Prestressed Concrete Box Girders Made from Precast Concrete Unsymmetrical Sections

Made 80

Prestressed

Unsymmetrical Department University University Zhongguo Graduate Environmental Department of Chuanbing of of Assistant Fairbanks, Research Alaska-Fairbanks Omaha, Nebraska-Lincoln Civil (John)

from Ph.D., Omaha, Maher Charles P.E., University Department Engineering Engineering of Professor Nebraska Assistant Civil FPCI Alaska J. Ma, P.E. Nebraska Sun K. Vranek of & of Tadros, Nebraska-Lincoln Civil Professor

Precast Engineering

Concrete Ph.D.,

Sections sections sections. assembling segmental combination many assembly control sections. reduced standard substitute builders, erection, removable percent tions girder concrete This

p example considerations includes trapezoidal are paper recast, America. 1 used

Concrete structures. advantages of placed bridges, and and AASHTO bridges (4) in for weight Design, implementation and gantry span-by-span prestressed for These prestressed box describes

Box short- void of increased I-sections. adjacent adjacent concrete Surveys In precast, (5) built girder and design most are forms, over and for required box production, include possible one-third in to concrete bridge box medium-span an the indicate box discussed. handling, concrete sections competition each prestressed typical This surface of

Girders box United innovative girder (2) beams other. of of (1) an solution for is elimination box simplified girders. that these presented. single-casting the or box bridges, States and external Since construction unsymmetrical inspection, girders assembled shipping, approximately trapezoidal bridges unsymmetrical A concept among girders are construction are concept can their numerical Discussion PCI the precast prestressed are provide quality JOURNAL introduc in box easily of from bridge widely North from as and box box the sec box for (3) of 50 a a tion in the 1950s, adjacent pre cast box girder bridges have gen erally performed very well. In ad 3f. dition, the conventional box fLft ]f[ girder systems offer an aestheti cally appealing solution for -7beams @4’-O’= bridge structures in large urban areas. Three box girder systems com Fig. 1. AASHTO Type BIH-48girders. monly used in the United States are the standard AASHTO box girder, the U-shaped girder with cast-in-place (CIP) deck, and the trapezoidal segmental box sys tem. Figs. 1, 2, and 3 illustrate these three systems, with a com mon bridge width of 28 ft (8.5 m) used for comparison purposes. When the standard AASHTO box girders are built as non-com posite structures, there is no need to place and cure a deck, making construction fast and economical. Adjacent box girder bridges also Fig. 2. Oregon standard have uniform soffits and large U-shaped girder system. span-to-depth 2ratios, making them attractive. As shown in Fig. 1, seven AASHTO Type BIII-48 box girders are needed for a 28 ft (8.5 m) wide bridge, for spans up to 100 ft (30.5 m). This corre sponds to a span-to-depth ratio of 100/3.25, or approximately 30. However, in the production pro cess, the void forms must be left in place unless removable col lapsible forms, which are expen sive and time consuming to re move, are used. In addition, the Fig. 3. AASHTO-PCI-ASBISBSsegmental box girder standard 1800. adjacent box girder bridges expe rience longitudinal reflective cracking in the topping directly over the longitudinal joints, is already gaining widespread acceptance. This system can causing water leakage, concrete staining and spalling, and span up to 200 ft (61.0 m). The resulting system is very aes corner strand corrosion. thetically appealing. However, the form costs, production Oregon, Washington,3 Texas and other states are using complexity, and specialized erection equipment limit its use standardized U-shaped girders with a CIP deck. Fig. 2 illus to large projects with enough segment and span repetition to trates a 28 ft (8.5 m) wide trapezoidal box girder bridge sec justify mobilization. The standard AASHTO-PCI-ASBI tion using typical Oregon girders. This is a good system, segment3is limited to about 10 ft (3.0 m) in length and 40 and void forms can be easily removed. The CIP deck, how tons (36 Mg) in weight. Because of the short segment ever, requires field forming, adding to cost and construction length, temporary support is required until the segments of time. In addition, the heavy weight of some large U-shaped an entire span are erected and post-tensioned together. Use girders may significantly increase shipping costs and limit of simple falsework may cause traffic disruption, rendering competition. the system unfeasible. Therefore, the span-by-span (SBS) Fig. 3 shows a 72 in. (1800 mm) deep standard AASHTO segmental construction is generally performed using a spe PCI-ASBI segmental box girder for the span-by-span (SBS) cial assembly truss spanning between permanent piers. This construction method. This standard precast segmental box solution is uneconomical without considerable repetition. girder section, developed by a joint committee of PCI and This paper proposes an innovative and economical solution the American Segmental Bridge Institute (ASBI), and ap for production of precast concrete box girders. Rather than proved by AASHTO, was introduced several years ago and “slicing” a segmental box girder span transversely, it is pro-

