Gap

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Gap

Gap
RELEASE 5
USER’S MANUAL

ENGINEERING DYNAMICS, INC.
2113 38TH STREET
KENNER, LOUISIANA 70065
U.S.A.

No part of this document may be
reproduced in any form, in an
electronic retrieval system or
otherwise, without the prior
written permission of the publisher.

Copyright © 1998 by
ENGINEERING DYNAMICS, INC.
Printed in U.S.A.

Gap

Gap
TABLE OF CONTENTS
1.0 INTRODUCTION .......................................................................................................................
1.1 OVERVIEW .........................................................................................................................
1.2 PROGRAM FEATURES ......................................................................................................
1.3 PROGRAM STRUCTURE ..................................................................................................

1-1
1-1
1-1
1-1

2.0 GAP MODELING AND INPUT ................................................................................................
2.1 MODELING REQUIREMENTS .........................................................................................
2.1.1 Member End Releases on Gap Elements .....................................................................
2.1.2 Defining Dummy Unit Load Case for a Gap Element ................................................
2.1.3 Simulating Compression or Tension Only Supports ...................................................
2.2 GAP ANALYSIS INPUT .....................................................................................................
2.2.1 Analysis Units .............................................................................................................
2.2.2 Designating Basic Load Cases ....................................................................................
2.2.3 Designating Load Cases to Analyze ............................................................................
2.2.3.1 Defining Output Load Cases ..............................................................................
2.2.4 Designating Gap Elements ..........................................................................................
2.2.4.1 Defining Force-Deflection Curve ......................................................................

2-1
2-1
2-1
2-1
2-2
2-2
2-2
2-3
2-3
2-3
2-3
2-4

3.0 GAP INPUT FILE .......................................................................................................................
3.1 INPUT FILE SETUP ............................................................................................................

3-1
3-1

4.0 COMMENTARY ........................................................................................................................
4.1 GAP ELEMENT FORCES ...................................................................................................

4-1
4-1

5.0 SAMPLE PROBLEMS ...............................................................................................................
5.1 SAMPLE PROBLEM 1 ........................................................................................................
5.2 SAMPLE PROBLEM 2 ........................................................................................................

5-1
5-2
5-9

i

Gap

ii

Gap

SECTION 1

INTRODUCTION

Gap

Gap
1.0 INTRODUCTION
1.1 OVERVIEW
The Gap program module allows for the analysis of non-linear one-way elements. Gap
uses linear combinations of gap element unit axial load cases to eliminate loading in any
gap element that contradicts the element type designation (i.e.. tension in a compression
only element, compression in a tension only element, etc.).

1.2 PROGRAM FEATURES
Gap requires a SACS input model file and a Gap input file for execution. The program
coupled with SACS IV and Combine creates a common solution file containing results of
the linear combination of the designated load combinations and gap element unit axial
load cases.
Some of the main features and capabilities of the Gap program module are:
1. Allows simulation of compression only, tension only and no load elements.
2. Simulation of non-linear springs defined by specified force/deflection curves.
3. Multiple load combinations may be analyzed in a single execution.
4. Ability to simulate loss of support and/or check differential settling problems
when used in conjunction with specified displacements.
5. Ability to simulate tension or compression only supports.
6. Ability to define load combinations in the Gap input file.

1.3 PROGRAM STRUCTURE
When executing a Gap analysis, a static analysis is performed for each load combination
and each gap element dummy unit load case. For each load combination the following
procedure is used to obtain gap analysis results:
1. The load in each gap element is checked. Any gap element having loading that
contradicts the element type specified (i.e.. compression only element with
tension load) is flagged.
2. The dummy unit load case corresponding to the gap element with the highest
contradicting load is added to the combination then factored until the loading in
that gap element is negated.
3. The load in each gap element is rechecked. If any gap element contradicts the
type specified, the procedure is repeated.
4. The load combination then consists of the original basic load conditions and any
gap dummy unit load cases factored to eliminate any contradicting gap element
loading.

1-1

Gap

1-2

Gap

SECTION 2

GAP MODELING AND INPUT

Gap

Gap
2.0 GAP MODELING AND INPUT
The Gap program requires a SACS model file and a Gap input file. The model file
requires some minor modeling consideration for the purpose of gap analysis.

2.1 MODELING REQUIREMENTS
Any element in the model may be regarded as a gap one-way element. While the gap
element type is designated in the Gap input file, some minor modeling considerations
may be required for execution of a gap analysis.
2.1.1 Member End Releases on Gap Elements
Member end releases may be used to remove shear, bending and/or torsion capacity of
elements that will be declared gap elements. For example, a guyed structure utilizing
tension only gap elements may require member end releases as follows:
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
MEMBER
MEMBER

102 201 GAP
102 301 GAP

011
011

103

Tension only

102

301
101

Note:

201

The axial degree of freedom at the ends of an element designated
as a compression or tension only element should not be released.

2.1.2 Defining Dummy Unit Load Case for a Gap Element
For each gap element, a dummy load case consisting of only a unit axial load for that gap
element must be defined in the model file. The net load of the dummy unit load case
must be zero. For example, load cases 12 and 13 define a unit load axial load for

2-1

Gap
members 102-201 and 102-301 from the preceding figure, respectively. Note that these
load cases produce no net load on the structure.

1.0

1.0

Load Case 12

Load Case 13

102

102

201

301

1.0

1.0

1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
LOADCN
LOAD X
LOAD X
LOADCN
LOAD X
LOAD X

12
102
201
13
102
301

Note:

Either a tension or compression unit axial load may defined
regardless of the gap element type designated.

201 0.0
102 0.0

1.0
-1.0

MEMB CONC
MEMB CONC

DUMMY12
DUMMY12

301 0.0
102 0.0

1.0
-1.0

MEMB CONC
MEMB CONC

DUMMY13
DUMMY13

The procedure illustrated above uses two ‘LOAD’ input lines per dummy unit load case.
The first load is defined as a compressive axial load at the begin joint while the second
load is defined as a compressive load at the end joint.
2.1.3 Simulating Compression or Tension Only Supports
Gap elements may be used to simulate compression only or tension only supports by
modeling two joints at the support. One joint is designated as the support joint and
assigned the appropriate fixities, while the other joint is attached to the structure. A gap
element is then modeled between the two joints. See the figure below.

Compression only elements

2.2 GAP ANALYSIS INPUT
Most Gap analysis input data is specified in the Gap input file. The following sections
address the specification of this input data.
2.2.1 Analysis Units

2-2

Gap
Gap analysis units are designated on the GAPOPT input line in columns 21-22.
2.2.2 Designating Basic Load Cases
Basic load cases in the model input file that are referenced by a load combination
defined in the Gap input file are called ‘Real’ load cases and must be designated as such.
The total number of ‘Real’ load cases referenced must be specified in columns 7-10 on
the GAPOPT input line. Each ‘Real’ load case must also be listed on the LCSEL input
line in the Gap input file. For example, load cases A1, A2, A3 and A7 may be defined as
‘Real’ basic load cases as follows:
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
GAPOPT
LCSEL

4

EN
A1
A2

A3

A7

2.2.3 Designating Load Cases to Analyze
The Gap program analyzes load combinations and basic load cases designated as
‘Output’ load cases in the Gap input file.
In general, ‘Output’ load cases are load combinations consisting of ‘Real’ load cases that
are defined in the model file and designated as such in the Gap input file. The number of
‘Output’ load cases must be specified in columns 11-14 on the GAPOPT line.
2.2.3.1 Defining Output Load Cases
An ‘Output’ load case or combination may consist of up to 48 ‘Real’ load cases
designated on the LCSEL and is defined in the Gap input file using LCOMB input lines.
The load combination name is specified in columns 7-10. For each ‘Real’ load case, the
load factor to be applied and the load case name are specified.
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
LCSEL
LCOMB CMB1
LCOMB CMB2

Note:

A1
A1 1.0
A1 1.0

A2
A3
A2 0.75
A2 3.00

A7

Output load case numbers must be sequential beginning with load
combination number one.

2.2.4 Designating Gap Elements
Elements may be designated as one of the following non-linear gap element types;
compression only, tension only, no load or force-deflection element. Elements that are to
be considered non-linear gap elements are designated in the Gap input file using the
GAPELM line.

