<%BANNER%>

Wave Loading on a Horizontal Plate

Permanent Link: http://ufdc.ufl.edu/UFE0024473/00001

Material Information

Title: Wave Loading on a Horizontal Plate
Physical Description: 1 online resource (212 p.)
Language: english
Creator: Marin, Justin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: forces, impact, loading, slamming, wave
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A theoretical, numerical, and experimental study of vertical forces due to non-breaking, monochromatic water waves propagating past a thin, horizontal rectangular plate structure is presented. A theoretical model is developed as the sum of the individual forcing components, drag, inertia, buoyancy, and slamming. A numerical model for evaluating the mathematical model is also developed that includes a stream function theory algorithm for computing the wave kinematics. Experimental tests were conducted for a range of water depths, wave conditions and structure locations relative to the still water level. Drag and inertia coefficients for the theoretical model were determined from the physical model test results. An empirical relationship for slamming was developed. There is good agreement between the numerical and experimental results. Also presented are recommendations for future work.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Justin Marin.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Sheppard, Donald M.
Local: Co-adviser: Thieke, Robert J.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024473:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024473/00001

Material Information

Title: Wave Loading on a Horizontal Plate
Physical Description: 1 online resource (212 p.)
Language: english
Creator: Marin, Justin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: forces, impact, loading, slamming, wave
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A theoretical, numerical, and experimental study of vertical forces due to non-breaking, monochromatic water waves propagating past a thin, horizontal rectangular plate structure is presented. A theoretical model is developed as the sum of the individual forcing components, drag, inertia, buoyancy, and slamming. A numerical model for evaluating the mathematical model is also developed that includes a stream function theory algorithm for computing the wave kinematics. Experimental tests were conducted for a range of water depths, wave conditions and structure locations relative to the still water level. Drag and inertia coefficients for the theoretical model were determined from the physical model test results. An empirical relationship for slamming was developed. There is good agreement between the numerical and experimental results. Also presented are recommendations for future work.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Justin Marin.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Sheppard, Donald M.
Local: Co-adviser: Thieke, Robert J.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024473:00001


This item has the following downloads:


Full Text

PAGE 1

1 WAVE LOADING ON A HORIZONTAL PLATE By JUSTIN M. MARIN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009

PAGE 2

2 2009 Justin M. Marin

PAGE 3

3 To Mom and Dad Cheers

PAGE 4

4 ACKNOWLEDGMENTS The following is a work that could not have b een com pleted without efforts and support of many besides the author. The extensive lab work completed on the topic would not have been possible without the (often unpaid) efforts of Jim Joiner, Vic Adams, and Sidney Schofield of the University of Florida Coastal Engineering Lab. I thank them for all the time, tools, and patience they have lent. I would also like to thank the entire staff at OEA Inc., especially Phil Dompe, for suffering silently through 76 versions of the model and counting. For the experience and the understanding, I thank Dr. D. Max Sheppard, who put up with the odd hours and the army of one attitude that drove him insane. The man gives laid back a new name. Thanks also go to my committee members, Dr. Robert J. Thieke and Dr. Arnoldo Valle-Levinson. Lastly, I thank my parents, Michelle and Juice, who have loved and backed me since the beginning, no matter how long I postpone the real world.

PAGE 5

5 TABLE OF CONTENTS Page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES.........................................................................................................................8 ABSTRACT...................................................................................................................................19 CHAP TER 1 INTRODUCTION..................................................................................................................20 Bridge Failures Due to Waves................................................................................................20 Problem Complexity............................................................................................................. ..20 The Structure...................................................................................................................21 The Wave Field............................................................................................................... 22 Plan of Study...........................................................................................................................22 2 LITERATURE SEARCH.......................................................................................................27 Previous Standardized Work.................................................................................................. 27 The Coastal Engineering Manual.................................................................................... 27 The Morison Equation..................................................................................................... 28 Previous Work on Bridges......................................................................................................28 Previous Work on Offshore Structures...................................................................................28 Offshore Platforms I........................................................................................................29 Offshore Platforms II....................................................................................................... 29 Offshore Jetties............................................................................................................... .30 Previous Work on Flat Plates................................................................................................. 31 3 DEVELOPMENT OF THE THEORETICAL MODEL........................................................32 The Problem............................................................................................................................32 Assumptions Made in Model Development.................................................................... 32 Dimensional Analysis......................................................................................................33 The Theoretical Model.......................................................................................................... .34 Drag Force.......................................................................................................................34 Inertia Forces...................................................................................................................35 Buoyancy.........................................................................................................................40 Slamming Force............................................................................................................... 40 Evaluating the Theoretical Model..........................................................................................42 4 PHYSICAL MODEL TESTS.................................................................................................47

PAGE 6

6 Test Facility............................................................................................................................47 The Physical Model................................................................................................................48 The Support Structure......................................................................................................49 Instrumentation................................................................................................................ 49 Physical Model Tests..............................................................................................................50 Data Processing......................................................................................................................50 Spectral Analysis............................................................................................................. 50 Signal Filtering................................................................................................................52 Assumption Verification................................................................................................. 52 Significant Parameters Ex tracted from the Data............................................................. 53 5 RESULTS AND ANALYSIS................................................................................................. 67 Evaluative Considerations...................................................................................................... 67 Added Mass Location......................................................................................................67 Change in Effective Mass................................................................................................68 The Quasi-steady Force..........................................................................................................69 Empirical Co efficients ..................................................................................................... 69 Accuracy of Predictive Equations................................................................................... 70 The Slamming Force...............................................................................................................71 Continuous Plate versus Finite Length Plate ..........................................................................71 6 CONLCUSIONS AND RECOMME NDATIONS................................................................. 80 Quasi-steady Force.................................................................................................................80 Slamming Force................................................................................................................. .....80 Recommendations................................................................................................................ ...81 APPENDIX A PHYSICAL MODEL DATA................................................................................................. 82 B MEASURED VERSUS PREDICTED fORCEs.................................................................... 99 LIST OF REFERENCES.............................................................................................................210 BIOGRAPHICAL SKETCH.......................................................................................................212

PAGE 7

7 LIST OF TABLES Table Page 4-1 Range of fluid variable values covered in the physical model testing............................... 66 A-1 Structure and fluid parameters for all physical model tests. .............................................. 83 A-2 Significant force values for all physical model tests......................................................... 91

PAGE 8

8 LIST OF FIGURES Figure Page 1-1 I-10 Bridge Escambia Bay superstr ucture rem oved by Hurricane Ivan............................ 24 1-2 I-10 Bridge Escambia Bay pile bents dam aged by Hurricane Ivan...................................24 1-3 I-10 Bridge Escambia Bay superstructure partially displaced by Hurricane Ivan. ............25 1-4 Bridge span-type classifications........................................................................................ 26 3-1 Definition sketch for wave load ing on a flat horizontal plate. ........................................... 43 3-2 Distribution of vertical wave kinem atics over structure subjected to wave attack............44 3-3 Variation of the time rate of change of effective mass over one wave period cycle. ........ 45 3-4 A spring-mass-dashpot system with damping................................................................... 46 3-5 Spring-mass-dashpot system a mplification effect............................................................. 46 4-1 Air/sea wave tank wave hei ght lim its by period and depth............................................... 54 4-2 Continuous flat plate model incl uding side panels (plan view). ........................................55 4-3 Definition sketch of the physical m odel setup (side profile view)....................................56 4-4 Definition sketch of the physical m odel setup (front profile view)................................... 57 4-5 Physical model setup showing the location of an upstream wave gauge.......................... 58 4-6 Total raw vertical force exampl es for a typical sub aerial case. ........................................ 59 4-7 Total raw vertical force exampl es for a typical subm erged case....................................... 60 4-8 Typical power spectral density of total vertical forcing. ...................................................61 4-9 Typical power spectral density of load cell pair vertical forcing. ......................................62 4-10 Total filtered (noise rem oved) vertical force examples for a typical sub aerial case. ....... 63 4-11 Total quasi-steady vertical force ex amples for a typical sub aerial case. .......................... 64 4-12 Total slamming force examples for a typical sub aerial case. ........................................... 65 5-1 Methods of estimating the adde d m ass distribution around the plate................................ 73 5-2 Variation of effective mass and re lated quantities over one wave period. ........................ 74

PAGE 9

9 5-3 Inertial coefficient data fit for c ontinuous plate tests w ith side panels. ............................. 75 5-4 Inertial coefficient data fit for finite length plate tests w ithout side panels. ...................... 75 5-5 Example of predicted versus measur ed values of the quasi-steady force. ......................... 76 5-6 Comparison of Florida model predictions versus independent experim ental data (Isaacson and Bhat 1996)...................................................................................................77 5-7 Slamming force empirical data fit for a continuous plate w ith side panels. ...................... 78 5-8 Slamming force empirical data fit for a fi nite length plate without side panels. ............... 78 5-9 Comparison of non-dimensionalized quasi -steady forces between continuous plate with side panel tests and finite le ngth plate without side panel tests. ................................79 5-10 Comparison of non-dimensionalized slammi ng forces between con tinuous plate with side panel tests and finite length plate without side panel tests. ........................................ 79 B-1 Measured vs. predicted quasi-st eady f orce for lab test FPWS-005................................. 100 B-2 Measured vs. predicted quasi-st eady f orce for lab test FPWS-006................................. 100 B-3 Measured vs. predicted quasi-st eady f orce for lab test FPWS-007................................. 101 B-4 Measured vs. predicted quasi-st eady f orce for lab test FPWS-008................................. 101 B-5 Measured vs. predicted quasi-st eady f orce for lab test FPWS-009................................. 102 B-6 Measured vs. predicted quasi-st eady f orce for lab test FPWS-011................................. 102 B-7 Measured vs. predicted quasi-st eady f orce for lab test FPWS-012................................. 103 B-8 Measured vs. predicted quasi-st eady f orce for lab test FPWS-013................................. 103 B-9 Measured vs. predicted quasi-st eady f orce for lab test FPWS-014................................. 104 B-10 Measured vs. predicted quasi-st eady f orce for lab test FPWS-015................................. 104 B-11 Measured vs. predicted quasi-st eady f orce for lab test FPWS-016................................. 105 B-12 Measured vs. predicted quasi-st eady f orce for lab test FPWS-017................................. 105 B-13 Measured vs. predicted quasi-st eady f orce for lab test FPWS-018................................. 106 B-14 Measured vs. predicted quasi-st eady f orce for lab test FPWS-021................................. 106 B-15 Measured vs. predicted quasi-st eady f orce for lab test FPWS-022................................. 107

PAGE 10

10 B-16 Measured vs. predicted quasi-st eady f orce for lab test FPWS-023................................. 107 B-17 Measured vs. predicted quasi-st eady f orce for lab test FPWS-024................................. 108 B-18 Measured vs. predicted quasi-st eady f orce for lab test FPWS-025................................. 108 B-19 Measured vs. predicted quasi-st eady f orce for lab test FPWS-026................................. 109 B-20 Measured vs. predicted quasi-st eady f orce for lab test FPWS-027................................. 109 B-21 Measured vs. predicted quasi-st eady f orce for lab test FPWS-028................................. 110 B-22 Measured vs. predicted quasi-st eady f orce for lab test FPWS-032................................. 110 B-23 Measured vs. predicted quasi-st eady f orce for lab test FPWS-034................................. 111 B-24 Measured vs. predicted quasi-st eady f orce for lab test FPWS-036................................. 111 B-25 Measured vs. predicted quasi-st eady f orce for lab test FPWS-038................................. 112 B-26 Measured vs. predicted quasi-st eady f orce for lab test FPWS-041................................. 112 B-27 Measured vs. predicted quasi-st eady f orce for lab test FPWS-042................................. 113 B-28 Measured vs. predicted quasi-st eady f orce for lab test FPWS-043................................. 113 B-29 Measured vs. predicted quasi-st eady f orce for lab test FPWS-044................................. 114 B-30 Measured vs. predicted quasi-st eady f orce for lab test FPWS-045................................. 114 B-31 Measured vs. predicted quasi-st eady f orce for lab test FPWS-046................................. 115 B-32 Measured vs. predicted quasi-st eady f orce for lab test FPWS-047................................. 115 B-33 Measured vs. predicted quasi-st eady f orce for lab test FPWS-049................................. 116 B-34 Measured vs. predicted quasi-st eady f orce for lab test FPWS-050................................. 116 B-35 Measured vs. predicted quasi-st eady f orce for lab test FPWS-051................................. 117 B-36 Measured vs. predicted quasi-st eady f orce for lab test FPWS-052................................. 117 B-37 Measured vs. predicted quasi-st eady f orce for lab test FPWS-055................................. 118 B-38 Measured vs. predicted quasi-st eady f orce for lab test FPWS-058................................. 118 B-39 Measured vs. predicted quasi-st eady f orce for lab test FPWS-059................................. 119 B-40 Measured vs. predicted quasi-st eady f orce for lab test FPWS-060................................. 119

PAGE 11

11 B-41 Measured vs. predicted quasi-st eady f orce for lab test FPWS-061................................. 120 B-42 Measured vs. predicted quasi-st eady f orce for lab test FPWS-062................................. 120 B-43 Measured vs. predicted quasi-st eady f orce for lab test FPWS-063................................. 121 B-44 Measured vs. predicted quasi-st eady f orce for lab test FPWS-068................................. 121 B-45 Measured vs. predicted quasi-st eady f orce for lab test FPWS-070................................. 122 B-46 Measured vs. predicted quasi-st eady f orce for lab test FPWS-071................................. 122 B-47 Measured vs. predicted quasi-st eady f orce for lab test FPWS-073................................. 123 B-48 Measured vs. predicted quasi-st eady f orce for lab test FPWS-074................................. 123 B-49 Measured vs. predicted quasi-st eady f orce for lab test FPWS-075................................. 124 B-50 Measured vs. predicted quasi-st eady f orce for lab test FPWS-076................................. 124 B-51 Measured vs. predicted quasi-st eady f orce for lab test FPWS-077................................. 125 B-52 Measured vs. predicted quasi-st eady f orce for lab test FPWS-078................................. 125 B-53 Measured vs. predicted quasi-st eady f orce for lab test FPWS-079................................. 126 B-54 Measured vs. predicted quasi-st eady f orce for lab test FPWS-081................................. 126 B-55 Measured vs. predicted quasi-st eady f orce for lab test FPWS-082................................. 127 B-56 Measured vs. predicted quasi-st eady f orce for lab test FPWS-083................................. 127 B-57 Measured vs. predicted quasi-st eady f orce for lab test FPWS-084................................. 128 B-58 Measured vs. predicted quasi-st eady f orce for lab test FPWS-085................................. 128 B-59 Measured vs. predicted quasi-st eady f orce for lab test FPWS-086................................. 129 B-60 Measured vs. predicted quasi-st eady f orce for lab test FPWS-087................................. 129 B-61 Measured vs. predicted quasi-st eady f orce for lab test FPWS-089................................. 130 B-62 Measured vs. predicted quasi-st eady f orce for lab test FPWS-090................................. 130 B-63 Measured vs. predicted quasi-st eady f orce for lab test FPWS-091................................. 131 B-64 Measured vs. predicted quasi-st eady f orce for lab test FPWS-092................................. 131 B-65 Measured vs. predicted quasi-st eady f orce for lab test FPWS-093................................. 132

PAGE 12

12 B-66 Measured vs. predicted quasi-st eady f orce for lab test FPWS-094................................. 132 B-67 Measured vs. predicted quasi-st eady f orce for lab test FPWS-095................................. 133 B-68 Measured vs. predicted quasi-st eady f orce for lab test FPWS-098................................. 133 B-69 Measured vs. predicted quasi-st eady f orce for lab test FPWS-100................................. 134 B-70 Measured vs. predicted quasi-st eady f orce for lab test FPWS-101................................. 134 B-71 Measured vs. predicted quasi-st eady f orce for lab test FPWS-102................................. 135 B-72 Measured vs. predicted quasi-st eady f orce for lab test FPWS-105................................. 135 B-73 Measured vs. predicted quasi-st eady f orce for lab test FPWS-106................................. 136 B-74 Measured vs. predicted quasi-st eady f orce for lab test FPWS-107................................. 136 B-75 Measured vs. predicted quasi-st eady f orce for lab test FPWS-108................................. 137 B-76 Measured vs. predicted quasi-st eady f orce for lab test FPWS-110................................. 137 B-77 Measured vs. predicted quasi-st eady f orce for lab test FPWS-111................................. 138 B-78 Measured vs. predicted quasi-st eady f orce for lab test FPWS-113................................. 138 B-79 Measured vs. predicted quasi-st eady f orce for lab test FPWS-114................................. 139 B-80 Measured vs. predicted quasi-st eady f orce for lab test FPWS-115................................. 139 B-81 Measured vs. predicted quasi-st eady f orce for lab test FPWS-116................................. 140 B-82 Measured vs. predicted quasi-st eady f orce for lab test FPWS-117................................. 140 B-83 Measured vs. predicted quasi-st eady f orce for lab test FPWS-118................................. 141 B-84 Measured vs. predicted quasi-st eady f orce for lab test FPWS-119................................. 141 B-85 Measured vs. predicted quasi-st eady f orce for lab test FPWS-121................................. 142 B-86 Measured vs. predicted quasi-st eady f orce for lab test FPWS-122................................. 142 B-87 Measured vs. predicted quasi-st eady f orce for lab test FPWS-124................................. 143 B-88 Measured vs. predicted quasi-st eady f orce for lab test FPWS-125................................. 143 B-89 Measured vs. predicted quasi-st eady f orce for lab test FPWS-126................................. 144 B-90 Measured vs. predicted quasi-st eady f orce for lab test FPWS-127................................. 144

PAGE 13

13 B-91 Measured vs. predicted quasi-st eady f orce for lab test FPWS-129................................. 145 B-92 Measured vs. predicted quasi-st eady f orce for lab test FPWS-130................................. 145 B-93 Measured vs. predicted quasi-st eady f orce for lab test FPWS-131................................. 146 B-94 Measured vs. predicted quasi-st eady f orce for lab test FPWS-132................................. 146 B-95 Measured vs. predicted quasi-st eady f orce for lab test FPWS-133................................. 147 B-96 Measured vs. predicted quasi-st eady f orce for lab test FPWS-134................................. 147 B-97 Measured vs. predicted quasi-st eady f orce for lab test FPWS-135................................. 148 B-98 Measured vs. predicted quasi-st eady f orce for lab test FPWS-137................................. 148 B-99 Measured vs. predicted quasi-st eady f orce for lab test FPWS-139................................. 149 B-100 Measured vs. predicted quasi-st eady f orce for lab test FPWS-140................................. 149 B-101 Measured vs. predicted quasi-st eady f orce for lab test FPWS-141................................. 150 B-102 Measured vs. predicted quasi-st eady f orce for lab test FPWS-142................................. 150 B-103 Measured vs. predicted quasi-st eady f orce for lab test FPWS-143................................. 151 B-104 Measured vs. predicted quasi-st eady f orce for lab test FPWS-145................................. 151 B-105 Measured vs. predicted quasi-st eady f orce for lab test FPWS-146................................. 152 B-106 Measured vs. predicted quasi-st eady f orce for lab test FPWS-147................................. 152 B-107 Measured vs. predicted quasi-st eady f orce for lab test FPWS-148................................. 153 B-108 Measured vs. predicted quasi-st eady f orce for lab test FPWS-149................................. 153 B-109 Measured vs. predicted quasi-st eady f orce for lab test FPWS-150................................. 154 B-110 Measured vs. predicted quasi-st eady f orce for lab test FPWS-151................................. 154 B-111 Measured vs. predicted quasi-st eady f orce for lab test FPWS-153................................. 155 B-112 Measured vs. predicted quasi-st eady f orce for lab test FPWS-154................................. 155 B-113 Measured vs. predicted quasi-st eady f orce for lab test FPWS-155................................. 156 B-114 Measured vs. predicted quasi-st eady f orce for lab test FPWS-156................................. 156 B-115 Measured vs. predicted quasi-st eady f orce for lab test FPWS-157................................. 157

PAGE 14

14 B-116 Measured vs. predicted quasi-st eady f orce for lab test FPWS-158................................. 157 B-117 Measured vs. predicted quasi-st eady f orce for lab test FPWS-159................................. 158 B-118 Measured vs. predicted quasi-st eady f orce for lab test FPWS-161................................. 158 B-119 Measured vs. predicted quasi-st eady f orce for lab test FPWS-162................................. 159 B-120 Measured vs. predicted quasi-st eady f orce for lab test FPWS-163................................. 159 B-121 Measured vs. predicted quasi-st eady f orce for lab test FPWS-164................................. 160 B-122 Measured vs. predicted quasi-st eady f orce for lab test FPWS-167................................. 160 B-123 Measured vs. predicted quasi-st eady f orce for lab test FPWS-170................................. 161 B-124 Measured vs. predicted quasi-st eady f orce for lab test FPWS-171................................. 161 B-125 Measured vs. predicted quasi-st eady f orce for lab test FPWS-172................................. 162 B-126 Measured vs. predicted quasi-st eady f orce for lab test FPWS-173................................. 162 B-127 Measured vs. predicted quasi-st eady f orce for lab test FPWS-174................................. 163 B-128 Measured vs. predicted quasi-st eady f orce for lab test FPWS-175................................. 163 B-129 Measured vs. predicted quasi-st eady f orce for lab test FPWS-186................................. 164 B-130 Measured vs. predicted quasi-st eady f orce for lab test FPNS-001.................................. 164 B-131 Measured vs. predicted quasi-st eady f orce for lab test FPNS-002.................................. 165 B-132 Measured vs. predicted quasi-st eady f orce for lab test FPNS-003.................................. 165 B-133 Measured vs. predicted quasi-st eady f orce for lab test FPNS-004.................................. 166 B-134 Measured vs. predicted quasi-st eady f orce for lab test FPNS-005.................................. 166 B-135 Measured vs. predicted quasi-st eady f orce for lab test FPNS-007.................................. 167 B-136 Measured vs. predicted quasi-st eady f orce for lab test FPNS-008.................................. 167 B-137 Measured vs. predicted quasi-st eady f orce for lab test FPNS-009.................................. 168 B-138 Measured vs. predicted quasi-st eady f orce for lab test FPNS-010.................................. 168 B-139 Measured vs. predicted quasi-st eady f orce for lab test FPNS-011.................................. 169 B-140 Measured vs. predicted quasi-st eady f orce for lab test FPNS-013.................................. 169

