BC 2011 Training Bridge

8/13/2019 BC 2011 Training Bridge

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SeventeenthStatewide Conferenceon Local BridgesTuesday, October 25, 2011

Training Session 1: Fundamentals & Applications of LRFR(Bridge Superstructures)

Presented by:

Bala SivakumarDirector Of Special Bridge Projects

HNTB (New York)

Bala Sivakumar, P.E.

HNTB

New York

LOAD & RESISTANCE FACTORRATING OF HIGHWAY BRIDGES

NY STATEWIDE CONFERENCE ON

LOCAL BRIDGES

INTRODUCTION

TO LRFR

LOAD RATING OF HIGHWAY BRIDGES

SESSION 1OUTLINE

SESSION 1: INTRODUCTION TO LRFR

SESSION 2: LOAD MODELS FOR LRFR

SESSION 3: LRFR LOAD RATING PROCESS &LOAD RATING EQUATION

SESSION 4: LRFR LIMIT STATES, RELIABILITYINDICES & LOAD FACTORS

SESSION 5: P/S GIRDER BRIDGE LRFR RATING

SESSION 6: STEEL GIRDER BRIDGE LRFR RATING



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FHWA MEMORANDUM: OCT. 30, 2006BRIDGE LOAD RATING FOR THE NATIONAL BRIDGE INVENTORY

After Oct 1, 2010 all LRFD designs shall be load ratingusing LRFR when reporting to the NBI

WHY LRFD / LRFR ?

1- More uniform reliability in allbridge designs and ratings

2- Increased Bridge Life

2- Meaningful Load Ratings and postings!

LRFD / LRFR RELIABILITY-BASED LIMIT STATESSPECIFICATIONS

USE PROBABILISTIC METHODS TO DERIVELOAD & RESISTANCE FACTORS

UNIFORM RELIABILITY ACROSS BRIDGETYPES AND SPAN LENGTHS

CALIBRATED LOAD AND RESISTANCEFACTORS FOR DESIGN AND RATING

LOAD FACTOR RATING METHOD

A Strength-based load rating method. Limitedguidance on serviceability ratings

Uncalibrated code. Load factors wereestablished based on engineering judgment(Unknown reliability)

No guidance on adjusting load and resistancefactors for changed uncertainty in loadings ormember resistance.


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LRFR GOAL : UNIFORM RELIABILITY

LFD

LFR

LRFD

LRFR

CALIBRATION OF LIMIT STATES

Only the Strength Limit State was calibrated based uponstructural reliability theory.

Service limit states were calibrated to past practice

Target reliability index of 3.5 was selected for design.

Target reliability index of 3.5 was selected for rating.

Design Reliability = 3.5 ; 1 in 10,000 notional failureprobability.

For evaluation =2.5 or a 1 in 100 notional failure

probability.

Q Q TR T R

Load Effect Resistance

Loads ( QT) Increase, Resistance ( RT)Decreases

Reliability Decreases with Time

Time Dependant ReliabilityBridge Reliability


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LRFD / LRFR ISSUES

The HL-93 loading does not bear anyresemblance to actual trucks.

HL-93 is a notional load not suitable for posting.

LRFD only addresses redundant superstructuresystems. Many existing bridges are non-redundant.

LRFD is focused on new bridges, not degradedbridges.

Older materials & connections (rivets) are notcovered in the LRFD Specs.

LRFD Live Load, HL-93Design Truck:

Design Tandem:

superimposed on

Design Lane Load 0.64 Kip/ft +

or or

25.0 KIP 25.0 KIP

AASHTO Manual for BridgeEvaluation

TABLE OF CONTENTS

SECTION 1 - INTRODUCTIONSECTION 2 - BRIDGE FILESECTION 3 - BRIDGE MANAGEMENT SYSTEMSSECTION 4 - INSPECTIONSECTION 5 - MATERIAL TESTINGSECTION 6 - LOAD RATING OF BRIDGESSECTION 7 - FATIGUE EVALUATION OF STEEL

BRIDGESSECTION 8 - NON-DESTRUCTIVE LOAD TESTINGSECTION 9 - SPECIAL TOPICSAPPENDIX - ILLUSTRATIVE LRFR EXAMPLES

2008 AASHTO MBE


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LOAD RATING BY LOAD AND RESISTANCEFACTOR EVALUATION METHOD

FINAL REPORT JUNE 2005

The objective of this project is to provide explicitcomparisons between the ratings produced by the LRFRmethod and Load Factor ratings (LFR).

The comparisons of 74 bridges are based upon flexural-strength ratings.

Design criteria failure rates & reliability indices

determined using Monte Carlo simulations.

NCHRP PROJECT 20-07/Task 122FAILURE RATE VERSUS LRFR HL-93

INVENTORY RATING FACTOR

RELIABILITY INDEX VERSUS LRFR & LFR DESIGNLOAD INVENTORY RATING FACTORS

FAILURE RATE VERSUS LRFR & LFR DESIGNLOAD INVENTORY RATING FACTORS


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FACTORS AFFECTING THERELIABILITY INDEX

Live load modelChange from HS20 to HL-93

Live load distribution factorsNew LRFD distribution factors

Load factorsNew calibrated load factors

RELIABILITY INDICES FOR AASHTO STD. SPECS.SIMPLE SPAN MOMENTS IN STEEL GIRDERS

Ref: NCHRP 12-33 Calibration of LRFD Bridge Design Code

Influenceof DF

FEDERAL TRUCK WEIGHT LIMITS FOUR BASIC FEDERAL WEIGHT LIMITS APPLY:

SINGLE AXLE (20,000 #) TANDEM AXLE (34,000 #) BRIDGE FORMULA B GROSS VEHICLE WEIGHT (80,000 #)

ONLY SEVEN STATES APPLY THESE LIMITS STATEWIDE WITHOUTMODIFICATION. OTHER STATES ALLOW TRUCKS EXCEEDING THESE LIMITS UNDER THEGRANDFATHER PROVISIONS.

500 12 361

LN W N

N

= + +

LOAD MODELS FOR LRFR


SESSION 2


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WHAT ARE EXCLUSION TRUCKS ?

