RTA Submission - DA APP A - Structural Design Calculations Mooring Pier 24-06-28.pdf

DESIGN WORK SHEET

PROJECT

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

Purpose

Design Fender Support System

Check Existing-to-Remain Components of Mooring Pier

General Assumptions

Assume Existing Connection Locations will be used for the proposed fender system.

Assume that the connection between the support members and the fender system will be determined by the manufacturer.

Assume breaking waves act as if the fenders are a solid wall with no water behind

Assume that atmospheric ice conditions will only control when concurrent with a Ice Impact or Thermal Expansion Load Condition.

Assume that the only dynamic loads that occur simultaneously with each other are Wave and Hydrodynamic Loads.

Assume that Debris Impact or Barge Impact doesn't occur with Thermally-Expanding Ice Loads

Assume that Impact and Wave loads do not occur in Usual or Unusual Load Combinations.

Assume that the Barge Impact is applied only to two Fender Supports

Assume that the maximum positive and the negative moments occur at the same locations for all load cases.

References

Name Edition Year Abbreviation

1968 Troy Lock & Dam Mooring Pier Contract Documents 1968 1968 TLDMP

AASHTO LRFD Bridge Design Specifications (2020, 9th Ed.) 9 2020 AASHTO LRFD

AASHTO LRFD Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals 2015 AASHTO Signs

AISC Steel Construction Manual (4th Ed.) 4 AISC 4

AISC Steel Construction Manual (15th Ed.) 15 2017 AISC 15

AISC Design Guide 9: Torsional Analysis of Structural Steel Members 2003 AISC DG9

International Building Code 2021 IBC

International Existing Building Code 2021 IEBC

USS Hot-Rolled Steel, Shapes and Plates 1963 USS

ASCE/SEI 7-16: Minimum Design Loads and Associated Criteria for Buildings and Other Structures 2016 ASCE 7-16

USACE UFC 3-301-01: Structural Engineering Change 1 2023 UFC 3-301-01

EM 1110-2-2107: Design of Hydraulic Steel Structures * 2022 EM 1110-2-2107

EM 1110-2-2502: Flood Walls and Other Hydraulic Retaining Walls 2022 EM 1110-2-2502

EM 1110-2-2607: Planning and Design of Navigational Dams 1995 EM 1110-2-2607

EM 1110-2-3402: Barge Impact Forces for Hydraulic Structures 2022 EM 1110-2-3402

* The Troy Lock & Dam Mooring Pier is not considered a "Hydraulic Steel Structure" since its primary purpose is not to retain water. However, EM 1110-2-2107 is still used as a reference for determining design loads and details since the Mooring Pier is a steel structure submerged in water.

1. General Input

1.1 Unit Weights

γC 0.150 kcf Unit Weight of Concrete AASHTO Bridge C3.5.1 γS 0.490 kcf Unit Weight of Steel AASHTO Bridge Table 3.5.1-1 γW 0.062 kcf Unit Weight of Water ASCE 7-16 5.4.4.2 γE 0.120 kcf Unit Weight of Compacted Soil AASHTO Bridge Table 3.5.1-1 γI 0.056 kcf Unit Weight of Ice ASCE 7-16 10.4.1 γCF 0.063 kcf Unit Weight of Composite Fender Material USACERL TR-98/123 Table 1

1.2 Datum Conversions

ZMLW-N88 2.620 ft Conversion from Mean Low Water to NAVD88 NOAA Datums for 8531680 Sandy Hook, NJ

ZSH-N88 0.240 ft Conversion from Mean Sea Level at Sandy Hook, NJ to NAVD88 NOAA Datums for 8531680 Sandy Hook, NJ

ZNG29-N88 3.600 ft Conversion from NGVD29 to NAVD88 USGS Conversion Factors and Datums

S:\STRUCTURES\Project Files\TLD Mooring Pier\RTA\RTA_TLD_Mooring Pier Fender Design.xlsx Revision 00

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

1. General Input (cont.)

1.3 Material Properties

f'c 4.500 ksi Deck Concrete Strength

K1 1.000 Correction Factor for Aggregate Source AASHTO Bridge 5.4.2.4

Ec 4435.31 ksi = 120,000 *K1 * γc (kcf) 2.0

* f'c (ksi) 0.33

Modulus of Elasticity of Concrete AASHTO Bridge Eq. 5.4.2.4-1 fy 50.000 ksi Yield Strength of Steel fu 65.000 ksi Ultimate Strength of Steel

Es 29000 ksi Modulus of Elasticity of Steel

G 11200 ksi Shear Modulus of Steel AISC 15 E4 n 6.54 = Es / Ec Transformational Factor AASHTO Bridge Eq. 4.6.2.2.1-2

2. Structural Component Properties

2.1 Existing Post Properties

SIZE 1968 TLDMP

LP 11.000 ft Proposed Span Length of Pile (between Channel Struts)

LP-T 14.000 ft Total Length of Pile (from Top to Bottom Fender Support) 1968 TLDMP

WP 53.000 plf Self Weight of Channel AISC 4 Pg. 52 dP 11.780 in Depth of Channel tP-w 0.436 in Web Thickness AISC 4 Pg. 52 bP-f 12.046 in Flange Width tP-f 0.436 in Flange Thickness AISC 4 Pg. 52

AP 15.580 in

Cross Sectional Area AISC 4 Pg. 52

IP-x 394.800 in

Major Axis Moment of Inertia IP-y 127.300 in

Minor Axis Moment of Inertia AISC 4 Pg. 52

SP-x 67.000 in

Major Axis Section Modulus SP-y 21.200 in

Minor Axis Section Modulus AISC 4 Pg. 52 rP-x 5.030 in Major Axis Radius of Gyration rP-y 2.860 in Minor Axis Radius of Gyration AISC 4 Pg. 52

2.2 Proposed Strut Properties

SIZE

LCS 2.500 ft Length of Strut Match Existing θCS 27.000 ° Angle between CL of Strut and CL of Post Match Existing

WP 20.000 plf Self Weight of Channel AISC 15 Table 1-5 dP 9.000 in Depth of Channel tP-w 0.448 in Web Thickness AISC 15 Table 1-5 bP-f 2.650 in Flange Width tP-f 0.413 in Flange Thickness AISC 15 Table 1-5

APF 5.870 in

Cross Sectional Area AISC 15 Table 1-5

IPF-x 60.900 in

Major Axis Moment of Inertia IPF-y 2.410 in

Minor Axis Moment of Inertia AISC 15 Table 1-5

SPF-x 13.500 in

Major Axis Section Modulus SPF-y 1.170 in

Minor Axis Section Modulus AISC 15 Table 1-5 rPF-x 3.220 in Major Axis Radius of Gyration rPF-y 0.640 in Minor Axis Radius of Gyration AISC 15 Table 1-5

ZPF-x 16.900 in

Major Axis Plastic Modulus ZPF-y 2.460 in

Minor Axis Plastic Modulus AISC 15 Table 1-5

12BP53

C9X20

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

2. Structural Component Properties (cont.)

2.3 Proposed Fender Support Properties

The proposed fender support will be a continuous beam between Hydraulic Cells with a intermediate support at the steel posts

SIZE

LPF 12.575 ft Maintain Span Length of Beam Between Hydraulic Cell and Post 1968 TLDMP

LPF-T 25.150 ft Total Length of a Single Piece of Beam

Lb-PF 25.150 ft Maximum Unbraced Length (Both Flanges)

WPF 58.000 plf Self Weight of Beam AISC 15 Table 1-1 dPF 12.200 in Depth of Beam tPF-w 0.360 in Web Thickness AISC 15 Table 1-1 bPF-f 10.000 in Flange Width tPF-f 0.640 in Flange Thickness AISC 15 Table 1-1

APF 17.000 in

Cross Sectional Area kdes 1.240 in Outside of Flange to Inside of Fillet AISC 15 Table 1-1

IPF-x 475.000 in

Major Axis Moment of Inertia IPF-y 107.000 in

Minor Axis Moment of Inertia AISC 15 Table 1-1

SPF-x 78.000 in

Major Axis Section Modulus SPF-y 21.400 in

Minor Axis Section Modulus AISC 15 Table 1-1 rPF-x 5.280 in Major Axis Radius of Gyration rPF-y 2.510 in Minor Axis Radius of Gyration AISC 15 Table 1-1

