Table of Contents
- Application Of Rock Bolts
- Bolting patterns
- Beams and roof ties
- Anchorage capacity and bolt loading
- Problems of bolt use
- Advantages of roof bolts
- Installation sequence
- Using Steel Timber Set Underground Support
- Use Of Concrete Sets
- Design Of Concrete Sets
- Ordinary set
- Loaded drift set — cap
- Spreader Bearing
- Calculation of concrete mix
- Placing sets in drift
- Wooden Headframes
- Wooden Ore Bin
When selecting a square-set design, one should adopt the design having the fewest number of saw-cuts but still providing the maximum support. An excessive number of cuts adds little to the strength of the set, and makes erection difficult. Furthermore, it is difficult to get even contact and bearing between the many faces. (In fact, too many cuts may actually prevent maximum support).
READ PART 1 of Timber Support in Underground Mining
It is important to remember that only three pieces of the set are used to describe a square-set or express its efficiency or economy. For example, the boardfeet of lumber in a set refers only to one each of a cap, post, and girt. Similarly, the number of saw cuts means the total number of cuts for these same three members.
Square-sets must be tightly blocked and closely filled with hydraulic fill or waste rock. Failure to adhere strictly to this principle may result in the loss of a stope.
Application Of Rock Bolts
(Figures 23 and 24)
Figure 23 illustrates four commonly used types of rock bolts. Types (a) and (b) are most widely used. There are many varieties of (b).
In (c) the wooden bolt shown was developed for use at the Day Mines in the Coeur d’Alene district, Idaho (Farmin and Sparks, 1953, p. 922). This bolt proved satisfactory in holding soft, wet ground in and near fault zones.
Figure 23d shows a type of bolt which is receiving considerable attention.
Use of the PERFO bolt may be briefly described as follows: the two perforated halves are filled with sand-cement-water mortar, the halves tightly wired together, and the filled tube pushed into the drill hole. Pushing the bolt or reinforcing rod into the tube forces the mortar out through the perforations to tightly fill the drill hole and cracks. Advantages of this method are:
- The entire length of the device supports the ground.
- Circulation of moist air through the hole is eliminated. (Remember the deleterious effect of moist air on many rock-forming minerals).
- It can be applied in soft rock.
- Less attention need be paid to uniformity of the diameter of the drill hole.
Unfortunately, a great deal of the more practical literature on rock bolting occurs in current technical journals or government publications of limited distribution. For this reason some parts of the article by Humphrey (May 1956, p. 491-495) will be quoted extensively.
Bolting patterns vary with rock conditions. A typical pattern in a 16- ft. opening in a coal mine would be four bolts per row, spaced 4 to 5 ft. in direction of the advance. The two center bolts would be driven vertically, or normal to the plane of the structure, while the outside bolts might be angled out about 30° to obtain anchorage over the rib. A steel angle washer is used to provide a bearing surface normal to the angled bolts.
In unstratified ground a pattern might consist of bolts driven in rows every 4 or 5 ft., one bolt vertically in the back; two bolts on each side, 4 ft. from the center bolt, at a 15° angle; two additional bolts 4 ft. down the side at a 30° angle. Special cast iron or steel beveled washers are used in that type of bolting to correct for angularity of the bolt, and to bring the bearing plate parallel to the rock’s surface. (Frequently the bolts are all driven normal to the surface of the opening).
In larger openings, such as motor rooms, intersections, and shaft stations, random pattern bolting is often employed. A typical pattern would find bolts installed on 5—ft. centers in both directions. To provide further stability and to minimize deterioration from moisture and air, permanent installations may be gunited after bolting.
Beams and roof ties
To increase the bearing area absorbing the load from the bolt, and to control spalling between bolts, steel channels, usually 4-in. at 5.4 lb. per foot or 5-in. at 6.7 lb. per foot, or steel mine roof ties are used in place of mild steel plate washers. Wooden headers are used for the same purpose; however, gradual failure of the wood results in loss of bolt tension, destroying
part of the effectiveness. Channels and roof ties are provided with holes punched for the spacing of bolts used in the particular formation. Holes are made large enough for either wedge or expansion shell to pass through. Special small plate and angle washers are used to distribute the load from the bolt to the channel or tie. In non-bedded structures they are more difficult to employ in long lengths. Roof ties, on the other hand, are flexible and can be adapted to surface irregularities of almost any ground condition.
Anchorage capacity and bolt loading
The USBM has developed testing procedures to determine the length and type of bolt that should be employed and to measure the possibility of anchoring bolts in any given underground opening. From test results and experimentation, the spacing or pattern necessary to obtain the support desired is determined.