2-3

Gap
The element connecting joints are specified in columns 7-11 and 12-16. The element
type is designated in columns 24-25 by ‘CO’ (compression only), ‘TO’ (tension only),
‘NL’ (no load), ‘FD’ (force-deflection) or ‘RP’ (repeat previous element type). The
dummy unit load case defined in the model file that corresponds to the element being
defined is specified in columns 17-21.

1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
GAPELM
GAPELM

101
103

201
203

4
5

CO
NL

Note:

The dummy load case corresponding to the element should contain
only unit axial load at each end of the element and should add no
net load to the overall structure.

2.2.4.1 Defining Force-Deflection Curve
The curve used for an element designated as force-deflection type gap element is defined
on the line labeled F-DEL immediately following the GAPELM line used to designate
the element as a force-deflection gap element.
Points on the curve are entered in columns 9-80 and must be entered in order of
increasing deflection. As many F-DEL lines as needed to define the curve may be used.
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
GAPELM
GAPELM
F-DEL
F-DEL
GAPELM

101 201
103 203
0.0
300.0
105 205

4 CO
5 FD
-10.0
10.0
6 CO

Note:

For deflections outside of the range of the curve, the force value
is assumed to be constant.

0.0

0.0

2-4

100.0

1.0

200.

2.0

Gap

SECTION 3

GAP INPUT FILE

Gap

Gap
3.0 GAP INPUT FILE
3.1 INPUT FILE SETUP
The Gap input file contains the gap analysis information required to execute the analysis.
The table below shows the standard input in the Gap input file.
INPUT LINE

DESCRIPTION

GAPOPT

Gap analysis options

LCSEL

Designates ‘Real’ load cases to be used

LCOMB

Defines output load combinations to be analyzed

GAPELM

Designates non-linear gap element information

F-DEL*

Defines the force-deflection curve for force-deflection type gap
elements

END

Designates end of input data

*Note:

F-DEL input is only required for force-deflection type gap
elements.

The following section illustrates the formats of the input data for Gap. The user should
be familiar with the basic guidelines for specifying input data. These guidelines are
located in the Introduction Manual.

3-1

GAP OPTIONS INPUT

FOUR REAL LOAD CASES DEFINED IN THE MODEL FILE ARE TO BE REFERENCED
BY THE SIX OUTPUT LOAD COMBINATIONS DEFINED IN THE GAP INPUT FILE.
THE ANALYSIS UNITS ARE ENGLISH AS SPECIFIED IN COLUMNS 21-22.

3-2
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4

6

EN

Gap

GAPOPT

GAP OPTIONS INPUT - INPUT LINE 1

COLUMNS

3-3
LINE
LABEL

COMMENTARY

GENERAL

THIS INPUT IS REQUIRED IN ANY NON-LINEAR GAP ELEMENT ANALYSIS.
IT SPECIFIES OVERALL ANALYSIS PARAMETERS.

( 7-10)

ENTER THE NUMBER OF REAL LOAD CASES IN THE SACS DATA.
THE REAL LOAD CASES ARE THOSE THAT REPRESENT ACTUAL LOADING
ON THE STRUCTURE AS OPPOSED TO THE DUMMY LOAD CASES THAT ARE
USED TO SIMULATE THE GAP ELEMENTS.

(11-14)

ENTER THE NUMBER OF OUTPUT LOAD CASES.
THESE ARE THE LOAD CASES THAT REPRESENT THE ACTUAL LOADING
CONDITIONS TO BE ANALYZED AND IN GENERAL THESE WILL BE
COMBINATIONS OF THE REAL LOAD CASES IN THE SACS DATA.

(15-18)

THIS OPTION IS PRIMARILY USED FOR DEBUGGING ANY
PROBLEMS THAT MAY EXIST. IT WILL PRODUCE A GREAT DEAL OF
OUTPUT THAT WILL NOT BE USEFUL FOR THE NORMAL CASE.

(21-22)

ENTER THE SYSTEM OF UNITS USED. THIS SYSTEM WILL
NORMALLY BE THE SAME AS USED IN THE SACS ANALYSIS BUT IS NOT
REQUIRED TO BE SO. SELECT FROM ONE OF THE FOLLOWING:
EN - ENGLISH UNITS
MN - METRIC UNITS WITH NEWTONS AS THE FORCE UNITS
ME - METRIC UNITS WITH KILOGRAMS AS THE FORCE UNITS

(23-26)

ENTER THE NUMBER OF ITERATIONS ALLOWED IN THE NON-LINEAR
SOLUTION.

(27-34)

ENTER THE CONVERGENCE TOLERANCE REQUIRED. THIS TOLERANCE
SHOULD BE SMALL SINCE THE GAP ELEMENTS MAY BE SHORT AND
RELATIVELY STIFF.

NUMBER
OF
REAL
LOAD
CASES

NUMBER
OF
OUTPUT
LOAD
CASES

DIAGNOSTIC
OUTPUT
PRINT
OPTION

UNITS
OPTION

MAXIMUM
NUMBER OF
ITERATIONS

CONVERGENCE
TOLERANCE

LEAVE BLANK

7))))) >10

11))))) >14

15))))) >18

21)))) 22

23)))) >26

27<)))34

35)))))))))))))))) 80

EN

600

0.00001

GAPOPT
1))))))) 6
DEFAULTS
ENGLISH
METRIC(KN)

Gap

METRIC(KG)

REAL LOAD CASE DESIGNATION INPUT

LOAD CASES A1, A3 AND B7 DEFINED IN THE SACS MODEL FILE ARE TO BE
CONSIDERED AS REAL LOAD CASES AND ARE REFERENCED BY OUTPUT LOAD
COMBINATIONS DEFINED IN THE GAP INPUT FILE.

3-4
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GAPOPT

6

EN
A1

A3

B7

Gap

LCSEL

4

GAP ANALYSIS LOAD CASE SELECTION - INPUT LINE 2

COMMENTARY

COLUMNS

THIS LINE IS USED TO SPECIFY THE LOAD CASES IN THE SACS
INPUT FILE THAT ARE TO BE USED IN THE GAP PROGRAM.
THIS LINE CAN BE REPEATED AS OFTEN AS NECESSARY
TO SELECT ANY OR ALL OF THE LOAD CASES.

(17-75)

ENTER THE LOAD CASE ID S FOR ALL LOAD CASES TO BE
INCLUDED FOR GAP ANALYSIS. THE LOAD CASES CAN BE IN ANY ORDER.

3-5

GENERAL

LINE
LABEL

LOAD CASE SELECTION
1ST

2ND

3RD

4TH

5TH

6TH

7TH

8TH

9TH

10TH

11TH

12TH

17)))))) >20

22))>25

27))>30

32))>35

37))>40

42))>45

47))>50

52))>55

57))>60

62))>65

67))>70

72))>75

LCSEL
1)))))) 5
DEFAULTS
ENGLISH

Gap

METRIC

OUTPUT LOAD CASE DEFINITION

THREE OUTPUT LOAD COMBINATIONS ARE DEFINED. THE REAL LOAD CASES
REFERENCED ARE SPECIFIED ON THE LDCASE INPUT LINE. NOTICE THAT
THE LOAD COMBINATION NAMES MAY BE ALPHA NUMERIC.

3-6
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839 40 414243444546474849505152535455565758596061626364656667686970717273747576777879 80

LCSEL

A1

A2

OP01

A1 1.0

A2 1.0

LCOMB CMB2

A1 1.0

A2 0.75

LCOMB CMB3

A1 1.0

OP01 1.0

Gap

LCOMB CMB1

GAP LOAD COMBINATION INPUT - INPUT LINE 3

COLUMNS

COMMENTARY

LOCATION LOAD COMBINATIONS FOLLOW THE BASIC LOAD CONDITION DATA.
(GENERAL) THIS LINE ENABLES THE USER TO GENERATE NEW
LOAD CONDITIONS, EACH DEFINED AS A LINEAR COMBINATION OF FROM
ONE TO FORTY EIGHT BASIC AND/OR OTHER COMBINED LOAD CONDITIONS
FOR THIS ANALYSIS.

3-7

( 1- 5)

ENTER LCOMB ON ALL LINES DEFINING COMBINATIONS. A HEADER
WITH LCOMB ONLY MUST PRECEDE ANY LOAD COMBINATION DATA.

( 7-10)

ENTER THE NAME FOR THE LOAD COMBINATION BEING DEFINED.