January-February 2004 81 Precast, prestressed concrete

WeldedWire Reinforcement unsymmetrical sections have been employed in the past with various degrees of success. The challenge of two-directional CrackControlBar 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 4risers. Fig. 4 shows a typical stadium Fig. 4. Typical stadium riser (unsymmetrical section). riser cross section. Initially, this type of product was convention ally reinforced with mild steel. In recent years, however, the bene fits of prestressing in reducing 7/8in. diameter - 150 ksi bars through 3”Bituminouswearing surface member size and controlling cracks have encouraged more ap F plications of prestressing. Refer ence 9 has provided assistance to precast concrete designers in considering the impact of the lack of symmetry on design, pro duction, and construction of these stadium risers. Fig. 5. Bridge cross section with AASHTO Type B111-48girders. Construction of the Ringling Causeway Bridge in Sarasota County, Florida, was under way at the time of writing this article. It is a segmental box girder bridge constructed using the balanced cantilever method. Due to the large width of the bridge, the single multi-cell box was precast using two unsymmetrical halves. Separately post-tensioning the seg ments of the two halves as the cantilevers progressed cre ated the same conditions as pretensioning of long unsym metrical sections. An equivalent to the conventional adjacent box girder sys tem is presented in the following sections. Precast concrete unsymmetrical beams combined with precast concrete I- beams are incorporated. It is also shown how the proposed concept can cost-effectively be substituted for a trapezoidal box system. The special design, production, and construc tion considerations that need to receive attention for these uncommon section shapes are discussed. This is followed by Fig. 6. AASHTO box girder Type BIIl-48. a numerical design example. posed that the girder be segmented longitudinally. Thus, the SYSTEMDEVELOPMENT girder is composed of two or more precast sections. A single void standard AASHTO-PCI-ASBI segmental box girder of Conventional Adjacent may be split, for example, into two half-boxes. These half- Description the Box System boxes would be unsymmetrical full-span pieces that are pre Girder cast, pretensioned in a plant, shipped separately, and assem The design example in Section 9.1 of the PCI Bridge De bled as box sections on the permanent piers without an sign Manual is referred to as a conventional adjacent box assembly truss or temporary shoring. High-strength threaded girder example. This example demonstrates the design of a rods can be used to connect the precast segments transversely 95 ft (29.05 m) single-span AASHTO Type BIII-48 girder and make them work as a single unit. Diaphragms or slab bridge. The superstructure consists of seven adjacent typical thickening may be needed at the locations of the threaded AASHTO Standard Type BIII-48 girders as shown in Fig. 5. rods, depending on the number of locations per span. A 3 in. (76 mm) bituminous non-composite overlay pro-

