20241204 Charlemont C05027 Deck Replacement Calculations.pdf

STRUCTURAL CALCULATIONS

for

SOUTH RIVER ROAD OVER ALBEE BROOK

BRIDGE NO. C-05-027 (0ET)

CHARLEMONT, MASSACHUSETTS

Prepared for:

TOWN OF CHARLEMONT

STRUCTURAL CALCULATIONS

NOVEMBER 2024

Prepared by:

63 Kendrick Street

Needham, MA 02494

INDEX TO CALCULATIONS

PAGE

EXISTING PLANS .......................................................................................... 2-3

VIRTIS INPUT FOR BEAM RATINGS ................................................................ 4-43

GENERAL INFORMATION ....................................................................... 4-7

DEAD LOADS .................................................................................. 8-16

LIVE LOAD DISTRIBUTION FACTORS ................................................... 17-36

ALTERNATE LIVE LOAD DISTRIBUTION FACTORS .................................. 37-43

DETERIORATION ............................................................................. 44-45

SECTION PROPERTIES .............................................................................. 46-50

VIRTIS INPUT FOR BEAM RATINGS .............................................................. 51-60

VIRTIS OUTPUT FOR BEAM RATINGS ........................................................... 61-68

1 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

TOWN OF CHARLEMONT

STRUCTURAL CALCS.

SHEAR CONNECTORS

Load Rating - Plans C-05-027

Plans

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PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - Plans C-05-027

3 68

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PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - General Information C-05-027

General Information

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PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

References:

1) AASHTO Standard Specifications, 17th Edition, 2002

2) MassDOT Bridge Manual 2024

3) 1995 Mass Highway Bridge Manual

4) AISC Steel Construction Manual, 15th Edition, 2017

5) AASHTO LRFD Bridge Design, 9th Edition, 2020 with 2021 Errata

6) AASHTO Manual for Bridge Evaluation, 3rd Edition, 2018 thru 2022 Interim

Bridge Geometry

Beam 1 Span = 30.34 ft

Beam 2 Span = 24.34 ft

Beams 3-8 Span = 21.0 ft

Beam 1-2 Shape = W14x68

Beam 3-8 Shape = W14x53

W14x68 tf = 0.060 ft = 0.720 in

W14x53 tf = 0.055 ft = 0.660 in

W14x68 wtf = 10.00 in

W14x53 wtf = 8.06 in

W14x68 tw = 0.415 in

W14x53 tw = 0.370 in

W14x68 A = 20.0 in²

W14x53 A = 15.6 in²

No. of Beams = 8

Beam 1-2 Spacing = 3.00 ft

Beam 3 Spacing = 2.97 ft

Beam 4-8 Spacing = 2.95 ft

Beam 1 Overhang = 1.63 ft

Beam 8 Overhang = 2.46 ft

Beam 1 Overhang Thickness= 0.813 ft

Beam 8 Overhang Thickness= 0.807 ft

Add'l. Deck Depth at Overhang = 0.083 ft

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Roadway Width = 21.6 ft

Safety Curb Width = 1.63 ft

Wearing Surface Depth = 0.250 ft

Deck Thickness = 0.667 ft

Haunch Height = 1.00 in

Diaphragm Shape = W10x21

Diaphragm Cut Length = 0.042 ft

Railing Type =

No. of Rail Posts South = 6

Railing Length South = 31.3 ft

Post Height = 2.00 ft

Curb Width = 1.63 ft

Height of Curb above WS = 0.667 ft

West Crown Depth = 1.15 ft

West Curb Depth = 1.03 ft

East Crown Depth = 1.02 ft

East Curb Depth = 0.91 ft

WS Depth = 0.250 ft

Beam 1 de = -0.017 ft = 1.63 ft - 1.63 ft - 0.017 ft

Beam 8 de = 0.818 ft = 2.46 ft - 1.63 ft - 0.015 ft

Thrie Beam Guardrail

*Assuming Diaphragms are cut 0.5" before reaching beam web allowing space for connection

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Material Properties

Unit Weights

Concrete = 0.150 kcf (1) 3.3.6

Wearing Surface = 0.150 kcf (1) 3.3.6

Gravel Borrow = 0.120 kcf (1) 3.3.6

Steel = 0.490 kcf (1) 3.3.6

Steel Member Weights

W14x53 = 0.053 klf (4) 1-25

W14x68 = 0.068 klf (4) 1-25

W10x21 = 0.021 klf

Material Properties f'c,deck = 5.00 ksi (6) 6B.5.2.1-1 n = 6.76

EB = 29,000 ksi (5) 6.4.1

ED = 4291 ksi (5) C5.4.2.4-2

Fy,1960 steel = 33 ksi (6) 6B.5.2.1-1

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PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - Dead Loads C-05-027

Dead Loads

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PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

1) AASHTO Standard Specifications, 17th Edition, 2002

2) MassDOT Bridge Manual 2024

3) 1995 Mass Highway Bridge Manual

4) AISC Steel Construction Manual, 15th Edition, 2017

5) AASHTO LRFD Bridge Design, 9th Edition, 2020 with 2021 Errata

Narrative:

Calculate proposed dead loads. Dead loads distributed per (2) 3.5.3 and 3.5.4.

Summary:

Beam DC1 DC2 DW BRR DC1

1 0.429 klf 0.573 klf 0.101 klf 0.048 klf

2 0.384 klf 0.452 klf 0.101 klf 0.016 klf

3 0.365 klf 0.452 klf 0.101 klf 0.015 klf

4 0.363 klf 0.452 klf 0.101 klf 0.015 klf

5 0.363 klf 0.452 klf 0.101 klf 0.015 klf

6 0.363 klf 0.452 klf 0.101 klf 0.015 klf

7 0.363 klf 0.452 klf 0.101 klf 0.015 klf

8 0.511 klf 0.583 klf 0.101 klf 0.064 klf

Bridge Geometry

No. of Beams = 8

Beam 1-3 Spacing = 3.00 ft

Beam 3-8 Spacing = 2.95 ft

Beam 1 Span = 30.3 ft

Beam 2 Span = 24.3 ft

Beams 3-8 Span = 21.0 ft

Beam 1 Trib. Width = 3.13 ft = 1.63 ft + 1.50 ft

Beam 2 Trib. Width = 3.00 ft = 3.00 ft

Beam 3 Trib. Width = 2.97 ft = 1.50 ft + 1.47 ft

Beam 4-7 Trib. Width = 2.95 ft = 2.95 ft

Beam 8 Trib. Width = 3.93 ft = 1.47 ft + 2.46 ft

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Calculate DC1 (Non-Composite DL) Loads

