05/197816

04/30/1974

11/11/1971

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Battelle Development Corporation (Columbus, OH)

52/340

428/379, 428/703, 428/401, 428/294.700, 14/73, 52/659, 428/213, 52/600, 428/390

E01C11/18; E01D19/12; E04C3/20; E04C5/01; E01C11/00; B32B5/08

161/340,151,158,143,59,162,170,175 52/600,659,177,181

2590685

Prestressed concrete structure

March 1952

Coff

Lesmes, George F.

Bell, James J.

Warburton, Kenneth Mase William Dunson Philip R. J. M.

1. In a load-bearing reinforced-concrete structural member having top and bottom surfaces and a thickness T measured between the top and bottom surfaces and composed of concrete and lower and upper stress-reinforcing means with the lower stress-reinforcing means being a plurality of reinforcing metal bars disposed in the lower halfmost region of the thickness T and in proximity to the bottom surface, the improvement in combination therewith of: the upper stress-reinforcing means consisting essentially of a fibrous-concrete material disposed as a wear-resistant top surface layer of said structural member with said top surface layer extending downwardly from the top surface to a depth between 20 percent and 45 percent of said thickness T and with said fibrous-concrete material consisting essentially of between 0.3 and 5.0 percent by volume of closely spaced short-wire metal segments uniformly distributed randomly in concrete at an average spacing between said wire segments of less than 0.3

2. The structural member of claim 1 in which said upper stress-reinforcing means consists essentially of the fibrous-concrete material whose short wire segments are uniformly distributed randomly in concrete at the

3. The structural member of claim 2 in which said top surface layer extends downwardly from the top surface to a depth between 25 percent and 35

4. The structural member of claim 3 in the form of a beam or slab adapted for use with span supports effectively spaced between 4'7" and 7'11" apart and with said beam or slab incorporating said top surface layer extending downwardly from the top surface to the depth of the thickness T providing

5. The structural member of claim 3 in which short wires of a diameter between 0.006 and 0.020 inch and of a length within 1/2 and 3 inches are the closely spaced short wire segments of the fibrous-concrete material.

DISCLOSURE

This invention relates to improvements in a loadbearing reinforced-concrete structural member which includes both upper and lower stress-reinforcing means and whose utility involves a load downwardly imposed on its upper surface, and more specifically relates to employing a special fibrous-concrete material as its upper stress-reinforcing means. More particularly, the invention concerns an improved load-bearing reinforced-concrete structural member which includes a combination of a plurality of metal reinforcing bars disposed in concrete in the member's bottom region, to provide its lower stress-reinforcing means, and a special fibrous-concrete material disposed as a significantly thick layer serving as a crack-resistant and wear-resistant upper surface and also concurrently providing its upper stress-reinforcing means with the special fibrous-concrete material consisting essentially of concrete including therein uniformly distributed and randomly dispersed short wires closely spaced at an average spacing therebetween or less than about 0.3 inch.

In general, concrete is prepared by mixing sand and coarse aggregate with cement and water to form a workable mass which upon setting and hardening provides a resultant material characteristically resembling stone in weight, hardness, brittleness, and strength. A unique characteristic of concrete is its hydraulicity or ability to harden under water as well as to set in air. The cement most commonly used is Portland cement. Concrete has a low tensile strength and it has long been recognized that its low tensile strength is an unavoidable limitation which must be taken into account in various applications in which concrete is to be employed. Thus, usages of unreinforced concrete usually are limited to applications where mass and weight are chiefly required and where tension and bending stresses are not to be encountered or are expected in only a limited amount. Typical and illustrative applications of unreinforced concrete are: thick foundation slabs of limited spread, walls, dams, and the like.

