Clp

Dynpac

Dynpac

RELEASE 5

USER’S MANUAL

ENGINEERING DYNAMICS, INC.

2113 38TH STREET

KENNER, LOUISIANA 70065

U.S.A.

No part of this document may bereproduced in any form, in anelectronic retrieval system orotherwise, without the prior

written permission of the publisher.

Copyright © 1998 by

ENGINEERING DYNAMICS, INC.

Printed in U.S.A.

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TABLE OF CONTENTS

1.0 INTRODUCTION 1-1.......................................................................................................................1.1 OVERVIEW 1-1.........................................................................................................................1.2 PROGRAM FEATURES 1-1......................................................................................................

2.0 DYNAMIC MODELING AND INPUT 2-1.....................................................................................2.1 RETAINED DEGREES OF FREEDOM 2-1.............................................................................2.2 STRUCTURAL MASS 2-1........................................................................................................

2.2.1 Generating Structural Mass Automatically 2-1.................................................................2.2.1.1 Default Structural Density 2-2.................................................................................2.2.1.2 Overriding Structural Density 2-2............................................................................

2.2.2 Converting Loads to Mass Automatically 2-2...................................................................2.2.2.1 Designating Load Cases to Convert to Mass 2-3.....................................................2.2.2.2 Factoring Load Cases 2-3.........................................................................................

2.2.3 User Input Joint Weight 2-4..............................................................................................2.3 FLUID MASS 2-4.......................................................................................................................

2.3.1 Generating Fluid Added Mass Automatically 2-4.............................................................2.3.1.1 Member Overrides for Fluid Added Mass Generation 2-4......................................2.3.1.2 Plate Overrides for Fluid Added Mass Generation 2-5............................................

2.3.2 Generating Fluid Entrapped Mass Automatically 2-5.......................................................2.3.2.1 Member Overrides for Fluid Entrapped Mass Generation 2-5................................

2.4 HYDRODYNAMIC MODELING USING SEASTATE 2-5.....................................................2.5 SIMULATING NON-LINEAR FOUNDATIONS 2-6...............................................................

2.5.1 Including Linearized Foundation Automatically 2-6........................................................2.6 INCLUDING P-DELTA EFFECTS 2-6.....................................................................................

3.0 DYNPAC INPUT FILE 3-1..............................................................................................................3.1 INPUT FILE SETUP 3-1............................................................................................................3.2 INPUT LINES 3-1......................................................................................................................

4.0 DYNPAC TROUBLE SHOOTING 4-1............................................................................................4.1 MODEL STIFFNESS MATRIX 4-1..........................................................................................4.2 MODEL MASS MATRIX 4-1....................................................................................................

5.0 COMMENTARY 5-1........................................................................................................................5.1 STIFFNESS MATRIX REDUCTION 5-1.................................................................................5.2 MASS MATRIX GENERATION 5-2........................................................................................

5.2.1 Consistent Mass Approach 5-2..........................................................................................5.2.2 Lumped Mass Approach 5-3.............................................................................................

5.3 MASS MATRIX REDUCTION 5-3...........................................................................................5.4 CALCULATING RESULTS 5-4................................................................................................5.5 FLUID ADDED OR VIRTUAL MASS 5-4...............................................................................

6.0 SAMPLE PROBLEMS 6-1...............................................................................................................6.1 SAMPLE PROBLEM 1 6-2........................................................................................................6.2 SAMPLE PROBLEM 2 6-12........................................................................................................6.3 SAMPLE PROBLEM 3 6-14........................................................................................................

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Dynpac

SECTION 1INTRODUCTION

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1.0 INTRODUCTION

1.1 OVERVIEWThe Dynpac program module generates dynamic characteristics including eigenvectorsor natural mode shapes, eigenvalues or natural periods and modal internal load and stressvectors for a structure.

Because the Dynpac module provides the mode shapes and masses required for modaldynamic analysis, its execution is required prior to execution of any of the SACSdynamic programs.

1.2 PROGRAM FEATURESDynpac requires a SACS input model file or output structural data file and a Dynpacinput file for execution. The program creates a common solution file containingnormalized mode shapes, frequencies, internal loads etc. and a mass file.

Some of the main features and capabilities of Dynpac program module are:1. Full six degree of freedom modes supported.2. Guyan reduction of non-inertially loaded (slave) degrees of freedom.3. Generates structural mass and fluid added or virtual mass automatically.4. Supports lumped or consistent mass generation.5. User input lumped or consistent mass capability.6. Ability to convert model input loading to mass.7. Utilizes hydrodynamic properties and modeling from Seastate module.8. Plate and beam element structural density overrides.9. Member and member group fluid added mass property overrides.10. Determines modal mass participation to allow determination of number of modes

required for subsequent dynamic analyses.11. Ability to override plate added mass coefficient.12. Ability to override plate properties by plate group.13. Includes P-Delta capabilities in addition to cable elements.

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Dynpac

SECTION 2DYNPAC MODELING AND INPUT

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2.0 DYNAMIC MODELING AND INPUTThe Dynpac program requires a SACS model file or output structural data file and aDynpac input file. The model file must contain minimal additional dynamic modelinginformation in order to perform the Dynpac analysis, namely, the dynamic analysisoption 'DY' must be specified in columns 19-20 on the 'OPTIONS' input line, jointretained (master) degrees of freedom (DOF) must be specified in the joint fixity columnson the appropriate 'JOINT' input line(s) and a 'LOAD' header must exist in the model fileeven if no loading is specified.

2.1 RETAINED DEGREES OF FREEDOMDynpac uses a set of master (retained) degrees of freedom, selected by the user, toextract the Eigen values (periods) and Eigen vectors (mode shapes). All stiffness andmass properties associated with the slave (reduced) degrees of freedom are included inthe Eigen extraction procedure. The stiffness matrix is reduced to the master degrees offreedom using standard matrix condensation methods. The mass matrix is reduced to themaster degrees of freedom using the Guyan reduction method assuming that the stiffnessand mass are distributed similarly. All degrees of freedom which are non-inertial (nomass value) must be slave degrees of freedom. After modes are extracted using themaster degrees of freedom, they are expanded to include full 6 degrees of freedom for alljoints in the structure. The expanded modes are used for subsequent dynamic responseanalysis.

Any joint degree of freedom, X, Y and Z translation and/or rotation, to be retained forextraction purposes must be designated in the model. A joint DOF may be retained byspecifying a '2' in the appropriate fixity column on the 'JOINT' input line. Specifying a '0'or leaving the fixity field blank designates the DOF as a slave degree of freedom to bereduced. For example, to retain the X and Z translation degrees of freedom, specify '202'or '2 2' in columns 55-57 on the 'JOINT' line defining the joint.Note: Columns 55, 56 and 57 pertain to global X, Y and Z translation

respectively and columns 58, 59, and 60 to X, Y and Z rotationrespectively.

Support degrees of freedom require no special modeling for dynamic purposes.Note: Specifying a ’2’ or ’0’ for a particular DOF, has no effect for

static analysis.

2.2 STRUCTURAL MASS

2.2.1 Generating Structural Mass Automatically

By default, Dynpac generates structural mass for modeled beam, plate and shell elementsautomatically. Structural masses are also generated if 'SA' is specified as one of theexecution options in columns 63-68 on the 'DYNOPT' line. Structural masses are notgenerated if option 'SO' is specified in columns 63-68.

Structural mass may be calculated as lumped or consistent mass by specifying 'LUMP' or'CONS' in columns 15-18 on the 'DYNOPT' line respectively. The lumped method placesall element mass at the nodes to which the element is connected while the consistent

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approach assumes mass is distributed along the element. Although, the default method islumped, consistent mass may be desirable for structures immersed in fluid.

The following example indicates that the mass of modeled elements is to be calculatedby the program in addition to converting some load cases in the model file to mass. Theconsistent mass approach is to be used.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

DYNOPT CONS SA-Z

Note: Because the lumped approach does not generate mass moments ofinertia, the weight moment of inertia for each rotational DOFretained must be specified in the Dynpac input file when using thelumped approach.

2.2.1.1 Default Structural Density

For a beam element, the density specified on the GRUP input line is used as the defaultwhen generating structural mass automatically, unless density is specified on theMEMBER line. If structural mass is not specified the density specified on the 'DYNOPT'line is used.

The density specified on the PGRUP or PLATE input lines located in the model file areused for plate elements. For shell elements on the other hand, the density specified incolumns 19-25 on the DYNOPT line is used. The density specified on the 'SHELL' lineis ignored by the Dynpac program module.

2.2.1.2 Overriding Structural Density

The density for individual members, plates, plate groups, shells and member groups maybe overridden for mass generation purposes. The member, plate, shell or group name,along with the structural density override, are specified in the Dynpac input file on theMBOVR, PLOVR, PGOVR, SHOVR and GROVR override lines, respectively.

The following example specifies that the density of member 101-157, member groupMM1, plate A101 and plate group PG1 is to be 100.0 for the purpose of determining thedynamic characteristics.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

MBOVR 101 157 100.0GROVR MM1 100.0PLOVR A101 100.0PGOVR PG1 100.0

2.2.2 Converting Loads to Mass Automatically

Loading contained in the SACS model file can be converted to structural joint ormember mass automatically by specifying 'SA' as one of the execution options incolumns 63-68 on the 'DYNOPT' input line.

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The direction of loads to be converted and whether the same sign or the opposite sign ofthe load is to be used when converting to mass must also be specified in the executionoptions. If loading in the model file defined in the X direction is to be converted to mass,then '±X' should be specified. To convert loading defined in the Y or Z directions, '±Y' or'±Z' should be specified as one of the execution options respectively. The sign of the loaddirection specified, denotes whether the mass calculated from the load line will have thesame sign as the load, designated by '+', or the opposite sign of the load designated by '-'.For example, when converting loading in the global -Z direction (such as gravity loading)to mass, the mass should have the opposite sign as the load specified (ie. positive mass).Therefore, execution options 'SA-Z' (or 'SO-Z') should be specified on the 'DYNOPT'input line.

The following example indicates that the mass of modeled elements is to be calculatedby the program in addition to converting load cases in the Z direction in the model file tomass. The sign of the mass will be the opposite of the sign of the load.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

DYNOPT CONS SA-Z

Note: When converting loading to mass, the sign of the net load for anyload vector must be such that no negative mass is introduced.

2.2.2.1 Designating Load Cases to Convert to Mass

When loads specified in the SACS model file or Seastate input file are to be converted tomass, only load cases specified on the LCSEL line(s) designated as dynamic load cases(ie. function ‘DY’) are converted. For example, the following designates that load cases4 and 5 are to be converted to mass by the program.Note: Either the SA or SO options must be specified on the DYNOPT

line in order to convert the designated load cases to mass.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

LCSEL DY 4 5

Note: It is recommended to generate structural mass of the modeledstructure automatically rather than converting the gravity loadingcreated by Precede or Seastate.

2.2.2.2 Factoring Load Cases

Load Cases may be factored when converting to mass using the LCFAC line in theSeastate or model input file. In order to factor a load case, specify the load case andfactor on the LCFAC using option ‘DY’. For example, the following designates that 50%of load cases 4 and 5 are to be converted to mass.Note: Load cases 4 and 5 are specified on the LCSEL and LCFAC lines.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

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LCSEL DY 4 5LCFAC DY 0.50 4 5

2.2.3 User Input Joint Weight

Joint weights not defined in load cases designated to be converted to mass, may bespecified as user defined concentrated joint weights in the Dynpac input file.Concentrated joint weights for X, Y and Z translational degrees of freedom and weightmoments of inertia for the X, Y and Z rotational degrees of freedom are specified alongwith the joint number on the JTWGT line and are converted to masses automatically.

