Adequacy of the U10 & L11 Gusset Plate Designs for the Minnesota Bridge No (I-35W over the Mississippi River) INTERIM REPORT

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1 FEDERAL HIGHWAY ADMINISTRATION TURNER-FAIRBANK HIGHWAY RESEARCH CENTER REPORT Adequacy o the U10 & L11 Gusset Plate Designs or the Minnesota Bridge No (I-35W over the Mississippi River) INTERIM REPORT Reggie Holt, PE Federal Highway Administration Joseph Hartmann, PhD, PE Federal Highway Administration JANUARY 11, 008

2 TABLE OF CONTENTS PAGE LIST OF FIGURES LIST OF TABLES iii iv INTRODUCTION 1 DESIGN SPECIFICATIONS 1 LOADS 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 ii

3 LIST OF FIGURES PAGE Figure 1. Live Load Lane Placement Used or Design. 3 Figure. 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 or Section A A o Upper Nodes. 11 Figure 6. Demand to Capacity Ratio or Section A A o Lower Nodes. 11 Figure 7. Demand to Capacity Ratio or Section B B o Upper Nodes. 1 Figure 8. Demand to Capacity Ratio or Section B B o Lower Nodes. 1 Figure 9. Gusset Plate Thickness Comparison. 14 iii

4 LIST OF TABLES PAGE Table 1. Gusset Plate U10 Section A A Demand to Capacity Ratios. 10 Table. Gusset Plate U10 Section B B Demand to Capacity Ratios. 10 Table 3. Demand to Capacity Ratios or the Primary Truss Gusset Plates. 13 Table 4. Gusset Plate Unsupported Edge Adequacy. 15 iv

5 INTRODUCTION The I-35W Bridge over the Mississippi River in Minneapolis, MN had 14 spans and a total length o 1,907 eet. The primary structure o this bridge was a variable depth steel deck truss o 1,064 eet in length that carried I-35W over the river and gorge. On August 1, 007 a ailure in the river span o the deck truss caused a complete collapse o the entire truss structure and some o the approach spans resulting in the tragic loss o 13 public motorist lives. The National Transportation Saety Board (NTSB) is the primary agency investigating this ailure to determine a probable cause. The Federal Highway Administration (FHWA) is assisting and collaborating with both the onsite and broader activities o the NTSB investigators. The FHWA team consists o personnel rom the Turner-Fairbank Highway Research Center (TFHRC), the Oice o Bridge Technology (HIBT), the Resource Center (RC) and several Division oices. One o the tasks perormed by the FHWA team was a review and assessment o the original bridge design calculations by Sverdrup & Parcel. This report will ocus on the indings o this assessment unique to the gusset plate design methodology used or the primary truss and more speciically the design o the gusset plates at locations U10 and L11. The initial onsite investigation o the collapsed structure identiied the ailure o 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 (herein reerred to as the I-35W Bridge) was designed by structural engineering consultant Sverdrup & Parcel or the Minnesota Department o Transportation (Mn/DOT) in the early 1960s. The General Notes on the construction drawings indicate that Mn/DOT commissioned the design to be in accordance with Division I o the A.A.S.H.O. Standard Speciication or Highway Bridges, 1961 Edition and 1961 and 196 Interim Speciications modiied by Minnesota Highway Department standards on allowable stresses. The ollowing sections summarize the appropriate provisions rom those speciications relevant to the design o the gusset plates on the I-35W Bridge. Section GENERAL The provisions o this section outline the various combinations o loads and orces or which structures are designed to withstand and what percentage o material allowable stress will be used or the design resistance calculations associated with each combination. The gusset plate design assessment conducted herein considered the Group I load combination which typically governs the design or this component. This combination includes the eect o dead load, live load, impact, earth pressure, buoyancy, and stream low. Designing or Group I loads is intended to produce a structure with adequate strength to resist a credible extreme orce eect. As this is an ultimate strength condition or the component, use o 100% o the appropriate allowable stresses are permitted in the design. 1

