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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STRUCTURES DESIGN ADVISORYCODE:
DATE: 14 Apr il 2008 PAGE: 3
SUBJECT:GUSSET PLATES DESIGN PROCESS
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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STRUCTURES DESIGN ADVISORYCODE:
DATE: 14 Apr il 2008 PAGE: 4
SUBJECT:GUSSET PLATES DESIGN PROCESS
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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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: 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.
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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.
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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.
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
positive value and compressive force as a negative value.
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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State of New York
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 11 of 77PIN: ________
Job Title: ____________________
Analysis of Horizontal Section A1-A1
LAA1 90.2in
YA1 19.618in
XA1 46.4in
Force Diagram
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 13 of 77PIN: ________
Job Title: ____________________
Case 2
Axial Force: FAA2 FB2y FC2y FD2y FAA2 210 kip
Shear Force: VAA2 FB2x FC2x FD2x VAA2 223 kip
Bending Moment: MAA2 FB2yeAA.B FC2yeAA.C FD2yeAA.D MAA2 4096 kip in
Case 3
Axial Force: FAA3 FB3y FC3y FD3y FAA3 178 kip
Shear Force: VAA3 FB3x FC3x FD3x VAA3 233 kip
Bending Moment: MAA3 FB3yeAA.B FC3yeAA.C FD3yeAA.D MAA3 4334 kip in
Case 4
Axial Force: FAA4 FB4y FC4y FD4y FAA4 195 kip
Shear Force: VAA4 FB4x FC4x FD4x VAA4 222 kip
Bending Moment: MAA4 FB4yeAA.B FC4yeAA.C FD4yeAA.D MAA4 4098 kip in
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Flexural Stress: AA2.b.left
MAA2
SAA.left
AA2.b.left 2.7ksi
AA2.b.right
MAA2
SAA.right
AA2.b.right 2.7 ksi
Uniform Average Shear Stress: AA2.vu
VAA2
AAA
AA2.vu 2.2 ksi
Maximum Average Shear Stress: AA2.v QLAA1
2tgp
LAA1
4
VAA2Q
IAAtgp
AA2.v 3.3 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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L R F D G u s s e t P l a t e A n a l y s i s
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Sheet: 15 of 77PIN: ________
Job Title: ____________________
Case 3
Axial Stress: AA3.a
FAA3
AAA AA3.a 1.8ksi
Flexural Stress: AA3.b.left
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
Maximum Average Shear Stress: AA3.v QLAA1
2tgp
LAA1
4
VAA3Q
IAAtgp
AA3.v 3.4 ksi
Case 4
Axial Stress: AA4.a
FAA4
AAA
AA4.a 1.9ksi
Flexural Stress: AA4.b.left
MAA4
SAA.left
AA4.b.left 2.7ksi
AA4.b.right
MAA4
SAA.right
AA4.b.right 2.7 ksi
Uniform Average Shear Stress: AA4.vu
VAA4
AAA
AA4.vu 2.2 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 16 of 77PIN: ________
Job Title: ____________________
Maximum Average Shear Stress: AA4.v QLAA1
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
R3 AA3.a AA3.b.right
R4 AA4.a AA4.b.right
c min R1 R2 R3 R4( )
n 0ksi
nreturn c 0if
creturn otherwise
C1 0.0ksi C4 1.1 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
21/81
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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
22/81
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: 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
R2 AA2.a AA2.b.right
R3 AA3.a AA3.b.right
R4 AA4.a AA4.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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
23/81
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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
24/81
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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