The following designates that X,Y and Z weight of 10.0 is to be applied at joints 601 and603.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

JTWGT 601 10.0 10.0 10.0JTWGT 603 10.0 10.0 10.0

2.3 FLUID MASS

2.3.1 Generating Fluid Added Mass Automatically

For structures immersed in fluid, the added or virtual mass and the mass of entrappedfluid can be generated automatically. The fluid mass, mudline elevation and the waterdepth must be specified on the DYNOPT line (in the Dynpac input file) in columns 26-32, 33-39 and 40-46, respectively. The normal and axial added mass coefficients formembers surrounded by fluid are input in columns 49-53 and 54-58 on the DYNOPTline.

By default, the virtual mass is calculated based on the added mass coefficient in columns49-53 on the DYNOPT line and actual member diameter unless an effective diameter isspecified in columns 73-78 on the MEMBER input line. For plate elements, the virtualmass is determined using the added mass coefficient specified in columns 49-53 unless avalue is indicated in columns 59-62 on the DYNOPT line.

The following specifies that the default added mass coefficient is 1.0 for beam elementsand 0.01 for plate elements (ie. effectively ignoring plate mass).

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

DYNOPT CONS 1.0 0.01

2.3.1.1 Member Overrides for Fluid Added Mass Generation

The effective member diameter used for added mass calculation may be overridden forindividual members or for member groups using the 'MBOVR' or the 'GROVR' linesrespectively in the Dynpac input file.

The following overrides the effective diameter of member 101-157 and member groupMM1 to 0.001, thus ensuring that no added mass is calculated for these members.

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1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

MBOVR 101 157 0.001 GROVR MM1 0.001

2.3.1.2 Plate Overrides for Fluid Added Mass Generation

The added mass coefficent for plates and plate groups may be overridden using thePLOVR and PGOVR lines, respectively in the Dynpac input file. The following specifiesthat the plate added mass coefficent for plate A101 and plate group PG1 is 0.001.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

PLOVR A101 0.001PGOVR PG1 0.001

2.3.2 Generating Fluid Entrapped Mass Automatically

Entrapped mass is calculated for members designated as flooded in the model file basedon the actual diameter of the member.

2.3.2.1 Member Overrides for Fluid Entrapped Mass Generation

The flood condition may be overridden for all members on the DYNOPT line in columns47-48. The flood condition for individual members or member groups may be changedusing the MBOVR or the GROVR line images in the Dynpac input file.

The following overrides the flood condition of member 101-157 and member groupMM1 to non-flooded, thus ensuring that no entrapped mass is calculated for thesemembers.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

MBOVR N 101 157 0.001 GROVR MM1 N 0.001

Note: The flood condition specified on the ’DYNOPT’ line overrides anyexisting flood condition for all members in the model unless floodcondition is changed with subsequent ’MBOVR’ or ’GROVR’ lines.

2.4 HYDRODYNAMIC MODELING USING SEASTATEThe Seastate program can be used to account for the hydrodynamic affects of unmodeledstructural items and/or marine growth. Seastate updates the member lines to account forthe density and effective diameter due to marine growth specified on 'MGROV' lines inthe SACS model or in the Seastate input file. Member density is also updated to reflectthe effective density based on any density and/or cross section area overrides specified inthe Seastate input. The effective member diameter in columns 73-78 on the 'MEMBER'input line is updated to account for any local Y and Z force dimension overridesspecified (in addition to effects of marine growth).Note: Seastate must be executed with ’DYN’ specified in columns 56-58 on

the ’LDOPT’ line in the Seastate input file or with the

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appropriate option specified in the Executive in order to generatehydrodynamic properties. The model updates are contained in theoutput structural data file created. See the Seastate User’sManual for a detailed discussion.

2.5 SIMULATING NON-LINEAR FOUNDATIONSBecause the dynamic capabilities in the SACS system use linear theory (ie. modalsuperposition), non-linear foundations must be represented with a linearly equivalentsystem. The equivalent linear foundation model must be incorporated into the SACSmodel for the purposes of dynamic analysis.Note: The Pile program module can be used to determine the length,

properties and offsets for equivalent pile stub elements used torepresent the soil-pile interaction. See the PSI/Pile programuser’s manual for a detailed discussion.

2.5.1 Including Linearized Foundation Automatically

The PSI program may be used to generate an equivalent foundation stiffness matrix orsuper-element to be used to represent the foundation for dynamic analysis. Theequivalent foundation super-element may be included as part of the model by specifying‘I’ in column 9 of the OPTIONS line in the model file or by selecting the appropriatesuperelement option in the Executive.

2.6 INCLUDING P-DELTA EFFECTSThe Dynpac program can include the effects of P-Delta on the dynamic characterisitcs ofthe structure. This feature allows the user to designate reference load case(s)representing static dead loading on the structure.

In order to include P-delta effects, the reference load cases must be designated in themodel file or the Seastate input file using the LCSEL line with the ‘PD’ option. Forexample, the following shows that dead loading defined by load cases DEAD, EQPT andAREA are to be used to determine the P-delta effects on the beam elements.

1 2 3 4 5 6 7 812345678901234567890123456789012345678901234567890123456789012345678901234567890

LCSEL PD DEAD EQPT AREA

Load factors may be applied to the reference load cases using the LCFAC line. Forexample, in the following, 50% of load cases DEAD EQPT and AREA are used to obtainthe reference axial load.

12345678901234567890123456789012345678901234567890123456789012345678901234567890

LCSEL PD DEAD EQPT AREALCFAC PD 0.5 DEAD EQPT AREA

Note: Dead loads are typically used as P-Delta loads. For cableelements, the pre-tension load should be designated as the P-Deltaload.

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SECTION 3DYNPAC INPUT FILE

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3.0 DYNPAC INPUT FILE

3.1 INPUT FILE SETUPThe Dynpac input file contains general dynamic analysis information and may includeadditional hydrodynamic property override information. The table below shows thestandard Dynpac file input lines.

INPUT LINE DESCRIPTION

TITLE Dynpac analysis title

DYNOPT* Dynamic analysis options

PLOVR Plate override data

PGOVR Plate group override data

GROVR Member group density and hydrodynamic property overrides

MBOVR Member density and hydrodynamic property overrides

SHOVR Shell element structural weight density overrides

JTWGT Specify joint concentrated weight data

END* Designates the end of input data

Note: Lines that are required are designated with an asterisk.

3.2 INPUT LINESThe following section illustrates the formats of the input lines for Dynpac. The usershould be familiar with the basic guidelines for specifying input data. These guidelinesare located in the Introduction Manual.

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1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334353637383940

DYNAMIC CHARACTERISTICS SAMPLE PROBLEM

ENGLISH UNITS CONSISTENT MASS APPROACH

DYNOPT +ZEN 15CONS

41424344454647484950515253545556575859606162636465666768697071727374757677787980

SA-Z

THE TITLE LINES DYNAMIC CHARACTERISTICS SAMPLE PROBLEM AND ENGLISH UNITS CONSISTENT MASS APPROACH ARE ENTERED BEFORE THEOPTIONS LINE.

DESCRIPTIVE TITLE LINES

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DESCRIPTIVE TITLE 2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 80

COLUMNS COMMENTARY

LOCATION IF INPUT, THIS OPTIONAL LINE IS FIRST IN THE DYNPAC INPUT FILE.

GENERAL THIS LINE IS OPTIONAL AND ALLOWS THE USER TO SPECIFY A TITLE FOR DYNPAC OUTPUT OTHER THAN THE TITLE OF THE SACS IV DECK.

( 2-80) ENTER ANY ALPHANUMERIC TITLE. THIS TITLE WILL APPEAR ON ALL PAGES OF DYNPAC OUTPUT.

DYNPAC TITLE - INPUT LINE 1

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DYNAMIC CHARACTERISTICS SAMPLE PROBLEM

ENGLISH UNITS 150 WATER DEPTH

DYNOPT +ZEN 15CONS 62.4 -150.

41424344454647484950515253545556575859606162636465666768697071727374757677787980

150. SA-Z

THE VERT COORDINATE DIRECTION IS +Z AND ENGLISH UNITS ARE TO BE USED FOR THE DYNAMIC CHARACTERISTIC ANALYSIS. 15 MODESHAPES ARE TO BE EXTRACTED AND THE CONSISTENT MASS APPROACHIS TO USED. THE MUDLINE ELEVATION IS AT -150. AND THE DEPTHTO BE USED FOR VIRTUAL MASS AND BUOYANCY CALCULATION IS 150.FEET. LOADS IN THE GLOBAL Z DIRECTION SPECIFIED IN THE SACSMODEL FILE ARE TO BE CONVERTED TO MASS WITH THE OPPOSITE SIGNAS SPECIFIED BY SA-Z IN COLUMNS 63-66.

DYNAMIC ANALYSIS OPTIONS LINE

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LINELABEL

VERT.COORD. UNITS NO.

MODES

MASSCALC.

OPTION

STRUCT.DENSITY

FLUIDDENSITY

MUDLINEELEV.

WATERDEPTH

FLOODOR

NON-FLOODOPTION

ADDEDMASS

COEFF.

AXIALADDEDMASS

COEFF.

PLATEADDEDMASS

COEFF.

EXECUTIONOPTIONS OUTPUT OPTIONS

1ST 2ND 3RD 1ST 2ND 3RD 4TH 5TH 6TH

DYNOPT

1) 6 8<) 9 10<)11 12)>14 15<)18 19<))25 26<))32 33<)39 40<)46 47<)48 49<)53 54<)58 59<)62 63)648

65)66 67)6869)70071)7273)7475)7677)78 79)80

DEFAULTS +Z 10 LUMP 490.0 0.0 0.0 0.0 1.0 ABOVE ABOVE

ENGLISH LB/CU FT LB/CU FT FT FT

METRIC TONNE/CU TONNE/CU M M

COLUMNS COMMENTARY

GENERAL THIS LINE IS REQUIRED IN ANY DYNAMIC CHARACTERISTICS EXECUTION. IT SPECIFIES THE OVERALL ANALYSIS OPTIONS AND PARAMETERS.

( 8- 9) ENTER THE VERTICAL COORDINATE DIRECTION SUCH AS +Z FOR THE Z COORDINATE IN THE POSITIVE VERTICAL DIRECTION.

(10-11) ENTER THE UNITS DESIRED FOR THIS ANALYSIS. IF LEFT BLANK, THE PROGRAM WILL USE THE UNITS SPECIFIED ON THE SACS OPTION LINE.

EN - ENGLISH UNITS (FEET,LBS,ETC.) MS - METRIC UNITS (METERS,KILOGRAMS,ETC.) MN - METRIC UNITS (METERS,KILONEWTONS,ETC.)

(12-14) ENTER THE NUMBER OF MODES DESIRED.

(15-18) ENTER THE MASS CALCULATION OPTION. LUMP - LUMPED MASS (DIAGONAL MASS MATRIX) CONS - CONSISTENT MASS NOTE THAT CONSISTENT MASS IS HIGHLY DESIRABLE FOR

STRUCTURES THAT ARE IMMERSED IN A FLUID.

(19-25) ENTER THE DEFAULT STRUCTURAL DENSITY FOR ALL PLATE AND SHELL ELEMENTS AND ANY BEAM ELEMENTS THAT DO NOT HAVE DENSITY SPECIFIED ON THE MEMBER OR GROUP LINE. THE DENSITY OF INDIVIDUALBEAM, PLATE OR SHELL ELEMENTS CAN BE OVERRIDDEN WITH SUBSEQUENT OVERRIDE CARDS.

