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CM - Jauregui - Sapienza University of Rome (60 min, part i, members modified)

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Slide del seminario del Prof. Jauregui su LOAD RATING OF RIVETED STEEL ARCH BRIDGE MEMBERS al corso di Costruzioni Metalliche.

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CM - Jauregui - Sapienza University of Rome (60 min, part i, members modified)

  1. 1. LOAD RATING of RIVETED STEEL ARCH BRIDGE MEMBERS Dr. David V Jáuregui Wells-Hatch Professor of Civil Engineering New Mexico State University Las Cruces, NM Graduate Seminar Sapienza University of Rome November 28th, 2013
  2. 2. OUTLINE of PRESENTATION BRIDGE BACKGROUND and DESCRIPTION AASHTO LOAD RATING ANALYSIS LOAD RATING of FLOOR SYSTEM LOAD RATING of COLUMNS LOAD RATING of ARCH RIB FINAL LOAD RATING CONCLUSIONS and RECOMMENDATIONS
  3. 3. BRIDGE BACKGROUND and DESCRIPTION • HISTORY: the Omega Bridge was designed by Finney and Turnispeed, fabricated by the American Bridge Company, and erected by the Vinson Construction Company. • ORIGINAL DESIGN (1951): based on ASD method and H-20 vehicular live load • REHABILITATION (1992): based on LFD method and HS-20 vehicular live load • CURRENT STUDY: determine the current capacity level of the Omega Bridge based on the LFR method
  4. 4. West Road Route e idg r aB g me O
  5. 5. Past Inspection and Evaluation Studies • 1973 – HNTB (Howard Needles Tammen & Bergendoff) Corporation; conducted an in-depth bridge inspection and structural analysis of deck and superstructure • 1983 – Holmes and Narver (with assistance from NMSU); assessed structural condition of original deck and pedestrian walkway which was later replaced • 1988 – Merrick & Company; investigated various alternatives along with construction cost estimates for rehabilitating the Omega Bridge (done in 1992)
  6. 6. 51' - 312" 7' - 6" 39' - 9" 9' - 1114" Lane 1 9' - 1114" Lane 2 9' - 1114" Lane 3 9' - 1114" Lane 4 Before 1992 Rehabilitation 7' - 412" 6' - 9" 6' - 9" 7' - 412" 6' - 9" 35' - 0" 55' - 6" 8' - 0" 44' - 0" 11' - 0" Lane 1 11' - 0" Lane 2 11' - 0" Lane 3 11' - 0" Lane 4 C Bridge L 1.5% West Outrigger Beam 6' - 9" After 1992 Rehabilitation Interior Stringer Exterior Stringer 3' - 6" 1.5% Spandrel Beam Floor Beam 7' - 412" 6' - 9" 6' - 9" 35' - 0" 6' - 9" 7' - 412 " 6' - 9" 3' - 6"
  7. 7. Details of Bridge Rehabilitation • Increased cross-section width (11’ traffic lanes) • Light-weight concrete deck (28-day strength of 4.5 ksi) • Shear studs and cover plates installed on interior stringers and spandrel beams • Exterior stringers supported by outrigger beams added on both sides of bridge width
  8. 8. BRIDGE DESCRIPTION • LAYOUT: 814.5-foot long with a 442.5-foot arch span and six 62-foot approach spans; three approach spans at each end of the bridge • CONFIGURATION: (1) Floor System: two spandrel beams; six stringers; 22 floor beams. (2) Column System: four pairs of pier columns; two pairs of skewback columns; 14 pairs of arch columns. (3) Arch Rib: a pair of two-hinge arch ribs. 62ft 62ft 62ft 15 spans (29.5ft each) 106.6ft 422.5ft 62ft 62ft 62ft
