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

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. 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. 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. West Road
Route
e
idg
r
aB
g
me
O

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. 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. 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. 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. 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. 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. 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. 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. 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. (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. LOAD RATING of FLOOR SYSTEM

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. LOAD RATING of COLUMNS

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. 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. 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. 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. LOAD RATING of ARCH RIB

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. 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. 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. 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. 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. Load Rating Analysis Summary: Columns and Arch Rib
62ft
62ft
62ft
15 spans (29.5ft each)
106.6ft
422.5ft
62ft
62ft
62ft

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. 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. 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. THANK YOU