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PERFORMANCE EVALUATION OF CONCRETE BRIDGE
DECKS SUBJECT TO STORM SURGE AND WAVE LOADS:
A CASE STUDY
Thuydu N. Tran
and
Ian N. Robertson
Research Report UHM/CEE/12-03 May 2012
iii
ACKNOWLEDGEMENTS
This report was prepared by Thuydu N. Tran under the guidance of Dr. Ian N. Robertson in
partial fulfillment of requirements for a Master of Science degree in Civil and Environmental
Engineering. The authors wish to thank Drs. Teng and Riggs of the Department of Civil and
Environmental Engineering at the University of Hawaii for their review of this report.
The reconnaissance survey of the I-10 Onramp Bridge was part of a larger survey of coastal
structures damaged during Hurricane Katrina, supported by funding from the National Science
Foundation under a Small Grant for Exploratory Research (grant #0553966). Analysis of the
bridge response was performed as part of a research project to develop Performance Based
Tsunami Engineering (PBTE) funded by the NSF George E. Brown, Jr. Network for Earthquake
Engineering Simulation (grant #0530759). This funding is gratefully acknowledged. The
opinions, recommendations, and conclusions given in this report are those of the authors and do
not necessarily reflect that of the funding agency.
iv
ABSTRACT
In 2005 Hurricane Katrina struck the Gulf Coast causing widespread devastation. Post-storm
assessments suggest that the majority of structural damage to buildings and bridges along the
Alabama and Mississippi coastlines stemmed from severe storm surge and associated wave
action. Numerous low lying bridges that lacked vertical and lateral restraints between their
superstructure and substructure were discovered with spans either displaced from supports or
collapsed into the bay. There was one bridge, however, that was equipped with sizeable tie-
downs— the I-10 Onramp. This paper presents the findings of a performance evaluation of the
I-10 Onramp and its connections. Recommendations are made for the retrofit and design of new
bridges vulnerable to coastal storms.
v
TABLE OF CONTENTS
1.0 INTRODUCTION ....................................................................................................................1
1.1 Scope .....................................................................................................................................1
2.0 I-10 ONRAMP DESCRIPTION AND OBSERVED DAMAGE ............................................2
2.1 Bridge Layout ........................................................................................................................2 2.2 Damage Description ..............................................................................................................6
3.0 ESTIMATED HYDRODYNAMIC AND HYDROSTATIC LOADS ..................................13
3.1 Hydrodynamic Forces .........................................................................................................14 3.2 Hydrostatic Uplift Force ......................................................................................................15
4.0 ESTIMATED RESISTANCE .................................................................................................16
5.0 RECOMMENDATIONS ........................................................................................................18
6.0 CONCLUSION .......................................................................................................................20
APPENDIX ....................................................................................................................................21
1
1.0 INTRODUCTION
Gulf Coast residents, state and federal agencies, and the engineering community at large,
along with the rest of the world suffered a rude awakening at the hands of Hurricane Katrina.
Post-storm assessments suggest that the majority of structural damage to buildings and bridges
along the Alabama and Mississippi coastlines stemmed from severe storm surge and associated
wave action (Robertson et al., 2007), both of which are not explicitly accounted for in current
design codes. Numerous low lying bridges that lacked vertical and lateral restraints between
their superstructure and substructure were discovered with spans either displaced from supports
or collapsed into the bay. These include stretches of U.S. Highway 90 over Biloxi Bay and Bay
St. Louis in Mississippi and an onramp to the I-10 East over Mobile Bay in Alabama. The I-10
Onramp was equipped with sizeable tie-downs, presumably to prevent dislocation of the low-
level bridge deck when subjected to wave loading. Its performance during Hurricane Katrina is
investigated herein. Section 2 of this report describes the I-10 onramp construction and post-
Katrina damage. Section 3 provides estimates of the hydrostatic and hydrodynamic loads on the
bridge superstructure. Section 4 estimates the resistance to these loads provided by self weight
and the tie-downs. Section 5 provides recommendations for retrofit of existing bridges and for
future bridge design and construction.
1.1 Scope
The intent of this study is to report the observed damage to the I-10 Onramp and to
evaluate the performance of the tie-down system installed to connect the superstructure to the
piers. Recommendations are made to improve future tie-down designs.