Measurement of anchorage capacity is obtained by pulling installed test bolts with a hydraulic pull tester. The tester is attached to the end of a bolt in the roof with the hydraulic jack bearing against the roof around the bolt, and load is applied until desired values are reached, or until slip occurs. Test results indicate the type and length of bolt that should be used to obtain maximum anchorage for the given rock condition.
Danger of overloading the bolt with the impact wrench used in tightening during installation has led to establishment of safe limits of initial loading. Overloading may not be apparent, and an unsound roof may go unnoticed unless proper procedures are strictly adhered to.
USBM tests have established the ratio of tension in pounds to torque on the nut or bolt head:
a) For 1-in. slotted bolts, tension in lb. = bolt load = 42.5 times torque (foot-pounds) – 1000 lb. (Barry, Panek, and McCormick, 1953, p. 6).
b) For ¾-in. headed bolts,tension in lb. = bolt load =39.8 times torque (foot-pounds) (Barry, Panek, and McCormick, 1954, p. 14).
Tests made by Bethlehem Steel Co. indicate wide variation and values in general lower than this unless hardened washers are used under the bolt heads, in which case the tension-torque ratio is 60 for ¾-in. bolts and 80 for 5/8-in. bolts.
For practical purposes a ratio of 40 to 1 may be used. Tests indicated that manufacturing methods, type of thread lubrication type of bearing plates
used, roof strata, and other factors appreciably affect the ratio. For commercial 1-in. bolts the advised limit of installation torque is 350 ft.-lb. or 14,000 lb. Tightening of ¾-in. headed or expansion shell bolts produces torsional (shear) stresses in addition to tension. Lowering the tensile load at which yield may occur, and a limit of 200 ft.-lb., or 8000 lb. is advised. The torque necessary to turn the nut or the head of the bolt can be read with a dial-type torque wrench. Provided that threads are free from rust and a straight pull is exercised, a true indication of load on the bolt can be obtained. Bolts should be spot checked after installation even though impact wrenches can be set for the desired driving torque. Periodic spot checks should also be made in permanent drifts and accesses to detect any shifting of load. Unless the bolt is in tension, it is not providing adequate support. Loosened bolts should be retightened to insure that rock surface is held in compression.
- Estimation of Ground Pressure with Selection of Support
- Timber Cap Selection
- Selection of Standing Posts
- Post in bending
- Force acting on spreader
- Suggested Change in Working Stress
- Treatment Of Timber
- Framing Of Timber
- Installation Of Timber
- Timber Repairing
- Discussion Of Illustrations
- Simple Drift Supports
- Squeeze Sets
- Erection Of Drift Sets
- Chute Construction
- Shaft Bearing Sets
- Application Of Stulls
- Loose Or Squeezing Ground
- Vertical And Inclined Shafts
- Square-Set Timbering
Problems of bolt use
In addition to torque limitations, adherence to prescribed patterns and the size and depth of hole drilled to install the bolt are of utmost importance. Successful (wedge-type) bolting requires strict adherence to prescribed procedure.
- A hole of accurate depth. A shallow hole does not allow sufficient takeup on the thread. A hole too deep does not allow proper wedging or tightening. For bolts using 3/8-in. or ½-in. plates, or washers, a hole 1½ to 2 in. shorter than the bolt is prescribed.
- Tight, hard material at the back and sides of the hole. Since the wedge is driven against the back of the hole, it must be sound to provide good anchorage.
- A hole 1¼-in. diameter finished size. A hole too large does not allow enough bite for the legs of the slot when they are wedged out. Thicker wedges may be used if holes are oversize.
For expansion type. Diameter of the hole drilled and protection of bolt threads and expansion shell are of primary importance for proper anchorage of the headed-type bolt. Protection is afforded by shipping and storing bolts with the expansion shell assembled on the bolt. Very good results are obtained where the hole at anchorage depth is of the prescribed size, usually 1 3/8 in. A larger hole reduces both anchorage capacity and effectiveness of the expansion shell. Most shell types are sufficiently strong to break a common steel bolt if the hole is drilled to the proper diameter and the rock structure is firm.
Advantages of roof bolts
Use of roof bolts instead of conventional timber sets offers many advantages, both from the safety and cost standpoint:
- Safer, more assured roof control. By systematic bolting BEFORE any sag has taken place and by providing sufficient tension in the bolts, roof sag can be limited and roof falls almost eliminated.
- Lower handling and timbering costs. Reduction of timber in the mine reduces fire hazard.
- Less storage space required.
- Cleaner ore and coal through better control of sloughing of waste rock.
- Reduced danger to men from falls caused by blasting and accidental dislodging of timber posts. Danger from falls in event of train wrecks also lessened.
- Increased head room and side clearance due to absence of timbers, resulting in increased productivity.
