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Special Report

Precast Prestressed ConcreteHorizontally Curved

Bridge Beams

prepared by

ABAM EngineersA MEMBER OF THE BERGER GROUP

33301 Ninth Avenue SouthFederal Way, Washington 98003-6395

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Substantial effort has been made to ensure that all data and infor-mation in this report are accurate. However, PCI cannot acceptresponsibility for any errors or oversights in the use of material orin the preparation of engineering plans. This publication isintended for use by professional personnel competent to evaluatethe significance and limitations of its contents and able to acceptresponsibility for the application of the material it contains.Special conditions on a project may require more specific evalu-ation and practical engineering judgment.

JR 350-88Copyright © 1988

Prestressed Concrete InstituteAll rights reserved. This report or any part thereof may notbe reproduced in any form without the written permission of the Prestressed Concrete. Institute.

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CONTENTS

1. Introduction ................................................................................42. Concept Description...................................................................43 Cost Comparisons .....................................................................64. Analysis and Design .................................................................75. Design Alternatives ...................................................................96. Fabrication Techniques ............................................................107. Conclusion ...............................................................................10Reference.....................................................................................11Appendix A – Conceptual Drawings and Details..........................11Appendix B – Design Charts........................................................19Appendix C – Design Example ....................................................33

This report discusses the concept, analysis anddesign procedures, design alternatives and fabricationtechniques recommended for precast prestressedhorizontally curved bridge beams. Comparisons ofcurved precast bridge superstructures with steel andcast-in-place concrete demonstrate the aesthetic andeconomic advantages a precast concrete solutionoffers to bridge owners and engineers. Three sepa-rate appendixes contain plans and details, designcharts and a design example applying the designaids.

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New interchanges off limited accesshighways often require horizontallycurved medium length bridge beams.These bridge beams have been madealmost exclusively of steel where false-work restrictions preclude cast-in-placeconcrete construction. This report presentsresults of a project sponsored by thePrestressed Concrete Institute (PCI) todevelop standards for precast prestressedhorizontally curved bridge beams.

The idea to develop horizontally curvedbridge beams won PCI’s IndustryAdvancement Award in 1985. This awardwinning idea was developed from a pre-cast prestressed curved beam project con-structed in Pennsylvania. PCI subsequent-ly issued a request for proposals to devel-op this idea. ABAM Engineers of FederalWay, Washington, was selected to pursuethis effort.

This report summarizes the concept,analysis and design procedures, and fabri-cation techniques recommended for pre-cast prestressed horizontally curved bridgebeams. Comparisons of curved precastbridge superstructures with steel andcast-in-place concrete demonstrate theaesthetic and economic advantages a pre-cast concrete solution offers to bridgeowners and design engineers.

1. INTRODUCTION

A concept for horizontally curved pre-cast prestressed concrete beams is pre-sented. The concept uses the basic ideathat won PCI’s Industry AdvancementAward for 1985. Several alternatives tothis basic idea for materials, fabricationand erection procedures, beam geometry,and beam cross sections were evaluated.Descriptions of these alternatives arelisted in Table 1. Concept 8, a trape-zoidal box beam, was selected for devel-opment in this report. Design charts andconceptual drawings are presented for 5and 6 ft (1.52 and 1.83 m) deep precastbox beams. These charts are intended topresent preliminary prestressing strandand concrete strength criteria for variousspans and beam spacings. Appendix Acontains conceptual design plans anddetails.

The concept uses long precast concrete

beams spanning between supports.Chorded sections [20 ft (6.10 m) long]are used to approximate curved geome-try (Figs. 1 and 2). Diaphragms are pro-vided at angle points between thesechorded sections. This chord length pro-duces a 2 in. (51 mm) offset on a 300 ft(91.5 m) radius curve. The beams arechorded in plan and in profile. Individualprecast beams are post- tensioned togeth-er in the field to form continuous struc-tures.

Trapezoidal box beams are used toproduce a torsionally rigid section that isaesthetically pleasing (Fig. 3). Span todepth ratios for bridge superstructuresconstructed with 5 ft (1.52 m) deep pre-cast box beam elements can be 27 to 1for interior spans and 23 to 1 for exteriorspans. These span to depth ratios arecomparable to bridges constructed from

composite welded steel girders and fromcast-in-place post-tensioned box girders.

