Outline of LRFR for Steel Bridges. Probabilistic Design and Evaluation

Transcription

1 ENCE717 Bridge Engineering Load and Resistance Factor Rating (LRFR) or Steel Bridges Chung C. Fu, Ph.D., P.E. (http: Outline o LRFR or Steel Bridges General AASHTO LRFR Rating or steel truss bridges Rating or steel line girders Rating or reined steel bridge analysis Rating actors or steel girder bridges Basic Rating Factor Equation or the LRFR Method C DW P LL DW P L C RF DW DW PP LL( 1 IM ) L is the structural capacity (= c s R; c: condition, s: system) is the dead-load eect o structural components and attachments is the dead-load eect o wearing suraces and utilities is the permanent loading other than dead loads is the live-load eect IM is the dynamic load allowance is the load actor or structural components and attachments is the LRFD load actor or wearing suraces and utilities is the load actor or permanent loads other than dead loads is the evaluation live-load actor Probabilistic Design and Evaluation Analysis used BIAS CO AASHTO S/D AASHTO LRFD AASHTO Reined Field Test 1.0 4

2 Federal Bridge Formula B (FBF B) Permit* load FEDERAL TRUCK WEIGHT LIMITS FOUR BASIC FEDERAL WEIGHT LIMITS APPLY: SINGLE AXLE (20,000 #) TANDEM AXLE (34,000 #) BRIDGE FORMULA B GROSS EHICLE WEIGHT (80,000 #) ONLY SEEN STATES APPLY THESE LIMITS STATEWIDE WITHOUT MODIFICATION. OTHER STATES ALLOW TRUCKS EXCEEDING THESE LIMITS UNDER THE GRANDFATHER PROISIONS. Any vehicle or combination o loads having a gross weight in excess o 40 tons (or 80 kips). * = Permits are also required or over-sized vehicles. But, or the purposes o load rating, we are reerring to permits that are required due to over-weight only. Superload 1) DESIGN LOAD RATING (HL-93) 2) LEGAL LOAD RATING (POSTING) Any vehicle or combination o loads having a gross weight in excess o 60 tons (or 120 kips). 3) PERMIT LOAD RATING (OERWEIGHT TRUCKS) IM = 33% Is Standard. Following alues are Optional: Legal Load rating Riding surace conditions: smooth IM = 10%; minor surace irregularities IM = 20%; major surace irregularities IM = 33% Permits same, except or: slow moving (< 5mph) vehicles IM = 0%

3 LRFR Flowchart or Load Ratings LRFR Limit States and Load Factor Factors Table 6A a-1 & 3b-1 Table 6A a-1 Routine Permit Truck (3, 3S2, 3-3, ) Special Permit Truck LRFR Live Loads Factors L From Elements to Analysis Models Element Rod/Bar Plate Brick Beam Shell Rigid link To orm Beam (DASH) Plane truss Plane rame Full 3D FEM (TRAP) Grid (DESCUS) Space truss Space rame

4 Ratings o Three Types o Steel Bridges 2D Truss Bridge Modeling Truss Bridges (TRAP Truss Rating and Analysis Program) Straight Steel Girder Bridges (DASH Design and Analysis o Straight Highway Bridges) Curved or Skewed Steel Girder Bridges (DESCUS I & II Design and Analysis o Curved I or Box Steel Girder Bridges) Member released rom resisting axial orces Truss Inluence Lines and Applied Loading Truss Bridge Load Rating Axial Tension P r = P n where Pr yfy Ag P F A U } lesser (LRFD Eq & -2) r u u n Axial Compression P r = P n where P n = 0.66 F y A s or λ 2.25 (LRFD Eq ) 0.88Fy As Pn or λ > 2.25 (LRFD Eq ) / DW P - r p a a LL where LL is based on ADTT FHWA Load Rating Guidance and Examples For Bolted and Riveted Gusset Plates In Truss Bridges