PAGE 15

15 B-141 Measured vs. predicted quasi-st eady f orce for lab test FPNS-014.................................. 170 B-142 Measured vs. predicted quasi-st eady f orce for lab test FPNS-015.................................. 170 B-143 Measured vs. predicted quasi-st eady f orce for lab test FPNS-016.................................. 171 B-144 Measured vs. predicted quasi-st eady f orce for lab test FPNS-017.................................. 171 B-145 Measured vs. predicted quasi-st eady f orce for lab test FPNS-019.................................. 172 B-146 Measured vs. predicted quasi-st eady f orce for lab test FPNS-020.................................. 172 B-147 Measured vs. predicted quasi-st eady f orce for lab test FPNS-021.................................. 173 B-148 Measured vs. predicted quasi-st eady f orce for lab test FPNS-022.................................. 173 B-149 Measured vs. predicted quasi-st eady f orce for lab test FPNS-023.................................. 174 B-150 Measured vs. predicted quasi-st eady f orce for lab test FPNS-025.................................. 174 B-151 Measured vs. predicted quasi-st eady f orce for lab test FPNS-026.................................. 175 B-152 Measured vs. predicted quasi-st eady f orce for lab test FPNS-027.................................. 175 B-153 Measured vs. predicted quasi-st eady f orce for lab test FPNS-028.................................. 176 B-154 Measured vs. predicted quasi-st eady f orce for lab test FPNS-029.................................. 176 B-155 Measured vs. predicted quasi-st eady f orce for lab test FPNS-031.................................. 177 B-156 Measured vs. predicted quasi-st eady f orce for lab test FPNS-032.................................. 177 B-157 Measured vs. predicted quasi-st eady f orce for lab test FPNS-033.................................. 178 B-158 Measured vs. predicted quasi-st eady f orce for lab test FPNS-034.................................. 178 B-159 Measured vs. predicted quasi-st eady f orce for lab test FPNS-035.................................. 179 B-160 Measured vs. predicted quasi-st eady f orce for lab test FPNS-036.................................. 179 B-161 Measured vs. predicted quasi-st eady f orce for lab test FPNS-037.................................. 180 B-162 Measured vs. predicted quasi-st eady f orce for lab test FPNS-038.................................. 180 B-163 Measured vs. predicted quasi-st eady f orce for lab test FPNS-039.................................. 181 B-164 Measured vs. predicted quasi-st eady f orce for lab test FPNS-040.................................. 181 B-165 Measured vs. predicted quasi-st eady f orce for lab test FPNS-041.................................. 182

PAGE 16

16 B-166 Measured vs. predicted quasi-st eady f orce for lab test FPNS-042.................................. 182 B-167 Measured vs. predicted quasi-st eady f orce for lab test FPNS-043.................................. 183 B-168 Measured vs. predicted quasi-st eady f orce for lab test FPNS-044.................................. 183 B-169 Measured vs. predicted quasi-st eady f orce for lab test FPNS-045.................................. 184 B-170 Measured vs. predicted quasi-st eady f orce for lab test FPNS-046.................................. 184 B-171 Measured vs. predicted quasi-st eady f orce for lab test FPNS-047.................................. 185 B-172 Measured vs. predicted quasi-st eady f orce for lab test FPNS-048.................................. 185 B-173 Measured vs. predicted quasi-st eady f orce for lab test FPNS-049.................................. 186 B-174 Measured vs. predicted quasi-st eady f orce for lab test FPNS-050.................................. 186 B-175 Measured vs. predicted quasi-st eady f orce for lab test FPNS-051.................................. 187 B-176 Measured vs. predicted quasi-st eady f orce for lab test FPNS-052.................................. 187 B-177 Measured vs. predicted quasi-st eady f orce for lab test FPNS-053.................................. 188 B-178 Measured vs. predicted quasi-st eady f orce for lab test FPNS-054.................................. 188 B-179 Measured vs. predicted quasi-st eady f orce for lab test FPNS-055.................................. 189 B-180 Measured vs. predicted quasi-st eady f orce for lab test FPNS-056.................................. 189 B-181 Measured vs. predicted quasi-st eady f orce for lab test FPNS-057.................................. 190 B-182 Measured vs. predicted quasi-st eady f orce for lab test FPNS-058.................................. 190 B-183 Measured vs. predicted quasi-st eady f orce for lab test FPNS-059.................................. 191 B-184 Measured vs. predicted quasi-st eady f orce for lab test FPNS-060.................................. 191 B-185 Measured vs. predicted quasi-st eady f orce for lab test FPNS-061.................................. 192 B-186 Measured vs. predicted quasi-st eady f orce for lab test FPNS-062.................................. 192 B-187 Measured vs. predicted quasi-st eady f orce for lab test FPNS-063.................................. 193 B-188 Measured vs. predicted quasi-st eady f orce for lab test FPNS-064.................................. 193 B-189 Measured vs. predicted quasi-st eady f orce for lab test FPNS-065.................................. 194 B-190 Measured vs. predicted quasi-st eady f orce for lab test FPNS-066.................................. 194

PAGE 17

17 B-191 Measured vs. predicted quasi-st eady f orce for lab test FPNS-067.................................. 195 B-192 Measured vs. predicted quasi-st eady f orce for lab test FPNS-068.................................. 195 B-193 Measured vs. predicted quasi-st eady f orce for lab test FPNS-069.................................. 196 B-194 Measured vs. predicted quasi-st eady f orce for lab test FPNS-070.................................. 196 B-195 Measured vs. predicted quasi-st eady f orce for lab test FPNS-071.................................. 197 B-196 Measured vs. predicted quasi-st eady f orce for lab test FPNS-072.................................. 197 B-197 Measured vs. predicted quasi-st eady f orce for lab test FPNS-073.................................. 198 B-198 Measured vs. predicted quasi-st eady f orce for lab test FPNS-074.................................. 198 B-199 Measured vs. predicted quasi-st eady f orce for lab test FPNS-075.................................. 199 B-200 Measured vs. predicted quasi-st eady f orce for lab test FPNS-076.................................. 199 B-201 Measured vs. predicted quasi-st eady f orce for lab test FPNS-077.................................. 200 B-202 Measured vs. predicted quasi-st eady f orce for lab test FPNS-078.................................. 200 B-203 Measured vs. predicted quasi-st eady f orce for lab test FPNS-079.................................. 201 B-204 Measured vs. predicted quasi-st eady f orce for lab test FPNS-080.................................. 201 B-205 Measured vs. predicted quasi-st eady f orce for lab test FPNS-081.................................. 202 B-206 Measured vs. predicted quasi-st eady f orce for lab test FPNS-082.................................. 202 B-207 Measured vs. predicted quasi-st eady f orce for lab test FPNS-083.................................. 203 B-208 Measured vs. predicted quasi-st eady f orce for lab test FPNS-084.................................. 203 B-209 Measured vs. predicted quasi-st eady f orce for lab test FPNS-085.................................. 204 B-210 Measured vs. predicted quasi-st eady f orce for lab test FPNS-086.................................. 204 B-211 Measured vs. predicted quasi-st eady f orce for lab test FPNS-087.................................. 205 B-212 Measured vs. predicted quasi-st eady f orce for lab test FPNS-088.................................. 205 B-213 Measured vs. predicted quasi-st eady f orce for lab test FPNS-089.................................. 206 B-214 Measured vs. predicted quasi-st eady f orce for lab test FPNS-090.................................. 206 B-215 Measured vs. predicted quasi-st eady f orce for lab test FPNS-093.................................. 207

PAGE 18

18 B-216 Measured vs. predicted quasi-st eady f orce for lab test FPNS-094.................................. 207 B-217 Measured vs. predicted quasi-st eady f orce for lab test FPNS-097.................................. 208 B-218 Measured vs. predicted quasi-st eady f orce for lab test FPNS-098.................................. 208 B-219 Measured vs. predicted quasi-st eady f orce for lab test FPNS-099.................................. 209 B-220 Measured vs. predicted quasi-st eady f orce for lab test FPNS-100.................................. 209

PAGE 19

19 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science WAVE LOADING ON A HORIZONTAL PLATE By Justin M. Marin May 2009 Chair: D. Max Sheppard Cochair: Robert J. Thieke Major: Coastal and Oceanographic Engineering A theoretical, numerical, and experimental study of vertical for ces due to non-breaking, monochromatic water waves propagating past a th in, horizontal rectangula r plate structure is presented. A theoretical model is developed as the sum of the individual forcing components, drag, inertia, buoyancy, and slam ming. A numerical model for evaluating the mathematical model is also developed that in cludes a stream function theory algorithm for computing the wave kinematics. Experimental tests were conducted fo r a range of water depths, wave conditions and structure locations relative to the still water level. Drag and inertia coefficients for the theoretical model were determined from the physical model test results. An empirical relationship for slamming was developed. Ther e is good agreement between the numerical and experimental results. Also presented are recommendations for future work.

PAGE 20

20 CHAPTER 1 INTRODUCTION Bridge Failures Due to Waves Over the course of 2004 and 2005, a num ber of bridges sustained critical damage during major storm events. The most notable of these incidents were the catast rophic failures of the I10 bridges over Escambia Bay, Florida during th e landfall of Hurricane Ivan in 2004, the I-10 Bridge over Lake Pontchartrain in Louisiana, and the US 90 bri dges over Biloxi and Saint Louis Bays in Mississippi during Hurricane Katrin a in 2005. The cause of these failures was determined to be elevated water levels and wave forces. In each of these cases numerous span superstructures (bridge deck, gi rder, and rail structures) were completely removed from the support structure (Figure 1-1). Pile groups and bents were also seriously damaged due to the displacement and collapse of the above spans (F igure 1-2). Some deck structures were not completely displaced by the waves but torn from their tie downs and shifte d in the direction of wave propagation (Figure 1-3). While wave loading is taken into account for most offshore and coastal structures, it has been overlooked in the design of bridges. A seemingly obvious solution to the problem of wave loading is to simply construct bridges at a high er elevation, thereby avoi ding any wave contact. However, the higher the bridge the greater the co st will be. Approach spans near the end would also have to be raised, requiring increased land use in many cases and additional costs. This expensive solution would also do little in the way of serving existing structures that are susceptible to wave attack. Problem Complexity In the coastal and nearshore environm ent, wa ve loading has long been studied for various types of structures. However, these structures are traditionally oriented vertically (caissons,

PAGE 21

21 seawalls, bulkheads, etc.) while in this case it is the vertical forcing on hori zontal structures that is of interest. In the few instances where vertical wave loading has been st udied, the structures in question were typically very small in size relativ e to the design wave length (offshore platforms subjected to open ocean waves). Only a few reported studies on wave loading on horizontal structures with wave lengths on the order of the structure width exis t (Isaacson and Bhat 1996; Denson 1978, 1980; Bea et al. 2001; Ka plan et al. 1995), all of whic h ignored partially or fully submerged structures. The scarcity of information on this subject was part of the motivation for this study. The Structure At its m ost basic, a bridge is little more th an a slab supported at both ends. At its most complex, a bridge is an amalgam of beams, di aphragms, decks, rails, overhangs, pile caps, pilings, bents, tie downs, box girders and in some cases, suspensions or arches. These individual components themselves are extremely varied in size and shape from bridge to bridge. To categorically define a bridge by a single set up, would exclude any number of components that would also be vulnerable to wave attack. Howe ver, it would be neither practical nor cost effective to conduct physical model tests for a wide range of these parameters. For comparison, cross sectional diagrams of a beam, slab and segmental box girder bridges are shown (Figure 1-4). Beam and slab are two of the more common designs used in the state of Florida. Slab spans are relatively simple in sh ape while girder spans are more complex and have the capability of entrapping air between the beams (girders). Segmental bridge spans have enclosed air spaces and have segments that exte nd over several bents, a linking that creates an indeterminate system of forcing. Obviously, each of these structures would experience different loading when encountered by a wave and would al so offer different resistive forces. Before

PAGE 22

22 tackling these complex structures, a detailed unde rstanding of a simple structure under similar conditions is necessary. Using a flat plate as the initial model pr ovides a geometrically simple structure for calculating various needed dynamic quantities. It also provide s an excellent platform for comparison with the limited previous work. An additional benefit of investigating thin plate structures is their similarity to many other coasta l structures that are not bridges (jetties, docks, piers, platforms, etc.), which can provide a basis for studies of other structure types. The Wave Field Actual wind wave fields are com plex and co mposed of waves with different heights and lengths propagating in a range of directions. The distribution of wave heights and therefore wave energy can be quantified w ith directional wave energy density spectra diagrams. From the information in these diagrams quantities such as significant wave heig ht, peak period, most probable maximum wave height as a function of duration, etc. can be obtained. For design purposes it is usually (but not always) the maxi mum wave height and its associated period (wave length) that is of interest. In general, forces produced by irregu lar or random waves are less than those produced by regular, monochromatic waves. Fo r this reason and the fact that it is difficult to produce irregular waves for l ong durations without contaminati on due to reflection in wave tanks, monochromatic waves were used in this study. Plan of Study The experim ental work reported on in this thesis is intended to be a first step in providing information on wave loading on a horizontal slab type structure subjected to waves with lengths on the same order as the structure width. The purpose of this study was to measure vert ical wave forces on thin, flat, horizontal structures and to initiate the development of a theoretical model that describes those forces. A

PAGE 23

23 numerical model was developed for the purpose of evaluating the theoretical model. Horizontal forces, while present, were not c onsidered due to their relatively small magnitude (a flat plate taken as having negligible thickness). A literature review resulted in a limited number of experimental and theoretical papers on this subject. These are summarized in Chapter 2. The theoretical model presented here has its foundation in the models described by Morison et al. (1950), Kaplan (1992), Kaplan et al. (1992), and Isaacson and Bhat (1996) and extends the range of application to situations wh ere the wave lengths are on the same order of magnitude as the width of the structure. This seemingly minor change introduces considerable complexity to the problem by creating large grad ients in the wave kinematics over the width of the structure as well as signifi cant changes in the added mass. To provide information needed to evaluate drag and inertia coefficients in the mathematical model and to test its validity, experi mental tests were carried out in a University of Florida Coastal Engineering Laboratory wave ta nk using an approximate scale model of an actual bridge deck. A wide range of structure positions, water elevations and wave conditions were investigated. The test results were used to obtain drag and inertia coefficients for the mathematical model. Good agreement between predicted and measured forces was obtained.

PAGE 24

24 Figure 1-1. I-10 Bridge Es cambia Bay superstructure removed by Hurricane Ivan. Figure 1-2. I-10 Bridge Es cambia Bay pile bents damaged by Hurricane Ivan.

PAGE 25

25 Figure 1-3. I-10 Bridge Escambi a Bay superstructure partially displaced by Hurricane Ivan.

PAGE 26

26 A B C Figure 1-4. Bridge span-type classifications. A) Beam and slab bridge with rails. B) Segmental (box girder) with rails. C) Slab span/flat plate.

PAGE 27

27 CHAPTER 2 LITERATURE SEARCH In the specif ic area of vertical wave forci ng on horizontal structures, there have been several previous studies conduc ted. These studies vary greatly in motivation, method, and application. In some cases, a theoretical basis is dismissed in lieu of a purely empirical model. Assumptions are often made to suit the specific scenarios of a variety of structure types and meteorological/oceanographic (met/ocean) conditions This results in a solution method with very limited application. However, the fundame ntals of previous relevant work, notably by Isaacson and Bhat (1996) and Kaplan et al. (1995) do provide an excellent platform from which to begin. Previous Standardized Work The im portance of vertical forcing in the st andardized literature is acknowledged in only two places, with the Morison equation being the mo st well documented work on the subject. In the Coastal Engineering Manual (U.S. Army Corp s of Engineers 2008) a small section on uplift forces is included, though only rudiment ary methods of calculation are provided. The Coastal Engineering Manual The Coastal Engineering Manual (U.S. Ar my Corps of Engineers 2008) breaks up the case of a horizontally oriented structure into two se parate groupssubmerged (o r partially submerged) structures and emergent (sub aerial) structures. For a submerged st ructure, forces are calculated using a lift-based flow equation with the force pr oportional to the square of the horizontal water velocity. An empirically determined lift coefficien t for each structure of interest is required. For an emergent structure, forces are calculated us ing a single slamming-type equation with the force proportional to the square of the vertical wate r velocity. An experimentally determined coefficient for each structure is required. Due to the limited work done on the topic, the Coastal

PAGE 28

28 Engineering Manual recommends the use of pr oblem-specific numerical and physical modeling for the purposes of design. The Morison Equation The Morison Equation was developed by Morison et al. (1950) for computing wave forces on a single vertical pile. Calculation of the forces using th e Morison Equation requires an analytical model for the wave kinematics a nd empirically determ ined drag and inertia coefficients. Keys to the validity of this equation are accurate wa ve field kinematics and accurate coefficients. Versions of this equation have been used by the offshore industry for a number of years. Application is limited to cases where the elements and structures are slender when compared to the lengths of the waves encountered. Previous Work on Bridges W ith regard to wave forces on bridges the onl y studies uncovered in the literature search were those conducted at Missi ssippi State University by Denson (1978, 1980), coincidentally motivated by hurricane-induced wave damage. Scale models (1:24) of the beam and slab Bay St. Louis Bridge and the box girder I-1 10 Biloxi Bridge. A series of tests were run in a wave tank at Mississippi State University. Di mensionless groups were devel oped and the test results for vertical and horizontal forces and rolling moment were presented in terms of dimensionless groups. All tests were conducte d using the same 3 second wave period and all waves were shallow water waves (kZD < /10, where k is the wave number and ZD is water depth). The effects of wave length and wave peri od on the wave forces were ignored. Previous Work on Offshore Structures Perhaps the most significant work o n the topi c of wave forcing on horizontal structures was that for offshore structures, nearly all of which deal with offshore petroleum platforms. A

PAGE 29

29 related problem area is that associated with open coast ship and LNG tanker docks (sometimes referred to as jetties). The need for structure specific coefficients and the difference in environmental and structural conditions between the offshore and coastal areas limit the direct application of this information to the current pr oblem. Useful comparative studies were done by Kaplan (1992), Kaplan et al. (1995), Bea et al. (1999, 2001), and McConnell et al. (2004). Offshore Platforms I Kaplan (1992) and Kaplan et al. (1995) deal t with vertical and hor izontal wave forces on offshore platfor m decks with steel plate bottoms The theoretical model used for horizontal structures was similar to Morisons equation for vertical piles but with additional terms to account for a time-varying added mass. Predictions using these equations were compared with experimental data from laboratory tests with offshore platform models (Murray et al. 1995). The equations consider the effects of finite le ngth structures and the in clusion of change in added mass effects, for sub aerial structures An equation for added mass was proposed. Nonlinear wave theory was used to determine wa ve kinematics, with single averaged velocities and single average accelerations applied over the entire length of the structure during submergence. Slamming force effects were filtered out of the laboratory and field data. The theoretical model results were in good agreement with the limited field data that was available. Offshore Platforms II Bea et al. (1999) concentrated on offshore platform decks that were suspended beneath the structure, specifically dealing wi th failed decks in the field. D ata was compared from laboratory tests for wave forces on offshore platforms (F innigan and Petrauskas 1997; Dean et al. 1985; Faltinsen et al. 1977; Jue 1993; Kjeldsen and Myrh aug 1979; Kjeldsen and Hasle 1985; Kjeldsen et al. 1986; Weggel 1997) with the gu idelines of the American Petr oleum Institute. The current methods were found excessively conservative and more extensive work and modifications to the

PAGE 30

30 guidelines were recommended. An analytical model was presented as the sum of forcing components derived from the Morison equation. While vertical components are discussed, the decks in question were porous or grated, maki ng the horizontal component the dominant load. 5th order Stokes wave theory was used to compute the wave kinematics. Bea et al. (2001) evaluated the analytical m odels numerically and compared the results with field data (Stear and Bea 1997; Imm et al. 1994; Cardone and Cox 1992; Vannan et al. 1994) for existing structures that had been subj ected to wave loads. The horizontal force predictions were found to be extr emely conservative. A slamming fo rce equation in the form of a drag equation using an empirical slamming coef ficient was also developed. The structural response characteristics were taken into account in the analysis. This required knowledge of the structures primary modes of vibr ation as well as the frequency of the slamming force. There was no method provided for estimatin g the slamming force frequency. Offshore Jetties Tirindelli et al. (2002) revealed the lack of m ethod for dealin g with offshore jetties. Engineers at HR Wallingford (McConnell et al. 2 004) conducted wave loading tests with model (1:25 scale) jetties (open coast piers). One of the models was a flat plate and one had beams under the slab. Dimensional analysis was used to develop predictive force equations and to provide a means of presenting the laboratory test results. Variables included in the dimensionless parameters were clearance height significant wave height maximum wave crest elevation, and the structural dimensions. Forces were normalized by a parameter based on static head pressures on the structure surface and st ructure dimensions. Similar to Denson (1978, 1980), the period and wave length were not cons idered in the analysis of data, though wave periods were varied during testing. Vertical forcing was separate d into two separate groups, the quasi-static force and th e slamming force. The magnitude of the slamming was acknowledged as

PAGE 31

31 important as well as the response characteristics of the structure when considering the slamming. Coefficients were developed for the quasi-sta tic predictive equations. No predictive equation was presented for the slamming force due to difficulties in accurately measuring this high frequency component. Previous Work on Flat Plates Studies of wave forces on hor izon tal structures with simple shapes are limited. The only tests with a flat plate and wa ves with lengths comparable to plate length were conducted by Isaacson and Bhat (1996). A theoretical/experimental study of vertical for ces on a rigid, suspended plate of negligible thickness was completed. The expression devel oped by was mathematically similar to that developed in Kaplan et al. (1995) The vertical force is assu med to be the sum of the time varying components (time rate of change of mo mentum, drag, and buoyancy). Included were the effects of added mass in his calculations. Th e added mass equation was for a general structure shape with only a single empirical coefficient. The equations were evaluated numerically. Due to the uncertainties associated with the change in added mass as the latt er portion of the wave strikes the structure no attempt wa s made to predict forces beyond the first half of the wave. IN total, 69 sub aerial tests were conducted. No subm erged or partially submerged structures were tested. Low pass filters were used to filter ou t the slamming force components from the force transducer signals. Selected results were pres ented in table form along with a single plot of predicted versus measured vertical force.