25/81
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: 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
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 1303 kip in
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
-
8/10/2019 SDA-08-001 Gusset Plate Design
26/81
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: 22 of 77PIN: ________
Job Title: ____________________
Case 2
Axial Force: FAA2 FB2y FC2y FD2y FAA2 210 kip
Shear Force: VAA2 FB2x FC2x FD2x VAA2 223 kip
Bending Moment: MAA2 FB2yeAA.B FC2yeAA.C FD2yeAA.D MAA2 1286 kip in
Case 3
Axial Force: FAA3 FB3y FC3y FD3y FAA3 178 kip
Shear Force: VAA3 FB3x FC3x FD3x VAA3 233 kip
Bending Moment: MAA3 FB3yeAA.B FC3yeAA.C FD3yeAA.D MAA3 1398 kip in
Case 4
Axial Force: FAA4 FB4y FC4y FD4y FAA4 195 kip
Shear Force: VAA4 FB4x FC4x FD4x VAA4 222 kip
Bending Moment: MAA4 FB4yeAA.B FC4yeAA.C FD4yeAA.D MAA4 1299 kip in
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 0.9ksi
AA1.b.right
MAA1
SAA.right
AA1.b.right 0.9 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
27/81
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: 23 of 77PIN: ________
Job Title: ____________________
Uniform Average Shear Stress: AA1.vu
VAA1
AAA
AA1.vu 2.1 ksi
Maximum Average Shear Stress: AA1.v QLAA2
2tgp
LAA2
4
VAA1Q
IAAtgp
AA1.v 3.2 ksi
Case 2
Axial Stress: AA2.aFAA2
AAA
AA2.a 2.1ksi
Flexural Stress: AA2.b.left
MAA2
SAA.left
AA2.b.left 0.8ksi
AA2.b.right
MAA2
SAA.right
AA2.b.right 0.8 ksi
Uniform Average Shear Stress: AA2.vu
VAA2
AAA
AA2.vu 2.2 ksi
Maximum Average Shear Stress: AA2.v QLAA2
2tgp
LAA2
4
VAA2Q
IAAtgp
AA2.v 3.3 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
28/81
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: 24 of 77PIN: ________
Job Title: ____________________
Case 3
Axial Stress: AA3.a
FAA3
AAA AA3.a 1.8ksi
Flexural Stress: AA3.b.left
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
Maximum Average Shear Stress: AA3.v QLAA2
2tgp
LAA2
4
VAA3Q
IAAtgp
AA3.v 3.4 ksi
Case 4
Axial Stress: AA4.a
FAA4
AAA
AA4.a 1.9ksi
Flexural Stress: AA4.b.left
MAA4
SAA.left
AA4.b.left 0.9ksi
AA4.b.right
MAA4
SAA.right
AA4.b.right 0.9 ksi
Uniform Average Shear Stress: AA4.vu
VAA4
AAA
AA4.vu 2.2 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
29/81
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: 25 of 77PIN: ________
Job Title: ____________________
Maximum Average Shear Stress: AA4.v QLAA2
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
R2 AA2.a AA2.b.right
R3 AA3.a AA3.b.right
R4 AA4.a AA4.b.right
c min R1 R2 R3 R4( )
n 0ksi
nreturn c 0if
creturn otherwise
2C1 0.0ksi 2C4 0.0ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
30/81
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: 26 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
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
31/81
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: 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
c max L1 L2 L3 L4( )
n 0ksi
nreturn c 0if
creturn otherwise
T4.g R1 AA1.a AA1.b.right
R2 AA2.a AA2.b.right
R3 AA3.a AA3.b.right
R4 AA4.a AA4.b.right
c max R1 R2 R3 R4( )
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
L3 AA3.aRgn AA3.b.left
L4 AA4.aRgn AA4.b.left
c max L1 L2 L3 L4( )
n 0ksi
nreturn c 0if
creturn otherwise
T4.n R1 AA1.aRgn AA1.b.right
R2 AA2.aRgn AA2.b.right
R3 AA3.aRgn AA3.b.right
R4 AA4.aRgn AA4.b.right
c max R1 R2 R3 R4( )
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
32/81
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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
33/81
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: 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
Calculated Maximum Average Shear Stress
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
-
8/10/2019 SDA-08-001 Gusset Plate Design