Because of concrete's relatively low tensile strength, when employed in applications where significant tension and bending stresses are expected, such as a structural member subjected to a load downwardly imposed on its upper surface, reinforcing means are customarily included in the concrete to compensate for the concrete's low tensile strength and thus make these applications feasible. In general, concrete containing conventionally employed reinforcing means is known as reinforced concrete. The conventionally employed reinforcements are of steel in the form of bars, rods, long wires, mesh, and the like. The concrete is reinforced by casting it around the steel reinforcements so disposed and proportioned as to provide the specific properties requisite for the intended application. The employed conventional reinforcements do not impart wear resistance and resistance to cracking of the top surface of reinforced concrete. The tensile strength improvement of reinforced concrete over unreinforced concrete, arises primarily because the employed reinforcements are of much greater tensile strength than concrete per se.

As illustrative of the foregoing, with favorable and proper materials, amounts thereof, and workmanship, concrete per se can be expected to have a crushing strength of at least 2,000 lbs/sq. in. in seven days and 3,000 lbs/sq. in. in 30 days, while only having a breaking strength in tension of 150 to 200 lbs/sq. in. in seven days and of 225 to 300 lbs/sq. in. in 30 days. Now if such an unreinforced concrete is in the form of a beam or like of particular width, depth, and length and is supported by support means at each end, mathematically and experimentally it has been shown in the art under an imposed downward load on its top surface that the top edge at midspan will be in compression and the bottom edge at midspan will be in tension with the two stresses being approximately equal. When the imposed load is such that the tensile stress on the beam's bottom exceeds about 300 lbs/in. ² then the 28-day old beam will break, even though the beam's top can withstand compressive stress in the order of ten times that magnitude. Thus concrete's excess compressive strength is wasted in such an application and not fully utilized due to inherent low tensile strength of concrete in tension at the beam's bottom. Whether such a beam application employs supports other than at its ends or a plurality of supports, a similar stressing is encountered between supports upon downwardly imposed surface loads thereon with resulting tensile stresses concentrating at the bottom edge's midpoint between two supports. Now, however, if one utilizes a reinforcing means, such as a plurality of steel bar reinforcements in the lower region of the beam, one is able to strengthen the beam's resistance to tensile stresses in its bottom region and thus make feasible applications wherein tensile stresses thereat are encountered. Thus, in conventional reinforced concrete, an underlying principle is to strengthen the beam's bottom region with steel reinforcements embedded therein to bring this region's strength up to more nearly that of the concrete in its upper region receiving compression stresses.

As already pointed out, if one considers unreinforced concrete in the form of a beam, slab, or like of particular width, depth, and extended length with the beam supported by end-support means, then the beam's top edge at mispan between two supports under an imposed downward load will be in compression and the bottom edge at midspan will be in tension. However, if the beam or like is extended or continuous to the extent that at least three support means are utilized therefor, then the beam will be subject to a location reversal of imposed compression and tensile stresses at the beam's region of a support means located other than at the ends. Thus, such a beam at its supported region intermediate its ends will be subject to tensile stresses on its top edge and compressive stresses on its bottom edge. This reversal of stresses at such a supported region also has been shown mathematically and experimentally in the art. Accordingly customarily the art hereto also reinforced the beam's concrete in this upper region, such as by conventional steel bar reinforcements embedded in the concrete, so as to strengthen the beam's upper region at this intermediate support means and to bring this region's strength up to more nearly that of the concrete in the supported region directly therebelow receiving compression stresses.

It is to the immediately proceedingly described type of structural member that the present invention is concerned and improves thereon for in such a load-bearing reinforced-concrete structural member there are included both upper and lower reinforcing means and utility of a downwardly imposed load on its surface. Typical where such a structural member is utilized, and its applications are beams, slabs, and the like supported by a plurality support means over their spread. Included therein are: slab panels for bridge decking; support beams for supporting floors and ceilings; multiple-point supported floor slabs and paving, such as highways and airport runways and taxi ramps of extended spread (it should be noted in the instance of top-loaded pavings, runways, and the like, even though overlying a substantially continuous base or foundation, that unless the base's supporting characteristics be essentially uniform throughout, at weakly supported areas the tensile stresses will be found at the bottom edges and compression stresses at the top thereof, while at strongly supported areas therebetween tensile stresses will dominate at top edges and compressive stresses at the bottom edges); and the like.

