US3010257A

US3010257A - Prestressed girder

Info

Publication number: US3010257A
Application number: US23540A
Authority: US
Inventors: Jacob D Naillon
Original assignee: Individual
Current assignee: Individual
Priority date: 1960-04-20
Filing date: 1960-04-20
Publication date: 1961-11-28
Anticipated expiration: 1978-11-28

Description

3 Sheets-Sheet 1 Filed April 20, 1960 INVENTOR.

Nov. 28, 1961 J. D. NAILLON PRESTRESSED GIRDER 3 Sheets-Sheet 2 Filed April 20, 1960 a 8 AL Q 2 4 L z a; a w

7 OJ .L F 8 Fig-'8 INVENTOR.

Nov. 28, 1961 J. D. NAILLON 3,010,257

PRESTRESSED GIRDER Filed April 20, 1960 a Sheets-Sheet 3 ...H.....H 2 a my w Q United States Patent 3,010,257 PRESTRESSED GIRDER Jacob D. Naillon, 1824 Magnolia Way, Walnut Creek, Calif.

Filed Apr. 20, 1960, Ser. No. 23,540 14 Claims. (Cl. 50-131) This is a continuation-in-part of my application Serial No. 390,995, filed November 9, 1953, now abandoned.

This invention relates to girders adapted to support distributed loads, such as roofs, suspended ceilings and floors, or concentrated loads, such as the ends of beams or structural bridge elements supported by the girder. The invention is applicable both to girders having positive bending moments, viz., with the upper flange in compression as in simply supported spans, and to those with negative bending moments, as in cantilevers.

The girders according to the invention have upper and lower flanges which comprise metallic members fixed to a metallic web, e.g., by continuous or intermittent welds. The said flanges may consist of the said metallic members or may include, in addition thereto, a body of concrete bonded to a flange for carrying a part of the flange stress. The girders have cable means, e.g., one or more tensioned cables, disposed to carry a part of the tensile stress of one of the flanges.

It is a principal object of the invention to provide an improved girder of the type indicated above which makes a more eflicient use of structural materials and especially of the metal than prior girders, thereby achieving a reduction in weight and cost for a given load-carrying capacity.

Another object is to provide an improved girder of the said type which can be designed with a lower height than prior girders having the same weight and load-carrying capacity, i.e., which can have a greater ratio of span to depth for a given load and amount of structural material than is possible with conventional girders; however, the invention is not restricted to such shallow designs.

A further object is to provide an improved girder of the said type which includes cable means, such as high tensile strength, spun metal cables or rods, situated essentially parallel and near to the flange which is stressed in tension due to loading (i.e., the lower flange in the case of a simply supported span or the upper flange in the case of a cantilever) for carrying a part of the tensile stress at the said flange, wherein a more effective use of the metal and cable means is achieved than in conventional constructions by making the flanges of different sizes to shift the neutral axis from the mid-height of the web and by pre-tensioning the cable means in a manner to achieve an improved stress relation between the flanges, the said relation being difierent under loaded and non-loaded conditions of the girder.

Another object is to provide a girder of the type indicated wherein the deflection due to loading can be controlled by adjusting the tension of the cable or the like.

Still another, specific object is to provide an improved girder of the said type which is suitable, for example, as an all-metal girder, particularly a roof girder, wherein one flange, such as the upper flange, is inclined with respect to the other so as to be spaced farther therefrom at an intermediate section of the girder than at the ends, and having the other flange straight and of smaller crosssectional area than the first, the cable means being positioned adjacently to the smaller flange and tensioned so as to utilize the structural materials most effectively. The inclined flange may be curved, 'e.g., be parabolic.

A further object is to provide an improved cable anchor for transmitting stress from the cable ends to the web.

ice

; Still other objects will become apparent from the following description.

In summary, the girder according to the invention includes vertically spaced upper and lower flanges having dilferent cross-sectional areas and each comprising a metallic flange member, a connecting metallic web fixed to both metallic flange members, and cable means positioned near the smaller flange and pretensioned. The cable means, which may comprise one or more spun metal wire cables, extends essentially parallel to the smaller flange and places it into initial compressive stress. Preferably the proportions of the web and flanges are such that the larger flange is placed into initial tensile stress. The cable pull is preferably great enough to place the smaller flange under initial unit compressive stress which is a major fraction of the allowable unit stress of the flange metal. These initial stresses prevail when the girder is not loaded; upon application of load, such as the dead weight of the girder or live loading, the said smaller flange becomes stressed in tension while the larger flange remains or is placed into compressive stress.

The cable means is provided with an adjustable conneotion to the girder near the ends thereof whereby the tension can be adjusted. According to a feature of the invention the cable means is made of high tensile strength steel and is stressed initially to a unit stress which is in excess of the yield point of the metal used in the metallic flange members, the latter being of structural steel, aluminum, or other suitable metal, including alloys.