82 PCIJOURNAL vides the wearing surface. The box girders are transversely post- tensioned through 8 in. (203 mm) wide full-depth diaphragms lo cated at quarter points along the IE L EH L JE1 span. Fig. 6 shows the dimen H sions of a standard AASHTO Type BIII-48 section. The weight of the box girder is 0.85 kips/ft Fig. 7. Option A: Equivalent adjacent box girder system. (12.40 kNIm). The total weight of a 95 ft (29.0 m) long girder is about 42 tons (38 Mg). Corrugated interface As mentioned previously, pro Corrugated interfce ducing closed box sections with internal voids is difficult. Usu 1 ally, either a collapsible reusable steel form or a stay-in-place ex panded polystyrene (EPS) form is used. The reusable steel form is not an option here because of the presence of quarter-point and end diaphragms. The stay-in- place EPS form provides a rela tively fast production 3cycle. However, some producers have expressed concern that the buoy (a) Precast I-section (b) Precast Unsymmetrical Section ancy forces of the vibrated con crete may push the expanded polystyrene form upward. Fur Fig. 8. Proposed girder sections with Option A. ther, if the concrete is not ade quately consolidated, voids may develop on the inside faces of the webs and bottom flange, are sloped 1/4 in. per ft (21 minIm) to allow void forms to be where they cannot be visibly inspected. There is also the removed in single pieces without disassembly. The web added expense of not amortizing the use of the forms over width of the I-section is 6 in. (152 mm), which is thinner numerous applications. than that of the sum of two web widths of the AASHTO box One advantage of the proposed unsymmetrical sections is girder. The precast I-girder can be produced in a similar that the void forming system is external and reusable. Two manner to standard precast concrete I-girders. The channel possible options are proposed herein. These are the equiva section with unsymmetrical prestressing will be discussed in lent adjacent box girder system (Option A) and the alterna more detail further on in the paper. tive trapezoidal box girder system (Option B). The weight of the precast channel girder and I-girder are 0.45 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 tons Equivalent Adjacent Box Girder System (Option A) (19 Mg) for the channel girder and 38 tons (35 Mg) for the Option A is illustrated in Fig. 7. For clarity, only the pre I-girder, which are significantly lighter than the AASHTO cast concrete section is shown in this figure. As can be seen, box girder. Thus, no additional handling and shipping equip instead 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 pro As shown in Fig. 8, the proposed girders would need to be posed cross section dimensions of the two types of girders produced with corrugated interfaces in their top and bottom are shown in Fig. 8. The bottom flange minimum thickness flanges, which is relatively simple to accomplish. These cor for both types of section is 6 in. (152 mm) so that two rows rugated interfaces would form shear-key joints that would be of pretensioning strands can be placed. A minimum thick grouted after the beams are erected. CIP diaphragms may be ness of 5.5 in. (140 mm), as that in the standard AASHTO used as in the conventional system. However, if long-line box, is also possible if a concrete cover of 1.75 in. (44 mm) prestressing beds with prismatic cross sections and reusable to the strand centerline is permitted. steel forms are to be used, then CIP diaphragms are best A transverse post-tensioning sleeve, 1.5 in. (38 mm) in di added in a second casting. A better solution is to avoid con ameter, can be placed in the 2 in. (50 mm) center-to-center crete diaphragms altogether. Recent practice with I-girder space between strands in the bottom flange, and a similar bridges, including that in Nebraska, Florida, and a number detail can be used in the top flange for transverse connection of other states, has demonstrated that intermediate concrete as discussed below. The top and bottom flange inside faces diaphragms are unnecessary. Because the spacing between

