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Effects of Time-Dependent Loss Models for Spliced-Girder Bridges

David A. Tomley, P.E., Manager, Engineering Services, LEAP Software, Inc.

LEAP Software, Inc.

P.O. Box 16827

Tampa, FL 33687-6827Telephone: (813) 985-9170

FAX: (813) 980-3642

e-mail address: [email protected]

Lee D. Tanase, President/CEO, LEAP Software, Inc.

LEAP Software, Inc.

P.O. Box 16827

Tampa, FL 33687-6827

Telephone: (813) 985-9170

FAX: (813) 980-3642

e-mail address: [email protected]

TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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Effects of Time-Dependent Loss Models for Spliced-Girder Concrete Bridges

Lee D. Tanase, President/CEO, LEAP Software, Inc. and


ABSTRACT (WORD COUNT 201)

In order to compare prestress losses over time, a time-dependent finite element analysis was performed on two

precast spliced-girder bridges using the industries currently recommended loss models (ACI-209, CEB-FIP, and

AASHTO LRFD). The same time-dependent analysis was also performed on a simple span conventional

precast/prestressed concrete bridge to compare the results using the current AASHTO prestress loss equations

compared to the prestress loss predictions using the ACI-209, CEB-FIP, and AASHTO LRFD loss models. The

CONSPLICE PT software program was used for the design studies. Key construction stages and the comparison

between prestress and post-tensioning losses over time and the critical beam stresses are highlighted using each of

the three loss models independently.

Simple Span Conventional Precast/Prestressed Bridge

40 ft. single span

prestressing only (16-0.5 270 ksi strands)

precast double-T beam

HS20 Live Load

Spliced-Girder Project Details

Example 1: Twisp River Bridge

Location: State of Washington

192 ft. single span

3 individual precast segments

Temporary supports Combination prestressing and post-tensioning

Option for 1 or 2 stage stressing sequence for post-tensioning

Example 2: Black Warrior Parkway Bridge

Location: State of Alabama

3-span (208-260-208 ft) continuous with drop-in segment

Combination prestressing and post-tensioning

Variable depth 10 ft. pier segments using constant web height


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Lee D. Tanase and David A. Tomley, LEAP Software, Inc.

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Effects of Time-Dependent Loss Models for Spliced-Girder Concrete Bridges



INTRODUCTION

A finite element-based, time-dependent analysis using either of the three code specified loss models (e.g., ACI-209,

CEB-FIP, and AASHTO LRFD) allows engineers to compare the analysis and design effects over time and more

accurately take into account the variation in material behavior (e.g., increases in concrete strength and modulus of

elasticity, creep and shrinkage effects, and prestress losses) over time. AASHTOs LRFD Commentary section

C5.9.5.1 states that For multistage construction and/or prestressing, the prestress losses should be computed in

consideration of the elapsed time between each stage. Such computation can be handled with the time-steps

method. Further, according to AASHTO LRFD article 5.4.2.3.1, when mix-specific data are not available,

estimates of shrinkage and creep may be made according to AASHTO LRFD using the provisions of; AASHTO

LRFD Articles 5.4.2.3.2 and 5.4.2.3.3, and the CEB-FIP model code, or ACI-209.

A time-dependent analysis, that considers the material variations over time, is important to owners from

which a more accurate computation of camber and deflections can be obtained over time by performing a time-

dependent analysis using either the ACI-209, CEB-FIP, or AASHTO LRFD loss models. This statement is backedup by AASHTO LRFDs article 5.9.5.4 on Refined Estimates of Time-Dependent Losses and parallel commentary

article C5.9.5.4.1 stating, Estimates of losses due to each time-dependent source, such as creep, shrinkage, or

relaxation, can lead to a better estimate of total losses compared with the values given in Table 5.9.5.3-1. Table

5.9.5.3-1 outlines AASHTO LRFDs approximate lump sum estimate of time-dependent losses as further outlined in

AASHTO LRFD article 5.9.5.3. Insight into the percent differences and the sensitivity between the loss model

results as applicable to spliced girder bridges will be discussed. The CONSPLICE PT software program (1)was

used for the design studies.

Should a time-dependent analysis be performed on a conventional simple span precast/prestressed concrete

girder? A simple span bridge was compared using the Standard AASHTO prestress loss equations (2) compared to

the results of a time-dependent analysis using the ACI-209 (3), CEB-FIP (4), and AASHTO LRFD models (5).