2
2.0 I-10 ONRAMP DESCRIPTION AND OBSERVED DAMAGE
This study relies heavily on observations and measurements collected during two
reconnaissance trips to the affected region in late 2005 (Robertson et al., 2007).
2.1 Bridge Layout
The I-10 onramp is positioned along an inclined horizontal curve (~2 degrees northward)
with superelevation that sets the south side higher (Figure 1). The onramp is composed of two
different structural systems. Adjacent to the approach roadway and west abutment (bottom right
of Figure 1), the bridge consists of a multi-span continuous flat slab deck integrally connected to
multiple closely-spaced foundation piles (Figure 2). The remainder of the onramp consists of a
multi-span prestressed girder bridge simply supported on pier bents (Figure 3). Girder spans
average 50 feet (15.25 m) in length and consist of four prestressed I-girders at 7.25 feet (2.21 m)
on center, supporting a 7.5 inch. (19 cm) thick concrete deck slab and “Jersey” barrier (Figure 4).
Each span is secured to its supports by 6”x8”x1” thick (15cmx20cmx2.5cm thick) galvanized
steel angles, each 10.5 inches (26.7 cm) long, bolted to either side of the bottom bulb of exterior
girders and to the top of the pier bents (Figure 5). There are eight sets of angle connectors per
span.
Figure 6 shows details of the bolted angle connection. Threaded sleeve anchors were
embedded horizontally in the bottom bulbs of the exterior girders during precasting, while 1.125
inch. (28.6 mm) diameter vertical anchor bolts were cast into the top of the bent cap. After
girder placement, the galvanized angles were installed over the vertical anchor bolts and 0.875
inch. (22 mm) diameter bolts were installed in the horizontal sleeve anchors. No washers were
provided under the nuts on the vertical anchor bolts.
5
Figure 5. Original Connector
Section
Elevation
Plan
3"
1 1/4" diam sleeve anchor
1 1/8" diam bolt
7/8" diam bolt
6" x 8" x 1" AngleShear Tab
312"1"
2 3/4"
5"2 3/4"
5"
1 3/4" 2" 3" 2"1 3/4"
2 1/2"
3 1/2"
312"
5" 7"
10"
1"
Vertical Leg
1 3/4" 2" 3" 2" 1 3/4"
5"
3"1"
Horizontal Leg
Figure 6. Existing Connection Detail
6
2.2 Damage Description
The first (and lowest) section of the onramp did not sustain any damage, attributing
survival to its “integral” design and construction. However, the first five spans of the girder
bridge broke free of their angle-bolt connections and displaced laterally to the north as much as 6
feet in certain places (Figure 7). Damage, in general, pertained to the connection failures and
was relatively uniform across spans, varying only in intensity.
Figure 7. Dislocation of Spans
7
78'-3"
80'-312"
78'
80'
48'-9"
50'-3"
48'-5"
50'
48'-10"
50'-312"
48'-10"
50'-212"
0 12 3 4
5B
C
A
D
BA
B AB
A
B A
B A
C
D C DC
D
C D
C D
25'
1'-3"
1'-3"5'-2"
5'-2"6"412"
7"
49'-1012"
49'-11"
Abutment
- Longitudinal measurements are along the inside of the base of the guardrail.- Transverse measurements are between the inside of the bae of the guardrail.- Elevation measurement from high water mark to top of roadway.
N
5'-0"6'-6" 7'-6" 9'-3"
10'-9"
4'-0"5'-4" 6'-3" 8'-0" 9'-6"
Figure 8. Plan Showing Absolute Movement and Roadway Elevation Above High Water Mark
8
Unbolted Connections
In a number of connections, the securing bolts appeared to have been left out during
construction. This may have been the result of misalignment of the embeds in the girder bulbs,
or complete absence of the inserts. Figure 9 shows evidence that the embeds have either been
forgotten during precasting or patched over due to misalignment. Note also the lack of washers
under the nuts on the vertical anchor bolts. This lack of connection at one corner of a bridge
section would result in increased loads at the other corners, leading to premature failure of the
bridge span.
Figure 9. Some Bolts were Never Installed
Connection Angle Failure
In a number of instances, significant damage had occurred to the connection angles (Figure 10).
This damage ranged from severe bending to rupture of the angle leg through the net area at the
9
bolt holes. These failures were likely due to crushing of the angles as the bridge deck was lifted
from its original position between the angles.