PAGE 32

32 CHAPTER 3 DEVELOPMENT OF THE THEORETICAL MODEL The theoretical m odel developed as part of this thesis builds on the work of Kaplan et al. (1995) and Isaacson and Bhat (1996). A definition sk etch of the problem is presented in Figure 3-1, which shows the pertinent parameters. The Problem The scope of this study is lim ited to inves tigating the vertical wave forces on flat, horizontal structures, for waves and structures with comparable size ratios. If the bottom of the structure is located above the trough of the wave then it will experien ce slamming as well as buoyancy, drag and inertia forces. An empirical equation was developed for the slamming force in terms of the wave steepness (H/ ) and the relative clearance (ZC/ ) using data from tests performed as part of this study. Assumptions Made in Model Development The flow and fluid-structure interaction processes associated with wave impact on horizontal structures are com plex. For this reason certain simplifying assumptions must be made for the mathematical model development: The structure is a rigid, horizontal, flat plate of negligible thickness. The waves are monochromatic, non-breaking a nd two-dimensional. The waves approach the structure normal to the leadi ng edge side of the structure. The effects of the structure on the waves can be accounted for through the experimentally determined drag and inertia coefficients. While the problem is treated two-dimensionally and the forces and moments computed on a per unit length basis, it should be noted that the eff ect of finite structure le ngth on the calculation of added mass must be taken into consideration as the variation of the added mass quantity is not linear with structure length. Considering the waves to be two-dimensional and to approach the

PAGE 33

33 structure normal to the leading edge side of the structure is thought to produce conservative estimates of the forces and moments. Dimensional Analysis Wave loads depend on the structure param eters as well as those associated with the water and waves. The wave forcing is thought to depend on twelve indepe ndent variables. A dimensional analysis was performe d with these variables. From the analysis, nine dimensionless groups were found. In some cases, two groups were combined to form a single group, so that the normalized force can be expressed as a func tion (Equation 3-1) of the remaining seven dimensionless groups. C 2 D DZ FWHLH Z gLH WgZ f,,,,, (3-1) In Equation 3-1, F is the total directional forcing, is fluid density, is dynamic fluid viscosity, g is gravity, L is the length of the structure perpendicular to direction of wave propagation, W is the width of structure parall el to direction of wave propagation, D is the thickness of the structure, ZC is the structure clearance height (distance from lowest structure chord to the still water level), ZD is water depth, H is wave height, max is maximum wave crest elevation, and is wave length. The absence of the wave period (T) in any of the parameters is due to it being uniquely defined by the wave length and water depth. The maximum wave elevation ( max) is also uniquely determined by the wave he ight, length and water depth. H/ is a measure of the wave steepness. W/ is the length of the structure in the di rection of wave propagation divided by the wave length, an important parameter in this study. The term ( max ZC)/D is the height of the wave above the bottom of the structure normaliz ed by the structure thic kness, an important parameter for the horizontal component of the force (but unimportant for a fl at plate). The last

PAGE 34

34 parameter is actually the rati o of the Froude Number to th e Reynolds Number. The force normalizing parameter, gLH is proportional to the total en ergy of the wave. When treating forces as per unit length, the structure length, L can be removed from the force normalizing parameter. The Theoretical Model While the vertical com ponent of the force is of primary interest in this study, expressions for the horizontal force are deve loped as well for completeness. The forces exerted on a completely submerge d body in an accelerating fluid are due to buoyancy, drag and inertia. If the structure is sub aerial then it will al so experience a slamming force. A partially submerged structure may al so experience a slamming force depending on the level of submergence and the height of the wave The horizontal and vertical force components can be expressed as shown in Equations 3-2 and 3-3. HorizontalxDragInertiaSlammingF = F = F+ F+ F (3-2) VerticalzDragInertiaBuoyancySlammingF = F = F+ F + F+ F (3-3) These force components contribute to the tota l forcing in varying degrees and are, in general, out of phase with each other. Each component was examined in detail and its mathematical representation obtained. Drag Force The drag force can be further divided into shear and norm al components with the normal (pressure drag) component resulting from fl ow separation on the body. Most analytical treatments of drag lump the two components toge ther with an expression that is proportional to the projected area of the structure, the mass density of the fluid and the square of the approach velocity. The experimentally determined consta nt of proportionality is the drag coefficient

PAGE 35

35 which is a function of the structure shape, the Reynolds Number (based on the structure width and approach velocity), surface roughness, etc. The drag functions are presented in Equation 3-4 and Equation 3-5. DragXDXX1 FC Auu 2 (3-4) DragZDZZ1 FC Aww 2 (3-5) In Equation 3-4 and Equation 3-5, u is horizonta l water particle velocity, w is vertical water particle velocity, AX is the projected area on a plane pe rpendicular to the horizontal axis, AZ the projected area on a plane perpe ndicular to the vertical axis, CDX the horizontal drag coefficient, and CDZ the vertical drag coefficient. The drag coefficients used in this study are those yielding the best fit between predicted and measured values from the wave tank tests co nducted as part of this study. The presence of large gradients in the particle kinematics over the length of the structure (direction of wave propagation) requires relatively hi gh resolution in the computati on scheme of the wave field kinematics. Inertia Forces The inertia f orces are a normal force that results from the acceleration-induced pressure gradient field in the vicinity of the structure. The force component is proportional to the time rate of change (the derivative) of linear moment um. For a small structure in the flow field, the linear momentum is the product of the mass of the water impacted by the presence of the structure (the sum of the wate r displaced by the structure and the mass of water in the flow affected by the presence of the structure) and th e velocity of the fluid at the centroid of the structure (if the structure were not present in the flow). The time derivative of this is taken and

PAGE 36

36 an experimentally determined constant of proportionality, the inertial coefficient, is added. The inertia function is presented in Equation 3-6 and Equation 3-7. InertiaXMXeFCmu t (3-6) InertiaZMZeFCmw t (3-7) In Equation 3-6 and Equation 3-7, me is the effective mass (total mass of water impacted by the presence of the structure), CMX is the horizontal inertial coefficient, and CMZ the vertical inertial coefficient. Complexities in the problem arise from the inte rmittent submergence of the structure. The varying inundation creates a ti me dependent effective mass value, which necessitates the inclusion of an additional term th at is not present in cases where the structure is fully submerged. This time rate of change in effective mass is dependent on the ratio of structure length (in the direction of wave propagation) to wa ve length. This ratio is small for a slender, vertical pile and thus can be neglected, as in the Morison Equati on. Similarly, when computing wave forces on offshore platforms, the deep water design wave s are much longer than the platform widths. While excluded in most models, Kaplan et al. (1 995) included the time dependent effective mass, but used averaged water veloci ties and accelerations over the width of the structure. For structures and waves of compar able lengths, though, the variation in wave kinematics over the width of the structure is signi ficant and averaged kinematics ca nnot be used. Figure 3-2 shows the discrepancy in wave kinematics for the different structure to wave size ratios. At any given moment, the structure will experience a multi-directional kinematic field. With the effective mass in constant flux and the second inertia term present, accurate values for wave kinematics and effective mass are essential. More discu ssion on this subject is presented in Chapter 5.

PAGE 37

37 The derived expressions for bot h the horizontal and vertical components of the inertia force (Equations 3-8 and 3-9) contain two terms, the first of which is referred to as the inertial term and the second as the change in effective mass term. e InertiaXMXeMXm u FCmCu tt (3-8) e InertiaZMZeMZm w FCmCw tt (3-9) In Equation 3-8 and Equation 3-9, me/ t is the time rate of ch ange of effective mass, u/ t is the horizontal water particle acceleration, w/ t the vertical water particle acceleration, CMX the horizontal inertial coefficient, and CMZ the vertical inertial coeffi cient. At this point, one could establish two separate coefficients, one for the inertial term and one for the change in effective mass term. While this would prove help ful in obtaining fits to experimental data in more complex structures, a single coefficient provid ed excellent results for a structure as simple as a flat plate. The effective mass (Equation 3-10) can be sepa rated into the sum of two components the mass of water displaced by the structure (displaced mass, ms) and the surrounding mass impacted by the structure ( added mass, ma). esammm (3-10) Payne (1981) developed an expression for the added mass of a fully submerged flat, rectangular plate of finite width for flow normal to the plate. In many situations of interest in this study the structure is not fully submerged and the width of the structure in contact with water varies with time. For this reason the structure width in Paynes expression was replaced with the time varying wetted lengths. This gives the expressions for the added mass in Equation 3-11 and Equation 3-12, where W is the wetted width of the structure and D is the wetted thickness of

PAGE 38

38 the structure. The wetted length of the structur e is a constant value due to the 90 angle of incidence of the wave an d is therefore excluded. 22 1 4 aX 22 LD m LD (3-11) 22 1 4 aZ 22 LW m LW (3-12) Ideally a plate with negligible thickness woul d not contribute to the effective mass. For the purposes of accurate comparis on, the actual thickness of the pl ate (D) must be taken into account. The displaced mass component of the eff ective mass is then eas ily calculated (Equation 3-13) as the product of flui d density and the volume (VS) the submerged portion of the structure. sSm V LDW (3-13) Combining the derived expressions for the structure displaced ma ss (Equation 3-13) and the added mass (Equation 3-11, Equation 3-12), th e expressions for the effective mass are obtained (Equation 3-14, Equation 3-15). 22 1 4 eX 22 LD m LWD LD (3-14) 22 1 4 eZ 22 LW m LWD LW (3-15) To obtain the time rate of change of effectiv e mass needed for the change in effective mass term of the inertia force equation, the time de rivatives (Equation 3-16, Equation 3-17) of the effective mass expressions (Equation 3-14, Equa tion 3-15) were taken with both the wetted width and length being functions of time. It s hould be noted that when evaluating the inertia equation numerically, either this complex derivativ e can be used to dete rmine the time rate of change of effective mass, or the time rate of chan ge of the effective mass can be calculated as the

PAGE 39

39 slope of the effective mass between time steps, providing that the resolution of the numerical model is sufficiently small. 3 1 2 4 eX 22 22D L m DWD t LWD1 ttt LD LD (3-16) 3 1 2 4 eZ 22 22W L m WDW t LDW1 ttt LW LW (3-17) For the case of a thin plate, the rate of change of the wetted width is equivalent to the wave celerity. Unlike a flat plate, for structures with finite thickness, the sl ope of the water surface must be taken into consideration when computi ng the displaced mass as the wetted width varies over the thickness of the structure. Complete expressions for the inertia for ce can now be obtaine d by substituting the effective mass (Equation 3-14, Equation 3-15) and the time rate of change of effective mass (Equation 3-16, Equation 3-17) into the origin al inertia force expr essions (Equation 3-8, Equation 3-9) and rearranging the terms. Notatio n for the time derivative has been replaced with dot notation in Equations 3-18 and 3-19 to save space. 22 2 11 44 InertiaXMX 22 2222 LD LD D FC LuDW++uWD+DW+1 L+D L+DL+D (3-18) 22 2 11 44 InertiaZMZ 22 2222 LW LW W FC LwDW++wWD+DW+1 L+W L+WL+W (3-19) Evaluating these equations can be difficult due to the rather complex nature of the time dependence of the effective mass. For example as the wave initially strikes the structure both the displaced and the added mass are changing with tim e (Figure 3-3). If th e trailing edge of the wave reaches the structure before the leading edge exits then there is a period of time when the

PAGE 40

40 effective mass is essentially constant (Figure 33). For a wave wider than the structure at elevation, a similar period of time occurs when th e mass is essentially constant as the plate is fully submerged (Figure 3-3). The effective mass becomes time dependent once again as the wave exits the structure (Figure 33). If one adheres to the stri ct mathematics of the equations, forces would cutoff and cutback with unnatural, as ymptotic like characteristics. Application of the equations when dealing with these problems is discussed in Chapter 5. Buoyancy The buoyancy force, which is sim ply the net hydro static force, is the most straightforward of the force components. All wetted portions of the structure will e xperience a buoyancy force equivalent in magnitude to the weight of the volume of water displaced by that part of the structure (Equation 3-20). BuoyancySF gV gLDW (3-20) It should be noted that the submerged volume is a function of time and is in phase with the inertial term in the inertia force equations. Slamming Force The slamm ing force occurs when the air/water interface of the wave strikes the surface of the structure. During this initial contact a signi ficant exchange of momentum takes place at a high frequency. Depending on structure location and the wave parameters, the magnitude of this force can be equal to or greater than the quasi-steady forces. The impact of the slamming force depe nds on, among other things, the response characteristics of the structure. The short dur ation/high frequency nature of the slamming force can either increase or attenuate its contribution to the total forcing depending on the response characteristics of the structure. If the slamming force frequency is sufficiently high, the structure

PAGE 41

41 may not have time to respond and therefore the impact will be minimal. If the frequency of the slamming force is in the range of the natural frequency of the stru cture, then the impact can be significant. As an example, consider a dampened spring-mass-dashpot system (Figure 3-7). The differential equation (Equation 3-21 ) that describes this forci ng motion is a function of the displacement (z), the mass (m), a spring cons tant (k), and a damping coefficient (c). 2 2dzdz F(t)mcmkz dt dt (3-21) There are three important frequencies to th is single degree of freedom system the systems forcing frequency ( ), the systems natural frequency ( n), and the systems damped frequency ( d). Expressions for the natural freq uency (Equation 3-22) and the damped frequency (Equation 3-23) are given. The critical damping occurs when c = 2m n. nk m (3-22) 2 dn nc 1 2m (3-23) Depending on how close the forcing frequency is to the structure dampened frequency, the magnitude of the displacement can be amplifie d or attenuated. The structure response as a function of damping magnitude and ratio of forci ng to natural frequency is shown in Figure 3-8. Note that as the forcing freque ncy approaches the natural freque ncy the response is significantly amplified. As the mass of the structure becomes la rge (as in the case of a bridge), the frequency of its fundamental mode of vibr ation becomes very low and thus far removed from the slamming frequencies For this reason the slamming force ma y not have a significant impact on the bridge superstructure response. However, more work is needed on this topic before accurate predictions

PAGE 42

42 of slamming force frequencies can be made and definite conclusions regarding bridge superstructure response can be drawn. Empirical equations for the slamming force in terms of structure and wave parameters were developed as part of this study. Evaluating the Theoretical Model Due to the c omplexity of the calculations i nvolved in computing wave forces using the theoretical model, a co mputer model was developed. Inputs to the model include structure dimensions and location relative to the still wa ter surface, water depth and properties and wave kinematics. The drag and inertia coefficients needed in the numerical model were those that yielded the best fit to the experimental data. This numerical model used a gridded system for applying the theoretical equations. The structure and wave field were di vided into fine resolution elements. Inside each element (each element consisting of a known mass and wave partic le kinematics), the equations were solved. For each time step, the results of all the indivi dual elements were summed together to produce the total forcing of each component. Wave particle kinematics inside this model was generated using stream function theory, a nonlinear wave theory. This pr oduces better results in nears hore environment as these waves tend to become nonlinear as they shoal.

PAGE 43

43 Figure 3-1. Definition sketch for wave loading on a flat horizontal plate.

PAGE 44

44 A B Figure 3-2. Distribution of vertic al wave kinematics over structure subjected to wave attack. A) Structure of small size relative to wave length. B) Structure of comparable size relative to the wave length. Darkened kinematics curve shows distribution over structure at a mome nt of inundation.

PAGE 45

45 A B C D Figure 3-3. Variation of the time rate of change of effective mass over one wave period cycle. A) Wave propagating into structure. B) Wave propagating during maximum inundation. C) Wave propagating during complete submergence. D) Wave propagating away from structure.

PAGE 46

46 Figure 3-4. A spring-mass-das hpot system with damping. 0.0 1.0 2.0 3.0 0.01.02.03.04.05.0 / nAmplification =0.1 =0.2 =0.4 = 0.5 = 1.0 = Damping Ratio (c/co) = Forcing Frequency n = Natural Frequency c = Damping Coefficient co = Critical Damping Coefficient Figure 3-5. Spring-mass-dashpot system amplifi cation effect versus damping and frequency ratios.

PAGE 47

47 CHAPTER 4 PHYSICAL MODEL TESTS Wave force data from previous physical model tests exhibit considerab le scatter. This can be attributed to the highly dynamic nature of the fo rces being measured. If load cells are used to measure the forces, any movement of the structure or its support can alter the indicated forces. In the theoretical analysis, treating the struct ure as a rigid body eliminates many of these difficulties, but in the actual physical testing, steps must be taken to insure that the structure is as close to a rigid body structure as practical. Wave loading is a combination of low fre quency drag and inertia forces, buoyancy, and high frequency slamming forces. While the low frequency forces are well within the range that can produce a structural response, it is not obvious whether many bridge superstructures can respond to the higher frequency slamming forces. While the magnitude of the slamming force is often significant, if its duration is sufficiently sh ort then the structure ma y not respond to it as shown in the spring-mass-dashpot system discussion in Chapter 3. Also, if the structure, support, or instrumentation response frequencies are in th e range of the loading frequencies, movement in these can alter the force signals from the load cells. To avoid these problems, the structure and s upport system was made as stiff as possible, producing a model that is functionally a rigid body. Sampling of a ll instrumentation must be at least twice the highest frequency of interest (i.e. the Nyquist Fr equency) so that all forcing frequency contributions can be resolved and separated later with filtering. The sampling frequency for all the tests conducted was 480 Hz, resolving frequencies up to 240Hz. Test Facility All tests were conducted in one of the wave tanks located at th e Coastal Engineering Laboratory at the University of Florida. The wa ve tank is 6 ft wide by 6 ft deep by 120 ft long.