TIME-DEPENDENT MATERIALS

Concrete material properties vary with time, and various models have been developed by different code developing

organizations to predict this behavior. The concrete material properties to be considered include:

fc = Concrete Compressive Strength

fr = Modulus of Rupture

E = Modulus of Elasticity

S = Shrinkage Strain

N = Creep Coefficient

It is well known that the behavior of the concrete material properties vary over time as shown in Figure 1.

As shown, the concrete strength (fc) varies and increases over time as does the modulus of elasticity (E).

A time dependent analysis for spliced-girder bridges is warranted because;

1. The ACI-209, AASHTO LRFD, and CEB-FIP material models take into account the variation of

concrete compressive strength (fc) and modulus of elasticity (E) over time, and

2. The following bridge elements that are typically a part of the spliced-girder bridge construction

have their own, (unique and/or different) material properties:

a. Precast concrete girders


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b. Cast-in-place concrete splices

c. Cast-in-place concrete deck slab

d. Prestressing strands

e. Post-tensioning tendons

3. Different construction stages and corresponding time durations associated with each bridge

element listed above in (2.). Note, each element enters the spliced-girder construction in different

stages. Therefore an accurate model and representation of the actual construction stages specific

to spliced-girder bridges is essential in order to obtain better analytical predictions regarding the

behavior of the structure.

4. According to AASHTO LRFD article 5.5.2.3 on shrinkage and creep and parallel commentary

C5.4.2.3.1, Creep and shrinkage of concrete are variable properties that depend on a number of

factors, some of which may not be known at the time of design. Without specific physical tests or

prior experience with the materials, the use of the empirical methods referenced in these

Specifications cannot be expected to yield results with errors less than (+/-) 50 percent.

SIMPLE SPAN CONVENTIONAL PRECAST/PRESTRESSED BRIDGE

The first design study using CONSPLICE PT will be for a simple span conventional precast/prestressed bridge with

the following design information:

40 ft. single span

prestressing only (16-0.5 270 ksi strands)

precast double-T beam

HS20 Live Load

Construction stages, duration, elements, and applied loads (Table 1)

The typical design assumptions used for simple span (prestressed only) girder construction includes performing 2analysis and designs (initial and final).

Due to owner assumptions regarding future wearing surface (FWS) and sacrificial wearing surface assumptions, it is

necessary to investigate the initial design for 2 reasons:

1. Used to compute camber and screed elevations (full deck thickness, 0 FWS, and no sacrificial wearing

surface provisions, this simulates the bridge open for traffic)

2. Verify stresses and ultimate capacity

Whereas, the final design is considered since the final design controls the number of prestressing strands because the

FWS and sacrificial wearing surface assumptions are included in the analysis and design.

What is not considered in either the initial or final analysis is the time dependent behavior of the materials.

AASHTO recognizes the need for a time-dependent analysis using either of the three loss models (AASHTO LRFD,

ACI-209, and CEB-FIP) according to AASHTO LRFD article 5.4.2.3 on shrinkage and creep. AASHTO article5.9.5.3 addresses approximate lump sum estimates of time-dependent losses which are only applicable to

posttensioned nonsegmental members with spans up to 160 ft. AASHTO article 5.9.5.4 provide guidelines for

estimating time-dependent losses using refined methods that consider construction stages, material variations due to

creep and shrinkage, and relaxation losses.

Typically the future wearing surface (FWS) is included in the analysis up front to account for any

additional future load applied to the structure due to resurfacing maintenance over time, whereas in reality, the FWS


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load is not applied until some time into the future (i.e., after the bridge is open to traffic). What happens to the

prestress losses when the FWS is applied in the future rather than when the bridge is open to traffic?

As Figure 2 indicates, at mid-span, the prestress force decreases from approximately 400 kips (stage 6) to

350 kips (stage 7). The AASHTO equation method (3)predicts a constant prestress force of approximately 400 kips

over time, whereas the ACI-209 (4), AASHTO LRFD (6), and CEB-FIP (5)loss models all indicate that there is an

additional loss of prestress over time as shown in stages 7 and 8. These results also indicate that, for this example,

using a time-dependent analysis with either loss model will predict more losses and less prestress force over time.