January-February 2004 83 ______

bridge section. Each trapezoidal 5’-O” 5’-O’ 2’-0’-f-2’-0” 5’-O” 5-0” 2’-O”j box section would be produced I I ”b20’- I I in two halves. The four unsym metrical sections would be de signed to have standard dimen sions such that only one form I 7’—21/2” I type would be required. As in -7-0 Option A, the section bottom flange starts with a 6 in. (152 mm) thickness and increases lin Fig.9. Option B:Alternativetrapezoidal box girder system. early at /4 in. per ft (21 mm/rn). The flange thickness may have to be increased to accommodate webs in this system is only 4 ft (1.2 m), and because of the transverse post-tensioning of the top and bottom flanges, de existence of inter-connected top and bottom flanges, it can pending on the detail used. The authors believe, based on re be justifiable to eliminate intermediate concrete diaphragms cent experience with precast concrete deck slabs, that a 6 in. in the proposed Option A system. (150 mm) thickness of the top and bottom flanges is ade Sleeves can be preplaced in the top and bottom flanges, at quate. Three examples of suitable connection details are de about 4 ft (1.2 m) spacing, for installation of high-strength scribed in Reference 3. threaded rods, which would transversely connect the seg Fig. 10 provides the cross-sectional dimensions of the sec ments in the total bridge cross section. It is estimated that 1 tion. The web has a slope of 2 to 1 to improve aesthetics of in. (25 mm) diameter, Grade 150 ksi (1034 MPa) rods at 4 ft the completed bridge and to reduce the bottom flange to an (1.22 m) spacing inserted in 1.5 in. (38 mm) diameter optimal size without sacrificing girder capacity. The typical sleeves would provide adequate capacity. If a larger connec unsymmetrical section weighs 1.03 kipslft (15.02 kN/m), or tion is required, the flange thickness would need to be in 49 tons (44.5 Mg), for a 95 ft (29.0 m) segment. This is creased accordingly. somewhat heavier than the AASHTO Type BIII-48 box To provide a smooth riding surface, a bituminous overlay girder. may be placed, similar to that shown for the standard box Option B uses fewer pieces than Option A. It is optimized system. Alternatively, the top surface of the concrete may be for the loading and span considered. Its total weight is less ground. The latter solution requires that the original precast than that of Option A, and significantly less than that of the concrete product be made with an extra 0.5 in. (13 mm) of conventional adjacent box system. It can be viewed as being concrete cover over the top layer of reinforcement. Either a structurally comparable system to the standard I-beam sys measure will compensate for misalignment between seg tem with relatively wide web spacing, but aesthetically more ments without having to place a cast-in-place composite attractive. The relatively shallow depth and low stiffness re concrete overlay. sults in a higher bridge live load deflection than Option A or Creating the shear-key joint between precast pieces at the a deeper conventional I-beam system. However, deflection top and bottom slabs is advantageous over connecting adja of short- to medium-span precast, prestressed concrete cent full boxes. In adjacent box construction, the individual bridges is generally not a controlling design criterion. Op precast concrete pieces have relatively large torsional stiff tion B retains some advantages of Option A, such as exter nesses because they are closed boxes. They require, there nal void forming and improved concrete inspectability. The fore, very large connecting forces for the total cross section additional advantages discussed above make it the more fa to act as one unit. The connecting forces are greatly reduced vorable option. in the proposed system because the component pieces are An owner would have to be willing to make a long-term open boxes with relatively small torsional stiffnesses, the commitment to use it to allow precasters and contractors in webs are not doubled, and the connections are made in the the owner’s jurisdiction to amortize the substantial invest relatively flexible thin slabs. This improvement results in ment in forms and to gain the necessary production and con elimination of longitudinal reflective cracking over the struction experience. The precast producer may find it more joints of adjacent boxes. With conventional adjacent box efficient to make the two halves of the box simultaneously girder production, concrete placement is more difficult. in one casting. This would require larger bed capacity and With the proposed solution, all faces are visible, greatly im width than that required for individual halves cast at sepa proving quality assurance. With the increasing use of self- rate times or in separate beds. consolidating concrete, production of I-girders and channel The concept of splitting a box girder into several segments girders of the shapes shown in Fig. 8 is no longer a problem. can also be applied to segmental box girder bridges. Currently, only a few precast producers are involved in segmental con struction because of the expensive forms, complex geometric Alternative Trapezoidal Box Girder System (Option B) adjustments, and sophisticated construction equipment, de Option B, shown in Fig. 9, is another possible substitute spite the significant annual volume of segmental construction for the adjacent standard box girder system of Fig. 5. Four in the United States, reportedly about $1 6billion. The pro pieces of precast unsymmetrical sections comprise the total posed concept can be applied to segmental box girder con-