  9. 9. Arch column # 62ft 62ft 15 spans (29.5ft each) 62ft 1 2 3 4 5 6 7 8 9 10 62ft 11 12 13 62ft 62ft 14 Pier column #1 Pier column #2 Pier column #4 106.6ft Pier column #3 46" x 3 4" 8" x 8" x 3 4" L 422.5ft Skewback column #1 Skewback column #2 24" 71 12" x 12" 48" 4" x 4" x 6" x 4" x 3 4" L 3 8" 1 24" x 2" L 72" 4" x 4" x 12" Pier and Arch Columns 24" x 12" 24" 4" x 4" x 12" 24" 48" x 12" Skewback Columns Arch Rib 24.5" back-to-back 25.5" inside to inside of PLs 48.5" back-to-back
  10. 10. 55' - 6" 8' - 0" 44' - 0" 11' - 0" Lane 1 11' - 0" Lane 2 11' - 0" Lane 3 11' - 0" Lane 4 C Bridge L 1.5% Interior Stringer Exterior Stringer West Outrigger Beam 3' - 6" 1.5% 7' - 412" 6' - 9" Spandrel Beam Floor Beam 6' - 9" 6' - 9" 6' - 9" 7' - 412 " 6' - 9" 25" - 6" 3' 35' - 0" 25" x 3 8" top plate L 8" x 6" x 9 16" L 8" x 6" x 5 8" 48.5" PL 48" x 3 8" x 32'-9" Floor Beams 4" x 4" x 3 8" L 66.875" N.A. 48.5" 66" x 3 8" web plate PL 48" x 3 8" x 32'-9" 31.789" Spandrel Beam 8" x 6" x 3 4" L L
  11. 11. AASHTO LOAD RATING ANALYSIS Components subject to single load effect where RF = rating factor (inventory or operating) Rn = nominal member capacity (flexure or compression) D = nominal dead load effect L = nominal live load effect I = live load impact factor = 50 / (L + 125) γD = dead load factor = 1.3 γL = live load factor = 2.17 (inventory) or 1.3 (operating) Components subject to combined loading Interaction equation for columns and arch rib (discussed later)
  12. 12. Rating Vehicles DESIGN LOADING: AASHTO HS-20 Truck or Lane Load LEGAL LOADING: AASHTO Type 3, 3S2, and 3-3 Trucks PERMIT LOADING: Emergency-One Titan Fire Truck
  13. 13. Rating Vehicles (cont.) HS-20 Truck: 72 kips 32 k 32 k 36 k 36 k 8k 14 to 30 ft 14ft AXLE NO.1 2 6ft 3 Fire Truck: 77.74 kips 18.98 k 18.98 k 5 ft AXLE NO.1 19.89 k 5 ft 12.7 ft 2 19.89 k 3 38.87 k 38.87 k 7.2 ft 4 Legal Trucks: 50, 72, and 80 kips
  14. 14. (a) TYPE 3: Unit Weight = 50 kips 16 k 25 k 17 k 17 k 15 ft 4 ft AXLE NO.1 2 25 k 6ft 3 (b) TYPE 3S2: Unit Weight = 72 kips 10 k 15.5 k 15.5 k 11 ft AXLE NO.1 4 ft 2 36 k 15.5 k 15.5 k 22 ft 4 ft 3 4 36 k 6ft 5 (c) TYPE 3-3: Unit Weight = 80 kips 12 k 12 k 12 k 15 ft AXLE NO.1 15 ft 4 ft 2 16 k 3 14 k 14 k 16 ft 4 4 ft 5 40 k 40 k 6ft 6
  15. 15. LOAD RATING of FLOOR SYSTEM
  16. 16. Description of Rating Model: Stringers Section #2: Negative moment, non-composite section (no cover plates) Interior Stringer N1 (Abutment) N2 N3 (Pier Col #1) N4 N5 (Pier Col #2) N6 N7 (Skewback Col #1) Section #3: Positive moment, non-composite section (no cover plates) Section #1: Positive moment, composite section (top and bottom cover plates) Section #2: Negative moment, non-composite section (no cover plates) Exterior Stringer N1 (Abutment) N2 N3 (Pier Col #1) N4 N5 (Pier Col #2) N6 N7 (Skewback Col #1) Section #3: Positive moment, non-composite section (no cover plates) Section #1: Positive moment, composite section (no cover plates) NOTE: The four interior stringers are W21x62 sections of ASTM A7 steel; The two exterior stringers are W21x62 sections of ASTM A36 steel.
