Introduction Bridge Background
• Name: The Los Alamos Canyon Bridge
(a.k.a. the Omega Bridge)
• Steel arch riveted bridge
• Designed & built in 1951 following 1944 AASHTO
specifications
• Carries traffic from town of Los Alamos and the LANL
(Los Alamos National Laboratory)
• Bridge reduced the travel distance from 1.9 miles on a
steep grade to 820 ft: critical for emergency vehicles
• Owned and maintained by the LANL
Introduction Research Objectives
Connections commonly assumed to have equal or greater
capacity than the members they adjoin
Failure of connections could be critical
• Provide the LANL with up-to-date rating factors for the
Omega Bridge splice connections
LRFD is the required method of design by FHWA since
October 2007: Need for rating methodology consistent
with the design method.
No guidance in rating connections
• Provide guidance in load rating connections using LRFR
method to bridge engineers
Introduction Research Aids
• 2003 AASHTO Manual for Condition Evaluation and Load
and Resistance Factor Rating of Highway Bridges
• Research by Tuyen (2005)
• RISA for structural analysis
• MathCAD to calculate rating factors
• Others: Original plans of the bridge, AISC steel manual, etc.
Load Rating Method:
LRFR
Load Rating Method LRFR
• Load rating provides the basis for determining the safe load
capacity of a bridge in terms of a rating factor.
• Rating factor is the ratio of the available to required live load
capacity:
Available live load capacity
RF =
≥ 1.0
Required live load capacity
Start
Load Rating Method LRFR
Design Load Check
RF > 1
(HL-93)
-No Restrictive Posting
Requireda
-May be evaluated for
permit vehicle
Inventory Level Reliability
• Three Stages of load rating in LRFR: Design Load Rating
RF <1
Check at operating
level reliability
RF <1
Legal load Rating
AASHTO or State legal loads
Legal Load Rating
RF > 1
a
b
RF > 1
Evaluation level reliability
RF <1
Higher Level Evaluation
(Optional)
-Refined analysis
RF <1
RF > 1
-Load testing
-Site-specific load factors
-Direct safety assessment
-Initiate load posting and/or repair/rehab
-No permit vehicles
-No restrictive
posting requiredb
-May be evaluated
for permit vehicles
Permit Load Rating
For AASHTO legal loads and state legal loads
within the LRFD exclusion limits
For AASHTO legal loads and state legal loads
having only minor variations from the
AASHTO legal loads
Load Rating Method LRFR
General Equation for LRFR:
φcφsφRn − γ DC DC − γ DW DW
RF =
γ LL LL(1 + IM )
where
RF = Rating Factor
φc, φs = Condition and system factor, respectively
φRn = Splice capacity
γDC, γDW, γLL = factors for dead load due to components and attachments,
wearing surface, and live load, respectively
DC, DW, LL = effects due to dead load due to components and
attachments, wearing surface, and live load, respectively
IM = Dynamic load allowance (or impact factor)
Load Rating Method LRFR
φcφsφRn − γ DC DC − γ DW DW
RF =
γ LL LL(1 + IM )
Super Structure Condition Ratings: 5.0 and higher:
Condition Factor, φc = 0.95 (LRFR Table C6-1 and 6-2)
System Factor, φs:
(LRFR Table 6-3)
1.0 for stringers
Redundant stringer systems
between floor beams
0.9 for spandrel beam, columns, and
arch ribs
Riveted members in twogirder/truss/arch bridges
Load Rating Method LRFR
φcφsφRn − γ DC DC − γ DW DW
RF =
γ LL LL(1 + IM )
Load Factors:
γDC = 1.25
γDW = 1.5
γLL = 1.75 for inventory
1.35 for operating
Load Rating Method LRFR
(a) TRUCK LOADS: HS-20 and Design Tandem
8k
φcφsφRn − γ DC DC − γ DW DW
RF = 32k
32k
25k
γ LL LL(1 + IM )
25k
For each member, distribution factor for different force effects
must be applied: i.e., to 30moment or DFshear
4 ft
14ft
14 DF ft
Live Load Effect = γ LL DF [Lane + Design Tandem IM)]
Truck (1 + (Longitudinal)
HS-20 (Longitudinal)
(b) LANE LOAD
Controlled by larger effect between HS-20 or Design Tandem
Lane Load = 0.64 klf
Load Rating Method LRFR
• Three Stages of load rating in LRFR: Design Load Rating
Legal Load Rating
Permit Load Rating
Load Rating of
Stringer Splice
Rating Stringer Splice Basic Information
CL Bearing
Abutment #1
Arch CL
South
407’-3”
• 2 Exterior Stringers: ASTM A36 Steel (Fy = 36 ksi) – W21x83
14’-9”
• 4 Interior Stringers: 31’ASTM A7 Steel 29.5’ y = 33 29.5’ ) – W21x62
(F 29.5’ ksi 29.5’ 29.5’ 29.5’
31’
31’
31’
31’
31’
29.5’
SP#1
SP#2
• Total of 27 spans:
6’-9”
SP#3
SP#4
SP#5
SP#6
SP#7
SP#8
SP#9
SP#10
SP#11
SP#12
Six approach spans of 31 ft on each end
SP#13
7’-4 1/2”
15 interior spans of 29.5 ft over arch
3@ 6’-9”
7’-4 1/2”
• 6’-9”
Total of 26 splices: 6 ft from the floor beam supports
6’-0”
(Typical)
Exterior Stringers
Stringer Splice
Interior Stringers
Spandrel Beams
Floor Beam
Rating Stringer Splice Splice Configuration
• Same splice configuration for both interior and exterior stringers
5 SPA @ 3”
= 1’- 3”
1 1/2” Min.