ZPF-x 86.400 in

Major Axis Plastic Modulus ZPF-y 32.500 in

Minor Axis Plastic Modulus AISC 15 Table 1-1

CPF-w 3570.000 in

Warping Constant JPF 2.100 in

Torsional Constant AISC 15 Table 1-1

WPF-no 28.900 in

SPF-w1 46.300 in

AISC DG9 Appendix A

2.5 Proposed Fender System

NFU 6 Number of Fender Supports

SFU 2.000 ft Maximum Vertical Spacing of Fender Support Beams

LFU 12.575 ft Length of one (1) Fender Unit 1968 TLDMP

3. Hydraulic Properties

3.1 Elevations

ZFB 1.000 Design Freeboard for Pier Extension EM 1110-2-2607 Section 5-6.d. & ASCE 7-16 5.4.2

ELLW -2.100 Low Water Elevation (January 1965) Mean Low Water 1968 TLDMP

ELHW 25.800 High Water Elevation (Peak at 12/31/1948 or 01/01/1949) Mean High Water 1968 TLDMP

ELBF 28.000 Base Flood Elevation NGVD 29 FEMA Firm Panel 360677002B

ELG -17.900 Ground Elevation (Riverbed) (between Cells 5 & 6) Mean Low Water 1968 TLDMP

ELT 16.000 Top of Mooring Pier Elevation Mean Low Water 1968 TLDMP

ELLW 0.520 Low Water Elevation (January 1965) Converted to NAVD88 Datum with ZMLW-N88

ELHW 28.420 High Water Elevation (Peak at 12/31/1948 or 01/01/1949) Converted to NAVD88 Datum with ZMLW-N88

ELBF 31.600 Base Flood Elevation Converted to NAVD88 Datum with ZNG29-N88

ELG -15.280 Ground Elevation (Riverbed) (between Cells 5 & 6) Converted to NAVD88 Datum with ZMLW-N88

ELT 18.620 Top of Mooring Pier Elevation Converted to NAVD88 Datum with ZMLW-N88

ELDF 32.600 = ELBF + ZFB Design Flood Elevation

3.2 Velocity of the stream

g 32.200 ft / s

Acceleration due to gravity

VW-max-f 3.470 ft / s Maximum velocity of water recorded USGS Water Data at Port of Albany, NY - 01359165

VW-min 30.47 ft / s = ds / 1 sec Approximate Lower Bound of Water Velocity ASCE 7-16 Eq. C5.4-1

VW-max 31.32 ft / s = (g * ds) 0.5

Approximate Higher Bound of Water Velocity ASCE 7-16 Eq. C5.4-2

W12X58

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations

4.1 General Parameters

CRISK I Risk Category Little to no risk to human life at failure UFC 3-301-01 Table 2-2

SRC D Surface Roughness Category, Water Surfaces ASCE 7-16 26.7.2

Exposure D Exposure Category, Water Surfaces ASCE 7-16 26.7.3

Exp. Roof Exposure of Roof ASCE 7-16 Table 7.3-1

IE 1.00 Importance Factor for Earthquake Loads UFC 3-301-01 Table 2-2

IS 0.80 Importance Factor for Snow Loads UFC 3-301-01 Table 2-2

Ii 0.80 Importance Factor for Ice Loads UFC 3-301-01 Table 2-2

ITSU N/A Importance Factor for Tsunami Loads UFC 3-301-01 Table 2-2

4.2 Vertical Loads

4.2.1 Dead Load of Fender Support System

Because the Fender product is to be chosen by the contractor, the following weight and center of gravity is assumed for the fender product ePANEL 2.000 ft Assumed Vertical Extension of Fender Panel Past Centerline of Support Beams

HPANEL 14.00 ft = (NFU - 1) * SFU + 2 * ePANEL Total Height of Assumed Fender Envelope

APANEL 2.33 ft

= tPANEL * HPANEL Cross-Sectional Area of Panel tHF 4.00 in = (2 * tPANEL) For Horizontal Members Assume a sides equal to 2 X the Panel Thickness

AHF 0.11 ft

= (tHF)

Assume a Rectangular Cross Section eHF 1.000 ft Assumed Distance from Outside of Fender Support Beam to Center of Gravity of Fender Product

WHF 0.200 klf Weight of Assumed Fender Product

WCF 0.02 klf = γCF * APANEL / NFU Weight of Assumed Composite Panel per Support Beam

WPF 0.06 klf Recall Self Weight of Fender Support Beam wDL 0.28 klf = 1.10 * (WHF + WPF) Total Assumed Dead Load per beam Assume 110% for contingency

Mv D-I -5.61 k-ft = -0.125 wDL * LPF

Maximum Moment due to Dead Loads at Center Support

Mv D-M 3.14 k-ft = 0.07 * wDL * LPF

Maximum Moment due to Dead Loads along Span

Vv D_E 1.34 kips = (3/8) * wDL * LPF Maximum Shear at End due to Dead Loads

Rv D_E 1.34 kips = (3/8) * wDL * LPF Maximum Reaction at End due to Dead Loads

Vv D_I 2.23 kips = (5/8) * wDL * LPF Maximum Shear at Intermediate Support due to Dead Loads

Rv D_I 4.46 kips = (10/8) * wDL * LPF Maximum Reaction at Intermediate Support due to Dead Loads

Full

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.2 Vertical Loads (cont.)

4.2.2 Dead Load of Grating, Channel, and Post

pGR 25.000 psf Assumed Weight of 1" Steel Grating

WCh 20.000 plf Weight of C9X20

WP 53.000 plf Weight of Existing 12 BP 53

Figure B.4: Tributary Width and Area of Channel Strut (in blue), Channel Cantilever (in pink) and Post (in Green)

Grating will be directly supported by the channels, which will transfer load to the post and the cell wall.

TLD 1968 Reconstruction Drawings, Drawing 5

WT-S 4.000 ft Average Tributary Width of Strut

AT-P 8.830 ft

Tributary Area of Post wv-D-Ch 0.12 klf = WCh + pGR * WT-S Dead Load Applied to Channel

Pv-D-P 0.22 kips = pGR * AT-P Maximum Dead Load Applied to Post

Mv D-Ch 0.06 k-ft = wv-D-Ch * LCS / 12 Maximum Moment due to Dead Load on Channel (with Welded Fixed Connections)

Vv D-Ch 0.15 kips = wv-D-Ch * LCS / 2 Maximum Shear due to Dead Load on Channel

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.2 Vertical Loads (cont.)

4.2.2 Gravity Loads

4.2.2.1 Mud / Sediment Accumulating on Section

Assume Mud Collects in Space between Beam Flanges hWELL 4.82 in = (bPF-f - tPF-w) / 2 Height of Empty Space above Beam Web bWELL 10.92 in = dPF - 2 * tPF-f Width of Empty Space above Beam Web wv G-m 0.05 klf = 1.10 * γE * (hWELL * bWELL) Assumed Weight of Mud Collected in Beam (Assume 110%)

4.2.2.2 Atmospheric Ice forming around Section

Assume that Ice forms in a certain thickness, tICE around every component and that an ice collar forms around the fender support beams. The size of the collar is assumed to be equal to the empty space between the fender support beams and the fender system components.