Figure 10. Bent and Fractured Angles
Oversized Bolt Holes
Presumably because of bolt alignment problems, a number of bolt holes in the connection angles
had been field modified using a cutting torch (Figure 11). Unfortunately, no attempt was made
to reinforce these oversized holes with plate washers, so the nuts were able to pull through. In
addition, damage to the galvanizing resulted in initiation of corrosion at the cut holes. All holes
in the connection angles were slotted to allow for field tolerances, however, the slots were all
aligned along the length of the bridge, providing no allowance for transverse misalignment. It
was also noted that washers were not provided on the vertical anchor bolts at these slotted holes.
10
Figure 11. Nuts and Bolts Pulled Through Oversized Field-Cut Holes
Threaded Insert Failure
Threaded inserts were embedded in the sides of the bottom bulb of the exterior prestressed
girders to accept bolts passing through the connection angles. These embeds extended only 3
inch. (7.6 cm) into the girder concrete and were secured with 0.25 inch. (6 mm) diameter bar
dove-tail anchors. Figure 12 shows a typical failure for anchors on the windward (South) side of
the girders. Concrete spalling and failure of the dove-tail anchors allowed the inserts to pull out
of the girder bulb. Note that some of the sleeves ruptured at the end of the bolt leaving the
remainder of the sleeve embedded in the girder. Schmidt hammer tests of the girder concrete
indicated a likely compressive strength of fc’ = 7500 psi (51.7 MPa).
11
Figure 12. Threaded Inserts Pulled Out, Spalling Girder Concrete
Concrete Spall and Embed Bolt Failure
The connection angles were bolted to the supporting bent cap by means of 1.125 inch. (28.5 mm)
diameter anchor bolts embedded during bent cap placement. The embedded anchor bolts in the
exterior angles were approximately 7 inch. (18 cm) from the end of the bent cap. Lateral load on
the bridge girders resulted in shear in these bolts, leading to concrete spalls followed by either
bending failure or rupture of the anchor bolts (Figure 13). This was the typical failure for angles
on the leeward (North) side of the bridge. Schmidt hammer tests of the bent cap concrete
indicated a likely compressive strength of fc’ = 5000 psi (34.5 MPa).
12
Figure 13. Loss of Anchor Bolts, Spalling Pier Bent Concrete
Dislocation of the spans would have been further exacerbated had the spans not been part of a
horizontal curve. This was evident by the presence of crushed concrete along span ends where
jamming occurred. Finally, the remaining spans at higher elevations were undamaged. Thus,
storm surge and wave action were clearly the critical loads responsible for damage to the I-10
Onramp, not wind, rain, floating debris, or scour.
13
3.0 ESTIMATED HYDRODYNAMIC AND HYDROSTATIC LOADS
Understanding fluid-structure interactions is a multifaceted problem. Flow complexities
(e.g., air entrainment and turbulence near the free surface as the wave encounters a structure),
laboratory modeling limitations (e.g., directional spreading, turbulence, and currents), and field
measurement inadequacies (e.g., simultaneous measurements of free surface, kinematics, and
forces) have yet to be resolved with certainty (Bea et al., 1999). This state of deficient
knowledge reflects the underdeveloped guidance in this area. Current Federal Highway
Administration (FHWA), individual State Department of Transportations (SDOTs), and
American Association of State Highway Transportation Officials (AASHTO) guidelines do not
include hydro-loading on bridge decks. While, earlier research pertained to offshore platforms
with structural geometries and deep water locations different from that of coastal bridges, thus
representing different wave loading conditions. Nevertheless, those findings can be adapted to
obtain preliminary estimates of wave forces.
The total force acting on a platform deck due to wave action is a linear combination of
buoyancy, slamming, drag (velocity dependent), lift (velocity dependent, normal to the wave
direction), and inertia (acceleration-dependent) forces (Bea et al, 1999). Based on an analysis of
the performance of bridge decks during Hurricane Katrina, Douglass et al. (2006) conclude that
the vertical hydrodynamic uplift force and the horizontal components of drag and inertia
hydrodynamic forces were the primary loads inducing failure. And in a recent report prepared
for FHWA, Douglass et al. (2006) recommend an interim method (presented next) to determine
these wave forces on bridge decks that is consistent with available technical knowledge.