(12-15)

ENTER THE NAME OF THE LOAD CASE OR COMBINATION TO BE USED AS
THE FIRST LOAD COMPONENT DEFINING THIS COMBINATION.
THE LOAD CONDITIONS BEING COMBINED MAY BE ENTERED IN RANDOM
ORDER.

(16-21)

ENTER THE FRACTION OF THE FIRST LOAD CASE TO BE INCLUDED IN
THIS COMBINATION.

(22-71)

REPEAT AS NECESSARY FOR THE REMAINING COMPONENTS MAKING UP
THIS COMBINATION.
THIS LINE MAY BE REPEATED TO ENTER A TOTAL OF FORTY EIGHT LOAD
COMPONENTS FOR EACH COMBINATION. EACH ADDITIONAL LCOMB LINE
MUST HAVE THE LOAD COMBINATION NAME SPECIFIED IN COLUMNS 7-10.

LINE
LABEL

COMBINATION
NAME

FIRST LOAD
COMPONENT

SECOND LOAD
COMPONENT

THIRD LOAD
COMPONENT

FOURTH LOAD
COMPONENT

FIFTH LOAD
COMPONENT

SIXTH LOAD
COMPONENT

LOAD
CASE
NAME

LOAD
FACTOR

LOAD
CASE
NAME

LOAD
FACTOR

LOAD
CASE
NAME

LOAD
FACTOR

LOAD
CASE
NAME

LOAD
FACTOR

LOAD
CASE
NAME

LOAD
FACTOR

LOAD
CASE
NAME

LOAD
FACTOR

12)))>15

16<)21

22)))>25

26<)31

32)))>35

36<)41

42)))>45

46<)51

52)))>55

56<)61

62)))>65

66<)71

LCOMB
1)) 5
DEFAULTS

7)))>10

1.0

1.0

1.0

1.0

1.0

1.0

ENGLISH

Gap

METRIC

GAP ELEMENT INPUT

THREE ELEMENTS ARE DESIGNATED AS GAP ELEMENTS. MEMBERS 101-201
AND 103-203 ARE COMPRESSION ONLY ELEMENTS. LOAD CASES 4 AND 5
DEFINED IN THE MODEL FILE CORRESPOND TO THE DUMMY UNIT LOAD CASES
FOR MEMBERS 101-201 AND 103-203, RESPECTIVELY. ELEMENT 105-205
IS A SPRING ELEMENT DEFINED BY A FORCED DEFLECTION CURVE. LOAD
6 IS THE DUMMY UNIT LOAD CASE DEFINED IN THE MODEL FILE
CORRESPONDING TO THIS ELEMENT.

3-8
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GAPELM

101

201

4

CO

GAPELM

103

203

5

CO

GAPELM

105

205

6

FD

0.0

-10.0

0.0

0.0

F-DEL

300.0

1.3

400.0

1.3

100.0

1.0

200.0

1.2

Gap

F-DEL

GAP ELEMENT INPUT - INPUT LINE 4

COLUMNS

THIS INPUT LINE IS REQUIRED FOR EACH NON-LINEAR GAP
ELEMENT. IT PROVIDES THE ELEMENT DEFINITION TO DUMMY LOAD
CASE CONNECTION.

( 7-11)

ENTER THE FIRST JOINT OF THIS GAP ELEMENT.

(12-16)

ENTER THE SECOND JOINT OF THIS GAP ELEMENT.

(17-21)

ENTER THE DUMMY LOAD CASE NUMBER ASSOCIATED WITH
THIS ELEMENT. THIS LOAD CASE WOULD HAVE A LOAD APPLIED ONLY
TO THIS ELEMENT.

(24-25)

ENTER THE GAP ELEMENT TYPE FROM THE FOLLOWING
CHOICES:
CO - COMPRESSION ONLY
TO - TENSION ONLY
NL - NO LOAD
FD - FORCE VERSUS DEFLECTION ELEMENT (SEE F-DEL DATA)
RP - REPEAT PREVIOUS GAP ELEMENT FORCE-DEFLECTION

3-9
LINE
LABEL

COMMENTARY

GENERAL

GAP ELEMENT
FIRST JOINT

DUMMY
LOAD CASE
NUMBER

ELEMENT
TYPE

LEAVE BLANK

SECOND JOINT

12))))))) >16

17)))))) >21

24))))) 25

26)))))))))))))))))))) 80

GAPELM
1)))))))))) 6
DEFAULTS

7)))))))) >11

CO

ENGLISH
METRIC(KN)

Gap

METRIC(KG)

FORCE VS. DEFLECTION CURVE DEFINITION

ELEMENT 105-205 IS DEFINED BY SIX POINTS ON A FORCE-DEFLECTION
CURVE AS DEFINED ON THE TWO F-DEL INPUT LINES IMMEDIATELY
FOLLOWING THE GAPELM LINE CORRESPONDING TO THIS ELEMENT.

3-10
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GAPELM

101

201

4

CO

GAPELM

103

203

5

CO

GAPELM

105

205

6

FD

0.0

-10.0

0.0

0.0

F-DEL

300.0

1.3

400.0

1.3

100.0

1.0

200.0

1.2

Gap

F-DEL

FORCE VS. DEFLECTION CURVE DEFINITION - INPUT LINE 5

COLUMNS

THIS INPUT IS REQUIRED FOR EACH NON-LINEAR GAP
ELEMENT THAT HAS A FD DESIGNATION.
THIS DATA FOLLOWS DIRECTLY AFTER THE GAPELM LINE
DEFINING THE GAP ELEMENT TO WHICH THIS FORCE VS.
DEFLECTION RELATIONSHIP APPLIES.

( 9-26)

ENTER THE FIRST FORCE-DEFLECTION POINT
TO DEFINE THIS CURVE.

(27-80)

ENTER THE SECOND,THIRD AND FOURTH POINTS AS
REQUIRED. THESE POINTS MUST BE ENTERED IN ORDER
OF INCREASING DEFLECTIONS. FOR DEFLECTIONS
OUTSIDE THE RANGE OF THE TABLE VALUES, THE PROGRAM
USES THE FIRST OR LAST FORCE VALUE IN THE TABLE AS
APPROPIATE. REPEAT THIS LINE AS OFTEN AS NECESSARY TO DEFINE
THE FORCE VERSUS DEFLECTION CURVE IN AS MUCH DETAIL
AS DESIRED. DO NOT USE BLANKS FOR ZEROES.

3-11
LINE
LABEL

COMMENTARY

GENERAL

FIRST POINT

SECOND POINT

THIRD POINT

FOURTH POINT

FORCE

DEFL.

FORCE

DEFL.

FORCE

DEFL.

FORCE

DEFL.

9)))))) 17

18))))) 26

27))))) 35

36))))) 44

45))))) 53

54))))) 62

63))))) 71

72))))) 80

F-DEL
1)))))) 5
DEFAULTS
KIPS

INCHES

KIPS

INCHES

KIPS

INCHES

KIPS

INCHES

METRIC(KN)

KN

CM.

KN

CM.

KN

CM.

KN

CM.

METRIC(KG)

KG

CM.

KG

CM.

KG

CM.

KG

CM.

Gap

ENGLISH

END OF INPUT

THE END OF THE GAP INPUT FILE IS DESIGNATED WITH THE
INPUT LINE.

END

3-12
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Gap

END

END OF INPUT - INPUT LINE 6

COLUMNS

COMMENTARY

3-13

LOCATION THIS LINE IS THE LAST LINE IN THE GAP INPUT FILE.
(GENERAL) THE

LINE
LABEL

END

LINE TERMINATES THE DATA READ BY THE GAP PROGRAM.THIS LINE IS OPTIONAL.

REMAINDER OF THIS INPUT LINE LEFT BLANK

END
4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 80

Gap

1))))) 3

Gap

3-14

Gap

SECTION 4

COMMENTARY

Gap

Gap
4.0 COMMENTARY
4.1 GAP ELEMENT FORCES
The Gap program module uses the relationship between force and load factors of
elements designated as non-linear gap elements.
For any output load condition, the total force Fi in a gap element i, can be expressed in
terms of the initial gap element force, Fio, and the force/load factor relationship of the
element as follows:
n
F i ' Fio % j
j'1

Aij P j

(1)

where n is the number of gap elements, Aij is the force in gap element i due to a unit load
factor, Pj, applied to the jth dummy load case.
Note:

The jth dummy load case corresponds to a unit load case applied to
the jth gap element.

