SDA-08-001 Gusset Plate Design

8/10/2019 SDA-08-001 Gusset Plate Design

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New York State Department of Transportation

OFFICE OF STRUCTURES

STRUCTURES DESIGN ADVISORYIssued by:MAIN OFFICE,OFFICE OFSTRUCTURES

SUBJECT:

GUSSET PLATES DESIGNPROCESS

CODE:SDA 08-001

DATE:14 Apr 2008

APPROVED BY: SUBJECT CODE: SUPERSEDES:NONE

PURPOSE

AASHTOs Standard Specifications for Highway Bridges and the Load and Resistance Factor Design(LRFD) Specifications do not prescribe hard and fast methods for gusset plate design. Rather, generalengineering principles and textbook methods are used for gusset plate design. This Design Advisory willprovide additional guidance, including an example, to designers of new or replaced non-load-path-

redundant steel truss bridges.

BACKGROUND

On August 1, 2007, the I-35W Interstate highway bridge over the Mississippi River in Minneapolis,Minnesota, experienced a failure in the superstructure of the steel deck truss. Physical examination of therecovered bridge structure showed that some gusset plates were fractured. Examination of the designmethodology used at the time was found to be sound. Although no problems were identified with thedesign methodology used for the bridge, the investigation discovered that some gusset plates on the maintrusses of the bridge were undersized.

Accordingly, NYSDOT put in place an implementation plan to address FHWA recommendations regardingLoad-carrying Capacity Considerations of Gusset Plates in Non-load path redundant Steel TrussBridges. On January 15, 2008 FHWA issued a Technical Advisory that made three recommendationscovering: new or replaced non-load-path-redundant steel truss bridges, future recalculations of loadcapacity on existing non-load-path-redundant steel truss bridges, and reviewing previous load ratings ofgusset plates on bridges subjected to significant changes in stress levels. This Structures Design

Advisory (SDA) addresses new or replaced non-load-path-redundant steel truss bridges.

A separate NYSDOT Load Rating Technical Advisory is being issued to address the otherrecommendations.

TRUSS GUSSET PLATE DESIGN AND ANALYSIS

Ordinarily, gusset plates are stronger than the truss members they connect and should not control thecapacity of the structure. There are several possible approaches to the design and analysis of truss gussetplates. A recommended procedure is outlined in this Structures Design Advisory (SDA). Other analysis

procedures may be used if they are soundly documented and considered to be applicable for the bridgeunder design.

The gusset plate design shall be made using AASHTOs Load and Resistance Factor Design (LRFD)Specifications with the HL-93 and NYSDOT Design Permit Vehicle for Live loads.

Truss member connections shall be designed at the strength limit state for not less than the larger of theaverage of the axial force due to the factored loadings at the point of splice or connection and the factoredaxial resistance of the member at the same point OR 75 percent of the factored axial resistance of themember per LRFD Article 6.13.1. The aforementioned LRFD article does not apply to sections ofinterest.

The maximum stress on a section due to the factored loads shall be checked in accordance with LRFDArticle 6.14.2.8.


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STRUCTURES DESIGN ADVISORYCODE:

DATE: 14 Apr il 2008 PAGE: 2

SUBJECT:GUSSET PLATES DESIGN PROCESS

LIVE LOAD CASES

Four live load cases will be considered at each truss joint:

1. Position the HL-93 live load plus impact such that the factored force in the higher loaded chord ismaximized while using the corresponding forces for that case in the diagonals and verticals at that

joint.

2. Position the HL-93 live load plus impact such that the factored force in the higher loaded diagonalis maximized while using the corresponding forces for that case in the chords and vertical at that

joint.

3. Position the NYSDOT Design Permit Vehicle live load plus impact such that the factored force inthe higher loaded chord is maximized while using the corresponding forces for that case in thediagonals and verticals at that joint.

4. Position the NYSDOT Design Permit Vehicle live load plus impact such that the factored force inthe higher loaded diagonal is maximized while using the corresponding forces for that case in thechords and vertical at that joint.

SECTIONS OF INTEREST

At least four sections, two horizontal sections located adjacent to the chord and two vertical sectionslocated on either side of the vertical member, shall be investigated at each truss joint. These sections areillustrated in the attached Math Cad worksheet. An additional section shall also be investigated at truss

joints where there is a break in the alignment of the chord. Additional sections should be investigated atunusual truss joint configurations.

At each of these sections the following are to be checked:

Maximum stress from combined factored flexural and axial loads on thegross and net sections.

Uniform and maximum shear stress on both the gross and net sections.

UNSUPPORTED EDGE DISTANCE

The unsupported edge distance of gusset plates should be designed in accordance with LRFD Article6.14.2.8

EDGE SLENDERNESS RATIO REQUIREMENT

The edge slenderness of gusset plates should be designed in accordance with LRFD Article 6.9.3


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MEMBER CONNECTION FORCE

Four cases will be considered at each member:

1. Maximum tensile force in the member due to dead load plus HL-93 live load plus impact.

2. Maximum compressive force in the member due to dead load plus HL-93 live load plus impact.

3. Maximum tensile force in the member due to dead load plus NYSDOT Design Permit Vehicle liveload plus impact.

4. Maximum compressive force in the member due to dead load plus NYSDOT Design PermitVehicle live load plus impact.

BOLT CAPACITY

The capacity of the bolts connecting the truss members to the gusset plates shall be designed for themaximum truss member force and in accordance with LRFD Articles 6.13.1 & 6.13.2.

BLOCK SHEAR RUPTURE RESISTANCEGusset plates should be designed for block shear rupture in accordance with LRFD Article 6.13.4.The analysis of block shear rupture involves the evaluation of several patterns of planes to arrive at thegoverning pattern.

ANALYSIS OF WHITMORE SECTION

The tensile stress on the gusset plate shall also be checked at the Whitmore Section. This considers the

axial load applied to the gusset plate individually by each truss member to the Whitmore Section.

The Whitmore Section is defined in the attached Math Cad worksheet.

BUCKLING CHECK OF COLUMN UNDER COMPRESSION MEMBERS

The resistance of gusset plates in compression shall be determined as that of idealized members incompression in accordance with the provisions of AASHTO LRFD Articles 6.9.2.1 and 6.9.4.

WORKED EXAMPLE

An example using a Math Cad worksheet is distributed along with this Structures Design Advisory.

CONTACT:

Direct questions regarding this SDA to Wahid Albert of the Structures Design Bureau at (518) 457 4539,or by e-mail to [email protected]
mailto:[email protected]:[email protected]


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REFERENCES

National Transportation Safety Board Safety Recommendation H-08-1, dated January 15, 2008.

FHWA Technical Advisory T 5140.29, Load Carrying Capacity Consideration of Gusset Plates inNon-Load-Path Redundant Steel Truss Bridges, dated January 15, 2008.

FHWA Bridge Design Guidance No. 1, Revision Date of February 28, 2008.

AASHTO LRFD Bridge Design Specifications, 4thEdition/2007, " Washington, DC, 2004.

AISCs Manual of Steel Construction, Load and Resistance Factor Design, Third Edition, Part 9,Dated November 2001.


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State of New York

Department of Transportation

L R F D G u s s e t P l a t e A n a l y s i s

J o i n t L 4

Sheet: 1 of 77PIN: ________

Job Title: ____________________

This Mathcad worksheet is intended to analyze gusset plates according to the AASHTO LRFD Bridge Design

Specifications, 4th Edition 2007. Gusset plates are analyzed for shear, bending, and axial force effects by theconventional "Method-of-Section" procedures. It should be noted that this sheet only investigates three common

sections of interest, two vertical and one horizontal section. Additional sections should be investigated at joints

that have a break in the alignment of the chord and/or unusual joint configurations. Member connections are

analyzed for bolt resistance, block shear rupture resistance, and Whitmore section stresses.

Disclaimer: This worksheet and sample calculations outline an acceptable method for designing truss gusset

plates. There may be other acceptable procedures for this design. While this Mathcad sheet has been checked,

it should be used by an engineer familiar with truss and gusset plate design. Sound engineering judgement is

required to apply this method to individual situations and to bridges that may vary from this example.

Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008


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State of New York



J o i n t L 4

Sheet: 2 of 77PIN: ________

Job Title: ____________________

Member Angles and Unsupported Edge Distances

A 90 deg

B 42.5 deg

C 0deg

D 40.2deg

E 90deg

B1 31.0in

B2 28.0in

B3 25.0in

B4 31.4in

Angle from Vertical: Input a positive angle for members that are clockwise from vertical and a negative angle for

members that are counter clockwise from vertical.

Unsupported Edge Distances: The unsupported edge distances of the top and side of the gusset plate should

be taken from the center to center of the outermost bolt holes.