6 Section HIGH STRENGTH LOW-ALLOY STRUCTURAL STEEL The provisions o this section speciy the allowable stresses that are to be used or design with high-strength low-alloy (HSLA) structural steels. These stresses are dependent on material thickness and direction o loading. For HSLA structural steel less than ¾ in thickness such as was used in the U10 and L11 gusset plates on the I-35W Bridge, the ollowing allowable stresses were used in this design assessment: 7,000 psi or axial tension 15,000 psi or shear,000 psi 0.56 (L/r) or compression where L (in.) is the unsupported length and r (in.) is the radius o gyration o the member being designed. These allowable stresses were not modiied by the Minnesota Highway Department design standards. Section GUSSET PLATES These provisions are intended to inorm the designer about elements and details associated with the design o gusset plates. They include the statement gusset plates shall be o ample thickness to resist shear, direct stress, and lexure, acting on the weakest or critical section o maximum stress. In addition, this section o the speciications indicates that i the length o an unsupported edge o a low-alloy steel gusset plate exceeds 48 times its thickness, the edge shall be stiened. LOADS As summarized above, the Group I load combination was used to determine the strength demands or this gusset plate design assessment. Dead load, live load and live load impact orce eects are needed or this load group. These loadings were generated based on the inormation contained on the original design plans and veriied by independent sources within and outside 1 o the assessment team. The generated loads were consistent with the values used in the Sverdrup & Parcel calculations and the truss member orces shown on the design plans. As such, the orces indicated on the design plans were used or the assessment o the gusset plate design. It is important to note that, consistent with accepted design practice, the member orces shown on the design plans are or the maximum orce carried by that member due to the varied application (envelope) o live load applied to the bridge. However, these orces are not necessarily produced concurrently or all the members connected by a gusset plate and, thereore, oten result in combinations o design loads that do not satisy static equilibrium at the node. The ollowing sections provide a brie description o how each component o loading was used in the reconstructed design calculation. 1 BSDI, Ltd., Coopersburg, Pennsylvania. Obtained rom Mn/DOT.

Dead Load The dead load was broken down into two load component sub-groups. The irst subgroup included the weight o the superstructure below the deck stringers.

7 Dead Load The dead load was broken down into two load component sub-groups. The irst subgroup included the weight o the superstructure below the deck stringers. That is, the weight o the primary truss, loor trusses, and all bracing members. The second subgroup included the weight o the components transerred to the primary truss at panel points through the deck stringers. The weight o the bridge deck, curb, barrier and deck stringers were included in this second sub-group. The dead load orces were assumed to be distributed equally to each truss line. That is, or the purposes o design, the east and west lines o the primary truss were considered to resist one-hal o the total dead load o the bridge. Live Load The General Notes on the construction drawings also speciied the live load model that was used or design: H0 S This model consists o a placing either a single three axle 7,000 pound truck (truck load) or a uniorm 640 pound/oot load in combination with one or more concentrated loads (lane load) in each lane o the bridge to produce the maximum orce eect or the component being designed. As expected or bridges with spans o this length lane load governed the live load design. The governing lane load case was generated by using seven traic lanes placed transversely across the deck in order to maximize the loading that occurs in one line o the primary truss. The application o live load indicated in Figure 1 placed a maximum demand o 4.3 lanes o lane load on one line o the primary truss. Figure 1. Live Load Lane Placement Used or Design. Impact Impact loadings were generated as per the Section 1..1 o the AASHO Speciications. These loadings account or the dynamic, vibratory and impact eects on the bridge caused by the moving live load. In application these eects scale up the governing live load by a small raction called an impact actor. For the I-35W Bridge, the impact actors computed in the original design were 9% or the main span and 13% or the back spans. 3

