Prestressed Concrete Bridge Decks

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25 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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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



s
?

q [F/L]

Assumption:

Linear behavior

L
C
Girders
Diaphragms
1
2
3
4
5
6
7
8
9
17
16
15
14
13
12
11
1
10
18
19
20
21
22
23
27
26
25
24
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

1.2ksi

1.2ksi

0.6ksi

)
psi
(
f
57
)
ksi
(
E
strain
measured
:
where
E
'
c
c
c
exp





s
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






42

38

38

40

Max

14

14

14

16

m

3D(III)

3D(II)

3D(I)

2D

Modeling Type

Top


Stresses

m 
mean[(
s
s
/
s
exp
)
-
1]x100%

M
ax

Max[(
s
s
/
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 ft
6 @ 8.83 ft
2.5 ft
q/h = 100

q/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 1
Location 2
Location 3
Location 4
Location 5
Location 6
Location 7
Location 13
Location 14
Location 18
Location 19
Stripe 1
Stripe 2
18 @ 25.33 in.
L
C
x

Normalized stress =
s
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.
Normalized Stress
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.
Normalized Stress
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.
Normalized Stress
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.
Normalized Stress
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)
Normalized Stress
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 Stress
(for Unit stress at middepth of flange)
Beff x h

Beff

Diaphragm Location vs. Effective Width

y = 30 x - 23.5
R2 = 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

0

50

100

150

200

250

300

350

400

Beff (in.)

Beff 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)
Normalized Stress
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