14
3.1 Hydrodynamic Forces
It has been widely accepted that the vertical hydrodynamic uplift force is proportional to
the weight of fluid that would be above the deck if the deck were not present (Lai and Lee, 1989;
and Douglass et al., 2006) and may be formulated as:
vvvavv AzcF )( (1)
where Fv is the estimated wave-induced uplift; cv-va is an empirical coefficient capturing ALL
uncertainties (e.g. design sea state), with a recommended value of 1.0; γ is the unit weight of
water taken as 64 lb/ft3 (1025 kg/m3) for seawater; Δzv is the difference between the elevation at
the crest of the maximum wave and the elevation at the underside of the deck slab; and Av is the
area of the projection of the bridge deck onto a horizontal plane.
Similarly, the horizontal hydrodynamic force and may be formulated as (Douglass et al.,
2006):
hhvahrh AzcNcF )()]1(1[ (2)
where Fh is the estimated wave-induced horizontal load; cr is a reduction coefficient for
horizontal load on all girders except the wave-ward girder, with a recommended value of 0.4; N
is the number of girders supporting the deck slab; ch-va is an empirical coefficient capturing ALL
uncertainties, with a recommended value of 1.0; Δzh is the difference between the elevation at the
crest of the maximum wave and the elevation at the centroid of Ah; and Ah is the area of the
projection of the bridge deck onto a vertical plane.
Assuming the storm surge elevation is at the bottom of the girders and a maximum wave
crest elevation of 7.28 feet (2.22 m) at the I-10 onramp site (Douglass et al., 2006), Fv = 388 k
(1726 kN) and Fh = 184 k (817 kN), per span.
15
Cyclical loads, Fv and Fh, are assumed to act in phase and refer to wave inundation
occurring after the initial impact. Impact or slamming forces, while may be up to three times
greater in the vertical direction and up to six times greater in the horizontal direction than wave
inundation forces, are much shorter in duration, thus of lesser influence (Douglass et al., 2006).
The equations prescribed by Douglass et al. (2006) are not without theoretical
shortcomings. First, it is implied that Fv and Fh act at the centroid of the deck cross-sectional
area. This is misleading since it is more likely that wave-induced loads will vary across the deck
section, thus imparting moment. Also, the equations do not consider variations in wave period,
even though past experiments have shown a correlation. Note: Fh does not differentiate between
drag and inertia forces. In addition, the expression for Fv tends to error once the water level
exceeds the bottom of the girders. In which case, hydrostatic uplift must be considered.
3.2 Hydrostatic Uplift Force
As defined by Robertson et al. (2007), hydrostatic uplift (Fb) is “a combination of
buoyancy due to submersion in water and the effect of air trapped below a structural element” (p.
10). Assuming full submergence occurred at some time during the storm, Fb = 187 k (831 kN)
per span. This value is conservative considering some of the existing intermediate and end
diaphragms have cut-out holes, presumably to allow for venting of cells during a flooding event.
The hydrostatic and hydrodynamic loads are composed of several components that, in
general, do not act in phase. For the sake of simplicity, the total uplift on the deck is Fv + Fb =
575 k (2557 kN), which is countered by the weight of the deck- 240 k (1069 kN), for a net effect
of 335 k (1488 kN) per span.
16
4.0 ESTIMATED RESISTANCE
The presence of angle-bolt connections between the substructure and superstructure
provided significant resistance to the estimated hydrostatic and hydrodynamic forces. Assuming
all eight were installed properly, the strength of these fasteners (Rn) was evaluated for various
failure modes in the Appendix. A summary of the analysis results is given in Table 1.
