Prestressed Concrete Box Girders Unsymmetrical Sections
Prestressed Concrete Box GirdersMade from Precast ConcreteUnsymmetrical SectionsZhongguo (John) Ma,Ph.D., P.E.Assistant ProfessorDepartment of Civil &Environmental EngineeringUniversity of Alaska-FairbanksFairbanks, AlaskaMaher K. Tadros, Ph.D.,P.E., FPCICharles J. Vranek ProfessorDepartment of Civil EngineeringUniversity of Nebraska-LincolnOmaha, NebraskaChuanbing SunGraduate Research AssistantDepartment of Civil EngineeringUniversity of Nebraska-LincolnOmaha, Nebraska80This paper describes an innovative concept forassembling prestressed concrete box girders from acombination of precast, prestressed unsymmetricalsections and I-sections. This solution can providemany advantages over typical single-casting boxsections. These include (1) external easilyremovable void forms, (2) simplified qualitycontrol and concrete surface inspection, (3)reduced weight for handling, shipping, anderection, (4) increased competition among bridgebuilders, and (5) possible elimination of theassembly gantry required for construction ofsegmental span-by-span box girders. Discussionincludes implementation of the concept as asubstitute for adjacent box beams assembled fromstandard AASHTO box sections or trapezoidal boxsections. Design, production, and constructionconsiderations are discussed. A numericalexample for design of an unsymmetricaltrapezoidal box girder bridge is presented.recast, prestressed concrete box girders are widelyused in short- and medium-span bridges in North1 Surveys indicate that approximately 50America.percent of bridges built in the United States are prestressedconcrete bridges, and one-third of these are precast boxgirder structures. In most box girder bridges, the box sections are placed adjacent to each other. Since their introducpPCI JOURNAL
tion in the 1950s, adjacent precast box girder bridges have generally performed very well. In addition, the conventional boxgirder systems offer an aesthetically appealing solution for-7 beams @ 4’-O’ bridge structures in large urbanareas.Three box girder systems comFig. 1. AASHTO Type BIH-48 girders.monly used in the United Statesare the standard AASHTO boxgirder, the U-shaped girder withcast-in-place (CIP) deck, and thetrapezoidal segmental box system. Figs. 1, 2, and 3 illustratethese three systems, with a common bridge width of 28 ft (8.5 m)used for comparison purposes.When the standard AASHTObox girders are built as non-composite structures, there is no needto place and cure a deck, makingconstruction fast and economical.Adjacent box girder bridges alsoFig. 2. Oregon standard U-shaped girder system.have uniform soffits and largespan-to-depth ratios,2 makingthem attractive. As shown in Fig.1, seven AASHTO Type BIII-48box girders are needed for a 28 ft(8.5 m) wide bridge, for spans upto 100 ft (30.5 m). This corresponds to a span-to-depth ratio of100/3.25, or approximately 30.However, in the production process, the void forms must be leftin place unless removable collapsible forms, which are expensive and time consuming to remove, are used. In addition, theFig. 3. AASHTO-PCI-ASBI SBS segmental box girder standard 1800.adjacent box girder bridges experience longitudinal reflectivecracking in the topping directly over the longitudinal joints,is already gaining widespread acceptance. This system cancausing water leakage, concrete staining and spalling, andspan up to 200 ft (61.0 m). The resulting system is very aescorner strand corrosion.3thetically appealing. However, the form costs, productionOregon, Washington, Texas and other states are usingcomplexity, and specialized erection equipment limit its usestandardized U-shaped girders with a CIP deck. Fig. 2 illusto large projects with enough segment and span repetition totrates a 28 ft (8.5 m) wide trapezoidal box girder bridge secjustify mobilization.3 The standard AASHTO-PCI-ASBItion using typical Oregon girders. This is a good system,segment is limited to about 10 ft (3.0 m) in length and 40and void forms can be easily removed. The CIP deck, howtons (36 Mg) in weight. Because of the short segmentever, requires field forming, adding to cost and constructionlength, temporary support is required until the segments oftime. In addition, the heavy weight of some large U-shapedan entire span are erected and post-tensioned together. Usegirders may significantly increase shipping costs and limitof simple falsework may cause traffic disruption, renderingcompetition.the system unfeasible. Therefore, the span-by-span (SBS)Fig. 3 shows a 72 in. (1800 mm) deep standard AASHTOsegmental construction is generally performed using a spePCI-ASBI segmental box girder for the span-by-span (SBS)cial assembly truss spanning between permanent piers. Thisconstruction method. This standard precast segmental boxsolution is uneconomical without considerable repetition.girder section, developed by a joint committee of PCI andThis paper proposes an innovative and economical solutionthe American Segmental Bridge Institute (ASBI), and apfor production of precast concrete box girders. Rather thanproved by AASHTO, was introduced several years ago and“slicing” a segmental box girder span transversely, it is pro-3f.January-February 2004fLft]f[81