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State of New York



J o i n t L 4

Sheet: 3 of 77PIN: ________

Job Title: ____________________

Unfactored Member Forces Due to Dead Load

Dead Load (DC) Dead Load (DW)

Member A ADC 1779kip ADW 103kip

Member B BDC 266kip BDW 15kip Tensile +Compressive -

Member C CDC 25 kip CDW 0kip

Member D DDC 5 kip DDW 0kip

Member E EDC 1940kip EDW 109kip

Dead Load (DC): Enter the unfactored member force due to dead load. Input tensile force as a positive value and

compressive force as a negative value.

Dead Load (DW): Enter the unfactored member force due to future wearing surface and utilities. Input tensile

force as a positive value and compressive force as a negative value.



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State of New York



J o i n t L 4

Sheet: 4 of 77PIN: ________

Job Title: ____________________

Unfactored Member Forces Due to HL-93 Live Load + Impact

Case 1 Case 2

Member A AHL1 415kip AHL2 345kip

Member B BHL1 110kip BHL2 142kip

Tensile +

Compressive -Member C CHL1 2kip CHL2 3kip

Member D DHL1 36 kip DHL2 11 kip

Member E EHL1 521kip EHL2 434kip

Case 1: Position the HL-93 live load such that the force in the higher loaded chord is maximized. Enter the

unfactored chord and corresponding vertical ,diagonal, and chord member forces. Input tensile force as a positive

value and compressive force as a negative value.

Case 2: Position the HL-93 live load such that the force in the higher loaded diagonal is maximized. Enter the

unfactored diagonal and corresponding vertical, diagonal, and chord member forces. Input tensile force as a

positive value and compressive force as a negative value.



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State of New York



J o i n t L 4

Sheet: 5 of 77PIN: ________

Job Title: ____________________

Unfactored Member Forces Due to NYSDOT Design Permit Vehicle + Impact

(LRFD 3.6.1.2.4a Blue Page)

Case 3 Case 4

Member A APV3 401kip APV4 414kip

Member B BPV3 166kip BPV4 170kip

Tensile +Compressive -

Member C CPV3 3kip CPV4 3kip

Member D DPV3 55 kip DPV4 27 kip

Member E EPV3 549kip EPV4 546kip

Case 3: Position the permit live load such that the force in the higher loaded chord is maximized. Enter the

unfactored chord and corresponding vertical, diagonal, and chord member forces. Input tensile force as a positive

value and compressive force as a negative value.

Case 4: Position the permit live load such that the force in the higher loaded diagonal is maximized. Enter the

unfactored diagonal and corresponding vertical, diagonal, and chord member forces. Input tensile force as a




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State of New York



J o i n t L 4

Sheet: 6 of 77PIN: ________

Job Title: ____________________

Gusset and Splice Plate Dimensions

tgp 1.125in

hsp 17.3in

t

sp

.75in

Lgs 1.6in

B 2.6in

Yield Strength of Steel: Fy 50ksi Ultimate Strength of Steel: Fu 65ksi

Modulus of Elasticity of Steel: E 29000ksi

Bolt Properties

Nominal Bolt Diameter: db 1in

Diameter of Hole: dh 1.0625in LRFD 6.13.2.4.2-1

Minimum Tensile Strength of Bolt: Fub 120ksi LRFD 6.4.3.1

Minimum Required Bolt Tension: Pt 51kip LRFD 6.13.2.8-1



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State of New York



J o i n t L 4

Sheet: 7 of 77PIN: ________

Job Title: ____________________

Resistance Factors

Resistance Factor for Flexure: f 1.0 LRFD 6.5.4.2

Resistance Factor for Shear: v 1.0 LRFD 6.5.4.2

Resistance Factor for Tension on Gross: y .95 LRFD 6.5.4.2

Resistance Factor for Tension on Net: u .80 LRFD 6.5.4.2

Resistance Factor for Compression: c

.90 LRFD 6.5.4.2

Resistance Factor for Shear on Gross: vy .95 FHWA Bridge Design Guidance No. 1, 2/28/08 Rev.

Resistance Factor for Shear on Net: vu .80 FHWA Bridge Design Guidance No. 1, 2/28/08 Rev.

Effective Length Factor: K 1.0 LRFD 4.6.2.5

Reduction factor for shear lag in connection: U 1.0 LRFD 6.8.2.2



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State of New York



J o i n t L 4

Sheet: 8 of 77PIN: ________

Job Title: ____________________

Factored Member Forces LRFD T3.4.1-1

Load Modifier based on ductility, redundancy, and operational importance: i 1.05 LRFD 1.3.2

Ac1 i 1.25ADC 1.5ADW 1.75 AHL1 Ac1 3260kipAc2 i 1.25ADC 1.5ADW 1.75 AHL2 Ac2 3131kipAc3 i 1.25ADC 1.5ADW 1.35 APV3 Ac3 3066kipAc4 i 1.25ADC 1.5ADW 1.35 APV4 Ac4 3084kip

Bc1 i 1.25BDC 1.5BDW 1.75 BHL1 Bc1 575 kipBc2 i 1.25BDC 1.5BDW 1.75 BHL2 Bc2 634 kipBc3 i 1.25BDC 1.5BDW 1.35 BPV3 Bc3 608 kipBc4 i 1.25BDC 1.5BDW 1.35 BPV4 Bc4 614 kip

Cc1 i 1.25CDC 1.5CDW 1.75 CHL1 Cc1 29 kipCc2 i 1.25CDC 1.5CDW 1.75 CHL2 Cc2 27 kipCc3 i 1.25CDC 1.5CDW 1.35 CPV3 Cc3 29 kip

Cc4 i 1.25CDC 1.5CDW 1.35 CPV4 Cc4 29 kip

Dc1 i 1.25DDC 1.5DDW 1.75 DHL1 Dc1 73 kipDc2 i 1.25DDC 1.5DDW 1.75 DHL2 Dc2 27 kipDc3 i 1.25DDC 1.5DDW 1.35 DPV3 Dc3 85 kipDc4 i 1.25DDC 1.5DDW 1.35 DPV4 Dc4 45 kip

Ec1 i 1.25EDC 1.5EDW 1.75 EHL1 Ec1 3675kipE

c2

i

1.25E

DC

1.5E

DW

1.75 EHL2

E

c2

3515kip

Ec3 i 1.25EDC 1.5EDW 1.35 EPV3 Ec3 3496kipEc4 i 1.25EDC 1.5EDW 1.35 EPV4 Ec4 3492kip



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State of New York



J o i n t L 4

Sheet: 9 of 77PIN: ________

Job Title: ____________________

Horizontal and Vertical Components of Member Forces

Note: The applied member forces are reduced by half to account for the member being supported on both

sides by a gusset plate.

Member A

FA1x .5Ac1sin A FA1x 1630 kip FA2x .5Ac2sin A FA2x 1566 kip

FA1y .5Ac1cos A FA1y 0 kip FA2y .5Ac2cos A FA2y 0 kip

FA3x .5Ac3sin A FA3x 1533 kip FA4x .5Ac4sin A FA4x 1542 kipFA3y .5Ac3cos A FA3y 0 kip FA4y .5Ac4cos A FA4y 0 kip

Member B

FB1x .5Bc1sin B FB1x 194 kip FB2x .5Bc2sin B FB2x 214 kip

FB1y .5Bc1cos B FB1y 212 kip FB2y .5Bc2cos B FB2y 234 kip

FB3x .5Bc3sin B FB3x 205 kip FB4x .5Bc4sin B FB4x 207 kipFB3y .5Bc3cos B FB3y 224 kip FB4y .5Bc4cos B FB4y 226 kip

Member C

FC1x .5Cc1sin C FC1x 0 kip FC2x .5Cc2sin C FC2x 0 kip

FC1y .5Cc1cos C FC1y 15 kip FC2y .5Cc2cos C FC2y 14 kip

F

C3x

.5C

c3

sin C

FC3x

0 kip FC4x

.5C

c4

sin C

FC4x

0 kip

FC3y .5Cc3cos C FC3y 14 kip FC4y .5Cc4cos C FC4y 14 kip



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State of New York



J o i n t L 4

Sheet: 10 of 77PIN: ________

Job Title: ____________________

Member D

FD1x .5Dc1sin D FD1x 23 kip FD2x .5Dc2sin D FD2x 9 kipFD1y .5Dc1cos D FD1y 28 kip FD2y .5Dc2cos D FD2y 10 kip

FD3x .5Dc3sin D FD3x 27 kip FD4x .5Dc4sin D FD4x 14 kip

FD3y .5Dc3cos D FD3y 32 kip FD4y .5Dc4cos D FD4y 17 kip

Member E

FE1x .5Ec1sin E FE1x 1838kip FE2x .5Ec2sin E FE2x 1758kipFE1y .5Ec1cos E FE1y 0 kip FE2y .5Ec2cos E FE2y 0 kip