SPLICED-GIRDER PROJECT DETAILS

Example 1: Twisp River Bridge

Location: State of Washington

192 ft. single span

3 individual precast segments

Temporary supports


Option for 1- or 2-stage stressing sequence for post-tensioning

Elevation view (Figure 3) Cross section details (Figure 4)

Pre-tension and post-tension details (Figure 5)

Construction stages, duration, elements, and loads (Table 2)

The construction stages for the Twisp River Bridge are more involved than the previous example for a conventional

precast/prestressed concrete girder. The spliced-girder stages as shown account for two stages of post-tensioning

(see stages 6 and 10). There are a total of 3 tendons; PT1 and PT2 are stressed during stage 6 prior to the deck pour

and the final PT3 tendon is stressed after the deck has cured during stage 10. If should be noted that the State of

Washington showed two options for post-tensioning in the contract bid documents. The first option, as depicted in

this example, utilizes two stages of post-tensioning. The second option, which was selected by the contractor, only

utilized one stage of post-tensioning. Also, note that during stage 15, a uniform temperature and temperature

gradient was included according to AASHTO specifications (3).

Figures 6 and 7 show the prestress and post-tensioning losses/force (at mid-span) over time using the three

loss models independently. As shown, the prestress and post-tension losses/force and corresponding beam stresses

are similar.

SPLICED-GIRDER PROJECT DETAILS:

Example 2: Black Warrior Parkway Bridge (As Shown in Figure 8)

Location: State of Alabama

3-span (208-260-208 ft) continuous with drop-in segment


Variable depth 10 ft. pier segments using constant web height

Elevation view (Figure 9) Cross section details (Figure 10)

End-span and drop-in beam details (Figure 11)

Construction stages, duration, elements, and loads (Table 3)

One important note to mention in looking at the construction stages is that a full depth deck replacement was

considered in the analysis because of the two stages of post-tensioning. Since the last tendon (PT4) was added to the

composite section (i.e., beam plus deck), engineers have to investigate the impacts of removing the deck in the

future on beam stresses since there will be 4 post-tensioning tendons acting on the non-composite (i.e., beam only)


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section. Instead of plotting prestress losses/force over time at mid-span, the bottom of beam stresses are shown in

Figure 12.

Bottom of Beam Stresses at Mid-Span (Compression Positive)

As a comparison, the allowable compressive stress of 4.2 ksi is shown in Figure 12. All computed/actual bottom of

beam stresses over time and for every construction stage are less than the allowable.

It should be noted, that the controlling stage of construction on the final design may not necessarily be thefinal construction stage. This depends on the material properties, loads, and cross section (composite or non-

composite). Also the design control could be due to shear, moment, or stresses for any construction stage, therefore

a time-dependent, finite element, analysis provides an engineer this information.

CONCLUSIONS

A time-dependent analysis is warranted for spliced-girder bridges in order to more accurately account for the time-

dependent material behavior and properties of concrete, and in order to reproduce/model the construction stages that

are specific to spliced-girder bridges, and for computing more accurate camber and deflections compared to lump

sum estimates.

For the Twisp River and Black Warrior Parkway spliced-girder bridges, the ACI-209 (3), CEB-FIP (4), and

AASHTO LRFD material models (2)produced similar prestress and post-tensioning losses over time. The 40 ft.

simple span conventional precast/prestressed concrete example study showed that a time-dependent analysis predicts

more losses and less prestress force over time compared to the current AASHTO equations (5)for losses.

RECOMMENDATIONS

The authors acknowledge the need for field measured data in order to compare and/or verify the time-dependent

analytical model responses against actual spliced-girder bridges constructed throughout the United States.

REFERENCES

1. LEAP Software, Inc., CONSPLICE PT (LRFD and AASHTO Standard Design and Analysis of Spliced

Prestressed/Precast Bridge Girders and CIP Concrete Slabs), Tampa, Florida, 2001.

2. American Association of State Highway and Transportation Officials (AASHTO),AASHTO LRFD Bridge

Design Specifications,Second Edition, Washington, D.C., 1998 (including the 2000 Interims).3. ACI Committee 209,Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures (ACI-

209R-92), America Concrete Institute, Detroit, 1992.

4. Comite Euro-International Du Beton, CEB-FIP Model Code, 1990.

5. American Association of State Highway and Transportation Officials (AASHTO), Standard Specifications for

Highway Bridges, 16thEd., Association of General Offices, Washington, D.C., 1996 (including the 1998

Interims).