Precast, prestressed concreteunsymmetricalsections haveWelded Wire Reinforcementbeen employed in the past withvarious degrees of success. Thechallenge of two-directionalCrack Control Barcamber at time of prestress release and the complexity of stresscalculations have discouragedwidespread application. The concept, however, has been successfully applied to stadium risers.4Fig. 4 shows a typical stadiumriser cross section. Initially, thisFig. 4. Typical stadium riser (unsymmetrical section).type of product was conventionally reinforced with mild steel. Inrecent years, however, the benefits of prestressing in reducing7/8 in. diameter 150 ksi bars throughmember size and controlling3” Bituminous wearing surfacecracks have encouraged more applications of prestressing. Reference 9 has provided assistance toprecast concrete designers inconsidering the impact of thelack of symmetry on design, production, and construction ofthese stadium risers.Fig. 5. Bridge cross section with AASHTO Type B 111-48 girders.Construction of the RinglingCauseway Bridge in SarasotaCounty, Florida, was under way at the time of writing thisarticle. It is a segmental box girder bridge constructed usingthe balanced cantilever method. Due to the large width ofthe bridge, the single multi-cell box was precast using twounsymmetrical halves. Separately post-tensioning the segments of the two halves as the cantilevers progressed created the same conditions as pretensioning of long unsymmetrical sections.An equivalent to the conventional adjacent box girder system is presented in the following sections. Precast concreteunsymmetrical beams combined with precast concrete Ibeams are incorporated. It is also shown how the proposedconcept can cost-effectively be substituted for a trapezoidalbox system. The special design, production, and construction considerations that need to receive attention for theseuncommon section shapes are discussed. This is followed bya numerical design example.Fig. 6. AASHTO box girder Type BIIl-48.-Fposed that the girder be segmented longitudinally. Thus, thegirder is composed of two or more precast sections. A singlevoid standard AASHTO-PCI-ASBI segmental box girdermay be split, for example, into two half-boxes. These halfboxes would be unsymmetrical full-span pieces that are precast, pretensioned in a plant, shipped separately, and assembled as box sections on the permanent piers without anassembly truss or temporary shoring. High-strength threadedrods can be used to connect the precast segments transverselyand make them work as a single unit. Diaphragms or slabthickening may be needed at the locations of the threadedrods, depending on the number of locations per span.82SYSTEM DEVELOPMENTDescription of the Conventional AdjacentBox Girder SystemThe design example in Section 9.1 of the PCI Bridge Design Manual is referred to as a conventional adjacent boxgirder example.5 This example demonstrates the design of a95 ft (29.0 m) single-span AASHTO Type BIII-48 girderbridge. The superstructure consists of seven adjacent typicalAASHTO Standard Type BIII-48 girders as shown in Fig. 5.A 3 in. (76 mm) bituminous non-composite overlay proPCI JOURNAL
vides the wearing surface. Thebox girders are transversely posttensioned through 8 in. (203 mm)wide full-depth diaphragms located at quarter points along thespan. Fig. 6 shows the dimensions of a standard AASHTOType BIII-48 section. The weightFig. 7. Option A: Equivalent adjacent box girder system.of the box girder is 0.85 kips/ft(12.40 kNIm). The total weightof a 95 ft (29.0 m) long girder isabout 42 tons (38 Mg).Corrugated interfaceCorrugated interfceAs mentioned previously, producing closed box sections with1internal voids is difficult. Usually, either a collapsible reusablesteel form or a stay-in-place expanded polystyrene (EPS) formis used. The reusable steel formis not an option here because ofthe presence of quarter-point andend diaphragms. The stay-inplace EPS form provides a relatively fast production cycle.3However, some producers haveexpressed concern that the buoy(a) Precast I-section(b) Precast Unsymmetrical Sectionancy forces of the vibrated concrete may push the expandedFig. 