Bridge I-35W -080115 -Safety Recommendation

7/31/2019 Bridge I-35W -080115 -Safety Recommendation

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National Transportation Safety BoardWashington, D.C. 20594

Safety Recommendation

Date: January 15, 2008

In reply refer to: H-08-1

The Honorable J. Richard Capka

AdministratorFederal Highway Administration

1200 New Jersey Avenue, S.E.

Washington, D.C. 20590

On Wednesday, August 1, 2007, about 6:05 p.m. central daylight time, the Interstate 35W(I-35W) highway bridge over the Mississippi River in north Minneapolis, Minnesota,

experienced a failure in the superstructure of the 1,000-foot-long deck truss portion of the1,900-foot-long bridge. Approximately 456 feet of the center span of the deck truss fell about

108 feet into the 15-foot-deep river. Approximately 110 vehicles were on the portion of the

bridge that collapsed, and 17 vehicles fell into the water. As a result of the bridge collapse, 13people died and 145 people were injured.

Roadway construction was being conducted on the deck truss portion of the bridge, andfour of the eight lanes were closed for repaving when the bridge collapsed. Machinery and

paving materials were being parked and stockpiled on the center span.

The National Transportation Safety Board dispatched investigators within hours of the

collapse and continues to investigate the circumstances of the accident. Although the SafetyBoards investigation is ongoing and no determination of probable cause has been reached,

investigators have a concern regarding certain elements of the bridge (gusset plates), which has

prompted issuance of this safety recommendation.

Bridge

Construction of the bridge (Federal bridge identification number 9340) began in 1964,

and it was opened to traffic in 1967. The bridge was designed by Sverdrup & Parcel(subsequently acquired by Jacobs Engineering) and was built by Hurcon Incorporated and

Industrial Construction Company. The steel deck truss portion of the bridge consisted of twoparallel main trusses (east and west) connected through transverse floor trusses supporting the

reinforced concrete deck. The ends of the beams in the main trusses were connected by rivetedgusset plates at 112 nodes (joints) along the deck truss portion of the bridge. The bridge was

considered to be fracture-critical because the load paths in the structure were nonredundant,

meaning that a failure of any one of a number of structural elements in the bridge would cause acomplete collapse of the entire bridge. This type of bridge is also referred to as a


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non-load-path-redundant bridge. The Federal Highway Administration (FHWA) estimates

that there are approximately 465 steel deck truss bridges within the National Bridge Inventory.

Since it was built, the deck truss portion of the bridge has undergone at least two major

renovations, one in 1977 and one in 1998. As part of these renovations, the average thickness of

the concrete deck was increased from 6.5 inches to 8.5 inches, and the center median barrier and

outside barrier walls were increased in size. These changes added significantly to the overallweight of the structure.

Gusset Plates

Physical examination of the recovered bridge structure showed that the gusset plates at

the east and west nodes U10, U10, L11, and L11 were fractured.1

The other major gusset platesin the main trusses were intact. Design methodology for gusset plates is normally very

conservative, with the result that a properly designed gusset plate should generally be stronger

than the beams it connects. Accordingly, one would not expect to find fractured gusset plates.However, the damage patterns and fracture features uncovered in the investigation to date

suggest that the collapse of the deck truss portion of the bridge was related to the fractured gusset

plates and, in particular, may have originated with the failure of the U10 gusset plates. Materials

testing performed to date has found no deficiencies in the quality of the steel or concrete used inthe bridge. Therefore, the Safety Board, with the FHWA, conducted a thorough review of the

design of the bridge, with an emphasis on the design of the gusset plates.

Gusset Plate Design Process Error

The investigation discovered that the original design process led to a serious error in

sizing of some of the gusset plates in the main trusses. Engineers working in the investigation

used generally accepted calculation methodologies to recalculate the stresses in these gussetplates. Their results indicate that some of the gusset plates were undersized and did not provide

the margin of safety expected in a properly designed bridge. These undersized gusset plates werefound at 8 (of the 112) nodes on the main trusses of the bridge (east and west upper nodes U10

and U10, and east and west lower nodes L11 and L11). These gusset plates were roughly halfthe thickness required. The results of the calculations are documented in the FHWAs interim

report, Adequacy of the U10 & L11 Gusset Plate Designs for the Minneapolis Bridge No. 9340

(I-35W over the Mississippi River).