Concrete Deck

Unit Weight = 0.150 kcf

Depth = 0.667 ft

Load = 0.100 ksf

Haunch

Beam 1

Unit Weight = 0.150 kcf

W14x68 wtf = 10.00 in

Haunch Width = 11.00 in *assuming add an inch on inside

Haunch Height = 1.00 in to account for haunch shape

Haunch Area = 0.076 ft² = (11.00 in x 1.00 in)/ 144

Load = 0.011 klf = 0.076 ft² x 0.150 kcf

Beam 8

Unit Weight = 0.150 kcf

W14x53 wtf = 8.06 in

Haunch Width = 9.06 in *assuming add an inch on inside

Haunch Height = 1.00 in to account for haunch shape

Haunch Area = 0.063 ft² = (9.06 in x 1.00 in)/ 144

Load = 0.009 klf = 0.063 ft² x 0.150 kcf

Beam 2

Unit Weight = 0.150 kcf

W14x68 wtf = 10.00 in

Haunch Width = 12.00 in *assuming add an inch on each side

Haunch Height = 1.00 in to account for haunch shape

Haunch Area = 0.083 ft² = (12.00 in x 1.00 in)/ 144

Load = 0.013 klf = 0.083 ft² x 0.150 kcf

Beam 3-7

Unit Weight = 0.150 kcf

W14x53 wtf = 8.06 in

Haunch Width = 10.06 in *assuming add an inch on each side

Haunch Height = 1.00 in to account for haunch shape

Haunch Area = 0.070 ft² = (10.06 in x 1.00 in)/ 144

Load = 0.010 klf = 0.070 ft² x 0.150 kcf

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Overhang

Beam 1

Overhang Length = 1.63 ft

Depth of Addt. Conc. = 0.146 ft = 0.813 ft - 0.667 ft

Unit Weight = 0.150 kcf

Load = 0.036 klf

Beam 8

Overhang Length = 2.46 ft

Depth of Addt. Conc. = 0.141 ft = 0.807 ft - 0.667 ft

Unit Weight = 0.150 kcf

Load = 0.052 klf

Girder Self Weight

Beam 1-2 = 0.068 klf

Beam 3-8 = 0.053 klf

Diaphragm Self Weight

W10x21 = 0.021 klf

Cut Length Int. Beams = 0.083 ft = 2 x 0.042 ft

Cut Length Ext. Beams = 0.042 ft

Beam 1 Diaphragm Length = 1.46 ft = 3.13 ft - 1.63 ft - 0.042 ft

Beam 2 Diaphragm Length = 2.92 ft = 3.00 ft - 0.083 ft

Beam 3 Diaphragm Length = 2.89 ft = 2.97 ft - 0.083 ft

Beam 4-7 Diaphragm Length = 2.86 ft = 2.95 ft - 0.083 ft

Beam 8 Diaphragm Length = 1.43 ft = 3.93 ft - 2.46 ft - 0.042 ft

No. of Diaphragms = 3

Beam 1 Diaphragm Load = 0.031 k = 1.46 ft x 0.021 klf

Beam 2 Diaphragm Load = 0.061 k = 2.92 ft x 0.021 klf

Beam 3 Diaphragm Load = 0.061 k = 2.89 ft x 0.021 klf

Beam 4-7 Diaphragm Load = 0.060 k = 2.86 ft x 0.021 klf

Beam 8 Diaphragm Load = 0.030 k = 1.43 ft x 0.021 klf

Angles Qty. = 4.00

L6x4x3/8 Weight = 12.30 plf

Angle Length = 0.500 ft

Angle Weight = 0.025 k = 0.50 ft x 12.30 plf x 4.00/ 1,000

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 1 Diaphragm Tot.Load = 0.045 k = (0.031 k + 0.012 k) x 1.050

Beam 2 Diaphragm Tot Load = 0.090 k = (0.061 k + 0.025 k) x 1.050

Beam 3 Diaphragm Tot. Load = 0.090 k = (0.061 k + 0.025 k) x 1.050

Beam 4-7 Diaphragm Tot. Load = 0.089 k = (0.060 k + 0.025 k) x 1.050

Beam 8 Diaphragm Tot. Load = 0.044 k = (0.030 k + 0.012 k) x 1.050

Table showing breakdown of each beams DC1 loading. Load units in klf

Beam # 1 2 3 4

Trib Width 3.13 ft 3.00 ft 2.97 ft 2.95 ft

Span Length 30.3 ft 24.3 ft 21.0 ft 21.0 ft

Deck 0.313 klf 0.300 klf 0.297 klf 0.295 klf

Haunch 0.011 klf 0.013 klf 0.010 klf 0.010 klf

Overhang 0.036 klf n/a n/a n/a

Girder Weight 0.068 klf 0.068 klf 0.053 klf 0.053 klf

Diaphragm Weight 0.001 klf 0.004 klf 0.004 klf 0.004 klf

DC1 = 0.429 klf 0.384 klf 0.365 klf 0.363 klf

Beam # 5 6 7 8

Trib Width 2.95 ft 2.95 ft 2.95 ft 3.93 ft

Span Length 21.0 ft 21.0 ft 21.0 ft 21.0 ft

Deck 0.295 klf 0.295 klf 0.295 klf 0.393 klf

Haunch 0.010 klf 0.010 klf 0.010 klf 0.010 klf

Overhang n/a n/a n/a 0.052 klf

Girder Weight 0.053 klf 0.053 klf 0.053 klf 0.053 klf

Diaphragm Weight 0.004 klf 0.004 klf 0.004 klf 0.002 klf

DC1 = 0.363 klf 0.363 klf 0.363 klf 0.511 klf

*Add 5% to total weight for connections exterior diaphragms only have 2 angles

12 68

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Calculate DC2 (Superimposed Load) Loads

Railing

Railing =

No. of Rail Posts South = 6.00

Railing Length South = 31.3 ft

Post Height = 2.00 ft

Post Unit Weight = 0.015 klf

Total Post Weight = 0.180 k = 0.015 klf x 2.00 ft x 6.00

Post Linear Weight = 0.006 klf = 0.180 k/ 31.3 ft

Thrie Beam Weight = 0.011 klf

Railing Weight = 0.017 klf = 0.011 klf + 0.006

Total Railing Weight = 0.019 klf = 0.003 klf + 0.017 klf

Safety Curb

Safety Curb assumed to be rectangle with dimensions using the average height of the curb through the span

Avg. Gravel Depth at Curb = 0.97 ft = (1.03 ft + 0.91 ft)/ 2.00

Avg. Curb Height = 1.89 ft = 0.67 ft + 0.25 ft + 0.97 ft

Unit Weight = 0.150 kcf

Curb Width = 1.63 ft

Load = 0.460 klf = 1.89 ft x 1.63 ft x 0.150 kcf

Gravel Borrow Type B

No. of Beams = 8

Unit Weight = 0.120 kcf

West Crown Depth = 1.15 ft

West Curb Depth = 1.03 ft

East Crown Depth = 1.02 ft

East Curb Deth = 0.91 ft

Avg. Crown Depth = 1.08 ft = (1.15 ft + 1.02 ft)/ 2.00

Avg. Curb Depth = 0.97 ft = (1.03 ft + 0.91 ft)/ 2.00

Avg. Depth = 1.03 ft = 1.08 ft + 0.97 ft/ 2.00

Rdwy Width = 21.6 ft

Gravel Load = 2.66 klf = 1.03 ft x 21.6 ft x 0.120 kcf

Beam # Railing Load Curb Load Gravel Load Total DC2 Load

Beam 1 0.019 klf 0.460 klf 2.66 klf 3.140 klf

Beam 2 0.039 klf 0.920 klf 2.66 klf 3.619 klf

Beam 3 0.039 klf 0.920 klf 2.66 klf 3.619 klf

Beam 4-7 0.039 klf 0.920 klf 2.66 klf 3.619 klf

Beam 8 0.019 klf 0.460 klf 2.66 klf 3.140 klf

Thrie Beam Guardrail

15% Additional Weight for

Connection =

0.003 klf = 0.017 klf x 0.150

*Interior beams have load from both railings and curbs

13 68

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Calculate and Distribute DW Loads

Wearing Surface

No. of Beams = 8

WS Unit Wt. = 0.150 kcf

Rdwy Width = 21.6 ft

WS Depth = 0.250 ft

WS Load = 0.101 klf = 0.150 kcf x 21.58 ft x 0.25 ft x 0.125

DW Load = 0.101 klf

Distribute DC2 Loads

Per (2) distribute DC2 loads to beams using the pile cap method to exterior stems.

DC2 loads shall be distributed to interior stems equally.

x= horizontal distance from left edge of bridge deck

A= Area of girder section

Beam x A x*A

Beam 1 1.625 1.000 1.625

Beam 2 4.625 1.000 4.625

Beam 3 7.625 1.000 7.625

Beam 4 10.575 1.000 10.58

Beam 5 13.525 1.000 13.53

Beam 6 16.475 1.000 16.48

Beam 7 19.425 1.000 19.43

Beam 8 22.375 1.000 22.38

∑ = 8.000 96.250

Stems will be treated as individual beams, where their sums will equal the load applied to the NEXTD beams for design.

��

Σ�

14 68

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BRIDGE NO.

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CALC BY

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SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

CG = 12.03 ft *from the left edge of bridge deck

Nb = number of beams e = eccentricity of load from C.G.

x = horizontal distance from C.G. of pattern of beams to each beam

Xext = horizontal dist from C.G. of pattern of beams to exterior beam

CG = 12.03 ft *from the left edge of bridge deck

Beam 1 Overhang = 1.63 ft

Beam 8 Overhang = 2.46 ft

Out to Out Dist. 24.83 ft xBeam1 = 10.41 ft (CL Beam 1 to CG Beam Group) xBeam2 = 7.41 ft (CL Beam 2 to CG Beam Group) xBeam3 = 4.41 ft (CL Beam 3 to CG Beam Group) xBeam4 = 1.46 ft (CL Beam 4 to CG Beam Group) xBeam5 = -1.49 ft (CL Beam 5 to CG Beam Group) xBeam6 = -4.44 ft (CL Beam 6 to CG Beam Group) xBeam7 = -7.39 ft (CL Beam 7 to CG Beam Group) xBeam8 = -10.34 ft (CL Beam 8 to CG Beam Group)

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BRIDGE NO.