PAGE 48

48 The wave maker has the capability of both paddl e and piston modes of op eration but was used solely in piston mode. Wave absorbers are lo cated behind the paddle and at the downstream end of the tank in order to minimize wave reflection. A series of glass panels run the length of one side of the tank for viewing. The range of wave heights and periods as a function of water depth achievable in this tank is shown in Figure 4-1. The Physical Model The horizontal dim ensions of the physical m odel are approximately that of a 1:8 scale model of the bridge decks on the old I10 Bridge over Escambia Ba y, Florida. This bridge was severely damaged by storm surge and wa ve loading during Hurricane Ivan in 2004. The instrumented model is intended to repr esent a strip through the span with the dimension parallel to wave propa gation being the width of the br idge (i.e., the waves approach the bridge normal to the roadway). To reduce th e effects of the wave tank walls the model was divided into three separate sect ions of equal length, with only the center section instrumented. The two, non-instrumented side sections also serv ed to minimize end effects for the instrumented section. Several tests were run w ithout the two side sections to determine the impact of cases where there would be free flow around the ends. Each of the three sections of panels were constructed of 1 inch thick polypropylene and measured 4 ft wide and 2 ft long. A diagram of the three panel layout is shown in Figure 4-2, with the center panel being the only one instrumented. To stiffen the individual panels, aluminum channe ls were added to all sides of the panels. To avoid possible effects from contact between pane ls, the side panels were spaced 1/8 away on either side of the instrumented panel. To main tain the effect of a si ngle continuous span across the tank, 3/8 plastic strips running the full widt h of the panels were mounted above and below the 1/8 gaps between panels. Mounted to the si de panels and overlapping with the instrumented

PAGE 49

49 panel, the strips prevented unwanted flow be tween panels while providing minimal impact on instrument measurements taken. The Support Structure The plate m odels were supported from above by 30 long steel pipes, 1 in diameter. For the dummy side plates, flanges were welded to th e pipe ends and attached to the plates by four bolts. For the center, instrumented panel, three-axis load cells were placed in aluminum housing on the end of the steel pipes and bolted into the deck. All 12 pipe supports were attached to a steel double H frame made with 6 x 2 channels. The H frame was connected to the main steel carriage by four 1 screws used to lower and raise the entire plate model and H frame structure. This allowed for easy adjustment of the model elevati on relative to the still water level. The main steel carriage is construc ted of 6 box tubing and is rigidly attached to the concrete and steel walls of the wave tank. A number of stiffeners were added to make the support structure more rigid. Steel bar cross bracing was placed between each set of pi pes running longitudinally down the length of the tank. Aluminum channel bracing was run laterally across the pipes as well Eight turnbuckles connecting the H frame to the solid steel carria ge were also added. The bracing was added in stages until the structure was deemed suffici ently rigid. The suppor t structure and model arrangement are shown in Figure 4-3 and Figure 4-4. Instrumentation Four m ulti-directional load cells were placed in aluminum housings and attached near the four corners of the center plate. The load cells measured forces in the X (longitudinally down the tank), Y (laterally across the tank), and Z (ver tical) directions. The electronics for the load cells were housed above the structure carriage. The wire leads and cables from the load cells were routed through the support pi pes. In the X and Y directions, the load cell maximum range

PAGE 50

50 was lbs per cell. In the Z direction, the load cell maximum ra nge was lbs per cell. The frequency response of the load cells was 1 kHz. Three capacitor-type wave gauges, developed by engineers at the Co astal Laboratory, were used to monitor the waves. The wave gauges we re located 32 ft and 8 ft upstream from the leading edge of the structure, and 8 ft downstream from the tra iling edge. The wave gauges were positioned so that the effects of the structure on the wave field could be estimated. The frequency response of the wave gauges was 1 kH z. All instrumentation was sampled at 480 Hz with all measurements taken and waves produced using LabView. The test section was located ne ar the center of the tank, 68 ft from the paddle. A working diagram of the model and wave gauge is shown in Figure 4-5. Physical Model Tests 192 tests were perform ed with al l 3 panels in place. 100 test s were performed without the side panels. For each test several monochromatic waves of the same height and period were run past the structure. Wave heights, wave periods clearance heights, and wa ter depths were varied over the tests. The range of pa rameters covered is shown in Ta ble 4-1. Forces were measured by four load cells, one at each corner of the inst rumented panel. Wave heights were recorded upstream and downstream of the structure. Example plots of the raw vertical force for the cases of a sub aerial (Figure 4-6) and a submerged plate (Figure 4-7) are shown. Data Processing Data from the experiments were reduced and analyzed as described below. Spectral Analysis Power spectra were com puted for the vertical component of each of the load cells as well as for the combined two upstream (and two downstr eam) cells. In all cases, the frequency with the highest power content was that of the wa ve frequency. Example power spectrums for sub

PAGE 51

51 aerial and submerged cases are shown in Figure 48. The wave frequency for these tests was 0.5 Hz (period = 2 sec). In tests where a slamming effect was pres ent, a smaller frequency peak (several orders of magnitude smaller than the pe ak of the wave frequency and its harmonics) can be seen in the range of 5 to 10 Hz. These two discernible peaks in forcing frequencies present a divi ding line between the forcing mechanisms. All forcing in the frequency range of the wave period is referred to as the quasi-steady force due to its smooth occurrence over the inunda tion cycle of the structure. Forcing in the range of the higher frequency p eak is referred to as the slamming force. A few notes can be made from Figure 4-8. In the submerged case, there is very little energy present in the harmonic multiples of the wa ve frequency and no energy at all in the range of slamming. For a structure in itially submerged or partially su bmerged, the natural frequency of the structure is lowered by the presence of the a dded mass of the water. There is also more damping for this situation. In this case, there is less st ructural response at the higher frequencies. In the sub aerial case the higher frequency slammi ng force excites the higher harmonics and also there is less damping. When considering the possible effects of slam ming in a design environment, the issue of partial submergence and added mass would then app ear to play an important part. The natural frequency of the structure as well as the response characteristics of the structure vary with the added mass quantity. A single stru cture could theoretically respond to the slamming force at one clearance height and not at a nother, depending on how the natu ral frequency is altered by the magnitude of the added mass. In the power spectra of the upstream and dow nstream load cell pairs, similar frequency content divisions were found as in the total forcing. However, from the upstream to the

PAGE 52

52 downstream pair a significant decrease in slamm ing frequency content was noticed (Figure 49). The presence of detectable action in the higher frequency range of the upstream load cell pairs did not always correspond to action in the downstream load cell pair. This difference points to the effects of slamming being limited to the upstream end of the structure during initial wave/structure interaction. In all tests a small amount of 60 Hz noise was present. Signal Filtering It was useful to separate the quasi-steady forces from the slamming forces. A low-pass 8th order Butterworth filter was used to filter out the higher frequency components of the force. To determine attenuation effects of the filter on the lower frequency forcing, maximums and minimums were compared for test cases where hi gher frequency components were not present. Attenuation of the quasi-static force due to the f ilter proved to be negligible. The slamming force signal was then determined by subtracting the filtered quasi-steady force from the original forcing. A sub aerial example of the original verti cal force time series and its filtered signals are shown for the same test case used in Figure 46. Included is the noise less signal (Figure 4-10), the quasi-steady signal (Figure 4-11), and the slamming signal (Figure 4-12). This filtering sequence was also done on the upstream and downstream load cell pairs. While the quasi-steady force readily appears in both pairs, for most cases the slamming force was not present in the downstream load cells. This confirms that the slamming force is somewhat confined to the upstream half of the structure. Assumption Verification To sim plify both the analysis of the data and create a practical pred ictive design tool, the wave is assumed to be two-dimensional and prop agates directly perpendicular to the structure (the orientation established as cr eating the largest forcing). This allows for the forcing to be

PAGE 53

53 treated as a force per unit length. However, wave tank wall shear and drag effects can affect the two-dimensionality of the wave as it propagate s. Waves propagating at an angle of incidence other than 90 would create altern ate forcing and phase shifts in lateral loading distribution. To check this, differences in force measurements in laterally located load cell pairs were compared. The differences between individual located load cells measured maximum force showed scatter in the range of 0-5%, sufficiently small enough fo r two-dimensionality to hold. As a further check, lateral axis load measurements in all load cells showed negligible forcing. Significant Parameters Extracted from the Data Once tim e series of the quasi-steady and slam ming force and water surface elevation were obtained, a number of important parameters could be computed. Maximum and minimum values of the quasi-steady forces were extracted and the maximum and minimum values of the moments about the downstream edge of structure comput ed. The maximum values of the slamming force were extracted as well as the slamming frequency and duration. From the water surface elevation data, wave heights and maximum wave crest elevations corresponding to the forces were obtained. Th is information is presented in Appendix A.

PAGE 54

54 Figure 4-1. Air/sea wave tank wave height limits by period and depth.

PAGE 55

55 Figure 4-2. Continuous flat plate model including side panels (plan view).

PAGE 56

56 Figure 4-3. Definition sketch of the phys ical model setup (side profile view).

PAGE 57

57 Figure 4-4. Definition sketch of the physic al model setup (front profile view).

PAGE 58

58 Figure 4-5. Physical model setup showing the location of an upstream wave gauge.

PAGE 59

59 -100 -50 0 50 100 150 0.02.04.06.08.010.012.014.0Time ( sec ) Force (lbs)A -100 -50 0 50 100 150 10.010.511.011.512.012.5Time ( sec ) Force (lbs)B Figure 4-6. Total raw vertical for ce examples for a typical sub aeria l case. A) Force time series resulting from the passage of several waves. B) Force time series resulting from a single wave.

PAGE 60

60 -100 -50 0 50 100 150 200 0.02.04.06.08.010.012.014.0Time ( sec ) Force (lbs)A -100 -50 0 50 100 150 200 11.111.311.511.711.912.112.312.512.712.913.1Time (sec)Force (lbs)B Figure 4-7. Total raw vertical for ce examples for a typical submerged case. A) Force time series resulting from the passage of several waves. B) Force time series resulting from a single wave.

PAGE 61

61 0 2000 4000 6000 8000 10000 12000 14000 16000 02468Fre q uenc y ( Hz ) Power Spectral Density A 0 100 200 300 400 500 600 700 800 900 02468Frequency (Hz)Power Spectral Density B Figure 4-8. Typical power spectral density of total vertical forcing. A) Submerged span case. B) Sub aerial span case. Wave period = 2.0 seconds in both cases.

PAGE 62

62 0 10 20 30 40 50 60 70 80 90 02468Fre q uenc y ( Hz ) Power Spectral Density A 0 5 10 15 20 25 30 35 40 45 50 02468Frequency (Hz)Power Spectral Density B Figure 4-9. Typical power spectral density of load cell pair vertical forcing. A) Upstream load cell pair. B) Downstream load cell pair. Wave period = 2.0 seconds in both cases.

PAGE 63

63 -100 -50 0 50 100 150 0.02.04.06.08.010.012.014.0 Time ( sec ) Force (lbs) Raw Noise removedA -100 -50 0 50 100 150 10.010.511.011.512.012.5 Time (sec)Force (lbs) Raw Noise removedB Figure 4-10. Total filtered (noise removed) vertical fo rce examples for a typi cal sub aerial case. A) Force time series resulting from the pa ssage of several waves. B) Force time series resulting from a single wave. Contains raw signal for comparison.

PAGE 64

64 -100 -50 0 50 100 150 0.02.04.06.08.010.012.014.0 Time ( sec ) Force (lbs) Raw Quasi-steadyA -100 -50 0 50 100 150 10.010.511.011.512.012.5 Time (sec)Force (lbs) Raw Quasi-steadyB Figure 4-11. Total quasi-steady ve rtical force examples for a typi cal sub aerial case. A) Force time series resulting from the passage of several waves. B) Force time series resulting from a single wave. Contains raw signal for comparison.

PAGE 65

65 -100 -50 0 50 100 150 0.02.04.06.08.010.012.014.0 Time ( sec ) Force (lbs) Raw SlammingA -100 -50 0 50 100 150 10.010.511.011.512.012.5 Time ( sec ) Force (lbs) Raw SlammingB Figure 4-12. Total slamming force examples for a typical sub aerial case. A) Force time series resulting from the passage of several waves. B) Force time series resulting from a single wave. Contains raw signal for comparison.

PAGE 66

66 Table 4-1. Range of fluid variable values covered in the physical model testing. Test setup Water depth (ft) Wave period (s) Wave height (ft) Clearance height (ft) Continuous plate with side panels 1.58 2.331.00 3.000.32 0.99 -0.42 0.25 Finite plate with no side panels 2.00 2.671.00 3.570.46 1.01 -0.35 0.29

PAGE 67

67 CHAPTER 5 RESULTS AND ANALYSIS Com parisons were made between the physical mo del data and the predictive mathematical model for quasi-steady forces. Empirical coeffici ents were determined. Developed relationships were tested against the physical model data as well as independent data (Isaacson and Bhat 1996). Effects of subjective evalua tion choices are discussed. An empirical relationship for the slamming force is developed and checked against the physical model data. The slamming force and dynamic effects are considered. Comparisons between tests with and without side panels are also made. Evaluative Considerations When evaluating the theoretical equations in the m athematical model, the physical effects inside the flow needed to be considered. While equations were developed for predicting quantities such as added mass and change in effective mass, there are no simple means for predicting the exact dist ribution of the added mass in the flow field. Added Mass Location W ith the large variation in kinematics along th e structure at any given point in time, the location of the fluid mass affected can radically alter not only the magnitude of the forces, but also the shape of force time series. While the variation of coefficients will most certainly manipulate the magnitudes of the forces produced, variation of the kinema tics applied to these calculated masses will, to a degree, govern the phas ing of the individual force components. This will in turn manipulate the overall shape of the for ce time series, an important factor in the least squares fit over a full wave period. While the kinematic variation is problematic, the time dependent change in effective mass term is equally difficult to evaluate. From one given time step to the next, there is the

PAGE 68

68 contribution of momentum transfer from the mass of water that is either newly part of the added mass or no longer a part of it. As that mass vari es, which velocities selected in the additional mass will also alter the phasing. Three separate methods for selecting added mass location were developed. The first method was a constant incrementing in the vertical direction originating from the areas of wetted structure and continuing perpe ndicular to those areas. The second method mimicked the first method with the addition of a linear spread fr om the structure 45 degrees outward to the perpendicular. The final method was a multi-di rectional diffusion radiating out from the wetted surface of the structure. Examples of each are shown in Figure 5-1. The best fit to the data was provided by the first method. Change in Effective Mass The single most difficult evaluati ve aspect of the m odel is in the evaluation of the change in effective mass equations as described in Chap ter 3. If the equations are used as defined, depending on the confluence of wave length, deck width, wave height, and structure clearance, the change in effective mass forcing will experi ence cutoffs in the force time series, creating choppy force curves with asymptotic-like transiti ons. These jagged transitions do not appear in the measured force time series of the physical mo del experiments, so a method of dealing with these erratic forces was needed. Example force time series for the change in e ffective mass were developed for a sub aerial case. In Figure 5-2, the mass quantities and fo rce time series are shown for a structure whose maximum wetted width is less than or greater than the length of wave at the clearance height. The effects of the disappearance in force and change in effective mass can be seen in both. Different methods of dealing with this problem have been used in previous work. Once the time rate of change of effective mass term in the inertial force reached a maximum, Isaacson

PAGE 69

69 and Bhat (1996) dropped the force linearly to zero at the moment where the wave crest was over the center of the plate. After this moment, the force was taken as zero. Kaplan et al. (1995) set the force to zero as soon as the plate reached the point of maximum inundation. Either method, though, continues to ignore the term even when time rate of change of the effective mass varies again once the wave begins to leave the plate. In the numerical model, when change in eff ective mass drops to zero, the force is brought down linearly to the point where the change in effective becomes negative as the wave leaves structure. Further work on this topic is recommended. The Quasi-steady Force Using the structural param eters and wave conditions from the physical model tests, predicted force time series were calculated usi ng the numerical model. Individual time series of the inertia force, the change in effective ma ss force, the drag force, and the buoyancy were output with a resolution of 480 Hz for ease of comparing with the experimental results. Comparisons were made between the predicte d numerical model and measured quasi-steady signal obtained from the filtered forcing time series. Fits were determined by varying the drag and inertia coefficients as well as certain characte ristics of the program to obtain a best fit using the least squares method for the forcing over a full wave period. Empirical Coefficients Sets of coefficien ts (drag and inertia) were created from the pr edicted versus measured fits. Relationships for these coefficients were dete rmined based on dimensionless groups obtained from the dimensional analysis in Chapter 3. For the test setups run as a continuous plate with side pa nels, values of the inertia coefficient ranged from 0.1 to 1.1. The coefficien t was found to be a function (Equation 5-1) of two of the groups derived in the dimens ional analysis the relative width (W/ ) and the relative

PAGE 70

70 height (ZC/ ). A plot of the data fit is shown in Figur e 5-3. For the test se tups run as a finite length plate with no side panels values of the inertia coefficient ranged from 0.2 to 1.8. The coefficient was similarly found to be a function (Equation 5-2) of the same two dimensionless groups. A plot of the data fit is shown in Figure 5-4. C MZZ W C031710195903531 L ..ln. (5-1) C MZZ W C089420381107163 L ln..ln. (5-2) With the system being inertia dominated, th e drag term did not provide a significant contribution to the overall forcing in either test setups. Alteri ng the drag coefficient produced little effect in the overall magnitude of the fo rces (the drag force of ten being an order of magnitude less than the inertia, buoyancy, and slamming terms). A ll determined values of the drag coefficient fell within the range of 1.8 to 2.3 for all tests. Due to both the small range of values and its slight contribution, a constant va lue was chosen for the drag coefficient (Equation 5-3), applicable to either test se tup (with and without side panels). DZC2.2 (5-3) Using the relationship developed for the inerti a and drag coefficients, the predictive model was rerun for all test cases. All cases showed excellent fit to maximum and minimum peak forces. Most cases showed good fit to the phasing of the force curve. Predicted versus measured plots are presented in Appendix B for the majority of the cases. An example of the predicted versus measured plots for both a sub aerial ca se and submerged case are shown in Figure 5-5. Accuracy of Predictive Equations W ith the relationships for the coefficients bei ng derived from the same data it was checked against, the success of the predictive capabilities of the model is biased towards the data that

PAGE 71

71 generated it. The data (quasi-steady force data for12 subaerial cases) presented by Isaacson and Bhat (1996) allows for an inde pendent data source to compar e against. Using the input parameters from the data, comparisons between the predicted and measured maximum and minimum forces were made. The results of th e comparison are presented in Figure 5-6. The predictive model shows good agreemen t with the independent data. The Slamming Force A relationship for the slamming forc e was dete rmined from a purely empirical standpoint, using dimensionless groups. An envelope fit was used on the data to insure a conservative estimate. The two dimensionless groups found to be influential were groups used before, the wave steepness and the relative height. The quantity used to non-dimensionalize the slamming force is a mass times acceleration system based on the mass of the water above the plate and the acceleration of the wave taken from linear wave theory. The equation for slamming for a continuous plat e with sides is presented in Equation 5-4 with the data fit shown in Figure 5-7. The equa tion for slamming for the plate with no sides is presented in Equation 5-5 with th e data fit shown in Figure 5-8. S C CFZ H 149991794012668 gHW Z ln..exp. / (5-4) S C CFZ H 926321095211647 gHW Z ln ..exp. / (5-5) Both equations for the slamming force are only valid for values -1.0 < ZC/ < 1.0. Outside of this range there is no slamming. Continuous Plate versus Finite Len gth Plate The continuous span nature of a bridge create s a structure that func tionally is infinitely long. This creates a situation wh ere there are no end flow effects. On a stand alone structure

PAGE 72

72 with a finite length, there will be end effects. Comparisons were made between tests run with side panels and without side panels ut ilizing important dimensionless groups. Figure 5-9 is a plot of norma lized quasi-steady force versus structure location for fixed wave steepness and relative width for the continu ous and finite width setups. Figure 5-10 is a plot of normalized slamming forcing versus st ructure location for fixed wave steepness and relative width for the same two plate setups. In both plots the forcing on th e finite width plate is noticeably less than that of the continuous plate. This is particularly true for the slamming force, where the continuous plate force is as much as three times larger than its counterpart.

PAGE 73

73 A B C Figure 5-1. Methods of estimating the added mass distribution around the plat e. A) 90 spread in direction of the forcing. B) 45 linear spread in direction of the forcing. C) Radiating uniform spread out from the structure.

PAGE 74

74 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.21.41.61.822.22.42.62.83 Time ( sec ) Effective Mass force Effective mass Slope of effective massA -1.2 -0.8 -0.4 0 0.4 0.8 1.2 11.21.41.61.82 Time (sec) Effective Mass force Effective mass Slope of effective massB Figure 5-2. Variation of effective mass and rela ted quantities over one wave period. A) For a structure with width greater th an the length of wave at the clearance height. B) For a structure with width less than the length of the wave at the clearance height.

PAGE 75

75 Figure 5-3. Inertial coeffici ent data fit for continuous plate tests with side panels. Figure 5-4. Inertial coefficient data fit for finite length plate test s without side panels.

PAGE 76

76 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5Time ( sec ) Force (lbs) Measured Predicted Figure 5-5. Example of predicted versus m easured values of the quasi-steady force.

PAGE 77

77 0 2 4 6 8 10 12 14 16 18012345678910111213CaseForce (lbs) Isaacson and Bhat ( 1996) University of Florida Figure 5-6. Comparison of Florid a model predictions versus i ndependent experimental data (Isaacson and Bhat 1996).

PAGE 78

78 Figure 5-7. Slamming force empirical data fit for a continuous plat e with side panels. Figure 5-8. Slamming force empirical data fit fo r a finite length plate without side panels.

PAGE 79

79 0.0 0.5 1.0 1.5 2.0 2.5 -1.5-1.0-0.50.00.51.0Zc/ F/ gH L WS NS H/ = constant = 0.03 W/ = constant = 0.2 Figure 5-9. Comparison of non-di mensionalized quasi-steady for ces between continuous plate with side panel tests and finite length plate without side panel tests. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 -1.50-1.00-0.500.000.501.00Zc/ F/ gH L WS NS H/ = constant = 0.03 W/ = constant = 0.2 Figure 5-10. Comparison of non-dimensionalized slamming forces between continuous plate with side panel tests and finite length plate without side panel tests.