(26-32) IF THE STRUCTURE IS IMMERSED IN A FLUID, ENTER THE DENSITY OF THE FLUID.

(33-39) ENTER THE MUDLINE ELEVATION. THIS IS THE STRUCTURAL COORDINATE VALUE IN THE POSITIVE VERTICAL DIRECTION.

(40-46) IF THE STRUCTURE IS IMMERSED IN FLUID, ENTER THE WATER DEPTH HERE.

COLUMNS COMMENTARY

(47-48) ENTER FL OR NF IF ALL MEMBERS ARE TO BE CONSIDERED FLOODED OR NON-FLOODED (THIS OVER-RIDES SEASTATE AND SACS IV MODELING). THE STATUS CAN BE CHANGED WITH SUBSEQUENT DYNPAC MODELING.

(49-53) ENTER THE ADDED MASS COEFFICIENT FOR MEMBERS SURROUNDED BY FLUID. THIS VALUE IS FOR THE MOTION OF THE STRUCTURE AND IS NOT NORMALLY THE SAME AS IF THE STRUCTURE IS IMMERSED IN A ACCELERATING FLUID.

(54-58) ENTER THE AXIAL ADDED MASS COEFFICIENT FOR MEMBERS SURROUNDED BY FLUID. THIS VALUE IS FOR THE AXIAL MOTION OF THE STRUCTURE AND THE DEFAULTS ARE 0.0 FOR CONSISTANT MASS AND 1.0 FOR LUMPED MASS OPTIONS.

(59-62) ENTER THE DEFAULT ADDED MASS COEFFICIENT FOR PLATES SURROUNDED BY FLUID. IF LEFT BLANK, THE VALUE INPUT IN COLS. 49-53 IS USED.

(63-68) ENTER THE EXECUTION OPTIONS DESIRED: Blank - USE ONLY MASSES CALCULATED BY DYNPAC. SA - USE LOADS IN THE SACS DATA AS MASSES IN ADDITION TO MASSES CALCULATED BY DYNPAC. SO - USE LOADS IN THE SACS DATA AS MASSES AND DO NOT USE ANY MASSES CALCULATED BY DYNPAC. +X - THE LOADS TO BE USED FROM THE SACS DATA FOR MASSES ARE THE X-DIRECTION LOADS ONLY, SAME SIGN AS LOAD RECORD. USE +Y AND +Z SIMILARLY. -X - THE LOADS TO BE USED FROM THE SACS DATA FOR MASSES ARE THE X-DIRECTION LOADS ONLY, OPPOSITE SIGN FROM LOAD RECORD. USE -Y AND -Z SIMILARLY.

(69-80) ENTER THE OUTPUT OPTIONS DESIRED: MA - PRINT MASS MATRIX ST - PRINT STIFFNESS MATRIX OT - PRINT ORTHOGONALTITY CHECK MATRIX THESE OPTIONS CAN BE ENTERED IN ANY ORDER.

DYNAMIC ANALYSIS OPTIONS - INPUT LINE 2

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1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334353637383940

DYNOPT +ZEN 15CONS

PLOVR AAAAAAAM 225.0

41424344454647484950515253545556575859606162636465666768697071727374757677787980

SA-Z

THE STRUCTURAL DENSITY FOR CERTAIN PLATES IS TO BE OVERRIDDENFOR THE PURPOSE OF DETERMINING THE DYNAMIC CHARACTERISTICS OFTHE STRUCTURE. 225.0 LB/CU FT. (TONNE/M*3) WILL BE USED AS THE DENSITY OF PLATES AAAA THROUGH AAAM .

PLATE OVERRIDE

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LINELABEL

PLATE RANGE STRUCTURALWEIGHT DENSITY

ADDEDMASS

COEFF.LEAVE BLANK

START NAME END NAME

PLOVR

1))))) 5 7)))))))))10 11)))))))14 21<)))))))30 31<))))))35 36))))))))))))))))))))))) 80

DEFAULTS

ENGLISH LB/CU FT

METRIC TONNE/M**

COLUMNS COMMENTARY

LOCATION THIS INPUT DATA IS OPTIONAL AND SHOULD FOLLOW THE DYNOPT INPUT LINE.

GENERAL THIS OPTIONAL INPUT ENABLES THE USER TO SPECIFY FOR ANY SET OF PLATES PROPERTIES THAT ARE DIFFERENT FROM THOSE SPECIFIED ON THE DYNOPT LINE.

( 7-10) ENTER NAME OF FIRST PLATE IN RANGE OF PLATES BEING SPECIFIED. THIS NAME MUST CORRESPOND TO A NAME IN THE SACS IV DATA DECK OR FILE. IF THIS DENSITY APPLIES TO ALL PLATES, THEN ENTER **** IN COLS 7-10 AND LEAVE COLS 11-14 BLANK.

(11-14) ENTER NAME OF LAST PLATE IN RANGE OF PLATES BEING SPECIFIED. THIS NAME MUST CORRESPOND TO A PLATE NAME IN THE SACS IV MODEL. ALL PLATES IN MODEL WHICH PHYSICALLY LIE BETWEEN THE FIRST AND LAST SPECIFIED PLATES WILL BE INCLUDED IN THIS PLATE RANGE. IF THIS FIELD IS LEFT BLANK, THE SINGLE PLATE SPECIFIED IN COLUMNS 7-10 WILL BE USED.

(21-30) ENTER STRUCTURAL WEIGHT DENSITY. IF LEFT BLANK OR ZERO, THE DEFAULT DENSITY IS THE DENSITY ENTERED ON THE DYNOPT LINE.

NOTE: THE DENSITY SPECIFIED ON THE DYNOPT LINE IS USED AS THE DEFAULT DENSITY FOR PLATE ELEMENTS.

(31-35) ENTER THE ADDED MASS COEFFICIENT IF DIFFERENT FROM THAT ENTERED ON THE DYNOPT LINE. NOTE THAT A ZERO OR BLANK WILL RESULT IN NO CHANGE.

PLATE OVERRIDE DATA - INPUT LINE 3

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DYNOPT +ZEN 15CONS

PGOVR PMM 225.0

41424344454647484950515253545556575859606162636465666768697071727374757677787980

SA-Z

THE STRUCTURAL DENSITY FOR CERTAIN PLATES IS TO BE OVERRIDDENFOR THE PURPOSE OF DETERMINING THE DYNAMIC CHARACTERISTICS OFTHE STRUCTURE. 225.0 LB/CU FT. (TONNE/M*3) WILL BE USED AS THE DENSITY OF PLATES ASSIGNED TO GROUP PMM.

PLATE GROUP OVERRIDE

Dynpac

3-9

LINELABEL

PLATEGRUPNAME

STRUCTURALWEIGHT DENSITY

ADDEDMASS

COEFF.LEAVE BLANK

PGOVR

1)))))))) 5 7)))))) 9 21<))))))))))30 31<))))))))35 36))))))))))))))))))))))))))))) 80

DEFAULTS

ENGLISH LB/CU FT

METRIC TONNE/M**

COLUMNS COMMENTARY

LOCATION THIS INPUT DATA IS OPTIONAL AND SHOULD FOLLOW THE DYNOPT INPUT LINE.

GENERAL THIS OPTIONAL INPUT ENABLES THE USER TO SPECIFY FOR ANY PLATE GRUP PROPERTIES THAT ARE DIFFERENT FROM THOSE SPECIFIED ON THE DYNOPT LINE.

( 7-9 ) ENTER THE PLATE GRUP ID OF THOSE PLATES WHOSE PROPERTIES ARE BEING SPECIFIED. THIS ID MUST CORRESPOND TO A PLATE GRUP ID IN THE SACS DATA FILE.

(21-30) ENTER STRUCTURAL WEIGHT DENSITY. IF LEFT BLANK OR ZERO, THE DEFAULT DENSITY IS THE DENSITY ENTERED ON THE DYNOPT LINE.

NOTE: THE DENSITY SPECIFIED ON THE DYNOPT LINE IS USED AS THE DEFAULT DENSITY FOR PLATE ELEMENTS.

(31-35) ENTER THE ADDED MASS COEFFICIENT IF DIFFERENT FROM THAT ENTERED ON THE DYNOPT LINE. NOTE THAT A ZERO OR BLANK WILL RESULT IN NO CHANGE.

PLATE GRUP OVERRIDE DATA - INPUT LINE 3A

Dynpac

3-10

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GROVR PL1 0.01

GROVR PL2 0.01

41424344454647484950515253545556575859606162636465666768697071727374757677787980

THE MASS OF THE PILE GROUPS PL1’ AND PL2’ IS DESIGNATED AS0.01 SO THAT NO EFFECTIVE MASS OF THE MEMBERS ASSIGNED TO THESEGROUPS WILL BE CONSIDERED.

MEMBER GROUP MASS DATA OVERRIDE LINE

Dynpac

3-11

LINELABEL

GROUPCODE

FLOODED CRITERIA‘F’ - FLOODED

‘N’ - NON-FLOODED

OUTSIDE DIAMETERFOR

FLUID ADDED MASSCALCULATION

STRUCTURALWEIGHT DENSITY LEAVE BLANK

GROVR

1)))))) 5 7))))) 9 11 13<)))))))))))20 21<)))))))30 31))))))))))))))))))))) 80

DEFAULTS SEE NOTE FOR COL 13-20

ENGLISH INCHES LB/CU FT

METRIC CM TONNE/M**

COLUMNS COMMENTARY

LOCATION THIS INPUT IS OPTIONAL AND SHOULD FOLLOW THE PLOVR DATA IF IT IS INPUT. IF IT IS NOT INPUT, THIS INPUT SHOULD FOLLOW THE DYNOPT LINE.

GENERAL THIS INPUT IS OPTIONAL. NORMALLY SEASTATE HAS BEEN EXECUTED BEFORE DYNPAC SO THAT ANY FLOODING STATUS, DENSITY DATA AND EFFECTIVE DIAMETER FOR FLUID ADDED MASS CALCULATIONS ARE INCLUDED ON THE MEMBER LINES IN THE SACS IV MODEL OUTPUT BY SEASTATE. DYNPAC USES THIS INFORMATION TO GENERATE MASS DATA.THIS INPUT LINE ENABLES THE USER TO SPECIFY THE WEIGHT DENSITY, BUOYANCY AND OR OUTSIDE DIAMETER TO BE DIFFERENT THAN THAT PREVIOUSLY DESIGNATED FOR A PARTICULAR GROUP OF MEMBERS. THE DATA SPECIFIED HERE WILL COMPLETELY REPLACE ALL PREVIOUS INPUT DATA INCLUDING SPECIFIED DEFAULTS.

THIS INPUT LINE CONSISTS OF GROUP MASS DATA OVERRIDE LINES FOR EACH GROUP WHOSE DATA IS BEING REPLACED.

( 7- 9) ENTER GROUP ID CODE FOR MEMBER GROUP WHOSE DENSITY, BUOYANCY AND/OR OUTSIDE DIAMETER ARE TO BE OVERRIDDEN. ANY GROUP ID CODE ENTERED HERE MUST CORRESPOND TO A GROUP CODE IN THE SACS IV DATA DECK OR FILE.

( 11 ) ENTER N TO INDICATE THIS GROUP OF MEMBERS IS NOT FLOODED. A F IN THESE COLUMNS WILL INDICATE THAT MEMBERS WITH THIS GRO

UP ID ARE FLOODED. IF LEFT BLANK, IT WILL NOT CHANGE THE FLOODING ON THESE MEMBERS.

