Evaluation Methods for Bridges in Categories C and D

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1 Evaluation Methods for Bridges in Categories C and D Presented by Ian Buckle Civil and Environmental Engineering University of Nevada Reno MULTIDISCIPLINARY CENTER FOR EARTHQUAKE ENGINEERING RESEARCH Yes Pass Pass Is Bridge Exempt? No Screen / prioritize Evaluate Fail Fail Review Next bridge Retrofit 1

2 Minimum requirements ACTION SEISMIC RETROFIT CATEGORY A B C D Screening/ Retrofitting NR Seats, connections, liquefaction B + columns, walls, footings C + abutments Evaluation Methods NR A1/A2 B/C/D1/D2 C/D1/D2/E Minimum requirements ACTION SEISMIC RETROFIT CATEGORY A B C D Screening/ Retrofitting NR Seats, connections, liquefaction B + columns, walls, footings C + abutments Evaluation Methods NR A1/A2 B/C/D1/D2 C/D1/D2/E 2

3 Detailed evaluation Methods of Evaluation (6). These include both demand and analyses/ assessments (exceptions exist). Tools for the Evaluation Methods. These include: Structural modeling Assessment of bridge for strength and deformation Geotechnical modeling Assessment of foundation for strength and deformation Methods of evaluation In general, all evaluation methods involve (figure 1-13): Demand analysis Capacity assessment Calculation of a / demand ratio either for each critical component in a bridge or for bridge as a complete system Exceptions exist 3

4 Methods of evaluation continued Three categories, six methods: I. No demand analysis 1.Method A1/A2 ( checks made for seats and connections) 2. Method B ( checks made for seats connections, columns, and footings) II. Component C/D evaluation 3. Method C (elastic analysis: uniform load method, multimode spectral analysis; prescriptive rules given for calculation of component ) Methods of evaluation continued III. Structure C/D evaluation 4. Method D1 (-spectrum method: elastic analysis for demands, simplified models for calculation of ; 5. Method D2 (pushover method: elastic analysis for demands, nonlinear static analysis used for calculation of pier ) 6. Method E (nonlinear time history analysis for calculation of both demand and ) 4

5 Evaluation methods (T5-1) A1/ A2 B C D1 D2 E METHOD Connection and Seat Width Checks Component Capacity Checks Component Capacity/Demand Method Capacity Spectrum Method Structure Capacity/Demand Method Nonlinear Dynamic Method CAPACITY ASSESSMENT Uses default due to non-seismic loads for connections and seat widths. Uses default due to non-seismic loads for connections, seats, columns and foundations. Uses component capacities for connections, seat widths, column details, footings, and liquefaction susceptibility (11 items). Uses bilinear representation of structure for lateral load, subject to restrictions on bridge regularity. Uses pushover curve from detailed analysis of superstructure, individual piers and foundation limit states. Uses component capacities for connections, seat widths, columns and footings. DEMAND ANALYSIS Not required SRC 1 A D B APPLICABILITY Bridge Type All single-span bridges. Bridges in low hazard zones. Not required C Regular bridges, but subject to limitations on FvS1. Elastic Methods 2 : ULM MM TH Elastic Methods 2 : ULM Elastic Methods 2 : ULM MM TH Inelastic Methods 2 TH C & D C & D Regular and irregular bridges that respond almost elastically, such as those in low-to-moderate seismic zones and those with stringent performance criteria. Regular bridges that behave as single-degree-of-freedom systems and have rigid in-plane superstructures. COMMENTS Hand method, spreadsheet useful. Hand method, spreadsheet useful. Calculates C/D ratios for individual components. This is the C:D Method of previous FHWA Highway Bridge Retrofitting Manuals. Software required for demand analysis. Calculates C/D ratios for complete bridge, for specified limit states. Spreadsheet useful. C & D Regular and irregular bridges. Calculates C/D ratios for bridge superstructure, individual piers, and foundations. Also known as Nonlinear Static Procedure or Displacement Capacity Evaluation Method. Software required for demand and analysis. D Irregular complex bridges, or when site specific ground motions are to be used such as for bridges of major importance. Most rigorous method, expert skill required. Software essential. Methods A1, A2 and B No demand analysis required, only a assessment A1/A2 previously described B - Component Capacity Method An extension of A1/A2 to columns, column/footing connections, column/superstructure connections, but not abutments. 5

