an investigation on transversely prestressed concrete bridge decks (1)
DESCRIPTION
llTRANSCRIPT
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