FE3x .5Ec3sin E FE3x 1748kip FE4x .5Ec4sin E FE4x 1746kip

FE3y .5Ec3cos E FE3y 0 kip FE4y .5Ec4cos E FE4y 0 kip



15/81

State of New York



J o i n t L 4

Sheet: 11 of 77PIN: ________

Job Title: ____________________

Analysis of Horizontal Section A1-A1

LAA1 90.2in

YA1 19.618in

XA1 46.4in

Force Diagram



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State of New York



J o i n t L 4

Sheet: 12 of 77PIN: ________

Job Title: ____________________

Section Properties

Area of Section: AAA LAA1t gp AAA 101 in2

Moment of Inertia of Section: IAA1

12

tgp LAA13

IAA 68800 in4

Neutral Axis: xNA .5LAA1 xNA 45.1 in

Section Modulus of Section:SAA.left

IAA

xNA SAA.left 1526 in

3

SAA.right

IAA

xNA

SAA.right 1526in3

Moment Arms: eAA.B XA1 xNA YA1tanB eAA.B 16.677 in

eAA.C XA1 xNA YA1tanC eAA.C 1.3in

eAA.D XA1 xNA YA1tan D eAA.D 17.9 in

Forces Acting on Section

Case 1

Axial Force: FAA1 FB1y FC1y FD1y FAA1 170 kip

Shear Force: VAA1 FB1x FC1x FD1x VAA1 218 kip

Bending Moment: MAA1 FB1yeAA.B FC1yeAA.C FD1yeAA.D MAA1 4050 kip in



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State of New York



J o i n t L 4

Sheet: 13 of 77PIN: ________

Job Title: ____________________

Case 2




Case 3




Case 4




Stress Along Section

Case 1

Axial Stress: AA1.a

FAA1

AAA

AA1.a 1.7ksi

Flexural Stress: AA1.b.left

MAA1

SAA.left

AA1.b.left 2.7ksi

AA1.b.right

MAA1

SAA.right

AA1.b.right 2.7 ksi



18/81

State of New York



J o i n t L 4

Sheet: 14 of 77PIN: ________

Job Title: ____________________

Uniform Average Shear Stress: AA1.vu

VAA1

AAA

AA1.vu 2.1 ksi

Maximum Average Shear Stress: AA1.v QLAA1

2tgp

LAA1

4

VAA1Q

IAAtgp

AA1.v 3.2 ksi

Case 2

Axial Stress: AA2.a

FAA2

AAA

AA2.a 2.1ksi


MAA2

SAA.left

AA2.b.left 2.7ksi

AA2.b.right

MAA2

SAA.right

AA2.b.right 2.7 ksi


VAA2

AAA

AA2.vu 2.2 ksi


2tgp

LAA1

4

VAA2Q

IAAtgp

AA2.v 3.3 ksi



19/81

State of New York



J o i n t L 4

Sheet: 15 of 77PIN: ________

Job Title: ____________________

Case 3

Axial Stress: AA3.a

FAA3

AAA AA3.a 1.8ksi


MAA3

SAA.left

AA3.b.left 2.8ksi

AA3.b.right

MAA3

SAA.right

AA3.b.right 2.8 ksi

Uniform Average Shear Stress: AA3.vuVAA3

AAA

AA3.vu 2.3 ksi


2tgp

LAA1

4

VAA3Q

IAAtgp

AA3.v 3.4 ksi

Case 4

Axial Stress: AA4.a

FAA4

AAA

AA4.a 1.9ksi


MAA4

SAA.left

AA4.b.left 2.7ksi

AA4.b.right

MAA4

SAA.right

AA4.b.right 2.7 ksi


VAA4

AAA

AA4.vu 2.2 ksi



20/81

State of New York



J o i n t L 4

Sheet: 16 of 77PIN: ________

Job Title: ____________________


2tgp

LAA1

4

VAA4Q

IAAtgp

AA4.v 3.3 ksi

Comparing Section A1-A1 Stresses to LRFD Allowable

Radius of Gyration of Gusset Plate: rgp

tgp

12

rgp 0.325in

Compressive Stress on Side Edges

C1 L1 AA1.a AA1.b.left

L2 AA2.a AA2.b.left

L3 AA3.a AA3.b.left

L4 AA4.a AA4.b.left

c min L1 L2 L3 L4( )

n 0ksi

nreturn c 0if

creturn otherwise

C4 R1 AA1.a AA1.b.right

R2 AA2.a AA2.b.right



c min R1 R2 R3 R4( )

n 0ksi

nreturn c 0if

creturn otherwise

C1 0.0ksi C4 1.1 ksi



21/81

State of New York



J o i n t L 4

Sheet: 17 of 77PIN: ________

Job Title: ____________________

Allowable Compressive Stress LRFD 6.9.4.1

C.all.1 Lc B1

K Lc

rgp

2 Fy

E

c 0.66

Fy 2.25if

c0.88 Fy

otherwise

C.all.1 23.2 ksi

C.all.4 Lc B4

K Lc

rgp

2 Fy

E

c 0.66

Fy 2.25if

c0.88 Fy

otherwise

C.all.4 22.8 ksi

Capacity/Demand

CD1 99return C1 0ksi=if

C.all.1

C1return otherwise

CD1 99.00 al1 C.all.1

ac1 C1

CD2 99return C4 0ksi=if

C.all.4

C4return otherwise

CD2 20.93 al2 C.all.4

ac2 C4



22/81

State of New York



J o i n t L 4

Sheet: 18 of 77PIN: ________

Job Title: ____________________

Tensile Stress on Side Edges

T1 L1 AA1.a AA1.b.left

L2 AA2.a AA2.b.left

L3 AA3.a AA3.b.left

L4 AA4.a AA4.b.left

c max L1 L2 L3 L4( )

n 0ksi

nreturn c 0if

creturn otherwise

T4 R1 AA1.a AA1.b.right




c max R1 R2 R3 R4( )