Trucks that exceed federal weight limitsThey are legal based on state weightregulationsAre not allowed on the Interstates but canoperate on state and local roadsThey induce the highest load effects onbridges

LIVE LOADS ON OUR HIGHWAYS

FEDERAL LEGAL LOADS

EXCLUSION VEHICLES(Grandfathered Trucks)

OVERWEIGHT PERMIT VEHICLES

< HS20

MICHIGAN EXCLUSION LOAD: 3-S3-5Total Weight = 149.4 Kips Total length = 72.4 Ft

Vehicle Load Effects Enveloped by HL-93

EXCLUSION TRUCKS


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LIVE LOADS ON OUR HIGHWAYS

FEDERAL / STATE LEGAL LOADS

EXCLUSION VEHICLES(GrandfatheredTrucks)

OVERWEIGHT PERMIT VEHICLES

HL-93

LRFR LEGAL LOADS FORRATING & POSTING

Truck Load ModelsRoutine Commercial Trucks

Specialized Hauling Trucks

Lane Load Models for spans > 200 ft

Lane Load Models for Continuous Spans

LRFR LEGAL LANE LOAD MODEL FOR SPANSBETWEEN 200 FT. and 300 FT.

15 4 15 4169K 9K 9K 12K 10.5K 10.5K

54LEGEND

Truck = 75% of Type 3-3

= 60 Kips

Lane Load = 0.2 KLF

Routine Commercial TrafficTruck Models

15.5k

11 422

15.5k 15.5k 15.5k 10k

4

Type 3S2 W=72 kips

1611 4 15 412k 12k 12k 15k 14k 14k

Type 3-3 W=80 kips

15 4

17k 17k 16k

Type 3 W=50 kips


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LRFR LEGAL LANE LOAD MODEL FORNEGATIVE MOMENTS

15 4 15 4169K 9K 9K 12K 10.5K 10.5K

54

15 4 15 4169K 9K 9K 12K 10.5K 10.5K

5430

LEGENDEach Truck = 75% of Type 3-3

= 60 Kips

Lane Load = 0.2 KLF

Headway Distance = 30 Ft

Trucking industry has in recent years introducedSpecialized Hauling Vehicles with closely-spacedmultiple axles:

Dump trucks, construction vehicles, solid wastetrucks and other hauling trucks.

Under 80,000 # and satisfy Bridge Formula B. They are legal in all states. New AASHTO posting loads adopted in 2005

SPECIALIZED HAULING VEHICLES (SHV)

7-AXLE SHV

SPECIALIZED HAULING VEHICLE

500 12 36

1

LN W N

N

= + +

FEDERAL BRIDGE FORMULA B

W = Maximum weight in pounds that can be carriedon a group of two or more axles

L = Distance in feet between the outer axles of anytwo or more consecutive axles.

N = Number of axles being considered.


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7-AXLE SHVSPECIALIZED HAULING VEHICLE Original AASHTO Single Unit Truck

AASHTO Type 3 posting load is not representative ofthese newer legal loads.

These SHVs may be severely overstressing short spanbridges.

TYPE 3

Weight = 50 Kips

AASHTO ADOPTED: NEW POSTING LOADS FOR SHVs A NEWNOTIONAL RATING LOAD FOR LOAD

RATING OF BRIDGES NEW POSTING LOAD MODELS FOR SINGLE

UNIT TRUCKS APPLIES TO: ALLOWABLE STRESS, LOAD

FACTOR, LOAD AND RESISTANCE FACTORMETHODS

2005 AASHTO BRIDGE MEETING

POSTING LOADS FOR SPECIALIZEDHAULING VEHICLES THAT MEET

BRIDGE FORMULA B

NCHRP Project 12-63

NCHRP Report 575


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A SINGLE NOTIONAL RATING LOAD

THERE ARE MANY VARIATIONS OF SHVs A SINGLE ENVELOPE RATING LOAD MODEL ISNEEDED FOR ALL SHV TRUCKS:

MAY NOT REPRESENT AN ACTUAL TRUCK(NOTIONAL TRUCK)

SIMPLIFIES THE RATING ANALYSIS GVW = 80 KIPS V 60 TO 14-0. SPACING

AXLES THAT DO NOT CONTRIBUTE TO THE MAXIMUM LOADEFFECT UNDER CONSIDERATION SHALL BE NEGLECTED .

2005 AASHTO ADOPTS: NOTIONAL RATING LOAD NRL

NOTIONAL RATING LOAD FOR SHVs

4

4

4

4

4

4

V

6K

8K

8K

17K

17K

8K

8K

8K

BRIDGE POSTING LOADS FOR SHVs

A wide variety of vehicle types cannot be effectivelycontrolled by any single posting load

A single posting load based on a short truck modelwould be too restrictive Setting weight limits for posting should consider

legal truck types that operate within a state.

SIMPLE SPAN MOMENTS

0.0

500.0

1000.0

1500.0

2000.0

2500.0

3000.0

3500.0

4000.0

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

Simple Span (Ft)

M o m e n

t ( K F T

)

NRL

AASHTOTrucks

HS20


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SU4 TRUCK

GVW = 54 KIPS

SU5 TRUCK

GVW = 62 KIPS

17K

2005 AASHTO POSTING LOADS

4410

12K 8K 17K17K

44410

12K 8K 8K 17K 17K

SU6 TRUCK

GVW = 69.5 KIPS

SU7 TRUCK

GVW = 77.5 KIPS

2005 AASHTO POSTING LOADS

444410

11.5K 8K 8K 17K 17K 8K

4444410

11.5K 8K 8K 17K 17K 8K 8K

LRFR FOR OVERWEIGHT PERMITCHECKING

LRFR provides permit load factors by permit type:- Routine/Annual Permits < 150 K- Special Permits > 150 K

Load factors calibrated to provide uniformreliability: = 2.5 for Routine Permits, = 3.5 forSpecial permits.

CHECKING OVERWEIGHT PERMITS

STRENGTH II LIMIT STATE


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ROUTINE PERMIT

8-AXLE CONTINUOUS TRIP PERMIT 105.5 K (Oregon)

Ohio Superload : TOTAL WEIGHT 848.6 k

SPECIAL PERMIT

LRFD Live Load Distribution Factors These factors were derived using refined methods ofanalysis. The LRFD formulas are lane-load distributions not wheel-

load distributions. Distribution formulas for beam-and-slab bridges arefound in the LRFD Specifications (Section 4). There are specific limitations on span and girderspacings.