The invention now will be more fully apparent from the following description and the drawings in which:

FIG. 1 is a transverse cross-sectional view of a portion of an improved load-bearing reinforced-concrete structural member of the invention;

FIG. 2 is a semi-diagrammatic cross-sectional view in the longitudinal direction of the improved structural member of the invention in an embodiment thereof as an improved bridge deck slab; and

FIG. 3 is a semi-diagrammatic cross-sectional view in the longitudinal direction of a conventional bridge-deck slab of the prior art over which the illustrated FIG. 2 embodiment of the invention provides significant improvement.

It will be noted that a like number or letter identifies a like component or element in each of the illustrated figures and that the drawings are not necessarily shown in true proportion and scale in order to present a more easily understood and clearer disclosure of the invention.

With reference to the drawings, in FIG. 1 there is shown a transverse cross-sectional portion of a structural member, generally designated 10; of the invention. Member 10 illustrates embodiments of applicant's invention such as an improved load-bearing beam (not otherwise illustrated) or alternatively a partial cross-section taken on line 1--1 of FIG. 2 of an improved bridge-deck slab 20 illustrated in FIG. 2. Structural member 10 is of an overall thickness T from its upper surface or edge 11 to its bottom surface or edge 12. Member 10 in its uppermost region is a layer 13 of special fibrous-concrete material, generally designated 14, of a thickness T _FC extending downward from upper surface 11. The fibrous concrete material 14 of layer 13 consists of concrete 15 and a multitude of short steel fibers 16 uniformly distributed randomly therein at an average spacing of less than 0.3 inch. The balance of member 10 is of a reinforced concrete, generally designated 17, consisting of concrete 15 containing a plurality of steel reinforcing bars 18. Reinforced concrete 17 in member 10 is of a thickness equaling T-T _FC . The illustrated reinforcing bars 18, are spaced a distance of S _RB apart and disposed longitudinally and parallel to each other in member 10 in a plane parallel to and located a distance of T _RB1 from the bottom surface 12.

In FIG. 2 there is shown a portion of a structural member of the invention which is an improved bridge-deck slab, generally designated 20. Alike the embodiment illustrated in FIG. 1, slab 20 includes an upper surface 11 and a bottom surface 12 with a thickness T therebetween. Slab 20 also includes an upper layer 13 of thickness T _FC of special fibrous-concrete material 14 containing a multitude of short steel fibers 16 uniformly distributed randomly therein at an average spacing of less than 0.3 inch. The balance of thickness T of slab 20 is of reinforced concrete 17 which includes longitudinal-disposed reinforcing bars 21 and transverse-disposed reinforcing bars 18 embedded in concrete 15. The transverse disposed reinforcing bars 18, alike those of the FIG. 1 embodiment are spaced a distance of T _RB1 from the bottom surface 12. A splice 22 of transverse reinforcing bars 18 is illustrated in the FIG. 2 embodiment. The FIG. 2 illustrated bridge-deck slab 20 includes two haunches, generally designated 23, projecting from bottom surface 12, for engagement each with a support means 24, which support means 24 as illustrated in part may be an I-shaped, or alternatively a T-shaped support means. Support means 24 is in engagement with haunch 23 over a distance F, with each support means 24 spaced from another support means 24 by an effective span distance S.

In FIG. 3 for comparison purposes there is shown a portion of a conventional bridge-deck slab, generally designated 30, made up of conventional reinforced concrete generally designated 17. In several respects slab 30 is closely akin to the slab 20, illustrated in FIG. 2. Slab 30 also has a top surface 11, a bottom surface 12, and a thickness T therebetween, and includes transverse disposed reinforcing bars 18 and longitudinal disposed reinforcing bars 21 embedded in concrete 15 with the transverse reinforcing bars 18 alike those in FIGS. 1 and 2 spaced a distance T _RB1 from bottom surface 12, as well as haunches 23 engaging support means 24 over a distance F with an effective span distance S between support means 24. Unlike slab 20, the slab 30 illustrated in FIG. 3 is composed completely of reinforced concrete 17 and does not include a layer 13 of special fibrous-concrete material 14. Slab 30 includes, in its upper region for its upper stress-reinforcing means, transverse disposed reinforcing bars 31 and longitudinal disposed reinforcing bars 32 embedded in the concrete 15 with a splice 22 of transverse bars 31 also being shown. The transverse reinforcing bars 31 are located a distance T _RB2 from top surface 11. The distances T _RB1 and T _RB2 not only serve to locate the position of the reinforcing bars but also designate the thicknesses of concrete cover for the embedded bars. Conventionally a concrete cover between 11/2 to 3 inches is utilized for embedded reinforcing bars.

