ENCE717 – Bridge EngineeringLoad and Resistance Factor Rating (LRFR)

for Steel Bridges

Chung C. Fu, Ph.D., P.E.(http: www.best.umd.edu)

Outline of LRFR for Steel Bridges• General

• AASHTO LRFR

• Rating for steel truss bridges

• Rating for steel line girders

• Rating for refined steel bridge analysis

• Rating factors for steel girder bridges

1969 W.V. Silver Bridge Collapse

LRFR Philosophy

• Reliability-based, limit state approach consistent with LRFD Rating done at Strength limit state and checked

for Service limit state

• Load Rating the Inventory Rating corresponds to that load

which can safely utilize an existing bridge for an indefinite period of time (, equivalent to the design level of stress)

the Operating Rating is the absolute maximum permissible load to which a structure should be subjected (, to the operating stress level)

Basic Rating Factor Equation for the LRFR Method

)1( IMLLPDWDCCRF

L

PDWDC

CDC

DW

P

LL IMDC

DWPL

is the structural capacity (=csR; c: condition, s: system)

is the dead-load effect of structural components and attachments

is the dead-load effect of wearing surfaces and utilities

is the permanent loading other than dead loads

is the live-load effect is the dynamic load allowance

is the load factor for structural components and attachments is the LRFD load factor for wearing surfaces and utilities

is the load factor for permanent loads other than dead loads is the evaluation live-load factor

Probabilistic Design and Evaluation

Analysis used BIAS COVAASHTO S/D 0.9 13AASHTO LRFD 1.0 10AASHTO Refined 1.0 7Field Test 1.0 4

Basic Rating for the LFR/LRFR Methods

• A strong, more linear correlation is demonstrated by the LRFR rating factors vs Reliability index β.

• Bridges designed with LRFD be load rated with LRFR

In LRFR Inventory & Operating Ratings are defined β=3.5 INV, β=2.5 OPR

LFR

LRFD Load Rating Process• 1) DESIGN LOAD RATING (HL-93)

• 2) LEGAL LOAD RATING (POSTING)

• 3) PERMIT LOAD RATING (OVERWEIGHT TRUCKS)

• IM = 33% Is Standard. Following Values are Optional:

• Legal Load rating Riding surface conditions: smooth IM = 10%; minor surface irregularities IM = 20%; major surface irregularities IM = 33%

• Permits – same, except for: slow moving (< 5mph) vehicles IM = 0%

AASHTO Live Loads considered in ASD and LRFD Methods

8

Vehicular load HS-20 used in ASD

HS-20 Truck

OR Concentrated Load plus Lane Load

OR Tandem (Interstate or Military)

Vehicular load HL-93 used in LRFD

OR

Federal Bridge Formula B (FBF B)

• 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 WITHOUT MODIFICATION.

• OTHER STATES ALLOW TRUCKS EXCEEDING THESE LIMITS UNDER THE “GRANDFATHER PROVISIONS”.

State Legal Loads• Bridge with RF < 1.0 for HL-93 should be rated for AASHTO &

State legal loads.

• Bridge with RF < 1.0 for legal loads should be posted (, not using HL-93 for posting.)

• Single load rating at β = 2.5 for legal loads, departure from current practice of INV & OPR ratings.

• Provides load ratings using AASHTO legal loads (Type 3, 3-3, 3S2 & specialized hauling vehicles.

• LRFR provides a single safe load capacity for indefinite use (comparable to Load Factor Operating Rating).

AASHTO Rating Truck vs FHWA Vehicles

FHWA Vehicle Classification

Permit* load

Any vehicle or combination of loads having a gross weight in excess of 40 tons (or 80 kips).

* = Permits are also required for over-SIZED vehicles. But, for the purposes of load rating, we are referring to permits that are required due to over-weight only.

Superload

Any vehicle or combination of loads having a gross weight in excess of 60 tons (or 120 kips).