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CALC BY

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SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

x Beam1 = 108.29 xBeam1 = 10.41 x Beam2 = 54.85 xBeam2 = 7.41 x Beam3 = 19.42 xBeam3 = 4.41 x Beam4 = 2.12 xBeam4 = 1.46 x Beam5 = 2.23 xBeam5 = -1.49 x Beam6 = 19.75 xBeam6 = -4.44 x Beam7 = 54.67 xBeam7 = -7.39 x Beam8 = 106.99 xBeam8 = -10.34

∑x = 368.32 xBeam1 / ∑x = 0.0283 xBeam8 / ∑x = 0.0281

South Railing e = 11.22 ft *Assuming Railing CG @ Center of Curb

North Railing e = 11.99 ft

South Curb e = 11.22 ft

North Curb e = 11.99 ft

Gravel e = 0.385 ft

Beam 1 South Railing DF = 0.442

Beam 8 North Railing DF = 0.462

Beam 2-7 Railing DF = 0.125

Beam 1 South Curb DF = 0.442

Beam 8 North Curb DF = 0.462

Beam 2-7 Curb DF = 0.125

Beam 1 Gravel DF = 0.136

Beam 8 Gravel DF = 0.136

Beam 2-7 Gravel DF = 0.125

Beam # Railing Load DF

DC2 Beam 1 0.019 klf 0.442

DC2 Beam 2-7 0.039 klf 0.125

DC2 Beam 8 0.019 klf 0.462

Beam # Curb Load DF

DC2 Beam 1 0.460 klf 0.442

DC2 Beam 2-7 0.920 klf 0.125

DC2 Beam 8 0.460 klf 0.462

Beam # Gravel Load DF

DC2 Beam 1 2.660 klf 0.136

DC2 Beam 2-7 2.660 klf 0.125

DC2 Beam 8 2.660 klf 0.136

0.333 klf

0.361 klf

0.203 klf

0.115 klf

0.212 klf

Factored DC2 Load

0.361 klf

Factored DC2 Load

0.009 klf

0.005 klf

0.009 klf

Factored DC2 Load

16 68

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BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - Live Loads C-05-027

Live Load Distribution Factors

17 68

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PROJECT

BRIDGE NO.

PAGE

CALC BY

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SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - Live Load Distribution Factors C-05-027

1) AASHTO Standard Specifications, 17th Edition, 2002

2) MassDOT Bridge Manual 2024

3) 1995 Mass Highway Bridge Manual

4) AISC Steel Construction Manual, 15th Edition, 2017

5) AASHTO LRFD Bridge Design, 9th Edition, 2020 with 2021 Errata

Narrative:

Calculate live load distribution factors per (2) and (5) Section 3.5.4.

Summary:

Beam LLDF M LLDF V LLDF M FAT. LLDF V FAT. LLDF DEFLECTION

1 0.333 0.333 0.278 0.278 0.250

2 0.346 0.480 0.248 0.400 0.250

3 0.349 0.479 0.253 0.399 0.250

4 0.347 0.478 0.252 0.398 0.250

5 0.347 0.478 0.252 0.398 0.250

6 0.347 0.478 0.252 0.398 0.250

7 0.347 0.478 0.252 0.398 0.250

8 0.365 0.365 0.304 0.304 0.250

Geometry:

Spacing, S Beam 1-2 = 3.00 ft

Spacing, S Beam 3 = 2.97 ft

Spacing, S Beam 4-8 = 2.95 ft ts = 0.67 ft

Span Length, L Beam 1 = 30.3 ft

Span Length, L Beam 2 = 24.3 ft

Span Length, L Beam 3-8 = 21.0 ft

Nb = 8

Roadway Width = 21.6 ft

Number of Lanes = 1

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BRIDGE NO.

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CALC BY

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SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam Geometry:

Beam 1-2 Type = W14x68

Beam 1-2 A = 20.0 in²

Beam 1-2 Depth = 14.0 in

Beam 1-2 Yt = 7.00 in

Beam 1-2 Ix = 722 in⁴

Beam 3-8 Type = W14x53

Beam 3-8 A = 15.6 in²

Beam 3-8 Depth = 13.9 in

Beam 3-8 Yt = 6.95 in

Beam 3-8 Ix = 541 in⁴

Calculate Kg:

Beam 1-2 eg = 11.0 in (8.00 in x 0.5) + 7.00 in

Beam 3 eg = 11.0 in (8.00 in x 0.5) + 6.95 in

Beam 4-8 eg = 11.0 in (8.00 in x 0.5) + 6.95 in n = 6.76 29000 ksi/ 4291 ksi (5) 4.6.2.2.1-2

Beam 1-2 Kg = 21,234 in⁴ (5) 4.6.2.2.1-1

Beam 3-8 Kg = 16,297 in⁴ (5) 4.6.2.2.1-1

19 68

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BRIDGE NO.

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CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Moment for Interior Beams:

Applicability

(5) Table 4.6.2.2.2b-1

Beam 2 Beam 2 Check

S = 3.00 ft NO GOOD ts = 8.00 in OKAY

L = 24.34 ft OKAY

Nb = 8 OKAY

Kg = 21,234 in⁴ OKAY

Beam 3 Beam 3-7 Check

S = 2.97 ft NO GOOD ts = 8.00 in OKAY

L = 21.0 ft OKAY

Nb = 8 OKAY

Kg = 16,297 in⁴ OKAY

Beam 4-7 Beam 3-7 Check

S = 2.95 ft NO GOOD ts = 8.00 in OKAY

L = 21.0 ft OKAY

Nb = 8 OKAY

Kg = 16,297 in⁴ OKAY

The existing beam spacing is below the minimum beam spacing specified in the Range of Applicability for live load distribution factors (LLDFs) for shear and moment of interior beams, as given in Tables 4.6.2.2.2b-1 and 4.6.2.2.3a-1.

Consequently, an alternate analysis is performed further on by theoretically increasing the beam spacing to the minimum value specified in these tables. By demonstrating that the beams are adequate at this larger spacing, which falls within the range of applicability, it is shown that they will be adequate for the actual smaller spacing. This is because the distribution factors would be lower in the real conditions at the smaller spacing. The interior beams were checked to rate above statutory with the alternate distribution factors. The results presented use the distribution factors from the actual beam spacing.

Per (2) - Section 3.5.3.8&9, Distribution of live load to interior beams shall be calculated using (5) - Section 4.6.2.2.2

20 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

(4) Table 4.6.2.2.2b-1

Beam 2

One Lane Loaded

DFMom.Beam2= 0.297 0.06 + 3.00 ft 3.00 ft

14 24.34 ft x

12.0 x 24.34 ft x 8.00 in

Two or More Lanes Loaded

DFMom.Beam2= 0.346 0.075 + 3.00 ft 3.00 ft

9.5 24.34 ft x

12.0 x 24.34 ft x 8.00 in

One Lane Loaded

DFMom.Beam2= 0.297

Two or More Lanes Loaded

DFMom.Beam2= 0.346

Critical Factor

DFMom.Beam2= 0.346

21,234 in⁴

21,234 in⁴

0.4 0.3

0.1

0.6 0.2

0.1

21 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 3

One Lane Loaded

DFMom.Beam3= 0.303 0.06 + 2.97 ft 2.97 ft

14 21.00 ft x

12.0 x 21.00 ft x 8.00 in

Two or More Lanes Loaded

DFMom.Beam3= 0.349 0.075 + 2.97 ft 2.97 ft

9.5 21.00 ft x

12.0 x 21.00 ft x 8.00 in

One Lane Loaded

DFMom.Beam3= 0.303

Two or More Lanes Loaded

DFMom.Beam3= 0.349

Critical Factor

DFMom.Beam3= 0.349

Beam 4-7

One Lane Loaded

DFMom.Beam4-7= 0.302 0.06 + 2.95 ft 2.95 ft

14 21.00 ft x

12.0 x 21.00 ft x 8.00 in

Two or More Lanes Loaded

DFMom.Beam4-7= 0.347 0.075 + 2.95 ft 2.95 ft

9.5 21.00 ft x

12.0 x 21.00 ft x 8.00 in

One Lane Loaded

DFMom.Beam4-7= 0.302

Two or More Lanes Loaded

DFMom.Beam4-7= 0.347

Critical Factor

DFMom.Beam4-7= 0.347

16,297 in⁴

16,297 in⁴

16,297 in⁴

16,297 in⁴

0.4 0.3

0.1

0.6 0.2

0.1

0.4 0.3

0.1

0.6 0.2

0.1

22 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Shear for Interior Beams:

Applicability (5) Table 4.6.2.2.3a-1

Beam 2 Beam 2 Check

S = 3.00 ft NO GOOD ts = 8.00 ft OKAY

L = 24.34 ft OKAY

Nb = 8.00 ft OKAY

Beam 3 Beam 3-7 Check

S = 2.97 ft NO GOOD ts = 8.00 ft OKAY

L = 21.00 ft OKAY

Nb = 8.00 ft OKAY

Beam 3-7 Beam 3-7 Check

S = 2.95 ft NO GOOD ts = 8.00 ft OKAY

L = 21.00 ft OKAY

Nb = 8.00 ft OKAY

(5) Table 4.6.2.2.3a-1

Per (2) - Section 3.5.3.8&9, Distribution of live load to interior beams shall be calculated using (5) - Section 4.6.2.2.2

23 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 2

One Lane Loaded

DFShear,Beam2 = 0.480 0.36 + 3.00 ft

Two or More Lanes Loaded

DFShear,Beam2 = 0.443 0.2 + 3.00 ft - 3.00 ft

12 35

One Lane Loaded

DFShear,Beam2 = 0.480

Two or More Lanes Loaded

DFShear,Beam2 = 0.443

Critical Factor

DFShear,Beam2 = 0.480

Beam 3

One Lane Loaded

DFShear,Beam3 = 0.479 0.36 + 2.97 ft

Two or More Lanes Loaded

DFShear,Beam3 = 0.441 0.2 + 2.97 ft - 2.97 ft

12 35

One Lane Loaded

DFShear,Beam3 = 0.479

Two or More Lanes Loaded

DFShear,Beam3 = 0.441

Critical Factor

DFShear,Beam3 = 0.479

2.0

2.0

24 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 4-7

One Lane Loaded

DFShear,Beam4-7 = 0.478 0.36 + 2.95 ft

Two or More Lanes Loaded

DFShear,Beam4-7 = 0.439 0.2 + 2.95 ft - 2.95 ft

12 35

One Lane Loaded

DFShear,Beam4-7 = 0.478

Two or More Lanes Loaded

DFShear,Beam4-7 = 0.439

Critical Factor

DFShear,Beam4-7 = 0.478

Moment for Exterior Beams:

Applicability

Beam 1 de = -0.017 ft OKAY

Beam 4 de = 0.818 ft OKAY

(5) Table 4.6.2.2.2d-1

Per (2) - Section 3.5.3.10, Distribution of live load to exterior beams under safety curb or barrier shall be calculated using (4) - Section 4.6.2.2.2

Per (4) - Section 4.6.2.2.2d - Exterior beam distribution factors shall be taken as the larger of those calculated using

Table 4.6.2.2.2d-1, or the pile cap analogy as outlined in C4.6.2.2.2d

2.0

25 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 1

One Lane Loaded

Lever Rule

0.5

D1 = 2.00 ft

S = 3.00 ft

DFMom.Beam1 = 0.167 = (1 - (2.00 ft/ 3.00 ft)) x

Two or More Lanes Loaded

Beam 1 de = -0.017 ft e = 0.768 ft = 0.77 + -(0.017 ft/ 9.1) g,interior = 0.346

DFMom.Beam1 = 0.266 = 0.768 ft x 0.346

"Rigid Superstructure" Pile Cap Analogy x= horizontal distance from left edge of bridge deck

A= Area of girder section

Beam x A x*A

Beam 1 1.625 0.139 0.226

Beam 2 4.625 0.139 0.642

Beam 3 7.625 0.139 1.059

Beam 4 10.575 0.139 1.47

Beam 5 13.525 0.139 1.88

Beam 6 16.475 0.139 2.29

Beam 7 19.425 0.139 2.70

Beam 8 22.375 0.139 3.11

∑ = 1.111 13.368

CG = 12.03 ft *from the left edge of bridge deck

��

Σ�

26 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Nb = number of beams e = eccentricity of load from C.G.

x = horizontal distance from C.G. of pattern of beams to each beam

Xext = horizontal dist from C.G. of pattern of beams to exterior beam

CG = 12.03 ft *from the left edge of bridge deck

Beam 1 Overhang = 1.63 ft

Beam 8 Overhang = 2.46 ft

Out to Out Dist. 24.83 ft xBeam1 = 10.41 ft (CL Beam 1 to CG Beam Group) xBeam2 = 7.41 ft (CL Beam 2 to CG Beam Group) xBeam3 = 4.41 ft (CL Beam 3 to CG Beam Group) xBeam4 = 1.46 ft (CL Beam 4 to CG Beam Group) xBeam5 = -1.49 ft (CL Beam 5 to CG Beam Group) xBeam6 = -4.44 ft (CL Beam 6 to CG Beam Group) xBeam7 = -7.39 ft (CL Beam 7 to CG Beam Group) xBeam8 = -10.34 ft (CL Beam 8 to CG Beam Group) x Beam1 = 108.29 xBeam1 = 10.41 x Beam2 = 54.85 xBeam2 = 7.41 x Beam3 = 19.42 xBeam3 = 4.41 x Beam4 = 2.12 xBeam4 = 1.46 x Beam5 = 2.23 xBeam5 = -1.49 x Beam6 = 19.75 xBeam6 = -4.44 x Beam7 = 54.67 xBeam7 = -7.39 x Beam8 = 106.99 xBeam8 = -10.34

∑x = 368.32

27 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

xBeam1 / ∑x = 0.0283 xBeam8 / ∑x = 0.0281 e1 = 5.41 ft = 10.41 ft - 2.00 ft - 3.00 ft e2 = -5.39 ft = 10.41 ft - 2.00 ft - 13.79 ft

1 + (0.0283 x 5.41 ft)

2 + (0.0283 x (5.41 ft +

One Lane Loaded (Lever Rule)

DFMom.Beam1 = 0.200 = 0.167 x 1.20

One Lane Loaded (Pile Cap)

DFMom.Beam1 = 0.333 = 0.278 x 1.20

Two or More Lanes Loaded (Formula)

DFMom.Beam1 = 0.266 0.266

Two or More Lanes Loaded (Pile Cap)

DFMom.Beam1 = 0.251 = 0.251 x 1.00

Critical Factor

DFMom.Beam1 = 0.333 e = Eccentricity of a design truck or a design lane load from the C.O.G. of the pattern of girders (ft)

NL = Number of loaded lanes under consideration

Xext = Horizontal distance from the C.O.G. of the pattern of girders to the exterior girder (ft) x = Horizontal distance from the C.O.G. of the pattern of girders to each girder (ft)

R2 = 0.251 =

R1 = 0.278 = b

L

N

N ext b

L x eX

N

N R

28 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 8

One Lane Loaded

Lever Rule

0.5

D1 = 1.17 ft

S = 2.95 ft

DFMom.Beam8 = 0.302 = (1 - (1.17 ft/ 2.95 ft)) x

Two or More Lanes Loaded

Beam 8 de = 0.818 ft e = 0.860 ft = 0.77 + (0.818 ft/ 9.1) g,interior = 0.347

DFMom.Beam8 = 0.298 = 0.860 ft x 0.347

29 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

"Rigid Superstructure" Pile Cap Analogy x= horizontal distance from left edge of bridge deck