Post-tensioning tendons are placedinside the beam void and are deflectedhorizontally and vertically at diaphragmsbetween chorded sections. The tendons,therefore, form a string polygon thatapproximates a parabolic shape in profileand the curve radius in plan (Fig. 4).Tendons are bonded to the cross sectionat each diaphragm but are not continu-ously bonded along the tendon length.

The concept allows individual beamlines to be bent horizontally to specificdesign radii and to provide different pro-files for individual beam lines to build invertical curves and varying supereleva-tions. A table of precast beam geometrywould be developed for each project.

Construction of a bridge made fromprecast prestressed horizontally curved-

2. CONCEPT DESCRIPTION

beams involves three basic steps, illus-trated in Figs. 5, 6 and 7.

■ Step 1 (Fig. 5): Beams are fabricatedfull length in the plant in speciallydesigned formwork. Beams are cast intwo stages. Stage 1 includes the soffit andwebs of the chorded sections, enddiaphragms, and diaphragms betweenchorded segments. Ducts are provided byplant post-tensioning tendons and forStage 1 and Stage 2 field post - tensioningtendons. The beam deck is cast in Stage 2.Beam casting is complete prior to remov-ing the beam from the form, Beams arelifted out of the form and transported to ayard storage/stressing area as reinforcedconcrete members. Plant post-tensioningtendons are stressed.

■ Step 2 (Fig. 6): Beams are transport-ed to the site and erected. Ducts for StageI and Stage 2 field post-tensioning ten-dons are spliced over interior supports.Closure pours are made between beamsover interior supports. Stage I tendons arestressed, creating continuous beams.

■ Step 3 (Fig. 7): Cross beams are castat the midpoint or at the third points alongthe span at the nearest diaphragm loca-tions. The bridge deck is cast. Stage 2 ten-dons are stressed, placing the deck intocompression. Traffic barriers, overlays,and expansion joints are placed, complet-ing the bridge construction.

This horizontally curved prestressedprecast beam concept was selected overthe other concepts (see Table 1) because itgenerally:

■ Improved quality■ Reduced costs■ Improved aestheticsQuality was enhanced using a twostage

casting with removable inner forms forStage 1. Inner surfaces and thicknesses ofthe I beam soffit and webs can be inspect-ed and positioning of post-tensioning ten-dons can be carefully established and ver-ified.

Labor costs to produce full lengthbeams are reduced by minimizing fabrica-tion steps. Also, sloping sides delete therequirement to move back beam sideforms to lift beams from the form.Material costs are reduced by eliminatingcostly inner void forms.

Aesthetics are improved by utilizingsloping beam sides in lieu of verticalsides.

Alternative design and fabrication vari-ations of this concept may be appropriatefor specific project conditions. Thesevariations are discussed later in thisreport.

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Cost estimates were developed forbridge superstructures of precast con-crete, cast-in-place concrete, and struc-tural steel. The precast alternativeincludes the cost of cast-in-place con-crete cross beams, bridge deck, and traf-fic barriers. The steel alternative includesthe cost of a concrete bridge deck andtraffic barriers.

A 24-beam project was assumed forthis cost comparison. Projects requir-ing fewer beams will be more costlyper square foot for the precast alterna-tive.

The unit superstructure cost range (persquare foot) for the precast concept ver-sus the cast-in-place concrete design andthe steel girder bridge design is shown inFig. 8. This figure shows that the precastbeam concept is cost competitive withthe steel beam design when the unit steelprice, in place and painted, is more than$1 per pound ($2000 per ton). Typicalunit prices on curved steel girders rangefrom $1.00 to $1.50 per pound.

Precast beams are competitive withcast-in-place concrete box girders whenthe in-place unit concrete price exceeds

$530 per cubic yard. Typicalcast-in-place concrete bridges will costbetween $400 and $700 per cubic yardcomplete with reinforcing bars andpost-tensioning). Difficult shoring con-ditions will add to this cost. Also, certainprojects will not allow shoring, thereforeexcluding cast-in-place concrete designs.

Horizontally curved bridges made ofprecast concrete beams are competitivewith steel girder bridges and cast-in-place concrete bridges. The amount ofcompetitive edge will vary with localproject and market conditions.

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3. COST COMPARISONS

Design of the curved precast beamsaddresses flexure, shear, torsion, distor-tion, and tendon anchoring and deflectionforces. A computer model was developedfor a 120 ft (36.6 m) span 5 ft (1.52 m)deep girder on a 300 ft (91.5 m) radius tobetter understand beam behavior. Thebeams, cross beams, and deck were mod-eled using a grillage of one-dimensionalelements. From this model, analysis tech-niques were developed for preliminarydesign.