84 PCI JOURNAL

January-February

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NUMERICAL An If at the 45.0 consistent Figs. in. top (55.2 as segments the service truck kPa). stress adequate post-tensioning bottom end. at an dimensions. Grade enough the provisions example box unsymmetrical kNIm), can needed, of (3.6 for Specifications11 boxes. in in. with and the release After horizontal assembly and MPa). m4), 13 at distance eight section. Fig. alignment loading, each be This Specifications.’° (1.14 changes m) at temporary post-tensioning, bottom box and a 270 approximately and overall to thus flange with removed. with and of shear-key tension release. Each jy during joint wide. will sections 12 pieces of of

f cause Prestressing example of flexural the girder ksi m). Area = 14. future becomes the of can the the sections EXAMPLE vertical = from open the allow deflection flanges. are 258,408 box bridge PCI (1862 provided Moments of dimensions This strength due 6 the section It significant four tie construc of alignment AASHTO AASHTO proposed be A Once ksi bridge are expected with the JOURNAL grouting concrete is wearing the strength is precast = focuses can precast for to made, design trape jack com MPa) cross used. 814.2 (41.4 one- vari sym 11 steel The two top the the in.4 No be the be as in in is is is of ft (0.1076 and I = —107 689 4),m xy 4in. (—0.04484).m

Loading Only the midspan section is considered in this example. Moment due to the weight of I’—4.369 a single precast piece (half-box) about the x axis is 1060.2 ft-kips kN-m). M (1437.6 3’. Moment due to weight of wearing surface and railing (acting on the whole box) is Md,, 2-4. S31” = 538.8 ft-kips (730.6 kN-m). Live load dis 1/2’ tribution factor (per whole box) 0.845. Live load moment per box is M = 1967.1 ft-kips (2667.4 kN-m). 11.710”

Coordinates of Critical Section Fibers The critical stress points are typically at Fig. 15. Details of typical unsymmetricalsection. the bottom and top fiber in a symmetrical section. However, in an unsymmetrical sec tion, the corner points are the critical stress points. The coordinates of Points P1 to P7 in Fig. 15 are (—28.631)(258408)— (30.232)(—107689) given in Table 1. For example, the coordinates of Point P3 27 + (—1882.2)(12) 814.2 221964(258408)— (_107689)2 are x3 = 30.232 in. (767.89 mm) and = —28.631 in. y (30.232)(221964)—(—28.631)(—107689) (—727.23mm), relative to the c.g. of the half-box section. +885 5(12) 221964(258408)— (_l07689)2

Required Number of Strands = 1.114 + 2.045 + 0.842 = 4.001 ksi (27.59 MPa)

Estimation of the required number of strands is governed Similarly, the stress at Point P3 due to self-weight equals by concrete tensile stresses at Point P1 at service, due to full —1.152ksi (—7.94MPa). Therefore, the total stress at this load plus effective prestress. The symmetrical bending for point at transfer of prestress is 2.849 ksi (19.64 MPa) mula can give a reasonable initial estimate. For this design (compression), which is below the compression limit of example, a total of 23 strands are estimated for each half- 0.6f= (0.6)(6.0) = 3.6 ksi (24.82 MPa). Table 1 shows the box. The horizontal center of the strands is arranged as close stresses at release at Points P1 to P7 due to prestress, self- as possible to the c.g. of the section, as shown in Fig. 15. weight, and the combined effect, respectively. Note that the maximum tensile stress occurs at P5 and is calculated Stress at Prestress Transfer to be —0.543ksi (—3.74MPa), which is within the limit of —7.5/ = = —0.581ksi (—4.01 The unsymmetrical bending formula in Eq. (3) is applied —7.5xf5/1000 MPa). From Table 1, note that all the calculated using the properties of the half-box to calculate stresses at stresses are within allowable limits. release. Using a steel stress of 181.8 ksi (1253.5 MPa), the total prestress force at release is: 0P = (23)(0.217)(181.8) = 907.4 kips (4032.9 kN) Strand Pattern Arrangement The coordinates of the c.g. of the prestressing strands The strand pattern shown in Fig. 15 is preferred over the (Point P in Fig. 15) relative to the c.g. of the cross section typical uniform pattern shown in Fig. 16 for three reasons: are x = 11.710 in. (297.43 mm) and y,,, = —24.892 in. (1) It minimizes the horizontal deflection, (2) it minimizes (—632.26mm). the extreme fiber (corner) concrete stresses at release, and Moments due to the prestressing force about the x-axis (3) it reduces horizontal deflection and thus minimizes the and y-axis are: alignment effort required in assembling the two halves of M = 0P(y) = 907.4(—24.892)/12 = —1882.2 ft-kips each box. (—2’52.3kN-m) To confirm this point, the analysis is repeated below for Mr.,.= 0P(x) 907.4(11.710)/12 = 885.5 ft-kips (1200.7 the stresses at release, using the strand pattern of Fig. 16. kN-th) The coordinates of Point P, the c.g. of the strand pattern, are xi,.= 15.710 in. (399.0 mm) and y,,, = —25.588in. (—649.9 The stress at Point P3 due to prestressing force at release mm). Moments due to the prestress force are M = —1934.8 is: ft-kips (—2623.6kN-m) and = 1187.9 ft-rips (1610.8 fP = p yl —xi xl —yl kN-m). Table 2 shows the stresses at the critical points at re + + M, lxxiv lease. — — The maximum compression stress at Point P3 is 3.195 ksi (22.03 MPa), which is still below the code limit. How-