- Availability of bolts for hanging air, water, and messenger lines.
- Increased height of working face. Timber sets limit roof heights to approximately 14 ft. before buckling of the legs becomes a problem. Roof bolts allow increased height and, therefore, increased recovery of coal or ore. (One Utah coal mine is now mining the full depth of a seam 25 to 30 ft. thick, removing 80 percent of the coal. Previous recovery limited to only 14 ft. of the seam depth was estimated at 40 to 45 percent,).
- More permanent support. Bolts are estimated to last 20 to 40 years, depending on corrosive conditions.
- Reduced sloughing of rock caused by attack of air and water. Fractures and faults are kept from opening.
- Decreased excavation costs. Opening need not be made larger than working space required. In a Butte mine of the Anaconda Co. , 2500 ft. of recent development was accomplished with 37 percent less excavation than would normally be required. Handling 10,000 tons of broken material was avoided through the use of roof bolts.
- Decreased ventilation costs through reduced resistance to air flow.
One mine reports that a single ventilation unit now handles two levels, where one unit per level was required with conventional timbering. Estimated cost per ventilation unit — $70,000.
Slotted type roof bolt
- Hole is drilled with stoper to depth 1½ to 3 in. shorter than bolt to be installed. Finish bit should be 1¼-in. in diameter.
- Back of hole is sounded with rod or bolt to insure soundness.
- Wedge is inserted into slot.
- Bearing plate is slipped over threaded end of bolt and nut is screwed on thread so that about ½-in. of thread protrudes from nut.
- Bolt with wedge inserted is started into the hole and threadless dolly fitted onto threaded end of the bolt.
- Bolt is driven to refusal with stoper. Driving bolt upward forces legs of slot over wedge and into surrounding rock, providing anchorage .
- Nut is tightened with impact wrench to approximately 350 ft.-lb. torque.
- Bolt is struck with rod or hammer. Experienced operator can tell by ring if bolt is tightened properly. Spot checks for tightness should later be made with torque wrench.
Wedges used with 1-in. bolts are usually ¾ x 7/8 x 5½ in. or 6 in. long. Plates are normally 6 x 6 in. or 8 x 8 x 3/8 or 1½ in. thick, with hole centrally punched.
Headed type bolts with expansion shell
- Hole is drilled slightly longer than the bolt to be installed. Finish bit size should be 1 3/8-in. for most expansion shells.
- Bearing plate is assembled on bolt and expansion shell threaded on end of bolt.
- Bolt is inserted in hole and turned to engage shell with sides of hole. As bolt is turned, plug of expansion shell is drawn downward, forcing the expandable sides outward into the rock, providing anchorage.
- Bolt is tightened with impact wrench and tested by measuring torque with torque wrench.
Among the outstanding articles on rock bolting is that by Thomas and Smedberg (1953-1959, sec. 22, p. 1). Their complete discussion of rock bolting deserves careful reading by anyone expecting to establish a rock-bolting program. This article states that in 1957 over 4,000,000 bolts per month were used in the United States.
Using Steel Timber Set Underground Support
While it is unlikely that the small mine operator will encounter ground conditions requiring the use of steel sets, he should know that such sets are available. Fault zones containing heavy, water-saturated gouge are not uncommon. Ground of this kind may best be supported with steel sets. For designing steel sets see Proctor and White (1946, p. 219-232).
The type of set shown in (b) is available in many varieties: circular rib (shown); elliptical rib; continuous rib separate from the posts and circular (for extremely heavy ground). For spacing between sets see Table 1.
Steel sets are usually blocked in place with wooden blocking. If a concrete lining is to be used, the wooden blocking should be removed. Wood will decay and leave weak sections in the lining.
Use Of Concrete Sets
There are localities where timber is not only scarce, but where the timber species available are not suitable for even light ground support. Concrete sets deserve consideration for these localities. In this paper I have made no effort to recommend concrete sets for heavy ground conditions. Such a recommendation would require careful analysis of ground pressures before the set was designed. Here I propose the use of concrete sets only for light ground support when suitable timber is difficult to get. Because this substitution of concrete for timber may be primarily an economic problem, the relative costs must be carefully compared.
For proportioning the ingredients of concrete for use under many of the following circumstances, complicated strength and proportioning rules are not necessary: Fuller’s rule is sufficient for most set work, as well as for other concrete work for the small operator (footings, walls, floors, foundations).
Fuller’s rule for proportioning cement, sand, and gravel is:
c = proportion of cement.
s = proportion of sand.
g = proportion of gravel.
C = barrels cement per cu. yd. of concrete.
4 sacks cement = one barrel.
This formula is used when the concrete mixture is expressed as a proportion of cement : sand : gravel : (for example, 1:2:4).