(13-20) ENTER HERE THE OUTSIDE DIAMETER FOR THE SPECIFIED MEMBER GROUP THAT IS TO BE USED IN CALCULATING FLUID ADDED MASS. IF LEFT BLANK THE DEFAULT IS THE STRUCTURAL O.D. FOR TUBULARS AND ZERO FOR PRISMATICS OR THE FLUID ADDED MASS O.D., IF SPECIFIED ON THE MEMBER LINES. THIS INPUT HAS NO EFFECT ON THE STRUCTURAL PROPERTIES OF THE MEMBERS.

(21-30) ENTER STRUCTURAL DENSITY IN WEIGHT PER UNIT VOLUME. IF LEFT BLANK OR ZERO, THE DENSITY WILL BE UNCHANGED.

MEMBER GROUP MASS OVERRIDE - INPUT LINE 4

Dynpac

3-12

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MBOVR 101 201 0.01

MBOVR 103 203 0.01

41424344454647484950515253545556575859606162636465666768697071727374757677787980

THE WEIGHT OF DUMMY MEMBERS 101-201 AND 103-203 ARE NOT TO BE CONSIDERED FOR THE DYNAMIC CHARATERISTIC CALCULATION. A WEIGHT DENSITY OF 0.01 IS THEREFORE SPECIFIED TO BE USED FOR MEMBER MASS CALCULATIONS.

MEMBER MASS DATA OVERRIDE LINE

Dynpac

3-13

LINELABEL

FLOODED CRITERIA‘F’ - FLOODED

‘N’ - NON-FLOODED

MEMBER DESIGNATION OUTSIDE DIAMETERFOR

FLUID ADDED MASSCALCULATION

STRUCTURALWEIGHT DENSITY LEAVE BLANK

STARTJOINT

ENDJOINT

MBOVR

1)))) 5 7 8)))))>11 12))))>15 16<)))))))))21 22<)))))30 45))))))))))))))))))80

DEFAULTS SEE NOTE FOR COL 16-21

ENGLISH INCHES LB/CU.FT

METRIC CM TONNE/CU.

COLUMNS COMMENTARY

GENERAL THIS INPUT IS OPTIONAL. NORMALLY SEASTATE HAS BEEN EXECUTED BEFORE DYNPAC SO THAT ANY FLOODING STATUS, DENSITY DATA AND EFFECTIVE DIAMETER FOR FLUID ADDED MASS CALCULATIONS ARE INCLUDED ON THE MEMBER LINES IN THE SACS IV MODEL OUTPUT BY SEASTATE. DYNPAC USES THIS INFORMATION TO GENERATE MASS DATA.THIS INPUT DATA ENABLES THE USER TO SPECIFY THE WEIGHT DENSITY, BUOYANCY AND OR OUTSIDE DIAMETER TO BE DIFFERENT THAN THAT PREVIOUSLY DESIGNATED FOR PARTICULAR MEMBERS.

THIS INPUT CONSISTS OF MEMBER MASS DATA OVERRIDE LINES FOR EACH MEMBER WHOSE DATA IS BEING REPLACED.

( 7 ) ENTER N TO INDICATE THAT THIS MEMBER IS NOT FLOODED. A F IN THESE COLUMNS WILL INDICATE THAT THIS MEMBER IS FLOODED. THE BUOYANT OR FLOODED CONDITION SPECIFIED ON THIS LINE FOR THIS MEMBER WILL OVERRIDE THE CONDITIONS SPECIFIED IN LINE 3 OR LINE 5. IF LEFT BLANK, THE MEMBER FLOODED CONDITION WILL REMAIN UNCHANGED.

( 8-11) ENTER MEMBER START JOINT. THIS JOINT SHOULD CORRESPOND TO MEMBER START JOINT IN SACS IV DATA DECK OR FILE.

(12-15) ENTER MEMBER END JOINT. THIS JOINT SHOULD CORRESPOND TO MEMBER END JOINT IN SACS IV DATA DECK OR FILE.

(16-21) ENTER HERE THE OUTSIDE DIAMETER FOR THE SPECIFIED MEMBER THAT IS TO BE USED IN CALCULATING FLUID ADDED MASS. IF LEFT BLANK THE DEFAULT IS THE STRUCTURAL O.D. FOR TUBULARS AND ZERO FOR PRISMATICS OR THE FLUID ADDED MASS O.D., IF SPECIFIED ON THE MEMBER LINES. THIS INPUT HAS NO EFFECT ON THE STRUCTURAL PROPERTIES OF THE MEMBERS.

(22-30) ENTER STRUCTURAL DENSITY IN WEIGHT PER UNIT VOLUME. IF LEFT BLANK OR ZERO, THE DENSITY WILL REMAIN UNCHANGED.

MEMBER MASS OVERRIDE - INPUT LINE 5

Dynpac

3-14

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SHOVR BAAA 225.0

SHOVR CAAACAAM 225.0

41424344454647484950515253545556575859606162636465666768697071727374757677787980

THE STRUCTURAL DENSITY SPECIFIED ON THE DYNOPT CARD IS TO BEOVERRIDDEN FOR THE PURPOSE OF CALCULATING THE MASS OF CERTAIN SHELL ELEMENTS. A DENSITY OF 225.0 LB/CU FT. (TONNE/M*3) ISDESIGNATED AS THE DENSITY OF SHELL BAAA AND SHELLS CAAA THROUGH CAAM .NOTE: THE STRUCTURAL DENSITY SPECIFIED ON THE DYNOPT CARD IMAGE IS USED AS THE DEFAULT DENSITY OF ALL SHELL ELEMENTS REGARDLESS OF THE DENSITY SPECIFIED ON THE SHELL CARD IMAGE.

SHELL MASS DENSITY OVERRIDE LINE

Dynpac

3-15

LINELABEL

SHELL RANGE STRUCTURALWEIGHT DENSITY LEAVE BLANK

START NAME END NAME

SHOVR

1))))))) 5 7))))))))))10 11)))))))))14 21<)))))))30 31))))))))))))))))))))))))))) 80

DEFAULTS

ENGLISH LB/CU FT

METRIC TONNE/M**

COLUMNS COMMENTARY

GENERAL THIS INPUT IS OPTIONAL INPUT WHICH ENABLES THE USER TO SPECIFY FOR ANY SET OF SHELLS WEIGHT DENSITIES THAT ARE DIFFERENT FROM THE SYSTEM WEIGHT DENSITY. AN INPUT WEIGHT DENSITY ON THIS LINE WILL OVERRIDE THE SYSTEM WEIGHT DENSITY FOR THE SPECIFIED RANGE OF SHELLS.

( 7-10) ENTER NAME OF FIRST SHELL IN RANGE OF SHELLS WHOSE DENSITY IS BEING SPECIFIED. THIS NAME MUST CORRESPOND TO A NAME IN THE SACS IV DATA DECK OR FILE. IF THIS DENSITY APPLIES TO ALL SHELLS, THEN ENTER **** IN COLS 7-10 AND LEAVE COLS 11-14 BLANK.

(11-14) ENTER NAME OF LAST SHELL IN RANGE OF SHELLS WHOSE DENSITY IS BEING SPECIFIED. THIS NAME MUST CORRESPOND TO A SHELL NAME IN THE SACS IV DATA DECK. ALL SHELLS IN THE DECK WHICH PHYSICALLY LIE BETWEEN THE FIRST AND LAST SPECIFIED SHELLS WILL BE INCLUDED IN THIS SHELL RANGE. IF THIS FIELD IS LEFT BLANK, THE SINGLE SHELL SPECIFIED IN COLUMNS 7-10 WILL BE USED.

(21-30) ENTER STRUCTURAL WEIGHT DENSITY. IF LEFT BLANK THE DEFAULT DENSITY IS THE DENSITY ENTERED ON THE DYNOPT LINE.

NOTE: THE DENSITY SPECIFIED ON THE DYNOPT LINE IS USED AS THE DEFAULT DENSITY FOR SHELL ELEMENTS. THE DENSITY SPECIFIED ON THE SHELL LINE IN THE MODEL FILE IS NOT USED FOR THE PURPOSE OF DETERMINING SHELL MASS.

SHELL MASS DENSITY - INPUT LINE 6

Dynpac

3-16

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JTWGT 354 10.5 10.5 10.5

JTWGT 355 10.5 10.5 10.5

41424344454647484950515253545556575859606162636465666768697071727374757677787980

ADDITIONAL JOINT WEIGHT OF 10.5 KIPS (TONNES) IS TO BE APPLIEDTO JOINTS 354 AND 355 IN THE GLOBAL X, Y AND Z DIRECTIONS. THE WEIGHT WILL BE CONVERTED TO TRANSLATIONAL MASS FOR THE X, Y AND Z DEGREES OF FREEDOM.

JOINT CONCENTRATED WEIGHT LINE

Dynpac

3-17

LINELABEL

JOINTNUMBER

JOINT CONCENTRATED WEIGHT DATA

WEIGHT(X DIRECTION)

WEIGHT(Y DIRECTION)

WEIGHT(Z DIRECTION)

WEIGHT MOMENTOF INERTIA

(X AXIS)


(Y AXIS)


(Z AXIS)

JTWGT

1))) 5 7)))>10 11<))))))))))))20 21<))))))30 31<))))))40 41<))))))50 51<))))))60 61<))))))70

DEFAULTS 0.0 0.0 0.0 0.0 0.0 0.0

ENGLISH KIPS KIPS KIPS KIP-IN**2 KIP-IN**2 KIP-IN**2

METRIC TONNES TONNES TONNES TONNES-CM**2 TONNES-CM**2 TONNES-CM**2

COLUMNS COMMENTARY

GENERAL THIS OPTIONAL INPUT LINE ENABLES THE USER TO SPECIFY ADDITIONAL WEIGHT AND WEIGHT MOMENT OF INERTIA DATA TO BE INPUT AS LUMPED DATA FOR SPECIFIED DEGREES OF FREEDOM. THIS DATA IS ADDED TO THE SYSTEM DATA GENERATED BY THE PROGRAM. A SEPARATE CARD SHOULD BE CODED FOR EACH JOINT TO WHICH MASS IS ADDED. THISLUMPED DATA MAY BE PLACED ON EITHER RETAINED OR REDUCED FREE DEGREES OF FREEDOM.

( 7-10) ENTER JOINT NUMBER. THIS JOINT NUMBER SHOULD CORRESPOND TO A JOINT NUMBER FOUND IN THE SACS IV DECK. RIGHT JUSTIFY INPUT.

(11-40) ENTER WEIGHTS FOR X , Y AND Z DIRECTION TRANSLATIONAL DEGREES OF FREEDOM, RESPECTIVELY, FOR THIS JOINT.

(41-70) ENTER WEIGHT MOMENTS OF INERTIA FOR X , Y AND Z ROTATIONAL DEGREES OF FREEDOM, RESPECTIVELY, FOR THIS JOINT.

JOINT CONCENTRATED WEIGHT - INPUT LINE 7

Dynpac

3-18

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END

41424344454647484950515253545556575859606162636465666768697071727374757677787980

THE END LINE DESIGNATES THE END OF INPUT DATA.

END OF DATA

Dynpac

3-19

LINELABEL LEAVE THIS FIELD BLANK

END

1))))) 3 4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 80

DEFAULT

ENGLISH

METRIC

COLUMNS COMMENTARY

GENERAL THIS LINE IS THE LAST CARD OF THE INPUT FILE.

( 1- 3) ENTER END .

