887-B399-03_ABS Removable Skeg Structural Calculations_Rev(-)_signed.pdf

NSF MCMURDO OFFLOAD INFRASTRUCTURE 9 June 2023 ABS Removable Skeg Structural Calculations Report 1 Doc. 887-B410-03, Rev -

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

PREPARED FOR:

Moffatt & Nichol Seattle, WA

BY:

Nate M. Seelig, PE

PROJECT ENGINEER

CHECKED:

Andrew L. Girdler, PE

NAVAL ARCHITECT

APPROVED:

Bradley G. Lamkin, PE

PRINCIPAL-IN-CHARGE

DOC. #:

887-B410-03

REV:

FILE:

22105.01

DATE:

9 June 2023

References

1. US Army Corps of Engineers, Scope of Work 3438 NSF McMurdo Station Offload Infrastructure Project Contract Level Design and Specification, MDC Project 3438, W912EE-21-D-0005, Tracking Number 0001.

2. ABS Marine Vessel Rules, 2023.

3. Glosten, Removable Skeg, 887-B410-04, Rev(-), 9 June 2023.

4. Glosten, 887_ABS Removable Skeg Structural Calculations_Rev(-).xlsx.

Revision History

Section Rev Description Date Approved

Summary

The United States Army Corps of Engineers (USACE) is supporting the US National Science Foundation (NSF) to develop a contract level design for the permanent offload infrastructure to support resupply operations at McMurdo Station, Antarctica (Ref. 1). The barge-like floating pier (barge) component of the proposed infrastructure will have a removable skeg attached to the topsides while being towed to its destination. This report presents the results of calculations performed on that removable skeg.

The vessel will be classed ✠A1, Deck Cargo Barge by the American Bureau of Shipping (ABS).

The calculations are based on established ABS regulations for rudders (Ref. 2). The calculations herein show that the proposed design of the removable skeg (Ref. 3) satisfies ABS Marine Vessel requirements for rudders (Ref. 2).

Calculations

Skeg geometry was adopted from other skegs on barges of similar size. The skeg was then modeled as a rudder, and the force and torque on the skeg was determined with standard equations for rudders. Skeg plating and structure were also evaluated (Ref. 2).

The skeg supports (or struts) holding the skeg on the side of the barge were designed to resist skeg torque, skeg force, and ice force. In this calculation, the skeg torque was resolved to a force couple. The capacity of the skeg support to resist bending and shear forces was evaluated (Ref. 2). The weld size and shear area of the skeg supports were also evaluated.

The calculations presented in Appendix A demonstrate that the removable skeg satisfies ABS Marine Vessel Rules Part 3 and 6 requirements for rudders (Ref. 2).

NSF MCMURDO OFFLOAD INFRASTRUCTURE 9 June 2023 ABS Removable Skeg Structural Calculations Report A-1 Doc. 887-B120-01, Rev -

Appendix A Removable Skeg Calculations

Skeg Forces File: 22105 Date: 9-Jun-23 By: NMS / ALG Checked: ZZM

References

1. ABS Marine Vessel Rules, 2023.

Purpose: To develop the force and torque on the skeg using ABS rules for rudders.

Rudder Calculations

Rudder Force

ABS MVR 3-2-14 / 3.1

CR = n kR kc kl A (VR)2 LTf

Ahead Astern CR 48.3 12.1 Ltf Force on rudder (transverse)

108,151 27,038 lb n 0.00123 0.00123 -kR 0.807 0.807 b 8.00 8.00 ft Mean height of submerged rudder area (WL is 8' above base of skeg)

At 152.00 152.00 ft2

A 152.00 152.00 ft2 Total projected area of rudder blade kc 1 1 kl 0.8 0.8 1 for Other/ 0.8 for outside propeller jet.

VR 20 10 kn 20 as indicated by MVR6-1-4/27.3.2

Vd 20.0 20.0 kn

Va 6.5 6.5 kn

Vmin 13.3 13.3 kn

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ABS Removable Skeg Structural Calculations Report

A-2 ABS Calculations: Forces

GLOSTEN | 9 June 2023 Doc. 887-B399-03, Rev -

Rudder Torque

ABS MVR 3-2-14 / 5.3

QR = CR r LTf-ft

Ahead Astern QR 91.7 104.0 Ltf-ft Torque on rudder stock (twist about stock)

2465838 2795365 lb-in

278602.3 315833.9 N-m

CR 48.3 12.1 Ltf r 1.9 8.615642 ft c 19.00 19.00 ft Mean breadth of rudder area α 0.33 0.75 k 0.296545 0.296545 Af 45.07 45.07 ft2 Area of rudder blade fwd stock centerline

A 152.00 152.00 ft2 Whole rudder area

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-3 ABS Calculations: Forces

Skeg Plating

Date: 9-Jun-23 By: NMS Checked: ALG

References

1. ABS Marine Vessel Rules, 2023.

2. 887_ABS Structure Calcs_Rev(-).xlsm

Purpose: To verify plating thickness of the skeg using ABS rules for rudders.