6 Method B: component method 1. Check applicability of method (restrictions) 2. Check all seats, bearings and connections as per Method A2 3. Check that reinforced concrete columns have minimum longitudinal reinforcement of 0.8% reinforcement details satisfying current AASHTO specifications for shear and confinement 4. Check steel columns for compactness Method B continued 5. Check adjacent members for strength to resist shears and moments caused by plastic hinging in columns, using an overstrength ratio of Check foundations for strength to resist shears and moments caused by plastic hinging in columns, using an overstrength ratio of 1.0 6

7 Restrictions on Method B Low to moderate hazard: Seismic Hazard Levels I and II Limitations on: column axial load longitudinal reinforcement ratio smallest column dimension or diameter M:VD ratio Bridge regularity (skew, curvature, span length, stiffness and mass distribution) Foundation type if a liquefiable site (piled) Method C: component /demand method Capacity/demand ratios calculated for all components r = R C ΣQ Q EQ NSi Based on elastic response In 1983 and 1995 FHWA Retrofit Manual 7

8 Required C/D ratios Component Seismic Retrofit Category B C and D EXPANSION JOINTS AND BEARINGS Support Length x x Connection Forces x x REINFORCED CONCRETE COLUMNS WALLS AND FOOTINGS Anchorage Splices Shear Confinement Footing Rotation ABUTMENTS Displacement LIQUEFACTION Lateral Spread x x x x x x x x Method C: component C/D ratio method Analysis methods for demand include Uniform Load Method Multi-mode Spectral Analysis Method Elastic Time History Method Assessment methods for in next section Two examples in Appendices E and F 8

9 Restrictions on Method C Applicable to bridges responding almost elastically ( essentially elastic behavior) such as those in low-moderate seismic zones and/or required to behave elastically to satisfy Performance Level requirements Method D1: -spectrum method Direct consideration of inelastic behavior; quick estimate Restricted to bridges that can be modeled as a single degree of freedom (SDOF); assumes the same deflection at the tops of all piers Uses a pushover curve 9

10 Capacity curves (pushover curves) Limit states: 1. End of essentially elastic behavior 2. Expansion joint closure and span lock-up 3. Bearing failure 4. Span collapse Displacement limit states, LS LS1 = y LS2 = θ p LS3 = N 0 LS4 = P- < θ p H (plastic hinge, θ p = 0.035) (seat width) (P- limit = max) ' W max 0.25CC H P 10

11 Idealized curves Method D1 continued Earthquake demand Long period bridges g FS v 1 Cd = fort TS Sd 2πBL 2 Short period bridges FS a S Cd = for T< TS BS 11

12 Demand spectrum Capacity/demand spectra 12

13 C/D ratios for each limit state LSi ( FS v ) ( FS ) 1 LSi r = fort T v 1 d S where LS ( FS ) = 2π B C v 1 LS L cls g LSi ( FS ) ( FS ) a S LSi r = fort< T a S d S where (FaSs) LS = Bs C cls Method D1 continued Can be used to calculate: Capacity demand ratios, r Bridge response, F- (iterative method) Restrictions: SDOF behavior Superstructure acts as rigid diaphragm Regular (stiffness, mass distribution) 13

14 Method D2: Capacity/Demand For bridges not satisfying restrictions on Method D1 Uses multi-modal or elastic time-history methods to find EQdi Capacity/demand ratios: r LSi = ( ) ci EQdi NSdi Method E: Nonlinear dynamic time history method Non-linear time history analysis for demands, using inelastic models for material behavior Compare results against calculated capacities r LSi = ( ) ci EQdi NSdi 14

