UNIVERSITY Load Capacity Evaluation of … 2003 prz.pdfStandard Design Dwgs. 1,651 Single Span...
Transcript of UNIVERSITY Load Capacity Evaluation of … 2003 prz.pdfStandard Design Dwgs. 1,651 Single Span...
Load Capacity Evaluation of Pennsylvania’s Single Span T-Beam Bridges
F. N. Catbas, A. E. Aktan, K. Ciloglu, O. Hasancebi, J. S. PopovicsDrexel Intelligent Infrastructure Institute
UNIVERSITY
Presentation at 2003 TRB Meeting, Washington, D.C.
Research Supported by:
Pennsylvania Department of TransportationFederal Highway Administration
Research Guidance & Contributions by:S. Christie, P. Kiehl, G. Hoffman, W. Williams, S. Chase
Profile of T-beam Bridges in PA
Two-span 1927
1922
Total Number in USA > 32,000Total Number in PA >2600Type Specific Design
Built Between ~1930 & 1950Span ~20 ft -40 ftWidth ~ 20 ft - 40 ftSkew ~ 0 - 45 degSlab Thickness ~ 8-8.5 inBeam Spacing ~ 5 ft on centerBeam Depth ~ 19 in - 40 in
Standard Design Dwgs.
1,651 Single Span T-beam Bridges in PA
Objectives
• Actual load capacity of RC single span T-
beam bridges in PA using state-of-the-art scientific measurement and analysis
techniques
• Load capacity for management purposes in
conformance with AASHTO provisions and
available resources
Scope of the Project
ü Fleet strategy and statistical sampling
ü Field evaluation of 27 bridges, analytical modeling and parameter studies
ü Rigorous field experiments, field-calibrated 3D FE modeling of four bridges and study of the mechanisms affecting rating
ü 3D FE Modeling and analysis of 40 bridges for rating and modified load distribution factors
Fleet Management Concept• Study a statistical sample and project observations to the entir e
fleet
• Major challenges in application to Constructed Systems
– Complexity and ambiguity of performance criteria
– Size, life cycle, variability (no twins)
– Uncertainties in loading and capacity over time
– Lack of measured data and knowledge on system parameters over time
• Load capacity rating of certain populations may be governed a
limited number of parameters. If these parameters are identified
and their variation within the population can be determined, it
should possible to implement fleet strategies.
Statistical Sampling(Location & Density)
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
> 55 ft 0%
16 ft to 32 ft64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span
Entire T-Beam Bridge Population
> 500%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
3
7%
7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
Statistical Representative 60 T-Beam Bridges
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
> 55 ft 0%
16 ft to 32 ft64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
> 55 ft 0%
16 ft to 32 ft64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span
> 55 ft 0%
16 ft to 32 ft64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span
Entire T-Beam Bridge Population
> 500%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span> 50
0%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)> 50
0%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
3
7%
7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
3
7%
7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
3
7%
7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
Statistical Representative 60 T-Beam Bridges
Typical Inspection by the Researchers
• Document the existing conditions– Collaborate with District engineers– Visual inspection and damage
mapping– Photographic/video image
