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ERRA'f.t.\.----Page 1 - First paragraph, 18~t sentence
. ClW,~g€; "lengths artd panel i, to !(?,sd "lengths a panel' n
P.ag.e: 2 ... Secof.1d p~ragraph~ second sentenceChimge; ffcompleted" to I completely"
Seem:;d p6:t'sgraph, Last sentence:Omit: "nO',," .
Page 3 ~ P'cog:;:sm ps:-t n.o, 3ctwnge to ~EGd; Function Be ~hich finds the zero root of a:lad order: paraboLic equation.by ul.dng NII!'\I1lon's Methoo 'f()':Find! ng Ze't'o8 o
Psge.5 Par:t U.-I) No. 2bC'hrm.ge; J'exce-ptable" to I eccl:~pt:C:lb1.l:.~"
P1I4le 6 ~ Var:b.b1e QICC'h:cnge; "j.ntet·~tiotli' to "ltFJr8{:io:rl"
Page 3 - ProgT~m part no o 3~;'hif.lng;e to :read; Function '\I'At. which (:omp.v.:tes' a valneusing 8 pa~abolic equ~tion<o
.~.~-~_....._--_...-----_..__._ ...----...--_.._.__.,.__....-"·-·--·---"-~r----"'-'-"·-·--·--"-_··_·-""---------""--~"'----'" --..,. ...-Po 9 of 1.3
0.5 * Q it C2)e12 :lr C3)
0,125 * ex * eIfe2 "
x(12) ~ ~(11) - C2 * (C13 += C3 *' (C14/REL + ,~.5 '*
I! Shou.l'd reed
iI1
~. ~
i,
'* (C3 .• (;.R '* CS).'K(17) + C12
x (18) "'" elf•.f' ell 't:' (''R * CS
x(12) = x(ll) • (C2 * eel3 - 00 5 • Qe2) + C3 * (Cl4 - 0.5 * C12 *(3»!REL
AL(K) '"" AL(K - Z) w <05 'ii," Cl ..,~ el/el
II,,I
I :;-r,(l8) "" CJ.4 + e12 Iii: cn. ~\' ilE".£. ~~ CS
II .AL(l() '" AL(K :'" 2}
" l ._.-'-----_.-..,.---_._-_.__ _..__ -.~". __ _.__.._-:. _--~_._._._._-~.-._-.._ __._-----_ _-_.__._------------
• BUILT-UP MEMBERS IN PLASTIC DESIGN
COMPUTER PROGRAM FOR
ULTIMATE STRENGTH OF
LONGITUDINALLY STIFFENED PANELS
(SMALL bit)
by
Bruce A.Bott
Jun Kondo
Alexis Ostapenko
This work has been carried out as a part ofan investigation sponsored by the Departmentof the Navy with funds furnished by theBureau of Ships Contract; NObs-94092
Reproduction of this report in whole or inpart is permitted for any purpose of theUnited States Government.
Fritz Engineering LaboratoryDepartment of Civil Engineering
Lehigh UniversityBethlehem, Pennsylvania
May, 1966
Fritz Engineering Laboratory Report No. 248.16
..
..
248.16
INTRODUCTION
One of the more common ship building elements are the longi
tudinally stiffened plates of Fig. l(a).(l) Their frequent use in
ships makes a thorough knowledge of their behavior important.
Consequently, a computer program was developed for the analysis of
such sections subjected to the combined transverse and axial loading
shown in Fig. l(b). The program described in this report is an
improved Fortran II version·of the program originally written in ~IZ*
Q
by Jun Kondo. The prog.ram analyzes a stiffened plate panel and
determines the maximum fixed and simply supported lengths and panel
can have under a given loading.
The analysis is basically a two step process. The main program
first develops'a moment-curvature-thrust curve for the given section.
Then the integration subroutine determines the maximum fixed and
simply supported lengths allowable for a series of midpoint starting
curvatures. Plotting these maximum lengths against the midpoint
starting curvatures produces a curve which is concave downward. The
peak on this curve is the maximum length the panel can have under
the given loading.
In the course of this analysis, the effects of residual
stresses and differing yield points in the stiffener and in-the
plate are considered. There are no limitations imposed on the
relative proportions of the cross section other than the requirement
* A GE compiler used at Lehigh University
248.16 -2
that the ratio of the stiffener spacing to the plate thickness (bit)
be sufficiently small (less than about 40) to prevent plate buckling.
In the integration procedure used in the program, the section
is called upon to resist both positive and negative bending moments.
However, it was found that, for hybrid sections (different yield
points in plate and stiffeners) subjected to high values of axial
load, the moment-curvature curve would shift under varying load until
it was completed on one side of the curvature axis (only positive or
only negative moments). Such a position indicates that under axial
load alone, the section requires the application of some internal
moment along its center line in order to maintain equilibrium. The
integration cannot be performed for such cases qnd this is now
printed out on the output.