LRFR Flowchart for Load Ratings

LRFR Limit States and Load Factor Factors

Special Permit Truck

Routine Permit Truck

(3, 3S2, 3-3,…)

Table 6A4.4.2.3a-1 & 3b-1 Table 6A4.5.4.2a-1

LRFR Live Loads Factors L

From Elements to Analysis Models

Element

• Rod/Bar • Plate • Brick

• Beam • Shell • Rigid link

To form

• Beam • Grid

• Plane truss • Space truss

• Plane frame • Space frame

• • Full 3D FEM

(DASH) (DESCUS)

(TRAP)

Ratings of Three Types of Steel Bridges

Truss Bridges (TRAP – Truss Rating and Analysis Program)

Straight Steel Girder Bridges(DASH – Design and Analysis of Straight Highway Bridges)

Curved or Skewed Steel Girder Bridges(DESCUS I & II – Design and Analysis of Curved I or Box Steel

Girder Bridges)

2D Truss Bridge Modeling

Member released from resisting axial forces

Truss Influence Lines and Applied Loading

Truss Bridge Load Rating• Axial Tension Pr = Pn

where } lesser (LRFD Eq. 6.8.2.1-1 & -2)

• Axial Compression Pr = Pn

where Pn = 0.66Fy As for λ 2.25 (LRFD Eq. 6.9.4.1-1)

for λ > 2.25 (LRFD Eq. 6.9.4.1-2)

where LL is based on ADTT

• FHWA Load Rating Guidance and Examples For Bolted and Riveted Gusset Plates In Truss Bridges

UAFPAFP

nuur

gyyr

sy

n

AFP

88.0

f

f - = RF

1LL+

/D

aLL

pDWC

arP

Line Girder (Approximate) Analysis Method

Assumptions:

• Single line girder

• Effective flange width(shear lag)

• Live load distribution factor

• Live load influence line

Since 2008, effective width be = tributary width b(AASHTO Art. 4.6.2.6)

Line Girder Modeling

• Assumed constant deck width, parallel beams with about the same stiffness

• Developed for “design” trucks• Developed to bound within that structural

type• Limited ranges of applicability. (When

exceeded, the LRFD specifications mandate refined analysis.)

AASHTO LRFD live load distribution factor design equations for shear and moment is recommended for rating.

Line girder

Influence Lines for Moment & Shear

Moment

Shear

Special Permit Review using Refined Analysis

• Refined analysis of Special Permits allows the input of different trucks and live load factors in each lane.

• Appropriate adjacent live load and permit load factors for use in refined analysis (Strength II Limit State)

Refined Analysis Methods

• Grillage analogy method

• Orthotropic plate method

• Articulated plate method

• Finite strip method

• Finite element method

• Software package

DESCUS Flowchart for the Curved Steel Bridge Design and Load Rating

Graphic Verification

DL & SDL Application

LL Influence Surface Generation

Geometry & Loading Data InputGeometry & Loading Data Input

LL Application by Inf. Surface

Stress Allowables

Load Rating

ReviseDESCUSPreprocessor

DESCUSMain processor

6+1 inflFiles

VISUAL-DESMESH

DESCUS-I & II Modeling

3D rendering

2D grid model

DESCUS-I

DESCUS-II

Positive moment of the inner exterior girder

Negative moment of the inner exterior girder

Moment Influence SurfacesPlacement of Live Load on Influence Surface

Consider a Influence surface as a 3D contour graph, instead of 2D influence line

Design or Legal Load CasePermit Load Case

DESCUS-I Positive Moment Influence Surface

By using the influence surface, DESCUS program places the load at the critical longitudinal position and move laterally to get the max/min values.

Fraction of vehicular loading

DESCUS-I Negative Moment Influence Surface

Components of Normal Stresses

AASHTO combined stresses due to warping with lateral loads to call it lateral bending stress

Strength Limit State (Flexure)• Flexural -Composite I-Sections in Positive Flexure• Compact Section (LRFD Eq. 6.10.7.1.1-1)

(not used in curved girder structures)

• Noncompact Sections Compression flange (LRFD Eq. 6.10.7.2.1-1)

Tension flange (LRFD Eq. 6.10.7.2.1-2)

nfxtu MSfM 31

ncfbu Ff

ntfbu Fff 31

Strength Limit State (Flexure)

• Flexural -Composite I-Sections in Negative Flexure and Noncomposite I-Sections

Discretely Braced Flanges in

Compression(LRFD Eq. 6.10.8.1.1-1)

Discretely Braced Flanges in

Tension(LRFD Eq. 6.10.8.1.2-1)

Continuously Braced

Flanges in Tension or

Compression

(LRFD Eq. 6.10.8.1.3-1)

ncfbu Fff 31

ntfbu Fff 31

yfhfbu FRf

Service Limit State (Flexure)

• For Composite I-sections: For the top steel flange:

(LRFD Eq. 6.10.4.2.2-1)

For the bottom steel flange: (LRFD Eq. 6.10.4.2.2-2)

• For Noncomposite I-Sections:(LRFD Eq. 6.10.4.2.2-3)

yfhf FRf 95.0

yfhf FRff 95.05.0

yfhf FRff 80.05.0

Components of Shear Stresses

AASHTO considers St. Venant torsional shear stress in steel boxes.