Flexure and shear forces can be com-puted as if the beam were tangent, giving

consideration to the extra length of theoutside beam line that results from hori-zontal curvature (Fig. 9). Critical stressconditions are identified for each step ofthe construction process.

The beam is post-tensioned at the plantto carry its own weight (Fig. 10). In thiscondition, long beams generally experi-ence downward deflection. Due to thebeam curvature, the banking, transporta-tion, and lifting locations are positionedinward from the ends of the beam over anappropriate diaphragm to provide over-turning stability. The beam prestressing is

also adjusted to minimize camber growthin the stored position. The beam profile inthe form is adjusted for the vertical geom-etry and for expected elastic and creepdeflections.

The critical stress condition due tostressing Stage I tendons is tension in thebeam soffit over interior supports (Fig.11). Temporary tension at this location isresisted by a positive moment connectionbetween beams. Upon placing the crossbeams and deck, the critical stress condi-tion becomes compression in the soffitover the piers.

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4. ANALYSIS AND DESIGN

Tension stresses in the top of the beamsover the piers and compressive stresses inthe top of the beams near midspan canalso control the design.

The critical stress conditions at Stage 2,with the full superimposed dead load andlive load in place, are tension in the bridgedeck and compression in the beam soffitover interior supports and compression inthe top of the beam near midspan (Fig.12). The compressive stress at midspan istheoretically large in the girder top flangeand small in the adjacent cast-in-placedeck. Creep effects, however, will redis-tribute the large compressive stress fromthe beam into the deck. Because the creepeffect is not considered in the preliminarycalculations, the beams designed in thisreport use a maximum compressive stressof 0.5 fc in the top flange of the precastbeam at midspan. Compression in thebeam soffit near interior supports general-ly determines the required concrete com-pressive stress, based on an allowablecompressive stress of 0.4 fc .

An ultimate strength check is required.It is recommended that the computationbe done using the capacity of unbondedpost-tensioned tendons. Additional mildsteel can be added to achieve the requiredflexural strength. Mild steel reinforce-ment is used acrossall cold joints along

the beam length. This controls crackingand improves ductility, which is especial-ly attractive in seismic risk areas.

Other considerations need to beaccounted for in horizontally curved pre-

cast prestressed concrete bridge beams.At each horizontal angle point, betweenchorded sections, the internal flexuralforces resisting the vertical bendingmoment turns through a horizontal angle

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(Fig. 13). Angular deflection of theseforces places horizontal forces in the topand bottom surfaces of the beams. Thesein-plane forces can be broken into tor-sional and distortion components (Fig.14). The torsional component is reactedby the box section and the distortion com-ponent is resisted by the diaphragmbetween chorded segments.

Significant beam torsions are producedonly by the beam self weight acting on asimple span and by the bridge deck deadload acting on a continuous beam.Subsequent twisting of the curved beams

is resisted by thebridge deck and crossbeams.

Shear and torsion design is performedby distributing the torsional resistanceinto individual web shears and addingweb shears reacting vertical forces.Thickening of webs may be required forlonger beams.

Tendon deflection and anchoring forcesare reacted by the end blocks and thediaphragms between chorded segments.

Beam span charts have been developedthat show the required number ofpost-tensioning strands per beam for vari-

ous spans and beam spacings. Requiredconcrete strengths for the design are alsoshown. High concrete strengths can beused to increase girder spacing. Bridgehorizontal curvature has little influenceon post-tensioning requirements. There-fore, designers can use design charts forany bridge having the same outside beamlength. Design charts use HS-20 live load.Beam charts are included in Appendix Band a design example using the charts isincluded in Appendix C.

Typical reinforcement and post-tension-ing (PT) placement are shown in Fig. 15.

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5. DESIGN ALTERNATIVES

Situations are presented that require aconcept to offer flexibility to suit the par-ticular requirements of an owner, bridgeengineer, or precaster. Several variationsin design can be employed to enhance theusefulness of horizontally curved precastconcrete beams.

Cross Section

A rectangular box section can be usedin lieu of a trapezoidal box section.Design curves for trapezoidal box crosssections may be used if rectangular crosssections have properties similar to trape-zoidal cross sections shown. Other varia-tions in the cross section will depend onthe configuration of the bridge and theintensity of the loads.