For gap elements with force that contradicts the element type designation, the total force
is set to zero thus negating the effects of the element. Therefore, for each contradicting
element, equation (1) can be expressed as:
n
j
j'1

Aij P j

' &Fio

(2)

Rewriting equation (2) in matrix form yields the following equation:
A

P

'& Fo

(3)

By pre-multiplying equation (3) by [A]-1, the load factors can be determined from:
P

Note:

'& A

&1

Fo

(4)

When determining the load factors for numerous gap elements, the
contradicting element with the highest load is balanced first. All
other gap elements are then rechecked before proceeding to balance
the remaining contradicting elements.

4-1

Gap

4-2

Gap

SECTION 5

SAMPLE PROBLEMS

Gap

Gap
5.0 SAMPLE PROBLEMS
Two sample problems are used to illustrate the various capabilities of the GAP program.
1. Sample Problem 1, is a guyed structure with three tension only gap elements used to
simulate wire cable.
2. Sample Problem 2 is a horizontal jacket structure supported at three pairs of support
points. Gap elements were used to simulate the load out condition where each set of
support points becomes ineffective (i.e.. when positioned between the barge and the
bulkhead).

5-1

Gap

5.1 SAMPLE PROBLEM 1
Sample Problem 1 is a tower structure supported laterally by four wire cables as shown
below. The wire cables, group ‘CBL’, are simulated using tension only gap elements
with shear capacity member releases at joint 2.

Two basic load conditions are specified; load case 1 is structure self weight and load
case 2 is a lateral load in the positive global X direction applied at joint 3. Additionally,
for each gap element, a dummy load case consisting of only a unit axial compressive
force applied to that gap element is specified.
Note:

In this sample, the dummy axial load was added as an unit axial
compressive load. Because the program can determine whether to use
a positive or negative load factor, the direction of the dummy
load may be added as either a tension or a compressive load.

The model file used for this sample problem follows:

5-2

Gap
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
GAP SAMPLE PROBLEM 1
OPTIONS
EN
SDUC
1 1 0 0
PT PTPT
PT
SECT
SECT CABLE
TUB 3.75
0.10
0.10
0.10
0.010.001
GRUP
GRUP CBL CABLE
13.0011.6036.00 1
1.001.00
GRUP FLG
24.00 0.625 29.0011.6036.00 1
1.001.00
MEMBER
MEMBER0
1
2 FLG
MEMBER0
2
3 FLG
MEMBER01001
2 CBL
011
MEMBER01002
2 CBL
011
MEMBER01003
2 CBL
011
MEMBER01004
2 CBL
011
JOINT
JOINT
1
0.000 0.000 0.000
111111
JOINT
2
0.000 0.000 30.000
JOINT
3
0.000 0.000 50.000
JOINT 1001 -15.000-15.000 0.000
111
JOINT 1002 15.000-15.000 0.000
111
JOINT 1003 -15.000 15.000 0.000
111
JOINT 1004 15.000 15.000 0.000
111
LOAD
LOADCN
1
LOAD Z
1
2
-0.033
-0.033
GLOB
LOAD Z
2
3
-0.033
-0.033
GLOB
LOADCN
2
LOAD
3
25.0000
GLOB
LOAD
2
25.0000
GLOB
LOADCN
3
LOAD X 1001
2
-1.0000
MEMB
LOAD X
21001
1.00000
MEMB
LOADCN
4
LOAD X 1002
2
-1.0000
MEMB
LOAD X
21002
1.00000
MEMB
LOADCN
5
LOAD X 1003
2
-1.0000
MEMB
LOAD X
21003
1.00000
MEMB
LOADCN
6
LOAD X 1004
2
-1.0000
MEMB
LOAD X
21004
1.00000
MEMB
END

0.50N490.00
0.50N490.00

UNIF
UNIF

DEADWT
DEADWT

JOIN
JOIN

LATERAL
LATERAL

CONC
CONC

DUMMY3
DUMMY3

CONC
CONC

DUMMY4
DUMMY4

CONC
CONC

DUMMY5
DUMMY5

CONC
CONC

DUMMY6
DUMMY6

The structure was analyzed for two load combinations of the self weight and the lateral
load. Below is the Gap input file used to perform the gap analysis. A detailed
description of each line of the input file follows:
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
A
B
C
D
E
F
G
H

GAPOPT
2
LCSEL
LCOMB CMB1
LCOMB CMB2
GAPELM 1001
GAPELM 1002
GAPELM 1003
GAPELM 1004
END

2

EN
1
1 1.0
1 1.0
2
3
2
4
2
5
2
6

2
2 1.0
2 -1.0
TO
TO
TO
TO

A. The GAPOPT input designates the gap analysis options as follows:

5-3

Gap
a. English units are designated in columns 21-22.
b. As specified in columns 7-10, two load cases specified in the model input file are
to be considered ‘Real’ load cases that are to be referenced by ‘Output’ load
combinations.
c. Two ‘Output’ load combinations will be analyzed as designated in columns 1114.
B. Load cases 1 and 2 defined in the SACS model file are ‘Real’ load cases that will be
referenced by ‘Output’ load combinations defined in the GAP input file.
C. The first ‘Output’ load combination is defined on the first line labeled LCOMB as
follows:
a. The load combination number is CMB1 as designated in columns 7-10.
b. The combination consists of 100% of load cases 1 and 2 defined in the model
input file.
D. The second ‘Output’ load combination is defined as follows:
a. The load combination number is CMB2 as designated in columns 7-10.
b. The combination consists of 100% of load case 1 and -100% of load case 2
defined in the model input file. (Note that the direction of the lateral load defined
in load case 2 was changed by specifying -100%).
E. Element 1001-2 was designated as a tension only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case 3 defined in the model file
corresponds to this element.
c. The element is defined as a tension only element by ‘TO’ in columns 24-25.
F. Element 1002-2 was designated as a tension only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case 4 defined in the model file
corresponds to this element.
c. The element is defined as a tension only element by ‘TO’ in columns 24-25.
G. Element 1003-2 was designated as a tension only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case 5 defined in the model file
corresponds to this element.
c. The element is defined as a tension only element by ‘TO’ in columns 24-25.
H. Element 1004-2 was designated as a tension only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case 6 defined in the model file
corresponds to this element.
c. The element is defined as a tension only element by ‘TO’ in columns 24-25.
The following is a portion of the output listing file created by the GAP program module:

5-4

GAP SAMPLE PROBLEM 1
1

DATE 03-JUN-1996

TIME 16:37:49

PRE

PAGE

PRE VERSION IV.F.002
** PROGRAM OPTIONS **

UNITS
....ENGLISH
EXECUTION
....SHEAR DEFORMATION INCLUDED
....UNITY CHECK
API RP2A 20TH EDITION
....NO SEGMENTS FOR PRISMATIC MEMBERS
1
....NO SEGMENTS/SECTION FOR NON-PRISMATIC MEMBERS

1

REPORTS SELECTED
....ELEMENT STRESS AT MAXIMUM UNITY CHECK...PRINT
....BEAM COMBINED AND SHEAR UNITY CHECK.....PRINT
....ELEMENT INTERNAL LOADS..................PRINT

5-5

LOAD
....NO. BASIC LOAD COND.
....NO. COMB. LOAD COND.

6
0

APPLIED LOAD SUMMARY
LOAD CASE

TOTAL FORCE(X)

KIPS

1
2
3
4
5
6

0.000000E+00
5.000000E+01
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

TOTAL FORCE(Y)

KIPS

0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

TOTAL FORCE(Z)

KIPS

-1.649993E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

Gap

GAP SAMPLE PROBLEM 1

DATE 03-JUN-1996

TIME 16:37:55

PAGE

2
LOAD CASE
NO.

GAP ELEMENT

1
2
3
4

1001100210031004-

LOAD CASE

2
2
2
2

TYPE

DEFLECTION
IN

TENS
TENS
TENS
TENS

0.71197
-0.76926
0.71197
-0.76926

CMB1

CMB1 CONVERGED IN

FORCE
KIPS
78.7
0.0
78.7
0.0

GAP ELEMENT

5-6

1
2
3
4

1001100210031004-

LOAD CASE

2
2
2
2

DEFLECTION
IN

TENS
TENS
TENS
TENS

-0.76926
0.71197
-0.76926
0.71197

CMB2

TYPE

CMB2 CONVERGED IN

0.000000E+00
-0.850543E+02
0.000000E+00
-0.850543E+02

30 ITERATIONS

LOAD CASE
NO.