END LINE - INPUT LINE 8

Dynpac

3-20

Dynpac

SECTION 4DYNPAC TROUBLE SHOOTING

Dynpac

Dynpac

4-1

4.0 DYNPAC TROUBLE SHOOTING

4.1 MODEL STIFFNESS MATRIXAs part of the dynamic characteristic analysis, the Solve module is used to generate thestiffness matrix properties of the structure. The structural model matrix created by Solvemust be 'Positive Definite' in order to determine the dynamic characteristics of thestructure. In general, if a degree of freedom for any joint or portion of the structure is notrestrained by fixity or by stiffness from other elements, the matrix will be 'Non'-PositiveDefinite'. For further discussion on matrix 'Non-Positive Definite', see the section titled'SACS IV Trouble Shooting' in the SACS IV user's manual.

The Solve module also determines the accuracy of the solution and reports it as the'Maximum Number of Significant Digits Lost'. In general, solutions with six or fewersignificant digits lost are sufficiently accurate while solutions with twelve or more lostare not. The SACS IV users's manual addresses possible causes for excessive numbers oflost significant digits.

4.2 MODEL MASS MATRIXThe structural mass matrix is developed by the Dynpac program module. Like thestiffness matrix, the structural mass matrix must be 'Positive Definite' in order for it to beinverted. When the mass matrix can not be inverted, the message 'Non-Positive DefiniteMass Matrix' is printed in the listing file. Some common reasons for the structural massmatrix becoming 'Non-Positive Definite' are as follows:

1. No degrees of freedom in the model are retained as master DOFs. The errormessage will normally refer to a degree of freedom for joint number 0.

2. All degrees of freedom are either retained or restrained as master DOFs so thatthere are no slave or unrestrained DOFs.

3. The mass for a particular degree of freedom is negative. This can occur whenconverting loads specified in the model file to mass using the 'SA' or 'SO' optionon the DYNOPT line. When negative loads in the model file are to be converted,ie. gravity loads, the '-X', '-Y' or '-Z' option should be specified so that the sign ofthe mass generated will be positive (opposite to that of the load).

4. A rotational degree of freedom is retained as a master DOF but no mass momentof inertia was generated (ie. lumped approach) or no weight moment of inertiawas specified in the input file for that DOF.

When a matrix 'Non-Positive Definite' occurs, the critical degree of freedom and the jointnumber are reported in the Dynpac listing file. For additional information on debuggingthe model, see the SACS IV user's manual.

Dynpac

4-2

Dynpac

SECTION 5COMMENTARY

Dynpac

Dynpac

5-1

K '

Kmm Kms

Ksm Kss

Fm

Fs

'

Kmm Kms

Ksm Kss

*m

*s

Fm ' Kmm*m % Kms*s (1) Fs ' Ksm*m % Kss*s

*s ' &Ksm

Kss

*m (2)

Fm ' Kmm*m % Kms(&Ksm

Kss

*m) ' (Kmm & Kms

Ksm

Kss

) *m (3)

Fm ' [ K ’mm ]*m (3)

5.0 COMMENTARY

5.1 STIFFNESS MATRIX REDUCTIONThe purpose of the Dynpac program module is to generate dynamic characteristics (modeshapes and frequencies) of a structure. A Guyan reduction is performed to reduce thestructural stiffness matrix K created by SACS IV as follows:

where the subscript m designates master degrees of freedom and the subscript sdesignates slave degrees of freedom. Knowing that F = K* or

the following relationships can be made.

If, by definition, no external forces are applied directly to the slave degrees of freedomsuch that Fs=0, *s can be expressed as follows:

Substituting for *s in equation (1) yields a relation that can be used to calculate theexternal forces on master degrees of freedom, namely,

or

Dynpac

5-2

* ' f(x,*a,2a,*b,2b) 0* ' f(x,0*a, 02a,0*b, 02b)

KE '12 m M 0*

2 dx

ddt

dKEd 0q

for 0q ' 0*a, 0*b, 02a, 02b

where K'mm is the reduced stiffness matrix. Once the master degrees of freedom arecalculated, relation (2) may be used to determine the slave degrees of freedom.

5.2 MASS MATRIX GENERATION

5.2.1 Consistent Mass Approach

The mass matrix may be generated based on the lumped or consistent mass approach.The consistent mass generation approach represents the kinetic energy of the distortedelement by the element joint velocities, as represented by the velocities of all degrees offreedom at the joint. The deflection * and velocity *' along a member may be expressedas follows:

The kinetic energy is defined as:

where M is the mass per unit length. Taking

results in

Dynpac

5-3

M

*̈a

2̈a

*̈b

2̈b

KE '12

[ 0*m0*

’s]

Mmm Mms

Msm Mss

0*m

0*s

0*s ' &Ksm

Kss

0*’m

where [M] is the elemental mass matrix for the element. The elemental mass matrix isthen transformed into the global coordinate system and added to the overall structuralmass matrix.Note: Because the consistent approach takes into account the

distribution of mass along the element, the mass matrix createdincludes off-diagonal coupling terms between all degrees offreedom, including rotational DOFs.

5.2.2 Lumped Mass Approach

In the lumped approach, a diagonal mass matrix is created by dividing each element massinto equal components along the global X, Y and Z directions and concentrating thesemasses at the end joints. Rotational mass or mass moments of inertia are neglected alongwith any off diagonal terms of the mass matrix.Note: Because off diagonal terms are assumed to be zero in the lumped

mass approach, it is not recommended when the element mass is notthe same in all three directions such as when including effects offluid added or virtual mass acting normal but not tangential tothe element.

5.3 MASS MATRIX REDUCTIONAfter the overall mass matrix has been generated by either the consistent or lumped massapproach, it is partitioned into the same form as the stiffness matrix such that:

Note: The terms Mms and Msm = 0 and Mmm and Mss are diagonal matrices forthe lumped approach.

Differentiating equation (2) with respect to time yields,

Dynpac

5-4

KE '12

[ 0*m] [I &Ksm

Kms

]Mmm Mms

Msm Mss

I

&Ksm

Kss

6 0*m >

KE '12

[ 0*m] [ M ’mm ] 6 0*

’m >

F ' Fn % Ft

Fn '12

CDnDDs*Vrel n*Vrel nrel

%14BCMnD

2Ds0Vn % (CMn&1)BD 2

4D 0Vssn

Ft '12

CDtDDs*Vrel t*Vrel t

%14BCMtD

2Ds0Vt % (CMt&1)BD 2

4D 0Vst

therefore, the equation for kinetic energy becomes

which is a standard Guyan reduction resulting in

where M'mm is the reduced mass matrix.

5.4 CALCULATING RESULTSOnce the reduced stiffness and reduced mass matrices are generated, theeigenvalues/eigenvectors for the master degrees of freedom are extracted using thestandard Householder-Givens extraction technique. The resulting eigenvectors at themaster degrees of freedom are expanded to obtain results for the reduced or slavedegrees of freedom which allows the calculation of modal reactions and modal elementalinternal loads.

5.5 FLUID ADDED OR VIRTUAL MASSMorrisons's equation is used to determine the hydrodynamic loading due to fluid addedor virtual mass. The resultant force per unit length, F, has a component normal to theelement, Fn, and a component tangential or along the cylinder axis, Ft.

where Fn and Ft are functions of the fluid relative velocity Vrel, fluid acceleration V' andthe acceleration of the structure V'

s, and are given by the following for tubular elements:

where the term (Cm-1)(BD2/4)D is the fluid added mass term. The normal added mass, mn,and axial or tangential added mass, mt, may be rewritten as follows:

Dynpac

5-5

mn ' (CMn&1)BD 2

4D ' Cvn

BD 2

4D mt ' (CMt&1) BD 2

4D ' Cvt

BD 2

4D

mnx ' mn cos "x mny ' mn cos "y mnz ' mn cos "yz

mtx ' mt sin "x mty ' mt sin "y mtz ' mt sin "yz

where Cvn and Cvt are the normal and axial added mass coefficients input into the Dynpacprogram, respectively.Note: Because the default tangential mass coefficient, Cvt, is zero,

tangential added mass is ignored by default unless the coefficientis overridden by the user.

The added mass normal to the member and the mass tangential, if applicable, are brokeninto global X, Y and Z direction masses then added to the elemental mass matrix.Including the hydrodynamic inertial terms due to structural acceleration in the massmatrix, results in the automatic inclusion of acceleration dependent hydrodynamic forcesincluding relative acceleration effects.

The global X, Y and Z components, mnx, mny and mnz, of the normal fluid added or virtualmass and the X, Y and Z components of the tangential fluid added mass, mtx, mty andmtz,are taken as:

where "x, "y and "z are the angle between the plane normal to the element and the globalX, Y and Z axes respectively. See the following figure.

Dynpac

5-6

Dynpac

SECTION 6SAMPLE PROBLEMS

Dynpac

Dynpac

6-1

Figure 1

6.0 SAMPLE PROBLEMSThe structure shown in Figure 1 was used to illustrate various capabilities of the Dynpacprogram. Three separate Dynpac analyses are illustrated:

1. The dynamic characteristics of the structure submerged in water weredetermined using the consistent mass approach. Seastate override lines wereused for the hydrodynamic modeling. The linearized foundation elements wereincluded in the model file.

2. Sample Problem 2 is the same as Sample Problem 1 except that instead ofmodeling linearized pile stubs, a linearized foundation superelement was used.The ability to convert loads from any load case to mass without copying the loadinto LC 1 is also illustrated.

3. The natural modes of the deck in Figure 1 were determined using the lumpedmass approach. Additional joint weight was added in the Dynpac input file.

Dynpac

6-2

6.1 SAMPLE PROBLEM 1The following example illustrates the use of the Seastate and Dynpac programs todetermine the dynamic characteristics of a structure submerged in a fluid.

The structure in Figure 1 stands in 82.02 feet of salt water (density 64.2 lb/ft3). Themember mass, mass of marine growth, mass of entrapped water and virtual or addedmass were calculated automatically using the consistent mass approach. The Seastateprogram was used to determine the effective member properties including diameter,density, etc. to account for the hydrodynamic properties of the members. Additionalmember and group overrides were specified in the Dynpac input file.

A load case consisting of miscellaneous loads, was specified in the SAC input file toaccount for unmodeled members and equipment weights that could affect the dynamiccharacteristics of the structure.

Dummy piles used to simulate the soil/pile interaction was developed using the Pileprogram and were added to the model. The degrees of freedom to be retained fordetermining the generalized masses and the eigenvectors were designated (usingPrecede) by specifying a '2' for the joint DOF.

A Seastate input file containing override lines to account for the hydrodynamics ofunmodeled members and appurtenances was used as the SACS input file. 50% of loadcase MISC in the model file contains miscellaneous loads to account for unmodeledmembers and equipment and is converted to mass.

The following is a portion of the Seastate input file:

12345678901234567890123456789012345678901234567890123456789012345678901234567890

A LDOPT IN NF+Z 64.20 490.00 -82.02 82.02 DYN NP KB LCSEL DY MISC C LCFAC DY 0.50 MISCD FILE JE CDM

CDM 11.81 1.000 1.400 1.200 1.400 CDM 23.62 1.000 1.500 1.200 1.500 CDM 47.24 1.000 1.600 1.200 1.600 CDM 70.87 1.000 1.700 1.200 1.700

E MGROVMGROV 0.000 26.247 MGROV 26.247 52.493 0.984 MGROV 52.493 82.021 1.969

E GRPOVGRPOV LG1 F GRPOV PL1 F 0.001 0.001 GRPOV PL2 F 0.001 0.001 GRPOV DK1 0.001 0.001 GRPOV DK2 0.001 0.001 LOADEND

The following is a description of the Seastate input file:

A. The LDOPT line specifies the physical parameters of the structure such as waterdepth, water and steel density etc. 'DYN' in columns 56-58 specifies that a SACShydrodynamic model is to be created for use by Dynpac.