Fuller’s rule offers a convenient way to express the ingredients of a concrete mixture in easily measured units.
Strength values of 28-day concrete for different mixtures may be taken from Table 4. These values are conservative.
Application of the formula may be shown with a 1:2:4 mixture.
To achieve maximum results for a water-cement ratio, consult the Portland Cement Association booklet. Gallons of water per sack of cement proportions shown in Table 4 will suffice for small batches and such construction requirements for which one usually uses Fuller’s rule. The least amount of water consistent with handling the mixture should be used. When necessary, tests may be made using representative samples of the aggregate and water. Final design is based on their results.
In addition, Tables 5, 6, and 7, and Figure 26k give information useful in concrete design.
Design Of Concrete Sets
Reinforced concrete design is based on various building and organization-sponsored codes, set up generally for structures directly connected with human safety. Furthermore, structures of this type invariably contain interdependent component parts; if one part fails, the entire project is endangered. In addition, the codes are not entirely uniform from locality to locality. Safety factors used are extremely conservative.
Concrete supports for mines serve a purpose much different from those for ordinary concrete structures. In this discussion concrete is proposed as a substitute for timber when the latter is difficult to obtain in quantity or when mine conditions are conducive to rapid deterioration of timber, or both. Reinforced concrete is unlikely to fail instantly. An unforeseen increase in the loading is invariably shown by progressive cracking of the concrete surface. Only under unusual conditions would the reinforcing steel completely fail to produce instant closure of the drift. Why then, should building code factors of safety be applied to drift sets? I propose that “ultimate strength design” be applied to mine supports (Urquhart, O’Rourke, and Winter, 1958, p. 434; ASCE, 1956). Such a design will save 25 percent (or more) of the materials (weight) in the usual reinforced concrete design. In those mine applications where rock pressures change rapidly and
are difficult to foretell, the procedure will require modification. In fact, instead of the ultimate strength method it would seem that even a much higher proportion of the 28-day strength for concrete could be used in the ordinary design formulas (40 to 50 percent is the limit recommended in the codes for compression; 75 to 80 percent might well be considered). Similarly for steel, at least the full yield strength should be used. Steel has a much higher ultimate strength than the yield point. For concrete mine-sets a value for steel in excess of the yield point could be considered. In any event, design formulas for concrete sets should be established on their own merits and not tied to building code limits.
When steel is used, costs are based on weight (these include fabricating, transportation, erecting, painting, etc.). When reinforcing bars are selected, weight is an important factor. Several small diameter bars may weigh much less for a given area than fewer large bars of equivalent area.
Two concrete drift sets will be examined:
- One—an ordinary set—to resist conditions under which an ordinary 8-in. x 8-in x 5-ft. timber cap would be ample. Here, the load is constant and seldom will increase sufficiently to cause destruction of a set; side pressure is negligible, but scarcity of timber and decay conditions are the reasons for considering concrete.
- Two—a loaded drift set—to resist the conditions given for the timber set investigated in Figure 5e.
An 8-in. x 8-in. x 5-ft. timber cap of the species usually found in mining regions would support an evenly distributed total load of about 15,000 lb. This weight is not the ultimate load but one based on the usual safety factors encountered when designing with timber. With this load the maximum bending moment on the cap is 102,400 in.- lb. and the load on each post is about 7600 lb.
Other data required for ultimate strength design are (Urquhart and others, 1958, p. 434; Baker, 1943):
Concrete: f’c = 3000 lb. per sq. in. , 28-day strength; ¾-in. aggregate with medium sized sand, n = 10 for 3000-lb. concrete.
Steel: fy = 40,000 lb. per sq. in. for intermediate grade deformed bars. This grade of steel will be used for all calculations to follow. (See Table 6).
Bond and Shear: Ordinary design procedures prevail (Report of ASCE, 1956, p. 13).
fs = 20,000 lb. per sq. in. working stress in steel.
fc = 0.45f’c = 1350 lb. per sq. in. working stress for concrete.
fv = 20,000 lb. per sq. in. working stress in shear for steel.
v = shear = 0.03f’c = 90 lb. per sq. in. with no web reinforcing.
= 0.08f’c = 240 lb. per sq. in. with web reinforcing
u = 0. 10f’c = 300 lb. per sq. in. bond for deformed bars.
Center of steel embedment, to concrete surface is 1½ in.
Application of the method requires a trial selection of dimensions of the steel. The ultimate moment or load for this selection is then calculated. A comparison with the maximum moment or load decides whether the section selected is satisfactory.
For this cap the following dimensions will be investigated. (See Figure 26c and d).
To resist shear, these simple beams (caps) will invariably require web reinforcing. Trial dimensions may be found by applying the shear formula,
v = 3/2 V/ba lb. per sq. in.