n 0ksi

nreturn c 0if

creturn otherwise

T1 4.8ksi T4 0.0ksi

Allowable Tensile Stress LRFD 6.14.2.8

T.all fFy T.all 50ksi

Capacity/Demand

al3 T.allCD3 99return T1 0ksi=if

T.all

T1return otherwise

CD3 10.52ac3 T1

CD4 99return T4 0ksi=if

T.all

T4return otherwise

CD4 99.00 al4 T.all

ac4 T4



23/81

State of New York



J o i n t L 4

Sheet: 19 of 77PIN: ________

Job Title: ____________________

Allowable Shear Stress on Section A1-A1 LRFD 6.14.2.8

xy.all

v.74 Fy

3 xy.all 21.4 ksi

Calculated Maximum Average Shear Stress

xy.max max AA1.v AA2.v AA3.v AA4.v xy.max 3.4ksi

Capacity/Demand

al5 xy.allCD5

xy.all

xy.max CD5 6.21

ac5 xy.max



24/81

State of New York



J o i n t L 4

Sheet: 20 of 77PIN: ________

Job Title: ____________________

Analysis of Horizontal Section A2-A2

LAA2 90.2in

YA2 7.0in

XA2 46.4in

Number of Bolt Holes Along Section Cut in Gusset Plate: NAgp 24

Force Diagram



25/81

State of New York



J o i n t L 4

Sheet: 21 of 77PIN: ________

Job Title: ____________________

Section Properties

Gross Area of Section: AAA LAA2t gp AAA 101 in2

Net Area of Section: AAAn LAA2 NAgpd h tgp hsptsp AAAn 86in2

Ratio of Gross to Net Area: Rgn

AAA

AAAn

Rgn 1.183

Moment of Inertia of Section: IAA1

12

tgp LAA23

IAA 68800 in4

Neutral Axis: xNA .5LAA2 xNA 45.1 in

Section Modulus of Section:SAA.left

IAA

xNA SAA.left 1526 in

3

SAA.right

IAA

xNA

SAA.right 1526in3

Moment Arms: eAA.B XA2 xNA YA2tanB eAA.B 5.114 in

eAA.C XA2 xNA YA2tanC eAA.C 1.3in

eAA.D XA2 xNA YA2tan D eAA.D 7.2in


Case 1






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State of New York



J o i n t L 4

Sheet: 22 of 77PIN: ________

Job Title: ____________________

Case 2




Case 3




Case 4





Case 1

Axial Stress: AA1.a

FAA1

AAA

AA1.a 1.7ksi


MAA1

SAA.left

AA1.b.left 0.9ksi

AA1.b.right

MAA1

SAA.right

AA1.b.right 0.9 ksi



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State of New York



J o i n t L 4

Sheet: 23 of 77PIN: ________

Job Title: ____________________


VAA1

AAA

AA1.vu 2.1 ksi


2tgp

LAA2

4

VAA1Q

IAAtgp

AA1.v 3.2 ksi

Case 2

Axial Stress: AA2.aFAA2

AAA

AA2.a 2.1ksi


MAA2

SAA.left

AA2.b.left 0.8ksi

AA2.b.right

MAA2

SAA.right

AA2.b.right 0.8 ksi


VAA2

AAA

AA2.vu 2.2 ksi


2tgp

LAA2

4

VAA2Q

IAAtgp

AA2.v 3.3 ksi



28/81

State of New York



J o i n t L 4

Sheet: 24 of 77PIN: ________

Job Title: ____________________

Case 3

Axial Stress: AA3.a

FAA3

AAA AA3.a 1.8ksi


MAA3

SAA.left

AA3.b.left 0.9ksi

AA3.b.right

MAA3

SAA.right

AA3.b.right 0.9 ksi

Uniform Average Shear Stress: AA3.vuVAA3

AAA

AA3.vu 2.3 ksi


2tgp

LAA2

4

VAA3Q

IAAtgp

AA3.v 3.4 ksi

Case 4

Axial Stress: AA4.a

FAA4

AAA

AA4.a 1.9ksi


MAA4

SAA.left

AA4.b.left 0.9ksi

AA4.b.right

MAA4

SAA.right

AA4.b.right 0.9 ksi


VAA4

AAA

AA4.vu 2.2 ksi



29/81

State of New York



J o i n t L 4

Sheet: 25 of 77PIN: ________

Job Title: ____________________


2tgp

LAA2

4

VAA4Q

IAAtgp

AA4.v 3.3 ksi

Comparing Section A2-A2 Stresses to LRFD Allowable

Radius of Gyration of Gusset Plate: rgp

tgp

12

rgp 0.325in

Compressive Stress on Side Edges

2C1 L1 AA1.a AA1.b.left

L2 AA2.a AA2.b.left

L3 AA3.a AA3.b.left

L4 AA4.a AA4.b.left

c min L1 L2 L3 L4( )

n 0ksi

nreturn c 0if

creturn otherwise

2C4 R1 AA1.a AA1.b.right




c min R1 R2 R3 R4( )

n 0ksi

nreturn c 0if

creturn otherwise

2C1 0.0ksi 2C4 0.0ksi



30/81

State of New York



J o i n t L 4

Sheet: 26 of 77PIN: ________

Job Title: ____________________


C.all.1 Lc B1

K Lc

rgp

2 Fy

E

c 0.66

Fy 2.25if

c0.88 Fy

otherwise

C.all.1 23.2 ksi

C.all.4 Lc B4

K Lc

rgp

2 Fy

E

c 0.66

Fy 2.25if

c0.88 Fy

otherwise

C.all.4 22.8 ksi

Capacity/Demand

CD6 99return 2C1 0ksi=if

C.all.1

2C1return otherwise

CD6 99.00 al6 C.all.1

ac6 2C1

CD7 99return 2C4 0ksi=if

C.all.4

2C4

return otherwise

CD7 99.00 al7 C.all.4

ac7 2C4



31/81

State of New York



J o i n t L 4

Sheet: 27 of 77PIN: ________

Job Title: ____________________

Tensile Stress on Side Edges

T1.g L1 AA1.a AA1.b.left

L2 AA2.a AA2.b.left

L3 AA3.a AA3.b.left

L4 AA4.a AA4.b.left


n 0ksi

nreturn c 0if

creturn otherwise

T4.g R1 AA1.a AA1.b.right





n 0ksi

nreturn c 0if

creturn otherwise

T1.g 2.9ksi T4.g 1.2ksi

T1.n L1 AA1.aRgn AA1.b.left

L2 AA2.aRgn AA2.b.left




n 0ksi

nreturn c 0if

creturn otherwise

T4.n R1 AA1.aRgn AA1.b.right

R2 AA2.aRgn AA2.b.right




n 0ksi

nreturn c 0if

creturn otherwise

T1.n 3.3ksi T4.n 1.6ksi

Allowable Tensile Stress on Gross Section LRFD 6.8.2

T.all.g yFy T.all.g 47ksi

Allowable Tensile Stress on Net Section LRFD 6.8.2

T.all.n uFu U T.all.n 52ksi



32/81

State of New York



J o i n t L 4

Sheet: 28 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

f1

m1

99

m2

"N/A"

m3

0

mreturn

T1.g 0ksi=if

all1 T.all.g

act1 T1.g

fs1all1

act1

all2 T.all.n

act2 T1.n

fs2 all2

act2

m1

min fs1 fs2( )

m2

all1

ksi fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD8 f11 f2

m1

99

m2

"N/A"

m3

0

mreturn

T4.g 0ksi=if

all1 T.all.g

act1 T4.g

fs1all1

act1

all2 T.all.n

act2 T4.n

fs2 all2

act2

m1

min fs1 fs2( )

m2

all1

ksi fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD9 f21

al8 f12 al9 f22

ac8 f13 ac9 f23

CD8 15.81 CD9 32.45



33/81

State of New York



J o i n t L 4

Sheet: 29 of 77PIN: ________

Job Title: ____________________

Allowable Shear Stress on Gross Section FHWA Bridge Design Guidance No. 1, 2/28/08 Rev.

xy.all.g vy.58 Fy .74 xy.all.g 20.4ksi

Allowable Shear Stress on Net Section FHWA Bridge Design Guidance No. 1, 2/28/08 Rev.

xy.all.n vu.58 Fu .74 xy.all.n 22.3 ksi


xy.max.g max AA1.v AA2.v AA3.v AA4.v xy.max.g 3.4ksi

xy.max.n xy.max.g Rgn xy.max.n 4.1ksi



34/81

State of New York



J o i n t L 4

Sheet: 30 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

f1

m1

99

m2

"N/A"

m3

0

mreturn

xy.max.g 0ksi=if

all1 xy.all.g

act1 xy.max.g

fs1all1

act1

all2 xy.all.n

act2 xy.max.n

fs2 all2

act2

m1

min fs1 fs2( )

