US 3323263 A
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June 6, 1967 R. K. ADAMS LONG-SPAN PRESTRESSED BEAM STRUCTURE Filed April 27, 1964 nu Lu Q r .It 1 4 x 1 a 1 1 Qdma Q BEAM DEPTH Invenror ROBERT K. ADAMS Hwne, Gvom Ole/M8 Hume.
United States Patent 3,323,263 LONG-SPAN PRESTRESSED BEAM STRUCTURE Robert K. Adams, 208 W. St. Paul Ave., Chicago, Ill. 60614 Filed Apr. 27, 1964, Ser. No. 362,815 4 Claims. (Cl. 52-423) This invention relates to structures and more particularly to long span vierendeel beam structures.
In T. Y. Lins text entitled Prestressed Concrete Structures the function of prestressing (i.e. the elimination of secondary stresses in a beam when in a dead load state) is thoroughly treated. Although the value of prestressing has heretofore been acknowledged, the applicability of this concept to vierendeel trusses has not previously been recognized.
In this latter connection, it has heretofore been thought that vierendeel beams have only limited utility, as short span trusses. This stems from the fact that the dead load characteristics of such vierendeel beams have previously precluded their use in long span applications. It has now been recognized that the advantages of vierendeel beams and the concept of prestressing can be employed to complement one another so that a long span beam structure having a preselected voiding pattern can be produced. The results achieved by the application of prestressing to selectively voided vierendeel beams pursuant to the pres ent invention is that the effective beam depth is optimized and while dead load is minimized.
It is an object of the present invention to provide a long span vierendeel beam structure suitable for use in roof structures, bridges, etc.
It is a further object of the present invention to provide a vierendeel type beam which is constructed so that the beam is lightest at the point where dead load contributes most to bending moment thereby effecting an advantageously varying reduction of dead load while at the same time facilitating optimum beam depth.
Still another object of the present invention is to provide a prestressed vierendeel beam structure having a preselected voiding pattern such that spans in excess of 150 feet and having optimum beam depth and minimum dead load characteristics can be readily produced and reliably utilized.
An additional object of the present invention is to provide a prcstressed vierendeel type beam structure as set forth above wherein the prestressing reduces secondary bending to a function of live load.
Other objects and advantages of the present invention will become apparent from the following description of one preferred embodiment thereof, particularly when considered in conjunction with the accompanying drawing wherein:
FIGURE 1 is a side elevational view of a beam structure embodying the principal features of the present invention;
'FIGURE 2 is a somewhat enlarged cross sectional view taken along the line 22 in FIGURE 1;
FIGURE 3 is an enlarged fragmentary view of a portion of the beam structure of FIGURE 1 with portions broken away to illustrate the reinforcing means for the beam; and
FIGURE 4 is a plot of beam depth versus dead load which illustrates the concept of optimum beam depth.
In general, the present invention relates to long span prcstressed vierendeel beam structures wherein dead load is minimized and beam depth dimensions are optimized. Spans well in excess of 150 feet can be realized as a result of the present invention whereby suitably voided vierendeel type structures are complementarily combined with parabolic prestressing tendons. In such a prcstressed vierendeel beam, secondary bending is caused by live load 3,323,263 Patented June 6, 1967 Whereas dead load secondary efiects are effectively eliminated.
It will be appreciated from the foregoing and from the following detailed description that the present invention has applicability to a variety of forms of long span beam structures. Accordingly, although the following description is directed toward a so-called T beam, the invention is clearly not limited to this particular configuration, and may be utilized in grid systems as well.
Referring particularly to FIGURE 1, there is shown a long span, prcstressed vierendeel type beam 10 formed of partially reinforced concrete. The selectively voided beam 10 is comprised of end blocks 11 and 12, a top chord 13, a bottom chord 14 and a plurality of web 15 which join the top and bottom chords. In the illustrated embodiment, the top chord 13 is joined to an upper flanged portion 16 which gives the beam 10 a T configuration. Other than these characteristics of the beam, it will be appreciated from FIGURE 3 that the beam may be formed by pouring the concrete into suitable forms (not shown) which house a plurality of conventional secondary reinforcing elements 18 and 19 as well as a prest-ressing tendon 17 (e.g. a cable, conduit, etc.).
More particularly, the beam 10 is partially reinforced by a plurality of the web reinforcing elements 18 and chord reinforcing elements 19 that are suitably positioned and joined together in a conventional manner through the use of bonding wire 20. These reinforcing elements 18 and 19 are utilized to effect the necessary reinforcement of the joints defined by the merging lower chord 14, web 15 and upper chord 13, with particular emphasis being placed on the reinforcement of the joints defined by the upper chord 13 and the top portions of the web 15.
The prestressing tendon 17, which may either be pretensioned or post-tensioned in accordance with any of the presently accepted techniques, is parabolically disposed along the bottom chord 14 of the beam 10. This parabolic prestressing tendon effectively compensates for the dead load of the vierendeel beam 10 which would otherwise substantially inhibit and effectively preclude the construction of a long span truss of this type. In this connection, the tendon 17, whether pre-tensioned or post-tensioned, supplies substantially uniform prestressing forces along the entire length of the beam, and secondary stresses and/ or bending in the beam is reduced to a function of live load. As in the usual case, the amount of prcstressing force supplied by the tendon 17 will be dictated in each given beam structure by the anticipated loading conditions and strengths of materials employed.
With particular reference to FIGURES 1 and 2, it will be noted that the illustrated beam 10 is preferably selectively voided so that the upper chord 13 has a linearly varying depth dimension between the end blocks 11 and 12. The web 15 are of uniform thickness but preferably each is of a different width with the width diminishing as the center of the beam is approached. In the illustrated embodiment, the lower chord 14 also has a linearly varying depth dimension between the end blocks, with a minimum depth dimension being maintained to insure that the prestressing cable 17 is suitably confined within the lower chord.
