2

Minimum requirements________________________________

C/D1/D2/EB/C/D1/D2A1/A2NREvaluation Methods

C + abutments

B + columns, walls, footings

Seats, connections,liquefaction

NRScreening/Retrofitting

DCBA

SEISMIC RETROFIT CATEGORYACTION

Minimum requirements________________________________

C/D1/D2/EB/C/D1/D2A1/A2NREvaluation Methods

C + abutments

B + columns, walls, footings

Seats, connections,liquefaction

NRScreening/Retrofitting

DCBA

SEISMIC RETROFIT CATEGORYACTION

3

Detailed evaluation

Methods of Evaluation (6). These include both demand and capacity analyses/ assessments (exceptions exist).

Tools for the Evaluation Methods. These include:Structural modelingAssessment of bridge capacity for strength and deformationGeotechnical modelingAssessment of foundation capacity for strength and deformation

Methods of evaluation

In general, all evaluation methods involve (figure 1-13):

Demand analysisCapacity assessmentCalculation of a capacity / demand ratio either

for each critical component in a bridge or for bridge as a complete system

Exceptions exist

4

Methods of evaluation continued

Three categories, six methods:I. No demand analysis

1.Method A1/A2 (capacity checks made for seats and connections)

2. Method B (capacity checks made for seatsconnections, columns, and footings)

II. Component C/D evaluation3. Method C (elastic analysis: uniform load

method, multimode spectral analysis;prescriptive rules given for calculation of component capacity)

Methods of evaluation continued

III. Structure C/D evaluation4. Method D1 (capacity-spectrum method:

elastic analysis for demands, simplified models for calculation of capacity;

5. Method D2 (pushover method: elastic analysis for demands, nonlinear static analysis used for calculation of pier capacity)

6. Method E (nonlinear time history analysis for calculation of both demand and capacity)

5

Evaluation methods (T5-1)_________________________________________________________

APPLICABILITY METHOD CAPACITY ASSESSMENT

DEMAND ANALYSIS SRC1 Bridge Type

COMMENTS

A – D All single-span bridges. A1/A2

Connection and Seat Width Checks

Uses default capacity due to non-seismic loads for connections and seat widths.

Not required B Bridges in low hazard zones.

Hand method, spreadsheet useful.

B Component Capacity Checks

Uses default capacity due to non-seismic loads for connections, seats, columns and foundations.

Not required C Regular bridges, but subject to limitations on FvS1.

Hand method, spreadsheet useful.

C Component Capacity/Demand Method

Uses component capacities for connections, seat widths, column details, footings, and liquefaction susceptibility (11 items).

Elastic Methods2:

• ULM • MM • TH

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.

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.

D1 Capacity Spectrum Method

Uses bilinear representation of structure capacity for lateral load, subject to restrictions on bridge regularity.

Elastic Methods2:

• ULM

C & D Regular bridges that behave as single-degree-of-freedom systems and have ‘rigid’ in-plane superstructures.

Calculates C/D ratios for complete bridge, for specified limit states. Spreadsheet useful.

D2 Structure Capacity/Demand Method

Uses pushover curve from detailed analysis of superstructure, individual piers and foundation limit states.

Elastic Methods2:

• ULM • MM • TH

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 capacity analysis.

E Nonlinear Dynamic Method

Uses component capacities for connections, seat widths, columns and footings.

Inelastic Methods2

• TH

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 capacity assessmentA1/A2 previously describedB - Component Capacity Method An extension of A1/A2 to columns, column/footing connections, column/superstructure connections, but not abutments.