Strength Limit State (Shear)

• Shear

nvu VV

LRFR Flexure Rating for AASHTO Load

• A1. Inventory Rating: The minimum of

(a)

(b)

• A2. Operating Rating: The minimum of

(a)

(b)

f

f - F = RF1LL+

b+

/Db

lINV

pDWC

lSTRN

f

f - F = RF 1LL+b+

Db+

IISERV l

DWClSERV

f

f - F = RF1LL+

b+

/Db

lOPER

pDWC

lSTRN

f

f - F = RF 1LL+b+

Db+

ISERV l

DWClSERV

LRFR Flexure Rating for Non-AASHTO Load

• FSTRN — Allowable flexural stress for Strength Limit State I or II

• FSERV — Allowable flexural stress for Service Limit State I or II

• fb+l — Bending + (1/3 for Strength LS & ½ for Service LS) * lateral bending stresses for dead load (DC or DW) or live load (LL+1)

• p — Dead load factor (default = 1.25 to DC and 1.5 to DW for Load and Resistance Factor rating)

• — Live load factor (default = 1.75 for Inventory, INV, 1.35 for Operating, OPER, 1.0 for Service-I or Permit Load SERV-I, 1.3 for Service-II or Legal Load SERV-II)

• LL — Live load factor based on LRFR Strength Limit State Table 6-5 for Legal Load and Table 6-6 for Permit Load

f

f - F = RF1LL+

b+

/Db

lLL

pDWC

lSTRN

f

f - F = RF 1LL+b+

Db+

IorIISERV l

DWClSERV

The minimum of

(a)

(b)

LRFR Shear Rating • A1. Inventory Rating (AASHTO):

• A2.Operating Rating (AASHTO):

• A3.Operating Rating (Non-AASHTO):

V

VV

INV

pDWC

STRN

1LL+b

/Db -

= RF

V

VVbOPER

pDWC

STRN

1LL+

/Db -

= RF

V

VV

LL

pDWC

STRN

1LL+b

/Db -

= RF

Load Rating for the FAST Act’s • EV2 – Set 1: Single-lane (EV2 One_Lane)

Set 2: With an adjacent unrestricted legal vehicle (EV2 w/SU7v)

• EV3 – Set 1: Single-lane (EV3 One_Lane)Set 2: With an adjacent unrestricted legal

vehicle (EV3 w/SU7v)

Example of EV Loaded Cases w/3 Lanes & 6 Girders

a. EV loaded on lane 1 with AASHTO live load on remaining lanes

b. EV loaded on lane 2 with AASHTO live load on remaining lanes

c. EV loaded on lane 3 with AASHTO live load on remaining lanes

• Multiple presence: If necessary, when combined with other unrestricted legal loads for rating purposes, the emergency vehicle needs only to be considered in a single lane of one direction of a bridge

FHWA Bridge Load Ratings for National Bridge Inventory

• For bridges and total replacement bridges designed by LRFD using HL-93 loading, prior to October 1, 2010, rating factors shall be based on LRFR methods using HL-93 loading or LFR methods using HS-20 (MS 18) loading

• For bridges and total replacement bridges designed by LRFD Specifications using HL-93, after October 1, 2010, RF shall be based on LRFR methods using HL-93 loading

• For bridges designed or reconstructed by either Allowable Stress Design (ASD) or Load Factor Design (LFD) Specifications, rating factors shall be based on LRFR methods using HL-93 loading or LFR methods using HS-20 (MS 18) loading.

• For bridges partially reconstructed resulting in the use of combination specifications (e.g. a reconstructed superstructure designed by LRFD supported by the original substructure designed by ASD) or unknown specifications, rating factors shall be based on LRFR methods using HL-93 loading or LFR methods using HS-20 (MS 18) loading.

• For bridges designed or reconstructed by either ASD or LFD Specifications and for bridges partially reconstructed resulting in the use of combination specifications or unknown specifications, after October 1, 2010, rating factors shall be based on LRFR methods using HL-93 loading or LFR methods using HS-20 (MS 18) loading