5 Line Girder (Approximate) Analysis Method Assumptions: Single line girder Eective lange width(shear lag) Since 2008, eective width b e = tritary width b (AASHTO Art ) Live load distrition actor Live load inluence line Line Girder Modeling AASHTO LRFD live load distrition actor design equations or shear and moment is recommended or rating. Assumed constant deck width, parallel beams with about the same stiness Developed or design trucks Developed to bound within that structural type Limited ranges o applicability. (When exceeded, the LRFD speciications mandate reined analysis.) Line girder Inluence Lines or Moment & Shear Moment Special Permit Review using Reined Analysis Reined analysis o Special Permits allows the input o dierent trucks and live load actors in each lane. Appropriate adjacent live load and permit load actors or use in reined analysis (Strength II Limit State) Shear

6 Reined Analysis Methods DESCUS Flowchart or the Curved Steel Bridge Design and Load Rating Grillage analogy method Orthotropic plate method Articulated plate method Finite strip method Finite element method Sotware package Revise 6+1 inl Files Geometry & Loading Data Input Graphic eriication DL & SDL Application LL Inluence Surace Generation LL Application by In. Surace Stress Allowables DESCUS Preprocessor ISUAL-DESMESH DESCUS Main processor Load Rating DESCUS-I & II Modeling Moment Inluence Suraces 3D rendering DESCUS-I DESCUS-II 2D grid model Positive moment o the inner exterior girder Negative moment o the inner exterior girder

7 Placement o Live Load on Inluence Surace Design or Legal Load Case Permit Load Case DESCUS-I Positive Moment Inluence Surace Fraction o vehicular loading Consider a Inluence surace as a 3D contour graph, instead o 2D inluence line By using the inluence surace, DESCUS program places the load at the critical longitudinal position and move laterally to get the max/min values. DESCUS-I Negative Moment Inluence Surace Components o Normal Stresses AASHTO combined stresses due to warping with lateral loads to call it lateral bending stress

8 Strength Limit State (Flexure) Flexural -Composite I-Sections in Positive Flexure Compact Section (LRFD Eq ) (not used in curved girder structures) M u 1 3 S Noncompact Sections xt M Compression lange (LRFD Eq ) F nc Tension lange (LRFD Eq ) 1 3 F nt n Strength Limit State (Flexure) Flexural -Composite I-Sections in Negative Flexure and Noncomposite I-Sections Discretely Braced Flanges in Compression Discretely Braced Flanges in Tension Continuously Braced Flanges in Tension or Compression R F nc F h F y nt (LRFD Eq ) (LRFD Eq ) (LRFD Eq ) Service Limit State (Flexure) Components o Shear Stresses For Composite I-sections: For the top steel lange: 0. 95R For the bottom steel lange: For Noncomposite I-Sections: h F R F R F y h h y y (LRFD Eq ) (LRFD Eq ) (LRFD Eq ) AASHTO considers St. enant torsional shear stress in steel boxes.

9 Strength Limit State (Shear) Shear u v n LRFR Flexure Rating or AASHTO Load A1. Inventory Rating: The minimum o (a) (b) A2. Operating Rating: The minimum o (a) (b) FSTRN - p bl b+ l IN F - SER b+ l SER II / DW b+ l DW FSTRN - p bl b+ l OPER / DW F - SER b+ l SER I b+ l DW LRFR Flexure Rating or Non-AASHTO Load The minimum o (a) (b) FSTRN - p b b+ l LL / DW l DW F - SER b+ l SER IorII b+ l F STRN Allowable lexural stress or Strength Limit State I or II F SER Allowable lexural stress or Service Limit State I or II b+l Bending + (1/3 or Strength LS & ½ or Service LS) * lateral bending stresses or dead load ( or DW) or live load (LL+1) p Dead load actor (deault = 1.25 to and 1.5 to DW or Load and Resistance Factor rating) Live load actor (deault = 1.75 or Inventory, IN, 1.35 or Operating, OPER, 1.0 or Service-I or Permit Load SER-I, 1.3 or Service-II or Legal Load SER-II) LL Live load actor based on LRFR Strength Limit State Table 6-5 or Legal Load and Table 6-6 or Permit Load LRFR Shear Rating A1.Inventory Rating (AASHTO): STRN - IN A2.Operating Rating (AASHTO): A3.Operating Rating (Non-AASHTO): D C / DW p b LL+1 b D C / DW STRN - p b LL+1 OPER b STRN - LL D C / DW p b LL+1 b