PAGE 80

80 CHAPTER 6 CONLCUSIONS AND RECOMMENDATIONS A theoretical m odel for wave loading on a flat plate was developed for situations where the wave length and structure width are approximately the same size. Physical model tests were conducted for a range of wave parameters and st ructure setups. The measured forces were separated into the lower frequency, quasi-stea dy and higher frequency sl amming components. A numerical model was developed to aid in the ev aluation of the theoretical model. Drag and inertia coefficients were chosen so as to minimize the difference between predicted and measured values of the force. The coefficien ts were found to depend on certain dimensionless groups of variables and these re lationships were also obtaine d from the data. Comparisons between the predictive model and independently obt ained experimental data (Isaacson and Bhat 1996) showed good agreement. As a basis for co mplex structures, the results are encouraging. Quasi-steady Force The quasi-steady force is the low frequency fo rcing com ponent that occurs over the full inundation cycle of a wave. It is composed of a momentum term, a drag term, and the buoyancy. The momentum term can be further separated into an inertial compone nt and a change in effective mass component. The change in effect ive mass component is a highly variable force dependent on the structure and wave parameters. For the range of parameters considered in this study the inertia force is dominant over the drag force. Accurate calculation of the added mass and where it is located in the wave field is important to accu rate predictions. Slamming Force The slamm ing force is the high frequency moment um exchange force that occurs when the air-water interface strikes the structure. Because of its short duration, the impact of this force on the structure response depends on several parame ters including the structures dynamic response

PAGE 81

81 characteristics and can vary greatly for similar conditions. A purely empi rical relationship was developed for the slamming force. Recommendations W ith the model developed for the quasi-steady force showi ng excellent agreement with experimental data, the next step is to apply to the model to more complex structures and adjust as needed. From a thin plate, the next setup is l ogically a rectangular plat e with a finite thickness with a physical model dimensioned similar to a bridge superstructure. For any more complex case, the horizontal forces must now be consider ed. With a working model for a finite thickness model, bridge superstructures can then be investigated using more expl icitly complex models, including girders, rails, and ove rhangs. For these cases, further work involving air entrapment and horizontal slamming is needed. The time rate of change in effective mass re quires further work. Discrepancies between theory and observed forces need to be resolved. While the empirical slamming equation agr ees well with the physical model data, a theoretical model is needed to practically expa nd the use for more complex models. A fully empirical model used for every structure type or setup would be unfeasible. Also needed is a better understanding of the duration of the slamming as well as the area over which the slamming force acts. In a controlled experimental envir onment, the structures dynamic properties can be manipulated, but in a prototype, dynamic properties will play a roll in the slamming force. As such, these effects must be considered in all mo dels. For the more complex bridge models, the effects of air entrapment on the slamming force also need to be investigated. In further work, means for reducing the total forcing should be considered. In complex structures, means of bleeding entrapment air via vents between either th e deck or girders are possible items of interest.

PAGE 82

82 APPENDIX A PHYSICAL MODEL DATA The following tables are a list of all physical m odel tests performed and the significant variables and values associated with each test. The tables are divided into variables and forces as well as tests done with and without side panels (i.e. continuous and finite width structures). The tests can be differentiated by the individual case prefix and reference number, FPWS for tests done with side panels, and FPNS for tests done without side panels. These reference numbers correspond to the same numbers given in the comparison plots in Appendix B. Table A-1 contains the relevant fluid and structure parameters for all tests. Table A-2 contains the measured significant forces and moments for all tests. All dimensions are in feet, all forces are in pounds, and all times are in seconds.

PAGE 83

83 Table A-1. Structure and fluid parameters for all physical model tests. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPWS-001 4.00 6.00 0.08 0.001.580.323.0020.65 4.00 0.16 FPWS-002 4.00 6.00 0.08 0.001.580.633.0020.65 4.00 0.31 FPWS-003 4.00 6.00 0.08 0.001.580.542.5016.92 4.00 0.27 FPWS-004 4.00 6.00 0.08 0.001.580.832.5016.92 4.00 0.42 FPWS-005 4.00 6.00 0.08 0.001.580.582.0013.12 3.51 0.29 FPWS-006 4.00 6.00 0.08 0.001.580.752.0013.12 3.73 0.38 FPWS-007 4.00 6.00 0.08 0.001.580.611.509.17 3.66 0.30 FPWS-008 4.00 6.00 0.08 0.001.580.671.509.17 2.41 0.33 FPWS-009 4.00 6.00 0.08 0.001.580.581.004.94 3.26 0.29 FPWS-010 4.00 6.00 0.08 0.001.580.521.004.94 2.47 0.26 FPWS-011 4.00 6.00 0.08 0.081.580.453.0020.65 4.00 0.22 FPWS-012 4.00 6.00 0.08 0.081.580.683.0020.65 4.00 0.34 FPWS-013 4.00 6.00 0.08 0.081.580.482.5016.92 4.00 0.24 FPWS-014 4.00 6.00 0.08 0.081.580.752.5016.92 4.00 0.38 FPWS-015 4.00 6.00 0.08 0.081.580.422.0013.12 4.00 0.21 FPWS-016 4.00 6.00 0.08 0.081.580.582.0013.12 4.00 0.29 FPWS-017 4.00 6.00 0.08 0.081.580.631.509.17 4.00 0.32 FPWS-018 4.00 6.00 0.08 0.081.580.671.509.17 4.00 0.34 FPWS-019 4.00 6.00 0.08 0.081.580.581.004.94 1.66 0.29 FPWS-020 4.00 6.00 0.08 0.081.580.501.004.94 1.98 0.25 FPWS-021 4.00 6.00 0.08 0.171.580.383.0020.65 3.17 0.19 FPWS-022 4.00 6.00 0.08 0.171.580.643.0020.65 4.00 0.32 FPWS-023 4.00 6.00 0.08 0.171.580.482.5016.92 4.00 0.24 FPWS-024 4.00 6.00 0.08 0.171.580.712.5016.92 4.00 0.35 FPWS-025 4.00 6.00 0.08 0.171.580.462.0013.12 3.25 0.23 FPWS-026 4.00 6.00 0.08 0.171.580.602.0013.12 4.00 0.30 FPWS-027 4.00 6.00 0.08 0.171.580.501.509.17 2.54 0.25 FPWS-028 4.00 6.00 0.08 0.171.580.651.509.17 3.25 0.32 FPWS-029 4.00 6.00 0.08 0.171.580.501.004.94 1.51 0.25 FPWS-030 4.00 6.00 0.08 0.171.580.441.004.94 1.19 0.22 FPWS-031 4.00 6.00 0.08 0.251.580.403.0020.65 0.00 0.20 FPWS-032 4.00 6.00 0.08 0.251.580.583.0020.65 3.53 0.29 FPWS-033 4.00 6.00 0.08 0.251.580.462.5016.92 0.00 0.23 FPWS-034 4.00 6.00 0.08 0.251.580.752.5016.92 4.00 0.38 FPWS-035 4.00 6.00 0.08 0.251.580.482.0013.12 0.00 0.24 FPWS-036 4.00 6.00 0.08 0.251.580.582.0013.12 2.21 0.29 FPWS-037 4.00 6.00 0.08 0.251.580.581.509.17 1.54 0.29

PAGE 84

84 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPWS-038 4.00 6.00 0.08 0.251.580.691.509.17 2.36 0.34 FPWS-039 4.00 6.00 0.08 0.251.580.511.004.94 0.00 0.26 FPWS-040 4.00 6.00 0.08 0.251.580.481.004.94 0.00 0.24 FPWS-041 4.00 6.00 0.08 0.081.790.413.0021.86 4.00 0.21 FPWS-042 4.00 6.00 0.08 0.081.790.783.0021.86 4.00 0.39 FPWS-043 4.00 6.00 0.08 0.081.790.492.5017.87 4.00 0.25 FPWS-044 4.00 6.00 0.08 0.081.790.832.5017.87 4.00 0.42 FPWS-045 4.00 6.00 0.08 0.081.790.582.0013.80 4.00 0.29 FPWS-046 4.00 6.00 0.08 0.081.790.752.0013.80 4.00 0.38 FPWS-047 4.00 6.00 0.08 0.081.790.691.509.54 4.00 0.35 FPWS-048 4.00 6.00 0.08 0.081.790.581.005.01 1.81 0.29 FPWS-049 4.00 6.00 0.08 0.001.790.493.0021.86 4.00 0.24 FPWS-050 4.00 6.00 0.08 0.001.790.783.0021.86 4.00 0.39 FPWS-051 4.00 6.00 0.08 0.001.790.512.5017.87 4.00 0.26 FPWS-052 4.00 6.00 0.08 0.001.790.752.5017.87 4.00 0.38 FPWS-053 4.00 6.00 0.08 0.001.790.702.0013.80 4.00 0.35 FPWS-054 4.00 6.00 0.08 0.001.790.792.0013.80 4.00 0.40 FPWS-055 4.00 6.00 0.08 0.001.790.721.509.54 4.00 0.36 FPWS-056 4.00 6.00 0.08 0.001.790.541.005.01 2.50 0.27 FPWS-057 4.00 6.00 0.08 0.171.790.363.0021.86 2.62 0.18 FPWS-058 4.00 6.00 0.08 0.171.790.723.0021.86 4.00 0.36 FPWS-059 4.00 6.00 0.08 0.171.790.512.5017.87 4.00 0.26 FPWS-060 4.00 6.00 0.08 0.171.790.752.5017.87 4.00 0.38 FPWS-061 4.00 6.00 0.08 0.171.790.502.0013.80 3.83 0.25 FPWS-062 4.00 6.00 0.08 0.171.790.672.0013.80 4.00 0.33 FPWS-063 4.00 6.00 0.08 0.171.790.631.509.54 3.20 0.31 FPWS-064 4.00 6.00 0.08 0.171.790.521.005.01 1.40 0.26 FPWS-065 4.00 6.00 0.08 0.251.790.363.0021.86 0.00 0.18 FPWS-066 4.00 6.00 0.08 0.251.790.673.0021.86 4.00 0.33 FPWS-067 4.00 6.00 0.08 0.251.790.442.5017.87 0.00 0.22 FPWS-068 4.00 6.00 0.08 0.251.790.672.5017.87 4.00 0.34 FPWS-069 4.00 6.00 0.08 0.251.790.502.0013.80 0.00 0.25 FPWS-070 4.00 6.00 0.08 0.251.790.752.0013.80 3.81 0.38 FPWS-071 4.00 6.00 0.08 0.251.790.641.509.54 2.01 0.32 FPWS-072 4.00 6.00 0.08 0.251.790.541.005.01 0.60 0.27 FPWS-073 4.00 6.00 0.08 0.002.060.513.0023.30 4.00 0.26 FPWS-074 4.00 6.00 0.08 0.002.060.863.0023.30 4.00 0.43

PAGE 85

85 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPWS-075 4.00 6.00 0.08 0.002.060.582.5019.00 4.00 0.29 FPWS-076 4.00 6.00 0.08 0.002.060.762.5019.00 4.00 0.38 FPWS-077 4.00 6.00 0.08 0.002.060.672.0014.58 4.00 0.33 FPWS-078 4.00 6.00 0.08 0.002.060.812.0014.58 4.00 0.41 FPWS-079 4.00 6.00 0.08 0.002.060.721.509.95 4.00 0.36 FPWS-080 4.00 6.00 0.08 0.002.060.501.005.06 2.53 0.25 FPWS-081 4.00 6.00 0.08 0.082.060.503.0023.30 4.00 0.25 FPWS-082 4.00 6.00 0.08 0.082.060.853.0023.30 4.00 0.42 FPWS-083 4.00 6.00 0.08 0.082.060.692.5019.00 4.00 0.34 FPWS-084 4.00 6.00 0.08 0.082.060.752.5019.00 4.00 0.38 FPWS-085 4.00 6.00 0.08 0.082.060.672.0014.58 4.00 0.33 FPWS-086 4.00 6.00 0.08 0.082.060.832.0014.58 4.00 0.42 FPWS-087 4.00 6.00 0.08 0.082.060.781.509.95 2.97 0.39 FPWS-088 4.00 6.00 0.08 0.082.060.541.005.06 1.71 0.27 FPWS-089 4.00 6.00 0.08 0.172.060.443.0023.30 4.00 0.22 FPWS-090 4.00 6.00 0.08 0.172.060.833.0023.30 4.00 0.42 FPWS-091 4.00 6.00 0.08 0.172.060.512.5019.00 4.00 0.26 FPWS-092 4.00 6.00 0.08 0.172.060.992.5019.00 4.00 0.49 FPWS-093 4.00 6.00 0.08 0.172.060.632.0014.58 4.00 0.31 FPWS-094 4.00 6.00 0.08 0.172.060.792.0014.58 4.00 0.40 FPWS-095 4.00 6.00 0.08 0.172.060.691.509.95 3.48 0.34 FPWS-096 4.00 6.00 0.08 0.172.060.521.005.06 1.35 0.26 FPWS-097 4.00 6.00 0.08 0.252.060.403.0023.30 0.00 0.20 FPWS-098 4.00 6.00 0.08 0.252.060.753.0023.30 4.00 0.38 FPWS-099 4.00 6.00 0.08 0.252.060.542.5019.00 1.88 0.27 FPWS-100 4.00 6.00 0.08 0.252.060.862.5019.00 4.00 0.43 FPWS-101 4.00 6.00 0.08 0.252.060.582.0014.58 2.40 0.29 FPWS-102 4.00 6.00 0.08 0.252.060.752.0014.58 4.00 0.38 FPWS-103 4.00 6.00 0.08 0.252.060.751.509.95 2.81 0.38 FPWS-104 4.00 6.00 0.08 0.252.060.541.005.06 0.61 0.27 FPWS-105 4.00 6.00 0.08 0.082.250.523.0024.23 4.00 0.26 FPWS-106 4.00 6.00 0.08 0.082.250.883.0024.23 4.00 0.44 FPWS-107 4.00 6.00 0.08 0.082.250.562.5019.71 4.00 0.28 FPWS-108 4.00 6.00 0.08 0.082.250.952.5019.71 4.00 0.47 FPWS-109 4.00 6.00 0.08 0.082.250.582.0015.06 4.00 0.29 FPWS-110 4.00 6.00 0.08 0.082.250.832.0015.06 4.00 0.42 FPWS-111 4.00 6.00 0.08 0.082.250.791.5010.18 4.00 0.40

PAGE 86

86 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPWS-112 4.00 6.00 0.08 0.082.250.541.005.09 2.03 0.27 FPWS-113 4.00 6.00 0.08 0.002.330.563.0024.62 4.00 0.28 FPWS-114 4.00 6.00 0.08 0.002.330.883.0024.62 4.00 0.44 FPWS-115 4.00 6.00 0.08 0.002.330.652.5020.01 4.00 0.32 FPWS-116 4.00 6.00 0.08 0.002.330.982.5020.01 4.00 0.49 FPWS-117 4.00 6.00 0.08 0.002.330.792.0015.26 4.00 0.40 FPWS-118 4.00 6.00 0.08 0.002.330.832.0015.26 4.00 0.42 FPWS-119 4.00 6.00 0.08 0.002.330.821.5010.27 4.00 0.41 FPWS-120 4.00 6.00 0.08 0.002.330.671.005.09 3.19 0.33 FPWS-121 4.00 6.00 0.08 0.082.330.583.0024.62 4.00 0.29 FPWS-122 4.00 6.00 0.08 0.082.330.963.0024.62 4.00 0.48 FPWS-123 4.00 6.00 0.08 0.082.330.592.5020.01 4.00 0.30 FPWS-124 4.00 6.00 0.08 0.082.330.792.5020.01 4.00 0.40 FPWS-125 4.00 6.00 0.08 0.082.330.672.0015.26 4.00 0.33 FPWS-126 4.00 6.00 0.08 0.082.330.832.0015.26 4.00 0.42 FPWS-127 4.00 6.00 0.08 0.082.330.831.5010.27 4.00 0.42 FPWS-128 4.00 6.00 0.08 0.082.330.631.005.09 2.69 0.31 FPWS-129 4.00 6.00 0.08 0.172.330.463.0024.62 4.00 0.23 FPWS-130 4.00 6.00 0.08 0.172.330.863.0024.62 4.00 0.43 FPWS-131 4.00 6.00 0.08 0.172.330.602.5020.01 4.00 0.30 FPWS-132 4.00 6.00 0.08 0.172.330.972.5020.01 4.00 0.49 FPWS-133 4.00 6.00 0.08 0.172.330.712.0015.26 4.00 0.35 FPWS-134 4.00 6.00 0.08 0.172.330.792.0015.26 4.00 0.40 FPWS-135 4.00 6.00 0.08 0.172.330.741.5010.27 3.74 0.37 FPWS-136 4.00 6.00 0.08 0.172.330.581.005.09 1.77 0.29 FPWS-137 4.00 6.00 0.08 -0.422.330.583.0024.62 4.00 0.29 FPWS-138 4.00 6.00 0.08 -0.422.330.903.0024.62 4.00 0.45 FPWS-139 4.00 6.00 0.08 -0.422.330.652.5020.01 4.00 0.33 FPWS-140 4.00 6.00 0.08 -0.422.330.852.5020.01 4.00 0.42 FPWS-141 4.00 6.00 0.08 -0.422.330.712.0015.26 4.00 0.35 FPWS-142 4.00 6.00 0.08 -0.422.330.792.0015.26 4.00 0.40 FPWS-143 4.00 6.00 0.08 -0.422.330.921.5010.27 4.00 0.46 FPWS-144 4.00 6.00 0.08 -0.422.330.501.005.09 4.00 0.25 FPWS-145 4.00 6.00 0.08 -0.172.080.523.0023.40 4.00 0.26 FPWS-146 4.00 6.00 0.08 -0.172.080.883.0023.40 4.00 0.44 FPWS-147 4.00 6.00 0.08 -0.172.080.582.5019.07 4.00 0.29 FPWS-148 4.00 6.00 0.08 -0.172.080.772.5019.07 4.00 0.39

PAGE 87

87 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPWS-149 4.00 6.00 0.08 -0.172.080.672.0014.63 4.00 0.33 FPWS-150 4.00 6.00 0.08 -0.172.080.832.0014.63 4.00 0.42 FPWS-151 4.00 6.00 0.08 -0.172.080.851.509.97 4.00 0.43 FPWS-152 4.00 6.00 0.08 -0.172.080.581.005.07 3.54 0.29 FPWS-153 4.00 6.00 0.08 -0.082.000.463.0022.98 4.00 0.23 FPWS-154 4.00 6.00 0.08 -0.082.000.793.0022.98 4.00 0.40 FPWS-155 4.00 6.00 0.08 -0.082.000.562.5018.74 4.00 0.28 FPWS-156 4.00 6.00 0.08 -0.082.000.792.5018.74 4.00 0.40 FPWS-157 4.00 6.00 0.08 -0.082.000.632.0014.40 4.00 0.31 FPWS-158 4.00 6.00 0.08 -0.082.000.752.0014.40 4.00 0.38 FPWS-159 4.00 6.00 0.08 -0.082.000.801.509.86 4.00 0.40 FPWS-160 4.00 6.00 0.08 -0.082.000.591.005.05 3.60 0.30 FPWS-161 4.00 6.00 0.08 -0.292.000.513.0022.98 4.00 0.25 FPWS-162 4.00 6.00 0.08 -0.292.000.793.0022.98 4.00 0.40 FPWS-163 4.00 6.00 0.08 -0.292.000.542.5018.74 4.00 0.27 FPWS-164 4.00 6.00 0.08 -0.292.000.782.5018.74 4.00 0.39 FPWS-165 4.00 6.00 0.08 -0.292.000.582.0014.40 4.00 0.29 FPWS-166 4.00 6.00 0.08 -0.292.000.832.0014.40 4.00 0.42 FPWS-167 4.00 6.00 0.08 -0.292.000.831.509.86 4.00 0.42 FPWS-168 4.00 6.00 0.08 -0.292.000.581.005.05 4.00 0.29 FPWS-169 4.00 6.00 0.08 -0.171.920.453.0022.54 4.00 0.23 FPWS-170 4.00 6.00 0.08 -0.171.920.773.0022.54 4.00 0.38 FPWS-171 4.00 6.00 0.08 -0.171.920.502.5018.41 4.00 0.25 FPWS-172 4.00 6.00 0.08 -0.171.920.772.5018.41 4.00 0.38 FPWS-173 4.00 6.00 0.08 -0.171.920.502.0014.17 4.00 0.25 FPWS-174 4.00 6.00 0.08 -0.171.920.712.0014.17 4.00 0.35 FPWS-175 4.00 6.00 0.08 -0.171.920.791.509.74 4.00 0.39 FPWS-176 4.00 6.00 0.08 -0.171.920.581.005.04 3.53 0.29 FPWS-185 4.00 6.00 0.08 -0.171.750.393.0021.62 4.00 0.19 FPWS-186 4.00 6.00 0.08 -0.171.750.753.0021.62 4.00 0.38 FPWS-187 4.00 6.00 0.08 -0.171.750.502.5017.69 4.00 0.25 FPWS-188 4.00 6.00 0.08 -0.171.750.752.5017.69 4.00 0.38 FPWS-189 4.00 6.00 0.08 -0.171.750.502.0013.67 4.00 0.25 FPWS-190 4.00 6.00 0.08 -0.171.750.672.0013.67 4.00 0.33 FPWS-191 4.00 6.00 0.08 -0.171.750.691.509.47 4.00 0.35 FPWS-192 4.00 6.00 0.08 -0.171.750.591.005.00 4.00 0.29 FPNS-001 4.00 2.00 0.08 -0.042.330.683.5629.69 4.00 0.34