January-February 2004 87 —1.119 —0.581 ever,

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P6’

758.6

814.2 jD

formula, =

16.

choice.

= properties =

load

the

ksi

(23)(0.217)(152.0) =

0.932

not be

ksi = A

the ft-kips

Unsymmetrical

ksi

—1573.6

740.3 at

at +

calculated M

maximum (1048.0 + at

used

y=-25.588”

+ and (—1573.6)(l2) be

(—7.72 Point

due

whole

Final

due

(—4.01

Point 740.3(12)

+ Eq.

used, Px yl IXI,

(1437.6

2.865 ft-kips

with

live

ft-kips (3), —XI Xy

Service

MPa):

MPa). — full

prestress box

P1 the

even —

with due load. MPa).

prestress

tensile — —

but

(4.232)(221964)

(1003.8 X

0.416

kN-m)

load section due

half-box

should

(—28.63 Xy =

(—2133.8

though with the =

Using

—1.930 Conditions +

prestress

significantly

758.6

221964(258408)_(_107689)2

Therefore,

1964(258408) to

stress,

plus

aid =

and

is: kN-m)

two

with service Py

3.381 l)(258408)

self-weight

be X=

an XIX

section

effective kips

kN-m)

girder ksi Xy

used sets appears

the

which

15.710”

is: effective — —

ksi

different

(—13.31 —

are:

(3374.3

(—28.631)(—107689)

YIXY

unsymmetrical

of j2

this

exceeds

weight. with

(23.31 X —(—107689) —

shown

section

(4.232)(—107689)

prestress

moment

strand

MPa)

superimposed

steel

kN)

MPa)

Point

The

the

in properties.

stress

pattern. obvious

Fig. pattern limit

proper

can

P4 P7

P5,

bend

is =

x-axis

combined

(—3.37 of stresses stresses Flexural fSID+LL

Thus,

Stress

Note j

Factored

f Stress

Flexural This f’

f’=

—6-,j

d y=0.28 = = = =

=f;[1_C*(p1 ======

is 1967.1

the

MPa)

7727.5 1.3[2(1060.2)+538.8+1.67(1967.l)]

2(23)0.217 41.261 270 0.65 8.0 538.8 (270)[1 that 263.3

Afd A5 8733.7 1 = = = =

are moment

in twice

.0(9.982)(263.3)(41

Strength

—0.417 —1.939

(538.8)12(—28.63

M5y effects section

all

Point

ksi prestressing

strength load 2I

all —

ksi

the

—0.537 ft-kips (tension),

ksi

seven

ft-kips

142(41.261)

2(221964) that

ft-kips

(55.2 in. within

ft-kips —

(1861.7

moment

[1_0.6’J

—J(O.OOl7) (0.28’\

9.982 (1815.5 —

isf1 ksi

strength (1048.0 =

1.522

is:

due

larger

points

MPa)

(2667.4

9.982

(—13.37

ksi

a the (730.6

(10478.5 =

(11842.9

half-box.