  17. 17. Load Rating Analysis Results: Stringers Interior Stringer Exterior Stringer Section #3 Section #1 Section #2 Section #3 2.46 1.09 1.16 2.07 1.21 1.29 TYPE 3 3.05 1.41 1.42 2.57 1.57 1.58 TYPE 3S2 3.19 1.03 1.80 2.69 1.15 2.01 TYPE 3-3 3.84 1.25 2.03 3.23 1.39 2.26 FIRE 2.55 0.97 1.23 2.14 1.08 1.37 HS-20 Operating Rating Section #2 HS-20 Inventory Rating Section #1 4.11 1.81 1.94 3.46 2.02 2.15 TYPE 3 5.10 2.36 2.36 4.29 2.62 2.63 TYPE 3S2 5.33 1.72 3.01 4.49 1.92 3.35 TYPE 3-3 6.41 2.09 3.38 5.40 2.33 3.77 FIRE 4.25 1.62 2.05 3.58 1.80 2.28 Controls
  18. 18. Description of Rating Model: Floor Beams 4'-9" 3'-6" 6'-9" 6'-0" 4'-0" 7'-4.5" Slab 6'-9" 6'-0" 4'-0" 6'-9" 35'-0" 6'-9" 6'-0" 4'-9" 7'-4.5" 6'-9" 3'-6" Exterior Stringer 0.872 x (36 kips) per force. Spandrel Beam 42.6 k 42.8 k 42.8 k 42.6 k Interior Stringer Floor beam 7'-4.5" 6'-9" 6'-9" 6'-9" 7'-4.5"
  19. 19. Description of Rating Model: Floor Beams (cont.) HS-20 Live Load Effects: FB#2 -42.6 k -42.8 k -42.8 k 630 k-ft -42.6 k 630 k-ft 919 k-ft 919 k-ft Dead Load Effects: FB#2 -22.1 k 153 k-ft -17.2 k -17.2 k -17.2 k 124 k-ft -17.2 k 134 k-ft 252 k-ft 255 k-ft 136 k-ft -19.5 k
  20. 20. Load Rating Analysis Results: Floor Beams Floor Beam 0.85* TYPE 3 1.22 1.17* TYPE 3S2 1.13 1.16* TYPE 3-3 1.21 1.29 0.91 0.88* HS-20 1.46 1.41 TYPE 3 2.04 1.96 TYPE 3S2 1.89 1.94 TYPE 3-3 2.03 2.15 FIRE Operating Rating 0.88 FIRE NOTE: FB#6 HS-20 Inventory Rating FB#2 1.51 1.47 Floor beam FB#2 is located one bay from the abutment. Floor beam FB#6 is located above the arch span. asterisk (*) symbol indicates the section does not satisfy the compact requirements of the AASHTO Specification.
  21. 21. Description of Rating Model: Spandrel Beam BEAM Model SOUTH Abutment Pier Col #1 Pier Col #2 Skewback Col #1 Arch Col #1 Arch Col #2 Arch Col #3 FRAME Model SOUTH NORTH Roller Roller Pinned Pinned Fixed Fixed
  22. 22. Description of Rating Model: Spandrel Beam (cont.) HS-20, Type 3, and Fire Trucks Section #4: Negative moment, non-composite section Section #2: Negative moment, composite section Abutment Pier Col #1 Pier Col #2 Skewback Col #1 Section #3: Positive moment, non-composite section Section #1: Positive moment, composite section Type 3S2 and Type 3-3 Trucks Section #2: Negative moment, composite section Section #4: Negative moment, non-composite section Abutment Pier Col #1 Pier Col #2 Section #3: Positive moment, non-composite section Section #1: Positive moment, composite section Skewback Col #1
  23. 23. Load Rating Analysis Results: Spandrel Beam BEAM Model FRAME Model Section #3 Section #4 Section #1 Section #2 Section #3 Section #4 1.17 1.19 1.15 1.21 1.17 1.19 1.17 1.31 TYPE 3 1.57 1.67 1.53 1.69 1.57 1.67 1.55 1.83 TYPE 3S2 1.52 1.44 1.55 1.53 1.52 1.45 1.57 1.46 TYPE 3-3 1.73 1.34 1.79 1.44 1.72 1.35 1.81 1.58 FIRE 1.20 1.18 1.21 1.20 1.20 1.18 1.23 1.30 HS-20 Operating Rating Section #2 HS-20 Inventory Rating Section #1 1.96 1.98 1.93 2.02 1.96 1.99 1.96 2.18 TYPE 3 2.62 2.78 2.55 2.82 2.62 2.79 2.59 3.05 TYPE 3S2 2.54 2.40 2.58 2.56 2.54 2.42 2.62 2.43 TYPE 3-3 2.88 2.23 2.99 2.40 2.88 2.26 3.02 2.64 FIRE 2.01 1.96 2.01 2.00 2.01 1.97 2.05 2.16 Controls
  24. 24. 31' 31' 31' 31' 31' 31' 29' - 6" FB#5 FB#5 FB#4 FB#3 FB#2 FB#2 FB#2 FB#2 FB#1 Load Rating Analysis Summary: Floor System 29' - 6" Floor Beam 6' - 9" 7' - 412" 6' - 9" 35' 6' - 9" 6' - 9" 7' - 412" 6' - 9" C Pier Col #1 L Exterior Stringers C Pier Col #2 L C Skewback Col #1 L Interior Stringers