Because of the extremely strong pull exerted by the cable means in the girder according to the invention it is desirable to provide means to prevent buckling of the girder and to distribute the cable stress to the girder. The former is eifected according to the invention by providing along the length of each cable a plurality of cableengaging members which are fixed to the girder and prevent lateral motion between the taut cable and the girder; any tendency of the girder to move laterally and lead to buckling is opposed by the cable. The latter is efieoted by providing an improved cable anchor at each end of the cable or group of cables, the said anchor comprising a plate which is fixed to the Web along a vertically extended region thereof (and which may be further fixed to both the upper and lower flanges) and has a stiffener extending longitudinally along the web and fixed tothe plate and web so as to distribute cable stress to the latter along a longitudinally extended region thereof. This anchor finds utility also in conventional girders, wherein,

the above-described preferred relation between the flange sizes and stresses and/or the pre-tensioning of the cable are absent.

The invention will be further described with reference to the accompanying drawings which form a part of this specification and show, by way of example, certain preferred embodiments, wherein:

FIGURE 1 is an elevation view of a girder according to the invention embodied as an all-metal roof girder;

FIGURE 2 is an enlarged elevation view of one end of the roof girder;

FIGURE 3 is a bottom plan view of a part of FIG- URE 2;

FIGURE 4 is a transverse sectional view taken on the line 4-4 of FIGURE 1 but drawn to an enlarged scale;

FIGURE 5 is a further enlarged detail view showing file welded connection between two sections of the upper ange;

FIGURE 6 is a similarly enlarged detail View showing the welded connection between the Web and the upper flange;

FIGURE 7 is an elevation view of a cantilever girder constructed according to the invention, illustrating a modified placement of the cable above the upper flange;

line 88 of FIGURE-7;

FIGURE 9 is a transverse sectional view taken on the Q line 9-9 of FIGURE 7;

{FIGURE 10 is a longittudinal sectional view taken on the line 10-10 of FIGURE 11 showing a third embodimnt using steel and concretein" the upper flange and usedas a highway bridge; V

FIGURE 11 is a horizontal sectional view. taken on the broken line 1111 of FIGURE 10; and

FIGURE 12 is a transverse sectional'view taken on the line 1212 of FIGURE 11 but drawn to an enlarged scale.

' Referring to FIGURES 1-6 in detail, the roof girder is made entirely of metal and comprises a web 1010c, an upper flange 11-110, a lower flange 1242c, and a pair of

cables

13 and 13a, situated respectively on opposite sides of the web near to and essentially parallel to the lower flange. The web may be a single metal plate which extends the full length of the girder; howeven'it is often advantageous, particularly in long girders to assemble it from'a plurality of plates, such as the

plates

10, 10a, 10b and 100, which are butt-welded along vertical lines 14. Similarly, the flanges may in some instances be continuous plates, but are often more conveniently constituted' of a plurality of sections placed in end-to-end relation; this facilitates a change in flange size along the length thereof. Thus, the upper flange may include the

plates

11, 11a, 11b and 110, which are butt-welded along horizontal lines at the locations indicated by reference numbers 15, and the lower flange may include a pair of I

main flange plates

12 and 12a, butt-welded along a horizontal line at 16, and a pair of short, terminal flagge plates 12b and 120 which are butt welded tothe main flange plates at 17. Double-welded butt joints are ad vantageosuly used at 14-17, but the inventionis not restricted thereto. A typical joint is shown in FIGURE 5' and includes two V-

weldments

18 and 18a. 'While this view specifically illustrates a weldment between the

sections

11 and 11a of the upper flange, this type of weldment is applicable to all butt welds.

'For the most eflectiveutilization of the structural material and to permit a roof to be'laid on the upper flange with a suitable pitch, the depth of the web is varied along its length so as to be greatest at an intermediate section, e.g., at the center, of the girder. In the girder illustrated the lower flange and the adjoining edge of the web are straight and the upper flange and the upper edge of the web are parabolic; however, it is evident that the top of the girder may have some other shape to suit the structure to be supported, e.g., arcuate or shaped as straight segments sloping downwards toward the ends of the girder. It may be further noted that the upper flange and web edge may in other embodiments be straight, e.g., in the case of a floor girder. The web is welded along its length to the upper and lower flanges by continuous or intermittent welds. Preferably the' upper and lower edges of the web are bevelled as is shown in FIGURE 6 and a pair of

longitudinal weldments

19 and 19a is provided between each edge of the web and the corresponding flange.