m

2

all1

ksi

fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD10 f11

al10 f12

ac10 f13

CD10 5.48



35/81

State of New York



J o i n t L 4

Sheet: 31 of 77PIN: ________

Job Title: ____________________

Analysis of Vertical Section B-B

LBB 59.4in

XB 6.339in

YB 9.842in

NBI 50

NBE 10

Number of Bolt Holes Along Section Cut in Gusset Plate: NBgp 11

Number of Bolt Holes Along Section Cut in Splice Plate: NBsp 5

Force Diagram



36/81

State of New York



J o i n t L 4

Sheet: 32 of 77PIN: ________

Job Title: ____________________

NBT NBI NBE NBT 60

Section Properties

Gross Area of Section: ABB LBBtgp hspt sp ABB 80in2

Net Area of Section: ABBn LBB NBgpdh tgp hsp NBspd h tsp ABBn 63in2


ABB

ABBn

Rgn 1.273

Bottom of Gusset Plate to Neutral Axis: yNA Agp tgpLBB

Asp tsphsp

y

AgpLBB

2

Asp Lgs

hsp

2

Agp Asp

yreturn

yNA 27in

Moment of Inertia of Section: IBB Igp 1

12tgp LBB

3

Isp 1

12tsp hsp

3

ygpLBB

2

ysp Lgs

hsp

2

I Igp tgpLBB yNA ygp 2

Isp tsph sp yNA ysp 2

Ireturn

IBB 24083 in4

Section Modulus of Section:SBB.top

IBB

yNA LBB SBB.top 733 in

3

SBB.bot

IBB

yNA

SBB.bot 907in3



37/81

State of New York



J o i n t L 4

Sheet: 33 of 77PIN: ________

Job Title: ____________________

Moment Arms: eBB.D yNA

XB

tan D

YB

eBB.D 9.2in

eBB.E yNA

XB

tan E YB

eBB.E 16.7 in


Case 1

Axial Force: FBB1 FD1x FE1x

NBT

NBE

NBT

FBB1 1508kip

Shear Force: VBB1 FD1y FE1y

NBT NBE

NBT

VBB1 28 kip

Bending Moment: MBB1 FD1xeBB.D FE1x

NBT NBE

NBT

eBB.E MBB1 25351 kip in

Case 2


NBT NBE

N

BT

FBB2 1456kip


NBT NBE

NBT

VBB2 10 kip


NBT NBE

NBT


Case 3


NBT NBE

NBT

FBB3 1429kip


NBT

NBE

NBT

VBB3 32 kip


NBT NBE

NBT




38/81

State of New York



J o i n t L 4

Sheet: 34 of 77PIN: ________

Job Title: ____________________

Case 4


NBT NBE

NBT

FBB4 1440kip


NBT NBE

NBT

VBB4 17 kip


NBT NBE

NBT



Case 1

Axial Stress: BB1.a

FBB1

ABB

BB1.a 18.9 ksi

Flexural Stress: BB1.b.top

MBB1

SBB.top

BB1.b.top 34.6 ksi

BB1.b.bot

MBB1

SBB.bot

BB1.b.bot 27.9ksi

Uniform Average Shear Stress: BB1.vu

VBB1

ABB

BB1.vu 0.3 ksi

Maximum Average Shear Stress: BB1.v Q1 yNAtgp yNA

2

Q2 h

sp

t

sp

y

NA

L

gs

hsp

2

Q Q1 Q2

VBB1Q

IBBtgp

return

BB1.v 0.6 ksi



39/81

State of New York



J o i n t L 4

Sheet: 35 of 77PIN: ________

Job Title: ____________________

Case 2

Axial Stress: BB2.aFBB2

ABB

BB2.a 18.2 ksi


MBB2

SBB.top

BB2.b.top 33.3 ksi

BB2.b.bot

MBB2

SBB.bot

BB2.b.bot 26.9ksi

Uniform Average Shear Stress: BB2.vuVBB2

ABB

BB2.vu 0.1 ksi


2

Q2 hspt sp yNA Lgshsp

2

Q Q1 Q2

VBB2QIBBtgp

return

BB2.v 0.2 ksi

Case 3

Axial Stress: BB3.a

FBB3

ABB

BB3.a 17.9 ksi


MBB3

SBB.top BB3.b.top 32.8 ksi

BB3.b.bot

MBB3

SBB.bot

BB3.b.bot 26.5ksi



40/81

State of New York



J o i n t L 4

Sheet: 36 of 77PIN: ________

Job Title: ____________________


VBB3

ABB

BB3.vu 0.4 ksi


2


2

Q Q1 Q2

VBB3Q

IBBtgp

return

BB3.v 0.7 ksi

Case 4

Axial Stress: BB4.a

FBB4

ABB

BB4.a 18.1 ksi


MBB4

SBB.top

BB4.b.top 33.0 ksi

BB4.b.bot

MBB4

SBB.bot

BB4.b.bot 26.6ksi


VBB4

ABB

BB4.vu 0.2 ksi



41/81

State of New York



J o i n t L 4

Sheet: 37 of 77PIN: ________

Job Title: ____________________


2


2

Q Q1 Q2

VBB4Q

IBBtgp

return

BB4.v 0.4 ksi

Comparing Section B-B Stresses to LRFD Allowable

Compressive Stress on Top Edge

C3 T1 BB1.a BB1.b.top

T2 BB2.a BB2.b.top

T3 BB3.a BB3.b.top

T4 BB4.a BB4.b.top

c min T1 T2 T3 T4( )

n 0ksi

nreturn c 0if

creturn otherwise

C3 15.7 ksi



42/81

State of New York



J o i n t L 4

Sheet: 38 of 77PIN: ________

Job Title: ____________________


C.all.3 Lc B3

K Lc

rgp

2 Fy

E

c 0.66

Fy 2.25if

c0.88 Fy

otherwise

C.all.3 29.3 ksi

Capacity/Demand

al11 C.all.3CD11 99return C3 0ksi=if

C.all.3

C3return otherwise

CD11 1.86 ac11 C3

Tensile Stress on Edges

Tbr.g B1 BB1.a BB1.b.bot

B2 BB2.a BB2.b.bot

B3 BB3.a BB3.b.bot

B4 BB4.a BB4.b.bot

c max B1 B2 B3 B4( )

n 0ksi

nreturn c 0if

creturn otherwise

T3.g T1 BB1.a BB1.b.top

T2 BB2.a BB2.b.top

T3 BB3.a BB3.b.top

T4 BB4.a BB4.b.top

c max T1 T2 T3 T4( )

n 0ksi

nreturn c 0if

creturn otherwise

Tbr.g 46.8ksi T3.g 0.0ksi



43/81

State of New York



J o i n t L 4

Sheet: 39 of 77PIN: ________

Job Title: ____________________

Tbr.n B1 BB1.aRgn BB1.b.bot

B2 BB2.aRgn BB2.b.botB3 BB3.aRgn BB3.b.bot

B4 BB4.aRgn BB4.b.bot


n 0ksi

nreturn c 0if

creturn otherwise

T3.n T1 BB1.aRgn BB1.b.top

T2 BB2.aRgn BB2.b.topT3 BB3.aRgn BB3.b.top

T4 BB4.aRgn BB4.b.top


n 0ksi

nreturn c 0if

creturn otherwise

Tbr.n 52.0 ksi T3.n 0.0ksi







44/81

State of New York



J o i n t L 4

Sheet: 40 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

f1

m1

99

m2

"N/A"

m3

0

mreturn

Tbr.g 0ksi=if

all1 T.all.g

act1 Tbr.g

fs1all1

act1

all2 T.all.n

act2 Tbr.n

fs2 all2

act2

m1

min fs1 fs2( )

m2

all1

ksi fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD12 f11 f2

m1

99

m2

"N/A"

m3

0

mreturn

T3.g 0ksi=if

all1 T.all.g

act1 T3.g

fs1all1

act1

all2 T.all.n

act2 T3.n

fs2 all2

act2

m1

min fs1 fs2( )

m2

all1

ksi fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD13 f21

al12 f12 al13 f22

ac12 f13 ac13 f23

CD12 1.00 CD13 99.00



45/81

State of New York



J o i n t L 4

Sheet: 41 of 77PIN: ________

Job Title: ____________________






xy.max.g max BB1.v BB2.v BB3.v BB4.v xy.max.g 0.7ksi




46/81

State of New York



J o i n t L 4

Sheet: 42 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

f1

m1

99

m2

"N/A"

m3

0

mreturn

xy.max.g 0ksi=if

all1 xy.all.g

act1 xy.max.g

fs1all1

act1

all2 xy.all.n

act2 xy.max.n

fs2 all2

act2

m1

min fs1 fs2( )