8. Proposed girder sections with Option A.polystyrene form upward. Further, if the concrete is not adequately consolidated, voids maydevelop on the inside faces of the webs and bottom flange,are sloped 1/4 in. per ft (21 minIm) to allow void forms to bewhere they cannot be visibly inspected. There is also theremoved in single pieces without disassembly. The webadded expense of not amortizing the use of the forms overwidth of the I-section is 6 in. (152 mm), which is thinnernumerous applications.than that of the sum of two web widths of the AASHTO boxOne advantage of the proposed unsymmetrical sections isgirder. The precast I-girder can be produced in a similarthat the void forming system is external and reusable. Twomanner to standard precast concrete I-girders. The channelpossible options are proposed herein. These are the equivasection with unsymmetrical prestressing will be discussed inlent adjacent box girder system (Option A) and the alternamore detail further on in the paper.tive trapezoidal box girder system (Option B).The weight of the precast channel girder and I-girder are0.45 and 0.79 kips/ft (6.56 and 11.52 kN/m), respectively.The total weight for a 95 ft (29 m) segment is about 21 tonsEquivalent Adjacent Box Girder System (Option A)(19 Mg) for the channel girder and 38 tons (35 Mg) for theOption A is illustrated in Fig. 7. For clarity, only the preI-girder, which are significantly lighter than the AASHTOcast concrete section is shown in this figure. As can be seen,box girder. Thus, no additional handling and shipping equipinstead of the seven AASHTO box girders shown in Fig. 5,ment capacity will be required.six I-girders and two channel-girders are needed. The proAs shown in Fig. 8, the proposed girders would need to beposed cross section dimensions of the two types of girdersproduced with corrugated interfaces in their top and bottomare shown in Fig. 8. The bottom flange minimum thicknessflanges, which is relatively simple to accomplish. These corfor both types of section is 6 in. (152 mm) so that two rowsrugated interfaces would form shear-key joints that would beof pretensioning strands can be placed. A minimum thickgrouted after the beams are erected. CIP diaphragms may beness of 5.5 in. (140 mm), as that in the standard AASHTOused as in the conventional system. However, if long-linebox, is also possible if a concrete cover of 1.75 in. (44 mm)prestressing beds with prismatic cross sections and reusableto the strand centerline is permitted.steel forms are to be used, then CIP diaphragms are bestA transverse post-tensioning sleeve, 1.5 in. (38 mm) in diadded in a second casting. A better solution is to avoid conameter, can be placed in the 2 in. (50 mm) center-to-centercrete diaphragms altogether. Recent practice with I-girderspace between strands in the bottom flange, and a similarbridges, including that in Nebraska, Florida, and a numberdetail can be used in the top flange for transverse connectionof other states, has demonstrated that intermediate concreteas discussed below. The top and bottom flange inside facesdiaphragms are unnecessary. Because the spacing betweenI E L EH H L J E 1January-February 200483
5’-O”’- ’—2 1/2”Fig. 9. Option B: Alternative trapezoidal box girder system.webs in this system is only 4 ft (1.2 m), and because of theexistence of inter-connected top and bottom flanges, it canbe justifiable to eliminate intermediate concrete diaphragmsin the proposed Option A system.Sleeves can be preplaced in the top and bottom flanges, atabout 4 ft (1.2 m) spacing, for installation of high-strengththreaded rods, which would transversely connect the segments in the total bridge cross section. It is estimated that 1in. (25 mm) diameter, Grade 150 ksi (1034 MPa) rods at 4 ft(1.22 m) spacing inserted in 1.5 in. (38 mm) diametersleeves would provide adequate capacity. If a larger connection is required, the flange thickness would need to be increased accordingly.To provide a smooth riding surface, a bituminous overlaymay be placed, similar to that shown for the standard boxsystem. Alternatively, the top surface of the concrete may beground. The latter solution requires that the original precastconcrete product be made with an extra 0.5 in. (13 mm) ofconcrete cover over the top layer of reinforcement. Eithermeasure