The upper flange has a greater cross-sectional area than the lower flange at least at the intermediate part of the girder and continuously throughout the major extent of the girder. Thus, the

interior sections

11a and 11b of the upper flange have greater cross-sectional areas than the

main plates

12 and 12a of the lower flange, so that the neutral axis of the above-mentioned girder parts (ignoring the cables) is situated well above the midheight of the web throughout the extent of the said

flange sections

11a and 11b. For example, the upper flange may have from two to ten times the cross-sectional area of the lower flange at least at the intermediate section of the girder where the greatest bending moment is developed. For economizing on metal and reducing" weight, at least the upper flange is advantageously made smaller at the endsthan at the intermediate part; thus the two

sections

11a and 11b are thicker than the end sections 11 and 110 (see FIGURE 5) although of like width. To facilitate welding the end portion of each thicker flange plate may be given a slighttaper or bevel as also shown in FIGURE 5. The terminal lower flange sections 12b and 12c are both thicker and wider than the main lower flange sections to serve as abutment supports adapted to rest on abutments (not shown) on which the girder is laid. Bolt holes 21, 21a, are provided in the terminal lower flange sections for securing the girder.

Ata short distance, e.g., one foot, inward from each end of the girder, preferably at the thick, terminal flange sections 12b and 120, is a pair of vertical cable anchor plates or

abutments

22, 22a, situated one on each side of the. web and welded to the web along a vertically extended zone and further to both the upper and lower flanges, asshown in FIGURES 2 and 3. It should be noted that attachment to the flanges is not in every case essential. Each of the cable anchor platesis apertured at a level intermediate the flanges to receive a threaded tensioning rod 23 having a nut 24 which bears against the longitudinally outer face of the respective anchor plate. Each rod 23 is fixed permanently within a tubular connector 25 which is further fixed to the end of a

cable

13 or 13a. According to an optional feature, a pair of longitudinal, substantially

horizontal stiifener plates

26, 26a, is welded to each anchor plate and also to theweb along a longitudinally extended region, the stiffener plates 1 plates reinforce the end structure of the girder and transmit cable stress from the anchor plates to the --Web, to which they distribute the stress over a longitudinally extended zone. They incidentally protect'the rod and connector and position them during assembly.

Each

cable

13, 13a, is further attached to the girder by a plurality of cable-engaging elements 27 which are fixed to the web at intervals along the lengths of the cables. As is best shown in FIGURES 2 and 4, the said elements are connectors arranged in pairs onopposite sides'of the web, and each connector includes a base block 28 situated adjacently to the web and a cap 29. Bolts 30 extend through the caps and base blocks and apertures in the web. The bases and caps are formed with concave recesses which define longitudinal holes cylindrical in shape and only slightly larger than the external cable diameter, whereby the cables can'slide therein. However, the connectors prevent any appreciable lateral motion between the cables and the web, thereby supporting the latter against buckling when the cables are tensioned as hereinafter described. The connectors shown are, of course, merely indicative of one specific arrangement that can be employed, and they may be omitted in some cases, e.g., when the flanges are so wide that lateral buckling of the girder is unlikely. However,

cable-engaging devices of some form are necessary in the embodiment under consideration when strong cable. pulls are applied and/or when it is desired to incline the ends of the cable upwards.

Although notia feature of the invention, it is

possible anchor plates

22 and 22a are situated at still higher levels,

to incline the cable ends as shown with some exaggerationin FIGURE 2. The inclination of the cable ends, when used, is small, usually about 1 to the lower flange.

It is evident that a greater number of cables can be employed. For best distribution of stresses and to insure stability against buckling it is desirableto arrange the cables and flanges symmetrically With respect to the longitudinal, vertical center plane of the girder. Thus, in the case of a girder having a single web the number of cables should be equal on the two sides of the web and spaced equally therefrom; however, with a girder having a box construction, providing a pair of Webs, a single or an odd number (as well as an even number) of cables can be used by mounting the cables between the webs.

The parts of the girder other than the cables may be constructed of metal of standard structural strength, e.g., structural steel having a working strength prescribed in building codes of 20,000 lbs. per sq. in., or of aluminum or other alloy. The

cables

13, 13a, are preferably made of high tensile strength steel or alloy having unit strengths in excess of, e.g., twice, the yield point of the other parts of the girder, such as 100,000 to 150,000 lbs. per sq. in.

When assembling the girder the cables are tensioned by means of the nuts 24 to prestress the cable to an initial tension which, when the girder is not loaded, is smaller than the Working strength of the cable by an amount which is determined by the change in cable length caused by elongation of the part of the girder at cable-level upon loading of the girder. The increment in cable stress due to the load can be determined by applying the principle of statically indeterminate structures. This increment may exceed the working strength of the metal in the smaller flange.