documentation– Measure geometry– Identify load test access and
traffic control requirements– GPS localization
• Local NDE application– Partial coring– Rebound hammer – Characterization of the deck
corrosion• Follow up studies
– Rating using AASHTO Manual– Documentation into GIS based
database
Visual Inspection
Concrete Coring
Visual Documentation of Deterioration
Cross Section of the Model
16.85
15.5
15.75
8.5
T-Beams
Parapet
End Diaphragm
Rebar Layout Structural Details and Boundary Conditions
Statistics of The ModelNumber of DOF =108243Number of Solid Elements = 22940Number of Frame Elements = 7636 3.375”
12”3.375”
3D FE Modeling of a RC T-beam Bridge using Solid and Frame Elements
Field Tests and Instrumentation
Swan Road Bridge
Displacement Sensor Location
Steel Strain Sensor Location Concrete Strain Gauge Location
A-A
A B C D E F
3
2
1
CL
CL
B-B
Truck and Sensor Locations:
Modal Analysis of the Swan Road Bridge
39.4334.1955.403
35.6927.3141.262
25.8314.6422.381
Calib. FEM(Hz)
Nominal FEM(Hz)
Test(Hz)
Modes
Mode 2 Mode 3
Mode 1
Measurements and Correlation of FE Models for Swan Road Bridge
Transverse Centerline Deflection of the Superstructure (Test vs. Models)
Def
lect
ion
(in
)
-0.010
-0.020
-0.030
0
-0.040
-0.050
-0.060
-0.070
Section A-A
A2 B2 C2 D2 E2 F2
K K
K = 1000 kip/in
Boundary Condition Idealization of Different Models:
Displacement Sensor Location
A-A
A B C D E F
3
2
1
CL
CL
Truck and Sensor Locations:
-0.010
-0.020
-0.030
0
Def
lect
ion
(in
)
-0.040
-0.050
-0.060
-0.070
Deflection of the T-Beam "C" (Test vs. Models)
Superstructure
C3 C2 C1
Section B-B
B-B
48.0 kips51.5 kips
3D FEM Stress Outputs to Compute Load Demand
Model Normal Stress Distribution (psi) due to the Most Critical Live Load
Configuration (Moment values are kip-in)
Shear Stress (psi) Distribution due to the Most Critical Live Load Configuration
(Shear values are in kips)
As-is Condition w/All Elements, End Restraints & Pin-pin supports
MD= 364 ML= 553 MU= 454
VD= 11.02 VL = 13.53 VU= 117.06
110 (psi) 0 -110 -220 0 36 72 (psi) 36 72
Current and Projected Condition for Swan Road Bridge
As-is Condition with All Elements, End Restraints, Pin-pin Supports (using calibrated FEM)
RFM=3.18, RFV=2.69
Projected Extreme Deterioration (using calib. FEM)
RFM=2.11, RFV=2.30
BAR7 AnalysisRFM=1.27, RFV=1.80
x DF
Parametric Study for Swan Road Bridge
BAR7 Analysis (Swan Road Bridge)
RFM=1.27,RFV=1.80
Pin-roller Supports with Parapets and Diaphragms (Nominal FEM) w/o pavement thrust
RFM=1.99, RFV=3.90
Pin-pin Supports with Parapets and Diaphragms (Nominal FEM) w/o pavement thrust
RFM=3.05, RFV=3.54
Pin-roller Supports without Parapets and Diaphragms (Nominal FEM) w/o pavement thrust
RFM=1.44, RFV=2.64
Pin-roller Supports with Parapets and without Diaphragms (Nominal FEM) w/o pavement thrust
RFM=1.88, RFV=3.10
Pin-roller Supports without Parapets and without Diaphragms (Nominal FEM) and with Extreme Deterioration w/o pavement thrust
RFM=0.88, RFV=1.97
X DF
BAR7 and FEM based Load Rating
Ratio (FEM/AASHTO) = 5.10
BAR7 Rating = 1.01
Field Calibrated FEM = 5.15Ratio (FEM/AASHTO) = 2.75
BAR7 Rating = 1.22
Field Calibrated FEM = 3.35
Ratio (FEM/AASHTO) = 2.50
BAR7 Rating = 1.27Field Calibrated FEM = 3.18
Ratio (FEM/AASHTO) = 3.46
BAR7 Rating = 0.92Field Calibrated FEM = 3.18
Mechanisms That Contribute To Higher Load Rating by FE Analysis
v Demand Mechanisms
• Compression due to Earth Pressure and Pavement Thrust
• Restrained Boundaries
• Reinforced Concrete Parapets