will compensate for misalignment between segments without having to place a cast-in-place compositeconcrete overlay.Creating the shear-key joint between precast pieces at thetop and bottom slabs is advantageous over connecting adjacent full boxes. In adjacent box construction, the individualprecast concrete pieces have relatively large torsional stiffnesses because they are closed boxes. They require, therefore, very large connecting forces for the total cross sectionto act as one unit. The connecting forces are greatly reducedin the proposed system because the component pieces areopen boxes with relatively small torsional stiffnesses, thewebs are not doubled, and the connections are made in therelatively flexible thin slabs. This improvement results inelimination of longitudinal reflective cracking over thejoints of adjacent boxes. With conventional adjacent boxgirder production, concrete placement is more difficult.With the proposed solution, all faces are visible, greatly improving quality assurance. With the increasing use of selfconsolidating concrete, production of I-girders and channelgirders of the shapes shown in Fig. 8 is no longer a problem.Alternative Trapezoidal Box Girder System (Option B)Option B, shown in Fig. 9, is another possible substitutefor the adjacent standard box girder system of Fig. 5. Fourpieces of precast unsymmetrical sections comprise the total84bridge section. Each trapezoidalbox section would be producedin two halves. The four unsymmetrical sections would be designed to have standard dimensions such that only one formtype would be required. As in-7-0Option A, the section bottomflange starts with a 6 in. (152mm) thickness and increases linearly at /4 in. per ft (21 mm/rn).The flange thickness may have tobe increased to accommodatetransverse post-tensioning of the top and bottom flanges, depending on the detail used. The authors believe, based on recent experience with precast concrete deck slabs, that a 6 in.(150 mm) thickness of the top and bottom flanges is adequate. Three examples of suitable connection details are described in Reference 3.Fig. 10 provides the cross-sectional dimensions of the section. The web has a slope of 2 to 1 to improve aesthetics ofthe completed bridge and to reduce the bottom flange to anoptimal size without sacrificing girder capacity. The typicalunsymmetrical section weighs 1.03 kipslft (15.02 kN/m), or49 tons (44.5 Mg), for a 95 ft (29.0 m) segment. This issomewhat heavier than the AASHTO Type BIII-48 boxgirder.Option B uses fewer pieces than Option A. It is optimizedfor the loading and span considered. Its total weight is lessthan that of Option A, and significantly less than that of theconventional adjacent box system. It can be viewed as beinga structurally comparable system to the standard I-beam system with relatively wide web spacing, but aesthetically moreattractive. The relatively shallow depth and low stiffness results in a higher bridge live load deflection than Option A ora deeper conventional I-beam system. However, deflectionof short- to medium-span precast, prestressed concretebridges is generally not a controlling design criterion. Option B retains some advantages of Option A, such as external void forming and improved concrete inspectability. Theadditional advantages discussed above make it the more favorable option.An owner would have to be willing to make a long-termcommitment to use it to allow precasters and contractors inthe owner’s jurisdiction to amortize the substantial investment in forms and to gain the necessary production and construction experience. The precast producer may find it moreefficient to make the two halves of the box simultaneouslyin one casting. This would require larger bed capacity andwidth than that required for individual halves cast at separate times or in separate beds.The concept of splitting a box girder into several segmentscan also be applied to segmental box girder bridges. Currently,only a few precast producers are involved in segmental construction because of the expensive forms, complex geometricadjustments, and sophisticated construction equipment, despite the significant annual volume of segmental construction6 The proin the United States, reportedly about 1 billion.posed concept can be applied to segmental box girder conI5-0”I 2’-O”jPCI JOURNAL