Pretensioning of the cables places the girder into axial compression and, because the cables act at a level below the neutral axis, they further create an initial negative bending moment (i.e., one which places the upper flange in tension and the lower flange in compression). The terms initial stress and initial bending moment are used herein to denote the stresses and moments that prevail in the girder and cable after the latter is pretensioned but while the girder is not subjected to loading, either dead or live, the weight of the girder itself being suitably carried by special support means. The consequence of these two effects is that the smaller flange is initially strongly stressed in compression. Because these effects are opposed at the larger flange, the greater effect prevails, and the stress therein may be tensile or compressive, depending upon the properties of the girder section, i.e., upon its configuration. In the preferred embodiment of the invention, whereby the benefits are best realized, the section properties are such that the larger flange is placed into initial tensile stress. The section properties will be described further hereinafter. To attain maximum economy of construction material or most eflicient utilization thereof for a given section, the cable pull is made so high that the smaller flange is stressed to a unit stress that is a major fraction of the allowable working stress of the flange metal, e.g., equal thereto or in excess of the allowable stress but not as high as the yield point of the metal.

For example, when the cable and the other parts of the girder have allowable working strengths of 150,000 and 20,000 lbs. per sq. in., respectively, and have about equal moduli of elasticity, e.g., are all of steel, the cable is pretensioned to an initial stress not greater than 150,000 lbs. per sq. in. less the cable stress increment due to loading. The cable pull is at least that which places the smaller flange into initial unit compressive stress which is a major part of 20,000 lbs. per sq. in., but not so large that the initial flange stress reaches its yield point, typically, 34,000 lbs. per sq. in. Usually initialflange stresses substantially abovethe allowable working stress are avoided.

When the girder is installed a positive bending moment is induced by loading, whereby the upper flange is.

placed into compression. This induced moment elongates the lower flange and cable by approximately equal amounts (or, more precisely, by amounts almost proportional to their distances from the neutral axis); hence tensile stresses are induced into these parts. The total tensile stress in the cable will, therefore, be the sum of the initial stress and the stress increment due to loading and concomitant cable elongation. It may be noted that the connectors 27 permit the cable to slide and so do not place longitudinal restraints on the cable. The net tensile stress in the lower flange will be the tensile stress induced by the said positive bending moment less the initial compressive stress. The girder parts and cable should, of course, be designed so that both flanges and the cable attain unit stresses substantially equal to their respective allowable unit working stresses when the girder is loaded.

When the lower flange has a modulus of elasticity different from that of the cable, the tensile stresses induced into these parts by loading will be approximately in the ratio of their moduli. For example, with a steel cable having a modulus of 28 million lbs. per sq. in. and a lower flange of aluminum having a modulus of 9.7 million lbs. per sq. in., the tensile stress induced in the cable by loading will be about 2.9 times the stress that would be induced in the aluminum flange for the same application.

It is evident that the relations given in the three preceding paragraphs are only approximate and that the relation of the load-induced stresses in the cable and flanges is influenced 'by the location and profile of the cable and the connection of the latter to the girder ends; the relations described are approximated most closely when the cable is parallel to and situated at the level of the smaller flange.

The initial cable tension is preferably applied by means of a device which indicates the tension, e.g., a hydraulic tensioning device that is attached to the end of the rod 23 beyond the nut 24 and bears against the

anchor plate

22 or 22a to apply the cable tensionwhile the nut 24 is turned to engage the anchor plate lightly. A torque wrench may, of course, be used instead to turn the nut 24 for applying the tension, but this technique is not usually preferred because the torque wrench is not sufficiently sensitive to permit accurate tensioning. A strain gage may be applied to the cable.

The initial tension imposes a slight initial camber to the girder; this is subsequently reduced, balanced or overcome by deflection of the girder due to loading. The magnitude of the final deflection can be adjusted by varying the tension on the cables.

When the cable ends are inclined upwards as shown some vertical load is transmitted by the cables, as in conventional girders. This is not, however, an essential feature of the invention, inasmuch as the inclination, when present, is slight and the cable is substantially straight. A slight upward slope in the cable ends is, however, often desirable to raise the points of attachment thereof and thereby avoid the danger of overloading the lower flange in compression by the extremely high initial cable forces, in view of the small cross-sectional area of the said flange.

The cross-sectional area of the main

lower flange sections

12 and 12a is typically between about one-half and four times the aggregate area of the cables; as a specific example, the lower flange area may be two sq. in. and each of the two cables may be one inch in diameter.

