an investigation on transversely prestressed concrete bridge decks (1)

An Investigation on Transversely Prestressed Concrete Bridge Decks

J. Paul Smith

Objective

Study of transverse post-tensioning of concrete bridge decks as an alternative to improve durability.

Types of Bridges in Indiana

0%

20%

40%

60%

80%

Slab & slab-on-girder Box-beam

Type of RC bridge

Scope

Develop design specifications applicable to:

– Slab bridges– Slab-on-Girder bridges

Problem Statement

?q [F/L]

Assumption:

Linear behavior

LC

Girders

Diaphragms

1 2 3 4 56

7

8

9

17161514131211

1

10

18 19 20 21 22 23

27262524

0.6

ksi

1.2

ksi

0.6

ksi

1.2

ksi

8.70ft

4.80ft

1.80ft

1.80ft

11 ft

5.5 ft

Specimen for Experimental Phase of Texas Study

Location of strain gages

1.2k

si1.

2ksi

0.6k

si

)psi(f57)ksi(E

strainmeasured:

where

E

'cc

cexp

3.78 in.

9.64 in.

3.48 in.

9.87 in.

3.14 in.

8.52 in.

4.82 in.

6.28 in.

9.64 in.

3.59 in.

4.82 in.

3.48 in.

3.78 in.

8.52 in.

beam

shell• 2D Model

Modeling Alternatives (SAP2000)

• 3D Model

(slab as shell)

Girders and diaphragms as beams (Type I)

Flanges as beams and webs as shells Diaphs. as beam (Type III)

Diaphs. as shells (Type II)

Comparison of Analytical (SAP2000) & Experimental (Texas Study) Results

42383840Max

14141416

3D(III)3D(II)3D(I)2D

Modeling TypeTop

Stresses

mean[(s/exp)-1]x100%ax Max[(s/exp)-1]x100%

Analysis using ANSYS 5.7

•Alternative modeling:

Use brick and shell elements

SAP2000 vs. ANSYS 5.7(Texas Model)

Variables of Interest

• Girders (spacing, stiffness)

• Diaphragms (spacing, stiffness, location)

• Boundary conditions

• Post-tensioning spacing

• Slab thickness

Base Case

22 in.

24.33 ft

25.34 ft

24.33 ft

1.00 ft

1.00 ft6 @ 8.83 ft

2.5 ftq/h = 100q/h = 100

7 in.

22 in.

14 in.

10.75 in.

8.25 in.

7.75 in.

21.5 in.27 in.

27 in.21.5 in.

8.25 in.

7.75 in.

10.75 in.

8 in.

Preliminary Evaluation of Variables (2D Modeling)

• Base Case:

Preliminary Evaluation of Variables (2D Modeling)

• Effect of Girder Spacing:

a) Half Spacing b) Quarter Spacing

Preliminary Evaluation of Variables (2D Modeling)

• Effect of Girder (No diaphragms):

a) Concrete girders b) Steel girders

Preliminary Evaluation of Variables (2D Modeling)

• Effect of Diaphragms:

Bottom half: diaphragms no present

Top half:

diaphragms present

Preliminary Evaluation of Variables (2D Modeling)

• Effect of boundary conditions:

Fully restrained except against displacement in x

Restrained against displacement in x

Preliminary Evaluation of Variables (2D Modeling)

• Effect of Post-tensioning Spacing:

a) Forces at every other node: b) Forces every four nodes:

@ 4’ @ 8’

Preliminary Evaluation of Variables (2D Modeling)

• Effect of Slab Thickness:

8” slab

6” slab

Preliminary Identification of Relevant Variables (2D Modeling)

• Diaphragms (stiffness, location, spacing)

• Boundary conditions

• Post-tensioning spacing

Effect of Diaphragms

Distribution of transverse stresses is mainly affected by diaphragm size and location.

Notation

y

Location 1Location 2Location 3Location 4Location 5Location 6Location 7

Location 13Location 14

Location 18Location 19

Str

ipe

1

Str

ipe

2

18 @ 25.33 in.

LC

x

Normalized stress = s/q

Effect of Diaphragm Size

Stripe 1 Stripe 2

y y

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

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

Location No.

Norm

aliz

ed S

tress

Ad (in2) =65

Ad (in2) =176

Ad (in2) =270

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

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

Location No.

Nor

mal

ized

Str

ess

Ad (in2) =65

Ad (in2) =176

Ad (in2) =270

Effect of Diaphragm Location(Exterior Diaphragms Only)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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

Location No.

Nor

mal

ized

Stre

ss

Location 1

Location 3

Location 5

Location 7

Location 9

Location 13

Location 17

Diaphragm Position

Stripe 1 Stripe 2

y y

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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

Location No.

Nor

mal

ized

Str

ess

Location 1

Location 3

Location 5

Location 7

Location 9

Location 13

Location 17

Diaphragm Position

Minimum Stress vs. Diaphragm Position

0.4

0.5

0.6

0.7

0.8

0.9

1

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

Location No. (of diaphragm)

No

rma

lize

d S

tre

ss

Effective Width of T Beam vs. Top Stress

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 50 100 150 200 250 300 350 400

Beff (in.)

Top S

tress

(f

or

Unit

stre

ss a

t m

iddep

th o

f fla

nge)

Beff x h

Beff

Diaphragm Location vs. Effective Width

y = 30 x - 23.5R2 = 0.99

20

100

180

260

340

420

500

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

Location No.

Beff (

in.)

0.40

0.50

0.60

0.70

0.80

0.90

1.00

050

100

150

200

250

300

350

400

Bef

f (in

.)

Bef

f x

h

0.4

0.5

0.6

0.7

0.8

0.9

1

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

Location No. (of diaphragm)

No

rma

lize

d S

tre

ss

Conclusions at this Stage

• Distribution of transverse stresses mainly influenced by:

» Diaphragm axial stiffness and position» Boundary conditions

• Influence of diaphragm position: Rationalized using T-beam analogy