m

2

all1

ksi

fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD14 f11

al14 f12

ac14 f13

CD14 24.22



47/81

State of New York



J o i n t L 4

Sheet: 43 of 77PIN: ________

Job Title: ____________________

Analysis of Vertical Section C-C

LCC 59.4in

XC 6.339in

YC 9.842in

NCI 50

NCE 10

Number of Bolt Holes Along Section Cut in Gusset Plate: NCgp 11

Number of Bolt Holes Along Section Cut in Splice Plate: NCsp 5

Force Diagram



48/81

State of New York



J o i n t L 4

Sheet: 44 of 77PIN: ________

Job Title: ____________________

LBB LCC NCT NCI NCE

FD1x FB1x FE1x FA1x FD2x FB2x FE2x FA2x

FD1y FB1y FE1y FA1y FD2y FB2y FE2y FA2y

FD3x FB3x FE3x FA3x FD4x FB4x FE4x FA4x

FD3y FB3y FE3y FA3y FD4y FB4y FE4y FA4y

Section Properties

Gross Area of Section: ABB LBBtgp hspt sp ABB 80in2

Net Area of Section: ABBn LBB NBgpdh tgp hsp NBspd h tsp ABBn 63in2


ABB

ABBn

Rgn 1.273

Bottom of Gusset Plate to Neutral Axis: yNA Agp tgpLBB

Asp t

sp

h

sp

y

AgpLBB

2

Asp Lgs

hsp

2

Agp Asp

yreturn

yNA 27in

Moment of Inertia of Section: IBB Igp 1

12tgp LBB

3

Isp 1

12tsp hsp

3

ygpLBB

2

ysp Lgs

hsp

2

I Igp tgpLBB yNA ygp 2

Isp tsph sp yNA ysp 2

Ireturn

IBB 24083 in4



49/81

State of New York



J o i n t L 4

Sheet: 45 of 77PIN: ________

Job Title: ____________________

Section Modulus of Section:SBB.top

IBB

yNA LBB SBB.top 733 in

3

SBB.bot

IBB

yNA

SBB.bot 907in3

Moment Arms: eCC.B yNA YC XC

tan B eCC.B 9.8in

eCC.A yNA YC XC

tan A eCC.A 16.7 in

eBB.D eCC.B eBB.E eCC.A


Case 1


NCT NCE

NCT

FBB1 1552kip


NCT NCE

NCT

VBB1 212 kip


NCT NCE

NCT


Case 2


NCT NCE

NCT

FBB2 1519kip

Shear Force: VBB2

F

D2y

F

E2y

NCT NCE

NCT

V

BB2

234 kip


NCT NCE

NCT




50/81

State of New York



J o i n t L 4

Sheet: 46 of 77PIN: ________

Job Title: ____________________

Case 3

Axial Force: FBB3 FD3x FE3xNCT NCE

NCT

FBB3 1483kip


NCT NCE

NCT

VBB3 224 kip


NCT NCE

NCT


Case 4


NCT NCE

NCT

FBB4 1492kip


NCT NCE

NCT

VBB4 226 kip


NCT NCE

NCT



Case 1


ABB

BB1.a 19.5 ksi


MBB1

SBB.top

BB1.b.top 33.5 ksi

BB1.b.bot

MBB1

SBB.bot

BB1.b.bot 27.1ksi


VBB1

ABB

BB1.vu 2.7 ksi



51/81

State of New York



J o i n t L 4

Sheet: 47 of 77PIN: ________

Job Title: ____________________


2


2

Q Q1 Q2

VBB1Q

IBBtgp

return

BB1.v 4.8 ksi

Case 2

Axial Stress: BB2.a

FBB2

ABB

BB2.a 19.0 ksi


MBB2

SBB.top

BB2.b.top 32.6 ksi

BB2.b.bot

MBB2

SBB.bot

BB2.b.bot 26.3ksi


VBB2

ABB

BB2.vu 2.9 ksi


2


2

Q Q1 Q2

VBB2Q

IBBtgp

return

BB2.v 5.2 ksi



52/81

State of New York



J o i n t L 4

Sheet: 48 of 77PIN: ________

Job Title: ____________________

Case 3


ABB

BB3.a 18.6 ksi


MBB3

SBB.top

BB3.b.top 31.8 ksi

BB3.b.bot

MBB3

SBB.bot

BB3.b.bot 25.7ksi


VBB3

ABB

BB3.vu 2.8 ksi


2


2

Q Q1 Q2

VBB3Q

IBBtgp

return

BB3.v 5.0 ksi

Case 4

Axial Stress: BB4.a

FBB4

ABB

BB4.a 18.7 ksi


MBB4

SBB.top

BB4.b.top 32.0 ksi

BB4.b.bot

MBB4

SBB.bot

BB4.b.bot 25.9ksi



53/81

State of New York



J o i n t L 4

Sheet: 49 of 77PIN: ________

Job Title: ____________________


VBB4

ABB

BB4.vu 2.8 ksi


2


2

Q Q1 Q2

VBB4Q

I

BB

t

gp

return

BB4.v 5.1 ksi

Comparing Section C-C Stresses to LRFD Allowable

Compressive Stress on Top Edge

C2 T1 BB1.a BB1.b.top

T2 BB2.a BB2.b.top

T3 BB3.a BB3.b.top

T4 BB4.a BB4.b.top

c min T1 T2 T3 T4( )

n 0ksi

nreturn c 0if

creturn otherwise

C2 14.1 ksi



54/81

State of New York



J o i n t L 4

Sheet: 50 of 77PIN: ________

Job Title: ____________________


C.all.2 Lc B2

K Lc

rgp

2 Fy

E

c 0.66

Fy 2.25if

c0.88 Fy

otherwise

C.all.2 26.2 ksi

Capacity/Demand

al15 C.all.2CD15 99return C2 0ksi=if

C.all.2

C2return otherwise

CD15 1.86 ac15 C2

Tensile Stress on Edges

Tbl.g B1 BB1.a BB1.b.bot

B2 BB2.a BB2.b.bot

B3 BB3.a BB3.b.bot

B4 BB4.a BB4.b.bot


n 0ksi

nreturn c 0if

creturn otherwise

T2.g T1 BB1.a BB1.b.top

T2 BB2.a BB2.b.top

T3 BB3.a BB3.b.top

T4 BB4.a BB4.b.top


n 0ksi

nreturn c 0if

creturn otherwise

Tbl.g 46.5ksi T2.g 0.0ksi



55/81

State of New York



J o i n t L 4

Sheet: 51 of 77PIN: ________

Job Title: ____________________

Tbl.n B1 BB1.aRgn BB1.b.bot

B2 BB2.aRgn BB2.b.botB3 BB3.aRgn BB3.b.bot

B4 BB4.aRgn BB4.b.bot


n 0ksi

nreturn c 0if

creturn otherwise

T2.n T1 BB1.aRgn BB1.b.top

T2 BB2.aRgn BB2.b.topT3 BB3.aRgn BB3.b.top

T4 BB4.aRgn BB4.b.top


n 0ksi

nreturn c 0if

creturn otherwise

Tbl.n 51.9ksi T2.n 0.0ksi







56/81

State of New York



J o i n t L 4

Sheet: 52 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

f1

m1

99

m2

"N/A"

m3

0

mreturn

Tbl.g 0ksi=if

all1 T.all.g

act1 Tbl.g

fs1all1

act1

all2 T.all.n

act2 Tbl.n

fs2 all2

act2

m1

min fs1 fs2( )

m

2

all1

ksi

fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD16 f11 f2

m1

99

m2

"N/A"

m3

0

mreturn

T2.g 0ksi=if

all1 T.all.g

act1 T2.g

fs1all1

act1

all2 T.all.n

act2 T2.n

fs2 all2

act2

m1

min fs1 fs2( )

m

2

all1

ksi

fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD17 f21

al16 f12 al17 f22

ac16 f13 ac17 f23

CD16 1.00 CD17 99.00



57/81

State of New York



J o i n t L 4

Sheet: 53 of 77PIN: ________

Job Title: ____________________






xy.max.g max BB1.v BB2.v BB3.v BB4.v xy.max.g 5.2ksi




58/81

State of New York



J o i n t L 4

Sheet: 54 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

f1

m1

99

m2

"N/A"

m3

0

mreturn

xy.max.g 0ksi=if

all1 xy.all.g

act1 xy.max.g

fs1all1

act1

all2 xy.all.n

act2 xy.max.n

fs2 all2

act2

m1

min fs1 fs2( )

m2

all1

ksi fs1 fs2if

m2

all2

ksi otherwise

m3

act1

ksi fs1 fs2if

m3

act2

ksi otherwise

mreturn

CD18 f11

al18 f12

ac18 f13

CD18 3.35



59/81

State of New York



J o i n t L 4

Sheet: 55 of 77PIN: ________

Job Title: ____________________

Unsupported Edge Requirement

Allowable Length of Unsupported Edges

ball 2.06 E

Fy

tgp ball 55.8 in LRFD 6.14.2.8

Capacity/Demand

al19 ballCD19

ball

B1 CD19 1.80

ac19 B1

al20 ballCD20

ball

B2

CD20 1.99ac20 B2

al21 ballCD21

ball

B3

CD21 2.23ac21 B3

al22 ballCD22

ball

B4

CD22 1.78ac22 B4

Edge Slenderness Ratio Requirement

Allowable Slenderness Ratio: SRall 120 LRFD 6.9.3

Calculated Slenderness Ratio

SR1K B1

rgp

SR1 95

SR2

K B2

rgp

SR2 86



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Sheet: 56 of 77PIN: ________

Job Title: ____________________

SR3

K B3

rgp

SR3 77

SR4

K B4

rgp

SR4 97

Capacity/Demand

al23 if min C1 2C1 0 "N/A" SRall CD23 99return min C1 2C1 0if

SRall

SR1

return otherwise

CD23 99.00ac

23

if minC1

2C1

0 "N/A" SR

1

al24 if C2 0 "N/A" SRall CD24 99return C2 0ifSRall

SR2

return otherwise

CD24 1.39ac24 if C2 0 "N/A" SR2

al25 if C3 0 "N/A" SRall CD25 99return C3 0ifSRall

SR3

return otherwise

CD25 1.56ac25 if C3 0 "N/A" SR3

al26 if min C4 2C4 0 "N/A" SRall CD26 99return min C4 2C4 0ifSRall

SR4

return otherwise

CD26 1.24ac26 if min C4 2C4 0 "N/A" SR4



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J o i n t L 4

Sheet: 57 of 77PIN: ________

Job Title: ____________________

Applied Force for Member Connection Analysis LRFD 6.13.1

Maximum HL-93 Live

Load + Impact Case 1

Maximum HL-93 Live


Member A AMHL1 499kip AMHL2 499kip

Member B BMHL1 144kip BMHL2 80 kip

Tensile +

Compressive -Member C CMHL1 3kip CMHL2 3kip

Member D DMHL1 118kip DMHL2 105 kip

Member E EMHL1 546kip EMHL2 546kip

Maximum Permit Live


Maximum Permit Live


Member A AMPV3 605kip AMPV4 605kip

Member B BMPV3 196kip BMPV4 119 kip

Tensile +

Compressive -Member C CMPV3 4kip CMPV4 4kip

Member D DMPV3 172kip DMPV4 150 kip

Member E EMPV3 662kip EMPV4 662kip



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Sheet: 58 of 77PIN: ________

Job Title: ____________________

Factored MemberResistance Case 1

Factored MemberResistance Case 2

Member A AR1 3894kip AR2 3894kip

Member B BR1 1236kip BR2 1236kip

Tensile +

Compressive -Member C CR1 1435kip CR2 1435kip

Member D DR1 2038kip DR2 927 kip

Member E ER1 3894kip ER2 3894kip

Maximum HL-93 Live Load + Impact Case 1: Enter the unfactored maximum member force due to HL-93 live load.