3.5 Spacing 16 ft.

20 Span 240 feet

LIVE LOAD DISTRIBUTION ANALYSIS

LRFR UTILIZES LRFD DISTRIBUTION FACTORS MORE ACCURATE THAN S/D FACTORS MORE COMPLEX DIFFERENT DF FOR MOMENT AND SHEAR


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LRFD DF for Moment:Interior Beams

One Lane Loaded

Two or More Lanes Loaded

= +

0.10.4 0.3

1 30.06 14 12g

ms

K S Sg L Lt

= +

0.10.6 0.2

2 30.075 9.5 12g

ms

K S Sg

L Lt

Longitudinal Stiffness Parameter, Kg

( ) ( )2 4.g g B

D

K n I Ae in

E n E

= +

=

g e A = Area of steelbeam

If section is non-composite e g = 0

Multiple Presence of Live LoadMultiple Presence Factor is used to Account for the Probability ofSimultaneous Lane Occupation by the full HL93 Live Load.

Table 3.6.1.1.2-1 -- Multiple Presence Factor m

Number of LoadedLanes

Multiple PresenceFactor m

1 1.202 1.003 0.85>3 0.65

LRFD DF for Shear:Interior Beams

One Lane Loaded

Two or More Lanes Loaded

1 0.36 25v Sg = +

2.0

2 0.2 12 35v S S

g = +


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LRFR LOAD RATING PROCESS &LOAD RATING EQUATION

.


SESSION 3

THE LRFR PHILOSOPHY

Reliability-based, limit states approach consistentwith LRFD.

Rating done at Strength limit state andchecked for serviceability.

Provides more flexible rating procedures withuniform reliability.

Calibrated live load factors for different liveload models and loading uncertainties.

Flow Chart for LRFR Load Rating

Start

Legal Load Rating

Design Load Rating(HL93)

Permit Load Rating

No Further

Action Required

Load Posting Strengthening

Pass / Fail

RF 1

RF 1

RF 1

RF < 1

RF < 1

THE LRFR LOAD RATING PROCESS

Three Rating Levels

1) DESIGN LOAD RATING (HL-93)

2) LEGAL LOAD RATING (POSTING)

3) PERMIT LOAD RATING (OVERWEIGHT TRUCKS)


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DESIGN LOAD RATING (HL 93)

HL93 is a notional representation of trucks permitted under Grandfather exclusion to weight laws.

Bridges that rate for HL93 are safe for all legal loads(including grandfather trucks).

RF < 1.0 Identifies vulnerable bridges for further evaluations(need for posting).

Results suitable for NBI reporting of LRFR Ratings (Similarto HS20).

DESIGN LOAD RATING (HL 93)

Do not convert HL-93 rating factors to tonnage. Its a notionalload that includes a lane load.

Report ratings as Rating Factors to the NBI. Provides a metric for assessing existing bridges to current

(LRFD) design standards .

1) For States that allow Exclusion Loads

= 3.5 (Inventory Level)

Live Load Factor = 1.75

2) For States that comply with federal weight laws (incl.Formula B):

= 2.5 (Operating Level)


RELIABILITY LEVELS FOR HL-93TWO RATING LEVELS FOR HL 93

Inventory Level Rating Suitable for screening bridges in states that allow

exclusion (grandfathered) trucks as legal loads

Operating Level Rating Suitable for screening bridges in states that limit trucks to

the federal weight limits and Formula B


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LRFR FLOW CHART FOR HL-93 FHWA REPORTING

FHWA Coding Guide allows reporting of HL-93LRFR Rating Factors (Items 63 and 65)

Allows reporting of Rating Factors instead of Tons.

LEGAL LOAD RATING Single load rating (beta = 2.5) for a given legal load.

Departure from current practice of INV & OPR ratings. Provides Load Ratings using AASHTO Legal Loads

(Type 3, Type 3-3, Type 3S2) & Specialized HaulingVehicles

Legal load ratings are used to establish need forposting (RF < 1.0) or bridge strengthening

Do not use HL-93 results for posting purposes

LEGAL LOAD RATING

Bridges with RF < 1.0 for HL-93 should be load ratedfor AASHTO & State legal loads.

Bridges with RF < 1.0 for legal loads should be posted.

Single load rating at = 2.5 for legal loads.

LRFR Provides a single safe load capacity forindefinite use.

Load Factor Operating Rating --- Maximum permissible live loadfor the structure, suitable for one-time or Limited Crossings.


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STRENGTH LIMIT STATEEVALUATION

General Load RatingEquation

Where:

RF = Rating Factor

DC = LRFD Load factor for structural components andattachments

DW = LRFD Load factor forwearing surfaces and

utilities

P = LRFD Load factor for permanent loads other thandead loads

L = Evaluation live loadfactor

RF =

C S DC DW PR DC DW P

L L(1+ IM)

C = Condition factor S = System factor

= LRFD resistance factor R = Nominal member resistanceDC = Dead load effect due to

structural components and attachmentsDW = Dead load effect due to

wearing surface and utilitiesP = Permanent loads other than dead loads.L = Live Load effect IM = Dynamic Load Allowance





LRFR LOAD FACTORS FOR HL-93

MBE Table 6A.4.3.2.2-1

Where: C = LRFR Condition factor (Optional) S = LRFR System factor (Optional)

= LRFD resistance factor f R = Allowable Stress Specified in the LRFD Code

C S

R

C R

C f

=

=

CAPACITY C

For the STRENGTH Limit States

For the SERVICE Limit States


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LOAD FACTORS FOR LEGAL LOADS

MBE Table 6A.4.4.2.3a-1 TRAFFIC VOLUME LOAD FACTOR

ADTT > 5000 1.80ADTT = 1000 1.65ADTT < 100 1.40

For ADTT between 100 and 5000 interpolatethe load factor.

= 2.5

LRFR RESISTANCE MODIFIERS

L

0.85

(LL+IM)C S DC DW

C S

R DC DW

=RF

s OPTIONAL SYSTEM FACTOR FOR REDUNDANCY

c OPTIONAL MEMBER CONDITION FACTOR

LRFD RESISTANCE FACTOR

BRIDGE SAFETY AND REDUNDANCY

LRFD IS CALIBRATED TO PROVIDE UNIFORM MEMBERSAFETY FOR REDUNDANT PARALLEL GIRDERSUPERSTRUCTURE SYSTEMS (CONSIDEREDREPRESENTATIVE OF CURRENT AND FUTURE TRENDS INBRIDGE CONSTRUCTION )

MANY EXISTING BRIDGES HAVE NON-REDUNDANTSUPERSTRUCTURE SYSTEMS

REDUNDANT SYSTEMS:

SYSTEM SAFETY > MEMBER SAFETY

NON-REDUNDANT SYSTEMS:

SYSTEM SAFETY = MEMBER SAFETY

LRFD Factors (for Design)R/C Concrete Flexure = 0.90

P/S Concrete Flexure = 1.00

Concrete Shear = 0.90

Steel Flexure & Shear = 1.00

Applies to new members in good condition.