8 DESIGN METHODOLOGY The original design calculations by Sverdrup & Parcel or the I-35W Bridge which were supplied by Mn/DOT did not include any inormation or the primary truss gusset plate designs. It was thereore impossible to check or comment on the original design calculations or the gusset plates in the main trusses. For this report, a basic design methodology was established to enable checking o the main truss gusset plates. This design methodology is consistent with the methodology used by Sverdrup & Parcel to design the gusset plates or the loor trusses in the I-35W Bridge. In addition, the gusset plate design methodology is consistent with that used in several more modern truss bridge 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 o these design calculation sets indicate that the basic design methodology or gusset plates has been consistent over time and has not changed or modern vintage bridges. All o the design calculations studied used the same general procedures to design gusset plates. The methodology employs general beam theory structural mechanics to analyze the gusset plates and estimate design stresses along a critical section. One o the assumptions o beam theory is that the individual components o stress caused by shear, axial orce and bending can be decoupled rom the aggregate complex stress state and analyzed independently without a signiicant loss in accuracy. This approach is consistent with the language used in the governing AASHO Speciications o the era which state that gusset plates shall be o ample thickness to resist shear, direct stress, and lexure, acting on the weakest or critical section o maximum stress. For the purposes o this investigation, this design methodology was used to establish the capacity o the primary truss gusset plates or the I-35W Bridge. In doing so, two gusset plate critical sections were considered. These two sections, herein reerred to as Section A A and Section B B, are shown in Figure. Section A A, is the plane located between the chords and diagonals o a node and is oriented parallel to the chord (essentially horizontally throughout most o the structure). Section B B is the typically vertical plane located between the chord and diagonal on one side o the node and the remainder o the node. The geometry and critical sections or gusset plate U10 are shown in Figure. Transposing the diagrams o Figure about a horizontal plane would result in drawings appropriate or gusset plate L11. 4

However, investigating the capacity o the gusset plate along these two sections will result in an adequate determination o overall perormance.

9 SECTION A A SECTION B B Figure. Gusset Plate Design Sections. Sections A A and B B are typical sections or gusset plate design. A complete design would not be limited to only capacity calculations at these two sections but would include capacity checks on several other planes o signiicance. However, investigating the capacity o the gusset plate along these two sections will result in an adequate determination o overall perormance. Using the truss member orces at each node, the equilibrating shear (V), moment (M) and axial (P) orces shown in Figure are easily determined. The demands o these equilibrating orces on the gusset plate can then be compared to the lexural stress, direct stress and shear stress limitations speciied in order to evaluate perormance. RECONSTRUCTED DESIGN CALCULATION RESULTS This section contains the reconstructed design calculations or the primary critical sections o the U10 gusset plate. The demonstrated methodology was then used to evaluate all o the I-35W Bridge primary truss gusset plates. GUSSET PLATE U10 GEOMETRY The geometry o gusset plate U10 and the location o Sections A A and B B are shown on Figure 3. The plate dimensions (other than thickness) shown were scaled rom the design plan set to provide the best estimate o the dimensions used by the original designers. The dierences between the as-built plate sizes and those shown (scaled) rom the plans were minimal. As the dimensions shown on the plan set are the best representative o the original design, the plate dimensions scaled rom the plans have been used to reconstruct the design calculations. 5

10 Figure 3. Gusset Plate U10 Geometry. It should be noted that the oset dimensions that locate Sections A A (14 inches rom the centerline o the top chord) and B B (6 inches rom the centerline o the vertical) in Figure 3 are or the geometry o gusset plate U10. The osets or these sections at other nodes can vary. This is particularly the case or Section B B as it is located such that there will be no contribution o the connection plates to the resistance supplied by the gusset plates. GUSSET PLATE U10 RECONSTRUCTED DESIGN CALCULATIONS Figure 4 shows the ree body diagrams used to evaluate the demands o the equilibrated loadings on the critical sections o the U10 gusset plate. 6

Figure 4. Gusset Plate U10 Free Body Diagrams. The reconstructed design calculations or each o the critical sections indicated on Figure 4 are shown below.

11 Figure 4. Gusset Plate U10 Free Body Diagrams. The reconstructed design calculations or each o the critical sections indicated on Figure 4 are shown below. Section A A Section Properties (1 Plate) A = h( t) = 100( 1 ) ( 1 )( 100) = 50 in 3 bh I = = = 41,667 in 1 1 I 41,667 3 S = = = 833 in h 100 Equilibrating Forces P =, ,975 = 130 k ( tension) V =,88 + 1,975 =,73 k M =, ( 14) 1,975 ( 14) = 38,118 k in 7

12 Stresses along section (1 Plate) a b v v P 130 = = 1 ksi A = M 38,118 = = 1.9 ksi S = 833 V,73 1 avg = = = 7. ksi A = v avg = ( 7.) = 40.8 ksi Principal Stresses (at neutral axis) R = ten comp a + ( ) = + ( 40.8) v 1.3 a 1.3 = R = 40.8 = 41.5 ksi a 1.3 = + R = = 40. ksi = 40.8 ksi Section B B Section Properties (1 Plate) A = h( t) = 7( 1 ) ( 1 )( 7) = 36 in 3 bh I = = = 15,55 in 1 1 I 15,55 3 S = = = 43 in h