This formula is solved for ba. For v, the value of 240 lb. per sq. in. is used and V = 7600 lb. , the post load of the problem.
240 = 3/2 7600/b a
b a = 47.5 sq. in.
A 6 x 8 has 48 sq. in. Deducting 1½ in. from the depth of 8 in. gives 6 x 6.5 in. for trial.
b = width = 6 in. ; d = depth to center of steel bar = 6.5 in. ; total depth of section = 6.5 + 1.5 = 8 in.
Two ¾-in. diameter bars; area one bar = 0.44 sq. in.
Area = As = 2 x 0.44 = 0.88 sq. in.
Perimeter = O = 2 x 2.36 = 4.72 in.
Pmax = 0.4 f’c/fy = 0.4 x 3000/40,000 = 0.03, maximum reinforcement ration, must be greater than p.
p = AS/bd = 0.88/6 x 6.5 = 0.0226
m = fy/0.85 f’c = 40,000/0.85 x 3000 = maximum steel to maximum concrete ratio.
TS = ASfy = 0.88 x 40,000 = 35,200 lb.
a = pmd = 0.0226 x 40,000/0.85 x 3000 x 6.5 = 2.30 in.
c = d – a/2 = 6.5 – 2.3/2 = 5.35 in., internal lever arm — center of “a” to center of steel
Mu = TSC = 35,200 x 5.35 = 188,300 in-lb. resistance of steel section.
Loading originally assumed on the cap was 102,400 in.-lb. The section chosen appears to provide more than sufficient area, although it is about as small as can be used because of shear, bond, and web spacing requirements. Here an inconsistency creeps into the design, because no values for shear and bond correlative to tension and compression have been recommended for ultimate strength design. This inconsistency becomes less serious when one recalls that construction of forms with proper placement of concrete mix becomes difficult as the cross-sectional size of the forms decreases. Dimensions much less than 6 in. x 8 in. will seriously complicate the manufacture of the concrete cap.
As found above, vc, the actual shear in the section, exceeds v, the allowable shear (90 lb. per sq. in.). Therefore, web reinforcement must be used. The ¾-in. bars should be extended to form a hook anchorage as shown in Figure 26b. Additional detail for specifying the anchorage is shown in Figure 26.
For web reinforcing, the diameter of the bars should approach 1/50 of d and the web bars be otherwise dimensioned as shown in Figure 26a.
Because ¼-in. diameter bars are the smallest obtainable, they must necessarily be used. There are two sides to the stirrup; hence, twice the area of one bar is used.
Baker (1943, part 2, p. 31) suggests grouping the stirrups as follows:
- About 1 to 2 in. from the face of the support for the first stirrup.
- At xc/4 spacing between stirrups is 4s/3 for first group.
- At xc/2 spacing between stirrups is 2s for second group.
- At 3xc/4 spacing between stirrups is 4s for third group.
- Last stirrup at xc, with spacing in 4th group not to exceed d/2.
- Spacing not to exceed d/2 at any position.
These spacings are only approximate, and Nv is the minimum number required. Additional stirrups may be used to balance the grouping. Because of the small cross- sections generally designed for mine support sets (compared to building construction sets), the stirrups occur closely spaced. In choosing between the minimum and maximum spacing, one may have to decide on the basis of convenience in placing the concrete.
After the above six suggestions were applied, the spacing and number of stirrups shown in Figure 26d (cap) were decided upon.
For the set under consideration very little pressure from ground movement is assumed to be acting against the posts. If the spreader is 1½ in. deep, it and the post should resist;
6 x 1½ x 750 lb. per sq. in. (see Table 4) = 6750 lb.
The given axial load on each post is 7600 lb. One dimension should correspond to the width of the cap (6 in.).
For a trial, a 6-in. x 6 in. section (Figure 26e) will be investigated. At each corner ½-in. diameter bars tied together will be used. This arrangement is known as rectangular reinforcing. (Spiral reinforcing is usually applied to round columns). In designing columns (posts), the total dimensions are used. Here the depth equals t or 6 in. Also, (Urquhart and others, 1958, p. 452) an eccentric loading is assumed. When an average eccentric load is used with this type of column, the eccentricity e’ is taken as 0. lt. Values for the concrete and steel are the same as those used for the cap.
Column design also depends on whether the member is a long or a short column. Short columns are those whose length does not exceed 15 times the least dimension.
For the post under consideration the maximum figure would be 15 x 6 in. or 90 in. Actually the post will not exceed about 6½ feet or 78 in. When the member is a long column (Urquhart and others, 1958, p. 459),
the allowable load = P(1.6 — 0.04L/t) where L = unsupported length in inches, and t = least dimension of the column.