7/8”φ H.S. Bolts
(Typical)
PL 5/16” x 12 1/2” x 1’- 6”
(Both Sides of Web)
1’- 6”
4 SPA @ 3”
= 1’- 0”
1 1/2” Min.
1 11/16”
2’- 6 1/2”
1 1/2” Min.
(Typ.)
1/2”
Max.
3” (Typ.)
1 1/2”
Min.
1 1/2”
Min.
12 1/2”
PL 7/8” x 8 1/4” x 2’- 6 1/2”
(Typ. Both Flanges)
Rating Stringer Splice Loads
• Dead load applied to the stringers:
•Interior Stringer – WDead = 556 lb/ft
•Exterior Stringer – WDead = 609 lb/ft
• Live load applied using moving load tool in RISA:
Rating Stringer Splice Loads
• Used Influence Line for lane load placement
0.64 klf
0.64 klf
0.64 klf
Rating Stringer Splice
Force Distribution on
the Cross-Section
CflangePL
CwebPL
Flange
PL
NA
Stress at outside
edge of Web PL
Web
PL
dwebPL
TwebPL
Stress at inside
edge of Flange PL
dflangePL
TflangePL
Stress at
outermost surface
Stress, σ
Force = σ x Ai
Splice 1 controls for both moment and shear!
c
Rating Stringer Splice Limit States
• Limit States for the Flange PL Group:
Yielding on the gross section
Fracture on the net section
Block Shear
Shear strength of the rivets
Bearing strength of the plates
• Limit States for the Web PL Group:
Yielding on the gross section
Fracture on the net section
Shear strength of the rivets (for a single rivet)
Bearing strength of the plates (for a single rivet)
Rating Stringer Splice Limit States
Tensile Limit States (kip)
Stringer
Yielding on
Gross Area
Fracture on
Net Area
Block
Shear
Shear Strength
of Rivets
Bearing Strength
of Plate
Interior
214.4
270.7
610.7
126.3
831.6
Exterior
233.9
237.9
550.5
126.3
730.8
Shear Limit States (kip)
Stringer
Yielding on
Gross Area
Fracture on
Net Area
Shear Strength
of Rivetsa
Bearing Strength
of Platea
Interior
200.5
222.8
25.26
24.50
Exterior
218.7
195.8
25.26
16.82
a
Values for a single rivet
Rating Stringer Splice Combined Loading at Web
V/12
V
c.g. of Web PL
R1
V/12
R2
V V
c.g. of Rivet Group
M
V/12
MT = M + Ve
R4
R3
Ry4
Rx4
e
Total Moment on web splice PL
MT = M +V ⋅e
Resultant shear due to moment and
direct shear:
VR = Rx
2
V
+ Ry +
12
2
Rating Stringer Splice Distribution Factors
Interior Stringer: LRFD Table 4.6.2.2.2b-1
Shear DF
Moment DF
One Lane
Loaded
Two or More
Lanes Loaded
0.1
g m.i.1
0.4
0.3
S S Kg
= 0.06 +
12.0 Lt 3
14 L
s
g m.i.2
S S Kg
= 0.075 +
12.0 Lt 3
9 .5 L
s
0.6
All Range of Applicability are met
0.2
g v.i.1 = 0.36 +
0.1
g v.i.2
S
25.0
S S
= 0 .2 + −
12 35
2.0