A= Area of girder section

Beam x A x*A

Beam 1 1.625 0.139 0.226

Beam 2 4.625 0.139 0.642

Beam 3 7.625 0.108 0.826

Beam 4 10.575 0.108 1.15

Beam 5 13.525 0.108 1.47

Beam 6 16.475 0.108 1.78

Beam 7 19.425 0.108 2.10

Beam 8 22.375 0.108 2.42

∑ = 0.928 10.618

CG = 11.44 ft *from the left edge of bridge deck

Nb = number of beams e = eccentricity of load from C.G.

x = horizontal distance from C.G. of pattern of beams to each beam

Xext = horizontal dist from C.G. of pattern of beams to exterior beam

CG = 11.44 ft *from the left edge of bridge deck

Beam 1 Overhang = 1.63 ft

Beam 8 Overhang = 0.00 ft

Out to Out Dist. 24.83 ft xBeam1 = 9.82 ft (CL Beam 1 to CG Beam Group) xBeam2 = 7.41 ft (CL Beam 2 to CG Beam Group) xBeam3 = 4.41 ft (CL Beam 3 to CG Beam Group) xBeam4 = 1.46 ft (CL Beam 4 to CG Beam Group) xBeam5 = -1.49 ft (CL Beam 5 to CG Beam Group) xBeam6 = -4.44 ft (CL Beam 6 to CG Beam Group) xBeam7 = -7.39 ft (CL Beam 7 to CG Beam Group) xBeam8 = -10.34 ft (CL Beam 8 to CG Beam Group)

��

Σ�

L

N

N ext b

L x eX

N

N R

��

Σ�

30 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

x Beam1 = 96.42 xBeam1 = 9.82 x Beam2 = 54.85 xBeam2 = 7.41 x Beam3 = 19.42 xBeam3 = 4.41 x Beam4 = 2.12 xBeam4 = 1.46 x Beam5 = 2.23 xBeam5 = -1.49 x Beam6 = 19.75 xBeam6 = -4.44 x Beam7 = 54.67 xBeam7 = -7.39 x Beam8 = 106.99 xBeam8 = -10.34

∑x = 356.45

-4.61 ft)) xBeam1 / ∑x = 0.0275 xBeam8 / ∑x = 0.0290 e1 = 6.18 ft = 10.34 ft - 1.17 ft - 3.00 ft e2 = -4.61 ft = 10.34 ft - 1.17 ft - 13.79 ft

1 + (0.0290 x 6.18 ft)

2 + (0.0290 x (6.18 ft +

One Lane Loaded (Lever Rule)

DFMom.Beam8 = 0.363 = 0.302 x 1.20

One Lane Loaded (Pile Cap)

DFMom.Beam8 = 0.365 = 0.304 x 1.20

Two or More Lanes Loaded (Formula)

DFMom.Beam8 = 0.298 = 0.298

Two or More Lanes Loaded (Pile Cap)

DFMom.Beam8 = 0.295 = 0.295 x 1.00

Critical Factor

DFMom.Beam8 = 0.365 e = Eccentricity of a design truck or a design lane load from the C.O.G. of the pattern of girders (ft)

NL = Number of loaded lanes under consideration

Xext = Horizontal distance from the C.O.G. of the pattern of girders to the exterior girder (ft) x = Horizontal distance from the C.O.G. of the pattern of girders to each girder (ft)

R2 = 0.295 =

R1 = 0.304 =

L

N

N ext b

L x eX

N

N R

31 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Shear for Exterior Beams:

Applicability

(5) 4.6.2.2.3b-1

Beam 1 de = -0.017 ft OKAY

Beam 8 de = 0.818 ft OKAY

Beam 1

One Lane Loaded

0.5

Per (2) - Section 3.5.3.10, Distribution of live load to exterior beams under safety curb or barrier shall be calculated using (4) - Section 4.6.2.2.2

32 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Lever Rule

Beam 1 D= 2.00 ft

Beam 1 S = 3.00 ft

DFShear,Beam1 = 0.167 = (1 - (2.00 ft/ 3.00 ft)) x

Two or More Lanes Loaded

Beam 1 de = -0.017 = e = 0.598 = 0.60 + -(0.017 ft/ 10.0) g,interior = 0.443

DFShear,Beam1 = 0.265 = 0.598 ft x 0.443

One Lane Loaded (Lever Rule)

DFShear,Beam1 = 0.200 = 0.167 x 1.20

One Lane Loaded (Pile Cap) *See Moment Calculation

DFShear.Beam1 = 0.333 = 0.278 x 1.20

Two or More Lanes Loaded

DFShear,Beam1 = 0.265 = 0.265

Two or More Lanes Loaded (Pile Cap) *See Moment Calculation

DFShear.Beam1 = 0.251 = 0.251 x 1.00

Critical Factor

DFShear,Beam1 = 0.333

33 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam 8

One Lane Loaded

0.5

Lever Rule

Beam 1 D= 1.17 ft

Beam 1 S = 2.95 ft

DFShear.Beam8 = 0.302 = (1 - (1.17 ft/ 2.95 ft)) x

34 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Two or More Lanes Loaded

Beam 8 de = 0.818 = e = 0.682 = 0.60 + (0.818 ft/ 10.0) g,interior = 0.439

DFShear.Beam8 = 0.299 = 0.682 ft x 0.439

One Lane Loaded (Lever Rule)

DFShear.Beam8 = 0.363 = 0.302 x 1.20

One Lane Loaded (Pile Cap) *See Moment Calculation

DFShear.Beam8 = 0.365 = 0.304 x 1.20

Two or More Lanes Loaded

DFShear.Beam8 = 0.299 = 0.299 x 1.00

Two or More Lanes Loaded (Pile Cap) *See Moment Calculation

DFShear.Beam8 = 0.295 = 0.295 x 1.00

Critical Factor

DFShear.Beam8 = 0.365

35 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Deflection for All Beams g = 2

No. of Beams = 8

DF = 0.250 = 2/ 8

36 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - Alternate Live Loads C-05-027

Alternate Live Load Distribution Factors

37 68

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PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Load Rating - Alternate Live Load Distribution Factors C-05-027

1) AASHTO Standard Specifications, 17th Edition, 2002

2) MassDOT Bridge Manual 2024

3) 1995 Mass Highway Bridge Manual

4) AISC Steel Construction Manual, 15th Edition, 2017

5) AASHTO LRFD Bridge Design, 9th Edition, 2020 with 2021 Errata

Narrative:

Calculate live load distribution factors per (2) and (5) Section 3.5.4.

Summary:

Beam LLDF M LLDF V LLDF M FAT. LLDF V FAT. LLDF DEFLECTION

1 x x x x x

2 0.382 0.500 0.382 0.417 0.250

3 0.387 0.500 0.387 0.417 0.250

4 0.387 0.500 0.387 0.417 0.250

5 0.387 0.500 0.387 0.417 0.250

6 0.387 0.500 0.387 0.417 0.250

7 0.387 0.500 0.387 0.417 0.250

8 x x x x x

Geometry:

Spacing, S Beam = 3.50 ft ts = 0.67 ft

Span Length, L Beam 1 = 30.3 ft

Span Length, L Beam 2 = 24.3 ft

Span Length, L Beam 3-8 = 21.0 ft

Nb = 8

Roadway Width = 21.6 ft

Number of Lanes = 1

The existing beam spacing is below the minimum beam spacing specified in the Range of Applicability for live load distribution factors (LLDFs) for shear and moment of interior beams, as given in Tables 4.6.2.2.2b-1 and 4.6.2.2.3a-

1. Consequently, an alternate analysis is performed by theoretically increasing the beam spacing to the minimum value specified in these tables. By demonstrating that the beams are adequate at this larger spacing, which falls within the range of applicability, it is shown that they will be adequate for the actual smaller spacing. This is because the distribution factors would be lower in the real conditions at the smaller spacing. The interior beams were checked to rate above statutory with the distribution factors. The results presented use the distribution factors from the actual beam spacing.