Because the Fender product is to be chosen by the contractor, a width of possible fender locations is assumed in this calculation.

bHF 2.00 ft = 2 * eHF Assumed Width of Fender Envelope tICE 1.000 in Nominal Ice Thickness ASCE 7-16 Fig. 10.4-2

Tc 5.000 °F Temperatures Concurrent with Ice Thicknesses from Freezing Rain ASCE 7-16 Fig. 10.6-1 h 18.10 ft = ELT - ELLW Conservatively Consider Height of Structure over Low Water Elevation fz 1.00 = (z / 33) 0.1

Height Factor, Maximum 1.4, Minimum 1.0 ASCE 7-16 Eq. 10.4-4 td 0.80 in = Ii * tICE * fz * Kzt 0.35

Design Ice Thickness for Freezing Rain ASCE 7-22 Eq. 10.4-5

Dc-HF 33.94 in = √(bHF

+ SFU

) Characteristic Dimension for Panel (Rectangular Envelope) ASCE 7-16 Fig. 10.4-1

Dc-BEAM 15.77 in = √(bPF-f + dPF

) Characteristic Dimension for Beam (W-Shape Cross Section) ASCE 7-16 Fig. 10.4-1

Ai-PANEL 7.12 in

Cross Sectional Area of Ice on Panel ASCE 7-16 Fig. 10.4-1

Ai-HF 7.12 in

Assumed Cross Sectional Area of Ice on Fender Envelope ASCE 7-16 Fig. 10.4-1

Ai-BEAM 3.32 in

Cross Sectional Area of Ice on Beam ASCE 7-16 Fig. 10.4-1

Ai-ES 585.60 in

= SFU * (2 * dPF) Cross Sectional Area of Ice Collar Between Fender Support Beams, Assume collar width is twice the depth of the beam wv G-i-PANEL 0.000 klf = γI * Ai-PANEL / NFU Weight of Atmospheric Ice on Assumed Panel wv G-i-HF 0.003 klf = γI * Ai-HF Weight of Atmospheric Ice on Assumed Horizontal Fender wv G-i-BEAM 0.001 klf = γI * Ai-BEAM Weight of Atmospheric Ice on Fender Support Beam wv G-i-COLL 0.228 klf = γI * Ai-ES Weight of Ice Collar Between Fender Support Beams wv G-i 0.23 klf = wv G-i-PANEL + wv G-i-HF + wv G-i-BEAM + wv G-i-ES Weight of Ice on each Beam

4.2.2.3 Snow Loads

pg 40.000 psf Ground Snow Load UFC 3-301-01 Tool

Ce 0.800 Exposure Factor ASCE 7-16 Table 7.3-1

Ct 1.200 Thermal Factor ASCE 7-16 Table 7.3-2 pf 21.50 psf = 0.7 * Ce * Ct * Is * pg ASCE 7-16 Eq. 7.3-1 bf 24.40 in = 2 * dPF Assume Snow resting on Surface Width Equal to twice the Fender Support Beam Depth wv G-s 0.04 klf = bf-SNOW * pf Weight of Snow on each Beam

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.2 Vertical Loads (cont.)

4.2.2.4 Total Gravity Loads

wv G-wI 0.28 klf = wv G-m + wv G-i Total Weight without snow & with Atmospheric Ice

Mv GwI-I -5.54 k-ft = -0.125 * wv-GwI * LPF

Maximum Moment due to Gravity Loads with Ice at Center Support

Mv GwI-M 3.10 k-ft = 0.07 * wv-GwI * LPF

Maximum Moment due to Gravity Loads with Ice along Span

Vv GwI_E 1.32 kips = (3/8) * wv-GwI * LPF Maximum Shear at End due to Gravity Loads with Ice

Rv GwI_E 1.32 kips = (3/8) * wv-GwI * LPF Maximum Reaction at End due to Gravity Loads with Ice

Vv GwI_I 2.20 kips = (5/8) * wv-GwI * LPF Maximum Shear at Intermediate Support due to Gravity Loads with Ice

Rv GwI_I 4.41 kips = (10/8) * wv-GwI * LPF Maximum Reaction at Intermediate Support due to Gravity Loads with Ice wv G-nI 0.09 klf = wv G-m + wv G-s Total Weight with snow & without Atmospheric Ice

Mv GnI-I -1.82 k-ft = -0.125 * wv-GnI * LPF

Maximum Moment due to Gravity Loads without Ice at Center Support

Mv GnI-M 1.02 k-ft = 0.07 * wv-GnI * LPF

Maximum Moment due to Gravity Loads without Ice along Span

Vv GnI_E 0.43 kips = (3/8) * wv-GnI * LPF Maximum Shear at End due to Gravity Loads without Ice

Rv GnI_E 0.43 kips = (3/8) * wv-GnI * LPF Maximum Reaction at End due to Gravity Loads without Ice

Vv GnI_I 0.72 kips = (5/8) * wv-GnI * LPF Maximum Shear at Intermediate Support due to Gravity Loads without Ice

Rv GnI_I 1.45 kips = (10/8) * wv-GnI * LPF Maximum Reaction at Intermediate Support due to Gravity Loads without Ice

4.2.3 Weight of Water (Hydrostatic Buoyancy)

Ab-PF 69.63 in

= APF + hWELL * bWELL Area of Beam + Air Trapped in Void below Web

Ab-T 4.00 ft

= bHF * SFU Total Area of Displaced Water per support beam wv Hs 0.00 klf = γW * Ab-T Total Buoyancy Force per Beam

Mv Hs-I 0.00 k-ft = 0.125 * wv-Hs * LPF

Maximum Moment due to Buoyancy Loads at Center Support

Mv Hs-M 0.00 k-ft = -0.07 * wv-Hs * LPF

Maximum Moment due to Buoyancy Loads along Span

Vv Hs_E 0.00 kips = -(3/8) * wv-Hs * LPF Maximum Shear at End due to Buoyancy Loads

Rv Hs_E 0.00 kips = -(3/8) * wv-Hs * LPF Maximum Reaction at End due to Buoyancy Loads

Vv Hs_I 0.00 kips = -(5/8) * wv-Hs * LPF Maximum Shear at Intermediate Support due to Buoyancy Loads

Rv Hs_I 0.00 kips = -(10/8) * wv-Hs * LPF Maximum Reaction at Intermediate Support due to Buoyancy Loads

Because the hydrostatic forces are significantly lower than that of the Dead + Gravity Loads, these loads will be conservatively ignored.

4.2.4 Vertical Live Loads on Top of Hydraulic Cell

pLL 100.000 lbs/ft

Live Load EM 1110-2-2107 4.2.11

There is no live load expected to be on top of the fenders or on their support members. However, there is expected live load on the grating at the top of the Post and its connected channels. Therefore, the live load as shown will be applied to the post and channel strut checks.

wv-L-Ch 0.40 klf = pLL * WT-S Live Load Applied to Channel

Pv-L-P 0.88 kips = pLL * AT-P Maximum Live Load Applied to Post

Mv L-Ch 0.21 k-ft = wv-L-Ch * LCS / 12 Maximum Moment due to Live Load on Channel (with Welded Fixed Connections)

Vv L-Ch 0.50 kips = wv-L-Ch * LCS / 2 Maximum Moment due to Buoyancy Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads

4.3.1 Flood Load

4.3.1.1 Hydrostatic Lateral Load

Because the fender supports do not retain water, the water level will be the same on either side of the fenders. Therefore, there is no net Hydrostatic

Lateral Load wl Hs 0.000 klf

Ml Hs-I 0.00 k-ft = -0.125 * wl-Hs * LPF

Maximum Moment due to Lateral Hydrostatic Loads at Center Support

Ml Hs-M 0.00 k-ft = 0.07 * wl-Hs * LPF

Maximum Moment due to Lateral Hydrostatic Loads along Span

Vl Hs_E 0.00 kips = (3/8) * wl-Hs * LPF Maximum Shear at End due to Lateral Hydrostatic Loads

Rl Hs_E 0.00 kips = (3/8) * wl-Hs * LPF Maximum Reaction at End due to Lateral Hydrostatic Loads

Vl Hs_I 0.00 kips = (5/8) * wl-Hs * LPF Maximum Shear at Intermediate Support due to Lateral Hydrostatic Loads

Rl Hs_I 0.00 kips = (10/8) * wl-Hs * LPF Maximum Reaction at Intermediate Support due to Lateral Hydrostatic Loads

4.3.1.2 Hydrodynamic Lateral Load

Hd 1.250 ft Hydrodynamic Temporal Head EM 1110-2-2107 E.2.8 wl Hd 0.16 klf = (γw * Hd) * SFU Hydrodynamic Temporal Head Assume 110% for contingency

Ml Hd-I -3.08 k-ft = -0.125 * wl-Hd * LPF

Maximum Moment due to Lateral Hydrodynamic Loads at Center Support

Ml Hd-M 1.73 k-ft = 0.07 * wl-Hd * LPF

Maximum Moment due to Lateral Hydrostatic Loads along Span

Vl Hd_E 0.74 kips = (3/8) * wl-Hd * LPF Maximum Shear at End due to Lateral Hydrodynamic Loads

Rl Hd_E 0.74 kips = (3/8) * wl-Hd * LPF Maximum Reaction at End due to Lateral Hydrodynamic Loads

Vl Hd_I 1.23 kips = (5/8) * wl-Hd * LPF Maximum Shear at Intermediate Support due to Lateral Hydrodynamic Loads

Rl Hd_I 2.45 kips = (10/8) * wl-Hd * LPF Maximum Reaction at Intermediate Support due to Lateral Hydrodynamic Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.1 Flood Load (cont.)