The use of an upper flange that has a substantially greater cross-sectional area than the lower flange and the consequent location of the neutral axis well above the mid-height of the web are important when strong cable pulls are used, and it is an important feature of the invention to use such relative flange areas in combination with such strong cable pulls. By designing the girder to place the neutral axis at a height above the smaller flange a distance equal to 0.6 to 0.8 times the depth of the web, nearly equal flange stresses, with the top flange in compression and the lower flange in tension, can be achieved when the load is applied to the girder. If the neutral axis "were located nearer the lowerflange and cable, 'i.e., if

the flange areas were more nearly equal, unequal flange stresseswould result when the load is applied to the girder, and this would lead to an insuflicient utilization of the structural materials in the girder. The neutral axis is preferably located so that the upper flange is placed into tensile stress by the initial cable pull.

It is evident that any tendency of the girder to buckle laterally would tend to elongate at least one of-the cables because of the connectors 27 hence the cables themselves stabilize'the girder against such lateral motion.

The completed girder can be installed by applying a hoisting device to the upper flange. The girder can, therefore, be completely assembled in a shop or on the ground near the construction site before being emplaced.

It is evident that the construction provides a girder wherein the cables can be prestressed to produce high cable forces, in excess of those feasible with conven-' tional constructions. While the advantages of the invention are realized fully only when such high cable forces are applied that the smaller flange is initially compressed 'near to or in excess of its allowable working stress, the invention finds utility also when lower cable stresses are used.

Example.-The girder to be described is assumed to be prismatic throughout its length and is suitable for a span of 110 feet, with a total load (including the weight of the girder) of 775 lbs. per linear foot, which causes a bending moment at the center of the span of 1,171 ft. kips (a kip being a force of 1,000 lbs). A girder in accordance with the invention suitable for these conditions can be constructed entirely of steel and include: an upper flange l2 inches wide and 1 inch thick; a lower flange 1.75 inches wide and 1 inch thick; a vertical web 50 inches high and inch thick; and a pair of cables, each about 1 inch in diameter with 0.623 sq. in. of efi'ective crosssectional area of high tensile strength steel, situated one on each side of the web with their centers 2.5 inches above the lowest part of the girder. The section properties are as tollows:

A, cross sectional area of web and flanges sq. in 32.5

C distance from lowest part of girder to the.

neutral axis n 34 I, moment of inertia about neutral axis in. 10,746 S section modulus below neutral axis in. 316 8;, section modulus above neutral axis in. 597.

e, distance from neutral axis to cable centers 20,000 lbs. per sq; in. and the upper flange to a maximum compressive stressof 19,380lbs. per sq. in. The total cable pull rises to 187,000 lbs., causing a unit stress in the cables of 150,000 lbs. per sq..in.

It should be noted that approximately equal unit stresses result in the two flanges when the girder is loaded.

FIGURES 7-9 illustrate a modified embodiment where.

in the girder is a'cantilever and a positive bending moment is induced initially by the cable, which is situated above the upper flange; It is evident that a pair of cables, situated one on each side of the web and just below the upper flange could be used. When loaded, the girder is subjected to a negative bending moment, which places the upper flange into tension.

Referring to FIGURES 7-9 in detail, the girder has a lower flange 3535a, an upper flange 36--36a of smaller cross-sectional area, and a connecting web 37 of uniform height and welded to the flanges along their lengths. The gi der is rigidly mounted on a support 38, e.g., a column, and a load (not shown) is applied to the left of the support as viewed in FIGURE 7. The flanges may, if desired, be composed of abutting sections; thus, the lower flange includes outer and

inner sections

35 and 35a, the latter having asrnaller cross-sectional area than the latter to provide more flange metal near the support, where the greatest bending moment prevails. Similarly, the upper flange includes a main flange plate 36 which is smaller in cross-sectional area than the lower flange section 35a and, preferably, also smaller than the outer section 35, and a terminal section 36a which is thickened to transmit cable stress. The girder is secured rigidly to the support by suitable fixtures, as indicated at 39 and 40, to develop bending moment when the girder is loaded. The web is reinforced by a plate 41 at its outer end and this plate is fixed to the web and to the upper and lower flanges, e.g., by welding. A pair of horizontal plates 42 and 42a are fixed within the support 38 in alingment with the lower flange to transmit compressive stress when the girder is loaded and function as parts of the lower flange. They may also be welded to the vertical web 38a of the support. 7

Cable means, such asa single rod 43 of high tensile strength steel, is provided above the upper flange and fastened at the ends to cable anchors. The anchor at the inner end comprises the support itself and an anchor cylinder 44 which is welded to the transverse uprights of the support, which have apertures for the rod 43. As appears in' FIGURE 9, this cylinder is fitted into a gap in the web 38a and welded thereto. The anchor at the outer end includes an anchor plate 45 which is fixed to the flange section 36a above the reinforcing plate 41 and is buttressed by a'pair of longitudinal stifiening plates 48 and 48a which extend at opposite sides of the. rod 43 and are welded to the anchor plate and along their lengths to'the flange section 36a. The ends of the rod have adjustable connectors as previously described for the cables, including threaded rods 46 and nuts 47. A plurality of cable connectors 49 is optionally fixed to the upper flange; these engage the rod 43 with a close sliding fit to prevent lateral movement between the rod and girder.