It has been determined that a voiding pattern which yields a chord and web configuration corresponding to that just described and as shown in FIGURE 1 yields a number of advantageous results which facilitate the construction of prcstressed vierendeel beams having lengths well in excess of feet. More particularly, the voiding reduces dead load directly so that this aspect of the beam structure directly complements the function preformed by the prestressing tendon 17. In addition, the voiding is effected so that an eccentric center of gravity is created 3 in the beam (i.e. stemming from the varying depth dimension of the bottom chord).
Depending upon the particular varying depth configuration of the bottom chord 14, the resulting eccentricity of the beam center of gravity places the line of action of the compressive bending forces in the upper chord closer to the center of gravity of this chord. In the illustrated embodiment, which is a beam structure having general utility, the linearly varying depth dimension of the bottom chord 14 results in a parabolically eccentric center of gravity being created in the beam 10. However, to accommodate other particular loading conditions on a given beam structure, the lower chord 14 might be formed with a curvilinearly varying depth dimension. In such cases, the eccentricity created in the beam center of gravity would be particularly designed to accommodate point load conditions.
Although an additional virtual reduction in dead load stems from the above characteristics of the beam 10, this is effected without sacrificing the structural stability of the beam. In fact, the vierendeel beam configuration as heretofore described results in compensating moment couples being created in the joined web and chord members when live loads are applied to the beam so that vertical shear created by such loads is effectively resisted. As generally outlined above, the prestressing of a vierendeel beam of this type reduces the moments at the joints of the chords and web members from a function of combined live and dead load to a function of live load only.
From the foregoing it will be appreciated that voiding of the beam not only reduces dead load as a result of the removal of material but also leads to added beam strength through effective compensation for forces created in response to applied live loads. However, pursuant to the present invention these results are achieved without sacrificing beam depth.
In this latter connection, it has been determined that a hyperbolic relationship between dead load and beam depth exists for beam structures embodying the present invention. This relationship, as depicted in FIGURE 4, is such that a region A exists on the curve X so that an optimum beam depth can be utilized while the dead load of the beam is, at the same time, minimized. Because of this characteristic of the prestressed concrete vierendeel beam structures of the present invention, long span beams of reasonable depth can be produced.
One example of a beam structure which clearly manifests the practical utility of the present invention is represented by the following:
Total length of beam200 end to end.
Span of beam-190' 0" between supports.
Webb spacings-l0' 0" center to center.
Total depth of beam8' 0".
Top chordintegral with a 4 /2 inch concrete slab forming a T-section.
Top chord-depth varies linearly from 9 inches at the beginning of first panel to 17 inches at the center of the span.
Bottom chordvaries in depth linearly from 52 inches at the beginning of first panel to inches at the center of span.
Web members-uniform thickness, varying width.
Thickness of chordsconstant at 10 inches.
From the foregoing, it will be appreciated that the present invention provides an improved beam structure which is ideally suited for long span roofing, bridging and similar applications. However, it should be understood that materials other than concrete (e.g., steel) which lend themselves to prestressing can be utilized to fabricate beam structures pursuant to the invention as heretofore described. For example, steel beams can be readily constructed wherein the prestressing tendon would be fabricated from a suitable mild steel. When concrete is utilized to fabricate beam structures of the present invention, such concrete can be precast or poured in place and the secondary reinforcing means might be of any suitable type. Moreover, the beam structure of the present invention lends itself to the fabrication of various forms of grid structures which would be constituted a number of beams as previously described suitably fabricated to form the selected grid.
These and other modifications and/or applications of the invention will be readily apparent to those skilled in the art and can be developed without departing from the invention, various features of which are set forth in the accompanying claims.
What is claimed is:
1. A long span vierendeel beam structure which oomprises a pair of spaced apart end blocks; means forming upper and lower chord members so that said chord members extend between and are connected to said end blocks in spaced relation to each other; a plurality of web members joined to and extending between said upper and lower chord members so as to define a plurality of voided regions therebetween and along the length of said beam structure; and a prestressing tendon confined within said lower chord member and extending along the entire length thereof and through said end blocks; said lower chord member having a diminishing cross-sectional area from the ends thereof toward the center of the beam span; said web members being selectively proportioned so that the voided regions defined thereby have a greater area as the center of the beam span is approached; said upper chord member having a cross-sectional area that increases as the center of the beam span is approached and in accordance with the dimensional characteristics of said lower chord member; said upper and lower chord members and said web members coacting with said prestressing tendon to establish a parabolic, force compensating eccentricity in the center of gravity of said beam.
2. A long span vierendeel beam structure in accordance with claim 1 and wherein said prestressing tendon is a parabolic prestressing tendon that is confined within said lower chord member so as to extend along the entire length thereof and through said end blocks.
3. A long span vierendeel beam structure in accordance with claim 2 and wherein said lower chord member has a linearly varying depth dimension.
4. A long span vierendeel beam structure in accordance with claim 1 wherein said end blocks, chord members and web members are formed of reinforced concrete.
References Cited UNITED STATES PATENTS 724,500 4/1903 Raymond 52 723 1,431,086 10/1922 Ault 52--723X 1,538,293 5/1925 Loyeau 52 723 2,925,727 2/1960 Harris et al. 52-725 x FOREIGN PATENTS 1,102,595 5/1955 France.
516,464 2/1955 Italy.
OTHER REFERENCES German printed application No. 1,134,407, August 1962.
FRANK L. ABBOTT, Primary Examiner.
M. O. WARNECKE, Assistant Examiner.