Presentation at 2003 TRB Meeting, Washington, D.C. UNIVERSITY Load Capacity Evaluation of Pennsylvania s Single Span T-Beam Bridges F. N. Catbas, A. E. Aktan, K. Ciloglu, O. Hasancebi, J. S. Popovics Drexel Intelligent Infrastructure Institute Research Supported by: Pennsylvania Department of Transportation Federal Highway Administration Research Guidance & Contributions by: S. Christie, P. Kiehl, G. Hoffman, W. Williams, S. Chase
Profile of T-beam Bridges in PA 1,651 Single Span T-beam Bridges in PA 1922 Standard Design Dwgs. Total Number in USA > 32,000 Total Number in PA >2600 Type Specific Design Built Between ~1930 & 1950 Span ~20 ft -40 ft Two-span Width ~ 20 ft - 40 ft 1927 Skew ~ 0-45 deg Slab Thickness ~ 8-8.5 in Beam Spacing ~ 5 ft on center Beam Depth ~ 19 in - 40 in
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 Fleet strategy and statistical sampling Field evaluation of 27 bridges, analytical modeling and parameter studies Rigorous field experiments, field-calibrated 3D FE modeling of four bridges and study of the mechanisms affecting rating 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 entire 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) Entire T-Beam Bridge Population > 55 ft 0% 41 ft to 55 ft 14% 33ft to 40 ft 22% Span Skew Angle (deg) 38 to 50 20% 64% 23 to 37 16 ft to 32 ft 22% > 50 1% 8 to 22 19% 0 to 7 38% Condition Rating 3 3% 7 to 8 18% 4 20% 6 23% 5 36% Age < 1929 >1948 24% 24% 1939 to 1948 1929 to 1938 18% 34% Statistical Representative 60 T-Beam Bridges Span > 55 ft 0% 41 ft to 55 ft 20% Skew 33ft to 40ft 62% Angle 18% (degrees) 16 ft to 32 ft Skew Angle (deg) > 50 0% Condition Rating 38 to 50 7 to 8 3 17% 15% 7% 0 to 7 6 4 23 to 37 17% 27% 22% 43% 8 to 22 5 34% 18% Age > 1948 < 1929 23% 30% 1939 to 1948 17% 1929 to 1938 30%
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
3D FE Modeling of a RC T-beam Bridge using Solid and Frame Elements Cross Section of the Model 16.85 15.5 Rebar Layout 15.75 8.5 Statistics of The Model Number of DOF =108243 3.375 Number of Solid Elements = 22940 Number of Frame Elements = 7636 3.375 Structural Details and Boundary Conditions 12 Parapet End Diaphragm T-Beams
Field Tests and Instrumentation
Swan Road Bridge Truck and Sensor Locations: A B CCL D E F 1 2 CL 3 A-A Displacement Sensor Location B-B Steel Strain Sensor Location Concrete Strain Gauge Location
Modal Analysis of the Swan Road Bridge Modes Test (Hz) Nominal FEM (Hz) Calib. FEM (Hz) 1 22.38 14.64 25.83 2 41.26 27.31 35.69 Mode 1 3 55.40 34.19 39.43 Mode 2 Mode 3
Measurements and Correlation of FE Models for Swan Road Bridge Section A-A Section B-B 51.5 kips 48.0 kips Superstructure A2 B2 C2 D2 E2 F2 0-0.010-0.020 0-0.010-0.020 C3 C2 C1 Deflection (in) -0.030-0.040-0.050-0.060-0.070 Transverse Centerline Deflection of the Superstructure (Test vs. Models) Deflection (in) -0.030-0.040-0.050-0.060-0.070 Deflection of the T-Beam "C" (Test vs. Models) Truck and Sensor Locations: A B CCL D E F Boundary Condition Idealization of Different Models: 1 K K Displacement Sensor Location 2 3 A-A CL B-B K = 1000 kip/in
3D FEM Stress Outputs to Compute Load Demand Model As-is Condition w/all Elements, End Restraints & Pin-pin supports Normal Stress Distribution (psi) due to the Most Critical Live Load Configuration (Moment values are kip-in) M D = 364 M L = 553 M U = 454 Shear Stress (psi) Distribution due to the Most Critical Live Load Configuration (Shear values are in kips) V D = 11.02 V L = 13.53 V U = 117.06-220 -110 0 110 (psi) 72 36 0 36 72 (psi)