FACTOR

FORCE
KIPS
0.0
78.7
0.0
78.7

FACTOR

-0.850543E+02
0.000000E+00
-0.850543E+02
0.000000E+00

30 ITERATIONS

GAP SAMPLE PROBLEM 1
LOAD
CASE
CMB1

CMB2

NUMB
COMB

LOAD CASE DESCRIPTION

SOURCE ORIG
LC

FACTOR

4

4

P
P
P
P

1
2
4
6

1.000
1.000
-85.054
-85.054

P
P
P
P

1
2
3
5

1.000
-1.000
-85.054
-85.054

Gap

GAP SAMPLE PROBLEM 1
PAGE
5

DATE 03-JUN-1996

SACS-IV SYSTEM

MEMBER
NUMBER

1-

MEMBER
END

2

1
2

2-

3

2

5-7

1001-

2

1001
2

1002-

2

1002
2

1003-

2

1003
2

1004-

2

1004
2

PST

MEMBER FORCES AND MOMENTS

******************* KIPS ********************
FORCE(X)
FORCE(Y)
FORCE(Z)

****************** IN-KIPS ******************
MOMENT(X)
MOMENT(Y)
MOMENT(Z)

FLG CMB1
CMB2
CMB1
CMB2

-130.1994
-130.1994
-129.2095
-129.2095

14.2754
-14.2754
14.2754
-14.2754

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

860.8597
-860.8597
6000.0005
-6000.0005

FLG CMB1

-0.6600

-25.0000

0.0000

0.0000

0.0000

6000.0005

CMB1
CMB2
2

0.0000
0.0000
-0.6600

-25.0000
25.0000
25.0000

0.0000
0.0000
0.0000

0.0000
0.0000
0.0000

0.0000
0.0000
0.0000

0.0000
0.0000
-6000.0005

CBL CMB1
CMB2
CMB1
CMB2

78.7206
-0.0004
78.7206
-0.0004

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

CBL CMB1
CMB2
CMB1
CMB2

-0.0004
78.7206
-0.0004
78.7206

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

CBL CMB1
CMB2
CMB1
CMB2

78.7206
-0.0004
78.7206
-0.0004

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

CBL CMB1
CMB2
CMB1
CMB2

-0.0004
78.7206
-0.0004
78.7206

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000

CMB

3

GROUP LOAD
ID
CASE

TIME 16:38:05

Gap

GAP SAMPLE PROBLEM 1
PAGE
6

DATE 03-JUN-1996

SACS-IV SYSTEM

MEMBER

GRP

MAXIMUM CRITICAL LOAD
UNITY
COND. CASE
CHECK
NO.

DIST
FROM
END
FT

TIME 16:38:05

PST

ELEMENT STRESS REPORT AT MAXIMUM UNITY CHECK

********** APPLIED STRESSES **********
AXIAL
** BENDING **
*** SHEAR ***
Y-Y
Z-Z
Y
Z
KSI
KSI
KSI
KSI
KSI

* CM VALUES *
Y

Z

* NEXT TWO HIGHEST CASES *
UNITY LOAD
UNITY LOAD
CHECK COND
CHECK COND

1-

2 FLG

0.999

C<.15 CMB1

30.00

-2.82

0.00

22.95

0.62

0.00

0.85

0.85

1.00

2

0.00

2-

3 FLG

0.851

C<.15 CMB1

0.00

-0.01

0.00

22.95

1.09

0.00

0.85

0.85

0.85

2

0.00

1001-

2 CBL

0.972

TENS

CMB1

0.00

20.99

0.00

0.00

0.00

0.00

0.85

0.85

0.01

2

0.00

1002-

2 CBL

0.972

TENS

CMB2

0.00

20.99

0.00

0.00

0.00

0.00

0.85

0.85

0.01

1

0.00

1003-

2 CBL

0.972

TENS

CMB1

0.00

20.99

0.00

0.00

0.00

0.00

0.85

0.85

0.01

2

0.00

1004-

2 CBL

0.972

TENS

CMB2

0.00

20.99

0.00

0.00

0.00

0.00

0.85

0.85

0.01

1

0.00

5-8

SACS-IV SYSTEM

HIGHEST CASES
MEMBER GRP
UNITY LD

MAX. CRIT

LOAD

DIST

UNITY COND

COND

FROM

CHECK
CHECK

NO.

AXIAL

END

I N T E R N A L

SHEAR

SHEAR

Y

Z

L O A D S
TORSION

* * * * * * * * *

NEXT TWO

BENDING

BENDING

UNITY

LD

Y-Y

Z-Z

CHECK

CN

IN-KIP

IN-KIP

CN
FT

1-

* * * * * * * * * *

MEMBER INTERNAL LOADS SUMMARY REPORT

2 FLG

1.00 C<.15 CMB1

3 FLG

10010.0

30.0

KIPS

KIPS

KIPS

IN-KIP

-129.21

14.275

0.44798E-07

0.0000

0.0000

6000.0

1.0

2

0.85 C<.15 CMB1

0.0 -0.66000

-25.000

0.12875E-21

0.0000

0.0000

6000.0

0.9

2

2 CBL

0.97 TENS

CMB1

0.0

78.721

0.00000

0.00000

0.0000

0.0000

0.0000

0.0

2

10020.0

2 CBL

0.97 TENS

CMB2

0.0

78.721

0.00000

0.00000

0.0000

0.0000

0.0000

0.0

1

1003-

2 CBL

0.97 TENS

CMB1

0.0

78.721

0.00000

0.00000

0.0000

0.0000

0.0000

0.0

2

0.0
20.0

Gap

Gap

5.2 SAMPLE PROBLEM 2
Sample Problem 2 is a simulation of a load out of a jacket type structure. The structure is
supported by four pairs of supports located at the leg hard points. In addition to checking
the structure when fully supported, the structure is to be checked when each of the pairs
of supports is considered ineffective (ie. located between the bulkhead and the barge or
not touching because of change in barge deck elevation).

The structure is modeled such that joints 2101, 2105, 2201, 2205, 2301, 2305, 2501 and
2505 are support points. Each of the load out cans are divided into two members. The
bottom member attached to the support joint is designated as a compression only gap
element.
The weight of unmodeled items such as walkways, lifting eyes and mudmats were
accounted for in Load case 1 of the SACS model file while load case 2 contains the
structure self weight.
Load case 3, used to simulate loss of support at joints 2101 and 2105, contains a
specified displacement of 50.0 in the global -Z direction at each of the joints. Load cases
4, 5 and 6 are used to simulate loss of support at joints 2201 and 2205, at joints 2301 and
2305 and at 2501 and 2503, respectively.
Additionally, for each gap element, a dummy load case consisting of only a unit axial
compressive force applied to that gap element is specified. The table below details the
load conditions specified in the model file:

5-9

Gap
Load Case

Description

1

Unmodeled steel and miscellaneous loading

2

Self weight of the structure

3

Simulates loss of support at joints 2101 and 2105

4

Simulates loss of support at joints 2201 and 2205

5

Simulates loss of support at joints 2301 and 2305

6

Simulates loss of support at joints 2501 and 2505

7

Dummy unit load on gap element 2101-1101

8

Dummy unit load on gap element 2105-1105

9

Dummy unit load on gap element 2201-1201

10

Dummy unit load on gap element 2205-1205

11

Dummy unit load on gap element 2301-1301

12

Dummy unit load on gap element 2305-1305

13

Dummy unit load on gap element 2501-1501

14

Dummy unit load on gap element 2505-1505

A portion of the SACS model file used for Sample Problem 2 follows:

5-10

Gap
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
GAP SAMPLE PROBLEM 2
OPTIONS
EN
SDUC
2 1 0 0
GRUP
GRUP LG1
41.339 1.378 29.0111.2050.00
GRUP LG2
41.339 1.378 29.0111.2050.00
GRUP LG2
40.551 0.984 29.0111.2036.00
GRUP LG2
41.339 1.378 29.0111.2050.00
GRUP LG3
41.339 1.378 29.0111.2050.00
GRUP LG3
40.551 0.984 29.0111.2036.00
GRUP LG3
41.339 1.378 29.0111.2050.00
GRUP LG4
41.339 1.378 29.0111.2050.00
GRUP T01
15.748 0.689 29.0111.2036.00
GRUP T02
19.685 0.787 29.0111.6036.00
GRUP T03
11.811 0.492 29.0111.6036.00
GRUP GAP
24.000 1.000 29.0011.6036.00
MEMBER
MEMBER0
1 101 LG1
MEMBER0
3 103 LG1
MEMBER0
5 105 LG1
MEMBER0
7 107 LG1
MEMBER1 101 109 T02
MEMBER OFFSETS
-20.83
MEMBER1 101 112 T02

PT
1
1
1
1
1
1
1
1
1
1
1
1

PT
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00
1.001.00

0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50

490.00
490.006.14
490.00
490.004.89
490.006.73
490.00
490.004.36
490.00
490.00
490.00
490.00
490.00

*********** Additional MEMBER data *************
MEMBER1 303 309
MEMBER OFFSETS
MEMBER0 303 403
MEMBER1 305 201
MEMBER OFFSETS
MEMBER1 305 307
MEMBER OFFSETS
MEMBER1 305 309
MEMBER OFFSETS
MEMBER0 305 405
MEMBER1 307 205
MEMBER OFFSETS
MEMBER1 307 309
MEMBER OFFSETS
MEMBER0 307 407
MEMBER01101 101
MEMBER01105 105
MEMBER01201 201
MEMBER01205 205
MEMBER01301 301
MEMBER01305 305
MEMBER021011101
MEMBER021051105
MEMBER022011201
MEMBER022051205
MEMBER023011301
MEMBER023051305
MEMBER025011501
MEMBER025051505

T03
-11.89

-17.20

3.59

5.20

LG4
T01
17.15 29.48

-26.54-45.63

T03
20.67

-20.77

T03
11.78

17.05 -3.59

-5.20

LG4
T01
-3.41 27.30-18.04
T03
11.89
LG4
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP
GAP

5-11

-17.20

3.91-31.28 20.67

Gap
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
*********** Additional JOINT data *************
JOINT 1101 38.550164.042 -4.000
JOINT 1105 -38.550164.042 -4.000
JOINT 1201 26.657 68.898 -4.000
JOINT 1205 -26.657 68.898 -4.000
JOINT 1301 17.224 -6.562 -4.000
JOINT 1305 -17.224 -6.562 -4.000
JOINT 2101 38.550164.042 -8.000
JOINT 2101
-50.000
JOINT 2105 -38.550164.042 -8.000
JOINT 2105
-50.000
JOINT 2201 26.657 68.898 -8.000
JOINT 2201
-50.000
JOINT 2205 -26.657 68.898 -8.000
JOINT 2205
-50.000
JOINT 2301 17.224 -6.562 -8.000
JOINT 2301
-50.000
JOINT 2305 -17.224 -6.562 -8.000
JOINT 2305
-50.000
JOINT 2501 34.920135.000 -8.000
JOINT 2501
-50.000
JOINT 2505 -34.920135.000 -8.000
JOINT 2505
-50.000
LOAD
LOADCN A1
LOAD
112
-4.0000
LOAD
109
-4.0000
LOAD
110
-4.0000
LOAD
111
-4.0000

111000
PERSET DFL2101
3
111000
PERSET DFL2105
3
111000
PERSET DFL2201
4
111000
PERSET DFL2205
4
111000
PERSET DFL2301
5
111000
PERSET DFL2305
5
111
PERSET DFL2501
111
PERSET DFL2505

GLOB
GLOB
GLOB
GLOB

JOIN
JOIN
JOIN
JOIN

6
6

MUDMAT
MUDMAT
MUDMAT
MUDMAT

********* Additional dead loading ****************
LOADCN A3
LOADCN A4
LOADCN A5
LOADCN A6
LOADCNDM07
LOAD X 21011101
LOAD X 11012101
LOADCNDM08
LOAD X 21051105
LOAD X 11052105
LOADCNDM09
LOAD X 22011201
LOAD X 12012201
LOADCNDM10
LOAD X 22051205
LOAD X 12052205
LOADCNDM11
LOAD X 23011301
LOAD X 13012301
LOADCNDM12
LOAD X 23051305
LOAD X 13052305
LOADCNDM13
LOAD X 25011501
LOAD X 15012501
LOADCNDM14
LOAD X 25051505
LOAD X 15052505
END

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

1.00000
-1.0000

MEMB CONC
MEMB CONC

DUMMY
DUMMY

5-12

Gap
Below is the Gap input file used for the non-linear gap analysis. A detailed description of
the input file follows:
1
2
3
4
5
6
7
8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
A
B
C

GAPOPT
LCSEL
LCOMB

6

5

1

EN
A1
A2
A3
1 1.0
2 1.0

D

LCOMB

2

1 1.0

2 1.0

3 1.0

E

LCOMB

3

1 1.0

2 1.0

4 1.0

E

LCOMB

4

1 1.0

2 1.0

5 1.0

E

LCOMB

5

1 1.0

2 1.0

6 1.0

F

GAPELM 2101 1101 DM07

CO

G

GAPELM 2105 1105 DM08

CO

H

GAPELM 2201 1201 DM09

CO

I

GAPELM 2205 1205 DM10

CO

GAPELM 2301 1301 DM11

CO

GAPELM 2305 1305 DM12

CO

GAPELM 2501 1501 DM13

CO

GAPELM 2505 1505 DM14

CO

A4
2

A5

A6

END

A. The GAPOPT input designates the analysis options as follows:
a. English units are designated in columns 21-22.
b. As specified in columns 7-10, six load cases specified in the model input file are
to be considered ‘Real’ load cases that are to be referenced by ‘Output’ load
combinations.
c. Five ‘Output’ load combinations will be analyzed as designated in columns 1114.
B. Load cases A1 through A6 defined in the SACS model file are ‘Real’ load cases that
will be referenced by ‘Output’ load combinations defined in the GAP input file.
C. The first ‘Output’ load combination represents the fully supported condition and is
defined on the first LCOMB input line as follows:
a. The load combination number is 1 as designated in column 10.
b. The combination consists of 100% of load cases A1 and A2 defined in the model
input file.
D. The second ‘Output’ load combination represents the load condition when support
joints 2101 and 2105 are not effective and is defined as follows:
a. The load combination number is 2 as designated in column 10.

5-13

Gap
b. The combination consists of 100% of load cases A1 and A2 along with 100% of
load case 3 defined in the model input file.
Note:

The factor applied to the specified deflection must ensure that
the total deflection induced at the support joint is greater than
the deflection that would occur if the joint was un-supported.

E. ‘Output’ load combinations 3-5 represent the condition when support joints 2201 and
2205, 2301 and 2305 and 2501 and 2505, respectively, are ineffective.
F. Element 2101-1101 was designated as a tension only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case DM07 defined in the model file
corresponds to this element.
c. The element is defined as a compression only element by ‘CO’ in columns 2425.
G. Element 2105-1105 was designated as a compression only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case DM08 defined in the model file
corresponds to this element.
c. The element is defined as a compression only element by ‘CO’ in columns 2425.
H. Element 2201-1201 was designated as a compression only gap element.
a. The member connecting joints were input in columns 7-11 and 12-16,
respectively.
b. As specified in column 21, dummy load case DM09 defined in the model file
corresponds to this element.
c. The element is defined as a compression only element by ‘CO’ in columns 2425.
I.

Elements 2205-1205, 2301-1301, 2305-2305, 2501-1201 and 2505-1505 were also
designated as compression only gap elements using GAPELM input lines.