What are the resistance factors for evaluation of existingmembers in deteriorated condition?


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SYSTEM FACTORsC = c s R

System Factors are Multipliers to the Nominal Resistance toReflect the Level of Redundancy of the Complete SuperstructureSystem. Non-Redundant Bridges will Have Their Factored MemberCapacities Reduced, and, Accordingly, will Have Lower Ratings.System Factors are Used to Maintain an Adequate Level ofSystem Safety.The Aim ofs is to Add Reserve Capacity (to non-redundantmember) such That System Reliability is Increased from anOperating Level Reliability to an Inventory Level Reliability

SYSTEM FACTORsC = c s R

Redundant Bridges s = 1.00

Non-redundant Bridges s = 0.85

NON-REDUNDANT MEMBERS WITH INTERNAL REDUNDANCY

Riveted Two-Girder/Truss Bridges s = 0.90Multiple Eyebar Members in Trusses s = 0.90Floorbeams with Spacing > 12 ft s = 0.85

SYSTEM FACTORS ARE NOT APPROPRIATE FOR SHEAR AS SHEARFAILURES TEND TO BE BRITTLE. WITHOUT DUCTILITY SYSTEM RESERVE ISNOT POSSIBLE.

CONDITION FACTOR c Condition Factor c is Tied to The Condition of The Member

Being Evaluated: Good or Satisfactory c = 1.00 Fair c = 0.95 Poor c = 0.85

If Element Level Condition Data is not Collected, NBI Ratingsfor the Superstructure May be Used

c = 0.85 for NBI Rating of 4c = 0.95 for NBI Rating of 5c = 1.00 for NBI Rating 6 or higher

Increases Beta from 2.5 to a target of about 3.5 to account for the increased

variability of resistance of deteriorated members.

CONDITION FACTOR cC = c s R

Resistance of Deteriorated BridgesLRFD Resistance Factors for New Members Must be ReducedWhen Applied to Deteriorated MembersThere is Increased Uncertainty and Variability in Resistance ofDeteriorated MembersThey are Prone to Accelerated Future Deterioration. (increased

additional losses between inspection cycles)Improved Inspections will Reduce, but not Totally Eliminate, theIncreased Resistance Variability in Deteriorated Bridges.


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POSTING BRIDGES FOR UNIFORM RELIABILITY

Relationship between posting load and rating factor isnot linear in a reliability based evaluation (LRFR).

The lower the posting load, the greater the possibility ofillegal overloads and multiple presence.

In Load Factor Rating

Posting Load = Rating Factor x Weight of Rating Truck

LRFR POSTING ANALYSIS

1) When 0.3 < RF < 1.0

Posting Load = (W /0.7) [ (RF) - 0.3 ]

W= Weight of rating vehicleRF= Legal load rating factor

2) When RF < 0.3 for all rating loads, bridge should beclosed

If a bridge cannot support the empty weight of a legaltruck, that truck should not be allowed on the bridge.

LRFR POSTING CURVES

Criteria: A bridge with acceptable capacity less than 3 tonsshould be closed.

Increase reliability index from operating target of 2.5to 3.5 to account for historical failure occurrences inposted bridges

Allow an overweight cushion of 10,000 lbs

POSTING LOAD vs RATING FACTOR


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LRFR LIMIT STATES,RELIABILITY INDICES & LOAD

FACTORS


SESSION 4

LIMIT STATES FOR LOAD RATING

STRENGTH LIMIT STATES Checks the strength and stability of members Checks the strength of connections

SERVICE LIMIT STATES Checks the level of stress under service load Checks for permanent deformation under overloads Checks for slip in bolted connections

1) For States that allow Exclusion Loads



2) For States that comply with federal weight laws &Formula B:


LRFR Live Load Factor = 1.35

RELIABILITY INDICES FOR HL-93Bridge Limit Dead Dead Design LoadA6.4.3.2.1

LegalLoad

A6.4.4.2.1

PermitLoad

A6.4.5.4.1Type State Load Load Inventory Operating

DC DW LL LL LL LL

Steel STRENGTH I 1.25 1.50 1.75 1.35 Table6.4.4.2.3-1

-

STRENGTH II 1.25 1.50 - - - Table6.4.5.4.2-1

SERVICE II 1.00 1.00 1.30 1.00 1.30 1.00

FATIGUE 0.00 0.00 0.75 - - -

Reinforced STRENGTH I 1.25 1.50 1.75 1.35 Table6.4.4.2.3-1

-

Concrete STRENGTH II 1.25 1.50 - - - Table6.4.5.4.2-1

SERVICE I 1.00 1.00 - - - 1.00

STRENGTH I 1.25 1.50 1.75 1.35 Table6.4.4.2.3-1

-

Prestressed STRENGTH II 1.25 1.50 - - - Table6.4.5.4.2-1

Concrete SERVICE III 1.00 1.00 0.80 - 1.00 -

SERVICE I 1.00 1.00 - - - 1.00

Wood STRENGTH I 1.25 1.50 1.75 1.35 Table6.4.4.2.3-1

-

STRENGTH II 1.25 1.50 - - - Table

LRFR LIMIT STATES AND LOAD FACTORS


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LRFR Evaluation: = 2.5 for redundant systems

= 2.5 comparable to upper range of reliability inherent inLoad Factor Operating ratings.

= 2.5 has been shown to be an acceptable minimum level ofsafety for bridge evaluation.Exposure period for evaluation is 2 to 5 years versus 75 yearsfor design.

RELIABILITY INDEX FOR LEGAL LOADS GENERALIZED LRFR LIVE LOAD FACTORSRoutine Commercial Traffic

For system-wide use nationally, tied to ADTT at the site.

