ENCE717 – Bridge Engineering Load 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 ( IM LL P DW DC C RF L P DW DC C DC DW P LL IM DC DW P L is the structural capacity (=c s R; 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
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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
• 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)
• 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
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