4.3.1.3 Wave Load

Without a detailed hydrodynamic study, ASCE 7-16 was used for wave loads ds 30.47 ft = 0.65 * (ELBF - ELG) Local Stillwater Depth ASCE 7-16 Eq. 5.4-3

Hb 23.77 ft = 0.78 * ds Breaking Wave Height ASCE 7-16 Eq. 5.4-2

Cp 1.60 Dynamic pressure coefficient ASCE 7-16 Table 5.4-1

Pmax 5.32 lbs/ft

= Cp * γW * ds + 1.2 * γW * ds Max Dynamic + Static Wave Pressures ASCE 7-16 Eq. 5.4-5

Ft-V 241.03 lbs/ft = 1.1 * Cp * γW * ds + 2.4 * γW * ds

Breaking Wave Force against wall ASCE 7-16 Eq. 5.4-6

From ASCE 7-16 dEP 11.780 in Depth of Post tEP-w 0.436 in Web Thickness AISC 4 bEP-f 12.046 in Flange Width tEP-f 0.436 in Flange Thickness AISC 4

D 16.86 in = 1.4 * bEP-f ASCE 7-16 Eq. 5.4.4

CD 2.250 Coefficient of drag for breaking waves (Used square piles or columns) ASCE 7-16 Eq. 5.4.4

FD 55.73 lbs/ft = 0.5 * γW * CD * D * Hb

ASCE 7-16 Eq. 5.4.4

Ft 241.03 lbs/ft = Max of Ft-V & FD ASCE 7-16 Eq. 5.4.9 α 45.000 degrees Assumed Angle of Wave Approach to Mooring Pier wl Hw 0.12 lbs/ft = Ft * sin α ASCE 7-16 Eq. 5.4.9

Ml Hw-I -2.38 k-ft = -0.125 * wl-Hw * LPF

Maximum Moment due to Lateral Wave Loads at Center Support

Ml Hw-M 1.33 k-ft = 0.07 * wl-Hw * LPF

Maximum Moment due to Lateral Wave Loads along Span

Vl Hw_E 0.57 kips = (3/8) * wl-Hw * LPF Maximum Shear at End due to Lateral Wave Loads

Rl Hw_E 0.57 kips = (3/8) * wl-Hw * LPF Maximum Reaction at End due to Lateral Wave Loads

Vl Hw_I 0.95 kips = (5/8) * wl-Hw * LPF Maximum Shear at Intermediate Support due to Lateral Wave Loads

Rl Hw_I 1.89 kips = (10/8) * wl-Hw * LPF Maximum Reaction at Intermediate Support due to Lateral Wave Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.2 Impact Load

Impact equations due to Debris, Ice Floe, and Barge assume that the impact forces are directed perpendicular to the structure. However, the mooring pier is oriented parallel to the Hudson River flow. EM 1110-2-3402 provides guidance on the design of lock walls which similarily aren't perpendicular to the flow of water. The EM provides angles of approach to break the impact force into force components parallel and perpendicular to the structure.

While these angles are preliminary estimates for Barge Impact Forces, it is assumed that they also apply to debris and ice floe. This is considered a a conservative assumption since barges have more control over their bearing and their speed.

θBI_US 10.0 ° Max Angle Between Fender and Barge Trajectory in Usual Conditions EM 1110-2-3402 Table D.3 θBI_UN 20.0 ° Max Angle Between Fender and Barge Trajectory in Unusual Conditions EM 1110-2-3402 Table D.3 θBI_EX 25.0 ° Max Angle Between Fender and Barge Trajectory in Extreme Conditions EM 1110-2-3402 Table D.3

Because all Impact Forces are applied in extreme principal loading in EM 1110-2-2107 Table 4.1, Only the Extreme Angle will be used for these calculations.

For Concentrated Impact Forces, the controlling location of the force differs depending on whether you are calculating the maximum moment or shear.

To determine these locations, the derivative of the shear and maximum moment equations were calculated to find the max and min based on, a, the distance from the end support to the concentrated load. See the next page for the derivative equations.

AISC 14 Table 3-23

Because b = L PF - a, and a has to be between 0 ft and L PF ...

Mmax = P * aM * (LPF - aM) / (4 * LPF

) * (4 * LPF

- aM * (LPF + aM)) Rearranged Equation for Maximum Moment along Span

M1 = P * aM1 * (LPF - aM1) / (4 * LPF ) * (LPF + aM1) Rearranged Equation for Moment at Center Support

V1 = P * (LPF - aV1) / (4 * LPF

) * (4 * LPF

- aV1 * (LPF + aV1)) Rearranged Equation for Shear at Near End Support

V2 = P * aV2 / (2 * LPF

) * (2 * LPF

+ (LPF - aV2) * (LPF + aV2)) Rearranged Equation for Shear at Center Support

V3 = P * aV3 * (LPF - aV3) / (4 * LPF ) * (LPF + aV3) Rearranged Equation for Shear at Far End Support

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.2 Impact Load (cont.)

Find Location of Applied Load that produces the Maximum Moment along the Span

Mmax = P / (4 * LPF ) * (LPF * aM - aM

) * (4 * LPF

- LPF * aM - aM

)) Expanded Equation for Maximum Moment along Span

Mmax = P / (4 * LPF ) * (aM

- 5 * LPF

* aM

+ 4 * LPF

* aM) Expanded Equation for Maximum Moment along Span dMmax / daM = P / (4 * LPF ) * (4 * aM

- 10 * LPF

* aM + 4 * LPF

) Derivation of Equation for Maximum Moment along Span dMmax / daM = 0 → aM = - 1.75233 * LPF Find values of a where maximum moment occurs

= 0.43232 * LPF

= 1.32001 * LPF

Because the solutions, -1.75233 * L PF & 1.32001 * L PF , are outside the limits of a, the solution, 0.43232 * L PF , will be used.

aM 5.44 ft = 0.43232 * LPF Location of Load that produces the Maximum Moment along Span

Find Location of Applied Load that produces the Maximum Moment along the Span

M1 = P / (4 * LPF

) * aM * (LPF

- aM

) Expanded Equation for Moment at Center Support

M1 = P / (4 * LPF

) * (LPF

* aM - aM

) Expanded Equation for Moment at Center Support dM1 / daM1 = P / (4 * LPF

) * (LPF

- 3 * aM

) Derivation of Equation for Moment at Center Support dM1 / daM1 = 0 → aM1 = ± LPF / √3 Find values of a where maximum moment occurs

Because the solution, -L PF / √3, is outside the limits of a, the solution, L PF / √3, will be used aM1 7.26 ft = LPF / √3 Location of Load that produces the Maximum Moment at Center Support

Find Location of Applied Load that produces the Maximum Shear at Near End Support

V1 = P / (4 * LPF

) * (LPF - aV1) * (4 * LPF

- LPF * aV1 - aV1

)) Expanded Equation for Shear at Near End Support

V1 = P / (4 * LPF

) * (aM

- 5 * LPF

* aM + 4 * LPF

) Expanded Equation for Shear at Near End Support dV1 / daV1 = P / (4 * LPF ) * (3 * aM

- 5 * LPF

) Derivation of Equation for Shear at Near End Support dV1 / daV1 = 0 → aV1 = ± 5 * LPF / √3 Find values of a where maximum shear occurs

Because the calculated solutions are outside the limits of a, the location of the support itself will be a V1 aV1 0.00 ft Location of Load that produces the Maximum Shear at Near End Support

Find Location of Applied Load that produces the Maximum Shear at Center Support

V2 = P * aV2 / (2 * LPF

) * (2 * LPF

+ LPF

- aV2

) Expanded Equation for Shear at Center Support

V2 = P / (2 * LPF

) * (3 * LPF

* aV2 - aV2

) Expanded Equation for Shear at Center Support dV2 / daV2 = P / (2 * LPF

) * (3 * LPF

- 3 * aV2

) Derivation of Equation for Shear at Center Support dV2 / daV2 = 0 → aV2 = LPF Find values of a where maximum shear occurs aV2 12.58 ft = LPF Location of Load that produces the Maximum Shear at Center Support

Find Location of Applied Load that produces the Maximum Shear at Far End Support

V3 = P * aV3 * (LPF

- aV3

) / (4 * LPF

) Expanded Equation for Shear at Far End Support

V3 = P * (LPF

* aV3 - aV3

) / (4 * LPF

) Expanded Equation for Shear at Far End Support dV3 / daV3 = P * (LPF

- 3 * aV3

) / (4 * LPF

) Derivation of Equation for Shear at Far End Support dV3 / daV3 = 0 → aM1 = ± LPF / √3 Find values of a where maximum shear occurs

Because the solution, -L PF / √3, is outside the limits of a, the solution, L PF / √3, will be used aV3 7.26 ft = LPF / √3 Location of Load that produces the Maximum Shear at Far End Support

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.2 Impact Load (cont.)