Thickening of Soffit Slab at Interior Piers

The soffit of the beam near the supportcan be thickened to reduce compressivestresses and therefore the required con-crete compressive stress. Design Chart 11can be compared to Design Chart 2(Appendix B) to determine the amount ofthis reduction. Similarly, the thickness ofthe top flange of the precast beam couldbe increased in the midspan region toreduce compressive stresses near midspan.

Elimination of the Second Stage ofField Post-Tensioning

The second stage of field post-tension-ing can be eliminated. Additional mild

steel is placed in the deck over the piers tocontrol cracking and provide ultimatemoment strength. This alternative is espe-cially attractive for areas where therequirement to totally remove the con-crete deck for future replacement exists.Comparison of Design Charts 12 and 2shows the effect this alternative has on thenumber of prestressing strands and on therequired concrete compressive strength.

Use of Lightweight Concrete

Lightweight or semi-lightweight con-crete can be used to reduce beam trans-portation and erection weight. Reductionsin beam weight can be seen in Charts 7and 10 (Appendix B).

A concept has been developed for pre-cast prestressed concrete horizontallycurved bridge beams. The concept usestrapezoidal box beams made of chordedsegments to approximate curved plan andprofile geometries. Tendons are placedin-

side the void of the beams. High strengthconcrete can be used to increase the beamspacing. Shipping restrictions limit practi-cal beam span lengths, especially for 6 ft1.83 m) deep units. Lightweight concreteor spliced beams can be used to overcome

this limitation. Precast prestressed bridgebeams can be a viable option for horizon-tally curved bridges, giving bridge ownersand engineers an alternative to steel gird-ers and to, cast-in-place concrete struc-tures.

Form Concept

A forming concept for fabricating fullspan length chorded beams was devel-oped. The segments move and rotatealong guide beams to provide the hori-zontal curvature (Fig. 16). The elevationsof the guide beams can be adjusted usingjacks to provide the vertical profile (Fig.17). The segments are not twisted orwarped. These variations can be accom-modated in the cast-in-place deck.

Beam Weight

The weight of precast concrete beams isa major concern. A maximum shippingweight of 314,000 lb (142,430 kg) (haul-ing equipment plus beam) was selected toidentify limiting span lengths. Thisweight is equal to the P13 permit designload used on California’s highway sys-tem.

Shipping these large loads requires spe-cial transporters (Fig. 18). There are unitsthat have been used to transport girders ofsimilar size. For instance, 13-axle trans-porters are available on the west coast.The 318,000 lb (144,245 kg) shippingweight places an axle load of 24 kips (107kN) on axles 41/2 ft (1.37 in) apart.

This is similar to the axle loads for theAASHTO military loading. The maxi-mum shipping weight translates into aneffective beam transportation weight of254,000 lb (115,214 kg). This beamweight limits the shipping length of the 6ft (1.83 in) deep section to 130 ft (39.6 in)and the 5 ft (1.52 in) deep section tion to150 ft (45.7 m).

Alternative Production Methods

Alternative production techniques alsowere investigated.

Individual 20 ft (6.10 m) long chordedbeam segments could be fabricated and

then assembled into span length beams atthe plant. This option reduces beam form-ing costs but increases the number of pro-duction steps. This alternative may beadvantageous on projects requiring asmall number of beams.

Optional void materials could be used.The concept was designed around atwo-pour beam casting using steel inner

forms with an expendable wood deck sof-fit form. Polystyrene or wood forms couldbe used. However, production problemswith these expendable voids need to becarefully considered.

Beams can also be spliced in the field toreduce shipping weight and to producelonger spans.

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6. FABRICATION TECHNIQUES

7. CONCLUSION

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• • •

APPENDIX• APPENDIX A — CONCEPTUAL DRAWINGS AND DETAILS

• APPENDIX B — DESIGN CHARTS

• APPENDIX C — DESIGN EXAMPLE

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APPENDIX A — CONCEPTUAL DRAWINGS AND DETAILS

1. Barnoff, Robert, M.; Nagle, Gordon;Suarez, Mario, G.; Geschwindner,Louis, F., Jr.; Merz, H. William, Jr.; andWest, Harry, H.; “Design, Fabrication,

and Erection of a Curved PrestressedConcrete Bridge With ContinuousGirders,” Transportation Research Record950,1985, pp. 136-140.

REFERENCE

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APPENDIX B - DESIGN CHARTS

GENERALFig. B. Key plan, sections, and notes to be used with charts.