The stress relations in the cantilever girder are similar to those previously described, with the difference that the upper flange is the smaller one and the neutral axis is below the mid-height of the web. Because the rod 43 is situated beyond the web it exerts a slightly greater bending moment. When it is pre-tensioned it induces a positive bending moment which places. the upper flange into imtial compression. The initial tension is advantageously at least suflicient to stras the upper flange to a major fractlon of its allowable working stress. Due to the greaterbending moment induced the lower flange will, inpractically all designs, be placed into initial tension. When thegir der is loaded the upper flange is placed into tensile stress and the lower flange into compressive stress, and the dimensions are preferably such that these stresses, as well asthe final cable stress, are substantially equal to the respective allowable working stresses when the girder is fully loaded.

It may be noted that the single cable or rod is less adapted to restrain the girder against lateral buckling than cablesspaced laterally apart as in the first embodiment and would, therefore, be used when the girder has wide flanges or is otherwise reinforced against buckling, as by structural members connected thereto. 7

It is evident that therigid mounting shown is merely illustrative of one specific arrangement; in most applications the girder would extend to both sides of the sup- POrt.

FIGURES 10-12 show an embodiment in which the larger flange includes, in addition to the metallic flange member, a body of concrete which carries a part of the flange stress and is a part of said flange. In most such embodiments the concrete is integral with a deck or floor, such as the roadway of a highway bridge, and a strip of such deck or floor, running along the girder flange, is considered as a part of the flange and regarded in computations as contributing to the flange action. Typically, the width of the said strip is ten to twenty times the width of the metallic flange member, and the said concrete strip is transformed into an equivalent steel section when computing the allowable compressive stress on the composite flange.

Referring to these views, the composite girder com prises a metallic lower flange 50, a composite upper flange which includes a metallic plate member 51 and a body of concrete 52, a metallic web 53 fixed along its length by continuous or intermittent welds to the lower flange and to the upper metallic member 51, and four cables 54, which are situated two on each side of the web near the lower flange and are pretensioned. As was described for the first embodiment, the metallic flange members and web may be formed of separate sections placed end-toend and welded together, and may have different crosssectional areas at different locations along the length of the girder in conformity to the magnitude of the bending moment. It should be noted that when the lower flange is subjected to high initial compression by the cable so as to be subjected to an initial compressive stress close to its allowable working stress it is not feasible to reduce its cross-sectional area at the ends.

The girder shown is one of several similar parallel girders, e.g., extending along the length of a highway bridge, and the concrete 52 is an integral part of the deck slab which extends over several girders. The concrete is bonded to the girder against relative longitudinal motion by a plurality of bonding strips 55, which may be formed from structural channels as shown and fixed to the flange member 51 at suitable intervals, typically eight to twelve inches, and which are embedded in the concrete. The interval between the bonding strips may be greater near the ends of the girder than at the center where the greatest bending moment is developed. The concrete has further embedded therein suitable metal reinforcing elements, such as longitudinal steel rods 56 and steel rods 57 which extend transversely, both near the upper and lower faces of the slab. For clarity these reinforcing rods are shown only in the enlarged view of FIGURE 12. The rods- 57 may be placed at intervals of three to ten inches along the length of the girder to reinforce the slab against bending moment developed between girders. They also aid in transmitting shearing stress to the part of the concrete which is bonded to the girder; however, the shear strength of concrete is usually suflicient and the transverse rods are not essential for transmitting stress to the upper metallic flange member.

The part of the concrete slab 52 which is regarded as contributing to the compressive strength of the upper flange and considered herein as forming a part thereof is a strip having the width W as indicated in FIGURE 12. The width W depends upon the properties of the concrete and its shear strength (inherent and imparted by the transverse rods 57); it is, of course, never greater than the distance between adjacent girders. For the purpose of the present invention the distance W is taken as the smaller of the said inter-girder distance and twelve times the slab thickness.

The cables 54 are distributed symmetrically with respect to the web and positioned near the lower flange. They are secured near the girder ends by anchor plates 58 which are mounted on each side of the web and buttressed by longitudinal stiflener plates 59. These plates are welded to the plates 58 and to the web to distribute the cable stress. As in prior embodiments, the cable tension can be adjusted by turning a nut 60 on a threaded rod 61 which is fixed to each cable end, each nut being in engagement with a plate 58. Connectors 62 are fixed to the web at intervals along the cables and. have apertures through which the cables extend with close sliding fits to prevent relative lateral motion between the girder and cables. The ends of the girder aresupported on abutments 63.