4.3.2.1 Debris/Ice Impact Load

4.3.2.1.1 Debris Impact Load

g 32.200 ft/s

Recall Gravitational Acceleration

W 1.000 kips Debris Weight ASCE 7-16 C5.4.5

Δt 0.030 seconds Impact Duration ASCE 7-16 C5.4.5

Vb 31.32 ft/s = VW-max Maximum Velocity of Object (Assume Equivalent to Velocity of Water)

CI 0.600 Importance Coefficient ASCE 7-16 Table C5.4-1

CO 0.800 Orientation Coefficient ASCE 7-16 Eq. C5.4-3

CD 1.000 Depth Coefficient A-Zone, Stillwater Depth > 5ft ASCE 7-16 Table C5.4-2

CB 1.000 Blockage Coefficient No Screening 100 ft upstream of Mooring Pier ASCE 7-16 Table C5.4-3

K 3.12E-04 k / ft = Δ / P = 0.015 * LPF / (Es * IPF-x) Stiffness of two-span continuous fender-support beam AISC 15th Ed. Table 3-23 30 mB 0.05 k / (ft/s ) = WPF * LPF-T / g Mass of two-span continuous fender-support beam fn 0.08 seconds = √(K / mB) Natural Frequency of Two-Span Continuous fender-support beam

Δt / fn 0.36 Ratio of Impact Duration to Natural Period for Response Ratio

RMAX 1.28 Interpolated Response Ratio for Half-Sine Wave Impulsive Loads ASCE 7-16 Table C5.4-4

Fd-IM 31.41 kips = π * W * Vb * CI * CO * CD * CB * RMAX / (2 * g * Δt) Debris Impact Load ASCE 7-16 Eq. C5.4-3

Fd-IM-EX 13.28 kips = Fd-IM * sin (θBI_EX) Debris Impact Load Perpendicular to Structure with impact force orientation

Fd-IMA-EX 28.47 kips = Fd-IM * cos (θBI_EX) Debris Impact Load Parallel to Structure with impact force orientation

Mmax 34.63 k-ft Maximum Moment at Point of Load due to Fd_IM See Figure for M max equation with F d_IM applied at a M

M1 -16.06 k-ft Maximum Moment at Center Support due to Fd_IM See Figure for M 1 equation with F d_IM applied at a M1

V1 13.28 kips Maximum Shear at near end support due to Fd_IM See Figure for V 1 equation with F d_IM applied at a V1

V2 -13.28 kips Maximum Shear at intermediate support due to Fd_IM See Figure for V 2 equation with F d_IM applied at a V2

V3 1.28 kips Maximum Shear at far end support due to Fd_IM See Figure for V 3 equation with F d_IM applied at a V3

Md-IM-I -16.06 k-ft See M1 at aM Maximum Moment due to Debris Impact Loads at Center Support

Md-IM-M 34.63 k-ft See Mmax at aM Maximum Moment due to Debris Impact Loads along Span

Vd-IM_E 13.28 kips Max of V1 at aV1 or V3 at aV3 Maximum Shear at End due to Debris Impact Loads

Rd-IM_E 13.28 kips Max of V1 at aV1 or V3 at aV3 Maximum Reaction at End due to Debris Impact Loads

Vd-IM_I -13.28 kips = V2 Maximum Shear at Intermediate Support due to Debris Impact Loads

Rd-IM_I 12.00 kips = -(V2 + V3) Maximum Reaction at Intermediate Support due to Debris Impact Loads

Pd-IM 28.47 kips = FBIA_EX Maximum Longitudinal Force Applied by Debris Impact Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.2 Impact Load (cont.)

4.3.2.1 Debris/Ice Impact Load

4.3.2.1.2 Ice Impact Load

wl-IM-p 0.500 klf Ice Impact Load EM 1110-2-2502 6.12.3 wl-IM 0.21 klf = wI-IM-p * sin (θBI_EX) Ice Impact Load Perpendicular to Structure with impact force orientation wl-IMA 0.45 klf = wI-IM-p * cos (θBI_EX) Ice Impact Load Parallel to Structure with impact force orientation

Ml IM-I -4.18 k-ft = -0.125 * wl-IM * LPF

Maximum Moment due to Ice Impact Loads at Center Support

Ml IM-M 2.34 k-ft = 0.07 * wl-IM * LPF

Maximum Moment due to Ice Impact Loads along Span

Vl IM_E 1.00 kips = (3/8) * wl-IM * LPF Maximum Shear at End due to Ice Impact Loads

Rl IM_E 1.00 kips = (3/8) * wl-IM * LPF Maximum Reaction at End due to Ice Impact Loads

Vl IM_I 1.66 kips = (5/8) * wl-IM * LPF Maximum Shear at Intermediate Support due to Ice Impact Loads

Rl IM_I 3.32 kips = (10/8) * wl-IM * LPF Maximum Reaction at Intermediate Support due to Ice Impact Loads

PI-IM 11.40 kips = wl-IMA * LPF-T Maximum Longitudinal Force Applied by Ice Impact Loads

4.3.2.2 Barge Impact Load

In the 2016 Troy Lock and Dam Miter Gate Design Computations, it is stated that this is a much larger barge than is expected at this location.

Therefore, this design is conservative.

IBARGE 112.0 kips Maximum Unsymmetric Barge Impact Force 2016 Troy Lock & Dam Miter Gate Design

IBARGE-s 179.2 kips Maximum Symmetric Barge Impact Force 2016 Troy Lock & Dam Miter Gate Design

Because of the size of the barge, assume that the impact load will be equally shared by three fender support beams

As per EM 1110-2-2107 Table 4.1, Only the Extreme Case Barge Impact Force is considered

FBI_EX 25.24 kips = MAX(IBARGE, IBARGE-s) * sin(θBI_EX) / 3 Barge Impact Force in Extreme Conditions Perpendicular to Mooring Pier

FBIA_EX 54.14 kips = MAX(IBARGE, IBARGE-s) * cos(θBI_EX) / 3 Barge Impact Force in Extreme Conditions Parallel to Mooring Pier

Mmax 65.85 k-ft Maximum Moment at Point of Load due to FBI_EX See Figure for M max equation with F BI_EX applied at a M

M1 -30.55 k-ft Maximum Moment at Center Support due to FBI_EX See Figure for M 1 equation with F BI_EX applied at a M1

V1 25.24 kips Maximum Shear at near end support due to FBI_EX See Figure for V 1 equation with F BI_EX applied at a V1

V2 -25.24 kips Maximum Shear at intermediate support due to FBI_EX See Figure for V 2 equation with F BI_EX applied at a V2

V3 2.43 kips Maximum Shear at far end support due to FBI_EX See Figure for V 3 equation with F BI_EX applied at a V3

MBI-I -30.55 k-ft See M1 at aM Maximum Moment due to Extreme Barge Impact Loads at Center Support

MBI-M 65.85 k-ft See Mmax at aM Maximum Moment due to Extreme Barge Impact Loads along Span

VBI_E 25.24 kips Max of V1 at aV1 or V3 at aV3 Maximum Shear at End due to Extreme Barge Impact Loads