Bridge Design Documentation

The Safety Board obtained copies of the original design and fabrication drawings, as well

as a partial set of design calculations from both Jacobs Engineering and the Minnesota

Department of Transportation (Mn/DOT), and compared the design documents with the actualbridge structure. So far, this comparison has indicated that the superstructure of the bridge was

generally built as specified in the design, with no significant discrepancies identified between thedesign documents and the as-built condition of the bridge. The gusset plates that were undersized

on the bridge were undersized on the drawings.

1The symbol is pronounced prime and indicates the corresponding node on the opposite end of the

bridge.

Ver P


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Design Calculation Methodology

Because the investigation has determined that some of the gusset plates were undersized,the Safety Board examined the design calculation methodology used at the time the bridge was

designed, in the 1960s, to verify that the methodology was sound. The design documents

reviewed included detailed calculations for the beams in the main trusses and detailed

calculations for the welded gusset plates joining the beams in the floor trusses, both of whichindicate sound calculation methodology. However, because the detailed calculations for the main

truss gusset plates could not be located, the Safety Board was unable to verify the calculationmethodology used for those gusset plates. As a result, the Safety Board has not yet determined

whether the error was due to a calculation mistake, a drafting error, or some other error in the

design process.

Design Review Process

The design error was not detected during the internal review process conducted by

Sverdrup & Parcel when the drawings were developed. The Safety Board is still evaluating thisreview process but notes that any effective review should be sufficient to detect and correct

design errors such as the one that resulted in the undersized gusset plates. Nevertheless, the

review process in place at the time of the design failed to detect the error.

For the most part, State departments of transportation rely on bridge designers to perform

accurate calculations and to check their work. Thus, beyond the designers internal review, theredoes not appear to be a process in place to identify original design errors in bridges.

In addition, gusset plate design calculations are not usually reviewed during majormodifications on bridges. Generally, the weakest point of a bridge is evaluated to determine if

the additional loads or stresses can be accommodated, with the assumption that the remaining

portions of the bridge can withstand the change. For example, as previously mentioned, the

accident bridge underwent two major renovations, which added significantly to the overallweight of the structure. Information obtained from Mn/DOT indicates that Mn/DOT engineersfollowed generally accepted practice and recalculated the anticipated stress levels in what they

believed at the time were the weakest members of the bridge. Normally, there would be no

reason for them to question the strength of the gusset plates relative to these weaker structuralmembers.

In summary, the gusset plate design error identified during this ongoing investigation was

not detected by any of the internal review procedures used by Sverdrup & Parcel during the

original bridge design, nor was there a reasonable expectation that it would be detected during

any review associated with the original submission of the design or any subsequent

modifications to the bridge.

Bridge Load Rating Calculations

The error in the design of the gusset plates would not have been identified by routine loadrating calculations because gusset plate stresses are not normally part of these calculations.

Bridge load rating calculations are used by bridge owners to determine if their bridge can

accommodate heavy vehicles and to make critical load posting and permitting decisions. A


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number of States use specialized bridge load rating computer programsBARS or its

successor Virtisto calculate load ratings. Mn/DOT currently uses the BARS program but is in

the process of switching to theVirtis software program. Although these two computer programs

can be used to evaluate the stresses in the truss beams for a specified load case, they do notconsider any aspect of the gusset plates connecting the truss beams. In summary, periodic

recalculations of the load ratings of bridges are not intended to verify or confirm the adequacy of

gusset plate designs.

Bridge Inspections

Bridge inspections would also not have identified the error in the design of the gusset

plates. The National Bridge Inspection Standards (NBIS) are aimed at detecting conditions suchas cracks or corrosion that degrade the strength of the existing structure; they do not, and are not

intended to, address errors in the original design. Although inspections of the accident bridge

identified and tracked some areas of cracking and corrosion, at this point in the investigation,there is no indication that any of those areas played a significant role in the collapse of the

bridge.

Summary

The Safety Board is concerned that, for at least this bridge, there was a breakdown in the

design review procedures that allowed a serious design error to be incorporated into the

construction of the I-35W bridge. The bridge was designed with gusset plates that wereundersized, and the design firm did not detect the design error when the plans were created.

Because of this design error, the riveted gusset plates became the weakest member of this

fracture-critical bridge, whereas normally gusset plates are expected to be stronger than thebeams they connect. Further, there are few, if any, recalculations after the design stage that

would detect design errors in gusset plates. Finally, other programs to ensure the safety of our

Nations bridges, such as the methods used in calculating load ratings and the inspections

conducted through the NBIS program, are not designed or expected to uncover original mistakesin gusset plate designs or calculations.