34/81
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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
35/81
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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
36/81
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: 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
Ratio of Gross to Net Area: Rgn
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
37/81
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: 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
Forces Acting on Section
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
Axial Force: FBB2 FD2x FE2x
NBT NBE
N
BT
FBB2 1456kip
Shear Force: VBB2 FD2y FE2y
NBT NBE
NBT
VBB2 10 kip
Bending Moment: MBB2 FD2xeBB.D FE2x
NBT NBE
NBT
eBB.E MBB2 24375 kip in
Case 3
Axial Force: FBB3 FD3x FE3x
NBT NBE
NBT
FBB3 1429kip
Shear Force: VBB3 FD3y FE3y
NBT
NBE
NBT
VBB3 32 kip
Bending Moment: MBB3 FD3xeBB.D FE3x
NBT NBE
NBT
eBB.E MBB3 24070 kip in
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
-
8/10/2019 SDA-08-001 Gusset Plate Design
38/81
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: 34 of 77PIN: ________
Job Title: ____________________
Case 4
Axial Force: FBB4 FD4x FE4x
NBT NBE
NBT
FBB4 1440kip
Shear Force: VBB4 FD4y FE4y
NBT NBE
NBT
VBB4 17 kip
Bending Moment: MBB4 FD4xeBB.D FE4x
NBT NBE
NBT
eBB.E MBB4 24158 kip in
Stress Along Section
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
39/81
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: 35 of 77PIN: ________
Job Title: ____________________
Case 2
Axial Stress: BB2.aFBB2
ABB
BB2.a 18.2 ksi
Flexural Stress: BB2.b.top
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
Maximum Average Shear Stress: BB2.v Q1 yNAtgp yNA
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
Flexural Stress: BB3.b.top
MBB3
SBB.top BB3.b.top 32.8 ksi
BB3.b.bot
MBB3
SBB.bot
BB3.b.bot 26.5ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
-
8/10/2019 SDA-08-001 Gusset Plate Design
40/81
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: 36 of 77PIN: ________
Job Title: ____________________
Uniform Average Shear Stress: BB3.vu
VBB3
ABB
BB3.vu 0.4 ksi
Maximum Average Shear Stress: BB3.v Q1 yNAtgp yNA
2
Q2 hspt sp yNA Lgshsp
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
Flexural Stress: BB4.b.top
MBB4
SBB.top
BB4.b.top 33.0 ksi
BB4.b.bot
MBB4
SBB.bot
BB4.b.bot 26.6ksi
Uniform Average Shear Stress: BB4.vu
VBB4
ABB
BB4.vu 0.2 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate Design
41/81
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: 37 of 77PIN: ________
Job Title: ____________________
Maximum Average Shear Stress: BB4.v Q1 yNAtgp yNA
2
Q2 hspt sp yNA Lgshsp
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 38 of 77PIN: ________
Job Title: ____________________
Allowable Compressive Stress LRFD 6.9.4.1
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
c max B1 B2 B3 B4( )
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
c max T1 T2 T3 T4( )
n 0ksi
nreturn c 0if
creturn otherwise
Tbr.n 52.0 ksi T3.n 0.0ksi
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 41 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
Calculated Maximum Average Shear Stress
xy.max.g max BB1.v BB2.v BB3.v BB4.v xy.max.g 0.7ksi
xy.max.n xy.max.g Rgn xy.max.n 0.9ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Ratio of Gross to Net Area: Rgn
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Forces Acting on Section
Case 1
Axial Force: FBB1 FD1x FE1x
NCT NCE
NCT
FBB1 1552kip
Shear Force: VBB1 FD1y FE1y
NCT NCE
NCT
VBB1 212 kip
Bending Moment: MBB1 FD1xeBB.D FE1x
NCT NCE
NCT
eBB.E MBB1 24575 kip in
Case 2
Axial Force: FBB2 FD2x FE2x
NCT NCE
NCT
FBB2 1519kip
Shear Force: VBB2
F
D2y
F
E2y
NCT NCE
NCT
V
BB2
234 kip
Bending Moment: MBB2 FD2xeBB.D FE2x