RBI_E 25.24 kips Max of V1 at aV1 or V3 at aV3 Maximum Reaction at End due to Extreme Barge Impact Loads

VBI_I -25.24 kips = V2 Maximum Shear at Intermediate Support due to Extreme Barge Impact Loads

RBI_I 22.82 kips = -(V2 + V3) Maximum Reaction at Intermediate Support due to Extreme Barge Impact Loads

PBI 54.14 kips = FBIA_EX Maximum Longitudinal Force Applied by Extreme Barge Impact Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.3 Wind Load

4.3.3.1 Wind Load

Vz 102.000 mph Basic Wind Speed for Risk Category I UFC 3-301-01 Tool α 11.50 Terrain Exposure Constant ASCE 7-16 Table 26.11-1 zg 1935.00 ft Terrain Exposure Constant ASCE 7-16 Table 26.11-1

Kh 0.89 = 2.01 * ((Maximum of h or 15 ft) / zg) 2 / α

Velocity Pressure Exposure Coefficient ASCE 7-16 Table 26.10-1

K1 The Wind is traveling over water, therefore Topographic Effects are not considered ASCE 7-16 Fig. 26.8-1

K2 The Wind is traveling over water, therefore Topographic Effects are not considered ASCE 7-16 Fig. 26.8-1

K3 The Wind is traveling over water, therefore Topographic Effects are not considered ASCE 7-16 Fig. 26.8-1

Kzt 1.00 = (1 + K1 * K2 * K3)

Topographic Factor ASCE 7-16 Eq. 26.8-1

Kd 0.850 Wind Directionality Factor for wall / open sign ASCE 7-16 Table 26.6-1

Ke 1.000 Ground Elevation Factor (Conservative) ASCE 7-16 Table 26.9-1 qh 0.02 ksf = 0.00256 * Kh * Kzt * Kd * Ke * Vb

ASCE 7-16 Eq. 26.10-1

Cf 2.000 Wind Force Coefficient ASCE 7-16 10.5.2, 10.5.3, Fig. 29.3-1 & 29.4-2

Fender System could be an open frame or a solid wall. The most conservative factor is used amongst the two.

G 0.850 Gust-Effect Factor ASCE 7-16 26.11.1 wl w-b 0.07 klf = qh * G * Cf * SFU Wind Load on each Fender Support Beam ASCE 7-16 Eq. 29.3-1 / Eq. 29.4-1

Ml w-b-I -1.36 k-ft = -0.125 * wl-w-b * LPF

Maximum Moment due to Lateral Wind Loads at Center Support

Ml w-b-M 0.76 k-ft = 0.07 * wl-w-b * LPF

Maximum Moment due to Lateral Wind Loads along Span

Vl w-b_E 0.32 kips = (3/8) * wl-w-b * LPF Maximum Shear at End due to Lateral Wind Loads

Rl w-b_E 0.32 kips = (3/8) * wl-w-b * LPF Maximum Reaction at End due to Lateral Wind Loads

Vl w-b_I 0.54 kips = (5/8) * wl-w-b * LPF Maximum Shear at Intermediate Support due to Lateral Wind Loads

Rl w-b_I 1.08 kips = (10/8) * wl-w-b * LPF Maximum Reaction at Intermediate Support due to Lateral Wind Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.3 Horizontal Loads (cont.)

4.3.3 Wind Load (cont.)

4.3.3.2 Wind Load Concurrent with Atmospheric Ice from Freezing Rain

Vc 45.000 mph Gust Speeds Concurrent with Ice Thicknesses from Freezing Rain ASCE 7-16 Fig. 10.4-2 qh-i 0.00 ksf = 0.00256 * Kh * Kzt * Kd * Ke * Vc

ASCE 7-16 Eq. 26.10-1 wl w-i 0.01 klf = qh-i * G * Cf * SFU Wind Load on each Fender Support Beam ASCE 7-16 Eq. 29.3-1 / Eq. 29.4-1

Ml w-i-I -0.26 k-ft = -0.125 * wl-w-i * LPF

Maximum Moment due to Lateral Wind Loads at Center Support

Ml w-l-M 0.15 k-ft = 0.07 * wl-w-I * LPF

Maximum Moment due to Lateral Wind Loads along Span

Vl w-i_E 0.06 kips = (3/8) * wl-w-i * LPF Maximum Shear at End due to Lateral Wind Loads

Rl w-i_E 0.06 kips = (3/8) * wl-w-i * LPF Maximum Reaction at End due to Lateral Wind Loads

Vl w-i_I 0.11 kips = (5/8) * wl-w-i * LPF Maximum Shear at Intermediate Support due to Lateral Wind Loads

Rl w-i_I 0.21 kips = (10/8) * wl-w-i * LPF Maximum Reaction at Intermediate Support due to Lateral Wind Loads

4.3.3.3 Serviceability Wind Load

Vc 75.000 mph Gust Speeds with 10 Mean Recurrence Interval (for Service Loads) ASCE 7-16 Fig. CC.2-1 qh-S 0.01 ksf = 0.00256 * Kh * Kzt * Kd * Ke * Vc

ASCE 7-16 Eq. 26.10-1 wl w-S 0.04 klf = qh-S * G * Cf * SFU Wind Load on each Fender Support Beam ASCE 7-16 Eq. 29.3-1 / Eq. 29.4-1

Ml w-S-I -0.73 k-ft = -0.125 * wl-w-S * LPF

Maximum Moment due to Lateral Wind Loads at Center Support

Ml w-S-M 0.41 k-ft = 0.07 * wl-w-S * LPF

Maximum Moment due to Lateral Wind Loads along Span

Vl w-S_E 0.18 kips = (3/8) * wl-w-S * LPF Maximum Shear at End due to Lateral Wind Loads

Rl w-S_E 0.18 kips = (3/8) * wl-w-S * LPF Maximum Reaction at End due to Lateral Wind Loads

Vl w-S_I 0.29 kips = (5/8) * wl-w-S * LPF Maximum Shear at Intermediate Support due to Lateral Wind Loads

Rl w-S_I 0.58 kips = (10/8) * wl-w-S * LPF Maximum Reaction at Intermediate Support due to Lateral Wind Loads

4.3.4 Thermally Expanding Ice

wl-ICE 5.0 klf Ice Impact Load Thermally Expanding Ice EM 1110-2-2107 4.2.7

Ml ICE 98.83 k-ft = 0.125 * wl-ICE * LPF

Maximum Moment due to Thermally Expanding Ice Loads at Center Support

Ml ICE-M -55.35 k-ft = -0.07 * wl-ICE * LPF

Maximum Moment due to Thermally Expanding Ice Loads along Span

Vl ICE_E -23.58 kips = -(3/8) * wl-ICE * LPF Maximum Shear at End due to Thermally Expanding Ice Loads

Rl ICE_E -23.58 kips = -(3/8) * wl-ICE * LPF Maximum Reaction at End due to Thermally Expanding Ice Loads

Vl ICE_I -39.30 kips = -(5/8) * wl-ICE * LPF Maximum Shear at Intermediate Support due to Thermally Expanding Ice Loads

Rl ICE_I -78.59 kips = -(10/8) * wl-ICE * LPF Maximum Reaction at Intermediate Support due to Thermally Expanding Ice Loads

4.4 Self-Straining Loads in Fender Support Beams

The bolted connections will be pretensioned. While they are not intended to be slip-critical, the design still assumes that any axial expansion in the steel beam is restrained.

αT-St 6.50E-06 / °F Steel Temperature Expansion Coefficient AISC 15 Page 2-39

Tlow -30.000 °F Design Low Temperature for Cold Climates AASHTO Bridge Table 3.12.2.1-1

Thigh 120.000 °F Design High Temperature for Cold Climates AASHTO Bridge Table 3.12.2.1-1

ΔT-St 0.15 in = αT-St * (Thigh - Tlow) * LPF Design Expansion in beam due to Extreme Temperature Changes

Size Slotted Hole to accommodate this expansion.