The following is a portion of the output listing file created by the Gap program module:

5-14

GAP SAMPLE PROBLEM 2
PAGE
1

DATE 04-JUN-1996

TIME 13:53:19

PRE

PRE VERSION IV.F.002
** PROGRAM OPTIONS **
UNITS
....ENGLISH
REPORTS SELECTED
....ELEMENT STRESS AT MAXIMUM UNITY CHECK...PRINT
....JOINT REACTIONS.........................PRINT
LOAD
....NO. BASIC LOAD COND. 14
....NO. COMB. LOAD COND.
0
APPLIED LOAD SUMMARY
LOAD CASE

5-15

A1
A2
A3
A4
A5
A6
DM07
DM08
DM09
DM10
DM11
DM12
DM13
DM14

TOTAL FORCE(X)
KIPS
0.000000E+00
-4.097748E-08
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

TOTAL FORCE(Y)
KIPS
0.000000E+00
1.240194E-06
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

TOTAL FORCE(Z)
KIPS
-3.483669E+01
-5.707035E+02
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

GAP SAMPLE PROBLEM 2
2

PAGE

EL NO. GAP ELEMENT

TYPE

LOAD CASE 1
DEFLECTION
IN
-0.00199
-0.00180
-0.00273
-0.00315
-0.00141
-0.00130
-0.00074
-0.00075
0 ITERATIONS

FORCE
KIPS
-87.0
-78.4
-119.2
-137.6
-61.5
-57.0
-32.3
-32.6

TIME 13:53:28

FACTOR

0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

Gap

1
2101-1101
COMP
2
2105-1105
COMP
3
2201-1201
COMP
4
2205-1205
COMP
5
2301-1301
COMP
6
2305-1305
COMP
7
2501-1501
COMP
8
2505-1505
COMP
LOAD CASE
1 CONVERGED IN

DATE 04-JUN-1996

NO.

GAP ELEMENT

TYPE

1
2101-1101
COMP
2
2105-1105
COMP
3
2201-1201
COMP
4
2205-1205
COMP
5
2301-1301
COMP
6
2305-1305
COMP
7
2501-1501
COMP
8
2505-1505
COMP
LOAD CASE
2 CONVERGED IN

LOAD CASE 2
DEFLECTION
IN
49.11930
49.14309
-0.00493
-0.00511
0.24707
0.25432
-0.00196
-0.00188
30 ITERATIONS

TYPE

LOAD CASE 3
DEFLECTION
IN

1
2101-1101
COMP
2
2105-1105
COMP
3
2201-1201
COMP
4
2205-1205
COMP
5
2301-1301
COMP
6
2305-1305
COMP
7
2501-1501
COMP
8
2505-1505
COMP
LOAD CASE
3 CONVERGED IN

-0.00306
-0.00309
49.70562
49.69422
-0.00301
-0.00294
-0.00085
-0.00092
30 ITERATIONS

NO.

5-16

NO.

GAP ELEMENT

GAP ELEMENT

TYPE

1
2101-1101
COMP
2
2105-1105
COMP
3
2201-1201
COMP
4
2205-1205
COMP
5
2301-1301
COMP
6
2305-1305
COMP
7
2501-1501
COMP
8
2505-1505
COMP
LOAD CASE
4 CONVERGED IN

LOAD CASE 4
DEFLECTION
IN
-0.00095
-0.00065
-0.00509
-0.00565
49.54753
49.55187
-0.00079
-0.00075
30 ITERATIONS

FORCE
KIPS
0.0
0.0
-215.0
-222.9
0.0
0.0
-85.5
-82.2

FORCE
KIPS
-133.8
-135.0
0.0
0.0
-131.4
-128.3
-37.2
-40.1

FORCE
KIPS
-41.4
-28.4
-222.1
-246.6
0.0
0.0
-34.5
-32.9

FACTOR

-0.214431E+07
-0.214534E+07
0.000000E+00
0.000000E+00
-0.107857E+05
-0.111024E+05
0.000000E+00
0.000000E+00

FACTOR

0.000000E+00
0.000000E+00
-0.216990E+07
-0.216940E+07
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00

FACTOR

0.873195E-01
0.849600E-01
0.000000E+00
0.000000E+00
-0.216300E+07
-0.216319E+07
0.000000E+00
0.000000E+00

Gap

NO.

GAP ELEMENT

TYPE

1
2101-1101
COMP
2
2105-1105
COMP
3
2201-1201
COMP
4
2205-1205
COMP
5
2301-1301
COMP
6
2305-1305
COMP
7
2501-1501
COMP
8
2505-1505
COMP
LOAD CASE
5 CONVERGED IN

LOAD CASE 5
DEFLECTION
IN
-0.00256
-0.00230
-0.00286
-0.00339
-0.00143
-0.00133
49.61086
49.60733
30 ITERATIONS

FORCE
KIPS

SACS-IV SYSTEM

JOINT LOAD
NUMBER CASE

-111.8
-100.3
-124.9
-148.0
-62.5
-58.0
0.0
0.0

FACTOR

0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
-0.216576E+07
-0.216561E+07

REACTION FORCES AND MOMENTS

******************** KIPS *******************
FORCE(X)
FORCE(Y)
FORCE(Z)

****************** IN-KIPS ******************
MOMENT(X)
MOMENT(Y)
MOMENT(Z)

-1.473
3.673
-1.690
-0.645
-3.934

-6.357
38.480
-9.433
0.925
-30.030

86.951
-0.060
133.794
41.324
111.840

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

2105

1
2
3
4
5

6.269
1.317
6.142
5.869
9.534

-6.982
32.471
-4.756
-4.012
-31.304

78.416
-0.060
135.014
28.314
100.350

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

2201

1
2
3
4
5

-14.783
-19.761
-14.381
-15.868
-12.565

-2.390
-48.786
-2.292
-7.669
24.035

119.173
215.041
-0.196
222.094
124.901

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

2205

1
2
3
4
5

5.686
11.561
4.613
6.922
2.356

-3.539
-45.860
-6.335
-6.333
22.283

137.592
222.949
-0.216
246.592
147.979

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

2301

1
2
3
4
5

-0.778
-3.311
0.980
-2.223
-0.151

17.219
-3.735
31.409
4.030
22.367

61.511
-0.052
131.443
-0.063
62.521

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

Gap

1
2
3
4
5

5-17

2101

2305

1
2
3
4
5

4.865
5.517
4.847
5.111
4.510

15.138
-0.960
24.508
6.463
20.093

56.958
-0.050
128.335
-0.063
58.029

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

2501

1
2
3
4
5

-6.809
-3.774
-8.544
-5.180
-7.670

-5.522
18.044
-17.930
6.469
-12.498

32.306
85.547
37.223
34.483
-0.040

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

2505

1
2
3
4
5

7.023
4.777
8.032
6.014
7.921

-7.567
10.345
-15.171
0.127
-14.945

32.632
82.228
40.143
32.861
-0.040

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000

SACS-IV SYSTEM

MEMBER

5-18

112201201201-

111
105
203
301

GRP

T01
T02
T01
LG3

MAXIMUM CRITICAL LOAD
UNITY
COND. CASE
CHECK
NO.