Rating Stringer Splice Distribution Factors
Exterior Stringer: LRFD Article 4.6.2.2.2d
Moment DF
One Lane
Loaded
Lever Rule
Shear DF
Lever Rule
Two or More
Lanes Loaded
g m.e.2 = e ⋅ g m.i.2
g v.e.2 = e ⋅ g v.i.2
One Lane
Loaded - RBM
Rigid Body Motion
Rigid Body Motion
Two or More
Lanes Loaded -RBM
Rigid Body Motion
Rigid Body Motion
Rating Stringer Splice Distribution Factors
DF Type
Interior Stringer
Moment
Shear
Exterior Stringer
Moment
Shear
One Lane Loaded
0.494
0.630
0.667
0.667
Two or More Lanes
Loaded
0.627
0.725
0.621
0.580
0.451
0.451
0.632
0.632
0.667
0.667
Rigid
Body
Motion
One Lane
Loaded
N/A
Two or more
Lanes Loaded
Controlling DF
0.627
0.725
Rating Spandrel Splice Basic Information
CL Bearing
• 2 Abutment #1 Beams:
Spandrel
South
ASTM A7 Steel (Fy = 33 ksi)
• Total of 21 spans:
Three approach spans of 62 ft on each 14’-9”
end
62’
6’-9”
62’
SP#1
SP#2
SP#3
Arch CL
407’-3”
62’
29.5’
15 interior spans29.5’ 29.5ft29.5’ 29.5’ 29.5’
of 29.5’ SP#9 SP#10 SP#11
over arch
SP#4
SP#5
SP#6
SP#7
SP#8
29.5’
SP#12
SP#13
7’-4 1/2”
• Total of 26 splices: First five splices: 15.5 ft from pier and
3@ 6’-9”
skewback column supports
7’-4 1/2”
6’-9”
15.5’ Typ.
Remaining splices: 7.25 ft from arch column
7.25’ Typ.
supports
Exterior Stringers
Spandrel Beams
Floor Beam
Interior Stringers
Rating Spandrel Splice Splice Configuration
3”
2.5”
4”
4”
1.5” 3” 1.75”
2.5”
3”
12 ½” x 5/16” x 2’-1”
4”
12 ½” x 5/16” x 1’-5”
3 ½” x 3 ½” x ½ x 2’-0 ½”
12 ½” x 5/16” x 5’-0”
12 ½” x 5/16” x 4’-8”
16 @ 3”
5 ¼” x 1/2” x 3’-6 ½”
3”
5”
6” x 1/2” x 3’-6 ½”
3”
3”
6” x 5/8” x 3’-6 ½”
7” x 1/2” x 3’-6 ½”
3”
Rating Spandrel Splice Limit States
Moment Limit States (kip)
Plate Group
Yielding on Fracture on
Shear Strength Bearing Strength of
Block Shear
Gross Area Net Area
of Rivets
Plate
Top Flange
464.1
556.9
544.5
353.6
722.8
Bottom Flange
382.4
426.9
643.5
353.6
1726
Shear Limit States (kip)
Plate Group
Yielding on Fracture on
Gross Area Net Area
Web
a
For a single rivet
623.7
881.7
Shear
Strenght of
Rivetsa
Bearing Strength
of Platea
25.3
23.0
Rating Spandrel Splice Distribution Factors
• One spandrel beam on each edge of the bridge width
Considered as an exterior beam for moment DF
• Use the lever rule to determine moment distribution factors:
1.764
2.094
1.929
1.328
4 lanes loaded
3 lanes loaded
2 lanes loaded
1 lane loaded
Controls!