In a conventional reinforced concrete bridge-deck slab, such as in slab 30 illustrated in FIG. 3, the embedded reinforcing bars 18, 21, 31, and 32 are present to compensate for the small tensile strength of unreinforced concrete and their enhancement of tensile strength generally does not become effective until cracking occurs of the concrete matrix in which they are embedded. Under usage conditions a conventional bridge-deck slab is subject to cracking. Cracking can and does occur at locations where tensile stresses dominate, i.e., particularly on bottom surface 12 intermediate haunches 23 and on top surface 11 directly over the location of haunches 23 in slab 30. In addition, impact loads cause stress cracking throughout because of fatigue in concrete, and changing environmental weather conditions also contribute to crack initiation and formation in the slab. On the top surface 11, abrasion and salt intrusion further hasten deck deterioration with crack formation.

The special fibrous-concrete material included in the structural member of the invention is the two-phase concrete and steel material described and claimed in U.S. Pat. No. 3,429,094, J. P. Romualdi, issued Feb. 25, 1969. In particular the present invention employs that patent's particular two-phase material, herein called fibrous concrete, in its embodiment thereof (FIG. 1a of U.S. Pat. No. 3,429,094) employing closely spaced short-wire segments uniformly distributed randomly in concrete. For clarity and harmony with descriptive language in that U.S. Pat. of Romualdi, in many locations the present disclosure also utilizes that patent's terminology of short-wire segments, wires, and the like in describing the patent's two-phase material employed as the fibrous-concrete material making up an integral portion of the structural member of the invention. It should be understood that more aptly descriptive terms of fibers, metal fibers, and the like also can be and have been utilized in some locations in the present disclosure in place of the short-wire segments, steel wires, and the like terms. As is apparent from the U.S. Pat. of Romualdi, it is necessary that the short wire elements in the fibrous concrete be closely spaced so that the average spacing between wires is not greater than 0.5 inch and preferably is less than about 0.3 inch. For employment in the present invention, the average wire spacing in the employed fibrous concrete should be less than 0.3 inch, and preferably less than 0.1 inch. For definition and determination of this average wire spacing in the fibrous concrete employed in the invention, one also can use herein the rule of thumb calculation and the S = 13.8d √1/P formula therefor set forth in U.S. Pat. No. 3,429,094. Likewise as will be apparent from that patent and this disclosure, most generally the short-wire segments included in the fibrous-concrete material employed in the present invention will be of a diameter from about 0.006 inch to 0.0625 inch, a length of about 1/2 inch to about 3 inches, a ratio of length to diameter from about 40 to 300, with the wire segments included in concrete in an amount between 0.3 and 5.0 percent by volume. The short-wire elements in the fibrous-concrete material employed in the invention may be of other than round or oval cross section, may be of elliptical, square, rectangular, or like cross section, and also may be of alloys and metals other than steel and iron. Insofar as to any portion and up to substantially all of the disclosure of U.S. Pat. No. 3,429,094, as may be necessary and/or aids in fully and adequately disclosing and describing the fibrous concrete employed in the present invention, then the same hereby by this statement is incorporated herein by this reference to the U.S. Pat. No. 3,429,094.