15 SEISMIC RETROFIT CATEGORY and BRIDGE TYPE METHOD A sec 5.2 METHOD B sec 5.3 METHOD C sec 5.4 METHOD D1/D2 sec 5.5 / 5.6 METHOD E sec 5.7 DEMAND ANALYSIS No analysis req'd Min. seat and force requirements are specified No modelling req'd No analysis req'd Min. seat and force requirements are specified No modelling req'd Elastic Analysis (Uniform Load (ULM) Multimode (MM) Time History (TH) Methods) Modeling as per sec 7.3 Elastic Analysis (Response spectrum methods ULM, SM, MM) Modeling as per sec 7.3 Nonlinear Analysis (3 Dimensional, Time History Method) Modeling as per sec 7.3 Demand on pier caps and footings calculated from column overstrength, sec 7.6 Combination of seismic force effects, sec 7.4 Combination of seismic force effects, sec 7.4 CAPACITY ASSESSMENT Seat widths by inspection Connection by calculation Seat widths by inspection Connection by calculation Columnns must satisfy min. shear and confining steel requirements Column overstrength, sec 7.7 Component capacities using Appendix D Capacity/Demand ratios for: Abutment displacement Anchorage length Bearing connection force Column moment Column shear Confinement steel Footing moment Footing rotation Liquefaction potential Seat width Splice length Either bridge curve (D1) or pier curve (D2) Forces and moments in piers due to overstrength, sec 7.6 Strength sec 7.7 Detailed bridge model includes member capacities Forces and moments in piers due to overstrength, sec 7.6 Strength sec 7.7 Deformation sec 7.8 Deformation sec 7.8 SEISMIC RETROFIT CATEGORY and BRIDGE TYPE METHOD A sec 5.2 METHOD B sec 5.3 METHOD C sec 5.4 METHOD D1/D2 sec 5.5 / 5.6 METHOD E sec 5.7 DEMAND ANALYSIS No analysis req'd Min. seat and force requirements are specified No modelling req'd No analysis req'd Min. seat and force requirements are specified No modelling req'd Elastic Analysis (Uniform Load (ULM) Multimode (MM) Time History (TH) Methods) Modeling as per sec 7.3 Elastic Analysis (Response spectrum methods ULM, SM, MM) Modeling as per sec 7.3 Nonlinear Analysis (3 Dimensional, Time History Method) Modeling as per sec 7.3 Demand on pier caps and footings calculated from column overstrength, sec 7.6 Combination of seismic force effects, sec 7.4 Combination of seismic force effects, sec

16 CAPACITY ASSESSMENT Seat widths by inspection Connection by calculation Seat widths by inspection Connection by calculation Columnns must satisfy min. shear and confining steel requirements Column overstrength, sec 7.7 Component capacities using Appendix D Capacity/Demand ratios for: Abutment displacement Anchorage length Bearing connection force Column moment Column shear Confinement steel Footing moment Footing rotation Liquefaction potential Seat width Splice length Either bridge curve (D1) or pier curve (D2) Forces and moments in piers due to overstrength, sec 7.6 Strength sec 7.7 Detailed bridge model includes member capacities Forces and moments in piers due to overstrength, sec 7.6 Strength sec 7.7 Deformation sec 7.8 Deformation sec 7.8 Structural modeling Load path Modeling recommendations Combination of seismic forces Member strength capacities Member deformation capacities 16

17 Load path Identify clear load path for lateral loads: Deck slab and connectors (studs) Cross frames (diaphragms) Longitudinal beams (girders) Bearings and anchorages Pier (cap beam, columns, walls) Abutments and foundations (back wall, footing, piles) Soils Structural modeling recommendations Distribution of mass Distribution of stiffness and strength Damping In-span Hinges Substructures Superstructures 17

18 Combination of seismic forces Loading in 2- or 3-orthogonal directions: SRSS Rule % Rule Response quantities in biaxial design: SRSS Rule % Rule Member strengths Nominal strength, S n Design strength, S d = φ S n (φ<1) Expected strength, S e = φ e S n (φ e >1) Overstrength, S o = φ o S n (φ o >1) 18

19 Member strength capacities Flexural and shear strength of reinforced concrete columns and beams Expected flexural strength Flexural overstrength Flexural strength of columns with lapsplices in plastic hinge zones Initial shear strength Final shear strength Strength capacities continued Shear strength of reinforced concrete beam-column joints Maximum beam-column joint strength Cracked beam-column joint strength 19

20 Member deformation capacities Plastic curvature & hinge rotations Deformation-based limit states Compression failure of confined and unconfined concrete Buckling longitudinal bars Tensile fracture longitudinal bars Low-cycle fatigue longitudinal bars Failure in lap-splice zone CAPACITY ASSESSMENT Seat widths by inspection Connection by calculation Seat widths by inspection Connection by calculation Columnns must satisfy min. shear and confining steel requirements Column overstrength, sec 7.7 Component capacities using Appendix D Capacity/Demand ratios for: Abutment displacement Anchorage length Bearing connection force Column moment Column shear Confinement steel Footing moment Footing rotation Liquefaction potential Seat width Splice length Either bridge curve (D1) or pier curve (D2) Forces and moments in piers due to overstrength, sec 7.6 Strength sec 7.7 Detailed bridge model includes member capacities Forces and moments in piers due to overstrength, sec 7.6 Strength sec 7.7 Deformation sec 7.8 Deformation sec

21 Geotechnical modeling Geotechnical Modeling and Capacity Assessment Foundation Modeling Equivalent linear stiffness models Capacity models Shallow footing, piles, shafts, abutments Ground Displacement Demands Settlement Liquefaction Induced Lateral Spreads 21

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