Table 1. Connection Strength Direction
Of Loading Failure Mode
Rn [k] (kN)
ea. set
Ver
tica
l
Tensile Yielding of 6” Leg 378 (1681) 3024 (13451)Tensile Rupture of 6” Leg 377 (1677) 3016 (13416)Block Shear of 6” Leg Shear Yield and Tension Fracturea
282 (1254)
2256 (10035)
Angle Leg Bending 12 (52) 94 (416)Bearing Strength and Tear Out of 6” Legb 203 (903) 1624 (7224)Bolt Shear 58 (257) 462 (2054)Bolt Tensile Capacity 86 (385) 692 (3077)Tension Strength (Concrete Pullout) of Stud Groups in 8” Leg 79 (353) 635 (2827)Shear Strength (Concrete) of Stud Groups in 6” Leg 10 (44) 80 (356)
Hor
izon
tal
Ten
sion
Tensile Yielding of 8” Leg 378 (1681) --Tensile Rupture of 8” Leg 377 (1677) --Block Shear of 8” Leg Shear Yield and Tension Fracturea
304 (1350)
--
Angle Leg Bending 38 (168) 302 (1345)Bearing Strength and Tear Out of 8” Legb 261 (1161) --Bolt Shear 46 (205) 369 (1641)Bolt Tensile Capacity 108 (481) --Tension Strength (Concrete Pullout) of Stud Groups in 6” Leg 15 (68) --
Com
pres
sion
Angle Leg Bending 38 (168) 302 (1345)Bearing Strength and Tear Out of 8” Leg** 261 (1161) --Bolt Shear 46 (205) 369 (1641)Shear Strength (Concrete) of Stud Groups in 8” Leg 20 (88) --
Note. See Appendix for calculations. aOther block shear possibilities do not control. bFor bolts in connection with long-slotted holes perpendicular to direction of force.
A comparison of connection strength with the applied loads indicates that in the vertical direction
failure was likely the result of concrete shearing, eventually spalling off the bottom corners of
17
exterior girders. With an edge distance of 3.5 inch. (9 cm) to the bottom of the girder bulb, the
concrete resistance to shear load in the sleeve anchors was estimated at 10 k (44 kN) per bolt
pair. With 8 bolt pairs securing each bridge span, this results in an estimated total resistance to
uplift of 80 k (356 kN), which is significantly less than the estimated uplift force. And in the
horizontal direction, concrete pullout of threaded bolt inserts on the south faces of exterior
girders coupled with concrete shearing along northern edges of supporting bents were the likely
modes of failure. For a bridge segment to move laterally, four groups of two sleeve anchors
must fail on the South side of the girders due to tension pull-out, estimated at 4 x 15 k = 60 k
(272 kN). In addition, two groups of vertical anchor bolts must fail due to concrete spalling at
the North side of the bridge deck, estimated at 2 x 20 k = 40 k (176 kN). Finally the two
connection angles on the North side of the South girder must fail due to bending of the vertical
leg, estimated at 2 x 38 k = 76 k (336 kN). Conservatively assuming that all peak resistance
forces occur simultaneously, the total resistance to lateral load is therefore R = 60 + 40 + 76 =
176 k (784 kN), which is less than the estimated lateral load applied by wave action. This
analysis is consistent with the observed damage (Refer to Section 2.2 and Figures 12 and 13).
More importantly, the analysis confirms the ineffectiveness of the existing angle-bolt
connections in resisting severe storm surge and associated wave action. This analysis shows that
even if all anchor bolts had been correctly installed, the bridge deck connections would still have
failed.
18
5.0 RECOMMENDATIONS
Improvements to the existing angle-bolt configuration could serve as a practical and
inexpensive means of preventing detachment of the superstructure in future low-lying bridges.
Angles should be larger and include a plate stiffener welded to the centerline to resist
overtopping and subsequent bending of the angle. For constructability purposes, angles should
be slotted for bidirectional adjustment in the field (versus torching oversized holes, which should
be provided with washer welded then cold galvanized in the field). In addition, a thru bolt with
PVC sleeve, anchored to the girder web by U-bars, should be utilized such that bolt shear
controls, not concrete. These modifications are shown in Figure 14. They should be applied to
all girders not only the two exterior girders.
Figure 14. Recommended Connection Detail
19
The proposed connection detail is one strategy designed to accommodate the full wave
loads, given the substructure can sustain the transmitted loads without failure. Another strategy
is to design the superstructure (or just the lower level spans) to break away at less than full loads,
thereby minimizing damage to the foundation system. Such a scheme proved to be a time and
cost savings for Owners of bridges missing spans but whose substructure remained largely intact
after Katrina. Lost spans were replaced with either temporary i.e. ACROW Panels or permanent
superstructures in much less time than if the substructure had been functionally destroyed.
Regardless of the chosen engineered response, mitigation of wave forces should always
be at the forefront of any good design strategy. The following should be considered to reduce
the hydrostatic and hydrodynamic forces acting on the superstructure:
Provide at least 1 ft of clearance over the 100-yr design wave crest wherever practical.