The cross-sectional area of the composite upper flange, as the expression is used herein, is the effective crosssection determined by adding the area of the metallic member 51 and a transformed area 64, indicated in FIGURE 12 as having a width W, and a height equal to the actual height of the concrete slab. The width W is related to the width W in accordance with the strength of the concrete, being one-tenth of W for concrete hav ing a strength of 3,000 lbs. per sq. in., and one-eighth of W for 4,000 lbs. per sq. in. concrete.

According to the invention the cross-sectional area of the lower flange is materially less than that of the upper flange, e.g., one-half tonne-tenth as great. The neutral axis of the web and flanges is, therefore, above the mid-height of the Web. When the cables are pre tensioned they induce a negative bending moment. Initial tension is preferably at least so great as to impose on the lower flange an initial compressive stress (prior to loading, as when the girder is supported along its length by scaffolding) which is a major fraction of its allowable stress. This places the upper flange into initial tensile stress, which is carried exclusively or principally by the metallic member 51, depending upon the method used in fabricating the girder: When the cables are stressed prior to casting the concrete slab no subsequent elongation of the upper flange occurs and the concrete is not in tension. However, when the cables are prestressed after the concrete has hardened, an initial tensile stress is developed therein. Such initial tension is a small fraction of that in the metal member 51; more particularly, the ratio of the stresses in the concrete and in the metallic member is approximately the same as the ratio of their moduli of elasticity, viz., about 1:8 in most cases when steel is used. It is desirable to keep the tensile stress in the concrete below about 10% of its compressive strength. It is understood that this tensile stress is temporary and endures only until the girder is loaded.

When the girder is loaded the cable tension increases. The lower flange is then placed in tension and the upper flange (including its metallic member and the concrete) is placed in compression.

Example.-The following example of a composite girder in accordance with the third embodiment is designed as an interior girder of a plurality of parallel girders spaced at least six feet center to center and carrying bonded thereto a continuous slab of concrete six inches thick containing longitudinal and transverse steel reinforcing rods as required to carry the superimposed load. The width W of the concrete strip which is reckoned as a part of the upper flange is six feet and the transformed equivalent steel section has a width W oneeighth of W, viz., nine inches, the concrete having a strength of 4,000 lbs. per sq. in. The area of the transformed section is, therefore, 54 sq. in.

The girder is designed for a span of 72 ft. 3 in., to carry a dead load of 922 lbs. per linear foot, which produces a positive bending moment of 602 ft. kips. The girder is designed to carry also a live load which produces an additional positive bending moment of 958 ft. kips. The girder dimensions are:

Upper flange:

Steel plate 8 x /2 in. Transformed concrete section, 9 x 6 in. Area: Steel, 4 sq. in.; concrete, 54 sq. in.; total,

58 sq. in. Lower flange:

Steel plate, 8 x /2 in. Area: 4 sq. in. Web: Steel plate, 54217 in.; area, 16.88 sq. in.

11 Cables: Four steel rods, each in.-diameter, mounted two on each side of the web at an average distance of in. above the lowest part of the girder.

The section properties of the steelparts, excluding the cables, are:

A, cross-sectional area of web andsteel members of the flanges sq. -in 24.88 I, moment of inertia about neutral axis (at the mid-heightof the web) in. 10,040 S, section modulus in. 378

The section properties of the composite girder are:

A, cross-sectional area of web and flanges sq. in 78.88 C distance from lowest part of girder to the neutral axis in 49.6 I, moment of inertia about neutral axis in. 27,800 S section modulus below neutral axis ..in. 560 S section modulus above neutral axis in. 2,070 e, distance from neutral axis to center of cables in 46.6

The cables are pretensioned to an initial unit stress of 86,800 lbs. per sq. in. to exert a combined pull of 153.5 kips before the dead load is applied. This produces initial stresses of 15,900 lbs. per sq. in. compression in the lower flange and 3,580 lbs. per sq. in. tension in the upper flange metallic member.

After application of the dead load of the concrete butproduces a top flange stress in the metallic member of 15,700 lbs. per sq. in. in compression and a bottom flange stress of 19,500 lbs. per sq. in.'in tension.

I claim as my invention: 1. A girder including upper and lower flanges, each said flange comprising a metallic member which extends continuously between the ends of the girder, a metallic web fixed to both said metallic members, the flange which is subjected to tension by the bending moment due to loading having, throughout a major extent thereof, a cross-sectional area which is substantially less than that of the other flange, whereby the neutral axis of the abovementioned girder parts is offset from the mid-height of the web toward the larger flange, and cable means extending longitudinally and situated adjacently to the smaller flange at least throughout said major extent, the ends of said cable means being secured tautly to opposite. end portions of the girder'by anchor means and being tensioned so as to induce a bending moment opposite to that due to loading and thereby place said smaller flange into compression when the girder is not loaded, said flanges and cable means being positioned symmetrically with respect to the web.