• Diaphragm Beams
• Lateral Load Distribution due Slab
• Effective Force Redistribution Due To Cracking
v Capacity Mechanisms
• Bi-axial State of Concrete due to Restraints at the Boundaries
• Higher Yield Strength and Strain Hardening of Steel
• Multiple Rebar Layers
• Yield Line Capacity of Slab
Lateral Distribution Factor -Justification
• Actual load capacity rating much greater than BAR7
• Utilizing the entire actual load capacity may not be justified as per AASHTO provisions/practice
– 3D FE analysis of all bridges impractical
– Relying on secondary elements (diaphragm beams, parapets) and boundary elements not typical
– Effects of continuing deterioration on capacity and failure modeunclear
Lateral Distribution Factor -Derivation
• Microscopic 3D FE Models of 40 bridges not
incorporating secondary elements and
mechanisms were analyzed to derive lateral
distribution factors for BAR7 analysis
• Resulting FE based RFs are 10% - 55% higher
than given AASHTO LFD RFs computed using
Load Distribution Factors
DF for Critical Moment
Live Load Moment Distribution Factors for 90 deg Skewed Bridges
0.200
0.300
0.400
0.500
0.600
0.700
0.800
22 24 26 28 30 32 34 36 38 40 42 44Span Length (ft)
Dis
trib
utio
n F
acto
rs
Drexel FEM Moment Distribution Factor for 90 deg SkewCurve Fit and Closed Form DF Formulation
AASHTO LFD Moment Distribution FactorAASHTO LRFD One Lane Moment Distribution Factor for 90 deg Skew
AASHTO LRFD Two Lane Moment Distribution Factor for 90 deg Skew
Distribution Factor Equations
32’-42’θ=30-45
24’-32’θ=30-45
32’-42’θ=0-30
24’-32’θ=0-30
Moment DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges)
Range
32’-42’θ=0-45
24’-32’θ=0-45
Shear DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges)
Range
[ ]
−∗++∗∗−∗= −
15101.0185.1106170115 52 θ
LLg
[ ]
−∗+∗+∗−= −
151013.0104007888.62 5 θ
Lg
[ ]
−∗++∗∗−∗= −
152
5021.0009.110506745.94 52 θLLg
[ ]
−∗+∗+∗= −
152
502.0103347606.36 5 θLg
AASHTO LRFD Bridge Design Specs.
if θ <30 then c1=0.0if θ >60 then θ =60
AASHTO Standard Specs for Highway Bridges (LFD)
If S exceeds 10 ft: Assume flooring between stringers acts as a simple beam with the load on each stringer being the wheel load reaction
Moment DF for Two Design Lane Loaded
Range
( )[ ]5.113
2.06.0
tan10.125.9
075.0 θcLt
K
LSS
gs
g −
+=
4
24020125.4
165.3
≥
≤≤≤≤
≤≤
b
s
N
Lt
S
AASHTO LRFD Bridge Design Specs.
AASHTO Standard Specs for Highway Bridges (LFD)For T-beams S < 6 ft
Shear DF for Two Design Lane LoadedRange
+
−
+= θtan
0.1220.01
35122.0
3.032
g
s
KLtSS
g
600
710
424020
125.4165.3
≤≤
≤≤
≥≤≤
≤≤≤≤
θ
MKK
NL
tS
g
b
s
621 S
g ∗=
−
+∗=S
Sg
41
21
Current AASHTO Equations T-Beam BridgesEquations Derived for Single Span T-Beam Population
[ ]
−∗++∗∗−∗= − 1
452
022.018664.2103.91455.124 52 θLLg
[ ]
−∗+∗+∗= − 1
452032.01030315744 5 θLg
S (beam spacing), L (span of beam), K g (long. Stiffness parameter), ts (slab thickess) (See AASHTO LRFD Specs for details)
=
5.025.0
31 1225.0
LS
Lt
Kc
s
g
g=distribution factorL=clear span as given in PA Standards for Old Bridgesθ=skew angle
Conclusions• Promise of fleet approach/Statistics
• Field-calibrated 3D microscopic FE Modeling
• Actual RF = 2.5 – 5 X BAR7 RF
• 10% - 55% increase in rating factors only due to proper simulation of lateral load distribution
• Whether shear or flexure governs the actual load capacity and rating is one remaining very important issue
• Tests of most deteriorated bridges should be conducted at higher load levels and up to failure