Dynpac

6-3

B. The LCSEL line designates that if the convert load case to mass option isspecified in the Dynpac input file, only load case MISC is to be converted.

C. The LCFAC line indicates that load case MISC is to be factored by 0.50 whenconverted to mass.

D. The FILE line indicates that only loading in the jacket geometry file is to beconsidered for this analysis (i.e. ‘J’ in column 6).

E. The CDM, MGROV and GRPOV lines ensure that entrapped water mass andadded or virtual mass are generated accurately.

The following is a portion of the model file used for this sample followed by adescription of the input:

Dynpac

6-4

12345678901234567890123456789012345678901234567890123456789012345678901234567890

A OPTIONS EN DY SDUC 1 1 1 0 PT PTSECTSECT CONDSM TUB 66.26 3032.45 1516.22 1516.22 19.690.551

B SECT PILSTUB PRI 71.86 13490.0 6745.00 6745.00 10.0 10.0 GRUP

C GRUP PST PILSTUB 29.00 11.6 36.0 9 0.01******************* ADDITIONAL SACS GROUP AND MEMBER Lines *********************

D MEMBER2 2 102 PSTMEMBER OFFSETS 12.5MEMBER2 4 104 PSTMEMBER OFFSETS 12.5MEMBER2 6 106 PSTMEMBER OFFSETS 12.5MEMBER2 8 108 PSTMEMBER OFFSETS 12.5JOINT

E JOINT 2 -20.505-20.505-88.583 FIXEDJOINT 4 20.505-20.505-88.583 FIXEDJOINT 6 20.505 20.505-88.585 FIXED JOINT 8 -20.505 20.505-88.583 FIXED**************** More Joints ******************************JOINT 309 0.000 0.000 -3.281 JOINT 310 0.000 0.000 -3.281

F JOINT 401 -9.842 -9.842 19.685 222 JOINT 403 9.842 -9.842 19.685 222 JOINT 405 9.842 9.842 19.685 222 JOINT 407 -9.842 9.842 19.685 222 JOINT 409 0.000 0.000 19.685 LOAD

G LOADCNMISCLOAD Z 405 466 2.65750-3.8892 GLOB CONC SKID1 LOAD Z 405 466 17.6575-4.0025 GLOB CONC SKID1 LOAD Z 466 468 24.0806-4.2753 GLOB CONC SKID1 LOAD Z 466 468 2.86744-4.0485 GLOB CONC SKID1 LOAD Z 467 468 17.0276-4.3356 GLOB CONC SKID1 LOAD Z 467 468 2.02758-4.4489 GLOB CONC SKID1 LOAD Z 401 403 -1.969 -1.969 GLOB UNIF WALK1LOAD Z 472 401 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 403 465 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 407 405 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 405 466 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 471 407 -1.969 -1.969 GLOB UNIF WALK1 END

The following is a description of the SACS input file:

A. The analysis Dynamic option specified in columns 19-20 on the OPTIONS line('DY').

B. The dummy pile section properties are defined using section PILSTUB.

C. The dummy pile group PST is defined.

D. Dummy pile members 2-102, 4-104, 6-106 and 8-108 are defined.

E. The dummy pile bottom joints 2, 4, 6 and 8 are fixed (joint fixity ‘FIXED’).

F. The retained degrees of freedom are specified by '2' in columns 55-60 on theappropriate JOINT lines. For example, Joint 401 is retained for translation in theX, Y, and Z directions as designated by '222' in columns 55-57.

Dynpac

6-5

G. The loads of Load Condition ‘MISC’ account for the weight of unmodeledmembers and equipment and will be converted to masses by Dynpac.

Seastate and Dynpac were executed in succession to determine the dynamiccharacteristics of the structure. The output structural data file created by Seastatecontaining the effective member properties was used as the model input file for Dynpac.Note: Seastate and Dynpac can be run as separate analysis steps or

together as a single step. When executing separately, specify theSeastate output structural data file as the SACS input file forthe Dynpac execution.

The following is the Dynpac input file used for this sample followed by a description ofthe input:

12345678901234567890123456789012345678901234567890123456789012345678901234567890

TITLE DYNPAC SAMPLE PROBLEM

A DYNOPT +ZEN 10CONS 490. 64.2 -80.2 80.2 NF SA-ZB GROVR PL1 N 1.0

GROVR PL2 N 1.0C MBOVR F 301 401 40.0

MBOVR F 201 301 40.0END

A. The DYNOPT line specifies the following:a. The vertical coordinate is the +Z direction and English units are to be used

as specified in columns 8-9 and 10-11 respectively.b. 10 modes are desired (columns 12-14).c. The consistent mass approach is specified by 'CONS' in columns 15-18.d. The structure and fluid density are 490.0 and 64.2 lb/ft3 respectively.e. The mudline elevation (-80.2) and the water depth (80.2) are specified in

columns 33-39 and 40-46 respectively.f. All members without flood condition designated, are to be considered non-

flooded for the Dynpac analysis as specified by 'NF' (columns 47-48).g. Loads from the SACS data are to be used as masses and the Z direction

masses will be opposite sign of the specified Z direction load ('SA-Z' incolumns 63-66).

B. The GROVR lines specify that groups 'PL1' and 'PL2' (the piles inside the legs)be non-flooded and have an effective outside diameter of 1 inch for fluid addedmass and entrapped water mass calculation.

C. The MBOVR lines specify that members 301-401 and 201-301 have an effectiveoutside diameter of 40.0 inches for fluid added mass calculation.

Dynpac

6-6

Six of the modes are displayed below. The output file follows.

Dynpac

6-7

DYNPAC SAMPLE PROBLEM DATE 19-JAN-1993 TIME 08:06:21 DYN PAGE 1

DYNAMIC ANALYSIS PARAMETERS

NO. JOINTS ......... 60 NO. MEMBERS......... 139 NO. PLATES ......... 16 NO. SHELL ELEMENTS.. 0 NO. REDUCED DOF..... 287 NO. RETAINED DOF.... 73 NO. MODES .......... 10 NO. VECTORS......... 10

EXPANDED MODE SHAPES REQUESTED

MASS PASSED FROM SACS DATA - ADDITIONAL DIRECTION - -Z

AUTOMATIC CONSISTENT MASS OPTION SELECTED

STRUCTURAL DENSITY = 490.00 LB/FT**3 FLUID DENSITY = 64.20 LB/FT**3

FLUID ADDED MASS COEFFICIENT = 1.000

MUDLINE ELEVATION = -80.20 FT WATER DEPTH = 80.20 FT

ALL TUBULAR MEMBERS CONSIDERED BUOYANT UNLESS OTHERWISE SPECIFIED

PLATE PROPERTIES

NAME ****** JOINTS ****** OFFSET THICKNESS DENSITY 1 2 3 4 (INCHES) (LB/CU FT)

A100 461 462 472 0 0 1.969 490.000 A101 401 472 462 0 0 1.969 490.000 A102 462 463 403 401 0 1.969 490.000 A103 463 464 465 0 0 1.969 490.000 A104 465 403 463 0 0 1.969 490.000 A105 403 465 466 405 0 1.969 490.000 A106 405 466 468 0 0 1.969 490.000 A107 467 468 466 0 0 1.969 490.000

PLATE WEIGHTS X 280.336 KIPS PLATE CG LOC X 0.000 FT Y 280.336 KIPS Y 0.000 FT Z 280.336 KIPS Z 19.684 FT

Dynpac

6-8

DYNPAC SAMPLE PROBLEM DATE 19-JAN-1993 TIME 08:06:21 DYN PAGE 2 MEMBER PROPERTIES

MEMBER TYPE GRUP FIXITY BUOY DENSITY BETA AREA OD AM-OD (LB/CUFT) (SQIN) (IN)

101- 102 TUB PL4 311000 YES 490.000 0.00 72.032 29.921 29.860 101- 111 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 117- 101 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 101- 151 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 101- 157 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 101- 201 TUB LG1 0 NO 490.000 0.00 70.341 29.921 30.680 102- 202 TUB PL1 0 YES 490.000 0.00 39.936 23.622 1.000 103- 104 TUB PL4 311000 YES 490.000 0.00 72.032 29.921 29.860 111- 103 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 103- 113 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680

103- 151 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 103- 153 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 103- 203 TUB LG1 0 NO 490.000 0.00 70.341 29.921 30.680 104- 204 TUB PL1 0 YES 490.000 0.00 39.936 23.622 1.000 105- 106 TUB PL4 311000 YES 490.000 0.00 72.032 29.921 29.860 113- 105 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 105- 115 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 105- 153 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 105- 155 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 105- 205 TUB LG1 0 NO 490.000 0.00 70.341 29.921 30.680

106- 206 TUB PL1 0 YES 490.000 0.00 39.936 23.622 1.000 107- 108 TUB PL4 311000 YES 490.000 0.00 72.032 29.921 29.860 115- 107 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 107- 117 TUB HB1 0 YES 490.000 0.00 37.714 19.685 19.680 107- 155 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 107- 157 TUB DB1 0 YES 490.000 0.00 37.714 19.685 19.680 107- 207 TUB LG1 0 NO 490.000 0.00 70.341 29.921 30.680 108- 208 TUB PL1 0 YES 490.000 0.00 39.936 23.622 1.000 109- 110 TUB CON 311000 YES 490.000 0.00 66.260 19.690 19.650

111- 109 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 113- 109 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 109- 115 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 109- 117 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 110- 210 TUB CON 0 YES 490.000 0.00 66.260 19.690 20.450 111- 113 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 117- 111 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 111- 151 TUB VB1 0 YES 490.000 0.00 37.714 19.685 19.680 113- 115 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960 113- 153 TUB VB1 0 YES 490.000 0.00 37.714 19.685 19.680 115- 117 TUB HD1 0 YES 490.000 0.00 24.944 14.961 14.960

Dynpac

6-9


MEMBER PROPERTIES

MEMBER TYPE GRUP FIXITY BUOY DENSITY BETA AREA OD AM-OD (LB/CUFT) (SQIN) (IN)

115- 155 TUB VB1 0 YES 490.000 0.00 37.714 19.685 19.680 117- 157 TUB VB1 0 YES 490.000 0.00 37.714 19.685 19.680 151- 201 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 151- 203 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 153- 203 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 153- 205 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 155- 205 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 155- 207 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 157- 201 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 157- 207 TUB DB1 0 YES 490.000 0.00 37.714 19.685 21.480 201- 202 TUB PL2 311000 YES 490.000 0.00 39.936 23.622 1.000 201- 203 TUB HB2 0 YES 490.000 0.00 24.944 14.961 16.930 207- 201 TUB HB2 0 YES 490.000 0.00 24.944 14.961 16.930 201- 209 TUB HD2 0 YES 490.000 0.00 18.031 14.961 16.930 201- 251 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 201- 257 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 201- 301 TUB LG2 0 NO 490.000 0.00 57.973 29.921 40.000 202- 301 TUB PL2 0 YES 490.000 0.00 39.936 23.622 1.000 203- 204 TUB PL2 311000 YES 490.000 0.00 39.936 23.622 1.000 203- 205 TUB HB2 0 YES 490.000 0.00 24.944 14.961 16.930

203- 209 TUB HD2 0 YES 490.000 0.00 18.031 14.961 16.930 203- 251 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 203- 253 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 203- 303 TUB LG2 0 NO 490.000 0.00 57.973 29.921 33.320 204- 303 TUB PL2 0 YES 490.000 0.00 39.936 23.622 1.000 205- 206 TUB PL2 311000 YES 490.000 0.00 39.936 23.622 1.000 205- 207 TUB HB2 0 YES 490.000 0.00 24.944 14.961 16.930 205- 209 TUB HD2 0 YES 490.000 0.00 18.031 14.961 16.930 205- 253 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 205- 255 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990