Includes the multiple
presence factor
• LRFD Table 4.6.2.2.3.b-1 states the distribution factor for
shear of an exterior beam is also determined using the lever
rule: DFmoment = DFshear
Rating Spandrel Splice Rating Factors
Moment Rating Factor
Critical Splice
Moment Rating
RFi
Shear Rating Factor
Critical Splice
RFi
RFo
Web Splice Plates
4.00
5.19
Single Rivet
0.90
1.16
RFo
Top FL Plate
Group
S1
1.27
1.65
S6
1.33
1.72
Bottom FL
Plate Group
S1
0.92
1.20
S6
0.92
1.20
Splice S1 had larger moment
due to truck load in magnitude
Shear Rating
Load Rating of
Column Splice
Rating Column Splice Basic Information
• Total of 20 columns:
4 Pier columns
2 Skewback columns
14 Arch columns
• Splices in six tallest columns: 55 ft below the deck grade
Arch Column Splices
S3
S1
Roller
S4
S5
S6
S2
Pinned
Skewback Column
Splice
Fixed
Skewback Column
Splice
Rating Column Splice Splice Configuration
Arch Column Splice
1.5”
5 @ 3”
4 Angles
4” x 4” x 1/2”
4 Angles
5” x 5” x 3/4” x 3’- 1/2”
3”
3.5”
24”
4 Plates
24” x 1/2”
1.25”
3.5”
3”
8 Plates
12” x 1/3” x 1’- 3”
1.25”
4 @ 3”
5 @ 3”
1.5”
24.5”
1.5”
1.5”
Rating Column Splice Splice Configuration
Skewback Column Splice
48.5” back to back
4” x 4” x ½”
24” x ½”
48” x ½”
16”
48”
12”
4 @ 3”
4 Angles: 5” x 5” x ¾” x 3’-6 ½”
8 Plates: 12” x 3/8” x 1’-4”
2 Plates: 12” x 3/8” x 3’-4”
2”
42.5”
Rating Column Splice Modeling: Member
• The riveted connection stiffness is uncertain
• Two models: COLUMN and BEAM-COLUMN
• Actual connection stiffness somewhere in between COLUMN
and BEAM-COLUMN models
• Previous work found that BEAM-COLUMN model yielded
significantly smaller rating factors: thus, chosen as critical model.
Rating Column Splice Limit States
Flange Plates:
Gross yielding
PL based
Limit States Net fracture
Block shear
Rivet based Shear strength of rivets
Limit States Bearing strength of PL
Total Capacity = smaller of
[φRnFlangePL + φRnAngles]PL-Based
[φRnFlangePL + φRnAngles]Rivet-Based
Angles:
Gross yielding
Net fracture
Block shear
Shear strength of rivets
Bearing strength of PL
Rating Column Splice Limit States
Splice
Component
Plate-Based Limit States (kips)
Rivet -Based Limit States
(kips)
Gross Yield Net Fracture Block Shear Rivet Shear Plate Bearing
Plates
Arch
Column
297.0
330.0
240.9
252.6
501.2
Angle
412.1
538.3
1073
151.5
1743
Control
=
653.0
=
404.1
Plates
Skewback
Column
356.4
429.0
419.5
252.6
501.2
Angle
412.1
538.3
1344
176.8
2055
Control
768.5
429.3
Controls tension capacity
for Arch Column Splice!
Rating Column Splice Second-Order Effect
• No bracing between columns: Sway Frame
• For a beam-column in sway frame, the maximum first order
moments are amplified using the second order effect given in
LRFD Article 4.5.3.2.2b
• Non-sway and sway moments must be amplified by non-sway
(δb) and sway (δs) magnification factors
• Previous work determined δb = δs = 1.0
Rating Column Splice Second-Order Effect
δb < 1.0
Amplified
Moment
First-Order
Moment
δb >1.0
Amplified
Moment
Max.
Moment
First-Order
Moment
Max. Moment
Splice Location
Moment
End Moment
Higher Limit
Lower Limit
Range
Splice Location
Moment
End Moment
Rating Column Splice Distribution Factors
• Columns in eastern arch rib controlled
• Live load distribution factors determined using the same
method as the spandrel beam
DFmoment = DFshear = 2.094
Rating Arch Rib Splice Basic Information
• Total of 15 arch rib segments per arch plane
• Center 13 arch rib segments are spliced
(Labeled as S7 through S19 below)
South
North
9
10
13 14
11 12
15
16
17
18
8
19
7
Pinned
Pinned
Arch Rib Splice #
Rating Arch Rib Splice Splice Configuration
46” x 3/4”
8” x 8” x 3/4”
18 1/2” x 3/4” x 3’ 9”
7 1/4” x 7 1/4”
x 7/8” x 3’ 6 ½”
18 1/2” x 3/4” x 9”
71 1/2” x 1/2”
12 1/2” x 5/8” x 2’ 0”
Rating Arch Rib Splice Modeling: Member
• Two models considered: RIGID and PINNED
• Used Influence Line to determine which model produces lower
rating factors
RIGID Model
PINNED Model
1.0
1.45
1.0 rad
Skewback
Column
Quarter Point
Arch Splice
Skewback
Column
1.0 rad
Quarter Point
Arch Splice
Rating Arch Rib Splice Second Order Effect