Target BETA used for calibration = 2.5

TRAFFIC VOLUME LOAD FACTORADTT > 5000 1.80ADTT = 1000 1.65ADTT < 100 1.40

200K

80K

MULTIPLE PRESENCE DURING HEAVYPERMIT CROSSINGS

LRFR LIVE LOAD FACTORS FOROVERLOAD PERMITS


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Overweight Permit Distribution Analysis

LRFD Two-Lane Distribution Factors assume Side-by-Side Presence of Two Equally Heavy Loads.

Applying LRFD Two-Lane Distribution Factors toPermits can be Overly Conservative as the loadsare unequal.

LRFR Manual Provides Specially Calibrated LoadFactors for Overweight Permits that Account forthe Side-by-Side Presence of Two UnequalTrucks.

LRFR LOAD FACTORS FOR OVERLOADPERMITS

Permit Load Factors by Permit Type- Routine/Annual Permits < 150 K- Special Permits > 150 K

Load factors calibrated to provide uniform reliabilityRoutine/Annual Permits : = 2.5Special Permits : = 3.5

LRFR Permit Load Factors are Tied to the Permit Type, No. ofCrossings, and Site ADTT.

One-Lane Distribution Factor is Used With Special Permits.

Two-Lane Distribution Factor is Used With Routine Permits

LRFR PERMIT LOAD FACTORSSpecial Permits > 150 K

Load FactorADTTDFTRIPS OTHER TRAFFIC

*

Single-Trip Escorted with

no othervehicles on One lane N/Athe bridge

Single-Trip Mix with traffic One lane >5000(other vehiclesmay be on thebridge)

5000 1.85

Trips (less (other vehiclesthan 100 may be on thecrossings) bridge)

150

100 KIPS KIPS

Two or > 5000 1.80 1.30more anes

< 100 1.40 1.10

Weight

= 1000 1.65 1.20

LRFR PERMIT LOAD FACTORS

Routine Permits Up to 150 K

Load FactorADTTDF

Use Two-Lane Distribution factors


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7-AXLE SHV

LRFR LIVE LOAD FACTORS FORSPECIALIZED HAULING VEHICLES

CALIBRATION OF LRFR LIVE LOAD FACTORSFOR SHVs

SHVs Usually Constitute a Very Small Percentage of TotalTruck Traffic. Multiple Presence Probabilities for SHVs are Similar toPermit Crossings. Two Fully Loaded SHVs Side-By-Side is not Likely. SHV in one lane and Type 3 truck in the other was used inthe load factor calibration Reduced Live Load Factors for SHVs Compared to LRFRFactors for AASHTO Legal Loads.

LRFR SERVICE LIMIT STATES

LRFR LOAD FACTORS FOR SHVs

Traffic Volume(One Direction)

Load Factor for NRL, SU4,SU5, SU6, SU7

Unknown 1.60

ADTT 5000 1.60

ADTT = 1000 1.40

ADTT 100 1.15

Table 6A.4.4.2.3b-1

Live Load Factors for Specialized Hauling Vehicles


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LRFR SERVICEABILITY RATING EQUATION

L(LL+IM) DC DW P R f DC DW P

=RF

f R = Allowable Stress Specified in the LRFD / LRFR Code

SERVICE & FATIGUE LIMIT STATES

Steel Bridges: SERVICE II

FATIGUE

Concrete Bridges: SERVICE I SERVICE III (p/s only)

LRFR SERVICEABILITY RATINGOF STEEL BRIDGES

Limit State Load Type Load FactorSERVICE II HL93 (Inv.) 1.3SERVICE II HL93 (Opr.) 1.0SERVICE II Legal 1.3SERVICE II Permit 1.0 (optional)

Allowable Steel Stress:fR = 0.95 Fyf (composite sections)

= 0.80 Fyf (non-composite sections)

LRFR STEEL SERVICEABILITY RATINGS

CHECK PERMANENT DERFORMATION OF STEEL MEMBERS SERVICE II Limit State HL-93, Legal loads, Permit loads.

CHECK FATIGUE OF STEEL MEMBERS FATIGUE Limit State Infinite Life Rating Finite Life Rating


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Permanent Deformation Check

Service II Load Combination

1.0 DL + 1.3 LL < 1.0 Rn

Load combination SERVICE II is applied to steel bridges fortwo considerations:

for members, to limit yielding and objectionablekinking, and

for bolted connections, to prevent repeated slippingor kinking of the connections

LRFR CONCRETE SERVICEABILITY RATINGS

CHECK PERMANENT DEFORMATION OF REINFORCING STEELIN REINFORCED AND PRESTRESSED CONCRETEMEMBERS

SERVICE I Limit State Required only for Permit loads

CHECK CRACKING OF PRESTRESSED CONCRETE MEMBERS SERVICE III Limit State HL-93 and Legal Loads Not Required for Permit Loads

LRFR SERVICE III CHECK FOR P/SCONCRETE BRIDGES

SERVICE III is a design level check for crackcontrol in prestressed components using an uncrackedsection analysis.

SERVICE III check is made optional for legal loads;not required for permit loads.

Permit loads will crack the p/s member but the crackshould close after the truck passes. Cracking is OK onan infrequent basis.

See SERVICE I check for permits

LRFR SERVICEABILITY RATING OFCONCRETE BRIDGES

Type Load Limit State Load Factor

Reinf. Conc. Permit SERVICE I 1.0 (optional)

P/S Conc. HL93 SERVICE III 0.8

P/S Conc. Legal SERVICE III 1.0 (optional)

P/S Conc. Permit SERVICE I 1.0 (optional)


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LRFR SERVICE I CHECK FOR CONCRETEBRIDGES

For all concrete bridges, permit loads should satisfySERVICE I check to ensure that cracks will closeonce the live load is removed

No yielding in reinforcing steel under permitcrossing. Check for: f DL + f LL+IM 0.9 f y

(SERVICE I check for R/C and P/S concrete bridgesis similar to SERVICE II check for steel bridges --permanent deformation under overloads)


SESSION 5

SIMPLE SPAN PRESTRESSED CONCRETEI-GIRDER BRIDGE --LRFR EVALUATION OF AN INTERIOR GIRDER

SIMPLE SPAN PRESTRESSED CONCRETE I-GIRDER BRIDGE -- LRFR EVALUATIONOF AN INTERIOR GIRDER

Bridge Data

Span: 80 ft. (Total Length = 81 ft.)Year Built: 1985Materials:Concrete: 4.0 ksi (Deck)

5 ksi (P/S Beam)4 ksi (P/S Beam at transfer)

c

c

ci

f

f f

=

=

=

Prestressing Steel: 1/2 in. diameter, 270 ksi, Low-Relaxation StrandsA ps = 0.153 in

2 per strand32 prestressing strands, 10 are debonded over the last 12 fton each end

Stirrups: #4 at 9 in. over end 20 ft.#3 at 12 in. over center 40 ft.