205- 305 TUB LG2 0 NO 490.000 0.00 57.973 29.921 33.320 206- 305 TUB PL2 0 YES 490.000 0.00 39.936 23.622 1.000 207- 208 TUB PL2 311000 YES 490.000 0.00 39.936 23.622 1.000 207- 209 TUB HD2 0 YES 490.000 0.00 18.031 14.961 16.930 207- 255 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 207- 257 TUB DB2 0 YES 490.000 0.00 24.944 14.961 17.990 207- 307 TUB LG2 0 NO 490.000 0.00 57.973 29.921 33.320 208- 307 TUB PL2 0 YES 490.000 0.00 39.936 23.622 1.000

Dynpac

6-10


MEMBER GROUP SUMMARY WEIGHT REPORT

******** CONSTRUCTION MATERIAL ******** ENTRAPPED *** FLUID ADDED MASS *** GRUP WEIGHT *** CENTER OF GRAVITY *** FLUID NORMAL AXIAL X Y Z WEIGHT WEIGHT WEIGHT (KIPS) (FT) (FT) (FT) (KIPS) (KIPS) (KIPS)

PL4 7.02 0.00 0.00 -85.06 0.00 8.98 0.00 CON 24.75 0.00 0.00 -34.54 0.00 14.59 0.00 HB1 20.21 0.00 0.00 -82.02 0.00 21.36 0.00 DB1 56.29 0.00 0.00 -60.70 0.00 64.28 0.00 LG1 41.47 0.00 0.00 -60.70 48.88 57.10 0.00 PL1 23.54 0.00 0.00 -60.70 0.00 0.06 0.00 HD1 16.14 0.00 0.00 -82.02 0.00 14.90 0.00 VB1 12.76 0.00 0.00 -69.69 0.00 13.48 0.00 PL2 20.19 0.00 0.00 -21.57 0.00 0.05 0.00 HB2 9.75 0.00 0.00 -39.37 0.00 11.52 0.00 HD2 4.98 0.00 0.00 -39.37 0.00 8.15 0.00 DB2 29.66 0.00 0.00 -21.33 0.00 41.27 0.00 LG2 28.92 0.00 0.00 -21.33 42.17 63.27 0.00 HB3 3.79 0.00 0.00 -3.28 0.00 6.84 0.00 HD3 2.68 0.00 0.00 -3.28 0.00 4.84 0.00 PL3 15.89 0.00 0.00 8.20 3.82 5.04 0.00 DK1 99.35 0.00 0.00 21.18 0.00 0.00 0.00 DK2 21.88 0.00 0.00 21.68 0.00 0.00 0.00

MEMBER WEIGHTS X 814.768 KIPS MEMBER CG LOC X -0.101 FT Y 814.768 KIPS Y -0.101 FT Z 644.355 KIPS Z -33.920 FT

WEIGHT OF CONSTRUCTION MATERIAL ........... 439.27 KIPS WEIGHT OF ENTRAPPED FLUID ................ 94.86 KIPS WEIGHT OF VIRTUAL MASS (NORMAL) .......... 335.75 KIPS WEIGHT OF VIRTUAL MASS (AXIAL) ........... 0.00 KIPS

SACS WEIGHTS X 373.783 KIPS SACS CG LOCATION X 1.342 FT Y 373.783 KIPS Y 1.341 FT Z 373.783 KIPS Z 19.685 FT

TOTAL WEIGHTS X 1468.887 KIPS TOTAL CG LOC X 0.285 FT Y 1468.887 KIPS Y 0.285 FT Z 1298.474 KIPS Z -6.916 FT

Dynpac

6-11

DYNPAC SAMPLE PROBLEM DATE 19-JAN-1993 TIME 08:06:21 DYN PAGE 5 SACS IV-FREQUENCIES AND GENERALIZED MASS NORMALIZED DEGREES OF FREEDOM

MODE FREQ.(CPS) GEN. MASS EIGENVALUE PERIOD(SECS) JOINT DOF

1 0.786448 1.5161639E+03 4.0954395E-02 1.2715403 467 DIS Y 2 0.948796 4.3537926E+03 2.8138093E-02 1.0539675 464 DIS X 3 0.950534 3.2428933E+03 2.8035291E-02 1.0520404 461 DIS Y 4 2.650600 5.9550148E+02 3.6053859E-03 0.3772730 467 DIS Z 5 2.681863 1.3067587E+03 3.5218186E-03 0.3728751 464 DIS Z 6 2.945156 2.3794883E+02 2.9202741E-03 0.3395406 467 DIS Z 7 3.257900 1.9377288E+03 2.3865185E-03 0.3069462 105 DIS X 8 3.582488 2.0453946E+02 1.9736532E-03 0.2791356 461 DIS Z 9 3.720677 2.0636038E+02 1.8297694E-03 0.2687683 464 DIS Z 10 4.165966 3.2289680E+02 1.4595155E-03 0.2400403 461 DIS Z

*** M O D A L R E A C T I O N S U M M A R Y ***

MODE X Y Z (KIPS) (KIPS) (KIPS)

1 3.24 -3.24 0.00 2 -85.42 -81.72 0.56 3 70.49 -73.70 0.01 4 -108.04 -108.23 -15.78 5 -169.83 169.50 -0.02 6 18.80 18.89 -19.70 7 -4.02 4.02 0.00 8 -36.23 -36.27 55.90 9 33.91 -33.90 -0.17 10 -5.88 -5.86 -518.96

*** M O D A L S P R I N G S U M M A R Y ***

MODE X Y Z (KIPS) (KIPS) (KIPS)

1 -0.29 0.29 0.00 2 7.87 7.52 -0.05 3 -6.50 6.80 0.00 4 20.78 20.82 1.12 5 32.40 -32.34 0.00 6 -3.32 -3.34 1.41 7 0.87 -0.87 0.00 8 4.85 4.85 -4.50 9 -4.16 4.16 0.01 10 0.48 0.47 45.19

Dynpac

6-12

6.2 SAMPLE PROBLEM 2The following example illustrates the ability to use an equivalent foundation super-element and to convert loading in any load case to mass, therefore eliminating the needto modify the model for dynamic analysis purposes. Only the degrees of freedom to beretained for determining the generalized masses and the eigen vectors were specified inthe model by inputting a '2' in the appropriate joint fixity column.Note: Because retaining DOFs has no effect on the model for static

analysis, the same model file can be used for static and dynamicanalyses.

The following is a portion of the model file to be sent through Seastate for hydrodynamicmodeling. The differences between the model requirements for sample 1 and this sampleare discussed below:

A. Unlike Sample Problem 1, pile stub members 2-102, 4-104, 6-106 and 8-108 arenot included in the model. An equivalent foundation super-element is to be usedas specified on the OPTIONS line. Therefore, pile stub section 'PILSTUB' andpile stub group 'PST' are not required in the model input file.

B. The retained degrees of freedom are specified by '2' in columns 55-60 on theappropriate JOINT lines.

C. The pile joints at the mudline are designated with PILEHD fixity.

12345678901234567890123456789012345678901234567890123456789012345678901234567890

DYNAMIC CHARACTERISTICS OPTIONS I EN DY SDUC 1 1 1 0 PT PTSECTSECT CONDSM TUB 66.26 3032.45 1516.22 1516.22 19.690.551

******************* SACS GROUP and MEMBER Lines *******************************

JOINTJOINT 102 -19.685-19.685-82.021 PILEHDJOINT 104 19.685-19.685-82.021 PILEHDJOINT 106 19.685 19.685-82.021 PILEHDJOINT 108 -19.685 19.685-82.021 PILEHD******************* More jonts *****************JOINT 257 -11.678 0.000-17.961 JOINT 301 -9.842 -9.842 -3.281 222 JOINT 303 9.842 -9.842 -3.281 222 JOINT 305 9.842 9.842 -3.281 222 LOADCNMISCLOAD Z 405 466 2.65750-3.8892 GLOB CONC SKID1 LOAD Z 405 466 17.6575-4.0025 GLOB CONC SKID1 LOAD Z 466 468 24.0806-4.2753 GLOB CONC SKID1 LOAD Z 466 468 2.86744-4.0485 GLOB CONC SKID1 LOAD Z 467 468 17.0276-4.3356 GLOB CONC SKID1 LOAD Z 467 468 2.02758-4.4489 GLOB CONC SKID1 LOAD Z 401 403 -1.969 -1.969 GLOB UNIF WALK1LOAD Z 472 401 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 403 465 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 407 405 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 405 466 -1.969 -1.969 GLOB UNIF WALK1 LOAD Z 471 407 -1.969 -1.969 GLOB UNIF WALK1 END

Dynpac

6-13

As in Sample Problem 1, Seastate and Dynpac were executed in succession to determinethe dynamic characteristics of the structure. The output structural data file created bySeastate containing the effective member properties was used as the SACS input file forDynpac.

The following is the Dynpac input file followed by a detailed explanation of the featuresimplemented:

12345678901234567890123456789012345678901234567890123456789012345678901234567890

TITLE DYNPAC SAMPLE PROBLEM 2

A DYNOPT +ZEN 10CONS 490. 64.2 -80.2 80.2 NF SA-ZB GROVR PL1 N 1.0

GROVR PL2 N 1.0C MBOVR F 301 401 40.0

MBOVR F 201 301 40.0


as specified in columns 8-9 and 10-11 respectively.b. 10 modes are desired (columns 12-14).c. The consistent mass approach is specified by 'CONS' in columns 15-18.d. The structure and fluid density are 490.0 and 64.2 lb/ft3 respectively.e. The mudline elevation (-80.2) and the water depth (80.2) are specified in

columns 33-39 and 40-46 respectively.f. All members without flood condition designated, are to be considered non-

flooded for the Dynpac analysis as specified by 'NF' (columns 47-48).g. Loads from the SACS data are to be used as masses and the Z direction


B. The GROVR lines specify that groups 'PL1' and 'PL2' (the piles inside the legs)be non-flooded and have an effective outside diameter of 1 inch for fluid addedmass and entrapped water mass calculation.

C. The MBOVR lines specify that members 301-401 and 201-301 have an effectiveoutside diameter of 40.0 inches for fluid added mass calculation.

Dynpac

6-14

Figure 1

6.3 SAMPLE PROBLEM 3The following example illustrates the use of the Dynpac program to determine thedynamic characteristics of a deck structure.

The deck of a structure modeled to the top of jacket elevation contains a piece ofreciprocating machinery. The weight of the machinery along with the weight of othernon-modeled equipment was specified in Load Case 1. The member mass and massescalculated from Load Case one will be applied as lumped masses. Figure 2 is a plot ofthe deck for this sample.

The following are the steps required to execute the Dynpac analysis:

Miscellaneous loads to account for unmodeled members and equipment were will beconverted to mass. The degrees of freedom to be retained for determining the generalizedmasses and the eigenvectors were designated (using Precede) by specifying a '2' for thejoint DOF.