PAGE 88

88 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPNS-002 4.00 2.00 0.08 -0.042.330.903.0224.80 4.00 0.45 FPNS-003 4.00 2.00 0.08 -0.042.330.872.4619.63 4.00 0.44 FPNS-004 4.00 2.00 0.08 -0.042.330.961.9915.16 4.00 0.48 FPNS-005 4.00 2.00 0.08 -0.042.330.921.5410.68 2.09 0.46 FPNS-006 4.00 2.00 0.08 -0.042.330.561.015.19 2.77 0.28 FPNS-007 4.00 2.00 0.08 -0.352.670.573.4230.21 4.00 0.29 FPNS-008 4.00 2.00 0.08 -0.352.670.593.0026.11 4.00 0.30 FPNS-009 4.00 2.00 0.08 -0.352.670.662.4921.04 4.00 0.33 FPNS-010 4.00 2.00 0.08 -0.352.670.822.0016.00 4.00 0.41 FPNS-011 4.00 2.00 0.08 -0.352.670.871.5511.15 4.00 0.43 FPNS-012 4.00 2.00 0.08 -0.352.670.551.015.21 4.00 0.28 FPNS-013 4.00 2.00 0.08 -0.352.670.503.5531.47 4.00 0.25 FPNS-014 4.00 2.00 0.08 -0.352.670.612.9926.01 4.00 0.31 FPNS-015 4.00 2.00 0.08 -0.352.670.632.4720.84 4.00 0.32 FPNS-016 4.00 2.00 0.08 -0.352.670.821.9815.79 4.00 0.41 FPNS-017 4.00 2.00 0.08 -0.352.670.841.5310.93 4.00 0.42 FPNS-018 4.00 2.00 0.08 -0.352.670.541.005.11 4.00 0.27 FPNS-019 4.00 2.00 0.08 -0.252.580.463.5230.73 4.00 0.23 FPNS-020 4.00 2.00 0.08 -0.252.580.642.9925.65 4.00 0.32 FPNS-021 4.00 2.00 0.08 -0.252.580.732.5521.36 4.00 0.37 FPNS-022 4.00 2.00 0.08 -0.252.580.862.0115.93 4.00 0.43 FPNS-023 4.00 2.00 0.08 -0.252.580.921.5310.85 4.00 0.46 FPNS-024 4.00 2.00 0.08 -0.252.580.551.005.11 4.00 0.27 FPNS-025 4.00 2.00 0.08 -0.252.580.463.5330.83 4.00 0.23 FPNS-026 4.00 2.00 0.08 -0.252.580.512.9725.46 4.00 0.26 FPNS-027 4.00 2.00 0.08 -0.252.580.682.5020.87 4.00 0.34 FPNS-028 4.00 2.00 0.08 -0.252.580.831.9915.72 4.00 0.41 FPNS-029 4.00 2.00 0.08 -0.252.580.811.5310.85 4.00 0.40 FPNS-030 4.00 2.00 0.08 -0.252.580.561.015.21 4.00 0.28 FPNS-031 4.00 2.00 0.08 -0.172.460.463.5029.86 4.00 0.23 FPNS-032 4.00 2.00 0.08 -0.172.460.542.9724.91 4.00 0.27 FPNS-033 4.00 2.00 0.08 -0.172.460.672.5120.54 4.00 0.33 FPNS-034 4.00 2.00 0.08 -0.172.460.902.0015.55 4.00 0.45 FPNS-035 4.00 2.00 0.08 -0.172.460.771.5410.83 4.00 0.38 FPNS-036 4.00 2.00 0.08 -0.172.460.593.4028.93 4.00 0.30 FPNS-037 4.00 2.00 0.08 -0.172.460.682.9624.82 4.00 0.34 FPNS-038 4.00 2.00 0.08 -0.172.460.932.4620.06 4.00 0.47

PAGE 89

89 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPNS-039 4.00 2.00 0.08 -0.172.461.011.9815.35 4.00 0.51 FPNS-040 4.00 2.00 0.08 -0.172.460.851.5310.72 2.89 0.43 FPNS-041 4.00 2.00 0.08 -0.082.420.663.5129.72 4.00 0.33 FPNS-042 4.00 2.00 0.08 -0.082.420.792.9824.82 4.00 0.39 FPNS-043 4.00 2.00 0.08 -0.082.420.872.4419.73 4.00 0.43 FPNS-044 4.00 2.00 0.08 -0.082.420.952.0015.46 4.00 0.48 FPNS-045 4.00 2.00 0.08 -0.082.420.861.5310.68 2.73 0.43 FPNS-046 4.00 2.00 0.08 -0.082.420.483.4629.26 4.00 0.24 FPNS-047 4.00 2.00 0.08 -0.082.420.652.9424.45 4.00 0.33 FPNS-048 4.00 2.00 0.08 -0.082.420.792.4619.92 4.00 0.39 FPNS-049 4.00 2.00 0.08 -0.082.420.972.0115.56 4.00 0.48 FPNS-050 4.00 2.00 0.08 -0.082.420.851.5210.57 2.64 0.43 FPNS-051 4.00 2.00 0.08 0.002.290.523.5529.36 4.00 0.26 FPNS-052 4.00 2.00 0.08 0.002.290.682.9523.97 4.00 0.34 FPNS-053 4.00 2.00 0.08 0.002.290.642.4819.68 4.00 0.32 FPNS-054 4.00 2.00 0.08 0.002.290.891.9814.97 4.00 0.44 FPNS-055 4.00 2.00 0.08 0.002.290.851.5310.53 4.00 0.43 FPNS-056 4.00 2.00 0.08 0.002.290.613.5629.45 4.00 0.31 FPNS-057 4.00 2.00 0.08 0.002.290.673.0524.88 4.00 0.34 FPNS-058 4.00 2.00 0.08 0.002.290.742.4519.40 4.00 0.37 FPNS-059 4.00 2.00 0.08 0.002.290.842.0015.16 4.00 0.42 FPNS-060 4.00 2.00 0.08 0.002.290.911.5710.94 4.00 0.46 FPNS-061 4.00 2.00 0.08 0.062.250.613.4528.23 4.00 0.31 FPNS-062 4.00 2.00 0.08 0.062.250.692.9723.96 4.00 0.35 FPNS-063 4.00 2.00 0.08 0.062.250.752.4319.07 4.00 0.37 FPNS-064 4.00 2.00 0.08 0.062.250.872.0115.15 4.00 0.43 FPNS-065 4.00 2.00 0.08 0.062.250.811.5310.48 4.00 0.41 FPNS-066 4.00 2.00 0.08 0.062.250.643.5729.29 4.00 0.32 FPNS-067 4.00 2.00 0.08 0.062.250.663.0624.76 4.00 0.33 FPNS-068 4.00 2.00 0.08 0.062.250.862.4419.16 4.00 0.43 FPNS-069 4.00 2.00 0.08 0.062.250.911.9914.96 4.00 0.46 FPNS-070 4.00 2.00 0.08 0.062.250.851.5610.78 2.08 0.42 FPNS-071 4.00 2.00 0.08 0.132.170.633.4627.83 4.00 0.31 FPNS-072 4.00 2.00 0.08 0.132.170.772.9323.21 4.00 0.38 FPNS-073 4.00 2.00 0.08 0.132.170.732.4218.68 4.00 0.37 FPNS-074 4.00 2.00 0.08 0.132.170.802.0114.94 4.00 0.40 FPNS-075 4.00 2.00 0.08 0.132.170.881.5210.28 4.00 0.44

PAGE 90

90 Table A-1. Continued. Test case Plate width Plate chord Plate thick Plate clear Water depth Wave height Wave period Wave length Wetted width Max water elevation FPNS-076 4.00 2.00 0.08 0.132.170.653.4327.57 4.00 0.32 FPNS-077 4.00 2.00 0.08 0.132.170.682.9823.65 4.00 0.34 FPNS-078 4.00 2.00 0.08 0.132.170.802.4318.77 4.00 0.40 FPNS-079 4.00 2.00 0.08 0.132.170.892.0014.85 4.00 0.45 FPNS-080 4.00 2.00 0.08 0.132.170.881.5110.18 2.18 0.44 FPNS-081 4.00 2.00 0.08 0.212.080.683.4226.99 4.00 0.34 FPNS-082 4.00 2.00 0.08 0.212.080.792.9222.72 4.00 0.40 FPNS-083 4.00 2.00 0.08 0.212.080.792.4118.28 4.00 0.40 FPNS-084 4.00 2.00 0.08 0.212.080.852.0014.63 4.00 0.43 FPNS-085 4.00 2.00 0.08 0.212.080.911.509.97 1.45 0.46 FPNS-086 4.00 2.00 0.08 0.212.080.663.5227.83 4.00 0.33 FPNS-087 4.00 2.00 0.08 0.212.080.753.0123.49 4.00 0.37 FPNS-088 4.00 2.00 0.08 0.212.080.772.4418.55 4.00 0.39 FPNS-089 4.00 2.00 0.08 0.212.080.812.0014.63 4.00 0.41 FPNS-090 4.00 2.00 0.08 0.212.080.891.489.78 4.00 0.44 FPNS-091 4.00 2.00 0.08 0.292.000.583.4526.73 0.00 0.29 FPNS-092 4.00 2.00 0.08 0.292.000.712.9022.14 4.00 0.36 FPNS-093 4.00 2.00 0.08 0.292.000.832.4918.66 4.00 0.41 FPNS-094 4.00 2.00 0.08 0.292.000.872.0314.67 4.00 0.43 FPNS-095 4.00 2.00 0.08 0.292.000.891.489.67 4.00 0.44 FPNS-096 4.00 2.00 0.08 0.292.000.583.5127.23 0.00 0.29 FPNS-097 4.00 2.00 0.08 0.292.000.733.0223.15 4.00 0.36 FPNS-098 4.00 2.00 0.08 0.292.000.822.4318.15 4.00 0.41 FPNS-099 4.00 2.00 0.08 0.292.000.792.0715.02 4.00 0.40 FPNS-100 4.00 2.00 0.08 0.292.000.821.5210.05 1.73 0.41

PAGE 91

91 Table A-2. Significant force values for all physical model tests. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPWS-001 132.59 -17.13 86.29-15.3949.19 286.04 -13.17 FPWS-002 191.57 -81.61 141.32-41.0371.20 448.86 -208.95 FPWS-003 172.96 -14.16 122.52-10.2761.54 334.40 -45.35 FPWS-004 190.74 -59.52 118.85-42.1879.97 395.96 -145.03 FPWS-005 111.42 -71.76 64.87-64.0649.52 190.28 -182.98 FPWS-006 169.11 -53.45 113.05-29.4057.40 322.02 -159.78 FPWS-007 111.47 -88.19 77.77-51.4578.80 239.67 -206.89 FPWS-008 92.18 -101.48 69.87-64.0434.99 245.86 -241.43 FPWS-009 20.21 -4.98 19.68-3.432.45 54.52 -10.49 FPWS-010 53.76 -41.23 42.65-35.0522.52 161.38 -116.73 FPWS-011 126.22 -49.42 63.47-39.6063.27 166.24 -118.54 FPWS-012 237.20 -148.86 138.53-94.99110.82 479.22 -385.91 FPWS-013 193.15 -32.76 115.84-26.4178.75 324.03 -86.56 FPWS-014 194.54 -148.14 76.11-122.17123.48 493.57 -339.71 FPWS-015 78.45 -45.67 56.24-29.7831.04 196.20 -112.72 FPWS-016 140.35 -62.03 94.10-39.6554.13 348.81 -146.30 FPWS-017 52.58 -71.51 40.23-46.3334.80 179.14 -171.72 FPWS-018 67.32 -96.47 56.96-72.7245.29 167.14 -225.17 FPWS-019 15.98 -21.47 9.80-18.107.50 58.68 -68.14 FPWS-020 3.58 -10.26 6.16-9.052.54 15.24 -28.28 FPWS-021 21.68 -19.44 9.57-16.3816.08 51.52 -42.46 FPWS-022 85.28 -82.11 67.94-56.2337.82 243.85 -177.35 FPWS-023 51.84 -31.28 31.54-23.5724.18 109.25 -72.64 FPWS-024 69.67 -78.07 61.28-47.6240.17 185.35 -176.58 FPWS-025 32.00 -27.69 14.67-19.5119.93 106.35 -60.64 FPWS-026 53.22 -53.76 35.64-34.0828.02 163.21 -127.14 FPWS-027 24.41 -35.40 10.62-21.3928.27 79.68 -99.05 FPWS-028 44.53 -47.43 32.68-36.7019.34 114.18 -118.11 FPWS-029 8.66 -12.50 2.70-11.047.76 35.25 -41.93 FPWS-030 7.84 -13.69 2.93-13.225.02 33.86 -48.88 FPWS-031 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-032 42.12 -70.70 30.13-45.9222.36 141.35 -149.22 FPWS-033 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-034 42.56 -52.20 27.52-32.1518.29 150.15 -108.64 FPWS-035 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-036 24.95 -33.98 13.78-26.7812.65 88.20 -79.95 FPWS-037 17.98 -17.02 3.82-14.4415.29 66.68 -51.07

PAGE 92

92 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPWS-038 15.74 -31.99 7.92-23.0915.20 67.62 -85.88 FPWS-039 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-040 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-041 95.87 -30.74 54.80-18.7447.47 167.53 -70.30 FPWS-042 163.48 -90.68 118.48-60.1561.58 369.88 -194.90 FPWS-043 106.38 -35.25 65.10-27.8244.34 209.30 -94.08 FPWS-044 134.57 -77.85 102.84-48.4755.80 307.70 -168.53 FPWS-045 95.98 -57.94 73.54-28.5940.89 228.46 -130.14 FPWS-046 182.92 -75.08 105.51-50.4178.48 430.56 -178.63 FPWS-047 71.02 -100.09 46.75-64.4640.71 163.39 -228.40 FPWS-048 18.25 -33.50 10.77-26.5512.57 70.90 -104.13 FPWS-049 126.03 -28.43 76.20-27.4355.39 234.53 -60.52 FPWS-050 265.58 -87.25 165.32-52.76100.26 541.44 -184.02 FPWS-051 127.88 -35.45 92.42-31.3145.47 240.44 -82.64 FPWS-052 217.66 -68.31 118.00-51.72115.42 391.41 -177.32 FPWS-053 138.92 -96.35 65.91-64.0794.24 203.46 -215.91 FPWS-054 115.36 -113.80 76.41-77.1767.65 210.93 -254.70 FPWS-055 117.79 -95.34 61.63-63.5180.05 173.64 -217.29 FPWS-056 75.38 -51.60 33.10-38.3042.94 160.44 -134.79 FPWS-057 20.23 -29.43 14.55-14.0013.03 54.23 -54.15 FPWS-058 113.72 -88.03 78.47-54.4752.65 198.38 -186.04 FPWS-059 43.04 -38.92 28.95-24.1428.28 118.67 -76.28 FPWS-060 90.85 -83.26 74.30-49.6546.13 213.51 -180.84 FPWS-061 39.91 -24.68 22.93-19.6719.43 127.12 -55.42 FPWS-062 77.61 -93.04 54.55-44.6754.30 211.45 -197.01 FPWS-063 59.50 -60.94 29.08-39.4347.03 123.77 -173.64 FPWS-064 7.91 -10.49 3.31-9.645.07 32.63 -35.34 FPWS-065 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-066 47.22 -77.60 45.40-42.7836.73 138.75 -154.12 FPWS-067 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-068 65.36 -62.83 41.80-37.6140.58 161.07 -125.39 FPWS-069 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-070 52.85 -66.02 34.67-41.4628.52 168.63 -137.22 FPWS-071 28.47 -27.92 12.35-17.9226.26 103.88 -76.76 FPWS-072 1.60 -4.71 0.79-3.962.94 3.91 -10.05 FPWS-073 123.87 -33.59 74.70-31.0554.22 252.08 -57.91 FPWS-074 193.96 -82.28 137.88-59.5363.78 370.46 -171.80

PAGE 93

93 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPWS-075 119.51 -38.76 95.04-36.2336.21 272.70 -95.14 FPWS-076 235.30 -88.57 137.51-63.13102.42 428.92 -177.32 FPWS-077 184.14 -53.85 111.87-40.8274.81 307.30 -130.89 FPWS-078 179.95 -77.15 119.51-61.8768.66 340.02 -179.45 FPWS-079 123.66 -104.70 69.22-69.8188.89 184.96 -253.43 FPWS-080 8.30 -12.91 8.35-12.762.43 16.28 -32.23 FPWS-081 68.50 -37.20 58.07-28.3225.95 161.68 -85.97 FPWS-082 160.62 -85.49 118.89-48.0875.16 351.16 -225.15 FPWS-083 171.63 -56.91 96.77-39.8877.53 306.46 -135.09 FPWS-084 174.93 -80.47 111.85-50.4880.79 435.43 -185.60 FPWS-085 118.23 -40.65 78.56-31.6852.42 258.02 -112.11 FPWS-086 213.09 -78.65 126.77-60.5899.66 485.26 -186.60 FPWS-087 73.67 -100.06 50.02-69.9429.25 186.69 -230.21 FPWS-088 14.67 -18.64 9.59-16.3710.97 59.61 -57.87 FPWS-089 46.02 -31.26 34.36-22.5723.48 105.41 -64.96 FPWS-090 148.03 -109.04 102.33-75.3756.19 325.91 -234.67 FPWS-091 48.51 -37.43 37.16-21.1528.85 111.12 -80.09 FPWS-092 100.98 -72.50 78.80-44.5135.68 228.29 -162.23 FPWS-093 77.47 -80.59 58.10-34.2556.63 172.69 -163.70 FPWS-094 192.04 -88.14 95.85-58.88106.13 347.89 -210.32 FPWS-095 57.45 -73.09 35.60-52.6632.85 137.70 -181.75 FPWS-096 12.62 -17.32 5.86-16.986.76 53.77 -56.39 FPWS-097 0.00 0.00 0.000.000.00 0.00 0.00 FPWS-098 79.91 -74.65 64.31-45.3843.39 181.98 -170.36 FPWS-099 9.36 -16.34 4.44-14.405.47 29.34 -35.72 FPWS-100 72.84 -59.27 61.22-38.8836.90 148.04 -137.69 FPWS-101 24.96 -28.11 14.47-21.9518.84 79.75 -66.04 FPWS-102 85.74 -103.28 54.86-57.7857.27 213.17 -215.20 FPWS-103 29.20 -52.82 20.31-38.5923.11 106.46 -131.67 FPWS-104 3.11 -10.37 0.95-8.063.82 14.63 -35.54 FPWS-105 98.64 -27.32 61.31-21.7037.33 175.37 -56.36 FPWS-106 192.26 -65.04 136.45-54.3769.32 361.75 -144.03 FPWS-107 120.33 -43.48 74.28-35.4249.35 216.09 -112.58 FPWS-108 235.30 -108.62 136.77-56.54111.66 597.68 -246.18 FPWS-109 120.99 -78.77 89.10-53.0947.23 293.81 -187.36 FPWS-110 211.64 -97.72 128.47-60.02107.59 525.75 -217.67 FPWS-111 67.64 -111.60 57.47-83.1233.71 174.27 -243.60

PAGE 94

94 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPWS-112 13.66 -24.44 10.36-20.154.44 58.12 -75.39 FPWS-113 105.80 -46.44 73.31-43.3232.58 218.83 -78.46 FPWS-114 224.44 -72.04 138.09-62.29110.28 410.39 -153.99 FPWS-115 161.33 -58.30 101.98-50.1964.58 300.46 -133.71 FPWS-116 217.86 -75.13 174.19-55.2554.99 441.90 -157.69 FPWS-117 177.61 -82.61 112.56-50.0172.02 371.78 -179.29 FPWS-118 226.16 -102.10 145.56-62.4091.65 503.75 -214.02 FPWS-119 164.61 -126.72 80.67-101.54121.66 229.72 -339.24 FPWS-120 48.81 -50.15 31.54-41.7419.18 140.23 -125.08 FPWS-121 83.00 -32.44 61.63-22.9934.13 163.64 -76.28 FPWS-122 169.70 -69.83 137.63-51.3449.35 338.27 -158.33 FPWS-123 142.82 -42.88 82.52-37.3561.64 242.33 -105.69 FPWS-124 177.31 -91.03 115.16-53.4771.25 375.61 -203.29 FPWS-125 147.31 -63.49 96.60-44.3870.36 398.44 -149.88 FPWS-126 228.76 -85.56 123.65-63.29123.30 613.14 -191.70 FPWS-127 61.38 -107.73 58.57-84.2734.73 200.16 -238.33 FPWS-128 9.00 -7.27 4.50-8.634.68 35.22 -26.10 FPWS-129 55.16 -26.62 34.56-13.6326.82 91.31 -58.09 FPWS-130 160.88 -77.75 113.91-48.2566.29 350.89 -178.74 FPWS-131 100.82 -39.57 62.75-24.3451.95 222.18 -104.28 FPWS-132 113.61 -85.36 97.09-51.3769.51 371.25 -186.46 FPWS-133 114.09 -73.02 79.78-48.1253.02 280.80 -164.07 FPWS-134 165.69 -90.50 99.64-66.9872.90 437.01 -221.99 FPWS-135 57.72 -102.99 41.80-72.6030.82 196.70 -238.65 FPWS-136 0.98 -4.79 0.71-3.012.41 1.87 -10.92 FPWS-137 127.55 -8.57 127.97-8.3646.31 200.43 -47.58 FPWS-138 187.73 -65.20 188.12-64.4457.33 340.47 -154.87 FPWS-139 156.33 -32.16 155.46-29.9449.85 262.36 -80.88 FPWS-140 193.06 -48.96 191.76-48.5650.26 340.53 -127.88 FPWS-141 147.85 -82.10 145.57-76.1056.46 258.51 -183.24 FPWS-142 185.93 -62.10 182.99-63.9752.65 315.22 -158.24 FPWS-143 132.00 -89.37 130.54-84.6158.88 303.68 -223.61 FPWS-144 85.08 -23.58 82.95-23.4447.53 175.11 -117.11 FPWS-145 103.35 -41.78 103.11-39.9145.59 161.94 -98.16 FPWS-146 175.61 -64.34 160.95-59.8485.24 343.95 -144.15 FPWS-147 115.44 -52.21 115.64-49.0347.99 211.21 -112.99 FPWS-148 176.95 -86.40 150.23-81.6092.66 359.03 -168.14