It is important to note that the Safety Board has no evidence to suggest that the

deficiencies in the various design review procedures associated with this bridge are widespreador even go beyond this particular bridge. In fact, this is the only bridge failure of this type of

which the Safety Board is aware. However, because of this accident, the Safety Board cannot

dismiss the possibility that other steel truss bridges with nonredundant load paths may havesimilar undetected design errors. Consequently, the Safety Board believes that bridge owners

should ensure that the original design calculations for this type of bridge have been made

correctly before any future major modifications or operational changes are contemplated.

Therefore, the National Transportation Safety Board makes the following

recommendation to the Federal Highway Administration:


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For all non-load-path-redundant steel truss bridges within the National Bridge

Inventory, require that bridge owners conduct load capacity calculations to verify

that the stress levels in all structural elements, including gusset plates, remain

within applicable requirements whenever planned modifications or operationalchanges may significantly increase stresses. (H-08-1)

Please refer to Safety Recommendation H-08-1 in your reply. If you need additionalinformation, you may call (202) 314-6177.

Chairman ROSENKER, Vice Chairman SUMWALT, and Members HERSMAN,

HIGGINS, and CHEALANDER concurred in this recommendation.

Original Signed By:

By: Mark V. Rosenker

Chairman


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FEDERAL HIGHWAY ADMINISTRATION

TURNER-FAIRBANK HIGHWAY RESEARCH CENTER REPORT

Adequacy of the U10 & L11 Gusset Plate Designs for the Minnesota Bridge No. 9340

(I-35W over the Mississippi River)

INTERIM REPORT

Reggie Holt, PEFederal Highway Administration

Joseph Hartmann, PhD, PE

Federal Highway Administration

JANUARY 11, 2008


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ii

TABLE OF CONTENTS PAGE

LIST OF FIGURES iii

LIST OF TABLES iv

INTRODUCTION 1

DESIGN SPECIFICATIONS 1

LOADS 2

DESIGN METHODOLOGY 4

RECONSTRUCTED DESIGN CALCULATION RESULTS 5

GUSSET PLATE U10 GEOMETRY 5

GUSSET PLATE U10 RECONSTRUCTED DESIGN CALCULATIONS 6

GUSSET PLATE U10 DEMAND TO CAPACITY RATIOS 9

I-35W GUSSET PLATE DEMAND TO CAPACITY RATIOS 10

I-35W GUSSET PLATE DETAILING 13

INTERPRETATION OF RESULTS 15


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LIST OF FIGURES PAGE

Figure 1 . Live Load Lane Placement Used for Design. 3

Figure 2 . Gusset Plate Design Sections. 5

Figure 3. Gusset Plate U10 Geometry. 6

Figure 4. Gusset Plate U10 Free Body Diagrams. 7

Figure 5. Demand to Capacity Ratio for Section AA of Upper Nodes. 11

Figure 6. Demand to Capacity Ratio for Section AA of Lower Nodes. 11

Figure 7. Demand to Capacity Ratio for Section BB of Upper Nodes. 12

Figure 8. Demand to Capacity Ratio for Section BB of Lower Nodes. 12

Figure 9. Gusset Plate Thickness Comparison. 14

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iv

LIST OF TABLES PAGE

Table 1. Gusset Plate U10 Section AA Demand to Capacity Ratios. 10

Table 2. Gusset Plate U10 Section BB Demand to Capacity Ratios. 10

Table 3. Demand to Capacity Ratios for the Primary Truss Gusset Plates. 13

Table 4. Gusset Plate Unsupported Edge Adequacy. 15


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INTRODUCTION

The I-35W Bridge over the Mississippi River in Minneapolis, MN had 14 spans and atotal length of 1,907 feet. The primary structure of this bridge was a variable depth steel

deck truss of 1,064 feet in length that carried I-35W over the river and gorge. On August

1, 2007 a failure in the river span of the deck truss caused a complete collapse of theentire truss structure and some of the approach spans resulting in the tragic loss of 13public motorist lives. The National Transportation Safety Board (NTSB) is the primary

agency investigating this failure to determine a probable cause. The Federal Highway

Administration (FHWA) is assisting and collaborating with both the onsite and broaderactivities of the NTSB investigators. The FHWA team consists of personnel from the

Turner-Fairbank Highway Research Center (TFHRC), the Office of Bridge Technology

(HIBT), the Resource Center (RC) and several Division offices. One of the tasksperformed by the FHWA team was a review and assessment of the original bridge design

calculations by Sverdrup & Parcel. This report will focus on the findings of this

assessment unique to the gusset plate design methodology used for the primary truss and

more specifically the design of the gusset plates at locations U10 and L11. The initialonsite investigation of the collapsed structure identified the failure of the U10 gusset

plates as occurring early in the event. The L11 gusset plates are detailed similarly to

those at U10.