This formula may also be expressed as
d = distance from the extreme face to the center of the reinforcing bar in the direction t.
d’ = distance from the surface of the concrete to the center of the steel (actually the embedment distance).
A’s= area of the steel bars for compression.
A’s = 4 x 0.20 = 0.80 sq. in. (½-in. bars used),
d’ = 1½ in.
d =6 in. – 1½ in. = 4½ in.
e’ = 0.1 x 6 = 0.6 in.
Regardless of this great excess in capacity, the section is about the smallest size practical. Anything smaller would, among other things, prevent proper distribution of the aggregate around the bars. This is not an unusual example of the selection of a member for reasons other than the stresses to be resisted.
To help hold the four longitudinal bars in position, ties will be used. Spacing between the ties is the minimum distance derived from either
16 x diameter of reinforcing bars;
48 x diameter of ties;
or the least dimension of the column.
Material used for the ties should have a minimum diameter of ¼-in. For the above column, ¼-in. diameter bars will be used for the ties.
16 x ½-in = 8 in.
48 x ¼-in. = 12 in.
Least dimension of the column = 6 in.
Therefore, the spacing will be 6 in. from center to center of the ties. Bearing between the posts and the cap is,
6 x 6 x 750 lb. per sq. in. = 27,000 lb., which is more than ample. Detail for the post is shown in Figure 26d (post).
Loaded drift set — cap
Data used for designing the timber set in Figure 5e were used for finding a concrete set capable of resisting the same conditions. Calculations are identical to those just presented. Values for the steel and concrete are the same as assumed for the ordinary set.
Figure 26f shows the section and dimensions selected. For reasons similar to those given for the previously designed cap (vertical shear at the post, bond, etc.), the section is somewhat larger than would be necessary for tension and compression alone.
Figure 26g shows the stirrup spacing and end anchorage.
Because this post may have a large bending stress, the design must consider both bending and axial load.
Loading to be resisted by the post is,
M = 170,800 in.-lb. in bending = (Mu).
P = 12,000 lb. axial load (includes weight of cap).
The first step is to determine whether compression or tension governs the design. Compression is first checked.
Pu = 12,000 lb. = axial load on column.
When Pb is greater than Pu, failure will occur from tension, and the member is designed as a beam.
Pb = (0.72 90,000/fy + 90,000 f’c) + A’-Asfy, lb.
Ag is area of steel in compression; for the column under examination, no steel is used in the compression side of the column (side next to wall rock).
Figure 26h shows the post section.
b = 8 in.; d = 6.5 in.; and t = 8 in.
(A preliminary check for the bond resistance indicates that the three 5/8-in. bars are suitable).
AS = 3 x 0.31 = 0.93 sq. in.
O = 3 x 1.96 in. = 5.88 in.
Pb = (0.72 x 90,000/40,000 + 90,000 x 3000 x 8 x 6.5) + 0 – 0.93 x 40,000 = 77,600 – 37,200 = 40,400 lb. which is greater than
Pu = 12,000 lb.
Therefore, tension governs and the section must be designed as a beam.
Mu = Cc (t/2 – a/2) + Asfy (d – t/2), in. lb.
Cc = 0.085 f’cba, lb.
a = Pu + Asfy/0.85f’cb in.
a = 12,000 + 0.93 x 40,000/0.85 x 3000 x 8 = 2.19 in.
Mu = 0.85 x 3000 x 8 x 2.19 (8/2 – 2.19/2) + 0.93 x 40,000 (6.5 – 8/2) = 130,000 + 93,000 = 223,000 in. lb
Section chosen is satisfactory.
8 x 1¾ x 750 = 10,500 lb. , which is greater than 9933 lb.
Bond, Shear, and Stirrup Spacing
Because of the unsymmetrical loading on the post (load increases from zero at the bottom of the post to a maximum at the top), the spacing of the stirrups is best found by using a shear diagram. (See Figure 26i).
s = fvAv/(vc – v) b, in.,
we note that fvAv/b is constant (20,000 x 0.10/8 = 250). Values of (vc – v) may be scaled from the shear diagram. Dividing these scaled values into the constant gives the spacing between segments. Stirrups are placed at the center of each segment.
It must be kept in mind that the maximum is still d/2 inches. In the post under consideration the spacing is between 2 in. and 3¼ in. The first stirrup will be placed 1½ in. from the top of the post as shown in Figure 26j. Succeeding stirrups will be spaced as shown.
There is a little shear in excess of v at the bottom of the post. Merely as a precautionary measure, stirrups are placed there as shown.
Ordinary set (Customary method of design)
To show the comparison in size and weight, the cap for the ordinary set will be selected.