PAGE 95

95 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPWS-149 118.01 -71.81 102.47-62.4964.92 215.40 -180.86 FPWS-150 171.13 -80.57 136.60-77.7181.81 343.73 -196.89 FPWS-151 152.33 -100.90 119.10-75.4689.29 338.65 -241.79 FPWS-152 63.04 -27.19 58.37-21.7551.56 104.72 -121.93 FPWS-153 105.09 -28.40 91.60-28.4558.64 172.69 -73.19 FPWS-154 179.92 -57.20 139.04-53.2782.63 344.29 -117.84 FPWS-155 150.69 -33.00 115.14-29.8477.58 267.99 -96.96 FPWS-156 208.99 -60.11 144.12-48.81106.30 382.74 -160.76 FPWS-157 149.81 -45.22 119.99-28.2877.65 275.75 -140.76 FPWS-158 300.98 -58.49 158.16-36.20184.69 517.04 -161.13 FPWS-159 121.64 -74.79 99.98-49.4779.20 247.64 -205.59 FPWS-160 53.53 13.72 52.8613.0744.15 80.24 -20.93 FPWS-161 122.32 -14.23 122.92-14.1148.77 193.53 -49.78 FPWS-162 170.02 -37.83 169.35-38.2651.47 294.37 -110.77 FPWS-163 133.93 -34.83 134.57-31.4347.35 210.72 -86.98 FPWS-164 173.11 -53.20 172.80-51.4250.81 296.51 -100.07 FPWS-165 122.32 -14.23 122.92-14.1148.77 193.53 -49.78 FPWS-166 170.02 -37.83 169.35-38.2651.47 294.37 -110.77 FPWS-167 116.26 -79.68 115.31-69.6869.42 260.52 -186.88 FPWS-168 44.65 34.86 44.4836.2743.93 49.59 28.03 FPWS-169 105.72 -31.40 105.00-30.1945.06 166.60 -81.31 FPWS-170 159.11 -63.95 158.09-58.8448.75 293.36 -131.77 FPWS-171 107.79 -48.24 106.49-42.1148.83 177.58 -124.15 FPWS-172 150.27 -67.13 149.65-65.1051.38 273.55 -143.77 FPWS-173 109.90 -69.39 102.25-58.0558.94 207.76 -171.67 FPWS-174 134.76 -66.57 123.28-60.4260.51 250.20 -167.25 FPWS-175 137.03 -93.34 109.30-68.2789.64 306.08 -221.45 FPWS-176 72.95 1.11 70.02-2.4347.95 120.53 -69.26 FPWS-185 96.89 -22.68 97.02-19.3247.67 150.98 -68.38 FPWS-186 164.77 -49.09 163.09-45.6147.95 291.54 -108.05 FPWS-187 112.22 -33.20 110.86-32.2046.00 183.91 -88.35 FPWS-188 152.29 -62.10 151.17-59.5253.28 280.61 -147.97 FPWS-189 97.35 -47.70 95.32-46.7854.78 176.11 -136.72 FPWS-190 109.72 -67.14 110.06-60.1957.86 221.35 -173.83 FPWS-191 91.01 -120.52 83.00-100.2469.47 216.38 -281.18 FPWS-192 84.64 -23.95 77.16-20.6554.27 160.63 -106.32 FPNS-001 81.65 -99.79 77.06-92.5113.25 182.21 -216.64

PAGE 96

96 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPNS-002 84.98 -118.90 75.99-103.5526.02 207.08 -249.36 FPNS-003 84.60 -82.67 85.81-77.3919.16 198.05 -165.13 FPNS-004 122.31 -91.00 81.87-78.8841.28 285.13 -201.26 FPNS-005 78.97 -138.40 54.22-97.2755.91 219.76 -300.88 FPNS-006 21.74 -12.53 19.61-14.613.91 65.40 -52.06 FPNS-007 47.86 -40.14 45.64-38.714.42 100.85 -81.67 FPNS-008 71.73 -51.62 68.70-49.404.65 156.03 -101.31 FPNS-009 95.24 -77.39 94.71-71.756.00 196.50 -156.17 FPNS-010 111.36 -99.33 111.51-91.857.94 258.14 -202.41 FPNS-011 107.59 -117.43 102.96-103.8115.95 287.90 -244.52 FPNS-012 8.76 -14.32 8.77-13.442.83 14.14 -40.57 FPNS-013 39.64 -41.15 38.04-39.924.22 85.26 -87.83 FPNS-014 83.40 -55.67 81.30-54.384.86 182.08 -113.27 FPNS-015 101.75 -75.28 101.12-73.876.39 224.53 -143.85 FPNS-016 109.19 -97.21 108.36-88.148.16 252.04 -206.44 FPNS-017 109.04 -106.58 104.09-98.829.15 287.88 -227.00 FPNS-018 23.32 -10.83 21.24-9.643.73 49.14 -16.53 FPNS-019 54.53 -44.95 51.93-42.754.13 114.00 -90.62 FPNS-020 74.87 -66.18 72.85-64.904.22 176.77 -129.81 FPNS-021 101.97 -80.81 100.38-75.005.37 226.34 -174.75 FPNS-022 93.58 -115.80 88.51-108.725.29 210.02 -257.12 FPNS-023 88.90 -130.67 83.49-124.3211.89 233.05 -292.94 FPNS-024 14.11 -12.08 11.47-10.653.42 40.43 -24.00 FPNS-025 49.85 -47.68 48.31-45.844.03 110.86 -92.67 FPNS-026 68.32 -63.45 66.40-56.926.65 160.26 -122.84 FPNS-027 101.68 -76.03 101.11-72.227.25 232.72 -166.08 FPNS-028 87.25 -119.69 86.71-108.864.89 208.00 -263.65 FPNS-029 65.74 -91.99 64.16-82.5211.23 188.07 -185.93 FPNS-030 3.62 -30.02 3.17-29.834.22 36.89 -89.67 FPNS-031 63.90 -52.82 60.86-49.634.40 131.61 -102.85 FPNS-032 61.03 -67.79 59.08-64.095.08 146.61 -150.09 FPNS-033 88.18 -111.27 86.49-104.214.79 201.87 -233.10 FPNS-034 78.72 -137.24 67.49-128.5520.12 195.66 -282.20 FPNS-035 78.94 -128.86 59.20-120.6820.44 171.26 -287.92 FPNS-036 74.99 -76.62 72.95-71.736.31 164.48 -164.17 FPNS-037 75.41 -78.76 73.56-73.8417.19 190.10 -170.35 FPNS-038 116.52 -118.13 104.47-109.3926.73 275.39 -253.49

PAGE 97

97 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPNS-039 165.86 -138.88 81.06-129.3588.66 374.61 -294.01 FPNS-040 58.87 -88.59 57.15-86.287.94 156.47 -196.28 FPNS-041 74.04 -112.80 71.90-107.6810.92 172.85 -244.95 FPNS-042 77.32 -112.68 64.45-106.0724.57 182.99 -254.32 FPNS-043 87.06 -136.28 79.58-120.7220.06 230.29 -279.69 FPNS-044 123.43 -143.59 64.13-118.7264.48 328.81 -291.18 FPNS-045 84.98 -132.46 39.68-117.1871.35 224.84 -280.39 FPNS-046 53.24 -102.22 47.23-95.7518.73 123.29 -218.78 FPNS-047 71.29 -103.75 62.36-98.5822.66 165.75 -226.24 FPNS-048 99.86 -140.61 78.32-122.0830.61 234.08 -296.70 FPNS-049 109.42 -133.02 68.50-120.0042.87 258.64 -288.40 FPNS-050 36.10 -88.55 32.41-85.784.30 100.76 -209.39 FPNS-051 88.67 -71.84 75.30-64.8013.55 206.72 -147.89 FPNS-052 101.11 -70.66 85.36-65.1423.64 228.17 -140.44 FPNS-053 83.07 -83.65 70.07-78.3122.94 210.11 -177.28 FPNS-054 132.40 -80.63 98.92-70.6733.67 340.92 -177.75 FPNS-055 145.73 -80.81 74.63-66.9776.75 248.20 -181.16 FPNS-056 98.76 -76.49 87.81-68.8911.00 222.77 -161.61 FPNS-057 87.34 -74.38 78.10-67.6519.50 201.53 -152.64 FPNS-058 89.22 -85.62 79.28-78.7217.51 215.94 -183.64 FPNS-059 93.13 -61.52 67.48-57.1529.25 248.68 -138.34 FPNS-060 107.49 -93.22 69.34-72.6857.41 231.43 -199.40 FPNS-061 79.86 -61.38 73.22-54.9326.11 179.12 -123.96 FPNS-062 85.40 -63.54 78.41-59.1027.38 255.72 -132.30 FPNS-063 84.25 -89.21 68.05-80.9735.21 195.26 -184.79 FPNS-064 139.13 -61.90 73.18-49.7169.87 364.15 -131.43 FPNS-065 127.98 -73.08 67.68-61.0261.62 242.30 -173.99 FPNS-066 83.99 -63.11 77.41-59.5824.05 210.82 -125.30 FPNS-067 85.67 -60.90 72.62-56.3818.32 187.73 -133.84 FPNS-068 92.42 -88.01 77.19-81.8118.30 217.05 -177.89 FPNS-069 109.62 -63.51 65.96-58.2548.88 313.19 -132.25 FPNS-070 140.39 -78.05 71.48-64.3671.88 260.13 -159.65 FPNS-071 68.31 -53.93 56.64-49.4825.35 196.13 -114.44 FPNS-072 86.48 -55.56 65.76-52.0128.19 243.98 -122.11 FPNS-073 94.81 -76.05 60.69-65.3448.92 254.19 -148.59 FPNS-074 87.93 -36.70 47.43-29.1340.66 247.06 -118.33 FPNS-075 61.01 -62.23 52.43-51.2225.10 207.54 -165.19

PAGE 98

98 Table A-2. Continued. Test case Maximum total Minimum total Maximum quasi-steady Minimum quasi-steady Maximum slamming Maximum moment Minimum moment FPNS-076 55.68 -58.26 51.84-56.959.02 141.50 -123.93 FPNS-077 105.40 -55.71 70.73-46.5340.06 288.83 -128.06 FPNS-078 109.35 -81.16 76.92-66.4442.91 299.31 -166.21 FPNS-079 197.31 -69.58 75.52-50.39122.33 506.77 -177.40 FPNS-080 59.21 -34.90 56.68-21.0524.01 195.89 -89.81 FPNS-081 56.20 -30.00 45.15-26.3112.33 115.22 -65.25 FPNS-082 76.25 -37.38 58.07-35.6824.46 231.59 -95.14 FPNS-083 44.90 -43.75 41.06-40.1320.30 136.00 -96.77 FPNS-084 51.08 -32.26 37.74-24.4218.60 173.29 -84.99 FPNS-085 48.87 -42.97 41.47-36.7118.34 157.33 -118.12 FPNS-086 56.85 -30.84 47.14-28.3011.15 122.22 -79.74 FPNS-087 69.76 -31.51 60.50-31.7228.17 224.12 -85.57 FPNS-088 57.92 -49.48 45.96-39.8621.01 147.34 -107.57 FPNS-089 53.35 -38.00 39.22-29.6317.54 176.19 -109.20 FPNS-090 50.01 -55.33 42.75-41.0619.04 157.57 -135.48 FPNS-091 14.64 -17.94 13.15-15.795.34 48.11 -39.24 FPNS-092 65.35 -24.32 31.24-21.7034.62 192.46 -74.12 FPNS-093 62.14 -51.00 44.13-36.1831.52 185.84 -133.78 FPNS-094 32.20 -28.03 23.76-21.0512.82 95.82 -71.43 FPNS-095 8.19 -22.10 3.22-18.075.02 31.78 -67.92 FPNS-096 25.25 -20.96 20.36-20.017.70 95.82 -53.27 FPNS-097 14.86 -20.42 10.97-18.718.84 62.29 -43.42 FPNS-098 45.11 -38.18 30.41-31.5716.90 125.96 -79.63 FPNS-099 26.93 -22.82 17.90-17.1013.54 93.35 -56.50 FPNS-100 32.49 -35.71 19.13-27.3318.63 111.60 -100.47

PAGE 99

99 APPENDIX B MEASURED VERSUS PREDICTED FORCES The following figures (Figure B-1 to Figur e B-220) are comparison plots between m easured and predicted quasi-steady forces for most of the physical model tests performed. The figures include tests done with and without si de panels (i.e. conti nuous and finite width structures). They can be differentiated by th e individual case prefix and reference number, FPWS for tests done with side panels, and FPN S for tests done without side panels. These reference numbers correspond to the same numbers given in the significan t variables and values tables in Appendix A.

PAGE 100

100 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time ( sec ) Force (lbs) Measured Predicted Figure B-1. Measured vs. predicted qu asi-steady force for lab test FPWS-005. -100 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-2. Measured vs. predicted qu asi-steady force for lab test FPWS-006.

PAGE 101

101 -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-3. Measured vs. predicted qu asi-steady force for lab test FPWS-007. -100 -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-4. Measured vs. predicted qu asi-steady force for lab test FPWS-008.

PAGE 102

102 -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-5. Measured vs. predicted qu asi-steady force for lab test FPWS-009. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-6. Measured vs. predicted qu asi-steady force for lab test FPWS-011.

PAGE 103

103 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-7. Measured vs. predicted qu asi-steady force for lab test FPWS-012. -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time(sec) Force (lbs) Measured Predicted Figure B-8. Measured vs. predicted qu asi-steady force for lab test FPWS-013.

PAGE 104

104 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-9. Measured vs. predicted qu asi-steady force for lab test FPWS-014. -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-10. Measured vs. predicted qua si-steady force for lab test FPWS-015.

PAGE 105

105 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-11. Measured vs. predicted qua si-steady force for lab test FPWS-016. -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-12. Measured vs. predicted qua si-steady force for lab test FPWS-017.

PAGE 106

106 -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-13. Measured vs. predicted qua si-steady force for lab test FPWS-018. -20 -15 -10 -5 0 5 10 15 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-14. Measured vs. predicted qua si-steady force for lab test FPWS-021.

PAGE 107

107 -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-15. Measured vs. predicted qua si-steady force for lab test FPWS-022. -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-16. Measured vs. predicted qua si-steady force for lab test FPWS-023.

PAGE 108

108 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-17. Measured vs. predicted qua si-steady force for lab test FPWS-024. -25 -20 -15 -10 -5 0 5 10 15 20 25 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-18. Measured vs. predicted qua si-steady force for lab test FPWS-025.

PAGE 109

109 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-19. Measured vs. predicted qua si-steady force for lab test FPWS-026. -25 -20 -15 -10 -5 0 5 10 15 20 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-20. Measured vs. predicted qua si-steady force for lab test FPWS-027.

PAGE 110

110 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-21. Measured vs. predicted qua si-steady force for lab test FPWS-028. -60 -40 -20 0 20 40 60 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-22. Measured vs. predicted qua si-steady force for lab test FPWS-032.

PAGE 111

111 -40 -30 -20 -10 0 10 20 30 40 50 60 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-23. Measured vs. predicted qua si-steady force for lab test FPWS-034. -40 -30 -20 -10 0 10 20 30 40 50 60 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-24. Measured vs. predicted qua si-steady force for lab test FPWS-036.

PAGE 112

112 -40 -30 -20 -10 0 10 20 30 40 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-25. Measured vs. predicted qua si-steady force for lab test FPWS-038. -40 -20 0 20 40 60 80 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-26. Measured vs. predicted qua si-steady force for lab test FPWS-041.

PAGE 113

113 -80 -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-27. Measured vs. predicted qua si-steady force for lab test FPWS-042. -40 -20 0 20 40 60 80 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-28. Measured vs. predicted qua si-steady force for lab test FPWS-043.

PAGE 114

114 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-29. Measured vs. predicted qua si-steady force for lab test FPWS-044. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-30. Measured vs. predicted qua si-steady force for lab test FPWS-045.

PAGE 115

115 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-31. Measured vs. predicted qua si-steady force for lab test FPWS-046. -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-32. Measured vs. predicted qua si-steady force for lab test FPWS-047.

PAGE 116

116 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-33. Measured vs. predicted qua si-steady force for lab test FPWS-049. -100 -50 0 50 100 150 200 250 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-34. Measured vs. predicted qua si-steady force for lab test FPWS-050.

PAGE 117

117 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-35. Measured vs. predicted qua si-steady force for lab test FPWS-051. -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-36. Measured vs. predicted qua si-steady force for lab test FPWS-052.

PAGE 118

118 -60 -40 -20 0 20 40 60 80 100 0.00.20.40.60.81.01.21.41.6 Time (sec)Force (lbs) Measured Predicted Figure B-37. Measured vs. predicted qua si-steady force for lab test FPWS-055. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-38. Measured vs. predicted qua si-steady force for lab test FPWS-058.

PAGE 119

119 -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-39. Measured vs. predicted qua si-steady force for lab test FPWS-059. -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-40. Measured vs. predicted qua si-steady force for lab test FPWS-060.

PAGE 120

120 -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-41. Measured vs. predicted qua si-steady force for lab test FPWS-061. -60 -40 -20 0 20 40 60 80 100 120 0.00.20.40.60.81.01.21.41.6 Time (sec)Force (lbs) Measured Predicted Figure B-42. Measured vs. predicted qua si-steady force for lab test FPWS-062.

PAGE 121

121 -40 -30 -20 -10 0 10 20 30 40 0.00.20.40.60.81.01.21.41.6 Time (sec)Force (lbs) Measured Predicted Figure B-43. Measured vs. predicted qua si-steady force for lab test FPWS-063. -40 -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-44. Measured vs. predicted qua si-steady force for lab test FPWS-068.

PAGE 122

122 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-45. Measured vs. predicted qua si-steady force for lab test FPWS-070. -30 -25 -20 -15 -10 -5 0 5 10 15 20 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-46. Measured vs. predicted qua si-steady force for lab test FPWS-071.

PAGE 123

123 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-47. Measured vs. predicted qua si-steady force for lab test FPWS-073. -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-48. Measured vs. predicted qua si-steady force for lab test FPWS-074.

PAGE 124

124 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-49. Measured vs. predicted qua si-steady force for lab test FPWS-075. -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-50. Measured vs. predicted qua si-steady force for lab test FPWS-076.

PAGE 125

125 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-51. Measured vs. predicted qua si-steady force for lab test FPWS-077. -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-52. Measured vs. predicted qua si-steady force for lab test FPWS-078.

PAGE 126

126 -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-53. Measured vs. predicted qua si-steady force for lab test FPWS-079. -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-54. Measured vs. predicted qua si-steady force for lab test FPWS-081.

PAGE 127

127 -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-55. Measured vs. predicted qua si-steady force for lab test FPWS-082. -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-56. Measured vs. predicted qua si-steady force for lab test FPWS-083.

PAGE 128

128 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-57. Measured vs. predicted qua si-steady force for lab test FPWS-084. -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-58. Measured vs. predicted qua si-steady force for lab test FPWS-085.

PAGE 129

129 -150 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-59. Measured vs. predicted qua si-steady force for lab test FPWS-086. -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.41.6 Time (sec)Force (lbs) Measured Predicted Figure B-60. Measured vs. predicted qua si-steady force for lab test FPWS-087.

PAGE 130

130 -30 -20 -10 0 10 20 30 40 50 60 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-61. Measured vs. predicted qua si-steady force for lab test FPWS-089. -100 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-62. Measured vs. predicted qua si-steady force for lab test FPWS-090.

PAGE 131

131 -30 -20 -10 0 10 20 30 40 50 60 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-63. Measured vs. predicted qua si-steady force for lab test FPWS-091. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-64. Measured vs. predicted qua si-steady force for lab test FPWS-092.

PAGE 132

132 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-65. Measured vs. predicted qua si-steady force for lab test FPWS-093. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-66. Measured vs. predicted qua si-steady force for lab test FPWS-094.

PAGE 133

133 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-67. Measured vs. predicted qua si-steady force for lab test FPWS-095. -80 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-68. Measured vs. predicted qua si-steady force for lab test FPWS-098.

PAGE 134

134 -80 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-69. Measured vs. predicted qua si-steady force for lab test FPWS-100. -25 -20 -15 -10 -5 0 5 10 15 20 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-70. Measured vs. predicted qua si-steady force for lab test FPWS-101.

PAGE 135

135 -80 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-71. Measured vs. predicted qua si-steady force for lab test FPWS-102. -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-72. Measured vs. predicted qua si-steady force for lab test FPWS-105.

PAGE 136

136 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-73. Measured vs. predicted qua si-steady force for lab test FPWS-106. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-74. Measured vs. predicted qua si-steady force for lab test FPWS-107.

PAGE 137

137 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-75. Measured vs. predicted qua si-steady force for lab test FPWS-108. -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-76. Measured vs. predicted qua si-steady force for lab test FPWS-110.

PAGE 138

138 -100 -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-77. Measured vs. predicted qua si-steady force for lab test FPWS-111. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-78. Measured vs. predicted qua si-steady force for lab test FPWS-113.