DIST
FROM
END
FT

ELEMENT STRESS REPORT AT MAXIMUM UNITY CHECK

********** APPLIED STRESSES **********
AXIAL
** BENDING **
*** SHEAR ***
Y-Y
Z-Z
Y
Z
KSI
KSI
KSI
KSI
KSI

* CM VALUES *
Y

Z

* NEXT TWO HIGHEST CASES *
UNITY LOAD
UNITY LOAD
CHECK COND
CHECK COND

0.132
0.387
0.509
0.091
0.122
0.052

C<.15
C<.15
C>.15A
C<.15
C<.15
TN+BN

5
5
2
4
4
3

0.00
0.00
53.96
0.00
6.73
76.05

-0.44
-0.21
-4.02
-0.37
-0.52
0.40

-2.52
-9.03
0.79
-2.71
-2.47
-1.45

0.46
-0.01
-1.96
0.00
-0.01
-0.02

0.15
0.38
0.04
0.26
0.31
0.20

-0.23
-0.02
-0.01
-0.05
-0.07
-0.05

0.85
0.85
0.85
0.85
0.85
0.85

0.85
0.85
0.85
0.85
0.85
0.85

0.13
0.38
0.50
0.08
0.10
0.04

4
2
4
2
2
2

0.13
0.37
0.20
0.06
0.08
0.03

1
4
1
5
3
4

203- 207 T01
0.115
203- 301 T01 101.258
203- 303 LG3
0.099
0.139
0.017
205- 107 T02
1.314

TN+BN
EULER
C<.15
C<.15
C<.15
C>.15A

4
3
4
4
4
4

0.00
89.12
0.00
6.73
72.06
0.00

0.57
-3.93
-0.02
-0.03
-0.04
-2.34

-2.40
-5.39
-3.69
-3.71
0.55
-8.56

0.02
0.35
-0.01
-0.01
0.03
0.14

0.20
0.23
0.28
0.34
0.07
0.33

0.02
-0.08
0.08
0.11
0.08
0.08

0.85
0.85
0.85
0.85
0.85
0.85

0.85
0.85
0.85
0.85
0.85
0.85

0.11
0.40
0.10
0.14
0.02
1.21

2
5
2
2
2
2

0.11
0.38
0.09
0.13
0.02
0.42

3
2
5
5
5
3

GAP
GAP
GAP
GAP

0.207
0.210
0.373
0.355

C<.15
C<.15
C<.15
C<.15

5
5
2
2

4.00
4.00
4.00
4.00

-1.53
-1.38
-2.96
-3.07

-3.61
-3.77
-5.87
-5.52

-0.47
1.15
-2.38
1.39

0.84
0.91
1.46
1.31

0.00
0.00
0.00
0.00

0.85
0.85
0.85
0.85

0.85
0.85
0.85
0.85

0.17
0.15
0.22
0.20

2
2
4
4

0.13
0.12
0.20
0.20

3
3
5
5

2301-1301
2305-1305
2501-1501
2505-1505

GAP
GAP
GAP
GAP

0.225
0.194
0.137
0.103

C<.15
C<.15
C<.15
C<.15

3
3
2
2

4.00
4.00
4.00
4.00

-1.81
-1.76
-1.17
-1.12

3.78
2.95
2.17
1.24

0.12
0.58
-0.45
0.57

0.87
0.69
0.51
0.32

0.00
0.00
0.00
0.00

0.85
0.85
0.85
0.85

0.85
0.85
0.85
0.85

0.14
0.13
0.11
0.10

5
5
3
3

0.12
0.11
0.07
0.08

1
1
5
5

Gap

2101-1101
2105-1105
2201-1201
2205-1205

SACS-IV SYSTEM

MEMBER
NUMBER
2101-1101

MEMBER
END
2101

GROUP LOAD
ID
CASE

2105

-1.4730
3.6731
-1.6902
-0.6451
-3.9336
-1.4730
3.6731
-1.6902
-0.6451
-3.9336

-6.3570
38.4800
-9.4330
0.9248
-30.0304
-6.3570
38.4800
-9.4330
0.9248
-30.0304

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
-305.1352
1847.0270
-452.7845
44.3950
-1441.4681

0.0000
0.0000
0.0000
0.0000
0.0000
-70.7041
176.3070
-81.1357
-30.9622
-188.8123

GAP

1
2
3
4
5
1
2
3
4
5

-78.4158
0.0600
-135.0141
-28.3137
-100.3496
-77.4318
1.0440
-134.0301
-27.3297
-99.3656

6.2689
1.3172
6.1418
5.8687
9.5335
6.2689
1.3172
6.1418
5.8687
9.5335

-6.9819
32.4712
-4.7557
-4.0117
-31.3042
-6.9819
32.4712
-4.7557
-4.0117
-31.3042

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
-335.1334
1558.6323
-228.2783
-192.5627
-1502.5996

0.0000
0.0000
0.0000
0.0000
0.0000
300.9077
63.2259
294.8047
281.6972
457.6105

GAP

1
2
3
4
5
1
2
3
4
5

-119.1732
-215.0407
0.1956
-222.0937
-124.9005
-118.1892
-214.0567
1.1796
-221.1097
-123.9165

-14.7830
-19.7610
-14.3811
-15.8679
-12.5655
-14.7830
-19.7610
-14.3811
-15.8679
-12.5655

-2.3901
-48.7861
-2.2921
-7.6687
24.0347
-2.3901
-48.7861
-2.2921
-7.6687
24.0347

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
-114.7239
-2341.7461
-110.0213
-368.1017
1153.6836

0.0000
0.0000
0.0000
0.0000
0.0000
-709.5855
-948.5327
-690.2904
-761.6568
-603.1403

GAP

1
2
3
4
5
1
2
3
4
5

-137.5916
-222.9486
0.2158
-246.5916
-147.9794
-136.6076
-221.9646
1.1998
-245.6076
-146.9954

5.6863
11.5610
4.6135
6.9224
2.3556
5.6863
11.5610
4.6135
6.9224
2.3556

-3.5390
-45.8596
-6.3347
-6.3329
22.2832
-3.5390
-45.8596
-6.3347
-6.3329
22.2832

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
-169.8722
-2201.2666
-304.0704
-303.9780
1069.5961

0.0000
0.0000
0.0000
0.0000
0.0000
272.9426
554.9236
221.4536
332.2755
113.0649

1201

2205-1205

2205

1205

Gap

-86.9513
0.0597
-133.7944
-41.3237
-111.8397
-85.9673
1.0437
-132.8104
-40.3397
-110.8557

5-19
2201

****************** IN-KIPS ******************
MOMENT(X)
MOMENT(Y)
MOMENT(Z)

1
2
3
4
5
1
2
3
4
5

1105

2201-1201

******************* KIPS ********************
FORCE(X)
FORCE(Y)
FORCE(Z)

GAP

1101

2105-1105

MEMBER FORCES AND MOMENTS

SACS-IV SYSTEM

MEMBER
NUMBER
2301-1301

MEMBER
END
2301

GROUP LOAD
ID
CASE

2305

-0.7779
-3.3113
0.9804
-2.2231
-0.1506
-0.7779
-3.3113
0.9804
-2.2231
-0.1506

17.2189
-3.7346
31.4089
4.0301
22.3667
17.2189
-3.7346
31.4089
4.0301
22.3667

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
826.5083
-179.2459
1507.6266
193.4536
1073.5979

0.0000
0.0000
0.0000
0.0000
0.0000
-37.3377
-158.9427
47.0575
-106.7132
-7.2291

GAP

1
2
3
4
5
1
2
3
4
5

-56.9585
0.0502
-128.3345
0.0630
-58.0293
-55.9745
1.0342
-127.3505
1.0470
-57.0453

4.8651
5.5175
4.8472
5.1107
4.5098
4.8651
5.5175
4.8472
5.1107
4.5098

15.1381
-0.9604
24.5078
6.4630
20.0932
15.1381
-0.9604
24.5078
6.4630
20.0932

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
726.6300
-46.0952
1176.3783
310.2241
964.4742

0.0000
0.0000
0.0000
0.0000
0.0000
233.5232
264.8390
232.6626
245.3151
216.4733

GAP

1
2
3
4
5
1
2
3
4
5

-32.3064
-85.5473
-37.2232
-34.4828
0.0400
-31.3224
-84.5633
-36.2392
-33.4988
1.0240

-6.8090
-3.7735
-8.5438
-5.1802
-7.6699
-6.8090
-3.7735
-8.5438
-5.1802
-7.6699

-5.5215
18.0441
-17.9301
6.4687
-12.4980
-5.5215
18.0441
-17.9301
6.4687
-12.4980

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
-265.0344
866.1160
-860.6477
310.4947
-599.9017

0.0000
0.0000
0.0000
0.0000
0.0000
-326.8343
-181.1304
-410.0985
-248.6480
-368.1559

GAP

1
2
3
4
5
1
2
3
4
5

-32.6320
-82.2276
-40.1427
-32.8614
0.0395
-31.6480
-81.2436
-39.1587
-31.8774
1.0235

7.0227
4.7771
8.0322
6.0145
7.9206
7.0227
4.7771
8.0322
6.0145
7.9206

-7.5675
10.3453
-15.1710
0.1268
-14.9454
-7.5675
10.3453
-15.1710
0.1268
-14.9454

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0.0000
0.0000
0.0000
0.0000
0.0000
-363.2393
496.5809
-728.2051
6.0871
-717.3825

0.0000
0.0000
0.0000
0.0000
0.0000
337.0882
229.3018
385.5427
288.6943
380.1901

1501

2505-1505

2505

1505

Gap

-61.5114
0.0516
-131.4432
0.0634
-62.5214
-60.5274
1.0356
-130.4592
1.0474
-61.5374

5-20
2501

****************** IN-KIPS ******************
MOMENT(X)
MOMENT(Y)
MOMENT(Z)

1
2
3
4
5
1
2
3
4
5

1305

2501-1501

******************* KIPS ********************
FORCE(X)
FORCE(Y)
FORCE(Z)

GAP

1301

2305-1305

MEMBER FORCES AND MOMENTS

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