Following this procedure for the design, the values used for the concrete and steel are,
fc = 0.45 f’c = 0.45 x 3000 = 1350 lb. per sq. in.
When intermediate steel deformed bars are used,
fs = 20,000 lb. per sq. in.
v = 90 lb. per sq. in.; n = 10; j = 0.866; k = 0.403.
For this procedure the design is based on the balanced section method.
bd² = 2M/fckj in.³ and As = M/ fsjd sq. in.
Members of these formulas have the same designation as before.
As in the ultimate strength design, the cap must be checked for vertical shear at the face of the post.
v = 3/2 V/ba lb. per sq. in.
With web reinforcing, v is equal to 240 lb. per sq. in.
240 = 3/2 x 7600/ba and
ba = 47.5 sq. in.
If b = 6 in. and a = 8 in. , sufficient area for the shear is available. For this selection d will be assumed at 8½ in. If the embedment is 1½ in. , the total depth becomes 10 in. Two ¾-in. deformed bars are used.
Calculation of concrete mix
If an occasional, small amount of concrete is needed and the exact strength is of little importance, Fuller’s rule will suffice. On the other hand, if concrete in quantity with a specified strength is desired, a more exact method for figuring the mix should be used, as would be true if a considerable number of sets were to be made. To make such calculations consult data for concrete mixtures. Design and Control of Concrete Mixtures (1952, p. 18) is recommended. Sets should be allowed to cure for at least 28 days. During this period the surface of the concrete should be kept well moistened.
To illustrate the calculations, we shall determine a mix for the concrete sets previously investigated.
Raw materials (sand, aggregate, and water) will vary widely. Care must be exercised to use materials free from dirt, clay, and organic substances. Absolutely dry sand or aggregate will seldom be available. Therefore, the percent of moisture in each must be closely estimated. Of the five types of Portland cement, only the normal or common type will be considered—this type will probably always be available and is used for most ordinary construction.
In the calculations for the sets a 3000-lb. per sq. in. concrete was used. To make this concrete, assume the following data:
- Medium sand, 2 percent moisture. Medium here refers to the average size of the sand grains, which is defined and explained in Design and Control of Concrete Mixtures (1952).
- Maximum size of aggregate, ¾-in. with 1 percent moisture.
- Water should be determined on the basis of a 15 percent stronger concrete (Design and Control of Concrete Mix., 1952, p. 7): 3000 x 1.15 = 3450 lb. per sq. in.
- From tabulated information (Design and Control of Concrete Mix, 1952, p. 5 and 16; Fig. 26k is from this publication), a 3450-lb. concrete requires 6¾ to 8¼ gal. of water per sack (94 lb.) of cement; nearest trial amount is 7 gal. For the ¾-in. aggregate, medium sand, and 7 gal. per sack, 49 percent of sand, 51 percent of aggregate, and 38 gal. of water are necessary per cubic yard. (See Table 7, extracted from Table 5, Design and Control of Concrete Mix.).
- Slump of concrete mix is to be 5 in. (See Table 5), to provide sufficient fluidity for filling the forms.
- Correction for slump (tabulated data figured on slump of 3 in.); for each 1-in. change in slump, increase or decrease water by 3 percent.
38 gal. x 1.06 = 40 gal. for 5-in slump.
- Specific gravity of cement, 3.15; of sand and aggregate, 2.65.
- Cement factor = 40/7 = 5.72 sacks per cu. yd.
For one cubic yard
Absolute volume of cement = 94 x 5.71/3.15 x 6.24 = 2.73 cu. ft.
Volume of water = 40/7.48 = 5.35 cu. ft.
Volume of cement-water = 8.08 cu. ft.
Absolute volume of aggregate = 27.00 – 8.08 = 18.92 cu. ft.
Absolute volume of sand = 0.49 x 18.92 = 9.26 cu. ft.
Weight of surface-dry sand = 9.26 x 2.65 x 62.4 = 1531 lb.
Absolute volume of aggregate = 0.51 x 18.92 = 9.65 cu. ft.
Weight of surface-dry aggregate = 9.65 x 2.65 x 62.4 = 1598 lb.
For each sack of cement:
Weight of surface-dry sand = 1531/5.71 = 268 lb.
Weight of surface-dry aggregate = 1598/5.71 = 280 lb.
Correction for moisture:
Free moisture in sand = 268 x 2% = 5.36 lb.
Free moisture in aggregate = 280 x 1% = 2.80 lb.
Total free moisture = 5.36 + 2.80/8.33 = 0.98 = 1 gal.
Weight of moist sand = 268 + 5 = 273 lb.
Weight of moist aggregate = 280 + 3 = 283 lb.
Water to be added = 7 gal. – 1 gal. = 6 gal.