DESIGN SPECIFICATIONS

Minnesota Bridge No. 9340 (herein referred to as the I-35W Bridge) was designed by

structural engineering consultant Sverdrup & Parcel for the Minnesota Department ofTransportation (Mn/DOT) in the early 1960s. The General Notes on the construction

drawings indicate that Mn/DOT commissioned the design to be in accordance withDivision I of the A.A.S.H.O. Standard Specification for Highway Bridges, 1961Edition and 1961 and 1962 Interim Specifications modified by Minnesota Highway

Department standards on allowable stresses. The following sections summarize the

appropriate provisions from those specifications relevant to the design of the gusset plateson the I-35W Bridge.

Section 1.4.1 GENERAL

The provisions of this section outline the various combinations of loads and forces for

which structures are designed to withstand and what percentage of material allowable

stress will be used for the design resistance calculations associated with eachcombination. The gusset plate design assessment conducted herein considered the Group

I load combination which typically governs the design for this component. This

combination includes the effect of dead load, live load, impact, earth pressure, buoyancy,and stream flow. Designing for Group I loads is intended to produce a structure with

adequate strength to resist a credible extreme force effect. As this is an ultimate strength

condition for the component, use of 100% of the appropriate allowable stresses are

permitted in the design.

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Section 1.4.7 HIGH STRENGTH LOW-ALLOY STRUCTURAL STEEL

The provisions of this section specify the allowable stresses that are to be used for designwith high-strength low-alloy (HSLA) structural steels. These stresses are dependent on

material thickness and direction of loading. For HSLA structural steel less than inthickness such as was used in the U10 and L11 gusset plates on the I-35W Bridge, thefollowing allowable stresses were used in this design assessment:

27,000 psi for axial tension 15,000 psi for shear 22,000 psi 0.56 (L/r)2 for compression

whereL (in.) is the unsupported length and r(in.) is the radius of gyration of the member

being designed. These allowable stresses were not modified by the Minnesota Highway

Department design standards.

Section 1.6.34 GUSSET PLATES

These provisions are intended to inform the designer about elements and details

associated with the design of gusset plates. They include the statement gusset plates

shall be of ample thickness to resist shear, direct stress, and flexure, acting on the weakest

or critical section of maximum stress. In addition, this section of the specificationsindicates that if the length of an unsupported edge of a low-alloy steel gusset plate

exceeds 48 times its thickness, the edge shall be stiffened.

LOADS

As summarized above, the Group I load combination was used to determine the strength

demands for this gusset plate design assessment. Dead load, live load and live load

impact force effects are needed for this load group. These loadings were generated basedon the information contained on the original design plans and verified by independent

sources within and outside1 of the assessment team. The generated loads were consistentwith the values used in the Sverdrup & Parcel calculations 2 and the truss member forces

shown on the design plans. As such, the forces indicated on the design plans were usedfor the assessment of the gusset plate design. It is important to note that, consistent with

accepted design practice, the member forces shown on the design plans are for the

maximum force carried by that member due to the varied application (envelope) of live

load applied to the bridge. However, these forces are not necessarily producedconcurrently for all the members connected by a gusset plate and, therefore, often result

in combinations of design loads that do not satisfy static equilibrium at the node.

The following sections provide a brief description of how each component of loading was

used in the reconstructed design calculation.

1 BSDI, Ltd., Coopersburg, Pennsylvania.2 Obtained from Mn/DOT.

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Dead Load

The dead load was broken down into two load component sub-groups. The first sub-

group included the weight of the superstructure below the deck stringers. That is, the

weight of the primary truss, floor trusses, and all bracing members. The second sub-group included the weight of the components transferred to the primary truss at panel

points through the deck stringers. The weight of the bridge deck, curb, barrier and deckstringers were included in this second sub-group. The dead load forces were assumed tobe distributed equally to each truss line. That is, for the purposes of design, the east and

west lines of the primary truss were considered to resist one-half of the total dead load of

the bridge.