Side, Top, and Bottom Plating

ABS MVR 3-2-14 / 17.3

toffered 0.625 in PASS: Margin = 1.89 treq'd 0.330 in t17.3,min 0.0055 s β SQRT(k1 d + (k2 CR / A) × SQRT(Q) + k3

0.285 in Minimum required

Q 0.76 Ref. 2 ABS MVR 3-2-1 / 5.3 k1 0.305 k2 10.7 k3 0.1 d 8 ft CR 48.28 Ltf

A 152.00 β 1 s 16 in b 24 in 1.5s = diaphragm spacing t_tank 0.25 Ref. 2, ABS MVR 3-2-10 / 3.1 t17.3,tank 0.33 (ABS SBR 3-2-7 / 3.1)

ABS MVR 6-1-4 / 29.5

treq'd 15.5 mm ABS MVR 6-1-2 / 7.3

0.61 in no corrosion/abrasion allowance

Diaphragm Plates

ABS MVR 3-2-14 / 17.5

toffered 0.50 in PASS: Margin = 1.17 treq'd 0.427 in

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-4 ABS Calculations: Plating

Strut Section Modulus

Date: 9-Jun-23 By: NMS Checked: ALG

References

1. ABS Marine Vessel Rules, 2023.

2. ABS Rules for Materials and Welding, 2023.

2. 887_ABS Structure Calcs_Rev(-).xlsm

Purpose: To evaluate section modulus of the skeg struts using ABS rules for rudders.

Strut Force Ahead Astern

QR 91.7 104.0 Ltf-ft Torque on single rudder stock

2,465,838 2,795,365 in-lbs d 80 80 in Distance between strut centerlines Fq 30,823 34,942 lbs Resolve rudder torque, Qr, into force couple in tandem struts CR 48.3 12.1 LTf Force on skeg

CR/2 24.1 6.0 LTf assume each strut shares half rudder force

54,075 13,519 lbs

Cr' 84,898 48,461 lbs total force on each strut

37.9 21.6 LTf

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-5 ABS Calculations: Section Modulus

Strut Moment

Strut-Side Shell Connection

ABS MVR 3-2-A5 / 3.3.2

Ahead Astern Mn 337.95 192.91 Ltf-ft Bending moment in strut (stock)

9,084,125 5,185,318 in-lbs CR = Cr' 37.9 21.6 LT Total force on each strut cl 19 19 ft cu 19 19 ft ll 4.92 4.92 ft lR 8.00 8.00 ft

Strut-Skeg Connection

ABS MVR 3-2-A5 / 3.1.2

Guidelines for calculating bending moment and shear force in rudders and rudder stocks

Ahead Astern M 152 87 Ltf-ft Bending moment in horizontal section of skeg (rudder)

4,075,122 2,326,124 in-lbs z 8.0 8.0 ft CR = Cr' 37.9 21.6 Ltf Total force on each strut

A 152.00 152.00 ft2 cl 19 19 ft cu 19 19 ft lR 8.00 8.00 ft

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-6 ABS Calculations: Section Modulus

Required Section Modulus

ABS Rudders ABS MVR 3-2-14 / 1.3 and 17.1.1

F_yield 51,000 psi AH 36, DH 36 s_umin 71,000 psi n_y 34,000 psi Ymax 49,700 psi Y 49,700 psi e 0.75 - Q 0.75 Ref. 2 (ABS MVR 3-2-14 / 1.3)

Kσ 15,900 psi Kτ 7,300 psi Ke 17,400 psi σb 21,200 psi Bending stress τ 9,733 psi Shear stress σe 27,086 psi Equivalent stress σe 23,200 psi Equivalent stress Q 0.75 allowable 21,200 psi Bending stress

Ahead Astern SMreqd_skeg 192.2 109.7 in3 SMreqd_side 428.5 244.6 in3

Overall Requirements Ahead Astern

SMreqd_skeg 192.2 109.7 SMactual_skeg 195.6 195.6

PASS

Margin is 1

PASS

Margin is

1.8

Ahead Astern SMreqd_shell 428.5 244.6

SMactual_shell 429.3 429.3

PASS

Margin is 1

PASS

Margin is 1.8

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-7 ABS Calculations: Section Modulus

Strut Shear Force

Date: 9-Jun-23 By: NMS Checked: ALG

References

1. 887_ABS Structure Calcs_Rev(-).xlsm

Purpose: To evaluate shear capacity of the skeg struts using ABS rules for rudders.