38 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Beam Geometry:

Beam 1-2 Type = W14x68

Beam 1-2 A = 20.0 in²

Beam 1-2 Depth = 14.0 in

Beam 1-2 Yt = 7.00 in

Beam 1-2 Ix = 722 in⁴

Beam 3-8 Type = W14x53

Beam 3-8 A = 15.6 in²

Beam 3-8 Depth = 13.9 in

Beam 3-8 Yt = 6.95 in

Beam 3-8 Ix = 541 in⁴

Calculate Kg:

Beam 1-2 eg = 11.0 in (8.00 in x 0.5) + 7.00 in

Beam 3-8 eg = 11.0 in (8.00 in x 0.5) + 6.95 in n = 6.76 29000 ksi/ 4291 ksi (5) 4.6.2.2.1-2

Beam 1-2 Kg = 21,234 in⁴ (5) 4.6.2.2.1-1

Beam 3-8 Kg = 16,297 in⁴ (5) 4.6.2.2.1-1

39 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

Moment for Interior Beams:

Applicability

(5) Table 4.6.2.2.2b-1

Beam 2 Beam 2 Check

S = 3.50 ft OKAY ts = 8.00 in OKAY

L = 24.34 ft OKAY

Nb = 8 OKAY

Kg = 21,234 in⁴ OKAY

Beam 3-7 Beam 3-7 Check

S = 3.50 ft OKAY ts = 8.00 in OKAY

L = 21.0 ft OKAY

Nb = 8 OKAY

Kg = 16,297 in⁴ OKAY

(4) Table 4.6.2.2.2b-1

Per (2) - Section 3.5.3.8&9, Distribution of live load to interior beams shall be calculated using (5) - Section

4.6.2.2.2

40 68

CLIENT

PROJECT

BRIDGE NO.

PAGE

CALC BY

CHECK BY

SUBJECT DATE

OF

GILL ENGINEERING ASSOCIATES, INC.

63 KENDRICK STREET, NEEDHAM, MA 02494

SOUTH RIVER ROAD

C-05-027

TRS

DCH

OCT 2024

One Lane Loaded

DFMom.Beam2= 0.324 0.06 + 3.50 ft 3.50 ft

14 24.34 ft x

12.0 x 24.34 ft x 8.00 in

Two or More Lanes Loaded

DFMom.Beam2= 0.382 0.075 + 3.50 ft 3.50 ft

9.5 24.34 ft x

12.0 x 24.34 ft x 8.00 in

One Lane Loaded

DFMom.Beam2= 0.324

Two or More Lanes Loaded

DFMom.Beam2= 0.382

Critical Factor

DFMom.Beam2= 0.382

Beam 3-7

One Lane Loaded

DFMom.Beam3-7= 0.333 0.06 + 3.50 ft 3.50 ft

14 21.00 ft x

12.0 x 21.00 ft x 8.00 in

Two or More Lanes Loaded

DFMom.Beam3-7= 0.387 0.075 + 3.50 ft 3.50 ft

9.5 21.00 ft x

12.0 x 21.00 ft x 8.00 in

One Lane Loaded

DFMom.Beam3-7= 0.333

Two or More Lanes Loaded

DFMom.Beam3-7= 0.387

Critical Factor

DFMom.Beam3-7= 0.387

16,297 in⁴

21,234 in⁴

21,234 in⁴

16,297 in⁴

0.4 0.3

0.1

0.6 0.2

0.1

0.4 0.3

0.1

0.6 0.2

0.1

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OCT 2024

Shear for Interior Beams:

Applicability (5) Table 4.6.2.2.3a-1

Beam 2 Beam 2 Check

S = 3.50 ft OKAY ts = 8.00 ft OKAY

L = 24.34 ft OKAY

Nb = 8.00 ft OKAY

Beam 3-7 Beam 3-7 Check

S = 3.50 ft OKAY ts = 8.00 ft OKAY

L = 21.00 ft OKAY

Nb = 8.00 ft OKAY

(5) Table 4.6.2.2.3a-1

Per (2) - Section 3.5.3.8&9, Distribution of live load to interior beams shall be calculated using (5) - Section

4.6.2.2.2

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OCT 2024

One Lane Loaded

DFShear,Beam2 = 0.500 0.36 + 3.50 ft

Two or More Lanes Loaded

DFShear,Beam2 = 0.482 0.2 + 3.50 ft - 3.50 ft

12 35

One Lane Loaded

DFShear,Beam2 = 0.500

Two or More Lanes Loaded

DFShear,Beam2 = 0.482

Critical Factor

DFShear,Beam2 = 0.500

Beam 3-7

One Lane Loaded

DFShear,Beam3-7 = 0.500 0.36 + 3.50 ft

Two or More Lanes Loaded

DFShear,Beam3-7 = 0.482 0.2 + 3.50 ft - 3.50 ft

12 35

One Lane Loaded

DFShear,Beam3-7 = 0.500

Two or More Lanes Loaded

DFShear,Beam3-7 = 0.482

Critical Factor

DFShear,Beam3-7 = 0.500

2.0

2.0

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OCT 2024

Load Rating - Deterioration C-05-027

Deterioration

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OCT 2024

Load Rating - Deterioration C-05-027

1) AASHTO Standard Specifications, 17th Edition, 2002

2) MassDOT Bridge Manual 2024

3) 1995 Mass Highway Bridge Manual

4) AISC Steel Construction Manual, 15th Edition, 2017

5) AASHTO LRFD Bridge Design, 9th Edition, 2020 with 2021 Errata

6) AASHTO Manual for Bridge Evaluation, 3rd Edition, 2018 thru 2022 Interim

Bottom Flange Deterioration

BM # Shape Top Flange Thickness Remaining Thickness Percent Loss

BM 1-2 W14x68 0.72 0.47 34.72

BM 3-8 W14x53 0.66 0.41 37.88

Top flange deterioration was estimated to be a 1/4'' loss of thickness to the top flange along the entire span of each beam.

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SECTION PROPERTIES C-05-027

Section Properties

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OCT 2024

COMPOSITE SECTION PROPERTIES

GIRDER DESCRIPTION

GIRDER NUMBER

GIRDER LOCATION

WELDED PLATE GIRDER

GROSS SECTION PROPERTIES

n value width y WIDTH DEPTH A Y AY AY 2 I0 n= 6.76 37.50 4.00 5.55 8.00 44.38 18.00 798.8 14378.7 236.7

Cover Plate 0.000 0 0 0.00 14.00 0.0 0.0 0.0

Flange Plate 0.360 10.00 0.72 7.20 13.64 98.2 1339.6 0.3

Web Plate 6.280 0.42 12.56 5.21 7.00 36.5 255.4 68.5

Flange Plate 0.360 10.00 0.72 7.20 0.36 2.6 0.9 0.3

Cover Plate 0.000 0 0 0.00 0.00 0.0 0.0 0.0

SUMS 64.0 - 936.1 15974.6 305.8

IZ =ΣI0+ΣAY

in in

Y' = ΣAY DEPTH (Incl Deck) in

ΣA CTOP DECK 7.37 in

SDECK TRANS 2372.0 in

19.6 in in

WEB AREA 5.8 in

CTOP ST -0.63 in CBOTTOM 14.63 in

STOP ST -4114.4 in 3 SBOTTOM 176.8 in

STATICAL MOMENT OF INERTIA OF TOP AND BOTTOM FLANGES - Q = ΣAd where: A is the area of each flange component & d is the distance from the N.A. of the section the C.G. of the area

Q - DECK A = 44.38 in d = Y-Y' 3.37 in Q DECK = 149.6 in

Q - TOP FLANGE cover plates + deck deck A = 44.38 in d = Y-Y' 3.37 in Q= 149.6 in cover plate A = 0.00 in d = Y-Y' -0.63 in Q= 0.0 in flange plate A = 7.20 in d = Y-Y' -0.99 in Q= -7.1 in

Q TOP FLANGE = Σ 142.5 in

Q - BOTTOM FLANGE cover plates flange plate A = 7.20 in d = Y'-Y 14.27 in Q= 102.7 in cover plate A = 0.00 in d = Y'-Y 14.63 in Q= 0.0 in

Q BOTTOM FLANGE = Σ 102.7 in

2586.499

14.63 in 22.00

MEMBER AREA MEMBER DEPTH (Less Deck) 14.00

22.00

16280 IGROSS = IZ - (ΣA)(Y')

COMPOSITE

DECK

Beam 1

BM1

EXTERIOR

ELEMENTS PROPERTIES

47 68

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DCH

OCT 2024

GIRDER DESCRIPTION

GIRDER NUMBER

GIRDER LOCATION

WELDED PLATE GIRDER

GROSS SECTION PROPERTIES

n value width y WIDTH DEPTH A Y AY AY 2 I0 n= 6.76 36.00 4.00 5.33 8.00 42.60 18.00 766.9 13803.6 227.2