struction, resulting in longer, possibly pretensioned, segments. Thesegments may be as long as thespan length, thus supported directly on the permanent piers.Shorter segments may require afew temporary supports betweenpier locations. Reduced demandon lifting equipment and specialized construction gantries wouldattract more producers and contractors to this system and improvethe economy. Reference 7 provides an example of application ofthe concept to segmental Fig. 10. Typical proposed girder section with Option B.UNSYMMETRICALSECTION ANALYSISMost precast concrete sections are symmetrical about thevertical, or y-axis. Because of symmetry, this axis and a perpendicular x-axis passing through the centroid of the sectionare the principal axes. Vertical loads, which create a moment M at a given section, produce stresses that are uniform across the member width at any given vertical distancefrom the x-axis. The stress is calculated using the wellknown flexural equation:fMXYI-tie(1)Outer edgof footprintFor this paper, the sign convention is that positive moment, M, creates tensile stress in the bottom fibers. Compressive stress is positive. Prestress force P on a concretecross section A is always positive since it creates compressive stress. Prestress eccentricity is an algebraic quantity andits sign must be accounted for in this analysis.In unsymmetrical sections, the stresses due to M alonemay be variable for a constant value of y, because the x- andy-axes are not the principal axes, and the impact of the product moment of inertia I must be considered. For a verticalload, producing M only, the stress at a point identified bythe coordinates x and y may be obtained from Eq. (2):8yl —xlf M2t yy(2)Eq. (2) is the more general form, and Eq. (1) is a specialcase applicable for symmetrical sections for whichiszero. If bending occurs about
Precast, prestressed concrete unsymmetrical sections have been employed in the past with various degrees of success. The challenge of two-directional camber at time of prestress re lease and the complexity of stress calculations have discouraged widespread application. The con cept, however, has been success fully applied to stadium risers.4
precast, prestressed concrete spliced bulb-tee girders. Its success means that it also won’t be the last. Opened last November, the DPRV Bridge combines the use of post-tensioned spliced bulb-tee concrete girders and pretensioned concrete bulb-tee girders. The post-tensioned sp
Lecture 24 – Prestressed Concrete Prestressed concrete refers to concrete that has applied stresses induced into the member. Typically, wires or “tendons” are stretched and then blocked at the ends creating compressive stresses throughout the member’s entire cross-section. Most Prestressed concrete is precast in a plant.
Section 11-8 Design Guidelines of Precast Prestressed Girder1 s Furthermore, precasprecast girders can be more effective and economical when the girder quantity is large and details are repeatable. Project Engineers encouraged to consider precast prestressed concrete girder superstructures as an a lt ernat ive during the planning phase.
Box 1 1865-1896 Box 14 1931-1932 Box 27 1949 Box 40 1957-1958 Box 53 1965-1966 Box 2 1892-1903 Box 14 1932-1934 Box 28 1950 Box 41 1959 Box 54 1966-1967 Box 3 1903-1907 Box 16 1934-1936 Box 29 1950-1951 Box 42 1958-1959 Box 55 1967 Box 3 1907-1911 Box 17 1936-1938 Box 30 1951-1952 Box 43 1959 Box 56 1967-1968 Box 5 1911-
Prestressed concrete girders are one of the primary structural components in highway bridges. Benefits of using precast members include accelerated construction time, favorable life-cycle expense, affordable maintenance and repair, quality control, aesthetics, and minimal disruption to traffic (Nawy 2006; Baker et al. 2018).
Introduction to Prestressed Concrete 1 / 7 In prestressed concrete, compressive stresses are applied to the concrete prior to loading. Under service loads, the entire cross section is essentially in compression, which takes advantage of concrete’s considerable compressive
prestressed concrete members, the bonding action between the prestressing element and the concrete is a result of friction as well as adhesion and mechanical resistance. In the fabrication of a pre-tensioned prestressed concrete member the prestressing strand is first tensioned to the desired stress level. Concrete is then cast about the strand and
Engineering Mathematics – I, Reena Garg, Khanna Book Publishing . AICTE Recommended Books for Undergraduate Degree Courses as per Model Curriculum 2018 AICTE Suggested Books in Engineering & Technology w.e.f. 2018-19 BSC103 – Mathematics – II 1. Advanced Engineering Mathematics, Chandrika Prasad & Reena Garg, Khanna Book Publishing 2. Higher Engineering Mathematics, Ramana B.V., Tata .