Compression Steel: six #6 Grade 60Condition: No Deterioration, NBI Item 59 Code = 6Riding Surface: Minor surface deviations (Field verified and documented)

ADTT (one direction) 5000


33/40

Summary of Section Properties

Type 4 Girder

2

4

3

3

54in.

789 in.

260730 in.

24.73 in.10543in.

8908 in.

b

b

t

h

A

I

Y S

S

=

=

=

=

=

=

2) Composite Section

Effective Flange Width b e = 102 in.

trans

3

3

3.64 10Modular Ratio 0.89

4.07 10Transformed Width, b 102 in. 0.89 90.8 in.

deck

beam

E n

E

= = =

= =

a) Distribution Factor for Moment m g One Lane Loaded:

( )

0.10.4 0.3

1 3

0.4 0.30.1

0.0614 12.0

8.5 8.50.06 2.28

14 80

0.514

g m

s

K S S g

L Lt

= +

= +

=Two or More Lanes Loaded:

( )

0.10.6 0.2

2 3

0.6 0.20.1

0.0759.5 12.0

8.5 8.50.075 2.28

9.5 800.724 0.514

use 0.724

g m

s

m

K S S g

L Lt

g

= +

= + = >=

Components and Attachments DC

a) Non-Composite Dead Loads DC 1

2 2

Girder Self Weight: 0.822 kip/ft.

Diaphragms: 0.150 kip/ft.

Slab haunch:

8.5in. 1in. 20in.8.5ft. 0.15kcf 0.925 kip/ft.12in./ft. 144in. / ft.

==

+

+ =

1Total per Girder 1.90 kip/ft. DC =

( )

1

1

2

80ft.1.90 kip/ft. 76 kip

21

1.90kip/ft. 80 ft. 1520 kip-ft.8

DC

DC

V

M

= =

= =


34/40

b) Distribution Factor for Shear v g

One Lane Loaded:

1 0.36 25vS

g = +

8.500.36

25= +

0.70=

Two or More Lanes Loaded:2

2

2

0.212 35

8.5 8.50.2

12 350.849 0.70

use 0.849

v

v

S S g

g

= +

= + = >=

Compute Maximum Live Load Effects

a) Maximum Design Live Load (HL-93)

= 33% IM 512 1160 1.33 LL IM M + = +

2054.8 kip-ft ..=

Distributed Live Load Moment at Midspan

2054.8

2054.8 0.724

1487.7 kip - ft.

LL IM m M g + =

=

=

Maximum Reinforcement

factor of compression controlled sections shall be reduced in accordance withLRFD Article 5.5.4.2.1.

The net tensile strain, t , is the tensile strain at nominal strength and determined bystrain compatibility.

Given an allowable concrete strain of 0.003 and depth to neutral axis c = 4.39 in.d p = 59.75 in.

0.0034.39" 59.75" 4.39"

0.0378

c t

t

t

c d c

=

=

=

For t = 0.0378 > 0.005, the section is tension controlled and Resistance Factor shall be taken as 1.0.

Compute Nominal Flexural Resistance at Midspan

1 ps pu p

c f f k

d

=

0.28 for low-relaxation strands270 ksi pu

k f

==

4.39

270 1 0.28 59.75264.4 ksi

ps f

= =

Nominal Flexural Resistance (Midspan):

2

3.73 14.896 264.4 59.75

2 12

6244.4 kip-ft.

n ps ps p

a M A f d

= =

=


35/40

Minimum Reinforcement

Amount of reinforcement must be sufficient to develop r M equal to the lesser of:

1.2 cr M or 1.33 u M = (1.0) (6244.4) 6244.4 kip-ft.

1) 1.33 1.33 [1.75 (1487.7) 1.25 (1520 200) 1.5 (162)]

6645.3 kip-ft. 6244.4 kip-ft.

R n

u

M M

M

= =

= + + +

= >

( )2) 1c

cr c r cpe dnc c r

S M S f f M S f S

= +

1.2 1.2 3492cr M = .4 kip-ft = 4190.9 kip-ft.

1.33 6645.3 kip-ft. (previously calculated)

1.2 1.33 therefore,1.2

6244.4kip-ft. (previously calculated)

6244.4kip-ft.> 4190.9 kip-ft. OK

u

cr u cr

r

r

M

M M M governs

M

M

=

<

=

=

The minimum reinforcement check is satisfied.

Summary of Moments and Shears

location support criticalshear

stirrup

change

midspan

x/L 0.0 0.067 0.25 0.5

X (ft.) 0.0 5.37 20 40

V DC1 ( kips) 76 65.8 38 -

V DC2 (kips) 10 8.7 5 -

V DW (kips) 8.12 7.03 4.1 -

g m V LL+IM (kips) - 85.3 63.7 -

V n (kips) simplified - 221.7 129.1 -

V n (kips) MCFT - 440.7 227 -

M DC1 (kip-ft.) - 380.7 1140 1520

M DC2 (kip-ft.) - 50.1 150 200

M DW (kip-ft.) - 40.7 121.8 162

g m M LL+IM (kip-ft.) - 390.5 1087 1487.7

M n (kip-ft.) - - - 6244.4

Design Load Rating HL-93

A) Strength I Limit Statea) Inventory Level

LOAD LOAD FACTOR DC 1.25 DW 1.50 Overlay thickness was not field measured. LL 1.75

Flexure at Midspan

[ ](1.0)(1.0)(1.0)(6244.4) (1.25)(1520 200) (1.5)(162)(1.75)(1487.7)1.48

RF + +

=

=

Shear at Critical Section[ ](1.0)(1.0)(0.9)(440.7) (1.25)(65.8 8.7) (1.50)(7.03)

(1.75)(85.3)= 1.96

RF + +

=

General Load Rating Equation( )( ) ( )( ) ( )( )

( )( )

= +

DC DW P

L

C DC DW P RF

LL IM

Evaluation Factors (for Strength Limit State)

a) Resistance Factor 1.0 for flexure (tension controlledsection)0.9 for shear

=

=

b) Condition Factor c

1.0 No member deterioration, NBI Item 59 Code = 6c =

c) System Factor s

1.0 4-girder bridge with spacing > 4 .ft s =


36/40

B) Service III Limit State (Inventory Level)( )( )

( )( ) R D D

L LL IM

f f RF

f +

=

Flexural Resistance R pb f f = + Allowable tensile stress

= Compressive stress due to effective prestress

= 2.548 Ksi pb f

Allowable Tensile Stress 0.19

0.19 5

0.425 ksi

=

=

=

c f

2.548 0.425

2.973 ksi R f = +

=

Determine Dead Load Stresses At Midspan:

M DC1 = 1520 kip-ft. and M DC2 = 200 kip-ft.