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Effects of Time-Dependent Loss Models for Spliced-Girder Bridges



LIST OF TABLES AND FIGURES

FIGURE 1 Variation of Concrete Strength (fc) Over Time

FIGURE 2 Prestress Force During Each Construction Stage (Simple Span Conventional Prestressed Bridge)

FIGURE 3 Elevation View of Twisp River Spliced-Girder Bridge

FIGURE 4 Cross Section of Twisp River Spliced-Girder Bridge

FIGURE 5 Pre-Tension & Post-Tension Details of Twisp River Spliced-Girder Bridge

FIGURE 6 Prestress Force During Each Construction Stage (Twisp River Spliced-Girder Bridge)

FIGURE 7 Post-Tension Force During Each Construction Stage (Twisp River Spliced-Girder Bridge)

FIGURE 8 Black Warrior Parkway, An Example of a Spliced-Girder Bridge

FIGURE 9 Elevation View of Black Warrior Parkway Spliced-Girder Bridge

FIGURE 10 Cross Section of Black Warrior Spliced-Girder Bridge

FIGURE 11 End-Span and Drop-In Beam Details (FLBT-72)

FIGURE 12 Bottom of Beam Stresses During Each Construction Stage (Black Warrior Parkway Spliced-GirderBridge)

TABLE 1 Construction Stages for Conventional Prestressed Bridge

TABLE 2 Construction Stages for Twisp River Spliced-Girder Bridge

TABLE 3 Construction Stages for Black Warrior Parkway Spliced-Girder Bridge


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FIGURE 1 Variation of Concrete Strength (fc) Over Time

ksi

(Days)


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FIGURE 2 Prestress Force During Each Construction Stage (Simple Span Conventional Prestressed Bridge)

40 f t. Single Span Do uble T Beam (Mid-span)

35 0

40 0

45 0

50 0

0 1 2 3 4 5 6 7 8

Stage

PrestressForce(Kips)

A C I-2 09 LR F D CE B -F IP A A S HT O


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195' -6"

6"

Brg.-to- Brg. = 194'-6"

Abut.- to- Abut.

LCLC

LC LC

LC LC

A

A

B

B

45' -7" 103' -4"

Post-Tensioning

45' -7"

C 2' -0" C.I.P.

Splice (TYP.)L

Temporary Bent (TYP.)

Segment 1 Segment 2 Segment 3(L= 101' -4")

(L= 45' -1")

Abutment Abutment

(L= 45' -1")

FIGURE 3 Elevation View of Twisp River Spliced-Girder Bridge


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5.275' 5.275'

45'-0"

5 SPA. @ 6.89' = 34.45'

1'-6" 1'-6"

8" Deck

W24PTMG

0.5" Haunch Thickness 0.5" Sacrificial Thickness

FIGURE 4 Cross Section of Twisp River Spliced-Girder Bridge


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4.25 in. O.D. DUCTS (TYP.)

10 -0.6"

Dia. Strand2in.

6"

6"

3.84"

PT3

PT2

PT1

FIGURE 5 Pre-Tension & Post-Tension Details of Twisp River Spliced-Girder Bridge


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FIGURE 6 Prestress Force During Each Construction Stage (Twisp River Spliced-Girder Bridge)

195 ft. Single Span 3 Segment Bulb-T (Mid-span)

300

350

400

450

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Stage

PrestressForce(Kips)

ACI-209 LRFD CEB-FIP


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FIGURE 7 Post-Tension Force During Each Construction Stage (Twisp River Spliced-Girder Bridge)

195 ft. Single Span 3 Segment Bulb-T (Mid-span)

1500

1750

2000

2250

2500

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Stage

PostTensionForce(Kip

s)

ACI-209 LRFD CEB-FIP


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FIGURE 8 Black Warrior Parkway, An Example of a Spliced-Girder Bridge


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260'-0"208' -0" 208' -0"

End-span Beam

Pier Segment

Drop-in Beam

A

A

A

A

A

A

676' -0"

Temporary Bent (TYP.)

149' -6" 117' -0" 143' -0" 117' -0" 149' -6"

(Beam 1) (Beam 3)

Pier Segment(Beam 4)

End-Span Beam(Beam 5)

C Bent 3L

(Beam 2)

1' -0" Cast-In-Place Splice (TYP.)

C Bent 6LC Bent 5LC Bent 4L

C StrongbackL

FIGURE 9 Elevation View of Black Warrior Parkway Spliced-Girder Bridge


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1' - 4 1/2"1' - 4 1/2"59' -11"

6 SPA. @ 9' -0" = 54' -0"4'-4"

62' -8"

4'-4"

Haunch

Thickness

= 2"

8"

FIGURE 10 Cross Section of Black Warrior Spliced-Girder Bridge


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4' -1"

1'-8 3/4"

4'-5"

11"

1'-8 3/4"

4"

2"

2' -7"

8"

8" 11"

R=6"

R=6"

6'-0"

7

1/2"

5

1/2"

4- #9

(full length)

End-span beam length = 149' -0"

Drop-in beam length = 142' -0"

FIGURE 11 End-Span and Drop-In Beam Details (FLBT-72) of Black Warrior Spliced-Girder Bridge


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Multiple Span w/ Drop-In

0

1

2

3

4

5

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Stage

Bot.Beam

Stress(ksi)

1990 CEB-FIP ACI-209 LRFD Allow.

FIGURE 12 Bottom of Beam Stresses During Each Construction Stage (Black Warrior Parkway Spliced-Girder Bridge)


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Stage # DescriptionDuration

(days)

Total

Duration

(days)

Elements

Activated

Elements

RemovedLoads

1Construct abutments and install

supports, Place Beams (beam age = 2)

0 0supports/

beams

n/a beam self wt.