PAGE 139

139 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-79. Measured vs. predicted qua si-steady force for lab test FPWS-114. -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-80. Measured vs. predicted qua si-steady force for lab test FPWS-115.

PAGE 140

140 -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-81. Measured vs. predicted qua si-steady force for lab test FPWS-116. -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-82. Measured vs. predicted qua si-steady force for lab test FPWS-117.

PAGE 141

141 -150 -100 -50 0 50 100 150 200 250 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-83. Measured vs. predicted qua si-steady force for lab test FPWS-118. -150 -100 -50 0 50 100 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-84. Measured vs. predicted qua si-steady force for lab test FPWS-119.

PAGE 142

142 -30 -20 -10 0 10 20 30 40 50 60 70 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-85. Measured vs. predicted qua si-steady force for lab test FPWS-121. -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-86. Measured vs. predicted qua si-steady force for lab test FPWS-122.

PAGE 143

143 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-87. Measured vs. predicted qua si-steady force for lab test FPWS-124. -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-88. Measured vs. predicted qua si-steady force for lab test FPWS-125.

PAGE 144

144 -150 -100 -50 0 50 100 150 200 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-89. Measured vs. predicted qua si-steady force for lab test FPWS-126. -100 -80 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-90. Measured vs. predicted qua si-steady force for lab test FPWS-127.

PAGE 145

145 -40 -30 -20 -10 0 10 20 30 40 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-91. Measured vs. predicted qua si-steady force for lab test FPWS-129. -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-92. Measured vs. predicted qua si-steady force for lab test FPWS-130.

PAGE 146

146 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-93. Measured vs. predicted qua si-steady force for lab test FPWS-131. -80 -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-94. Measured vs. predicted qua si-steady force for lab test FPWS-132.

PAGE 147

147 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-95. Measured vs. predicted qua si-steady force for lab test FPWS-133. -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-96. Measured vs. predicted qua si-steady force for lab test FPWS-134.

PAGE 148

148 -80 -60 -40 -20 0 20 40 60 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-97. Measured vs. predicted qua si-steady force for lab test FPWS-135. -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-98. Measured vs. predicted qua si-steady force for lab test FPWS-137.

PAGE 149

149 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-99. Measured vs. predicted qua si-steady force for lab test FPWS-139. -150 -100 -50 0 50 100 150 200 250 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-100. Measured vs. predicted qua si-steady force for lab test FPWS-140.

PAGE 150

150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-101. Measured vs. predicted qua si-steady force for lab test FPWS-141. -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-102. Measured vs. predicted qua si-steady force for lab test FPWS-142.

PAGE 151

151 -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-103. Measured vs. predicted qua si-steady force for lab test FPWS-143. -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-104. Measured vs. predicted qua si-steady force for lab test FPWS-145.

PAGE 152

152 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-105. Measured vs. predicted qua si-steady force for lab test FPWS-146. -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-106. Measured vs. predicted qua si-steady force for lab test FPWS-147.

PAGE 153

153 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-107. Measured vs. predicted qua si-steady force for lab test FPWS-148. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-108. Measured vs. predicted qua si-steady force for lab test FPWS-149.

PAGE 154

154 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-109. Measured vs. predicted qua si-steady force for lab test FPWS-150. -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-110. Measured vs. predicted qua si-steady force for lab test FPWS-151.

PAGE 155

155 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-111. Measured vs. predicted qua si-steady force for lab test FPWS-153. -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-112. Measured vs. predicted qua si-steady force for lab test FPWS-154.

PAGE 156

156 -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-113. Measured vs. predicted qua si-steady force for lab test FPWS-155. -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-114. Measured vs. predicted qua si-steady force for lab test FPWS-156.

PAGE 157

157 -60 -40 -20 0 20 40 60 80 100 120 140 160 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-115. Measured vs. predicted qua si-steady force for lab test FPWS-157. -100 -50 0 50 100 150 200 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-116. Measured vs. predicted qua si-steady force for lab test FPWS-158.

PAGE 158

158 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-117. Measured vs. predicted qua si-steady force for lab test FPWS-159. -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-118. Measured vs. predicted qua si-steady force for lab test FPWS-161.

PAGE 159

159 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-119. Measured vs. predicted qua si-steady force for lab test FPWS-162. -60 -40 -20 0 20 40 60 80 100 120 140 160 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-120. Measured vs. predicted qua si-steady force for lab test FPWS-163.

PAGE 160

160 -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-121. Measured vs. predicted qua si-steady force for lab test FPWS-164. -100 -50 0 50 100 150 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-122. Measured vs. predicted qua si-steady force for lab test FPWS-167.

PAGE 161

161 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-123. Measured vs. predicted qua si-steady force for lab test FPWS-170. -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-124. Measured vs. predicted qua si-steady force for lab test FPWS-171.

PAGE 162

162 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-125. Measured vs. predicted qua si-steady force for lab test FPWS-172. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-126. Measured vs. predicted qua si-steady force for lab test FPWS-173.

PAGE 163

163 -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-127. Measured vs. predicted qua si-steady force for lab test FPWS-174. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-128. Measured vs. predicted qua si-steady force for lab test FPWS-175.

PAGE 164

164 -150 -100 -50 0 50 100 150 200 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-129. Measured vs. predicted qua si-steady force for lab test FPWS-186. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-130. Measured vs. predicted qua si-steady force for lab test FPNS-001.

PAGE 165

165 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-131. Measured vs. predicted qua si-steady force for lab test FPNS-002. -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-132. Measured vs. predicted qua si-steady force for lab test FPNS-003.

PAGE 166

166 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-133. Measured vs. predicted qua si-steady force for lab test FPNS-004. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-134. Measured vs. predicted qua si-steady force for lab test FPNS-005.

PAGE 167

167 -20 -10 0 10 20 30 40 50 60 70 80 90 0.00.51.01.52.02.53.03.54.0 Time (sec)Force (lbs) Measured Predicted Figure B-135. Measured vs. predicted qua si-steady force for lab test FPNS-007. -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.54.0 Time (sec)Force (lbs) Measured Predicted Figure B-136. Measured vs. predicted qua si-steady force for lab test FPNS-008.

PAGE 168

168 -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-137. Measured vs. predicted qua si-steady force for lab test FPNS-009. -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-138. Measured vs. predicted qua si-steady force for lab test FPNS-010.

PAGE 169

169 -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-139. Measured vs. predicted qua si-steady force for lab test FPNS-011. -10 0 10 20 30 40 50 60 70 80 90 0.00.51.01.52.02.53.03.54.0 Time (sec)Force (lbs) Measured Predicted Figure B-140. Measured vs. predicted qua si-steady force for lab test FPNS-013.

PAGE 170

170 -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.03.54.0 Time (sec)Force (lbs) Measured Predicted Figure B-141. Measured vs. predicted qua si-steady force for lab test FPNS-014. -100 -50 0 50 100 150 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-142. Measured vs. predicted qua si-steady force for lab test FPNS-015.

PAGE 171

171 -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-143. Measured vs. predicted qua si-steady force for lab test FPNS-016. -150 -100 -50 0 50 100 150 200 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-144. Measured vs. predicted qua si-steady force for lab test FPNS-017.

PAGE 172

172 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-145. Measured vs. predicted qua si-steady force for lab test FPNS-019. -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-146. Measured vs. predicted qua si-steady force for lab test FPNS-020.

PAGE 173

173 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-147. Measured vs. predicted qua si-steady force for lab test FPNS-021. -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-148. Measured vs. predicted qua si-steady force for lab test FPNS-022.

PAGE 174

174 -150 -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-149. Measured vs. predicted qua si-steady force for lab test FPNS-023. -20 0 20 40 60 80 100 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-150. Measured vs. predicted qua si-steady force for lab test FPNS-025.

PAGE 175

175 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-151. Measured vs. predicted qua si-steady force for lab test FPNS-026. -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-152. Measured vs. predicted qua si-steady force for lab test FPNS-027.

PAGE 176

176 -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-153. Measured vs. predicted qua si-steady force for lab test FPNS-028. -100 -50 0 50 100 150 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-154. Measured vs. predicted qua si-steady force for lab test FPNS-029.

PAGE 177

177 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-155. Measured vs. predicted qua si-steady force for lab test FPNS-031. -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-156. Measured vs. predicted qua si-steady force for lab test FPNS-032.

PAGE 178

178 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-157. Measured vs. predicted qua si-steady force for lab test FPNS-033. -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-158. Measured vs. predicted qua si-steady force for lab test FPNS-034.

PAGE 179

179 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-159. Measured vs. predicted qua si-steady force for lab test FPNS-035. -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-160. Measured vs. predicted qua si-steady force for lab test FPNS-036.

PAGE 180

180 -60 -40 -20 0 20 40 60 80 100 120 140 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-161. Measured vs. predicted qua si-steady force for lab test FPNS-037. -100 -50 0 50 100 150 200 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-162. Measured vs. predicted qua si-steady force for lab test FPNS-038.

PAGE 181

181 -150 -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-163. Measured vs. predicted qua si-steady force for lab test FPNS-039. -100 -50 0 50 100 150 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-164. Measured vs. predicted qua si-steady force for lab test FPNS-040.

PAGE 182

182 -100 -50 0 50 100 150 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-165. Measured vs. predicted qua si-steady force for lab test FPNS-041. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-166. Measured vs. predicted qua si-steady force for lab test FPNS-042.

PAGE 183

183 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-167. Measured vs. predicted qua si-steady force for lab test FPNS-043. -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-168. Measured vs. predicted qua si-steady force for lab test FPNS-044.

PAGE 184

184 -100 -80 -60 -40 -20 0 20 40 60 80 100 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-169. Measured vs. predicted qua si-steady force for lab test FPNS-045. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-170. Measured vs. predicted qua si-steady force for lab test FPNS-046.

PAGE 185

185 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-171. Measured vs. predicted qua si-steady force for lab test FPNS-047. -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-172. Measured vs. predicted qua si-steady force for lab test FPNS-048.

PAGE 186

186 -100 -50 0 50 100 150 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-173. Measured vs. predicted qua si-steady force for lab test FPNS-049. -100 -80 -60 -40 -20 0 20 40 60 80 100 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-174. Measured vs. predicted qua si-steady force for lab test FPNS-050.

PAGE 187

187 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-175. Measured vs. predicted qua si-steady force for lab test FPNS-051. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.03.5 Time (sec)Force (lbs) Measured Predicted Figure B-176. Measured vs. predicted qua si-steady force for lab test FPNS-052.

PAGE 188

188 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-177. Measured vs. predicted qua si-steady force for lab test FPNS-053. -100 -50 0 50 100 150 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-178. Measured vs. predicted qua si-steady force for lab test FPNS-054.

PAGE 189

189 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-179. Measured vs. predicted qua si-steady force for lab test FPNS-055. -100 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-180. Measured vs. predicted qua si-steady force for lab test FPNS-056.

PAGE 190

190 -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-181. Measured vs. predicted qua si-steady force for lab test FPNS-057. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-182. Measured vs. predicted qua si-steady force for lab test FPNS-058.

PAGE 191

191 -60 -40 -20 0 20 40 60 80 100 120 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-183. Measured vs. predicted qua si-steady force for lab test FPNS-059. -80 -60 -40 -20 0 20 40 60 80 100 120 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-184. Measured vs. predicted qua si-steady force for lab test FPNS-060.

PAGE 192

192 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-185. Measured vs. predicted qua si-steady force for lab test FPNS-061. -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-186. Measured vs. predicted qua si-steady force for lab test FPNS-062.

PAGE 193

193 -100 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-187. Measured vs. predicted qua si-steady force for lab test FPNS-063. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-188. Measured vs. predicted qua si-steady force for lab test FPNS-064.

PAGE 194

194 -60 -40 -20 0 20 40 60 80 100 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-189. Measured vs. predicted qua si-steady force for lab test FPNS-065. -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-190. Measured vs. predicted qua si-steady force for lab test FPNS-066.

PAGE 195

195 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-191. Measured vs. predicted qua si-steady force for lab test FPNS-067. -100 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-192. Measured vs. predicted qua si-steady force for lab test FPNS-068.

PAGE 196

196 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-193. Measured vs. predicted qua si-steady force for lab test FPNS-069. -80 -60 -40 -20 0 20 40 60 80 100 0.00.20.40.60.81.01.21.41.6 Time (sec)Force (lbs) Measured Predicted Figure B-194. Measured vs. predicted qua si-steady force for lab test FPNS-070.

PAGE 197

197 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-195. Measured vs. predicted qua si-steady force for lab test FPNS-071. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-196. Measured vs. predicted qua si-steady force for lab test FPNS-072.

PAGE 198

198 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-197. Measured vs. predicted qua si-steady force for lab test FPNS-073. -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-198. Measured vs. predicted qua si-steady force for lab test FPNS-074.

PAGE 199

199 -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-199. Measured vs. predicted qua si-steady force for lab test FPNS-075. -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-200. Measured vs. predicted qua si-steady force for lab test FPNS-076.

PAGE 200

200 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-201. Measured vs. predicted qua si-steady force for lab test FPNS-077. -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-202. Measured vs. predicted qua si-steady force for lab test FPNS-078.

PAGE 201

201 -80 -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-203. Measured vs. predicted qua si-steady force for lab test FPNS-079. -60 -40 -20 0 20 40 60 80 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-204. Measured vs. predicted qua si-steady force for lab test FPNS-080.

PAGE 202

202 -40 -30 -20 -10 0 10 20 30 40 50 60 70 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-205. Measured vs. predicted qua si-steady force for lab test FPNS-081. -60 -40 -20 0 20 40 60 80 100 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-206. Measured vs. predicted qua si-steady force for lab test FPNS-082.

PAGE 203

203 -60 -40 -20 0 20 40 60 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-207. Measured vs. predicted qua si-steady force for lab test FPNS-083. -40 -30 -20 -10 0 10 20 30 40 50 60 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-208. Measured vs. predicted qua si-steady force for lab test FPNS-084.

PAGE 204

204 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-209. Measured vs. predicted qua si-steady force for lab test FPNS-085. -40 -30 -20 -10 0 10 20 30 40 50 60 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-210. Measured vs. predicted qua si-steady force for lab test FPNS-086.

PAGE 205

205 -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-211. Measured vs. predicted qua si-steady force for lab test FPNS-087. -60 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-212. Measured vs. predicted qua si-steady force for lab test FPNS-088.

PAGE 206

206 -40 -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-213. Measured vs. predicted qua si-steady force for lab test FPNS-089. -40 -30 -20 -10 0 10 20 30 40 50 60 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-214. Measured vs. predicted qua si-steady force for lab test FPNS-090.

PAGE 207

207 -40 -20 0 20 40 60 80 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-215. Measured vs. predicted qua si-steady force for lab test FPNS-093. -40 -30 -20 -10 0 10 20 30 40 50 0.00.20.40.60.81.01.21.4 Time (sec)Force (lbs) Measured Predicted Figure B-216. Measured vs. predicted qua si-steady force for lab test FPNS-094.

PAGE 208

208 -20 -15 -10 -5 0 5 10 15 20 25 0.00.51.01.52.02.53.0 Time (sec)Force (lbs) Measured Predicted Figure B-217. Measured vs. predicted qua si-steady force for lab test FPNS-097. -50 -40 -30 -20 -10 0 10 20 30 40 50 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-218. Measured vs. predicted qua si-steady force for lab test FPNS-098.

PAGE 209

209 -25 -20 -15 -10 -5 0 5 10 15 20 25 0.00.51.01.52.02.5 Time (sec)Force (lbs) Measured Predicted Figure B-219. Measured vs. predicted qua si-steady force for lab test FPNS-099. -40 -30 -20 -10 0 10 20 30 0.00.51.01.52.0 Time (sec)Force (lbs) Measured Predicted Figure B-220. Measured vs. predicted qua si-steady force for lab test FPNS-100.

PAGE 210

210 LIST OF REFERENCES Bea, R. G., Iversen, R., and Xu, T. (2001). W ave-in-deck forces on offshore platforms. J. Offshore Mech. Arctic Eng. 123, 10-21. Bea, R. G., Xu, T., Stear, J., and Ramos, R. (1999). Wave forces on decks of offshore platforms. J. Waterway, Port, Coastal, Ocean Eng., 125(3), 136-144. Cardone, V. J., and Cox, A. T. (1992). Hindcas t study of Hurricane Andr ew, offshore Gulf of Mexico. Joint Industry Project Rep. Ocean-weather Inc., Cos Cob, Conn. Dean, R. G., Torum, A., and Kjeldsen, S. P. ( 1985). Wave forces on a pile in the surface zone from the wave crest to wave trough. Proc., Int. Symp. on Separated Flow Around Marine Structures Norwegian Institute of Technology, Trondheim, Norway. Denson, K. H. (1978). Wave forces on causeway-type coastal bridges. Misc. Rep., Water Resources Research Institute, Mississi ppi State University, Starkville, Miss. Denson, K. H. (1980). Wave forces on causeway-type coastal bridges: Effects of angle of wave incidence and cross-section shape. Technical Rep. No. MSHD-RD-80-070 Water Resources Research Institute, Mississi ppi State University, Starkville, Miss. Faltinsen, O., Kjarland, O., Nottveit, A., and Vinje, T. (1977). Water impact loads and dynamic response of horizontal circular cy linders in offshore structures. Proc., Offshore Technology Conf. SPE, Richardson, Tex. Finnigan, T. D., and Petrauskas, C. (1997). Wave-in-deck forces. Proc., 6th Int. Offshore and Polar Engineering Conf. ISOPE, Golden, Colo. Imm, G. R., OConnor, J. M., and Stahl, B. (1994). South Timbalier 161A: A successful application platform requalification technology. Proc., Offshore Technology Conf., SPE, Richardson, Tex. Isaacson, M., and Bhat, S. (1996). Wave forces on a horizontal plate. Int. J. Offshore Polar Eng., 6(1), 19-26. Kaplan, P. (1992). Wave impact forces on offshore structures: Re -examination and new interpretations. Proc., Offshore Tech. Conf. SPE, Richardson, Tex. Kaplan, P., Murray, J. J., and Yu, W. C. (1995). T heoretical analysis of wave impact forces on platform deck structures. Proc., 14th Int. Conf. Offshore Mech. and Arctic Eng. ASME, New York. Kjeldsen, S. P., and Myrhaug, D. (1979). Break ing waves in deep water and resulting wave forces. Proc., Offshore Technology Conf. SPE, Richardson, Tex. Kjeldsen, S. P., and Hasle, E. K. (1985) Ekofisk jacket Model experiments. Rep. No. NHL 85-0295, Norwegian Hydrodynamics Laboratory, Trondheim, Norway.

PAGE 211

211 Kjeldsen, S. P., Torum, A., and Dean, R. G. ( 1986). Wave forces on vertical piles caused by 2 and 3-dimensional breaking waves. Proc., Coastal Engineering Conf. ASCE, New York. Morison, J. R., OBrien, M. P., Johnson, J. W., a nd Schaaf, S. A. (1950). The force exerted by surface waves on piles. Petrol. Trans., 189, 149-154. McConnell, K. J., Allsop, N. W. H., Cuomo, G., and Cruicksha nk, I. C. (2003). New guidance for wave forces on jetties in exposed locations. Proc., 6th Int. Conf. on Coastal and Port Engineering in Developing Countries COPEDEC, Columbo, Sri Lanka. Murray, J. J., Kaplan, P., and Yu, W. C. (1995). Experimental and analytical studies of wave impact forces on Ekofisk platform structures. Proc., Offshore Tech. Conf. SPE, Richardson, Tex.. Payne, P. R. (1981). The virtual mass of a rect angular flat plate of finite aspect ratio. Ocean Eng., 8(5), 541-545. Stear, J., and Bea, R. G. (1997). Ultimate limit st ate capacity analysis of two Gulf of Mexico platforms. Proc., Offshore Technology Conf., SPE, Richardson, Tex. Tirindelli, M., Cuomo, G., Allsop, N. W. H., and McConnell, K. J. (2002). Exposed jetties: Inconsistencies and gaps in design methods for wave-induced forces. Proc., 28th Int. Conf. on Coastal Engineering ASCE, Cardiff, UK. Vannan, M. T., Thompson, H. M., Griffin, J. J., and Gelpi, S. L. (1994). An automated procedure for platform strength assessment. Proc., Offshore Technology Conf. SPE, Richardson, Tex. U.S. Army Corp of Engineers (2008 ). Coastal Engineering Manual. Manual No. EM 1110-21100, U.S. Army Corp of Engineers, Coastal and Hydraulics Laboratory, Vicksburg, Miss. Weggel, J. R. (1997). Breaking-wave loads on ve rtical walls suspended above mean sea level. J. Waterway, Port, Coastal, Ocean Eng., 123(3), 143-148.

PAGE 212

212 BIOGRAPHICAL SKETCH Justin Marin was born in 1981 in New Orleans, L ouisiana, the son of two civil engineers. He m oved to south Florida in 1995 and attended high school in Ft. La uderdale. He began attending the University of Florida in August 1999 and graduated with a B.S. in civil engineering in May 2003. Remaining at the University of Florida throughout gradua te school, he received his M.S. in coastal and oceanographic engineering in May 2009 and his Ph.D. in coastal and oceanographic engineering in August 2009. His furt her graduate studies included expanding the work on wave loading to bridge decks and more complex shapes. While at the University of Florida, he was pa rt of the Coastal Engineering Lab field dive team, installing and retrieving instruments from the field and inspecting bridge foundations for scour effects. His favorite color is grey.