5 FT (1.52 M) DEEP BOX BEAM

Chart 1. Total post-tensioned strand requirement (interior span beam).

Chart 2. Total post-tensioned strand requirement (exterior span beam).

Chart 3. Post-tensioned strand requirement (interior span beam, beam spacing = 13 ft).

Chart 4. Post-tensioned strand requirement (exterior span beam, beam spacing = 8 ft).

Chart 5. Post-tensioned strand requirement (exterior span beam, beam spacing = 10 ft).

Chart 6. Post- tensioned strand requirement (exterior span beam, beam spacing = 13 ft).

Chart 7. Beam shipping weight.

6 FT (1 .83 M) DEEP BOX BEAM

Chart 8. Total post-tensioned strand requirement (interior span beam).

Chart 9. Total post-tensioned strand requirement (exterior span beam).

Chart 10. Beam shipping weight.

DESIGN ALTERNATIVES, 5 FT (1.52 M) DEEP BOX BEAM

Chart 11. Total post-tensioned strand requirement (exterior span beam, thickened

bottom slab).

Chart 12. Total post-tensioned strand requirement (exterior span beam, no Stage 2

post-tensioning).

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Perform Preliminary Flexural Design

Bridge ge length= 380 ft 16 (116 m)Roadway width W = 38 ft (I 11.6m)Roadway radius R = 300 ft (91.5 m)Use beam depth = 5 ft (1.52 m)Number of spans: 380/3 = 127 ft (38.7 m)avgTry three spans.380/4 = 95 ft (29.0 m) avg

The number of beams, Ng (or beamspacing, S), can be determined from thedesign charts.

Try three beams [spacing = 13 ft (3.92m)].

To optimize the post-tensioning design,enter 5 ft (1.52 m) beam depth charts(exterior and interior span beams) withplot of strand required versus span forthree beams (see Figs. C1 and C2).

Find the combination of exterior andinterior span lengths that add up to thetotal bridge length and that has the samenumber of strands required for each stageof field post-tensioning.

The plant post-tensioning supports thebeam as a simple span and is not continu-

ous; therefore, the required number ofstrands will be greater for the longer inte-rior spans. It does not control the ratio ofspans.

Stage 1 field post-tensioning is to sup-port the cast-in-place bridge deck deadload and is continuous across interior sup-ports. The number of strands is the samein the tendon. There will be some differ-ence in the final stresses of the strandalong the span from the end anchor to thecenter of the bridge (assuming stressing isdone from both ends of the bridge) due tolosses.

From the charts, find the spans that addup to the total length for the same numberof strands in Stage 1:

Using the same charts, similar calcula-tions are done for determining the spansfor Stage 2 post-tensioning:

The vertical lines plotted on the chartswill bracket an efficient design solution.Any choice in between will require a fewmore strands. By inspection, use:

Span= 120 + 140 + 120= 380 ft (1 16m)

The sketch below shows the final spanarrangement of the bridge structure.

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APPENDIX C - DESIGN EXAMPLE

Strand Required (Figs. C3 and C4):

AdjustedBy chart strandstrand require-

required mentExterior span:5 ft beam depth,three beams (S = 13 ft)

Plant post-tension 36 36Stage 1 post-tension 36 36Stage 2 post-tension 32 36*

104 108

Interior span: 5 ft beam depth,three beams (S = 13 ft)

Plant post-tension 49 49Stage I post-tension 33 36*Stage 2 post-tension 36 36

118 121*Increase

Required 28-Day CompressiveStrength (see Figs. C3 and C4)

Exterior span: fc = 7300 psi (50.4 MPa)Interior span: fc = 7200 psi (49.7 MPa)Say: fc = 7500 psi (51.7 MPa)

This requirement can be significantly

reduced by thickening the bottom slab theinterior continuous supports, because thecompressive strength requirements shownon the charts are generally governed bycompression in the bottom slab at theinterior support (see Fig. C5.

There are significant compressive stress-es at the top of the bare beam at midspanprior to casting the deck; however, servicelevel stresses in the deck are relatively low,allowing creep effects to reduce the com-

pressive stress in the beam.fc might be reduced to 6000 psi (41.4

MPa). Exterior span = 4500 psi (31.0 MPa)

Beam Shipping Weight (see Fig. C6)

Exterior span beam shipping weight =210 kips (934 kN)

Interior span beam shipping weight =240 kips (1067 kN)

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