If the member has both a tensile and compressive maximum, input the tensile maximum. Input tensile force as a


Maximum HL-93 Live Load + Impact Case 2: Enter the unfactored maximum member force due to HL-93 live load.

If the member has both a tensile and compressive maximum, input the compressive maximum. Input tensile force

as a positive value and compressive force as a negative value.

Maximum Permit Live Load + Impact Case 3: Enter the unfactored maximum member force due to permit live

load. If the member has both a tensile and compressive maximum, input the tensile maximum. Input tensile force

as a positive value and compressive force as a negative value.

Maximum Permit Live Load + Impact Case 4: Enter the unfactored maximum member force due to permit live

load. If the member has both a tensile and compressive maximum, input the compressive maximum. Input tensile

force as a positive value and compressive force as a negative value.

Factored Member Resistance Case 1: Enter the factored LRFD axial member resistance. If the member is

subject to both tensile and compressive forces, input the tensile resistance. Input tensile resistance as a positive

value and compressive resistance as a negative value.

Factored Member Resistance Case 2: Enter the factored LRFD axial member resistance. If the member is

subject to both tensile and compressive forces, input the compressive resistance. Input tensile resistance as a

positive value and compressive resistance as a negative value.



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J o i n t L 4

Sheet: 59 of 77PIN: ________

Job Title: ____________________

AM1 i 1.25ADC 1.5ADW 1.75 AMHL1 AM1 3414kipAM2 i 1.25ADC 1.5ADW 1.75 AMHL2 AM2 3414kipAM3 i 1.25ADC 1.5ADW 1.35 AMPV3 AM3 3355kipAM4 i 1.25ADC 1.5ADW 1.35 AMPV4 AM4 3355kip

BM1 i 1.25BDC 1.5BDW 1.75 BMHL1 BM1 637 kipBM2 i 1.25BDC 1.5BDW 1.75 BMHL2 BM2 226 kipBM3 i 1.25BDC 1.5BDW 1.35 BMPV3 BM3 651 kipBM4 i 1.25BDC 1.5BDW 1.35 BMPV4 BM4 204 kip

CM1 i 1.25CDC 1.5CDW 1.75 CMHL1 CM1 27 kipCM2 i 1.25CDC 1.5CDW 1.75 CMHL2 CM2 27 kipCM3 i 1.25CDC 1.5CDW 1.35 CMPV3 CM3 27 kipCM4 i 1.25CDC 1.5CDW 1.35 CMPV4 CM4 27 kip

DM1 i 1.25DDC 1.5DDW 1.75 DMHL1 DM1 210 kipDM2 i 1.25DDC 1.5DDW 1.75 DMHL2 DM2 200 kipDM3 i 1.25DDC 1.5DDW 1.35 DMPV3 DM3 237 kipDM4 i 1.25DDC 1.5DDW 1.35 DMPV4 DM4 219 kip

EM1 i 1.25EDC 1.5EDW 1.75 EMHL1 EM1 3721kipEM2 i 1.25EDC 1.5EDW 1.75 EMHL2 EM2 3721kipEM3 i 1.25EDC 1.5EDW 1.35 EMPV3 EM3 3656kipEM4 i 1.25EDC 1.5EDW 1.35 EMPV4 EM4 3656kip



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J o i n t L 4

Sheet: 60 of 77PIN: ________

Job Title: ____________________

PA1 f max AM1 AM3

fa max mean f AR1 .75AR1 fareturn

PA2 f min AM2 AM4

fa min mean f AR2 .75AR2 fareturn

PA1 3654kip PA2 2920kip

PB1 f max BM1 BM3

fa max mean f BR1 .75BR1

fareturn

PB2 f min BM2 BM4

fa min mean f BR2 .75BR2

fareturn

PB1 943 kip PB2 720 kip

PC1 f max CM1 CM3

fa max mean f CR1 .75CR1

fareturn

PC2 f min CM2 CM4

fa min mean f CR2 .75CR2

fareturn

PC1 1076kip PC2 704 kip

PD1 f max DM1 DM3 fa max mean f DR1 .75DR1

fareturn

PD2 f min DM2 DM4 fa min mean f DR2 .75DR2

fareturn

PD1 1529kip PD2 695 kip

PE2 f min EM2 EM4

fa min mean f ER2 .75ER2

fareturn

PE1 f max EM1 EM3

fa max mean f ER1 .75ER1

fareturn

PE2 2920kipPE1 3808kip



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J o i n t L 4

Sheet: 61 of 77PIN: ________

Job Title: ____________________

Slip Connection Applied Force LRFD 6.13.2.2

PsA1 i 1.00ADC 1.00ADW 1.30 AMHL1 PsA1 2657kipPsA2 i 1.00ADC 1.00ADW 1.30 AMHL2 PsA2 2657kip

PsB1 i 1.00BDC 1.00BDW 1.30 BMHL1 PsB1 492 kipPsB2 i 1.00BDC 1.00BDW 1.30 BMHL2 PsB2 186 kip

PsC1 i 1.00CDC 1.00CDW 1.30 CMHL1 PsC1 22 kipPsC2 i 1.00CDC 1.00CDW 1.30 CMHL2 PsC2 22 kip

PsD1 i 1.00DDC 1.00DDW 1.30 DMHL1 PsD1 156 kipPsD2 i 1.00DDC 1.00DDW 1.30 DMHL2 PsD2 149 kip

PsE1 i 1.00EDC 1.00EDW 1.30 EMHL1 PsE1 2897kipPsE2 i 1.00EDC 1.00EDW 1.30 EMHL2 PsE2 2897kip

Member Connection Resistance

Number of Shear/Slip Planes Number of Bolts Bolt Clear Distance

Member A Ns.A 2 NA 120 LcA 1.26in

Member B Ns.B 1 NB 48 LcB 1.26in

Member C Ns.C 1 NC 48 LcC 1.26in

Member D Ns.D 1 ND 64 LcD 1.26in

Member E Ns.E 2 NE 120 LcE 1.26in

Number of Bolts: Input the total number of bolts connecting the member to the gusset plate. This

includes bolts on both sides of the member.

Bolt Clear Distance: Input the clear distance between the holes or between the hole and the edge of the

material in the direction of the applied force.



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J o i n t L 4

Sheet: 62 of 77PIN: ________

Job Title: ____________________

Area of Bolt: Ab .25 db2

Ab 0.785in2

Resistance Factor for Bolts In Shear: sb 0.80 LRFD 6.5.4.2

Bolt Group Shear Resistance LRFD 6.13.2.7

Member A RA sb.38 Fub Ab NA Ns.A RA 6876kip

Member B RB sb.38 Fub Ab NB Ns.B RB 1375kip

Member C R

C

sb

.38 Fub

Ab

NC

Ns.C

RC

1375kip

Member D RD sb.38 Fub Ab ND Ns.D RD 1834kip

Member E RE sb.38 Fub Ab NE Ns.E RE 6876kip

Note: If the length between extreme fasteners measured parallel to the line of action of the force is greater than

50 inches, the above equations shall be multiplied by .80 per LRFD 6.13.2.7.