M DW = 162 kip-ft

S b (nc) =10542 in 3 S b (comp) =17471 in 3

1520 12 200 121.87 ksi

10542 17471162 12

0.11 ksi17471

Total 1.98 ksi

= + =

= =

=

DC

DW

D

f

f

f

Live Load Stress At Midspan:

M LL+IM = 1487.7 kip-ft

S b (comp ) =17471 in 3

1487.7 12 1.02 ksi

174712.973 (1.0)(1.98)

(0.8)(1.02)1.22

LL IM f

RF

+

= =

=

=

Use One-Lane Distribution Factor and divide out the 1.2 multiple presencefactor.

1

1

10.514 0.428

1.21

0.70 0.5831.2

= 20% (Minor Surface Deviations)

m

v

g

g

IM

= =

= =

Maximum Live Load Effect:= (2950.5)(0.428)(1.20)

= 1515.4 kip-ft. at Midspan

= (157.9)(0.583)(1.20)= 110.5 kips

+

+

LL IM

LL IM

M

V

a) Flexure:

(1.0)(1.00)(1.0)(6244.4) [(1.25)(1520 200) (1.5)(162)](1.5)(1515.4)

1.69 1.0 OK

RF + +

=

= >

b) Shear (Using MCFT):

(1.0)(1.0)(0.9)(440.7) [(1.25)(72.0) (1.50)(6.7)](1.5)(110.5)

1.79 1.0 OK

RF +

=

= >

Legal Load Rating

Inventory Design Load Rating RF > 1.0, therefore the legal load ratings do notneed to be performed and no posting is required.

Permit Load RatingPermit Type: Special , Single-Trip, Mix with traffic,

No escortPermi t Weigh t: 220 kips ADTT (one direction): 5000Undistributed Maximum M LL = 2950.5 kip-ft.Undistributed Maximum V LL = 157.9 kips

PERMIT LOAD 220 K


37/40

Summary of Rating Factors

Design Load Rating (HL-93)Limit State

Inventory OperatingPermit Load Rating

Strength I

Flexure (@ midspan) 1.48 1.92

Shear (@ 64 in) 1.96

Shear (@ 20 ft) 1.30

Strength II

Flexure (@ midspan) 1.69

Shear 1.79

Service III

Flexure (@ midspan) 1.22

Service I Stress Ratio= 1.08

SESSION 6

LOAD RATING EXAMPLE

LRFR METHOD

SIMPLE SPAN COMPOSITE STEEL STRINGER BRIDGE

Evaluation of an Interior Stringer

Bridge Data

Span: 65 ftYear Built: 1964Str inger Spacing 7-4D ec k T hi ck ne ss 7 .2 5Material: A36 Steel

F y = 36 ksi f c = 3 ksi

Condi tion: No deter iorat ion (NBI I tem 59 = 7)Member is in good condition

Section Properties

Noncomposite Section Properties

W 33 130 and PL 5/8 in. 101/2 in.

Cross SectionInterior Stringer, Noncomposite

38293 436.0 in.19.02

DLt t S S = = =

38293 563.7 in.14.71

DLb bS S = = =

Composite Section Properties

Effective Flange Width

1/4 (65)(12) = 195 in.(7.33)(12) = 88 in.(7.25)(12) = 87 in. Controls

T H E

M A N U A L F O R

B R I D G E

E V A L U A T I O N

r i d g e


38/40

Modular Ratio n

for 3, 000 psi 10c f n = =

Composite n = n: W 33 130, PL 5/8 in. 10 1/2 in. and Conc. 71/4 in. 87 in.

Cross SectionInterior Stringer, Composite n = n

322007 3801 in.5.79t

S = = Section modulus at top of steel

322007 787.7 in.27.94

Lb bS S = = =

Use with Live Load.

Composite n = 3n: W 33 130, PL 5/8 in. 101/2 in.

Cross SectionInterior Stringer, Composite n = 3 n

21.94 in. y =

3

3

157251333.8 in. (Section modulus at top of steel)

11.7915725

716.7 in.21.94

t

SDLb b

S

S S

= =

= = =

Use with Superimposed Dead Load ( SDL).

Composite Dead Loads, DC 2

Curb: ( ) ( )10 in. 2 curbs1 ft 0.150 kcf 12 4 beams

= 0.062 kip/ft

Parapet:

( )6 in. 19 in. 18 in. 12 in. 2 parapets0.150 kcf 144 144 4 beams

+ = 0.172 kip/ft

Railing: Assume 2 railings0.020kip/ft4 beams

= 0.010 kip/ft

Total per stringer = 0.244 kip/ft

( )22

0.244 65129 kip-ft at midspan

8 DC M = =

265

0 .2 44 8 ki ps at be ar in g2 DC

V = =

Wearing Surface

DW = 0

Live Load AnalysisInterior Stringer

Compute Live Load Distribution Factors (Type (a) cross section)

Longitudinal Stiffness Parameter, K g

( )2 g g K n I Ae= +

( )1.533000 D c c E w f =

Dead Load AnalysisInterior Stringer

Components and Attachments, DC

Noncomposite Dead Loads, DC 1

Deck: ( ) ( )( )7.25 in.

7.33 ft 0.150 kcf 12

= 0.664 kip/ft

Stringer: (0.130 kip/ft) (1.06) = 0.138 kip/ft(six percent increase for connections)

Cover Plate:

( )( ) ( )( )0.490 kcf

0.625 in. 10.5 in. 1.06 38 ft144

65 ft

= 0.014 kip/ft

Diaphragms: ( ) ( )( )( )3 0 .0427 k ip /f t 7 .33 ft 1 .0665 ft

= 0.015 kip/ft

Total per stringer = 0.831 kip/ft

( )1

20.831 65

439 kip-ft at midspan8

DC M = =

1

650 .8 31 2 7 k ip s a t b ea ri ng

2 DC V = =


39/40

( )1.5 3 3000 0 .145 3=

3155.9 ksi=

29000 ksi B E =

Beam + Cov. PL

I = 8 29 3 i n. 4

A = 4 4. 82 i n. 2

e g = 1/2 (7.25) + 19.02 = 22.65 in.