Mix to be used: 94 lb. cement, 273 lb. sand, 283 lb. aggregate, and 6.0 gal. of water.
To make one cubic yard of concrete mix:
Cement: 94 lb. x 5.71 sacks = 537 lb.
Sand: 273 x 5.71 = 1560 lb.
Aggregate: 283 x 5.71 = 1615 lb.
Water: 6 gal. x 5.71 = 34.2 gal.
For very important work, the preceding calculations would be used for a test batch, Adjustment of succeeding batches would follow until the required strength was obtained.
Placing sets in drift
To insure a tight, even-bearing contact between the top of the post and the cap, a thin layer of thick grouting should be used. A quick setting type of cement is best.
Concrete sets must be designed to permit the construction of chutes between sets. Figure 26m suggests a design for facing the posts with timber. (Wooden sets could be used instead of concrete when chutes are required). To provide ample thickness for spiking the chute to the set, 4-in. thick material is recommended. When spiking to the facing, incline spikes to the surface; thus, if the spikes pass clear through the timber facing, they will tend to bend at the concrete face instead of at the spike-head.
Some of the plastic adhesives on the market might be investigated for fastening the wooden facing to the concrete.
To support the side lagging, 5-in. , ¼-in. diameter rods or large spikes (say 40d) may be embedded 2 inches in the back of the post. Spacing is selected for the conditions under consideration. Lagging simply rests on the 3-in. projection of the bolt or spike. It is not necessary to bolt the boards in place.
Instead of casting these bolts integral with the post, cast a hole of sufficient diameter to receive the bolt or spike, and about 2 in. deep in the concrete (See Figure 26j). Spikes may then be inserted in these holes to support the lagging after the set is erected.
Two designs for a wooden headframe are shown in the figure. Additional information may be found in Staley (1949, p. 105-186); (1937, p. 1-37); and Tillson (1938, p. 30-48).
For the construction shown, the use of solid material is assumed. However, the construction may be built up (laminated) with planks. If the headframe is designed in this way, an additional two inches should be added to the dimensions shown for the solid members. The right number of two-inch planks to give width and thickness will be used. Odd lengths are used so that there will be overlapping. Not only is the assembly well spiked together but a pair of ¾-in. bolts are used every 30 inches. Center-of-bolt holes are spaced 2 inches from the edges, and set in 3 inches from the ends. Planks for laminated construction must be carefully selected to be free of knots, checking, and crossgrain.
The structures shown were designed for a load of 5000 lb., which includes cage, car, ore, and rope. Acceleration or other forces were not included.
If a headframe higher than the 40 ft. shown is necessary, the design given may be altered as long as the height is divided into sections not exceeding 10 to 12 ft. each. The overall height should not exceed 60 ft. unless the stresses in the struts and bracing are checked.
The distance between the back posts and the front posts should always be such that the resultant stress between the vertical and inclined portion of the rope falls well within the back post, as shown in Figure 27.
Table 8 gives size of solid timbers for main members if a rope pull greater than 5000 lb. is desired (Staley, 1937). This table is based on the assumption that the dry timber has allowable working stresses similar to any species of Douglas fir, hemlock tamarack, or longleaf southern yellow pine. For species with lower working stresses, the next larger commercial size is suggested (for example, an 8 x 10 would be increased to 10 x 12).
Guides for the cage should be made of the best grade of selected Douglas fir or longleaf southern yellow pine. Joints for guides should occur at the shaft timbers. For making the connection, the half-lap scarf joint should be used. All bolts or lagscrews used on the face of the guide (contact with cage guide shoes) should be countersunk well below the surface of the guide.
Splices for posts and struts may be butt joints with a splice plate on each side, or the half-lap scarf joint may be used. Splices in the posts should be as near the panel joint as convenient.
For details on timber joints consult the Wood Handbook (1935, p. 119-136).
Wooden Ore Bin
Figure 28 shows an ore bin designed for a capacity of 100 tons. The lumber for this bin is assumed to be common grade of fir (nearly everything other than pine and cedar seems to be called fir), tamarack, or carefully selected grades of pine. If greater capacity is desired, the bin may be lengthened by additional chute sections. Further information on ore bins may be obtained from Staley (1949, p. 187-211) or Taggart (1945, sec. 18, p. 1-19).
Concrete footings for bins are preferable to timber sills. For the bin shown the dimensions of the footings are:
Top: 1 ft. 8 in. by 1 ft. 2 in.
Bottom: 2 ft. 7½ in. by 1 ft. 10½ in.
Depth: 1 ft. 3 in.
Top: 1 ft. 2 in. by 1 ft. 2 in.
Bottom: 1 ft. 10½ in. by 1 ft. 10½ in.
Depth: 11 in.