MPa)

steel

which

3.38

acting of

AASHTO

MPa)

(—3.70

mm)

is =

superimposed

than

1) inertia

.261

acceptable. at kN-m) 0.0017

kN-m)

final

MPa)

in. + — is

ultimate

kN-m)

(1967.

the

)(1

The 1.930

MPa). (6440.0 x within

the

service

(270N1

limits. —0.6

is:

—,)j

factored

and

2(221964)

stress

the

whole

1)12(—28.63 —

flexure

the Table

1.939

dead

live mm4)

0.0017(263.3)

full

conditions.

AASHTO

box

Point

load load

load

3 =

is:

PCI

girder

—0.488

shows

about

JOURNAL

moment

moment. moment

due

These

limit

is:

the the

ksi

1 Table 1. Stresses of critical checking points at release. Points Parameter P1 P2 P3 P4 P5 P6 P7 J x (in.) 4.232 30.232 30.232 30.232 —40.768 —40.768 30.232 y (in.) —28.631 —22.631 - —28.63! - 16.369 16.369 10.369 10.369 Stress due to prestress at release (ksi) 4.043 3.386 4.001 —0.613 —0.498 0.117 0.002 Stress due to self-weight (ksi) —1.930 —0.721 —1.152 2.081 —0.045 —0.476 1.650 Total stress at release (ksi) 2.1 13 2.665 2.849 1.468 —0.543 —0.359 1.652

Note: 1 in. = 25.4 mm; 1 ksi = 6.895MPa.

Table 2. Stresses of critical checking points at release with a different strand pattern. Points Parameter P1 P2 P3 P4 P6 P7 Stress due to prestress at release (ksi) 3.969 3.761 4.346 —0.044 —1.074 —0.489 0.541 Stress due to self-weight (ksi) - —1.930 J__0.721 —1.152 2.081 —0.045 —0.476 1.650 Total stress at release (ksi) 2.039 3.040 3.195 2.037 —1.119 —0.964 2.191 J Note: 1 ksi = 6.895 MPa.

Table 3. Stresses of critical checking points at service. Points

: - Parameter P1 P2 P3 P4 P5 P6 P7 Stress due to prestress at service (ksi) 3.381 2.831 3.346 —0.512 —0.417 0.098 0.002 Stress due to self-weight (ksi) —1.930 —0.721 —1.152 2.081 —0.045 —0.476 1.650 Stress due to SID (ksi) —0.417 —0.330 —0.417 0.238 0.238 (1.151 0.151

. Stress due toLL (ksi) —1.522 —1.203 —1.522 0.870 0.870 0.55! 0.55!

• Total stress at service (ksi) —0.489 0.577 0.254 2.678 0.648 0.325 2.354

Note: I ksi = 6.895 MPa.

CONCLUSIONS proposed system improves construction efficiency and helps reduce the reflective cracking problem that is frequent in ad This paper has demonstrated the advantages of using jacent standard AASHTO box beam systems. closed box beams cast in two or more longitudinal seg 8. It is possible to convert some of the segmental post- ments. If designers accept using biaxial bending analysis tensioned box girder bridges to an assembly of span-length and if producers and contractors accept handling vertically pretensioned partial box segments. Erection would thus be unsymmetrical products, the market penetration of precast greatly simplified, compared to the currently required span- concrete in bridge applications can be greatly increased. by-span gantry, or incremental cantilever post-tensioning. Among the advantages of this system are the following: Stress and deflection analyses require the use of more 1. Fabrication of partial box products is comparable in complex formulas to account for the effects of asymmetry. simplicity to that of the popular, but less aesthetically attrac Handling requires careful analysis to account for biaxial tive, I-beams. camber and possible tilting. Construction is complicated by 2. External void forms can be utilized for numerous pro the extra step of forcing alignment of the components of the duction cycles. box before they are joined to form the closed cells, Methods 3. All faces of the box are visible and can be easily in discussed in this paper and previous experience with other spected upon removal from the prestressing bed. products such as stadium risers can be utilized to facilitate 4. Lighter segment weights facilitate handling and encour performance of the additional design and construction tasks. age application in longer span. 5. The number of webs can be reduced in substitute op tions to the popular adjacent AASHTO standard box beam bridge, resulting in material savings and improved structural ACKNOWLEDGMENT efficiency. The authors would like to thank the PCI JOURNAL re 6. Reduced product weights and lack of need for special viewers, who contributed detailed and constructive review ized construction equipment should increase competition comments. Our appreciation is also extended to Morad and lower total cost. Ghali of PBS&J, who provided information on the Ringling 7. Absence of intermediate concrete diaphragms in the Causeway Bridge.

