1. Load Rating of Segmental Concrete Bridges Consistent with LRFR Requirements Corven Engineering Inc. November, 2003 American Segmental Bridge Institute Annual Convention, 2003

2. Inventory Rating: for design loads. The design load level that can safely use a bridge for an indefinite period of time. Operating Rating: for design, legal and permit loads. The absolute maximum load level to which a structure may be subjected. Takes advantage of conservatism in design. Definitions

3. For Segmental Bridges Inventory and Operating Ratings are performed at both the strength limit state and service limit state. Clearing Up A Misconception FDOT Manual 1995 - Section II.B.8 “The load factor method is the required method for load rating structures, unless circumstances dictate that other methods should be used. …”

4. Existing Criteria based on AASHTO Standard Specification (LFD) and Guide Specification for Segmental Bridges. When allowable Service stress is zero, ratings for Inventory and Operating are same – i.e. no benefit for Operating Introduction of AASHTO LRFD & LRFR. Current Issues in Rating Segmental Bridges

5. An AASHTO approved guide specification for rating all bridge types consistent with LRFD. Uses target reliability, β, of 2.5 for rating v. 3.5 for design ( via e.g. γ L = 1.35 OP vs. 1.75 DES ) Primarily a strength limit state specification Does not address, specifically, bridges governed by Service (e.g. zero tension) = Segmental Bridges. Load Resistance Factor Rating - LRFR

6. R-Q (R-Q) mean  Graphical definition of reliability index 

7. LFD LRFD β ~ 3.5 β ~ 2.5 LRFR (Inv) LRFR (Op)

8. To develop Load Rating Guidelines that: Are consistent with LRFR. Address Segmental Bridges. Goal

9. Rating Equation Where,

10. LRFR - Segmental Bridges at Inventory Level (= LRFD Design) Service Limit State Strength Limit State ok

11. ? LRFR - Segmental Bridges at Operating Level Service Limit State Strength Limit State ? ? ok

12. Capacity Factors – Strength Limit State

13. LRFR – Condition Factor ranges from 0.85 to 1.00 Structural Condition Good or satisfactory Fair Poor 1.00 0.95 0.85 NBI Rating > 6 5 < 4 Condition Factors - General

14. Examples: PC Balanced Cantilever, to new criteria1.00 PC Bal Cant, old, no leaks or corrosion1.00 PC Bal Cant, old, joint leaks, stains0.85 Span-by-Span, no damage or corrosion1.00 Condition Factors –Segmental PT

15. NCHRP 406: many simple and continuous I-beam bridges (conc. and steel) – determined reliability, β, and φ S Results = basis of LRFR:φ S 2 girders / truss / arch (welded)0.85 ditto(riveted)0.90 3 girders, spacing < 6 ft0.85 4 girders, spacing < 4 ft0.95 All other girders and slabs1.00 Floorbeams spacing > 12 ft0.85 System Factor (φ s ) – AASHTO LRFR

16. φ s =.85 2 Girders, Truss or Arch System Factor (φ s ) – AASHTO LRFR

17. φ s = 1.00 Multiple I-girders – (non-continuous) System Factor (φ s ) – AASHTO LRFR

18. Longitudinal Continuity (redundancy) Transverse Continuum of Closed Box Number of Tendons per Web (Multiple Tendon Paths) Number of webs System Factor for Segmental Bridges Need to account for:

19. φ s = 0.85 to 1.30 Established by applying NCHRP 406, engineering studies, known performance System Factor (φ s ) – Segmental LRFR

20. Simple Span = 1 hinge System Factor (φ s ) – Longitudinal Continuity End Span = 2 hinges Interior Span = 3 hinges φ S interior 0.10 > φ S simple φ S end 0.05 > φ S simple φ S simple = 1.0

21. Continuum of closed cell box: increase φ s by 0.10 (Box > I-girders w. multi-diaphragms 0.07 > no diaphragms) System Factor (φ s ) – Continuum of Box

22. Multiple load-paths considered in AASHTO LRFR as number of girders per deck multiple rivets or bolts versus single welds LRFR does not address PT segmental bridges FDOT “New Directions” requires accounting for “Multiple Post-Tensioning Tendon Paths” (MTP) φ S “pivotal values” established from case history … (φ S improves by 0.10 going from 2 to 4 tendons / web) System Factor (φ s ) – No. of Tendons / Web (MTP)

23. MTP, φ S pivotal values – Cantilever End Span 2 tendons / web / face: φ S > = 1.00 (O.K., conservative) But, 1 tendon / web / face: φ S = 0.85 (no PT redundancy) Existing / experience: Critical Section

24. 2 tendons / web (minimal, “old doing O.K”): φ S = 1.00 However, 1 tendon / web = (not allowed): (φ S = 0.85) Existing / experience: Critical Section MTP, φ S pivotal values – Interior Span-by-Span

25. Interior Span:φ S = 1.20 End Span: φ S = 1.15 Simple Span: φ S = 1.10 “New Directions” – Min. 4 tendons / web: MTP, φ S pivotal values – Span-by-Span