Live Load

The General Notes on the construction drawings also specified the live load model that

was used for design: H20S1644. This model consists of a placing either a single threeaxle 72,000 pound truck (truck load) or a uniform 640 pound/foot load in combination

with one or more concentrated loads (lane load) in each lane of the bridge to produce the

maximum force effect for the component being designed. As expected for bridges withspans of this length lane load governed the live load design. The governing lane load

case was generated by using seven traffic lanes placed transversely across the deck in

order to maximize the loading that occurs in one line of the primary truss. The

application of live load indicated in Figure 1 placed a maximum demand of 4.23 lanes oflane load on one line of the primary truss.

Figure 1. Live Load Lane Placement Used for Design.

Impact

Impact loadings were generated as per the Section 1.2.12 of the AASHO Specifications.

These loadings account for the dynamic, vibratory and impact effects on the bridgecaused by the moving live load. In application these effects scale up the governing liveload by a small fraction called an impact factor. For the I-35W Bridge, the impact factors

computed in the original design were 9% for the main span and 13% for the back spans.

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DESIGN METHODOLOGY

The original design calculations by Sverdrup & Parcel for the I-35W Bridge which weresupplied by Mn/DOT did not include any information for the primary truss gusset plate

designs. It was therefore impossible to check or comment on the original design

calculations for the gusset plates in the main trusses. For this report, a basic designmethodology was established to enable checking of the main truss gusset plates. Thisdesign methodology is consistent with the methodology used by Sverdrup & Parcel to

design the gusset plates for the floor trusses in the I-35W Bridge. In addition, the gusset

plate design methodology is consistent with that used in several more modern trussbridge designs reviewed by the assessment team:

Sewickley Bridge over the Ohio River, Pennsylvania, 1979 Chelyan Bridge over the Kanawha River, West Virginia, 1993 I-90 over the Grand River (Condition evaluation calculations), Ohio, 1996

The similarity of these design calculation sets indicate that the basic design methodology

for gusset plates has been consistent over time and has not changed for modern vintage

bridges.

All of the design calculations studied used the same general procedures to design gusset

plates. The methodology employs general beam theory structural mechanics to analyzethe gusset plates and estimate design stresses along a critical section. One of the

assumptions of beam theory is that the individual components of stress caused by shear,

axial force and bending can be decoupled from the aggregate complex stress state andanalyzed independently without a significant loss in accuracy. This approach is

consistent with the language used in the governing AASHO Specifications of the era

which state that gusset plates shall be of ample thickness to resist shear, direct stress,

and flexure, acting on the weakest or critical section of maximum stress.

For the purposes of this investigation, this design methodology was used to establish the

capacity of the primary truss gusset plates for the I-35W Bridge. In doing so, two gussetplate critical sections were considered. These two sections, herein referred to as Section

AA and Section BB, are shown in Figure 2. Section AA, is the plane located between

the chords and diagonals of a node and is oriented parallel to the chord (essentiallyhorizontally throughout most of the structure). Section BB is the typically vertical plane

located between the chord and diagonal on one side of the node and the remainder of the

node. The geometry and critical sections for gusset plate U10 are shown in Figure 2.Transposing the diagrams of Figure 2 about a horizontal plane would result in drawings

appropriate for gusset plate L11.

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SECTION AA SECTION BB

Figure 2. Gusset Plate Design Sections.

Sections AA and BB are typical sections for gusset plate design. A complete designwould not be limited to only capacity calculations at these two sections but would include

capacity checks on several other planes of significance. However, investigating the

capacity of the gusset plate along these two sections will result in an adequate

determination of overall performance. Using the truss member forces at each node, theequilibrating shear (V), moment (M) and axial (P) forces shown in Figure 2 are easily

determined. The demands of these equilibrating forces on the gusset plate can then becompared to the flexural stress, direct stress and shear stress limitations specified in order

to evaluate performance.

RECONSTRUCTED DESIGN CALCULATION RESULTS

This section contains the reconstructed design calculations for the primary critical

sections of the U10 gusset plate. The demonstrated methodology was then used to

evaluate all of the I-35W Bridge primary truss gusset plates.