Utilizing open or sacrificial parapets reduces the amount of area exposed to waves.
Allowing for ventilation of cells through cored holes in the intermediate and end
diaphragms minimizes the buoyancy forces associated with trapped air during a flooding
event.
Utilizing continuous superstructures would increase resistance.
Since the piers were capable of resisting loads for the integral section this is likely the
case for pier bents.
A multi span continuous slab bridge with integral abutment and piers (frame bridge) could
satisfy all of these conditions. (AASHTO, 2008).
20
6.0 CONCLUSION
Reconnaissance survey of the devastation left behind after Katrina and subsequent
performance evaluation of the I-10 onramp revealed numerous design and construction
deficiencies. This is relevant to other hurricane prone regions, particularly the state of Hawaii,
where a significant number of low lying coastal bridges exist. Efforts must be made to
appropriately assess the vulnerability of these existing structures to severe storm surge and wave
action. Estimates of wave forces should be based on the best available methods. During the
course of this study, AASHTO released Guide Specifications for Bridges Vulnerable to Coastal
Storms guidelines, a first of its kind. The AASHTO guide specifications provide a more
comprehensive approach to determine hydrodynamic and hydrostatic forces and addresses many
of the theoretical shortcomings previously identified with the Douglass et al. equations.
21
APPENDIX-- CONNECTION RESISTANCE CALCULATIONS
Uplift Tensile Yielding and Rupture of 6” Leg
kAFR gyn 378)5.101(36
kRn 3024 for (8) angles
kAFR eun 377)2125.10(58
kRn 3016 for (8) angles
Block Shear of 6” Leg Shear Yield and Tension Fracture:
kAFAFR ntugvyn 282)25(158)51(366.06.0
kRn 2256 for (8) angles
**other block shear possibilities do not control. Angle Leg Bending
ke
MR
inkbd
FZFM
nn
yxyn
7.115
5.58
5.584
15.636
4
22
kRn 6.93 for (8) angles
Bearing Strength and Tear Out of 6” Leg for bolts in connection with long-slotted holes perpendicular to direction of force:
uucn dtFtFLR 0.20.1
)58)(1)(8
7(0.2)58)(1)(
2
15.3(0.1
kk 5.101174
kRn 203 for (2) bolts
kRn 1624 for (16) bolts
Bolt Shear
kAFR bvn 87.288
7
448
2
kRn 58 for (2) bolts
kRn 462 for (16) bolts
**assuming A325 threads included.
22
Bolt Tensile Capacity
kAFAFR bubtn 24.438
9
4)5875.0()75.0(
2
kRn 86 for (2) bolts
kRn 692 for (16) bolts
**assuming A36 anchor rod. Tension Strength (Concrete Pullout) of Stud Groups in 8” Leg case 4: free edges on 2 adjacent sides:
minhh
kdlydlxfP eeeecc 4.79)7100)(75.9105(5000)1(67.2))((67.2 31'
kPc 635 for (8) stud groups
for a single stud:
kCAfP escc 8010
7)310(1025000)1(8.28.2 0
'
Shear Strength (Concrete) of Stud Groups in 6” Leg
ctwcc CCCVV '
where kfdV cec 09.77500)1()5.3(5.125.12 5.1'5.1'
se
w nd
bC
5.31
2)5.3(5.3
51
241.1
PLAN
SECTION
23
0.13.1
e
t d
hC
0.1)5.3(3.1
18
0.1956.3
0.17.04.0 e
cc d
dC
0.15.3
25.67.04.0
0.165.1
kVc 10)1)(1)(41.1(09.7
kVc 80 for (8) stud groups
**existing girder reinforcement does not add shear strength because bolt to short.
Lateral Tension: Tensile Yielding and Rupture of 8” Leg
kAFR gyn 378)5.101(36
kAFR eun 377)2125.10(58
Block Shear of 8” Leg Shear Yield and Tension Fracture*:
kAFAFR ntugvyn 304)31(58)321)(36(6.06.0
*other block shear possibilities do not control.
PLAN SECTION
24
Angle Leg Bending
ke
MR
inkbd
FZFM
nn
yxyn
8.375.2
5.94
5.944
15.1036
4
22
kRn 302 for (8) angles
Bearing Strength and Tear Out of 8” Leg for bolts in connection with long-slotted holes perpendicular to direction of force:
uucn dtFtFLR 0.20.1
)58)(1)(8
9(0.2)58)(1)(
2
25.13(0.1
kk 5.13075.137
kRn 261 for (2) bolts
Bolt Shear
kAFAFR bubvn 06.238
9
4)58(4.04.0
2
kRn 46 for (2) bolts
kRn 369 for (16) bolts
Bolt Tensile Capacity
kAFR btn 12.548
7
4)90(
2
kRn 24.108 for (2) bolts
Tension Strength (Concrete Pullout) of Stud Groups in 6” Leg case 1: not near a free edge*:
minhh
klylxfP eecc 26.15)320)(325(7500)1(67.2)2)(2(67.2 '
for a single stud:
kAfP cc 74.13)25.13(327500)1(8.28.2 0'
*since ee ld other cases do not produce appropriate values.
**values represent rough estimates since equations are for welded head studs. ***concrete shear failure of stud groups in 8” leg unlikely on the tension side.
25
Compression: Angle Leg Bending same value as in tension. Bearing Strength and Tear Out of 8” Leg for bolts in connection with long-slotted holes perpendicular to direction of force:
uucn dtFtFLR 0.20.1
)58)(1)(8
9(0.2)58)(1)(375.4(0.1
kk 5.13075.253
kRn 261 for (2) bolts
Bolt Shear same value as in tension. Shear Strength (Concrete) of Stud Groups in 8” Leg
ctwcc CCCVV '
where kfdV cec 37.165000)1()7(5.125.12 5.1'5.1' for single stud
se
w nd
bC
5.31
2)7(5.3
51
220.1
0.13.1
e
t d
hC
0.1)7(3.1
29
0.119.3
PLAN
SECTION
26
0.17.04.0 e
cc d
dC
0.17
75.97.04.0
0.1375.1
kVc 64.19)1)(1)(20.1(37.16
Concrete Shear Strength
kdbfV vvcc 127)2972.0)(43(5)2(0316.00316.0 '
PLAN
SECTION
27
REFERENCES
American Association of State Highway and Transportation Officials (2007). AASHTO LRFD Bridge Design Specifications. Washington, DC American Association of State Highway and Transportation Officials (2008). Guide Specifications for Bridges Vulnerable to Coastal Storms. Washington, DC American Institute of Steel Construction (2001). Manual of Steel Construction- Load and Resistance Factor Design. United States of America. Bea, R.G., Xu, T., Stear, J., and Ramos, R. (1999). Wave Forces on Decks of Offshore
Platforms. Journal of Waterway, Port, Coastal and Ocean Engineering, 125(3), 136-144.
Cheung, K.F., Phadke, A.C., Wei, Y., Rojas, R., Douyere, Y.J.M., Martino, C.D., Houston, S.H.,
Liu, P.L.F., Lynette, P.J., Dodd, N., Liao, S., and Nakazaki, E. (2003). Modeling of Storm-Induced Coastal Flooding for Emergency Management. Ocean Engineering, 30, 1353-1386.
Douglass, S.L., Chen, Q., Olsen, J.M., Edge, B.L., and Brown, D. (2006). Wave Forces on Bridge Decks. Office of Bridge Technology, Washington, D.C.: U.S. Department of Transportation. FEMA http://www.fema.gov/
Lai, C.P. and Lee, Jiin-Jen (1989). Interaction of Finite Amplitude Waves with Platforms or Docks. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(1), 19-39.
NOAA http://www.noaa.gov/
Robertson, I.N., Riggs, H.R., Yim, S.C.S., and Young, Y.L. (2007). Lessons from Hurricane Katrina Storm Surge on Bridges and Buildings. Journal of Waterway, Port, Coastal and
Ocean Engineering, 133(6), 463-483. Robertson, I.N., Yim, S.C.S., and Tran, T.N. (2011). Case Study of Concrete Bridge Subjected to Hurricane Storm Surge and Wave Action. Proceedings of the 2011 ASCE Solutions to Coastal Disasters Conference. doi:10.1061/41185(417)63 Precast/Prestressed Concrete Institute (1999). PCI Design Handbook. U.S. Army Corps of Engineers (2006). Coastal Engineering Manual-Part II. Retrieved from http://chl.erdc.usace.army.mil