2 Store beams on site 60 60 n/a n/a n/a

3 Time Step (form deck) 20 80 n/a n/a n/a

4 Pour Deck + Added DL 0 80 slab n/a slab self wt.

5 Time Step 30 110 n/a n/a n/a

6 Add Live Load 0 110 n/a n/a Live Load


8Add Future Wearing Surface + Live

Load0 4110 n/a n/a SDL + Live Load

TABLE 1 Construction Stages for Conventional Prestressed Bridge


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(days)

Total

Duration

(days)

Elements

Activated

Elements

RemovedLoads

1Construct abutments & install

temporary bents, active beams0 0 n/a n/a beam self wt.

2 Place Beams #1, 2, 3 in storage 60 60 n/a n/a n/a3 Time Step (forming) 20 80 n/a n/a n/a

4Pour Cast-in-Place Splices +

Diaphragms0 80 splice n/a

self wt.

diaphragms

5 Time Step (splice curing) 10 90 n/a n/a n/a

6 Stress PT1 & PT2 0 90 tendons strongback n/a

7 Time Step (form deck) 20 110 n/a n/a n/a

8Pour Deck + Supplemental Thickness

0.50 110

slab +

suppl.n/a

self wt. of

slab

9 Time Step (slab curing) 14 124 n/a n/a n/a

10 Stress PT3 0 124 tendons n/a n/a


12 Remove Temporary Bents 0 135 n/atemporary

bents

n/a

13Add Superimposed Dead Loads

(Barrier)0 135 n/a n/a

superimposed

dead load


15Add Live Load + Uniform Temp +

Temp Gradient0 165 n/a n/a

live load +

temperature


17 Sacrificial Wearing Surface 0 4165sacrificial

thicknessn/a n/a

18 Time Step (Infinity) + Live Load 6000 10165 n/a n/a n/a

19 Deck Removal 0 10165 n/a slab n/a

20 Redeck + Live Load 0 10165 redeck n/a n/a

TABLE 2 Construction Stages for Twisp River Spliced-Girder Bridge


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(days)

Total

Duration

(days)

Elements

Activated

Elements

RemovedLoads

1Install temporary bents in end spans,

add Pier Segment beams0 0

supports/

beamsn/a beam self wt.

2 Storage Time for Pier Segment Beams 20 20 n/a n/a n/a3

Place End Span Beams (assumed time

for cutting strands on these beams)0 20 beam n/a beam self wt.

4 Time Step (storage of end beams) 20 40 n/a n/a n/a

5Place Drop-In Beams (assumed time

for cutting strands on this beam)0 40 beam n/a beam self wt.

6 Time Step (storage of drop-in beam) 10 50 n/a n/a n/a

7Pour Cast-In-Place Splices and

Diaphragms0 50 splice n/a

dead load +

diaphragms

8 Time Step (splice curing) 14 64 n/a n/a n/a

9 Stress PT1 & PT2 & PT3 0 64 tendons strongback n/a

10Time Step (form deck using stay-in-

place forms)30 94 n/a n/a n/a

11 Pour Deck 0 94 slab n/a slab self wt.12 Time Step (slab curing) 7 101 n/a n/a n/a

13 Stress PT4 0 101 tendons n/a n/a

14 Remove Temporary Bents 0 101 n/atemporary

bentsn/a

15Add Superimposed Dead Loads

(Barrier)2 103 n/a n/a

superimposed

dead load


17 Add Live Load 0 133 n/a n/a live load


19Add Future Wearing Surface + Live

Load0 4133 n/a n/a

superimposed

dead load +

live load

20 Time Step 4000 8133 n/a n/a n/a21 Full depth deck replacement/removal 0 8133 n/a deck n/a

22 Pour Deck 0 8133 redeck n/a dead load

23 Time Step (infinity) 3000 11133 n/a n/a n/a

24 Live Load (infinity) 0 11133 n/a n/a live load

TABLE 3 Construction Stages for Black Warrior Parkway Spliced-Girder Bridge

trb2003-001620

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