GUSSET PLATE U10 GEOMETRY

The geometry of gusset plate U10 and the location of Sections AA and BB are shown

on Figure 3. The plate dimensions (other than thickness) shown were scaled from thedesign plan set to provide the best estimate of the dimensions used by the original

designers. The differences between the as-built plate sizes and those shown (scaled) from

the plans were minimal. As the dimensions shown on the plan set are the bestrepresentative of the original design, the plate dimensions scaled from the plans have

been used to reconstruct the design calculations.

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Figure 3. Gusset Plate U10 Geometry.

It should be noted that the offset dimensions that locate Sections AA (14 inches from

the centerline of the top chord) and BB (6 inches from the centerline of the vertical) in

Figure 3 are for the geometry of gusset plate U10. The offsets for these sections at othernodes can vary. This is particularly the case for Section BB as it is located such that

there will be no contribution of the connection plates to the resistance supplied by thegusset plates.

GUSSET PLATE U10 RECONSTRUCTED DESIGN CALCULATIONS

Figure 4 shows the free body diagrams used to evaluate the demands of the equilibrated

loadings on the critical sections of the U10 gusset plate.

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Figure 4. Gusset Plate U10 Free Body Diagrams.

The reconstructed design calculations for each of the critical sections indicated on Figure

4 are shown below.

Section AA

Section Properties (1 Plate)( )

( )( )

3

4

3

213

22

1

833

2

100

667,41

2

667,4112

100

12

50100)(

inh

IS

in

bh

I

inthA

=

=

=

===

===

Equilibrating Forces

( ) ( ) inkM

kV

tensionkP

=

+

=

=

+

=

=

=

118,388.39

0.3814

1.55

8.39975,1

3.51

0.3814

9.63

3.51288,2

723,21.550.38975,1

9.630.38288,2

)(1301.55

8.39975,1540

9.63

3.51288,2

7


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Stresses along section (1 Plate)

( ) ksiff

ksiA

Vf

ksiSMf

ksiA

Pf

avgvv

avgv

b

a

8.402.272

3

2

3

2.2750

723,2

9.22833

118,38

3.150

130

21

21

21

=

=

=

=

==

=

==

=

==

Principal Stresses (at neutral axis)

( ) ( )

ksiRf

f

ksiRf

f

ksiff

R

acomp

aten

v

a

2.408.402

3.1

2

5.418.402

3.1

2

8.408.402

3.1

2

2

2

2

2

=+

=+=

=

==

=+

=+

=

Section BB

Section Properties (1 Plate)( )

( )( )

3

4

3

213

22

1

432

2

72

552,15

2

552,1512

72

12

3672)(

inh

IS

inbh

I

inthA

=

=

=

===

===

8


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Equilibrating Forces

( )

inkM

M

kV

tensionkP

rivets

rivets

=

+

=

=

=

=

=

826,14

0.38

3.5161436

9.63

0.38288,21436

56

1656147,2

839,19.633.51288,2

)(17356

1656147,2

9.63

0.38288,2

Stresses along section (1 Plate)

( ) ksiff

ksiA

Vf

ksiS

Mf

ksiA

Pf

avgvv

avgv

b

a

3.385.252

3

2

3

5.2536

839,1

2.17432

826,14

4.236

173

21

21

2

1

=

=

=

=

==

=

==

=

==

Principal Stresses (at section neutral axis)

( ) ( )

ksiRf

f

ksiRf

f

ksiff

R

a

comp

a

ten

v

a

1.373.382

4.2

2

5.393.382

4.2

2

3.383.382

4.2

2

2

2

2

2

=+

=+=

=

==

=+

=+

=

GUSSET PLATE U10 DEMAND TO CAPACITY RATIOS

Comparing the reconstructed design stresses computed for the U10 gusset plate shownabove to the allowable stresses specified in the AASHO Specification, Section 1.4.7results in demand to capacity (D/C) ratios that illustrate the expected performance of the

gusset plate. The D/C ratio is a comparative measure of the efficiency of the design. A

D/C value less than 1 indicates a conservative design; a D/C ratio of 1 indicates anefficient design, and a D/C ratio greater that 1 indicates a liberal design with a reduction

in the intended factor of safety. Liberal designs are not common but are sometimes

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acceptable based on the professional judgment of an engineer. The D/C ratios for theU10 gusset plate along Sections AA and BB are summarized in Tables 1 and 2.

Table 1. Gusset Plate U10 Section AA Demand to Capacity Ratios.