2. A girder as defined in claim 1 wherein the area of said larger flange is at least twice that of'the smaller flange and said larger flange is in tension when the girder is not loaded. I a Y 3. In combination with the girder as defined in claim 1, a plurality of cable-engaging elements secured to the girder along the cable means for preventing relative lateral movement between the cable means and the girder.

4. A girder as defined in claim 1 wherein said cable means is substantially straight and the ends thereof are secured to the girder at a level displaced from the midheight of the web at the girder endstoward the smaller flange.

12 1, acable anchor at each end of the girder extending through a major part of the web height and fixed thereto for stiftening the web and transmitting thereto stress from the cable means, the ends of said cable -means being fastened to saidv anchors at levels intermediate said flanges.

6. In combination with the girder as defined in claim 5, said anchor being a plate, and at least one longitudinal stifiener plate extending along the web and fixed to the anchor plate and to the web along a longitudinally extended region for distributing stress from the anchor to the web.

7. A girder according to claim 5 wherein said cable anchors are fixed to both of said flanges.

8. A girder as defined in claim 1 wherein said flanges consist of said metallic members.

9. A girder as defined in claim 1 wherein said larger flange includes as a part thereof, in addition to said metallic member, a body of concrete extending longitudinally throughout the major extent of and bonded to the said metallic member so as to becompressed longitudinally when the said metallic member is under compressive stress.

10. A girder including upper and lower flanges, each said flange comprising a metallic member which extends continuously between the ends of the girder, a metallic web fixed to each of said metallic members, oneof said flanges having throughout the major extent thereof, including the intermediate section thereof, a cross sectional area which is substantially less than that of the other flange, whereby the neutral axis of the above-mentioned girder parts is offset from the mid-height of the web toward the larger flange, a plurality of cables of highv tensile strength extending longitudinally with respect to the girder and positioned adjacently to the smaller flange,.

and cable anchor means fixed to the girder near opposite ends thereof, said cables being secured tautly to said anchor means between the mid-height of the web and the said smaller flange and being pre-tensioned, the smaller flange being under compression to a unit stress which is at least a major fraction of the allowable stress therein and the larger flange being under tension due to said pre-tensioned cable when the girder is not loaded, said flanges and cables being positioned symmetrically with respect to the web;

11. A girder as defined in claim 10 wherein the relative cross-sectional areas of said flanges is such that the neutral axis is spaced from the smaller flange by a distance between 0.6 and 0.8 of the depth of the web at the said intermediate section.

12. An all-metal roof girder including a straight lower flange, an upper flange spaced above said lower flange by a distance which is greater at an intermediate girder section than at the ends of the girder, said flanges extending continuously between the ends of the girder and the cross-sectional area of said upper flange being at least twice that of the lower flange throughout the major 5. In combination with the girder as defined in claim, 5

extent thereof including said intermediate section, whereby the neutral axis of the above-mentioned girder parts is above the mid-height of the web, 'a cable extending longitudinally for substantially the full length of the girder on each side of the web and continuously adjacently to said lower flange, the ends of said cables being' secured tautly to'said girder near the opposite ends thereof and being pre-tensioned, said lower flange being in compressive stress and said upper flange being in tensile stress due to said pre-stressed cables when the girder is not loaded, and a plurality of cable-retaining elements hired to the girder at spaced pointsalong each cable for securing the cables and girder against relative lateral movement while permitting" relative longitudinal movement, said flanges and cables being positioned symmetrically with respect to the web.

13. A girder comprising, in combination, an upper flange, a lower flange, a web fixed to both said flanges, a pair of cable-anchor plates situated on each side of the web, one plate of each pair being near each end of the girder, said plates extending throughout major parts of web height in engagement therewith and having means for attaching longitudinal cables thereto at levels intermediate said flanges, a cable on each side of the web secured tautly to said anchor-plates by said attachment means, and a stiffener plate for each anchor-plate fixed thereto and extending longitudinally along the web, said stiffener plates being fixed to the web along the lengths of the stiffener plates for distributing cable stress from 10 the anchor-plates to the web.

14. In a girder comprising an upper flange, a lower flange, a web fixed to both said flanges and a tensioned cable extending longitudinally, the improvement of a plate and further fixed to the web along a longitudinally 7 extended region for distributing stress from the anchorplate to the web.

References Cited in the file of this patent UNITED STATES PATENTS 998,479 Eisen July 18, 1911 1,936,147 Young Nov. 21, 1933 2,510,958 Coif June 13, 1950