Shear Stress Athwartship Maximum shear in strut due to rudder force & torque V 37.9 Ltf Total force on each strut

84,898 lbs

Shear area of one strut Av 15.3 in2 Area of middle plates at skeg connection τ_actual 5,544 psi τ_allow 9,733 psi

PASS

Margin is

1.8

Fore/Aft

ABS MVR 6-1-4 / 27.3.3

F 379 LT Shear force for PC6 is using 20 kn speed 849,383 lbs

K3 3.3

D 3961 LT

t 10 in

0.83 ft

Shear area of both struts Av 80.00 in2 Area of top/bottom plates at skeg connection τ_actual 10,617 psi

Yield 50,000 psi τ_allow 28,850 psi

PASS

Margin is

2.7

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-8 ABS Calculations: Shear Force

Welded Attachment

Date: 9-Jun-23 By: NMS Checked: ALG

References

1. Blodgett, O., Design of Welded Structures , 1966.

Rudder Force/Torque

Fp 84,898 lb force normal to connection plane (total force on each strut) r 11 ft moment arm M 969,256 lb-ft moment at center of welded connection

11,631,076 in-lb b 32 in d 60 in Lw 488 in Total weld length (all welds effective as load is normal to connection plate) Zw 7,440 in2 Weld modulus; DC --> x2 w 0.5 in tw 0.35 in f1f 174 lb/in f1m 1,563 lb/in f1 1,737 lb/in τ_actual 4,964 psi τ_allowable 9,733 psi

PASS

Margin is 2

Ice Force

F 424,692 lb force parallel to connection plane (ice load per strut) r 11 moment arm M 4,848,563 lb-ft torque about center of welded connection

58,182,761 in-lb

Lw 128 in only welds aligned with force (fore/aft) are effective Jw 295,563 in3 Weld torsional modulus; DC --> x2 r 34 in f2f 3,318 lb/in f2m 6,693 lb/in f2 10,011 lb/in τ_actual 28,603 psi τ_allowable 28,850 psi

PASS

Margin is

1.01

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-9 ABS Calculations: Welded Attachment

Strut Section Properties

Date: 9-Jun-23 By: NMS Checked: ALG

Side Shell Box Depth 16.5 in

Item Base Height Centroid * Area A*Y A*Y2 Inertia in in in in2 in3 in4 in4

Top Plate 32.00 0.75 0.38 24.00 9.00 3.38 1.13 Short Plate 1 0.75 15.00 8.25 11.25 92.81 765.70 210.94 middle support 0.50 15.00 8.25 7.50 61.88 510.47 140.63 Short Plate 2 0.75 15.00 8.25 11.25 92.81 765.70 210.94 Bottom Plate 32.00 0.75 16.13 24.00 387.00 6240.38 1.13

Totals 16.50 78.00 643.50 8285.63 564.75

* Reference Distance is to Plate bottom of plate

Combined Properties About xx:

Neutral Axis NAx 8.25 in

Inertia About NA Ix 3,541.50 in4

Radius of Gyration rx 6.74 in

Weight (Stiff Only, No PL) Wt 158.2 lb/ft SM of Top Plate SMtopx 429.27 in3

SM of BTM Plate SMbtmx 429.27 in3

Shear Area Asx 78.0 in2

Shear Center ex 8.25 in

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ABS Removable Skeg Structural Calculations Report

A-10 ABS Calculations: Strut Section Properties

At Skeg Box Depth 10 in

Item Base Height Centroid * Area A*Y A*Y2 Inertia in in in in2 in3 in4 in4

Top Plate 32.00 0.63 0.31 20.00 6.25 1.95 0.65 Short Plate 1 0.63 8.75 5.00 5.47 27.34 136.72 34.89 middle support 0.50 8.75 5.00 4.38 21.88 109.38 27.91 Short Plate 2 0.63 8.75 5.00 5.47 27.34 136.72 34.89 Bottom Plate 32.00 0.63 9.69 20.00 193.75 1876.95 0.65

Totals 10.00 55.31 276.56 2261.72 99.00

* Reference Distance is to Plate bottom of plate

Combined Properties About xx:

Neutral Axis NAx 5.00 in

Inertia About NA Ix 977.91 in4

Radius of Gyration rx 4.20 in

Weight (Stiff Only, No PL) Wt 105.3 lb/ft SM of Top Plate SMtopx 195.58 in3

SM of BTM Plate SMbtmx 195.58 in3

Shear Area Asx 55.3 in2

Shear Center ex 5.00 in

Material Yield Stress σyield 50 ksi

Factor of Safety FS 1.67 Allowable Stress σallow 29.9 ksi σyield/FS

Allowable Shear Stress τallow 18.0 ksi 0.6*σallow

Modulus of Elasticity E 29,000 ksi Poisson's Ratio v 0.3

NSF MCMURDO OFFLOAD INFRASTRUCTURE

ABS Removable Skeg Structural Calculations Report

A-11 ABS Calculations: Strut Section Properties