  25. 25. 31' 31' 29' - 6" 29' - 6" 29' - 6" 29' - 6" C Skewback Col #1 L 29' - 6" Spandrel Beams Floor Beam Interior Stringers 29' - 6" FB#6 FB#6 FB#6 FB#6 FB#5 FB#5 FB#5 FB#4 FB#3 Load Rating Analysis Summary: Floor System (cont.) 29' - 6" 14' - 9" Wind Bracing Outrigger Beam Column
  26. 26. LOAD RATING of COLUMNS
  27. 27. Description of Rating Model: Columns BEAM-COLUMN Model (axial-bending interaction) COLUMN Model (axial load only) 62ft 62ft 62ft 15 spans (29.5ft each) 106.6ft 422.5ft 62ft 62ft 62ft
  28. 28. AASHTO Interaction Equation (rewritten for side-sway case): P 0.85A F s cr where + B M +B M 1 nt 2 M lt ≤1 u P = maximum axial compression As = cross-sectional area of column Fcr = critical buckling stress Mu = maximum flexural strength (equal to yield moment for all columns) Mnt = first order moment assuming no lateral end translation (i.e., non-sway case) Mlt = first order moment due to lateral end translation (i.e., sway-case) B1 = MAF for second order effect of Mnt (i.e., P-δ effects) δ C B = ≥1 1 P B1 = 1 since C ≤ 0.6 1− AF s e1 B2 = MAF for second order effect of Mlt (i.e., P-∆ effects) ∆ B2 = 1 ≥1 ∑P 1− ∑ As Fe2 B2 = 1 since ∑ As Fe2 is large compared to C = equivalent moment factor Fe1, Fe2 = Euler Buckling stress for non-sway and side-sway buckling, respectively. ∑P
  29. 29. Load Rating Analysis: Columns P 0.85A F B M +B M 1 + nt 2 M s cr lt ≤1 u B1 = B2 = 1 0.85A F s cr + M = u A P +A P 1 D 2 L 0.85A F + s cr A M +A M 1 D 2 SF L ≤1 y Solve for RF A P + A P ( RF ) 1 D 2 L 0.85A F s cr + A M + A M ( RF ) 1 D 2 L SF y =1
  30. 30. Load Rating Analysis Results: Columns Column HS-20 TYPE 3 TYPE 3S2 TYPE 3-3 FIRE RFi,b-c RFi,col RFi,b-c RFi,col RFi,b-c RFi,col RFi,b-c RFi,col RFi,b-c RFi,col Pier Col #3 1.42 3.26 2.03 4.64 1.48 3.51 1.37 3.37 1.40 3.22 Pier Col #4 N/A 3.19 N/A 4.55 N/A 3.39 N/A 3.22 N/A 3.15 Arch Col #6 0.80 4.38 1.13 6.07 0.89 6.03 0.86 6.67 0.80 4.37 Arch Col #7 0.91 4.40 1.29 6.09 0.98 6.06 0.94 6.69 0.90 4.38 Arch Col #10 0.76 4.33 1.07 6.00 0.84 5.97 0.81 6.59 0.76 4.32 Arch Col #11 0.84 4.20 1.19 5.81 0.92 5.78 0.89 6.39 0.83 4.18 Arch Col #12 0.90 3.93 1.27 5.45 0.98 5.41 0.93 5.99 0.89 3.92 Arch Col #13 1.02 3.41 1.46 4.72 1.11 4.70 1.05 5.19 1.01 3.40 Arch Col #14 1.31 2.69 1.87 3.72 1.43 3.65 1.36 4.03 1.30 2.67 Skewback Col #2 2.63 4.56 3.71 6.45 3.10 5.14 3.18 5.13 2.61 4.51
  31. 31. LOAD RATING of ARCH RIB
  32. 32. Description of Rating Model: Arch Rib RIGID Model: “rigid” behavior of riveted connections; same as BEAM-COLUMN Model used to analyze columns PINNED Model: “pinned” behavior of riveted connections; same as COLUMN Model used to analyze columns 62ft 62ft 62ft 15 spans (29.5ft each) 106.6ft 422.5ft 62ft 62ft 62ft
  33. 33. AASHTO Interaction Equation (for solid rib arches):   1  MD + ML   1 − 1.18 TD + TL  AFe  + ( where f a fb N D + N L + = Fa Fb AFa SFb )        ≤1 fa = computed axial stress Fa = allowable axial stress fb = computed bending stress Fb = allowable bending stress ND , NL = unfactored axial forces under dead and live load (plus impact) MD , ML = unfactored, first-order bending moments under dead and live load (plus impact) A , S = cross-sectional area and section modulus (at extreme fiber) of the arch rib TD , TL = unfactored thrust at the quarter point under dead and live load (plus impact) Fe = Euler buckling stress