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.5 Earthquake Loading

The Earthquake Loading was determined assuming site class B ground

PGA 10.60% G Peak Ground Acceleration UFC 3-301-01 Tool

SS 19.80% G MCER Spectral Response Acceleration Parameter at 0.2 seconds for Site Class BC UFC 3-301-01 Tool

S1 6.00% G MCER Spectral Response Acceleration Parameter at 1 second for Site Class BC UFC 3-301-01 Tool

SMS 17.80% G MCER Spectral Response Acceleration Parameter at short periods, Adjusted for Site Class Effects UFC 3-301-01 Tool

SM1 4.80% G MCER Spectral Response Acceleration Parameter at 1 second, Adjusted for Site Class Effects UFC 3-301-01 Tool

4.5.1 Earthquake-Generated Inertial Forces Loading

HPIER 33.90 ft = ELT - ELG Pool Depth to Riverbed. Assume entire Pier is submerged EM 1110-2-2107 Figure 4.1 y 7.00 ft = HPANEL / 2 Distance of applied force below pool surface, assume 1/2 Panel EM 1110-2-2107 Figure 4.1 ac 10.60% G = PGA Acceleration at inertial fluid pressures for short, stiff structures EM 1110-2-2107 4.4.6.6 pEQ-W 0.09 ksf = (7/8) * γW * ac * √(H* y) Earthquake-Generated Inertial Pressures at depth, y EM 1110-2-2107 Eq. 4.3 wEQ-W 0.18 klf = pEQ-W * SFU Earthquake-Generated Inertial Loading on Single Fender Support Beam

MEQ-i -3.52 k-ft = -0.125 * wEQ-W * LPF

Maximum Moment due to Earthquake Loads at Center Support

MEQ-M 1.97 k-ft = 0.07 * wEQ-W * LPF

Maximum Moment due to Earthquake Loads along Span

VEQ_E 0.84 kips = (3/8) * wEQ-W * LPF Maximum Shear at End due to Earthquake Loads

REQ_E 0.84 kips = (3/8) * wEQ-W * LPF Maximum Reaction at End due to Earthquake Loads

VEQ_I 1.40 kips = (5/8) * wEQ-W * LPF Maximum Shear at Intermediate Support due to Earthquake Loads

REQ_I 2.80 kips = (10/8) * wEQ-W * LPF Maximum Reaction at Intermediate Support due to Earthquake Loads

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.5 Unfactored Load Summary

4.5.2 Unfactored Loads at Fender Support Members

Gravity Gravity Impact Impact Impact Wind Wind w/ Ice w/o Ice Debris Ice Barge on Ice (Service)

D GICE G L Hd Hw IX IMD IMICE BI WICE W WS EQ

Mv-I (k-ft) -5.61 -5.54 -1.82

Mv-M (k-ft) 3.14 3.10 1.02

Vv_E (kip) 1.34 1.32 0.43

Rv_E (kip) 1.34 1.32 0.43

Vv_I (kip) 2.23 2.20 0.72

Rv_I (kip) 4.46 4.41 1.45

Ml-I (k-ft) -3.08 -2.38 98.83 -16.06 -4.18 -30.55 -0.26 -1.36 -0.73 -3.52

Ml-M (k-ft) 1.73 1.33 -55.35 34.63 2.34 65.85 0.15 0.76 0.41 1.97

Vl_E (kip) 0.74 0.57 -23.58 13.28 1.00 25.24 0.06 0.32 0.18 0.84

Rl_E (kip) 0.74 0.57 -23.58 13.28 1.00 25.24 0.06 0.32 0.18 0.84

Vl_I (kip) 1.23 0.95 -39.30 -13.28 1.66 -25.24 0.11 0.54 0.29 1.40

Rl_I (kip) 2.45 1.89 -78.59 12.00 3.32 22.82 0.21 1.08 0.58 2.80

P (kip) 28.47 11.40 54.14

T (k-ft)* 5.99 6.16 0.31

*Because the Fender Support Beam Connects to the Post at the Flange, there will be torsion on the connection. Assuming that the connection at the post resists all the torsion from the beam, this calculates the expected torsion in the beam and the connection. Assume that only vertical loads on the fender support beams apply torsion to the connection.

Moment Arm of Fender Support Beam from Outside Face of the Vertical Post xPF 6.10 in = dPF / 2 Moment Arm of Fender Support Beam from Outside Face of the Vertical Post xHF 24.20 in = dPF + eHF Moment Arm of Assumed Fender Product from Outside Face of the Vertical Post xCF 17.20 in = dPF + tHF + tPANEL / 2 Moment Arm of Assumed Fender Panel from Outside Face of the Vertical Post

Recall Vertical Forces

WHF 0.22 klf 110% of the Weight of Assumed Horizontal Fender Dead Load

WCF 0.03 klf 110% of the Weight of Assumed Composite Panel per Support Beam Dead Load

WPF 0.06 klf 110% of the Self Weight of Fender Support Beam Dead Load wv G-m 0.05 klf Recall Assumed Weight of Mud Collected in Beam (Assume 110%) Gravity Load wv G-i-PANEL 0.000 klf Recall Weight of Atmospheric Ice on Assumed Panel Gravity Load wv G-i-HF 0.003 klf Recall Weight of Atmospheric Ice on Assumed Horizontal Fender Gravity Load wv G-i-BEAM 0.001 klf Recall Weight of Atmospheric Ice on Fender Support Beam Gravity Load wv G-i-COLL 0.228 klf Recall Weight of Ice Collar Between Fender Support Beams Gravity Load

Calculate Torsion at Beam

LPF-T 12.58 ft Recall Length of Span Between Hydraulic Cell and Post

TDLb 5.99 k-ft = (WPF * xPF + WHF * xHF) * LPF Torsion on Beam due to Dead Load

TGL-Nib 0.31 k-ft = (wv-G-m * xPF) * LPF Torsion on Beam due to Gravity Load without Ice

TGL-Wib 6.16 k-ft = TGL-NIb + ((wv G-i-HF + wv G-i-COLL) * xHF + wv G-i-BEAM * xPF) * LPF Torsion on due to Gravity Load w/ Ice

Load

Earth-quake WindLiveDead

Hydro-

Dynam.

Wave Ice T Exp

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.5 Unfactored Load Summary (cont.)

4.5.3 Unfactored Loads at Post

4.5.3.1 Torsion at Post Connection

See Equations and Parameters from Previous Section

LPF-T 25.15 ft Recall Total Length of Single Fender Support Beam

TDL 11.97 k-ft = (WPF * xPF + WHF * xHF) * LPF-T Torsion on Connection due to Dead Load

TGL-NI 0.62 k-ft = (wv-G-m * xPF) * LPF-T Torsion on Connection due to Gravity Load without Ice

TGL-WI 12.32 k-ft = TGL-NI + ((wv G-i-HF + wv G-i-COLL) * xHF + wv G-i-BEAM * xPF) * LPF-T Torsion on due to Gravity Load w/ Ice

4.5.3.2 Unfactored Loads applied to the strut per fender support beam

PT = Rv_I + Pv-P

MT = T + Rv_I * dP / 2

VT = Rl_I

Gravity Gravity Impact Impact Impact Wind Wind w/ Ice w/o Ice Debris Ice Barge on Ice (Service)

D GICE G L Hs Hd Hw IX IMD IMICE BI WICE W EQ

Pv-P (kips) 0.22 0.88

PT (kips) 4.68 4.41 1.45 0.88 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

MT (k-ft) 14.16 14.49 1.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

VT (kips) 0.00 0.00 0.00 0.00 2.45 1.89 -78.59 12.00 3.32 22.82 0.21 1.08 0.58 2.80

4.5.4 Unfactored Loads at Struts

Load Dead

Earth-quake Live

Hydro-

Dynam.

Wave Ice T Exp Wind

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.6 Factored Load Combination

4.6.1 Load Factors

By inspection of the unfactored loads, the load combinations that will control in lateral forces towards the mooring pier are those with Ice

Thermal Expansion and Barge Impact as the principal loads. The load combinations that will control in lateral forces away from the mooring pier are those with Earthquake Loads as the principal load. Hydrodynamic, Live, and Wind loads will be companion loads. Wave, Debris Impact, Ice

Impact, Wind on Ice, and Earthquake Forces will not be included as they will not control by inspection.