The fibrous concrete included in the structural member of the invention differs significantly from both unreinforced and conventional reinforced concretes. In particular, the multitude of short-wire segments in fibrous concrete in combination with the very close spacing of the wire segments restrain and hinder initiation and propagation of cracks in the concrete matrix in which the wires are uniformly distributed randomly. Unreinforced concrete contains no added means to hinder and avoid crack initiation and propagation. Conventional reinforced concrete, such as concrete reinforced with steel reinforcing bars also inherently is subject to cracking of its concrete matrix alike unreinforced concrete. Its reinforcing bars are larger than short-wire segments, are not distributed randomly, and their amounts fail to provide average spacings therebetween of less than a mere fraction of an inch. Additionally in the employed herein fibrous-concrete material, the short-wire elements do not impart significant tensile strength to the fibrous-concrete because of their own tensile strength. The extremely close spacing of the wire elements in fibrous concrete is of essence to providing significantly improved crack resistance. Through restriction of the growth of cracks the useful tensile strength, both ultimate and firstcrack, of fibrous concrete are increased significantly over that of unreinforced concrete. Additionally fibrous concrete possesses a high fatigue endurance limit, an excellent wear resistance, an enhanced resistance to surface cracking and spalling upon exposure to heat and weather, an ability to remain intact upon appearance of cracks, an extensive plastic flow before disintegration, an ability to absorb energy impacts more efficiently than unreinforced concrete, and other most desirable and advantageous properties and characteristics uniquely employed to advantage in the present invention.

For presenting and illustrating a specific embodiment of the invention, the invention's embodiment of the improved bridge-deck slab 20 of FIG. 2 now will be described in greater detail and a comparison drawn therewith to the conventional bridge-deck slab 30 of FIG. 3.

Turning to the illustrated comparison, note that the conventional bridge-deck slab panel 30 in FIG. 3 is that of The Commonwealth of Pennsylvania, Department of Transportation, Concrete Deck Slab for Steel I-Beam Bridges, shown on their Standards for Bridge Design, Dwg. BD 101, September, 1970. For that typical and conventional slab 30, details on the required reinforcing bars at prescribed slab overall thicknesses along with the maximum normal effective span permitted at the specified reinforcements are presented by the following Table I; details for the haunches 23 are presented in the following Table II; and some additional instructions and notes are provided as well as a Table III presenting calculations verifying design of slab 30.

Table I ____________________________________________________________ ______________ No. 5 Reinforcing Bars 21 S T Reinforcing Bars 18 & 31 m ₁ Spacing ____________________________________________________________ ______________ 4'7" 71/2" No. 5 at 8" = 0.47 in. ² 3 11" 4'11" 71/2" No. 5 at 71/2 = 0.50 in. ² 4 11" 5'3" 71/2" No. 5 at 7" = 0.53 in. ² 4 10" 5'5" 71/2" No. 5 at 61/2 = 0.57 in. ² 5 9" 5'7" 71/2" No. 5 at 6" = 0.62 in. ² 5 9" 5'10" 8" No. 5 at 7" = 0.53 in. ² 5 10" 6'4" 8" No. 5 at 61/2" = 0.57 in. ² 6 9" 6'7" 8" No. 5 at 6" - 0.62 in. ² 7 9" 6'10" 8" No. 5 at 51/2" = 0.68 in. ² 8 8" 7'0" 81/2" No. 5 at 61/2" = 0.57 in. ² 7 9" 7'7" 81/2" No. 5 at 6" = 0.62 in. ² 8 9" 7'11" 81/2" No. 5 at 51/2" = 0.68 in. ² 9 81/2" ____________________________________________________________ ______________ S = maximum normal effective span permitted for given Reinforcing Bars 18 and 31, m ₁ = number of Reinforcing Bars 21 spaced at m equal spaces. Note: Reinforcing Bars 32 are No. 4 at 12 in. maximum spacing. ##SPC1##

Variation in flange thickness is not included in "A"

"a" shall be modified for a concave (sag) vertical curve.

Additional instructions:

1. Place transverse reinforcement in deck slab parallel to Brgs. for skew angles 75° and more. For skew angles less than 75°, the bars shall be placed normal to of bridge and length cut to fit.

2. To determine the required area of bars 18 and 31:

a. For values of skew angles α, less than 75°, use area of bars shown in table.

b. For values of skew angles α, 75° and greater, increase area of bars by Cosec α.

c. Spacing of bars shall be measured along of bridge.