NCT NCE
NCT
eBB.E MBB2 23874 kip in
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Case 3
Axial Force: FBB3 FD3x FE3xNCT NCE
NCT
FBB3 1483kip
Shear Force: VBB3 FD3y FE3y
NCT NCE
NCT
VBB3 224 kip
Bending Moment: MBB3 FD3xeBB.D FE3x
NCT NCE
NCT
eBB.E MBB3 23334 kip in
Case 4
Axial Force: FBB4 FD4x FE4x
NCT NCE
NCT
FBB4 1492kip
Shear Force: VBB4 FD4y FE4y
NCT NCE
NCT
VBB4 226 kip
Bending Moment: MBB4 FD4xeBB.D FE4x
NCT NCE
NCT
eBB.E MBB4 23481 kip in
Stress Along Section
Case 1
Axial Stress: BB1.aFBB1
ABB
BB1.a 19.5 ksi
Flexural Stress: BB1.b.top
MBB1
SBB.top
BB1.b.top 33.5 ksi
BB1.b.bot
MBB1
SBB.bot
BB1.b.bot 27.1ksi
Uniform Average Shear Stress: BB1.vu
VBB1
ABB
BB1.vu 2.7 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 47 of 77PIN: ________
Job Title: ____________________
Maximum Average Shear Stress: BB1.v Q1 yNAtgp yNA
2
Q2 hspt sp yNA Lgshsp
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
Flexural Stress: BB2.b.top
MBB2
SBB.top
BB2.b.top 32.6 ksi
BB2.b.bot
MBB2
SBB.bot
BB2.b.bot 26.3ksi
Uniform Average Shear Stress: BB2.vu
VBB2
ABB
BB2.vu 2.9 ksi
Maximum Average Shear Stress: BB2.v Q1 yNAtgp yNA
2
Q2 hspt sp yNA Lgshsp
2
Q Q1 Q2
VBB2Q
IBBtgp
return
BB2.v 5.2 ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 48 of 77PIN: ________
Job Title: ____________________
Case 3
Axial Stress: BB3.aFBB3
ABB
BB3.a 18.6 ksi
Flexural Stress: BB3.b.top
MBB3
SBB.top
BB3.b.top 31.8 ksi
BB3.b.bot
MBB3
SBB.bot
BB3.b.bot 25.7ksi
Uniform Average Shear Stress: BB3.vu
VBB3
ABB
BB3.vu 2.8 ksi
Maximum Average Shear Stress: BB3.v Q1 yNAtgp yNA
2
Q2 hspt sp yNA Lgshsp
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
Flexural Stress: BB4.b.top
MBB4
SBB.top
BB4.b.top 32.0 ksi
BB4.b.bot
MBB4
SBB.bot
BB4.b.bot 25.9ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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Sheet: 49 of 77PIN: ________
Job Title: ____________________
Uniform Average Shear Stress: BB4.vu
VBB4
ABB
BB4.vu 2.8 ksi
Maximum Average Shear Stress: BB4.v Q1 yNAtgp yNA
2
Q2 hspt sp yNA Lgshsp
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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J o i n t L 4
Sheet: 50 of 77PIN: ________
Job Title: ____________________
Allowable Compressive Stress LRFD 6.9.4.1
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
c max B1 B2 B3 B4( )
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
c max T1 T2 T3 T4( )
n 0ksi
nreturn c 0if
creturn otherwise
Tbl.g 46.5ksi T2.g 0.0ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
c max B1 B2 B3 B4( )
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
c max T1 T2 T3 T4( )
n 0ksi
nreturn c 0if
creturn otherwise
Tbl.n 51.9ksi T2.n 0.0ksi
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 53 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
Calculated Maximum Average Shear Stress
xy.max.g max BB1.v BB2.v BB3.v BB4.v xy.max.g 5.2ksi
xy.max.n xy.max.g Rgn xy.max.n 6.7ksi
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Load + Impact Case 2
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
Load + Impact Case 3
Maximum Permit Live
Load + Impact Case 4
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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
positive value and compressive force as a negative value.
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.
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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.
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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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: 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
Prep. By: J. Scarlata Date: 3/26/2008 Checked By: W. Albert Date: 4/2/2008
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8/10/2019 SDA-08-001 Gusset Plate D