13 Equilibrating Forces P =,88,147 = 173 k ( tension) V =,88 = 1,839 k 63.9 M rivets =, M = 14,86 k in ( 36 14) Stresses along section (1 Plate) a b v v rivets P 173 = = 1 ksi A =.4 36 M 14,86 = = ksi S = 43 V 1,839 1 avg = = = 5.5 ksi A = v avg = , ( 5.5) = 38.3 ksi Principal Stresses (at section neutral axis) R = ten comp a + ( ) = + ( 38.3) v.4 a.4 = R = 38.3 = 39.5 ksi a.4 = + R = = 37.1 ksi = 38.3 ksi GUSSET PLATE U10 DEMAND TO CAPACITY RATIOS Comparing the reconstructed design stresses computed or the U10 gusset plate shown above to the allowable stresses speciied in the AASHO Speciication, Section results in demand to capacity (D/C) ratios that illustrate the expected perormance o the gusset plate. The D/C ratio is a comparative measure o the eiciency o the design. A D/C value less than 1 indicates a conservative design; a D/C ratio o 1 indicates an eicient design, and a D/C ratio greater that 1 indicates a liberal design with a reduction in the intended actor o saety. Liberal designs are not common but are sometimes 9

14 acceptable based on the proessional judgment o an engineer. The D/C ratios or the U10 gusset plate along Sections A A and B B are summarized in Tables 1 and. Table 1. Gusset Plate U10 Section A A Demand to Capacity Ratios. Force Type AASHO Allowable Stress Reconstructed Design Demand to Capacity Ratio Stress Bending ( b ) 7.0 ksi.9 ksi 0.85 Shear ( v-avg ) 15.0 ksi 7. ksi 1.81 Principal ( ten ) 7.0 ksi 41.6 ksi 1.54 Principal ( comp ).0 ksi 40.3 ksi 1.83 Table. Gusset Plate U10 Section B B Demand to Capacity Ratios. Force Type AASHO Allowable Stress Reconstructed Design Demand to Capacity Ratio Stress Bending ( b ) 7.0 ksi 17.0 ksi 0.63 Shear ( v-avg ) 15.0 ksi 5.5 ksi 1.70 Principal ( ten ) 7.0 ksi 39.5 ksi 1.46 Principal ( comp ).0 ksi 37.1 ksi 1.69 I-35W GUSSET PLATE DEMAND TO CAPACITY RATIOS Using the method and procedures demonstrated or the design o the U10 gusset plate above, demands and capacities were determined or all o the unique primary truss gusset plates on the I-35W Bridge except those at node U0. This two member node at the end o the bridge was not considered because its geometry is very dierent than the typical ive member nodes elsewhere in the structure. Due to the symmetry o the I-35W Bridge, a complete review o the gusset plate designs needs to only consider one hal o the primary truss. The results or the Section A A design calculations are shown graphically on Figures 5 and 6. Similarly, the results or the Section B B calculations are shown graphically on Figure 7 and 8. The results o all o these calculations are summarized numerically in Table 3. For the entire set o primary truss gusset plates, the principal stress demands and capacities were determined at the neutral axis o the critical section. Thereore, the data shown in the igures and tables o this section may not represent the actual maximum principal stress along a critical section at locations where combined bending and axial stresses are a signiicant portion o the aggregate stress state. However, when shear stress dominates (as is the case in these gusset plate analyses), the principal stress calculated at the neutral axis o the critical section is also the most likely maximum principal stress. Figures 5 through 8 contain bar charts indicating the demand and capacity or a given gusset plate which is located on an accompanying igure o the primary truss. There are individual igures to address shear stress and principal stress comparisons. Demands that are greater than capacities are highlighted with a red box. 10

Demand to Capacity Ratio or Section A A o Upper Nodes.