3. For skew angles under 75°, a minimum of 3 No. 5 bars at 6" ± shall be placed in top and bottom of the deck slab parallel to abutment, or pier joint over the end supports.

Notes:

Design Specifications: Design Division of 1969 AASHO, "Standard Specifications for Highway Bridges."

Live Load: HS20-44.

Dead Load: Dead load includes 30 lbs. per sq ft for future wearing surface on the deck slab.

Design Stresses:

f _s = 20,000 lbs. per sq in.

f _c = 1,000 lbs. per sq in.

n = 10

D. l. moment = W S ² /10 ft kips/ft width.

(L. L. + Imp.) Moment = P(S+2)/32 × 1.30 × 0.80 = 0.52 (S+2) ft kips/ft width.

W = Dead load weight in kips per linear feet per ft width of slab.

S = Effective span

Impact factor = 1.30

Continuity factor = 0.80

P = Wheel load = 16 kips

Design is based on decks having 3 or more beams. The effects of haunch shall not be considered in the design. ##SPC2##

As a specific example of the invention, the specific embodiment of the improved bridge-deck slab 20, illustrated in FIG. 2, employs as its upper reinforcing member a layer 13 of thickness T _FC of the special fibrous-concrete material 14 described earlier as the two-phase material embodiment, in U.S. Pat. No. 3,429,094, Romualdi, employing closely spaced short-wire segments uniformly distributed randomly in concrete. Of essence to the invention is employment of a layer 13 of this special fibrous-concrete material 14 of a thickness T _FC with this layer also providing the top surface 11 of the invention's structural unit. The required thickness T _FC should be from about 20 percent to 45 percent of thickness T, which T is the distance from the upper surface 11 to the bottom surface 12 of the improved structural member. For example, for a structural member whose thickness T is 10 inches, the thickness T _FC would be between about 2 and 41/2 inches. Preferably T _FC is between 25 percent and 35 percent of overall thickness T. Were T _FC less than about 20 percent of T, then layer 13 would provide an improved upper wearing surface with crack resistance but the enhanced strength provided by layer 13 would be inadequate and additional reinforcement would be required in the upper region in order to provide a satisfactory and adequate upper stress-reinforcing means for the structural member. Were T _FC to be greater than about 45 percent of T, significant deviation from a balanced reinforced structural unit results along with increased cost for the structural member. Moreover a T _FC - thickness greater than 45 percent of T, were T to be constant, will provide a unit of overdesigned load capacity, and were T decreased so as not to overdesign then redesign and adjustment would be necessary of the overall structure in which the structural unit is to be employed in order to accommodate the thinner structural unit. As is known in the art, a load-bearing structural unit is over-reinforced when the stress in its steel reinforcements is less than the building code allows upon its concrete reaching code-allowable stress; a load-bearing structural unit is under-reinforced when the stress in its steel reinforcement is greater than the building code allows upon its concrete reaching code-allowable stress; and a balanced reinforcement is provided when the stress in its steel reinforcements closely approximates code-allowable stress when its concrete is at its code-allowable stress. Most desirably thickness T is a thickness as provides, or closely approximates, balanced reinforcement.

Now as an illustrative more specific example of the invention, let us employ the invention's improved slab 20 to replace the conventional slab 30 having an effective span S of 7 ft. 7 in. in its bridge application and compare the two slabs. A highly useful and improved slab 20 is provided for such purposes with improved slab 20 having a T _FC of 2 in. and a T of 81/2 in. To verify these values of T _FC and T for slab 20 in this application, one gives consideration to providing an adequate safety factor for the fibrous-concrete material and considers that 1,000 psi in tension is an allowable stress for fibrous-concrete. Note: Ultimate tensile strengths of 2,500 psi and higher and first-crack tensile strengths of 1,800 psi and higher are readily provided by fibrous-concrete material, such as obtainable with 28-day cured 1 : 2.4 concrete mix including 2.8 percent by volume of 0.020 in. diameter × 1.5 in. long steel wires uniformly distributed randomly therein.