K g = ( )229000 8 29 3 4 4. 82 2 2. 653155.9 +

K g = 287498 in. 4

Distribution Factor for Moment, g m

3 3

2874980.967

12.0 12 65 7.25 g

s

K

Lt = =

One Lane Loaded:

0.10.4 0.3

1 30.06 14 12.0 g

m s

K S S g

L Lt

= +

( )0.4 0.3

0.17.33 7.33 0.06 0.96714 65

= +

0.460=

Two or More Lanes Loaded:

0.10.6 0.2

2 30.075 9.5 12.0 g

m s

K S S g

L Lt

= +

( )0.6 0.2

0.17.33 7.33 0.075 0.967

9.5 65

= +

0.626 0.460= >

use 0.626m g =

Distribution Factor for Shear, g vOne Lane Loaded:

10.36

25.0vS g = + Table 4.6.2.2.3a-1

7.33 0.36

25.0= +

0.653=

Two or More Lanes Loaded:

2.0

20.2

12 35vS S

g = +

Table 4.6.2.2.3a-1

2.07 .3 3 7 .3 3

0.212 35

= +

0.767 0.653= >

use 0.767v g =

Tandem Axles Shear 2525 256 5 f t 4 ft= 25 25 48.5 kips

65 ftk k x P P

+ = + =

LL IM V + = 20.8 kips + 61.7 kips 1.33

= 102.9 k ips

Distributed Live Load Moments and Shears

Design Live-Load HL-93:

LL IM M + = 1521.7 g m

= 1521.7 0.626

= 952.6 kip-ft

LL IM V + = 102.9 g v

= 102.9 0.767

= 78.9 kips

Compute Nominal Resistance of Section at Midspan

The plastic moment M p is the sum of the moments of the plastic forces about the PNA.

M p =[ ]

2

t2 s

c c w w t s

Y P Prtdrt+Prbdrb+ P n + P d +P d

t

+ LRFD Design Table D6.1-1

= [ ]27 .1 3 1 62 6. 9

0+0+354.30.55+ 655.416.67+590.4 33.092 7 .2 5

+

= 36361 kip-in. or 3030 kip-ft

Maximum Design Live Load (HL-93) Moment at Midspan

Design Lane Load Moment ( )22 0.640klf 65ft

= 338kip-ft8 8

wl = =

Design Truck Moment ( )8 3232=4

P P xb P ++

( )8 32 32 .5 ft 18 .5 ft32 65 ft4 65ft

k k k + = +

Design Truck Moment = 890 kip-ft Governs

Tandem Axles Moment 25= 25 30.5ft= 762.5 kip-ftk P a =

IM = 33%

LL IM M + = 338 + 890 1.33

= 1521.7 kip-ft

Maximum Design Live Load Shear at Beam Ends

Design Lane Load Shear ( )0.640klf 65ft= 20.8kips2 2

w = =

Design Truck Shear 32 832 32 8= x x

P P P + +

65ft 14ft 65ft 28ft 32 32 8

65ft 65ftk k k = + +

Design Truck Shear = 61.7 kips Governs


40/40

Nominal Flexural Resistance, M n

p D 0.1 t D LRFD Design Eq. 6.10.7.1.2-1

Therefore, 1.07 0.7 pn pt

D M M

D

=

Shear Resistance

where 0.58 p yw wV F Dt = LRFD Design Eq. 6.10.9.2-2

= 1.0 x 0.58 36 29.75 0.580

= 3 60 .3 ki ps

Summary for Interior Stringer

Dead Load DC 1

Dead Load DC 2

LiveLoadDistribution

Factor Dist. Live Load

+ Im pa ct N om in al Ca pa ci tyMoment, kip-ft 439.0 129.0 gm = 0.626 952.6 2873.0Shear, kips 27.0 8.0 gv = 0.767 78.9 360.3

LRFR Load-Rating Equation

( )( ) ( )( ) ( )( )( )( )

DC DW P

L

C DC DW P RF

LL IM

=

+

Evaluation Factors (for Strength Limit States)

1. Re sistance Factor, = 1.0 for flexure and shear

2. Condition Factor, c c = 1.0 Member is in good condition. NBI Item 59 = 7.

3. System Factor, s s = 1.0 4-girder bridge, spacing > 4 ft (for flexure and shear).

Design Load Rating

Strength I Limit State

( ) ( ) ( )Capacity c s nC R=

( )( )( ) ( )( ) ( )( )( )( )

c s n DC DW

L

R DC DW RF

LL IM

=

+

Inventory Level

Load Load Factor

DC 1.25 LL 1.75

Flexure: RF =( )( )( )( ) ( )( ) ( )( )

( )( )1.0 1.0 1.0 2873 1.25 439 1.25 129

1 .75 952 .6

= 1 .2 97 5

Shear: RF =( )( )( )( ) ( )( )

( )( )1.0 1.0 1.0 360.3 1.25 27 8

1 .7 5 7 8. 9

+

= 2.29

Operating Level

Lo ad L oa d Factor

DC 1.25 LL 1.35

Flexure: RF = 1.751.291.35

= 1.67

Shear: RF =1.75

2.291.35

= 2.97

Service II Limit State

( )( )( )( ) R DC DC

LL LL IM

f f RF

f +

=

Inventory Level

Allowable Flange Stress for tension flange f R = 0.95 Rh F yf ( f = 0)

Checking the tension flange as compression flanges typically do not govern for compositesections.

Rh = 1.0 for non-hybrid sections

f R = 0.95 1.0 36

= 3 4. 2 k si

f D = 1 2 DC DC f f +

= 439 12 129 12563.7 725

+

= 9.35 + 2.14 = 11.49 ksi

f LL+ IM =9 52 .6 1 2

14.42 ksi793

=

LL = 1.30 DC = 1.0 Table 6A.4.2.2-1

RF = ( )( )( )( )

3 4. 2 1 .0 1 1. 49

1.3 14.42

= 1.21

BC 2011 Training Bridge

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