• LRFD Article 4.5.3.2.2c specifies live load moments in arch ribs
including impact “shall be increased by the moment magnification
factor, δb”
Cm
δb =
≥ 1.0
Pu
1−
φPe
Pe =
lu = half of the arch length
π 2 EI
K = f (type of arch, rise-to-span ratio of
arch)
(Klu )2
Cm = 1.0
Axial Forces (kips)
Dead Load
HS-20
Lane
Moment Amplification
Factor, δb
S9
1015
43.8
70.4
1.31
S17
1015
42.5
52.8
1.30
Splice
Rating Arch Rib Splice Distribution Factors
• Arch ribs in eastern arch rib controlled
• Live load distribution factors determined using the same
method as the spandrel beam
DFmoment = DFshear = 2.094
Conclusions Floor System
Splice
Moment
Shear
Web Splice Plates
Single Rivet
RFi
RFo
RFi
RFo
RFi
RFo
Interior Stringer
1.10
1.43
2.30
2.98
1.19
1.54
Exterior Stringer
1.02
1.32
2.43
3.15
1.33
1.72
Spandrel Beam
0.92
1.20
4.00
5.19
0.90
1.16
All splices rated
greater than 1.0 at
operating:
South
CL Bearing
Abutment #1
31’
Arch CL
Critical Interior and Exterior Stringer
Splice (S1) for Shear and Moment
31’
31’
31’
31’
31’
29.5’
29.5’
No posting required
Safe for AASHTO
and State legal loads
without major
Critical Spandrel Splice
variation from
(S1) for Moment
AASHTO legal loads
Critical Spandrel Splice
(S4) for Shear
29.5’
29.5’
14’-9”
29.5’
29.5’
29.5’
Conclusions Columns & Arch Ribs
Splice
Moment
Shear
Web Splice Plates
Single Rivet
RFi
RFo
RFi
RFo
RFi
RFo
Arch Column
1.03
1.34
8.39
10.88
1.93
2.50
Skewback Column
2.81
3.65
36.85
47.77
6.95
9.01
Arch Rib
0.82
1.06
8.05
10.4
2.37
3.07
All splices rated
greater than 1.0 at
operating:
Critical Arch Column Splice (S5)
for Shear and Moment
South
North
No posting required
Safe for AASHTO
and State legal loads
without major
variation from
AASHTO legal loads
Critical Arch Rib Splice (S9)
for Moment
Critical Arch Rib Splice (S11)
for Shear – Single Rivet
Critical Skewback Column Splice
(S2) for Shear and Moment
Critical Arch Rib Splice (S14)
for Shear - Web Splice Plates
Recommendations
• Load test recommended to better estimate the rotational
stiffness of the riveted connections for the spandrel beams,
columns, and arch ribs
• Uncertainty in second-order effect of column splice moments:
Lower end amplified moment rated as low as 0.84 at operating.
A thorough examination of column splice strongly
recommended
A more detailed analysis of the second-order effect
recommended in future analysis
Recommendations
• Several rivets reported missing during last inspection
Recommended to identify missing rivets and replace them
• Lateral load analysis due to wind and earthquake load
recommended
• 3-D finite element model recommended to better evaluate the
member and splice forces and refine the analysis
References
American Association of State Highway and Transportation Officials (AASHTO). (2003). Manual for Condition Evaluation
and Load and Resistance Factor Rating (LRFR) of Highway Bridges, Washington, DC.
American Association of State Highway and Transportation Officials (AASHTO). (2004). LRFD Bridge Design Specifications,
3rd Edition, Washington, DC.
American Institute of Steel Construction (AISC). (2001). Manual of Steel Construction: Load and Resistance Factor Design,
3rd Edition, Chicago, IL.
FDOT (Florida Department of Transportation). 2007. 24 August 2007
<http:www.dot.state.fl.us/structures/LoadRatingSummit/AskTheProfessor.htm>
Garrett, Gregory P. “Analytical Load Rating of an Open-Spandrel Arch Bridge: Case Study.” Journal of Bridge Engineering
(January/February 2007): 13-20.
Gaylord, Edwin H., Charles Gaylord, and James Stallmeyer. Design of Steel Structures, 3rd Edition. New York: McGraw-Hill,
1992
McCormac, Jack C., and James K. Nelson Jr. Structural Steel Design: LRFD Method, 3rd Edition.Upper Saddle River, NJ:
Prentice Hall, 2002
Salmon, Charles G. and John E. Johnson. Steel Structures: Design and Behavior, 4th Edition. New York: Harper Collins, 1996
Tuyen, Nguyenngoc. Load Rating of a Riveted Steel Arch Bridge. Las Cruces, NM: New Mexico State University, 2005
Vinnakota, Sriramulu. Steel Structures: Behavior and LRFD. New York: McGraw-Hill, 2006
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