\ \ ^.\^>^

kk \k \, K\

^\ \ \\ \\ \ \ \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 length1.5 1 10 15 20

ENTRYWIDTH, ft

FIGURE 10. - Nomogram for determining support loads.

Four different types of beam loadingsare shovm in figure 11. They includeconcentrated loading, uniform loading,uniformly varying loading, and parabolicloading. Formulas for calculating endreaction, maximum shear, maximum moment,and maximum deflection are presented foreach case.

rock to be carried by each support. Themaximum moment to be resisted in terms ofthe total load and beam length is

M 5WL 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 entryis to be supported. The roof is composedof shale rock with a density of 160 lb/ft-'. Support envelope height is esti-mated as 24 ft (3b/2), indicating thatheavy loading is expected. The supportswill be spaced 4 ft apart along the en-try. Parabolic loading of the supportsby the roof rock (case 4) is assumed. Atypical yield strength of structuralsteel is 36,000 psi. It is assumed thatthe critical load condition causes yield-ing of the section. In other words, thefailure load is defined when one elementof the supporting structure has reachedyield strength of the steel.

The nomograph of figure 10 gives a sup-port load of 41 kips per foot of entrylength for a 16-ft-wide entry, 160-lb/ft^rock density, and 24-ft-high support en-velope. Multiplying this number by the4-ft support spacing gives 164 kips or164,000 lb as the total weight of roof

The required section modulus is obtainedby converting the maximum moment to inchpounds and dividing by the yield strengthof 36,000 psi.

S =M (410,000) (12)

36,000= 137 in^. (5)

Referring to the "W Shapes, Propertiesfor Designing" section of a steel con-struction manual (_5 ) , and using the plas-tic modulus (Zj

12

W

R

End reaction; R = W

Maximum shear; V,

Maximum moment: M

W

WLmax

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*^ WLMaximum 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 ^ 60EICase 3-uniformly varying load

A n-* L

Total load ; W = qL

End reaction; R = qL W

Maximum shear; V, W2

Maximum moment;Mmax =

Maximum deflection; '^

qJLf_^WL8 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 checkedfor 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 wEnd r e a c t i on: R = -- =

q L wMaximum s h e a r: V^ a x ~ ""T~~T5qL^

_

5WL32Maximum moment:M max 48

Maximum d e f le c t io n:5 , eiqL^ 6 1WL'f"^^ 5,760EI 3,840EICase 4-parabolic loading

beam loading conditions.

All steel design and review calcula-tions are based on the specifications ofthe American Institute of Steel Construc-tion. Plastic design methods have beenused throughout this example.

Shear Capacity

The maximum shear on the beam is

V,, . f .i^MOO , 82.000 lb. (6)

13

ill1,375

+ 25, (8)

'w

Yf

ZxPlastic section m o d u I u s = 1 4 4 In-'d:beam depth=21 intyy:web thick ness=04 inr;radlus of gyration about Y axis=1.77 inl:tnoment of inertia about X axis1,330 in^bfiflange width=8.24 int|:flange t tiic k ness= . 6 1 5 ink:distance from outer face of flange to web toe

of fillet* 1 25 inE: modulus of e la s 1 1 c i t y= 2 9 , , 00 psiFyiyield strengfti of steel36.000 psi

FIGURE 12. Pertinent properties for selectedbeam.

The allowable shear for the selected beamin terms of the yield strength (Fy), webthickness, and beam depth (see figure 12for 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 thanthe 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.

1,37536

+ 25

(9)

As the beam is 16 ft long, it should bebraced (struts from beam to beam) on thecompression flange at the midspan of thebeam. This lateral bracing will preventbuckling of the compression flange.

Deflection

The deflection formula (figure 11, cased) is

= 61 WL^"^x 3^840 EI

= 61 (164,000) (16)^ (12)33,840 (29,000,000) (1,330)

= 0.478 = 0.5 in. (10)

Measurement of beam deflection permits aquick check on the condition of the beam.The midspan deflection can be measuredwith a pocket tape by stretching a stringfrom one support to the other. For exam-ple, if 0.25-in deflection is measured,the beam still retains approximately 50pet of its load capacity.

Localized Flange or Web Buckling

Beams are made with different flangeand web thicknesses and may be subjectto localized buckling, even though theirsection modulus is adequate for the load.

Flange thickness is checked with thefollowing formula:

14

2t,< 8.5. (11)

R

Substituting the selected beam valuesin the formula.

8.24= 6.70 < 8.5;

2 (0.615)

beam is acceptable. (12)

The equation for checking web thicknessassuming 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

210.4

412= 52.5 < -7^ = 68.7;7jh

beam is acceptable. (13)

Support Length (Web Crippling)

This test is to check for localized webbuckling from the concentrated loadingthat 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 theequation,

82,000N =

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 postof less than 6.3 in is used, a stiff-ener should be used at the end of thebeam. This reinforcement can be providedby welding plates to both sides of theweb.

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 assumedloading conditions.

SUMMARY

The major source of injuries appears tobe handling the steel supports, primarilydue to their weight and awkwardness. Ac-ceptable mechanical methods for quickerand safer installation of the heavy steelsupports in the confining mine environ-ment are needed.

The arch is a more efficient configura-tion than the flat crossbar, as the loadis transmitted as compression rather thanbending forces. Yielding arches are moreeffective than rigid arches under se-vere conditions that produce large de-formations. The void space between thearch and the strata must be backfilled

or blocked to provide uniform load-ing. Steel supports should be installedclose to the faceexposure.

and shortly after roof

The load to be carried by steel sup-ports can be calculated by assuming aparabolic-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 supportloads per foot of entry length for vari-ous entry widths, rock densities, andsupport envelope heights. The supportbeam can then be designed by referring to

15

any steel construction manual. A designexample is provided with pertinent equa-tions and calculations. Equations areprovided 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 OFR121(2)-82, 1980, 61 pp.; NTIS PB 82-251968.

3. Spruth, F. Steel Roadway Supports:A Practical Handbook. Collier GuardianCo., 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 SteelDesign. Harper & Row, 3d ed., 1982, 662pp.

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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