  34. 34. Load Rating Analysis: Arch Rib   1  MD + ML   1 − 1.18 TD + TL  AFe  + ( f a fb N D + N L + = Fa Fb AFa SFb )        ≤1 Solve for RF MD + ML ( N D + N L ( RFi ) + AFa    1 RFi   1.18 TD + TL RFi  1−  AFe  ) ( SFb ( ))         =1
  35. 35. 62ft 62ft 15 spans (29.5ft each) 62ft C2 E C1 A 62ft D2 106.6ft F D1 422.5ft Case 1: Nmax @ Point A, Mmax @ Point C2, T @ Point E Case 2: Nmax @ Point B, Mmax @ Point D2, T @ Point F Case 3: Mmax @ Point C1, Nmax @ Point A, T @ Point E Case 4: Mmax @ Point D1, Nmax @ Point B, T @ Point F B 62ft 62ft
  36. 36. Load Rating Analysis Results: Arch Rib Rating Vehicle HS20 TYPE 3 TYPE 3S2 TYPE 3-3 FIRE Case RIGID Model PINNED Model IRi RFi RFo IRi RFi RFo 1 0.56 2.53 4.23 0.57 2.41 4.02 3 0.63 2.14 3.57 0.69 1.77 2.96 1 0.48 3.58 5.98 0.48 3.47 5.79 3 0.53 3.05 5.10 0.58 2.53 4.23 1 0.53 2.81 4.69 0.56 2.35 3.92 3 0.60 2.32 3.87 0.66 1.80 3.01 1 0.54 2.68 4.48 0.58 2.54 4.24 3 0.62 2.21 3.68 0.69 1.91 3.19 1 0.56 2.49 4.17 0.57 2.39 3.99 3 0.63 2.12 3.54 0.70 1.76 2.93 Controls
  37. 37. Load Rating Analysis Summary: Columns and Arch Rib 62ft 62ft 62ft 15 spans (29.5ft each) 106.6ft 422.5ft 62ft 62ft 62ft
  38. 38. FINAL LOAD RATING Bridge Component Design Load Legal Load Permit Load RFo RFi RFo RFi RFo Stringer 1.09 1.81 1.03 1.72 0.97 1.62 0.85 1.14 1.13 1.89 0.88 1.47 Spandrel beam 1.15 1.93 1.34 2.23 1.18 1.96 Pier Column PINNED Model RFi Floor beam BEAM or FRAME Model 1.18 1.97 1.13 1.89 1.16 1.94 Arch Column 0.76 1.27 0.81 1.36 0.76 1.26 Skewback Column 2.63 4.39 3.10 5.18 2.61 4.35 Arch Rib 1.77 2.96 1.80 3.01 1.75 2.93 BEAM-COLUMN Model
  39. 39. Discussion 1. The rating factors of the columns are inversely proportional to the stiffness of the riveted connections. In actuality, the connection stiffness may be somewhere between fully rigid and pinned behavior and thus, the rating factors of the columns will fall somewhere between the rating values of BEAM-COLUMN and COLUMN models. 2. Another important observation is that, while the rigidity of the end-column connection helps to increase the capacity of the spandrel beam and the arch rib, it significantly reduces the capacity of the columns. 3. In the scope of this study, the rating factor of the arch column and the floor beam controlled the final rating of the entire bridge. However, it is anticipated that the rating factors of the columns may no longer control if the actual connection stiffness is taken into account (recommended for future work to improve column rating factors).
  40. 40. CONCLUSIONS and RECOMMENDATIONS • Column rating factors are inversely proportional to the stiffness of the riveted connections while arch rib rating factors are directly proportional; spandrel beam was not affected by connection stiffness at critical sections. • In general, the Omega Bridge is structurally sound with some concerns for the floor beams and arch columns. • Since the smallest rating factors for legal loads are RFi = 0.81 and RFo = 1.36, posting of the bridge is not required but additional inspection and traffic monitoring may be warranted. • Further studies (i.e., field testing along with 3D finite element analysis) are recommended to improve the rating factors.
  41. 41. THANK YOU

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