Cover Plate 0.000 0 0 0.00 14.00 0.0 0.0 0.0

Flange Plate 0.360 10.00 0.72 7.20 13.64 98.2 1339.6 0.3

Web Plate 6.280 0.42 12.56 5.21 7.00 36.5 255.4 68.5

Flange Plate 0.360 10.00 0.72 7.20 0.36 2.6 0.9 0.3

Cover Plate 0.000 0 0 0.00 0.00 0.0 0.0 0.0

SUMS 62.2 - 904.2 15399.4 296.4

IZ =ΣI0+ΣAY

in in

Y' = ΣAY DEPTH (Incl Deck) in

ΣA CTOP DECK 7.47 in

SDECK TRANS 2314.1 in

19.6 in in

WEB AREA 5.8 in

CTOP ST -0.53 in CBOTTOM 14.53 in

STOP ST -4800.9 in 3 SBOTTOM 175.9 in

STATICAL MOMENT OF INERTIA OF TOP AND BOTTOM FLANGES - Q = ΣAd where: A is the area of each flange component & d is the distance from the N.A. of the section the C.G. of the area

Q - DECK A = 42.60 in d = Y-Y' 3.47 in Q DECK = 147.7 in

Q - TOP FLANGE cover plates + deck deck A = 42.60 in d = Y-Y' 3.47 in Q= 147.7 in cover plate A = 0.00 in d = Y-Y' -0.53 in Q= 0.0 in flange plate A = 7.20 in d = Y-Y' -0.89 in Q= -6.4 in

Q TOP FLANGE = Σ 141.3 in

Q - BOTTOM FLANGE cover plates flange plate A = 7.20 in d = Y'-Y 14.17 in Q= 102.0 in cover plate A = 0.00 in d = Y'-Y 14.53 in Q= 0.0 in

Q BOTTOM FLANGE = Σ 102.0 in

MEMBER AREA MEMBER DEPTH (Less Deck) 14.00

22.00

15696 IGROSS = IZ - (ΣA)(Y')

2556.280

14.53 in 22.00

Beam 2

BM2

INTERIOR

ELEMENTS PROPERTIES

COMPOSITE

DECK

48 68

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OCT 2024

GIRDER DESCRIPTION

GIRDER NUMBER

GIRDER LOCATION

WELDED PLATE GIRDER

GROSS SECTION PROPERTIES

n value width y WIDTH DEPTH A Y AY AY 2 I0 n= 6.76 35.38 4.00 5.23 8.00 41.86 17.90 749.4 13413.6 223.3

Cover Plate 0.000 0 0 0.00 13.90 0.0 0.0 0.0

Flange Plate 0.330 8.06 0.66 5.32 13.57 72.2 979.6 0.2

Web Plate 6.290 0.37 12.58 4.65 6.95 32.3 224.8 61.4

Flange Plate 0.330 8.06 0.66 5.32 0.33 1.8 0.6 0.2

Cover Plate 0.000 0 0 0.00 0.00 0.0 0.0 0.0

SUMS 57.2 - 855.7 14618.6 285.0

IZ =ΣI0+ΣAY

in in

Y' = ΣAY DEPTH (Incl Deck) in

ΣA CTOP DECK 6.93 in

SDECK TRANS 2043.1 in

15.3 in in

WEB AREA 5.1 in

CTOP ST -1.07 in CBOTTOM 14.97 in

STOP ST -1957.2 in 3 SBOTTOM 139.9 in

STATICAL MOMENT OF INERTIA OF TOP AND BOTTOM FLANGES - Q = ΣAd where: A is the area of each flange component & d is the distance from the N.A. of the section the C.G. of the area

Q - DECK A = 41.86 in d = Y-Y' 2.93 in Q DECK = 122.7 in

Q - TOP FLANGE cover plates + deck deck A = 41.86 in d = Y-Y' 2.93 in Q= 122.7 in cover plate A = 0.00 in d = Y-Y' -1.07 in Q= 0.0 in flange plate A = 5.32 in d = Y-Y' -1.40 in Q= -7.4 in

Q TOP FLANGE = Σ 115.2 in

Q - BOTTOM FLANGE cover plates flange plate A = 5.32 in d = Y'-Y 14.64 in Q= 77.9 in cover plate A = 0.00 in d = Y'-Y 14.97 in Q= 0.0 in

Q BOTTOM FLANGE = Σ 77.9 in

MEMBER AREA MEMBER DEPTH (Less Deck) 13.90

21.90

14904 IGROSS = IZ - (ΣA)(Y')

2094.403

14.97 in 21.90

Beam 3-7

BM3-7

INTERIOR

ELEMENTS PROPERTIES

COMPOSITE

DECK

49 68

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C-05-027

TRS

DCH

OCT 2024

GIRDER DESCRIPTION

GIRDER NUMBER

GIRDER LOCATION

WELDED PLATE GIRDER

GROSS SECTION PROPERTIES

n value width y WIDTH DEPTH A Y AY AY 2 I0 n= 6.76 47.19 4.00 6.98 8.00 55.84 17.90 999.6 17892.7 297.8

Cover Plate 0.000 0 0 0.00 13.90 0.0 0.0 0.0

Flange Plate 0.330 8.06 0.66 5.32 13.57 72.2 979.6 0.2

Web Plate 6.290 0.37 12.58 4.65 6.95 32.3 224.8 61.4

Flange Plate 0.330 8.06 0.66 5.32 0.33 1.8 0.6 0.2

Cover Plate 0.000 0 0 0.00 0.00 0.0 0.0 0.0

SUMS 71.1 - 1105.9 19097.7 359.6

IZ =ΣI0+ΣAY

in in

Y' = ΣAY DEPTH (Incl Deck) in

ΣA CTOP DECK 6.35 in

SDECK TRANS 2410.1 in

15.3 in in

WEB AREA 5.1 in

CTOP ST -1.65 in CBOTTOM 15.55 in

STOP ST -1376.4 in 3 SBOTTOM 145.7 in

STATICAL MOMENT OF INERTIA OF TOP AND BOTTOM FLANGES - Q = ΣAd where: A is the area of each flange component & d is the distance from the N.A. of the section the C.G. of the area

Q - DECK A = 55.84 in d = Y-Y' 2.35 in Q DECK = 131.5 in

Q - TOP FLANGE cover plates + deck deck A = 55.84 in d = Y-Y' 2.35 in Q= 131.5 in cover plate A = 0.00 in d = Y-Y' -1.65 in Q= 0.0 in flange plate A = 5.32 in d = Y-Y' -1.98 in Q= -10.5 in

Q TOP FLANGE = Σ 121.0 in

Q - BOTTOM FLANGE cover plates flange plate A = 5.32 in d = Y'-Y 15.22 in Q= 80.9 in cover plate A = 0.00 in d = Y'-Y 15.55 in Q= 0.0 in

Q BOTTOM FLANGE = Σ 80.9 in

MEMBER AREA MEMBER DEPTH (Less Deck) 13.90

21.90

19457 IGROSS = IZ - (ΣA)(Y')

2265.380

15.55 in 21.90

Beam 8

BM8

EXTERIOR

ELEMENTS PROPERTIES

COMPOSITE

DECK

50 68

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OCT 2024

SHEAR CONNECTORS

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OCT 2024

SHEAR STUDS C-05-027

1. MassDOT LRFD Bridge Manual, 2024 Part II

2. AASHTO LRFD Bridge Design Specifications, 9th Edition, 2020 with 2021 Errata

Material Properties:

Shear Connector Diameter, d = 0.750 in (Ref 1 - Dwg. 8.4.2)

Shear Connector Area, Asc = 0.44 in

Shear Connector Height, h = 6.00 in

Number of Studs in a Line, n = 2

Minimum Edge Clear Distance, e = 1.00 in (Ref 2 - 6.10.10.1.3)

Deck f'c = 5 ksi

Deck Ec = 4287 ksi

Shear Connector Fu = 60 ksi (Ref 2 - 6.4.4)

Girder Web Fy = 33 ksi

Girder Flange Fy = 33 ksi

Beam 1-2 Top Flange Width, bf = 10.00 in

Beam 3-8 Top Flange Width, bf = 8.06 in

Deck Thickness, td = 8.00 in

Haunch Thickness, th = 1.00 in

Load Factor Fatigue 1 = 1.75 (Ref 2 - Table 3.4.1-1)

Load Factor Fatigue II = 0.80 (Ref 2 - Table 3.4.1-1)

Per Ref (2) 6.3.7 Shear studs shall be designed for the controlling fatigue limit state, then checked with the controlling strength limit state.