January-February 2004 89 REFERENCES

1. Hassanain, M. A., “Design of Adjacent Precast Box Girder Interchange Bridges,” PCI JOURNAL, V. 42, No. 5, Septem Bridges According to AASHTO LRFD Specifications,” Pro ber-October 1997, pp. 32-42. ceedings of CE World: ASCE’s First Virtual World Congress 7. Ma, Z., and Tadros, M. K., “Prestressed Concrete Box Girders for Civil Engineering, July 2002, 12 pp. Made from Unsymmetrical Precast Z-Sections,” Proceedings 2. Miller, R. A., Hlavacs, G. M., Long, T., and Greuel, A., “Full- of the International Conference on New Technologies in Struc Scale Testing of Shear Keys for Adjacent Box Girder tural Engineering, V. 1, IABSE and FIP, Lisbon, Portugal, July Bridges,” PCI JOURNAL, V. 44, No. 6, November-December 2-5 1997, pp. 657-664. 1999, pp. 80-90. 8. Boresi, A. P., Schmidt, R. J., and Sidebottom, 0. M., Ad 3. Badie, S. S., Kamel, M. R., and Tadros, M. K., “Precast Pre vanced Mechanics of Materials, Fifth Edition, John Wiley and tensioned Trapezoidal Box Girder for Short Span Bridges,” Sons, Inc., New York, NY, 1993, 832 pp. PCI JOURNAL, V. 44, No. 1, January-February 1999, pp. 48- 9. Kelly, I. B., and Pike, K. J., “Design and Production of Pre 59. stressed L-Shaped Bleacher Seat Units,” PCI JOURNAL, V. 4. PCI Design Handbook: Precast and Prestressed Concrete, 18, No. 5, September-October 1973, pp. 73-84. Fifth Edition, Precast/Prestressed Concrete Institute, Chicago, 10. AASHTO, Standard Specifications for Highway Bridges, 16th IL, 1999. Edition, American Association of State Highway and Trans 5. Precast Prestressed Concrete Bridge Design Manual, Pre portation Officials, Washington, DC, 1996. cast/Prestressed Concrete Institute, Chicago, IL, 1997. 11. AASHTO, LRFD Bridge Design Specifications, Second Edition, 6. Freyermuth, C. L., “AASHTO-PCI-ASBI Segmental Box 1998, and Interims 1999 and 2000, American Association for Girder Standards: A New Product for Grade Separations and State Highway and Transportation Officials, Washington, DC.

APPENDIX — NOTATION

A = area of concrete section = moment about y-axis due to prestress = area of prestressed tension reinforcement M = nominal moment strength of section b = top flange width of box girder = factored moment at section d = distance from extreme compression fiber to cen = moment about x-axis troid of tension reinforcement M = moment about y-axis f = concrete stress P = effective prestressing force at service load ft 7=tof concrete stress at critical checking Points ito 7 0P = effective prestressing force at transfer of prestress = specified compressive strength of concrete x1 to ,x7 y1 to y7 = coordinates of critical checking Points f = specified compressive strength of concrete at 1 to 7 transfer of prestress x1,, y,, = coordinate of strand center f’ = ultimate strength of prestressing steel = concrete strength factor f = stress in prestressing steel at ultimate load = strength reduction factor I, Ii,,I = second moments of inertia about x- and y p = tension reinforcement ratio axes of cross section y = factor for type of prestressing steel M, 1M Mp, = moment about x-axis due to girder , self-weight, live load, prestress and superimposed dead load

90 PCI JOURNAL