26. Number of Webs: Segmental boxes are internally redundant by the closed cell continuum Most segmental bridges have two webs Recognition of enhancement of third web is appropriate Ties in to MTP and closed continuum For three or more webs increase φ S by 0.10 System Factor (φ s ) – Number of Webs

27. Base system factor for concrete girders= 1.00 Longitudinal continuity (statically indeterminacy)+0.10 Transverse continuum of segmental box +0.10 Multiple tendons per web (MTP) +0.10 Added webs (also relates to MTP)+0.10 Other (reliability) considerations +0.10 Possible total=1.50 Use maximum of 1.30 (LRFR max of 1.20 not intended for bridges as redundant as closed cell boxes with multiple load and tendon paths) - Summary

28. Span number of tendons / web Type 1 2 3 > 4 Interior0.90 1.05 1.15 1.20 End Span0.85 1.00 1.10 1.15 Stat. Det.n/a 0.90 1.00 1.10 (For 3 or more webs, add 0.10) φ S – Balanced Cantilever (2 Webs)

29. Spannumber of tendons / web Type 1 2 3 > 4 Interiorn/a 1.00 1.10 1.20 End Spann/a 0.95 1.05 1.15 Simplen/a n / a 1.00 1.10 (For 3 or more webs, add 0.10) φ S – Span-by-Span (2 Webs)

30. Preceding values were for longitudinal flexure. Longitudinal Shear and Torsion Transverse Flexure & Other Effects

31. ? LRFR - Segmental Bridges at Operating Service Limit State Strength Limit State ? ok

32. 2 Conditions – at precast joints or not. When tension is permissible, to achieve β = 2.5, use φ S to increase allowable stress … but… Increasing φ S has no effect on a precast joint – so use φ S = 1.00 and reduce live load to get β ~ 2.5 Capacity Factors – Service Limit State

33. Use γL = 0.80 for Service III tension check for Inventory Rating under notional (HL 93) loads Use γL = 1.00 (Service I) to check tension under specific truck loads (i.e. HL 93 truck / tandem / legal / permit) Live Load Factors (γ L ) – Service Limit State

34. Use number of striped lanes v. full lanes for Longitudinal Operating Rating at Service – multi-presence m OP < m DES / INV Limit m max < 1.00 (multi-presence) for Inventory and Operating Ratings for specific truck or axle loads. (for new Design m max = 1.20 for 1 lane - allows for notional load / rogue trucks) Live Load Factors (γ L ) – Service Limit State

35. LRFR - Segmental Bridges at Operating Level Service Limit State Strength Limit State ok

36. Load Combinations at Strength and Service Limit States

37. Load Factors – Permanent and Thermal Longitudinal Service Strength DC1.00 1.25 DW1.00 1.50 EL 1.00 1.00 FR1.00 1.00 CR, SH1.00 0.50 TU1.00 0.50 TG (Inventory)0.50 0 TG (Operating) 0 0 Transverse Service Strength 1.001.25 1.001.50 1.001.00 n / an / a

38. Number of lanes as per LRFD Lanes loaded with HL93 (truck and lane)* Multiple Presence Factor “m” as per LRFD 0.5TG only with Live Load at Service Service III tension, γL = 0.80 (notional live load *) Load factor, γL = 1.75 at Strength ( LRFD LRFR ) * Except for transverse – use no uniform lane load Inventory Rating – Design Loads

39. Service: Number per striped lanes (place for max. effect) Strength: Number per full LRFD design lanes Same Legal Load in each load lane No TG Multiple Presence Factor “m” - cap at 1.0 (specific load) Service I for tension, γL = 1.00 (specific live load) Load Factor, γL = 1.35 at Strength (deviation from LRFR) * Transverse = axle loads only Operating Rating – Legal Loads

40. Service: Number per striped lanes (place for max. effect) Strength: Number per full LRFD design lanes Permit load in one lane, HL93 in others * No TG Multiple Presence Factor “m” - cap at 1.0 (specific load) Service I for tension, γL = 1.0 (specific live load) Load Factor, γL = 1.35 to 1.15 (deviation from LRFR) * Transverse = axle loads only, no uniform Operating Rating – Permit Loads

41. Allowable Stresses

42. CIP joints (Type A) New DesignLoad Rating and transverse tension aggressive3√f’c 4.5√f’c moderate6√f’c 6√f’c Epoxy joints (A) 0 tension 0 tension Dry joints (B) 100 psi comp 100 psi @ Inv 0 tens @ Op Principal Tension at N.A. 3√f’c final 4√f’c (4.5√f’c temp constn.) Allowable Stresses at Service Limit State

43. Selected LRFR Ratings of Two FDOT Segmental Bridges July 24, 2003 Florida Department of Transportation

44. Mid-Bay Bridge 136 ft span x span, 2 webs, external PT

45. Mid-Bay Bridge - Controlling Ratings Load LFD LRFR 0.59 0.55 0.59 0.99 Des Inv * Des Op * LFD: Inventory and Operating = HS 20 Longit Flex at Service 100 psi comp. 3 lanes live load LRFR: Inventory = HL 93 Longitudinal Flexure at Service 100 psi comp. for 3 lanes live load LRFR:Operating = HL 93 Longitudinal Flexure at Strength Limit for 3 lanes live load (Op. Service @ 100 psi; RF = 1.25)