Moreover wherein improved slab 20 replaces conventional slab 30 in its particular PENNDOT bridge design application, a T _FC of 2 in. for slab 20 provides a sufficient capacity over the range of various useful specified effective spans of from 4 ft, 7 in. to 7 ft, 11 in. This is shown by an analysis summary presented in the following Table IV over these various specified effective spans of slab 20 upon including a 2 in. T _FC thickness of the special fibrous-concrete material 14 as the upper reinforcing means. ##SPC3##

To provide and verify the summarized determinations in preceding Table IV, one proceeds through a series of calculations as illustrated below for the instance of T = 81/2 in. and T _FC = 2 in.

Ec = w ¹ .5 33 √f'c = 2.7 × 10 ⁶ psi f'c = 2250 psi w = 145 pcf ##SPC4##

n' = Ew/Ec = 1.2 × 10 ⁶ /2.7 × 10 ⁶ = 0.44

fw = 1,000 psi

f'w = 2,270 psi

1. For Transformed Fibrous Concrete d = 8.5 - 0.5 = 8.0"

kd = d (1000/1000 + 2270) = 0.306d = 0.306(8.0") = 2.45" Δf' _x = 3270 psi 1.5/8.0" = 613 psi f'x = 2270 - 613 = 1657 psi

Tc = 1657 psi (1.5") (12") + 613 (1/2)(1.5")(12")

= 29,826 + 5,517

= 35,343 lb.

id = 8.00 - 2.45(1/3) - 0.71

= 6.47

Mc = Cid = 14.7 ^k (6.47/12) = 7.93 ^k -ft

M-applied = 5.8 ^k -ft

X = 29,826(0.75") + 5517(1/2")/35,343

x = 0.71

c = 1000 psi (2.45) 1/2 (12")

= 14,000 lb.

Mt = Tcd = 35.3 (6.47"/12") = 19.0 ^k -ft

Sufficient capacity

(2) For nontransformed fibrous concrete

Then

kd = 8.0"/2 = 4.00"

fx = 1000 psi 2.50/4.00 = 625 psi

1000 psi - 625 psi = 375 psi

Tc = 625 psi (1.5")(12") + 375 psi (1.5") 1/2 (12")

= 11,250 lb. + 3375 lb.

= 14,625

id = 8.00" - 4.00(1/3) -0.69

= 5.98"

X = 11,250(0.75) + 3375(1/2")/14,625

= 0.69"

c = 1000 (1/2)(4.00)(12)

= 6000 (4.00)

= 24,000

mc = Cid = 24.0 ^k (5.98/12.0) = 12.0 ^k -ft ;

M applied = 5.8 ^k -ft

M _T = Tc id = 14.6 ^k 5.98/12.0 = 7.28 ^k -ft

∴ Sufficient capacity

In the exemplorary instance wherein improved slab 20 replaces conventional slab 30 in its particular PENNDOT bridge design application, details for requisite reinforcing bars 18 and 21 making up the lower reinforcing means of improved slab 20 are presented in the following Table V:

Table V ____________________________________________________________ ______________ Bars 21 S T Bars 18 M ₁ Spacing ____________________________________________________________ ______________ 4'7" 71/2" No. 5 at 8" = 0.47 in. ² 3 11" 4'11" 71/2" No. 5 at 71/2" = 0.50 in. ² 4 11" 5'3" 71/2" No. 5 at 7" = 0.53 in. ² 4 10" 5'5" 71/2" No. 5 at 61/2" = 0.57 in. ² 5 9" 5'7" 71/2" No. 5 at 6" = 0.62 in. ² 5 9" 5'10" 8" No. 5 at 7" = 0.53 in. ² 5 10" 6'4" 8" No. 5 at 61/2" = 0.57 in. ² 6 9" 6'7" 8" No. 5 at 6" = 0.62 in. ² 7 9" 6'10" 8" No. 5 at 51/2" = 0.68 in. ² 8 8" 7'0" 81/2" No. 5 at 61/2" = 0.57 in. ² 7 9" 7'7" 81/2" No. 5 at 6" = 0.62 in. ² 8 9" 7'11" 81/2" No. 5 at 51/2" = 0.68 in. ² 9 81/2" ____________________________________________________________ ______________ S = Maximum normal effective span permitted for given reinforcing bars 18

Also in such application the details for haunches 23 as presented precedingly in Table II as well as those additional instructions and notes earlier presented for conventional slab 30, so far as appropriate, continue to apply for defining and describing improved slab 20.

Improved slab 20 can be prepared in several relatively simple ways. In a preferred and illustrative preparation thereof, forms of boards or the like are placed to provide the requisite geometric contour for haunches 23, bottom surface 12, and side and end walls of the particularly desired size slab, and then lower reinforcing bars 18 and 21 are installed and tied down in their requisite placement. At this stage if one were preparing the conventional slab 30, the upper reinforcing bars 31 and 32 also would be installed and tied down, but such installation of upper reinforcing bars is eliminated and not required in preparing improved slab 20. To proceed further, one then pours the requisite concrete mix into the forms in an amount providing a depth of T-T _FC with the reinforcing bar 18 being embedded in the concrete at a distance T _RB1 from the forms providing the bottom surface's contour. To further complete preparation of slab 20, then on top of this poured concrete and before it has set significantly, one places a mix of the requisite special fibrous-concrete containing typically 2.0 percent by volume of 0.015 to 0.025 in. diameter by 1.0 to 1.5 in. long steel wires randomly dispersed and thoroughly mixed therein in an amount to provide a top layer 13 of thickness T _FC . By placing the fibrous-concrete mix directly upon the unset first-poured concrete, one assures a good bonding of the two together so that they together function as a unit to provide an integral member 20. In pouring and placement of the concrete and special fibrous-concrete mixes, if desired, one may use conventional tampers, immersion or exteriorly applied vibrators, and like means to assure proper and dense placement. Also, if desired, the exposed top surface 11 may be screeded conventionally as is known in the art. The employed concrete mix and the special fibrous concrete mix are prepared by methods taught in the art.

In an alternative prepartion of an improved slab of the invention, one commences with a preset mass of thickness T-T _FC of reinforced concrete containing embedded therein the requisitely placed lower reinforcing bars 18 and 21. Such a preset mass can be obtained as upon renovation of a conventional bridge-deck slab 30 by removing therefrom its upper portion containing upper reinforcing bars 31 and 32 and concrete to a depth of T _FC . One then thoroughly moistens the upper surface of the present mass of thickness T-T _FC , desirably sprinkles thereon powdered cement or neat cement, and then places thereover a thickness T _FC of the special fibrous-concrete material. The wetting of the upper surface of the preset mass as well as the dusting thereof assists in obtaining satisfactory bonding of the fibrous-concrete layer to the reinforced concrete so that together they function as a unitary and integral improved member 20.

From the foregoing it will be apparent that the present invention provides a unique structural member with significant advantages and improvements, as follows, over conventional load-bearing reinforced concrete structural members which include both upper and lower stress-reinforcing means:

a. Through employment of the special fibrous-concrete material both as the upper reinforcing means and as the upper surface of the improved member, one obtains an adequate upper reinforcing means with the member's capacity unaltered plus providing an upper surface having significant crack resistance;

b. A structural member requiring less maintenance and of longer life expectancy than conventional load-bearing upper and lower reinforced-concrete structural members;

c. A reduction and elimination of in the order of 50 percent of the conventionally employed reinforcing bars while still providing a member of equivalent load capacity;

d. A saving and ease of construction from elimination of conventional reinforcing bars and their installation as upper reinforcing means;

e. A providing of a member of unaltered overall geometry and capacity so that upon replacement of a conventional member thereby one does not need to alter, revise, or redesign other members associated therewith in its particular end application.

From the foregoing it also will be apparent to those in the art that the invention can be varied and modified without departing from its true scope and spirit. It is to be understood that the invention is to be limited in scope only as set forth in the appended claims.