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OCT 2024

Geometry Checks:

h 6.00 in d 0.75 in

Min. Pitch = 10.00 in > 4.50 in OK

Beam 1-2:

Sprovided = 7.25 in > 3.00 in OK

Edge Dist. = 1.38 in > 1.00 in OK

Beam 3-8:

Sprovided = 5.31 in > 3.00 in OK

Edge Dist. = 1.38 in > 1.00 in OK

Cover Top = 9.00'' - 6.00'' = 3.00'' OK

Pen. Bot = 6.00'' - 1.00'' = 5.00'' OK

Ref 2 - 6.10.10.1.2, The center-to-center pitch of shear connectors shall also not be less than six stud diameters.

Ref 2 - 6.10.10.1.3, stud shear connectors shall not be closer than 4.0 stud diameters center-to-center transverse to the longitudinal axis of the supporting member.

Ref 2 - 6.10.10.1.1, ratio of the height to the diameter of a stud shear connector shall not be less than 4.0.

= = 8.00 OK

Ref 2 - 6.10.10.1.4, the clear depth of concrete cover over the tops of the shear connectors should not be less than 2.0 in. Shear connectors should penetrate at least 2.0 in. into the concrete deck.

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OCT 2024

Traffic Information:

ADT = 154

ADTT = 9.24

p = 0.85 (Ref 2 - Table 3.6.1.4.2-1)

ADTTSL = p x ADTT (Ref 2 - Eq. 3.6.1.4.2-1)

ADTTSL = 0.85 x 9 = 7.854 n = 1.00 (Ref 2 - Table 6.6.1.2.5-2, L > 40ft, simple span)

(Ref 2 - Eq. 6.6.1.2.5-3)

N = 365 x 75 x 1 x 7.85 = 215003.25

From Routine & Special Member Inspection Report dated November 1, 2022

N = (365)(75)n(ADTT)SL

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OCT 2024

Shear Connector Fatigue Resistance:

Ref 2 - 6.10.10.2:

Zr = 5.5d = 3.1 k

Zr = αd = 6.6 k where α = 34.5-4.28 log N α = 34.5 - 4.28 x 5.33 = 11.68

ADTTSL = 7.854 <1090

Therefore Zr = 6.57 k

If (ADTT)SL >= 1090, use Fatigue I load combination and the fatigue shear resistance for infinite life shall be taken as:

Otherwise, the Fatigue II load combination shall be used and the fatigue shear resistance for finite life shall be taken as:

55 68

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DCH

OCT 2024

Required Pitch:

Ref 2 - 6.10.10.1.2, The pitch, p, of shear connectors shall satisfy:

n x Zr

Where Vsr = [(Vfat) + (Ffat)

1/2

(Ref 2 - Eq. 6.10.10.1.2-2)

Calculate Vsr and required p for each beam:

*Fatigue Shear Loads taken from BrR

Beam 1:

Span = 30.34

I (in ) = 2586 (See Section Properties Calc)

Q (in ) = 150 (See Section Properties Calc)

Point Distance Vf Vsr=Vfat=VfQ/I p = nZr/Vsr

0 0 11.59 k 0.67 k 19.59

0.1 3.034 11.33 k 0.66 k 20.04

0.2 6.068 11.07 k 0.64 k 20.52

0.3 9.102 10.82 k 0.63 k 20.99

0.4 12.136 10.56 k 0.61 k 21.51

0.5 15.17 10.41 k 0.60 k 21.82

0.6 18.204 10.56 k 0.61 k 21.51

0.7 21.238 10.82 k 0.63 k 20.99

0.8 24.272 11.07 k 0.64 k 20.52

0.9 27.306 11.33 k 0.66 k 20.04

1 30.34 11.59 k 0.67 k 19.59

Actual: Min:

Spacing Spacing

10.00 in < 19.59 ok p < (Ref 2 - Eq. 6.10.10.1.2-1) Vsr

Ref 2 - 6.10.10.1.2, for straight spans or segments, the radial fatigue shear range from Eq.

6.10.10.1.2-4 may be taken equal to zero.

Ref 2 - 6.10.10.1.2, the center-to-center pitch of shear connectors shall not exceed 24.0 in.

and shall not be less than six stud diameters.

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OCT 2024

Beam 2:

Span = 24.34

I (in ) = 2556 (See Section Properties Calc)

Q (in ) = 148 (See Section Properties Calc)

Point Distance Vf Vsr=Vfat=VfQ/I p = nZr/Vsr

0 0 16.28 k 0.94 k 13.96

0.1 2.434 15.91 k 0.92 k 14.29

0.2 4.868 15.54 k 0.90 k 14.63

0.3 7.302 15.18 k 0.88 k 14.97

0.4 9.736 14.81 k 0.86 k 15.35

0.5 12.17 14.72 k 0.85 k 15.44

0.6 14.604 14.81 k 0.86 k 15.35

0.7 17.038 15.18 k 0.88 k 14.97

0.8 19.472 15.54 k 0.90 k 14.63

0.9 21.906 15.91 k 0.92 k 14.29

1 24.34 16.28 k 0.94 k 13.96

Actual: Min:

Spacing Spacing

10.00 in < 13.96 ok

Beam 3-7:

Span = 21

I (in ) = 2094 (See Section Properties Calc)

Q (in ) = 123 (See Section Properties Calc)

Point Distance Vf Vsr=Vfat=VfQ/I p = nZr/Vsr

0 0 15.91 k 0.93 k 14.10

0.1 2.1 15.55 k 0.91 k 14.43

0.2 4.2 15.18 k 0.89 k 14.78

0.3 6.3 14.81 k 0.87 k 15.15

0.4 8.4 14.69 k 0.86 k 15.27

0.5 10.5 14.68 k 0.86 k 15.28

0.6 12.6 14.69 k 0.86 k 15.27

0.7 14.7 14.81 k 0.87 k 15.15

0.8 16.8 15.18 k 0.89 k 14.78

0.9 18.9 15.55 k 0.91 k 14.43

1 21 15.91 k 0.93 k 14.10

Actual: Min:

Spacing Spacing

10.00 in < 14.10 ok

*To be conservative, using the fatigue DF from Beam 3 as it is slightly higher than Beams 4-7

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OCT 2024

Beam 8:

Span = 21

I (in ) = 2265 (See Section Properties Calc)

Q (in ) = 131 (See Section Properties Calc)

Point Distance Vf Vsr=Vfat=VfQ/I p = nZr/Vsr

0 0 12.13 k 0.71 k 18.49

0.1 2.1 11.85 k 0.69 k 18.93

0.2 4.2 11.57 k 0.68 k 19.39

0.3 6.3 11.29 k 0.66 k 19.87

0.4 8.4 11.20 k 0.66 k 20.03

0.5 10.5 11.20 k 0.66 k 20.03

0.6 12.6 11.20 k 0.66 k 20.03

0.7 14.7 11.29 k 0.66 k 19.87

0.8 16.8 11.57 k 0.68 k 19.39

0.9 18.9 11.85 k 0.69 k 18.93

1 21 12.13 k 0.71 k 18.49

Actual: Min:

Spacing Spacing

10.00 in < 18.49 ok

Shear Connector Strength Resistance:

Calculate shear resistance of single shear stud:

Qr = φscQn (Ref 2 - Eq. 6.10.10.4.1-1) φsc = 0.85 (Ref 2 - 6.5.4.2)

(Ref 2 - Eq. 6.10.10.4.3-1)

0.5

Qn = 0.50 x x 0.44 in2 5 ksi x 4287 ksi = 32.340 k

AscFu = 0.44 in2 x 60.00 ksi = 26.507 k

Qr = 26.51 k x 0.85 = 22.5 k

�� � 0.5��

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