Current and Projected Condition for Swan Road Bridge x DF BAR7 Analysis RFM=1.27, RFV=1.80 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
Parametric Study for Swan Road Bridge X DF BAR7 Analysis (Swan Road Bridge) RF M =1.27,RF V =1.80 Pin-pin Supports with Parapets and Diaphragms (Nominal FEM) w/o pavement thrust RF M =3.05, RF V =3.54 Pin-roller Supports with Parapets and Diaphragms (Nominal FEM) w/o pavement thrust RF M =1.99, RF V =3.90 Pin-roller Supports with Parapets and without Diaphragms (Nominal FEM) w/o pavement thrust RF M =1.88, RF V =3.10 Pin-roller Supports without Parapets and Diaphragms (Nominal FEM) w/o pavement thrust RFM=1.44, RFV=2.64 Pin-roller Supports without Parapets and without Diaphragms (Nominal FEM) and with Extreme Deterioration w/o pavement thrust RF M =0.88, RF V =1.97
BAR7 and FEM based Load Rating BAR7 Rating = 0.92 Field Calibrated FEM = 3.18 Ratio (FEM/AASHTO) = 3.46 BAR7 Rating = 1.27 Field Calibrated FEM = 3.18 Ratio (FEM/AASHTO) = 2.50 BAR7 Rating = 1.22 Field Calibrated FEM = 3.35 Ratio (FEM/AASHTO) = 2.75 BAR7 Rating = 1.01 Field Calibrated FEM = 5.15 Ratio (FEM/AASHTO) = 5.10
Mechanisms That Contribute To Higher Load Rating by FE Analysis Demand Mechanisms Compression due to Earth Pressure and Pavement Thrust Restrained Boundaries Reinforced Concrete Parapets 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 Diaphragm Beams Lateral Load Distribution due Slab Effective Force Redistribution Due To Cracking
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 mode unclear
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 Distribution Factors Live Load Moment Distribution Factors for 90 deg Skewed Bridges 0.800 0.700 0.600 0.500 0.400 AASHTO LRFD Two Lane Moment Distribution Factor for 90 deg Skew AASHTO LFD Moment Distribution Factor AASHTO LRFD One Lane Moment Distribution Factor for 90 deg Skew 0.300 0.200 Drexel FEM Moment Distribution Factor for 90 deg Skew Curve Fit and Closed Form DF Formulation 22 24 26 28 30 32 34 36 38 40 42 44 Span Length (ft)
Distribution Factor Equations Range 24-32 θ=0-30 32-42 θ=0-30 24-32 θ=30-45 32-42 θ=30-45 Equations Derived for Single Span T-Beam Population g g Moment DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges) [ 2 ] 5 θ 115 L 6170 L 10 + 1.185 + 0.01 1 = g 15 [ + ] 5 θ 62.88 L 40078 10 + 0.013 1 = 15 [ 2 ] 5 2θ 94.45 L 5067 L 10 + 1.009 + 0.021 5 = g 15 [ + ] 5 θ 36.06 L 33476 10 + 0.02 5 = 2 15 Current AASHTO Equations T-Beam Bridges Range 3.5 S 16 4.5 t 12 20 L 240 s N b 4 if θ <30 then c 1 =0.0 if θ >60 then θ =60 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 AASHTO LRFD Bridge Design Specs. [ 1 c ( tan ) ] 1.5 0.6 0.2 S S K g g = 0.075 + 3 1 θ 9.5 L 12.0Lt s 0.25 0.5 K g S c 1 = 0.25 3 12Lt s L AASHTO Standard Specs for Highway Bridges (LFD) g = 1 S 2 6 Range 24-32 θ=0-45 32-42 θ=0-45 Shear DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges) g = g = 5 2θ [ 744 L + 30315] 10 + 0.032 1 2 5 2θ [ 124.5 L 9145.3 L] 10 + 2.18664 + 0.022 1 45 g=distribution factor L=clear span as given in PA Standards for Old Bridges θ=skew angle 45 Range 3.5 S 16 4.5 t 20 L 240 N b s 4 10 K K 12 0 θ 60 7M For T-beams S < 6 ft g Shear DF for Two Design Lane Loaded AASHTO LRFD Bridge Design Specs. 2 0.3 3 S S 12.0Lt + s g = 0.2 + 1 0.20 tanθ 12 35 K g AASHTO Standard Specs for Highway Bridges (LFD) 1 S 4 g = 1+ 2 S S (beam spacing), L (span of beam), K g (long. Stiffness parameter), t s (slab thickess) (See AASHTO LRFD Specs for details)
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