Force Type AASHO

Allowable Stress

Reconstructed

DesignStress

Demand to Capacity

Ratio

Bending (fb) 27.0 ksi 22.9 ksi 0.85

Shear (fv-avg) 15.0 ksi 27.2 ksi 1.81

Principal (ften) 27.0 ksi 41.6 ksi 1.54

Principal (fcomp) 22.0 ksi 40.3 ksi 1.83

Table 2. Gusset Plate U10 Section BB Demand to Capacity Ratios.

Force Type AASHO

Allowable Stress

Reconstructed

Design

Stress

Demand to Capacity

Ratio

Bending (fb) 27.0 ksi 17.0 ksi 0.63Shear (fv-avg) 15.0 ksi 25.5 ksi 1.70

Principal (ften) 27.0 ksi 39.5 ksi 1.46

Principal (fcomp) 22.0 ksi 37.1 ksi 1.69

I-35W GUSSET PLATE DEMAND TO CAPACITY RATIOSUsing the method and procedures demonstrated for the design of the U10 gusset plate

above, demands and capacities were determined for all of the unique primary truss gussetplates on the I-35W Bridge except those at node U0. This two member node at the end of

the bridge was not considered because its geometry is very different than the typical fivemember nodes elsewhere in the structure. Due to the symmetry of the I-35W Bridge, a

complete review of the gusset plate designs needs to only consider one half of theprimary truss. The results for the Section AA design calculations are shown graphicallyon Figures 5 and 6. Similarly, the results for the Section BB calculations are shown

graphically on Figure 7 and 8. The results of all of these calculations are summarized

numerically in Table 3.

For the entire set of primary truss gusset plates, the principal stress demands and

capacities were determined at the neutral axis of the critical section. Therefore, the data

shown in the figures and tables of this section may not represent the actual maximumprincipal stress along a critical section at locations where combined bending and axial

stresses are a significant portion of the aggregate stress state. However, when shear stress

dominates (as is the case in these gusset plate analyses), the principal stress calculated atthe neutral axis of the critical section is also the most likely maximum principal stress.

Figures 5 through 8 contain bar charts indicating the demand and capacity for a givengusset plate which is located on an accompanying figure of the primary truss. There are

individual figures to address shear stress and principal stress comparisons. Demands that

are greater than capacities are highlighted with a red box.

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Demand to capacity ratios greater than 1.00 in Table 3 are indicated with a gray field.

Figure 5. Demand to Capacity Ratio for Section AA of Upper Nodes.

Figure 6. Demand to Capacity Ratio for Section AA of Lower Nodes.

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Figure 7. Demand to Capacity Ratio for Section BB of Upper Nodes.

Figure 8. Demand to Capacity Ratio for Section BB of Lower Nodes.

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Table 3. Demand to Capacity Ratios for the Primary Truss Gusset Plates.

Demand/Capacity

Section AA Section BB

GussetPlate

Thickness

(in.) Shear

Princip

al

Tension

Princip

al

Compression

Shear

Princip

al

Tension

Princip

al

Compression

Upper Nodes

U2 5/8 0.89 0.77 0.88 0.71 0.50 0.86

U4 1/2 0.67 0.60 0.64 0.50 0.70 0.30

U6 1 0.98 0.94 0.99 0.48 0.55 0.36

U8 1 3/8*

0.05 0.03 0.07 0.31 0.46 0.20

U10 1/2 1.81 1.54 1.83 1.70 1.46 1.69

U12 1 0.11 0.11 0.10 0.71 0.37 1.15

U14 1 0.00 0.00 0.37 0.23 0.10 0.47

Lower Nodes

L1 1*

0.47 0.48 0.40 0.31 0.39 0.21

L3 1/2 0.76 0.59 0.82 0.45 0.45 0.38

L5 5/8 0.71 0.67 0.65 0.65 0.87 0.42

L7 1 0.58 0.54 0.52 0.75 0.97 0.50

L9 1 0.90 0.83 0.83 0.83 0.83 0.71

L11 1/2 2.07 1.80 2.03 1.55 1.11 1.84

L13 1 0.36 0.31 0.36 0.30 0.10 0.73*Thickness of built-up (multi-ply) gusset plate.