Bolt Group Slip Resistance LRFD 6.13.2.8

Hole size factor: Kh 1.0 LRFD 6.13.2.8-2

Surface condition factor: Ks .33 LRFD 6.13.2.8-3

Member A RsA KhKs Pt NA Ns.A RsA 4039kip

Member B RsB KhKs Pt NB Ns.B RsB 808 kip

Member C RsC KhKs Pt NC Ns.C RsC 808 kip

Member D RsD KhKs Pt ND Ns.D RsD 1077kip

Member E RsE KhKs Pt NE Ns.E RsE 4039kip



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J o i n t L 4

Sheet: 63 of 77PIN: ________

Job Title: ____________________

Bearing Resistance LRFD 6.13.2.9

Resistance Factor for Bolts Bearing on Material: bb 0.80 LRFD 6.5.4.2

Member A RbA bb1.2 LcA tgp tsp Fu NA RbA 17690kip

Member B RbB bb1.2 LcB tgp Fu NB RbB 4246kip

Member C RbC bb1.2 LcC tgp Fu NC RbC 4246kip

Member D RbD bb1.2 LcD tgp Fu ND RbD 5661kip

Member E RbE bb1.2 LcE tgp tsp Fu NE RbE 17690 kip

Shear Capacity/Demand

al27 RACD27

RA

max PA1 PA2 CD27 1.88

ac27 max PA1 PA2

al28 RBCD28

RB

max PB1 PB2 CD28 1.46

ac28 max PB1 PB2

al29 RCCD29

RC

max PC1 PC2 CD29 1.28

ac29 max PC1 PC2

al30 RDCD30

RD

max PD1 PD2 CD30 1.20

ac30 max PD1 PD2

al31 RECD31

RE

max PE1 PE2 CD31 1.81

ac31 max PE1 PE2



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J o i n t L 4

Sheet: 64 of 77PIN: ________

Job Title: ____________________

Slip Capacity/Demand

al32 RsACD32

RsA

max PsA1 PsA2 CD32 1.52

ac32 max PsA1 PsA2

al33 RsBCD33

RsB

max PsB1 PsB2 CD33 1.64

ac33 max PsB1 PsB2

al34 RsCCD34

RsC

max PsC1 PsC2 CD34 36.46

ac34 max PsC1 PsC2

al35 RsDCD35

RsD

max PsD1 PsD2 CD

35

6.91ac35 max PsD1 PsD2

al36 RsECD36

RsE

max PsE1 PsE2 CD36 1.39

ac36 max PsE1 PsE2

Bearing Capacity/Demand

al37 RbACD37

RbA

max PA1 PA2 CD37 4.84

ac37 max PA1 PA2

al38 RbBCD38

RbB

max PB1 PB2 CD38 4.50

ac38 max PB1 PB2

al39 RbCCD39

RbC

max PC1 PC2 CD39 3.94

ac39 max PC1 PC2

al40 RbDCD40

RbD

max PD1 PD2 CD40 3.70

ac40 max PD1 PD2

al41 RbECD41

RbE

max PE1 PE2 CD

41

4.65ac41 max PE1 PE2



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J o i n t L 4

Sheet: 65 of 77PIN: ________

Job Title: ____________________

Block Shear Rupture Resistance LRFD 6.13.4

LvA 43.6in nbrA 5

LvB 19.3in nbrB 4

LvC 19.3in nbrC 4

LvD 26.3in nbrD 4

LvE 41.0in nbrE 5

LtA 14.0in nrbA 11

LtB 12.6in nrbB 6

LtC 12.2in nrbC 6

LtD 12.7in nrbD 8

LtE 14.0in nrbE 11

Gross Area Subject to Shear

AvgA 2 LvA tgp 2 LvA tsp AvgA 163 in2

AvgB 2 LvB tgp AvgB 43in2

AvgC 2 LvC tgp AvgC 43in2

AvgD 2 LvD tgp AvgD 59in2

AvgE 2 LvE tgp 2 LvE tsp AvgE 154 in2



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J o i n t L 4

Sheet: 66 of 77PIN: ________

Job Title: ____________________

Net Area Subject to Shear

AvnA 2 LvA nrbA .5 dh tgp 2 LvA nrbA .5 dh tsp AvnA 122 in2

AvnB 2 LvB nrbB .5 dh tgp AvnB 30in2

AvnC 2 LvC nrbC .5 dh tgp AvnC 30in2

AvnD 2 LvD nrbD .5 dh tgp AvnD 41in2

AvnE 2 LvE nrbE .5 dh tgp 2 LvE nrbE .5 dh tsp AvnE 112in2

Gross Area Subject to Tension

AtgA LtAt gp LtAt sp AtgA 26in2

AtgB LtBtgp AtgB 14in2

AtgC LtCtgp AtgC 14in2

AtgD LtDt gp AtgD 14in

2

AtgE LtEtgp LtEtsp AtgE 26in2

Net Area Subject to Tension

AtnA LtA nbrA 1 dh tgp LtA nbrA 1 dh tsp AtnA 18in2

AtnB LtB nbrB 1 dh tgp AtnB 11in2

AtnC LtC nbrC 1 dh tgp AtnC 10in2

AtnD LtD nbrD 1 dh tgp AtnD 11in2

AtnE LtE nbrE 1 dh tgp LtE nbrE 1 dh tsp AtnE 18in2



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Sheet: 67 of 77PIN: ________

Job Title: ____________________

Block Shear Rupture Resistance LRFD 6.13.4

Strength Reduction Factor for Block Shear: bs 0.80 LRFD 6.5.4.2

RrbsA bs 0.58 Fy AvgA FuAtnA AtnA 0.58 AvnAif

bs 0.58 Fu AvnA FyAtgA otherwise

RrbsA 4719kip

RrbsB bs 0.58 Fy AvgB FuAtnB AtnB 0.58 AvnBif

bs 0.58 Fu AvnB FyAtgB otherwise

RrbsB 1480kip

RrbsC bs 0.58 Fy AvgC FuAtnC AtnC 0.58 AvnCif

bs 0.58 Fu AvnC FyAtgC otherwise

RrbsC 1462kip

RrbsD bs 0.58 Fy AvgD FuAtnD AtnD 0.58 AvnDifbs 0.58 Fu AvnD FyAtgD otherwise

RrbsD 1815kip

RrbsE bs 0.58 Fy AvgE FuAtnE AtnE 0.58 AvnEif

bs 0.58 Fu AvnE FyAtgE otherwise

RrbsE 4425kip



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Sheet: 68 of 77PIN: ________

Job Title: ____________________

Capacity/Demand

fA all R rbsA

act .5PA1

fs all

act

m1

fs fs 0if

m1

99 otherwise

m2

all

kip

m3

act

kip fs 0if

m3

"N/A" otherwise

mreturn

CD42 fA1 fB all R rbsB

act .5PB1

fs all

act

m1

fs fs 0if

m1

99 otherwise

m2

all

kip

m3

act

kip fs 0if

m3

"N/A" otherwise

mreturn

CD43 fB1

al42 fA2 al43 fB2

ac42 fA3 ac43 fB3

CD42 2.58 CD43 3.14

fC all R rbsC

act .5PC1

fs all

act

m1

fs fs 0if

m1

99 otherwise

m2

all

kip

m3

act

kip fs 0if

m3

"N/A" otherwise

mreturn

CD44 fC1 fD all R rbsD

act .5PD1

fs all

act

m1

fs fs 0if

m1

99 otherwise

m2

all

kip

m3

act

kip fs 0if

m3

"N/A" otherwise

mreturn

CD45 fD1

al44 fC2 al45 fD2

ac44 fC3 ac45 fD3

CD44 2.72 CD45 2.38



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J o i n t L 4

Sheet: 69 of 77PIN: ________

Job Title: ____________________

fE all R rbsE

act .5PE1

fs all

act

m1

fs fs 0if

m1

99 otherwise

m2

all

kip

m3

act

kip fs 0if

m3

"N/A" otherwise

mreturn

CD46 fE1

al46 fE2

ac46 fE3

CD46 2.32

Analysis of Whitmore Section

LwA 39.2in

LwB 32.9in

LwC 32.4in

LwD 41.0in

LwE 39.2in

LA 5.7in

L

B

30.3in

LC 23.2in

LD 21.9in



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J o i n t L 4

Sheet: 70 of 77PIN: ________

Job Title: ____________________

Allowable Tensile Force on Gross Section LRFD 6.8.2

PTGA yFy LwAtgp hspt sp PTGA 2711kip

PTGB yFy LwBt gp PTGB 1758kip

PTGC yFy LwCt gp PTGC 1731kip

PTGD yFy LwDtgp PTGD 2191kip

PTGE yFy LwEt gp hspt sp PTGE 2711kip

Allowable Tensile Force on Net Section LRFD 6.8.2

PTNA uFu U LwA nbrA 1 dh tgp LwA nbrA 1 dh tsp PTNA 3408kip

PTNB uFu U LwB nbrB 1 dh tgp PTNB 1738kip

PTNC uFu U LwC nbrC 1 dh tgp PTNC 1709kip

PTND uFu U LwD nbrD 1 dh tgp PTND 2212kip

PTNE uFu U LwE nbrE 1 dh tgp LwE nbrE 1 dh tsp PTNE 3408kip

Controlling Allowable Tensile Force

PTA min PTGA PTNA PTA 2711kip

PTB min PTGB PTNB PTB 1738kip

PTC min PTGC PTNC PTC 1709kip

PTD min PTGD PTND PTD 2191kip

PTE min PTGE PTNE PTE 2711kip



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J o i n t L 4

Sheet: 71 of 77PIN: ________

Job Title: ____________________

Gusset and Splice Plate Radius of Gyration

w 1in

yNA Agp tgpw

Asp tspw

y

Agptgp

2

Asp tgp B

tsp

2

Agp Asp

yreturn

yNA 2.0in

IGS Igp 1

12w tgp

3

Isp 1

12w tsp

3

ygptgp

2

ysp tgp Btsp

2

I Igp tgpw yNA ygp 2

Isp tspw yNA ysp 2

Ireturn

IGS 6 in4

rgs

IGS

tgpw tspw rgs 1.757in


8/10/2019 SDA-08-001 Gusset Plate D

Date post:	02-Jun-2018
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SDA-08-001 Gusset Plate Design

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