6

Method B: component capacity method

1. Check applicability of method (restrictions)2. Check all seats, bearings and connections as

per Method A23. 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 1.4

6. Check foundations for strength to resist shears and moments caused by plastic hinging in columns, using an overstrength ratio of 1.0

7

Restrictions on Method B

Low to moderate hazard:Seismic Hazard Levels I and II

Limitations on: column axial loadlongitudinal reinforcement ratio smallest column dimension or diameterM:VD ratioBridge regularity (skew, curvature, span length, stiffness and mass distribution)Foundation type if a liquefiable site (piled)

Method C: component capacity/demand method

Capacity/demand ratios calculated for all components

Based on elastic responseIn 1983 and 1995 FHWA Retrofit Manual

EQ

NSiCQQRr Σ−=

8

Required C/D ratios__________________________________

Seismic Retrofit Category Component

B C and D

EXPANSION JOINTS AND BEARINGS

Support Length x x Connection Forces x x REINFORCED CONCRETE COLUMNS WALLS AND FOOTINGS

Anchorage x Splices x Shear x Confinement x Footing Rotation x ABUTMENTS

Displacement x LIQUEFACTION Lateral Spread x x

Method C: component C/D ratio method

Analysis methods for demand includeUniform Load MethodMulti-mode Spectral Analysis MethodElastic Time History Method

Assessment methods for capacity in next section Two examples in Appendices E and F

9

Restrictions on Method C

Applicable to bridges responding almost elastically (‘essentially elastic’behavior) such as those

in low-moderate seismic zones and/orrequired to behave elastically to satisfy Performance Level requirements

Method D1: capacity-spectrum method

Direct consideration of inelastic behavior; quick estimateRestricted 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

10

Capacity curves (pushover curves)__________________________________Limit states: 1. End of essentially elastic behavior2. Expansion joint closure and span lock-up3. Bearing failure4. Span collapse

Displacement limit states, ∆LS

∆LS1 = ∆y

∆LS2 = ∆θp < θp H (plastic hinge, θp = 0.035)

∆LS3 = N0 (seat width)∆LS4 = ∆P-∆ (P-∆ limit = ∆max)

'

max CW0.25C HP

⎛ ⎞∆ ≤ ⎜ ⎟⎜ ⎟

⎝ ⎠

11

Idealized capacity curves__________________________________

Method D1 continued

Earthquake demand

Long period bridges

Short period bridges

2

v 1d S

d L

F SgC for T TS 2 B⎡ ⎤ ⎡ ⎤

= ≥⎢ ⎥ ⎢ ⎥π⎣ ⎦⎣ ⎦

a Sd S

S

F SC for T T

B= <

12

Demand spectrum__________________________________

Capacity/demand spectra__________________________________

13

C/D ratios for each limit state

where

where (FaSs)LS = Bs CcLS

( ) LSv 1 L cLSLS

F S 2 B Cg

∆= π

( )( )

v 1 LSiLSi S

v 1 d

F Sr for T T

F S= ≥

( )( )

a S LSiLSi S

a S d

F Sr for T T

F S= <

Method D1 continued

Can be used to calculate:Capacity demand ratios, rBridge response, F-∆ (iterative method)

Restrictions:SDOF behaviorSuperstructure acts as rigid diaphragmRegular (stiffness, mass distribution)

14

Method D2: Capacity/Demand

For bridges not satisfying restrictions on Method D1Uses multi-modal or elastic time-history methods to find ∆EQdi

Capacity/demand ratios:

( )ci NSdiLSi

EQdi

r∆ −∑∆

=∆

Method E: Nonlinear dynamic time history method

Non-linear time history analysis for demands, using inelastic models for material behaviorCompare results against calculated capacities

( )ci NSdiLSi

EQdi

r∆ −∑∆

=∆

15

METHOD Asec 5.2

No analysis req'd

Min. seat and forcerequirements are

specified

No modelling req'd

METHOD Bsec 5.3

No analysis req'd


specified

No modelling req'd

Demand on piercaps and footingscalculated from

columnoverstrength,

sec 7.6

METHOD Csec 5.4

Elastic Analysis(Uniform Load (ULM)

Multimode (MM)Time History (TH)

Methods)Modeling as per

sec 7.3

Seat widths byinspection

Connectioncapacity bycalculation



Columnns mustsatisfy min. shear

and confining steelrequirements

Columnoverstrength,

sec 7.7

Component capacitiesusing Appendix D

Capacity/Demandratios for:

AbutmentdisplacementAnchoragelengthBearingconnection forceColumn momentColumn shearConfinementsteelFooting momentFooting rotationLiquefactionpotentialSeat widthSplice length