46. Port of Miami Bridge PC Balanced cantilever, 3 webs, internal PT

47. Port of Miami - Controlling Ratings Load LFD LRFR 1.09 1.42 1.71 1.70 Des Inv * Des Op * LFD: Inventory = HS 20 Longitudinal Shear at Strength Limit for 4 lanes live load LFD:Operating = HS 20 Longitudinal Flexure at Service Limit for 4 lanes live load LRFR: Inventory = HL 93 Longitudinal Shear at Strength Limit for 4 lanes live load LRFR:Operating = HL 93 Tandem - Transverse Flexure at Service Limit

48. FDOT – William Nickas, Larry Sessions Corven Engineering – John Corven, Alan Moreton Expert Assistance – Dr. Dennis Mertz Acknowledgements Key Participants Florida Department of Transportation

49. Q mean R mean Q n R n  Q n RnRnRnRn f(R,Q) R,Q

50. MTP, φ s pivotal values – I-Girders Full continuity, interior span: φ S = 1.10 Full continuity, end span:φ S = 1.05 Simple Span (AASHTO LRFR):φ S = 1.00 “New Directions” minimum of 3 tendons / web

51. Mid-Bay Bridge - Transverse Ratings Trans: @ 4.5√f’cTrans Flexure: StrengthLoad LFD LRFR 1.12 1.05 LFD (γ L ) LRFR (γ L ) 1.59 (2.17) 1.71 (1.75) 2.59 (1.33) 2.21 (1.35) Des Inv * Des Op * * LFD = HS 20 Truck only LRFR = HL 93 Tandem only - no uniform lane load

52. Mid-Bay Bridge – Longitudinal Ratings Long. Flex - ServiceLong. Flex - StrengthLoad LFDLRFR (n @ γ L ) 0.590.55 (3 @ 0.80) 0.591.25 (2 @ 1.00) LFD (γ L )LRFR (γ L ) 0.92 (2.17)0.76 (1.75) 1.50 (1.33)0.99 (1.35) Des Inv * Des Op * * LFD = HS 20 (max of truck or uniform + point load) LRFR = HL 93 (including uniform lane load) 3 lanes except LRFR Operating Service = 2 striped 100 psi comp LFD Inv, Op & LRFR Inv; zero LRFR Op 0.5 TG with LRFR Service live load Load Des Inv * Des Op * Web Principal TensionWeb Shear - Strength LFD (γ L )LRFR (γ L ) 1.54 (2.17)1.43 (1.75) 2.52 (1.33)1.85 (1.35) LFDLRFR (n @ γ L ) 3.272.95 (3 @ 0.80) 3.272.36 (2 @ 1.00)

53. Port of Miami - Transverse Ratings Trans: @ 4.5√f’cTrans Flexure: StrengthLoad LFD LRFR 1.82 1.70 LFD (γ L ) LRFR (γ L ) 2.41 (2.17) 2.80 (1.75) 3.92 (1.33) 3.64 (1.35) Des Inv * Des Op * * LFD = HS 20 Truck only LRFR = HL 93 Tandem only - no uniform lane load

54. Port of Miami – Longitudinal Ratings Long. Flex - ServiceLong. Flex - StrengthLoad LFDLRFR (n @ γ L ) 1.712.15 (4 @ 0.80) 1.712.05 (3 @ 1.00) LFD (γ L )LRFR (γ L ) 2.30 (2.17)2.57 (1.75) 3.59 (1.33)3.33 (1.35) Des Inv * Des Op * * LFD = HS 20 (max of truck or uniform + point load) LRFR = HL 93 (including uniform lane load) 4 lanes except LRFR Operating Service = 3 striped Zero tension longitudinal service Load Des Inv * Des Op * Web Principal TensionWeb Shear - Strength LFD (γ L )LRFR (γ L ) 1.09 (2.17)1.42 (1.75) 1.78 (1.33)1.84 (1.35) LFDLRFR (n @ γ L ) 2.963.40 (4 @ 0.80) 2.962.83 (3 @ 1.00)

55. Posting Avoidance

56. Reduce dead load by accurate survey, γDC = 1.15 Reduce dead load using weighed segments, γDC = 1.10 Reduce dynamic allowance, grind smooth, IM = 1.10 Reduce for single Permit at crawl speed, IM = 1.00, γL = 1.10 More sophisticated analysis (F.E. / barrier stiffening) Zero tension in dry joints / some tension in epoxy joints Raise allowable transverse tensile limit, if possible Posting Avoidance

57. Normalize LRFD/LRFR so m = 1.00 for 1 lane (not 1.20) No uniform lane load for transverse ratings – but in order to use m = 1.00 for 1 lane, increase axle loads by 20% Use SERVICE III with γL = 0.80 for Operating Ratings instead of using “number of striped lanes” with γL = 1.00 (reducing from 3 design to 2 striped lanes calibrates OK - but reducing from 4 to 3 not so well) Would rather have: