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

ii

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

vi

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.

3

Figure 1. Bridge Overview

Figure 2. Flat Slab Bridge Section

4

Figure 3. Bridge Side View

Figure 4. Bridge Cross Section

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

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