LC 1 D Max 1.60 1.40

LC 2 D Min 0.00 1.40

LC 3 IX Max 1.20 1.60 1.30 1.00 1.00

LC 4 IX Min 0.90 0.00 1.30 1.00 1.00

LC 5 BI Max 1.20 1.60 1.30 1.00 1.00

LC 6 BI Min 0.90 0.00 1.30 1.00 1.00

LC 7 Max 1.20 1.60 0.00 1.00 0.50

LC 8 Min 0.90 0.00 0.00 1.00 0.50

LC 9 Max 1.20 1.60 0.00 1.00 1.00

LC 10 Min 0.90 0.00 0.00 1.00 1.00

LC S 1 D Max 1.00 1.00

LC S 2 D Min 0.00 1.00

LC S 3 IX Max 1.00 1.00 1.00 1.00 1.00

LC S 4 IX Min 1.00 0.00 1.00 1.00 1.00

LC S 5 BI Max 1.00 1.00 1.00 1.00 1.00

LC S 6 BI Min 1.00 0.00 1.00 1.00 1.00

LC S 7 Max 1.00 1.00 1.00 1.00 1.00

LC S 8 Min 1.00 0.00 1.00 1.00 1.00

LC S 9 Max 1.00 1.00 1.00 1.00 1.00

LC S 10 Min 1.00 0.00 1.00 1.00 1.00

LC F 1 D Max 1.00 1.00

LC F 2 D Min 0.00 1.00

LC F 3 IX Max 1.00 1.00 1.00 1.00 1.00

LC F 4 IX Min 1.00 0.00 1.00 1.00 1.00

LC F 5 BI Max 1.00 1.00 1.00 1.00 1.00

LC F 6 BI Min 1.00 0.00 1.00 1.00 1.00

LC F 7 Max 1.00 1.00 1.00 1.00 1.00

LC F 8 Min 1.00 0.00 1.00 1.00 1.00

LC F 9 Max 1.00 1.00 1.00 1.00 1.00

LC F 10 Min 1.00 0.00 1.00 1.00 1.00

LC N 1 D Max 2.00 2.00

LC N 2 D Min 0.00 2.00

LC N 3 IX Max 2.00 2.00 2.00 2.00 2.00

LC N 4 IX Min 2.00 0.00 2.00 2.00 2.00

LC N 5 BI Max 2.00 2.00 2.00 2.00 2.00

LC N 6 BI Min 2.00 0.00 2.00 2.00 2.00

LC N 7 Max 2.00 2.00 2.00 2.00 2.00

LC N 8 Min 2.00 0.00 2.00 2.00 2.00

LC N 9 Max 2.00 2.00 2.00 2.00 2.00

LC N 10 Min 2.00 0.00 2.00 2.00 2.00

* The Load Factor for Dead Loads will be Shown in γPR for Load Combinations LC 1, LC 2, LC S 1, LC S 2, LC F 1, LC F 2, LC N 1, and LC N 2 as the dead load is the principal load in these combinations.

SERVICE

FINITE FATIGUE

INFINITE FATIGUE

STRENGTH /

EXTREME

Impact (BI)

Service Wind Companion Load

Only

Hydrodynamic Companion

Load Only

Dead (Usual)*

Ice, Thermal Exp

Impact (BI)

Dead (Usual)*

Ice, Thermal Exp

Impact (BI)

Dead (Usual)*

Ice, Thermal Exp

Basic Wind Companion Load

Only

Hydrodynamic Companion

Load Only

Basic Wind Companion Load

Only

Hydrodynamic Companion

Load Only γc_Hd γc_W γc_WS

Dead (Usual)*

Ice, Thermal Exp

Impact (BI)

Basic Wind Companion Load

Only

Hydrodynamic Companion

Load Only

Comb. # Limit State Principal Load Max /

Min γp_D γp_G γp_GICE γpr γc_L

Troy Lock Dam Mooring Pier

SUBJECT

Fender Support Framing Design

Designed by:DSK

Date: 05/02/2024

Checked by: BLP

Date: XX/XX/2024

4. Load Calculations (cont.)

4.6 Factored Load Combination

4.6.2 Factored Loads at Fender Support Members

U = Σγp * Lp + γpr * Lpr + Σγc * Ltc + γc * Ldc Factored Applied Load on Hydraulic Steel Structures EM 1110-2-2107 Eq. 4.2

Axial Torsion

Lateral Vertical Lateral Vertical Lateral Vertical Lateral Vertical (kips) (k-ft)

LC 1 D 0.00 -16.72 0.00 9.37 0.00 3.99 0.00 6.65 0.00 18.24

LC 2 D 0.00 -7.85 0.00 4.40 0.00 1.87 0.00 3.12 0.00 8.38

LC 3 IX 125.40 -15.60 -70.22 8.74 -29.92 3.72 -49.86 6.20 0.00 17.04

LC 4 IX 125.40 -5.05 -70.22 2.83 -29.92 1.20 -49.86 2.01 0.00 5.39

LC 5 BI -42.79 -9.64 87.33 5.40 33.55 2.30 -31.59 3.83 70.38 7.68

LC 6 BI -42.79 -5.05 87.33 2.83 33.55 1.20 -31.59 2.01 70.38 5.39

LC 7 -0.68 -9.64 0.38 5.40 0.16 2.30 0.27 3.83 0.00 7.68

LC 8 -0.68 -5.05 0.38 2.83 0.16 1.20 0.27 2.01 0.00 5.39

LC 9 -3.08 -9.64 1.73 5.40 0.74 2.30 1.23 3.83 0.00 7.68

LC 10 -3.08 -5.05 1.73 2.83 0.74 1.20 1.23 2.01 0.00 5.39

LC S 1 D 0.00 -11.15 0.00 6.25 0.00 2.66 0.00 4.44 0.00 12.15

LC S 2 D 0.00 -5.61 0.00 3.14 0.00 1.34 0.00 2.23 0.00 5.99

LC S 3 IX 95.75 -11.15 -53.62 6.25 -22.84 2.66 -38.07 4.44 0.00 12.15

LC S 4 IX 95.75 -5.61 -53.62 3.14 -22.84 1.34 -38.07 2.23 0.00 5.99

LC S 5 BI -33.63 -7.43 67.57 4.16 25.98 1.77 -24.02 2.95 54.14 6.30

LC S 6 BI -33.63 -5.61 67.57 3.14 25.98 1.34 -24.02 2.23 54.14 5.99

LC S 7 -0.73 -7.43 0.41 4.16 0.18 1.77 0.29 2.95 0.00 6.30

LC S 8 -0.73 -5.61 0.41 3.14 0.18 1.34 0.29 2.23 0.00 5.99

LC S 9 -3.08 -7.43 1.73 4.16 0.74 1.77 1.23 2.95 0.00 6.30

LC S 10 -3.08 -5.61 1.73 3.14 0.74 1.34 1.23 2.23 0.00 5.99

LC F 1 D 0.00 -11.15 0.00 6.25 0.00 2.66 0.00 4.44 0.00 12.15

LC F 2 D 0.00 -5.61 0.00 3.14 0.00 1.34 0.00 2.23 0.00 5.99

LC F 3 IX 95.75 -11.15 -53.62 6.25 -22.84 2.66 -38.07 4.44 0.00 12.15

LC F 4 IX 95.75 -5.61 -53.62 3.14 -22.84 1.34 -38.07 2.23 0.00 5.99

LC F 5 BI -33.63 -7.43 67.57 4.16 25.98 1.77 -24.02 2.95 54.14 6.30

LC F 6 BI -33.63 -5.61 67.57 3.14 25.98 1.34 -24.02 2.23 54.14 5.99

LC F 7 -1.36 -7.43 0.76 4.16 0.32 1.77 0.54 2.95 0.00 6.30

LC F 8 -1.36 -5.61 0.76 3.14 0.32 1.34 0.54 2.23 0.00 5.99

LC F 9 -3.08 -7.43 1.73 4.16 0.74 1.77 1.23 2.95 0.00 6.30

LC F 10 -3.08 -5.61 1.73 3.14 0.74 1.34 1.23 2.23 0.00 5.99

LC N 1 D 0.00 -22.31 0.00 12.49 0.00 5.32 0.00 8.87 0.00 24.30

LC N 2 D 0.00 -11.22 0.00 6.28 0.00 2.68 0.00 4.46 0.00 11.97

LC N 3 IX 191.50 -22.31 -107.24 12.49 -45.68…