METHOD D1/D2sec 5.5 / 5.6

Elastic Analysis(Response

spectrum methodsULM, SM, MM)

Modeling asper sec 7.3

Either bridgecapacity curve (D1)

or pier capacitycurve (D2)

Forces andmoments in piers

due to overstrength,sec 7.6

Strengthcapacity

of bridge members,sec 7.7

Deformationcapacity


Combination ofseismic force effects,

sec 7.4

Combination ofseismic force

effects,sec 7.4

METHOD Esec 5.7

Nonlinear Analysis (3 Dimensional,

Time HistoryMethod)

Modeling as persec 7.3

Detailed bridgemodel includes

member capacities



Strengthcapacity


Deformationcapacity


SEISMIC RETROFIT CATEGORY and BRIDGE TYPE

DEMAND ANALYSIS

CAPACITY ASSESSMENT

METHOD Asec 5.2

No analysis req'd


specified

No modelling req'd

METHOD Bsec 5.3

No analysis req'd


specified

No modelling req'd

Demand on piercaps and footingscalculated from

columnoverstrength,

sec 7.6

METHOD Csec 5.4

Elastic Analysis(Uniform Load (ULM)

Multimode (MM)Time History (TH)

Methods)Modeling as per

sec 7.3

METHOD D1/D2sec 5.5 / 5.6

Elastic Analysis(Response

spectrum methodsULM, SM, MM)

Modeling asper sec 7.3

Combination ofseismic force effects,

sec 7.4

Combination ofseismic force

effects,sec 7.4

METHOD Esec 5.7

Nonlinear Analysis (3 Dimensional,

Time HistoryMethod)

Modeling as persec 7.3

SEISMIC RETROFIT CATEGORY and BRIDGE TYPE

DEMAND ANALYSIS

16





Columnns mustsatisfy min. shearand confining steel

requirements

Columnoverstrength,

sec 7.7








Strengthcapacity


Deformationcapacity



member capacities



Strengthcapacity


Deformationcapacity


CAPACITY ASSESSMENT

Structural modeling

Load pathModeling recommendationsCombination of seismic forcesMember strength capacitiesMember deformation capacities

17

Load path

Identify clear load path for lateral loads: Deck slab and connectors (studs)Cross frames (diaphragms)Longitudinal beams (girders)Bearings and anchoragesPier (cap beam, columns, walls)Abutments and foundations (back wall, footing, piles)Soils

Structural modeling recommendations

Distribution of massDistribution of stiffness and strengthDampingIn-span Hinges

SubstructuresSuperstructures

18

Combination of seismic forces

Loading in 2- or 3-orthogonal directions:SRSS Rule100-40% Rule

Response quantities in biaxial design:SRSS Rule100-40% Rule

Member strengths

Nominal strength, Sn

Design strength, Sd = φ Sn (φ<1)Expected strength, Se = φe Sn (φe>1)Overstrength, So = φo Sn (φo>1)

19

Member strength capacities

Flexural and shear strength of reinforced concrete columns and beams

Expected flexural strength Flexural overstrengthFlexural strength of columns with lap-splices in plastic hinge zonesInitial shear strengthFinal shear strength

Strength capacities continued

Shear strength of reinforced concrete beam-column joints

Maximum beam-column joint strengthCracked beam-column joint strength

20

Member deformation capacities

Plastic curvature & hinge rotationsDeformation-based limit states

Compression failure of confined and unconfined concreteBuckling longitudinal barsTensile fracture longitudinal barsLow-cycle fatigue longitudinal barsFailure in lap-splice zone





Columnns mustsatisfy min. shearand confining steel

requirements

Columnoverstrength,

sec 7.7








Strengthcapacity


Deformationcapacity



member capacities



Strengthcapacity


Deformationcapacity


CAPACITY ASSESSMENT

21

Geotechnical modeling

Geotechnical Modeling and Capacity Assessment

Foundation ModelingEquivalent linear stiffness modelsCapacity modelsShallow footing, piles, shafts, abutments

Ground Displacement DemandsSettlement Liquefaction Induced Lateral Spreads

evaluation methods for bridges in categories c and...

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