The following is the SACS input file used for the analysis:

Dynpac

6-15

12345678901234567890123456789012345678901234567890123456789012345678901234567890

DYNPAC SAMPLE PROBLEM OPTIONS EN DY SDUC 1 1 1 0 PT PTLCSEL DY 1 2 SECTSECT CONDSM TUB 66.26 3032.45 1516.22 1516.22 19.690.551 GRUPGRUP CON CONDSM K 29.0111.6035.97 1 1.001.00 0.50 GRUP DK1 W36X210 29.0111.6035.97 1 1.001.00 0.50 GRUP DK2 W24X131 29.0111.6035.97 1 1.001.00 0.50 GRUP DUM 18.000 2.500 29.0011.6036.00 1 1.001.00 0.50 0.010 GRUP EQ1 24.000 1.500 29.0011.6036.00 1 1.001.00 0.50 0.010 GRUP HB3 11.811 0.394 29.0111.6035.97 1 .800.800 0.50 MEMBERMEMBER0 301 309 HD3 MEMBER0 301 401 PL3

********************* SACS MEMBER AND PLATE MODEL DATA *************************

JOINTJOINT 1 0.000 0.000-13.281 111001 JOINT 301 -9.842 -9.842 -3.281 111 JOINT 303 9.842 -9.842 -3.281 111 JOINT 305 9.842 9.842 -3.281 111 JOINT 307 -9.842 9.842 -3.281 111 JOINT 309 0.000 0.000 -3.281 JOINT 310 0.000 0.000 -3.281 JOINT 401 -9.842 -9.842 19.685 222 JOINT 403 9.842 -9.842 19.685 222 JOINT 405 9.842 9.842 19.685 222 JOINT 407 -9.842 9.842 19.685 222 JOINT 409 0.000 0.000 19.685 JOINT 461 -29.528-29.528 19.685 222 JOINT 510 -19.685 3.281 28.185 222 LOADLOADCN 1LOAD Z 401 403 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 472 501 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 403 465 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 407 405 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 405 466 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 471 503 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 461 462 -0.984 -0.984 GLOB UNIF 100PSF LOAD Z 462 463 -0.984 -0.984 GLOB UNIF 100PSF LOAD Z 463 464 -0.984 -0.984 GLOB UNIF 100PSF LOAD Z 468 467 -0.984 -0.984 GLOB UNIF 100PSF LOAD Z 469 468 -0.984 -0.984 GLOB UNIF 100PSF LOAD Z 470 469 -0.984 -0.984 GLOB UNIF 100PSF LOAD Z 501 502 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 502 401 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 503 504 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 504 407 -1.969 -1.969 GLOB UNIF 100PSF LOAD Z 472 501 0.984 0.984 GLOB UNIF 100PSF LOAD Z 471 503 0.984 0.984 GLOB UNIF 100PSF LOAD Z 501 502 0.984 0.984 GLOB UNIF 100PSF LOAD Z 502 401 0.984 0.984 GLOB UNIF 100PSF LOAD Z 503 504 0.984 0.984 GLOB UNIF 100PSF LOAD Z 504 407 0.984 0.984 GLOB UNIF 100PSF LOADCN 2LOAD 509 -15.000 GLOB JOIN MACHINE LOAD 510 -15.000 GLOB JOIN MACHINE END

Dynpac

6-16

The following is a description of the SACS input file:

A. The analysis option specified in columns 19-20 on the OPTIONS line is 'DY'.

B. The loads of load cases 1 and 2 account for the weight of unmodeled membersand equipment and will be converted to masses by Dynpac. The weight of thereciprocating machinery for example, was modeled as joint loads at joints 509and 510.

C. Joints 1, 301, 303, 305 and 307 are pinned in the global X, Y and Z directions(joint fixity 111000), the conductor bottom joint 1 is also restrained againstglobal Z rotation.

D. The retained degrees of freedom are specified by '2' in columns 55-60 on theappropriate JOINT lines. For example, Joint 401 is retained for translation in theX, Y, and Z directions as designated by '222' in columns 55-57.

The Dynpac analysis was executed specifying the SACS input file and the followingDynpac input file:

12345678901234567890123456789012345678901234567890123456789012345678901234567890

TITLE DYNPAC SAMPLE PROBLEM

A DYNOPT +ZEN 20LUMP 490. -80.2 NF1.0 SA-ZB PLOVR A100A101 400.0C JTWGT 464 15.0 15.0 15.0

JTWGT 465 10.0 10.0 10.0JTWGT 466 10.0 10.0 10.0JTWGT 467 15.0 15.0 15.0END


as specified in columns 8-9 and 10-11 respectively.b. 20 modes are desired (columns 12-14).c. The lumped mass approach is specified by 'LUMP' in columns 15-18.d. The structure density is 490.0 lb/ft3.e. The mudline elevation (-80.2) is specified in columns 33-39.f. Loads from the SACS data are to be used as masses and the Z direction


B. The PLOVR input line specifies that the density of plates A100 and A101 is400.0 lb/ft3.

C. The JTWGT lines specify an additional mass equivalent to 15.0 kips in all threedirections is to be applied at joints 464 and 467. Likewise, a mass equivalent to10.0 kips in all three directions is to be applied at joints 465 and 466.

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Modes 1 through 9 are displayed below.

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Modes 10 through 18 are displayed below.

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DYNAMIC ANALYSIS PARAMETERS

NO. JOINTS ......... 34 NO. MEMBERS......... 64 NO. PLATES ......... 15 NO. SHELL ELEMENTS.. 0 NO. REDUCED DOF..... 139 NO. RETAINED DOF.... 65 NO. MODES .......... 20 NO. VECTORS......... 20

EXPANDED MODE SHAPES REQUESTED MASS PASSED FROM SACS DATA - ADDITIONAL

DIRECTION - -Z

AUTOMATIC LUMPED MASS OPTION SELECTED STRUCTURAL DENSITY = 490.00 LB/FT**3

PLATE PROPERTIES

NAME ****** JOINTS ****** OFFSET THICKNESS DENSITY 1 2 3 4 (INCHES) (LB/CU FT)

A100 461 462 472 0 1 1.969 400.000 A101 401 472 462 0 1 1.969 400.000 A102 462 463 403 401 1 1.969 490.000 A103 463 464 465 0 1 1.969 490.000 A104 465 403 463 0 1 1.969 490.000 A105 403 465 466 405 1 1.969 490.000 A106 405 466 468 0 1 1.969 490.000 A107 467 468 466 0 1 1.969 490.000 A108 468 469 407 405 1 1.969 490.000 A109 469 470 471 0 1 1.969 490.000 A110 471 407 469 0 1 1.969 490.000 A112 401 403 409 0 1 1.969 490.000 A113 403 405 409 0 1 1.969 490.000 A114 405 407 409 0 1 1.969 490.000 A115 407 401 409 0 1 1.969 490.000

PLATE WEIGHTS X 243.467 KIPS PLATE CG LOCATION X 2.981 FT Y 243.467 KIPS Y 0.463 FT Z 243.467 KIPS Z 21.185 FT

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MEMBER GROUP SUMMARY WEIGHT REPORT

******** CONSTRUCTION MATERIAL ******** GRUP WEIGHT *** CENTER OF GRAVITY *** X Y Z (KIPS) (FT) (FT) (FT)

HB3 0.00 0.00 0.00 -3.28 HD3 0.00 0.00 0.00 -3.28 PL3 0.00 0.00 0.00 8.20 CON 7.55 0.00 0.00 3.11 DK1 99.35 0.00 0.00 19.68 DK2 27.04 -3.75 0.00 20.16 EQ1 0.00 -19.68 0.00 28.18 DUM 0.00 -19.68 0.00 25.18

MEMBER WEIGHTS X 133.939 KIPS MEMBER CG LOCATION X -0.758 FT Y 133.939 KIPS Y 0.000 FT Z 133.939 KIPS Z 18.847 FT

*** ADDITIONAL JOINT WEIGHTS ***

JOINT ********* WEIGHTS ********* ** ROTARY INERTIAL WEIGHTS ** NO. X Y Z X Y Z ---------- KIPS ----------- --------- KIP-IN**2 ---------

464 15.00 15.00 15.00 0.00 0.00 0.00 465 10.00 10.00 10.00 0.00 0.00 0.00 466 10.00 10.00 10.00 0.00 0.00 0.00 467 15.00 15.00 15.00 0.00 0.00 0.00

JOINT WEIGHTS X 50.000 KIPS JOINT CG LOCATION X 29.528 FT Y 50.000 KIPS Y 0.000 FT Z 50.000 KIPS Z 19.685 FT

SACS WEIGHTS X 340.042 KIPS SACS CG LOCATION X 0.517 FT Y 340.042 KIPS Y 0.000 FT Z 340.042 KIPS Z 20.435 FT

TOTAL WEIGHTS X 767.447 KIPS TOTAL CG LOCATION X 2.966 FT Y 767.447 KIPS Y 0.147 FT Z 767.447 KIPS Z 20.347 FT

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SACS IV-FREQUENCIES AND GENERALIZED MASS * NORMALIZED DEGREES OF FREEDOM * MODE FREQ.(CPS) GEN. MASS EIGENVALUE PERIOD(SECS) JOINT DOF

1 0.668508 1.5977576E+03 5.6679639E-02 1.4958685 464 DIS Y 2 1.204053 1.7117122E+03 1.7472265E-02 0.8305284 509 DIS X 3 1.216031 1.4562797E+03 1.7129737E-02 0.8223472 470 DIS Y 4 2.395002 2.6866102E+02 4.4159954E-03 0.4175363 467 DIS Z 5 3.066141 3.3052186E+02 2.6943626E-03 0.3261429 464 DIS Z 6 3.417816 1.8185404E+02 2.1684169E-03 0.2925845 470 DIS Z 7 4.118304 1.6742868E+02 1.4934935E-03 0.2428184 461 DIS Z 8 6.458744 2.9443903E+02 6.0721728E-04 0.1548289 471 DIS Z 9 8.467087 1.5583728E+02 3.5332323E-04 0.1181044 470 DIS Z 10 9.795757 5.9579742E+02 2.6397589E-04 0.1020850 467 DIS Z 11 10.206057 1.2855483E+02 2.4317798E-04 0.0979810 510 DIS X 12 10.692706 1.7687723E+02 2.2154655E-04 0.0935217 510 DIS Y 13 12.274257 2.6919242E+02 1.6813177E-04 0.0814713 461 DIS Z 14 17.472221 1.8179860E+02 8.2974378E-05 0.0572337 471 DIS Z 15 19.275712 1.2561250E+02 6.8174093E-05 0.0518788 510 DIS Z 16 25.025570 7.8744867E+02 4.0445693E-05 0.0399591 405 DIS Z 17 28.310761 1.5727741E+02 3.1603644E-05 0.0353223 504 DIS Y 18 28.949107 3.9549732E+02 3.0225250E-05 0.0345434 403 DIS Z 19 29.743578 3.6317182E+02 2.8632142E-05 0.0336207 501 DIS Y 20 32.023928 7.3039937E+02 2.4699663E-05 0.0312267 504 DIS Z

*** M O D A L R E A C T I O N S U M M A R Y *** MODE X (KIPS) Y (KIPS) Z (KIPS) 1 0.24 -4.86 0.00 2 -104.84 -3.97 1.54 3 3.66 -97.45 0.02 4 -0.18 -6.52 0.69 5 -25.34 1.42 -95.07 6 -0.26 -21.51 -34.46 7 9.00 2.30 -266.63 8 21.79 6.90 -53.23 9 -19.42 17.12 13.34 10 48.24 34.81 483.60 11 -16.38 5.37 166.34 12 -0.05 16.18 83.23 13 3.63 -31.03 1282.43 14 -1.53 -3.65 144.60 15 3.30 -3.54 -694.19 16 -21.33 -79.34 -3207.64 17 -8.57 -9.91 -1935.18 18 -26.69 1.34 -10697.06 19 1.41 -14.91 4884.61 20 95.12 10.35 -9763.67

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