15 Demand to capacity ratios greater than 1.00 in Table 3 are indicated with a gray ield. Figure 5. Demand to Capacity Ratio or Section A A o Upper Nodes. Figure 6. Demand to Capacity Ratio or Section A A o Lower Nodes. 11

16 Figure 7. Demand to Capacity Ratio or Section B B o Upper Nodes. Figure 8. Demand to Capacity Ratio or Section B B o Lower Nodes. 1

17 Table 3. Demand to Capacity Ratios or the Primary Truss Gusset Plates. Gusset Thickness Demand/Capacity Plate Section A A Section B B (in.) Shear Principal Tension Principal Compression Shear Principal Tension Principal Compression Upper Nodes U 5/ U4 1/ U U8 1 3/8 * U10 1/ U U Lower Nodes L1 1 * L3 1/ L5 5/ L L L11 1/ L * Thickness o built-up (multi-ply) gusset plate. I-35W Gusset Plate Detailing Figure 9 presents a visual survey o the primary truss gusset plate thicknesses rom the as-built I-35W Bridge. In the back-span o the primary truss, a gradual decrease in gusset plate thickness is observed as the distance to the node rom the points o support increases. In the main-span, a less gradual transition in plate size is evident. For this comparison, the thickness o the built-up gusset plates at nodes L1 and U8 are represented in the igure. 13

Figure 9. Gusset Plate Thickness Comparison. The AASHO Speciications o the era also included a detailing requirement or gusset plates in Section 1.6.34.

18 Figure 9. Gusset Plate Thickness Comparison. The AASHO Speciications o the era also included a detailing requirement or gusset plates in Section For low alloy steels o the type used in the construction o the gusset plates o this bridge, the speciication limited the slenderness o the unsupported edge length to 48 times the plate thickness. I the unsupported edge length exceeded this limit, stiening was required. Stiening o the edge in these cases was needed in order to avoid prematurely compromising the capacity o the gusset plate due to buckling potentially caused by compression rom the primary truss diagonals. Table 4 assesses the adequacy o the unsupported edge lengths o the gusset plates provided on the I-35W Bridge. An initial comparison o the unsupported edge lengths and limits presented indicates that the gusset plates at L3, U8, L8 and U10 did not meet the speciied slenderness limit. However, the diagonals at L3 and U8 carry a net tension load due to all the load groups considered mitigating the need or edge stiening, and edge stiening was provided at L8 to bring that gusset plate into compliance with the speciication. Thereore, based on the reconstructed design assessment, only the gusset plates provided at U10 were not in compliance with the speciied limits (indicated by the gray shading in the table). 14

19 Gusset Plate Thickness o Unsupported Edge (in.) Table 4. Gusset Plate Unsupported Edge Adequacy. Unstiened Unsupported Assessment/Compliance Unsupported Edge Length Edge Limit (in.) (in.) Upper Nodes U 5/ OK U4 1/ 4 16 OK U OK U8 5/ Tension Diagonals Only OK U10 1/ 4 30 Inadequate No Good U OK U OK Lower Nodes L OK L3 1/ 4 6 Tension Diagonals Only OK L5 5/ OK L OK L Edge Stiening Provided OK L OK L11 1/ 4 OK L OK INTERPRETATION OF RESULTS Contrasting a review o the D/C ratios in Table 3 with the assessment o unsupported edge lengths shown in Table 4 indicates that the thickness o some o the primary truss gusset plates were dictated by the demands o the applied loading while others were determined by the geometric needs o the connection or the resulting slenderness requirements o the unsupported edge. It is clear that the thickness o the gusset plates supplied at U, L5, U6, L7 and L9 were the result o the demands o the applied loading. All o these gusset plates have at least one D/C ratio equal to or greater than 0.87 indicating an eicient design. The thickness o 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 rom the overall geometric requirements o the node. That is, the required shape o these gusset plates was determined by the layout and the number o asteners required or each o the connecting members o the primary truss. Combining the shape requirements with a 15

20 minimum plate thickness o 1/-inch suiciently met the reconstructed design and detailing requirements. From the reconstructed design and detailing inormation, it is less clear why the gusset plate 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 violate the slenderness limit o the unsupported edge but that requirement is mitigated by the act the 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 ineicient design considering the thickness supplied greatly exceeds the needs o the slenderness requirement. The gusset plates at U10 and L11 consistently ailed the D/C ratio checks conducted and the U10 gussets also violated the unsupported edge limitations. The capacity inadequacies were considerable or all conditions investigated with the plate providing approximately one-hal o the resistance required by the design loadings. The gusset plate at U1 ailed one o the six D/C ratio checks investigated. The recreated design indicated a 15% overstress condition associated with the principal compressive stress component along critical Section B B. A 15% overstress is signiicant 16

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