I-35W Gusset Plate DetailingFigure 9 presents a visual survey of the primary truss gusset plate thicknesses from the

as-built I-35W Bridge. In the back-span of the primary truss, a gradual decrease in gusset

plate thickness is observed as the distance to the node from the points of supportincreases. In the main-span, a less gradual transition in plate size is evident. For this

comparison, the thickness of the built-up gusset plates at nodes L1 and U8 are

represented in the figure.

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Figure 9. Gusset Plate Thickness Comparison.

The AASHO Specifications of the era also included a detailing requirement for gusset

plates in Section 1.6.34. For low alloy steels of the type used in the construction of thegusset plates of this bridge, the specification limited the slenderness of the unsupported

edge length to 48 times the plate thickness. If the unsupported edge length exceeded this

limit, stiffening was required. Stiffening of the edge in these cases was needed in orderto avoid prematurely compromising the capacity of the gusset plate due to buckling

potentially caused by compression from the primary truss diagonals.

Table 4 assesses the adequacy of the unsupported edge lengths of the gusset plates

provided on the I-35W Bridge. An initial comparison of the unsupported edge lengths

and limits presented indicates that the gusset plates at L3, U8, L8 and U10 did not meetthe specified slenderness limit. However, the diagonals at L3 and U8 carry a net tension

load due to all the load groups considered mitigating the need for edge stiffening, and

edge stiffening was provided at L8 to bring that gusset plate into compliance with thespecification. Therefore, based on the reconstructed design assessment, only the gusset

plates provided at U10 were not in compliance with the specified limits (indicated by the

gray shading in the table).

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Table 4. Gusset Plate Unsupported Edge Adequacy.

GussetPlate

Thicknessof

Unsupported

Edge

(in.)

UnstiffenedUnsupported

Edge Limit

(in.)

UnsupportedEdge Length

(in.)

Assessment/Compliance

Upper Nodes

U2 5/8 30 30 OK

U4 1/2 24 16 OK

U6 1 48 22 OK

U8 5/8 30 36 Tension Diagonals Only

OK

U10 1/2 24 30 Inadequate No Good

U12 1 48 22 OK

U14 1 48 16 OK

Lower Nodes

L1 1 48 36 OKL3 1/2 24 26 Tension Diagonals Only

OK

L5 5/8 30 20 OK

L7 1 48 16 OK

L8 1 48 54 Edge Stiffening Provided

OK

L9 1 48 22 OK

L11 1/2 24 22 OK

L13 1 48 18 OK

INTERPRETATION OF RESULTS

Contrasting a review of the D/C ratios in Table 3 with the assessment of unsupported

edge lengths shown in Table 4 indicates that the thickness of some of the primary trussgusset plates were dictated by the demands of the applied loading while others were

determined by the geometric needs of the connection or the resulting slenderness

requirements of the unsupported edge. It is clear that the thickness of the gusset plates

supplied at U2, L5, U6, L7 and L9 were the result of the demands of the applied loading.All of these gusset plates have at least one D/C ratio equal to or greater than 0.87

indicating an efficient design.

The thickness of the gusset plate supplied at L1 was needed to meet the unsupported edge

limitations.

The gusset plate sizes at locations L3 and U4 were seemingly derived from the overall

geometric requirements of the node. That is, the required shape of these gusset plates

was determined by the layout and the number of fasteners required for each of theconnecting members of the primary truss. Combining the shape requirements with a

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minimum plate thickness of 1/2-inch sufficiently met the reconstructed design anddetailing requirements.

From the reconstructed design and detailing information, it is less clear why the gussetplate thickness at locations U8, L13, and U14 were chosen. The gusset plates at U8 and

U14 have load demands well below their capacities. The gusset plates at U8 do violatethe slenderness limit of the unsupported edge but that requirement is mitigated by the factthe connected diagonals carry a net tension load. The gusset plate thicknesses at L13

may have been supplied to meet the load demands at the node (D/C=0.73). However, the

assessment team views this as an inefficient design considering the thickness suppliedgreatly exceeds the needs of the slenderness requirement.

The gusset plates at U10 and L11 consistently failed the D/C ratio checks conducted andthe U10 gussets also violated the unsupported edge limitations. The capacity

inadequacies were considerable for all conditions investigated with the plate providing

approximately one-half of the resistance required by the design loadings.

The gusset plate at U12 failed one of the six D/C ratio checks investigated. The recreated

design indicated a 15% overstress condition associated with the principal compressivestress component along critical Section BB. A 15% overstress is significant

Documents

Bridge I-35W -080115 -Safety Recommendation