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