In addition to this alteration, provision has also been made for
some identifying run or data set number to be included on the output.
This humber which is part of the input data, appears on the various
pages of the output and aids in correlating results with input datq.
The text of this report deals primarily with the preparation of
data for the program, technical information about the program and its
operation, and an explanation of the output. The appendices include
a program listing (the main program, integration subroutine, and two
required functions) and a series of exa~ple runs. The arrangement of
the explanatory text conforms to the standards of Ship Design,
Division Instruction 10462 of the Bureau of Ships, U. S. Navy.
...
•
248.16
PART I - IDENTIFICATION
-3
•
..
..
1. Title: Ultimate Strength of Longitudinally Stiffened Panels
(SMALL bit)
2. Brief Description: On the basis of a computed M-0-P curve
for the section under analysis, the program makes successive
computations of the fixed and simply supported panel lengths
corresponding to a given loading for each of a series of
mid-point curvatures. By comparing each new set of lengths
with those obtained on the last try, the maximum length is
determined.
The program consists of four parts:
1) The main program which provides the M-0-P relationship
for the section .
2) Subroutine INTEG (integration) which determines the simply
supported and fixed lengths corresponding to a given combi
nation of axial and lateral load for some midpoint curvature.
3) Function BC which computeq, by parabolic interpolation, the
peak value between 3 pts. on a curve.
4) Function VAL which computes, by parabolic interpolation,
the peak value between 3 points on a curve.
Input data is read directly from cards into the main program.
Termination occurs when an END card is read. (The main program
will iterate through successive sets of data and within each of
these sets, subroutine INTEG will iterate the value of lateral
loading) .
3. a) .Author: JunKondo, Bruce A. Bott, and Alexis Ostapenko,
Lehigh University .
b) Date: May, 1966
.;:~ 248.16
4. Code: Fortran II
5. Machine: GE225 (any other machine accepting Fortran II may
be used).
6. Security Classification: Unclassified
.7. Estimated Running Time: Punch input data 1.0 min
-4
Run time
Total
PART II - PURPOSE & METHOD
2.5 min
3.5 min
..
1 .. Description of Theory: See "Ultimate Strength of Longitudinally
Stiffened Plate Panels Subjected ,to Combined Axial and Lateral
Loading", by Jun Kondo, Fritz Engineering Laboratory Report
No. 248.13, Lehigh University, 1965.
2. Assumptions:
1) No buckling - as a result, the program is applicable only
to sections with low bit ratios.
2) The edges of the plate are assumed.free.
3) The distribution of the residual stresses in the plate is
assumed to be rectangular. The residual stress distri
bution in the stiffener flange iS,assumed to be triangular.
The residual stresses in the web of the stiffener have
small effect and are therefore neglected. (See Fig. 2).
3. References: See report listed in 1) above .
..
248.16
PART III - RESTRICTIONS
1. General Restriction$: None
2. Limitations For Use:
a) The condition of GFC = GFT = 0 (no residual stress in the
stiffener flange) will not run. (It results in division
by zero).
b) Ratios of GST > 2.0 do not produce exc.eptable results in
all cases and the output should be closely examined.
3. Nonstandard Hardware &- Tapes: None
4. Maximum Array Sizes: 6 Arrays are used: FI (200)
CM (200)
EPS (200)
AL (30)
X (25)
B (14)
PART IV - NONSTANDARD MACHINE
OPERATING INSTRUCTIONS
1. Special Operating Instructions: None
2. Restart Instructions: None
3. Error Correction: None
-5
248.16 -6
PART V - DATA PREPARATION
J
l. Card .Input Form:"
Card Format Variable Name
1 15 IRUN
2 7F10 .4 AST
D
AFF
GRC
. GST
GFC
GFT
3 6F1O.4 P
QI
QIC
QMAX
DSI
FIC
. Comment
Label for data set (i. e. -set #15)
Nondimensional area of stiffener
Nondimensionaldepth
Nondimensional area of flange
Nondimensional residual stressin plate
Ratio of yield stress in stiffenerto yield stress in plate
Nondimensional compressive residual stress in stiffener flange
,Nondimensional tensile residualstress in stiffener flange
Nondimensional axial load
Nondimensional initial value oflateral load (for iteration insubroutine)
Nondimensional increment of lateralload (for interation in subroutine)
Nondimensional maximum value oflateral load to be run
Increment of panel length to beused in subroutine Integ
Increment of curvature for subrOl:l.tine Integ
For additional data sets repeat the above sequence.
Last card - End (1st 3 columns) this terminates the run with an
illegal character on a data card.
248.16 -7
Format2. . Sample Input: Comment
55 IS
.3 10.0 .45 0.0 1.0 0.3 0.3 7F1O.4
.4 0.0 3.0 3.0 .18 .15 6F10.4
3. Output Form Description:
Comment
..
1 &- 2
5
Lists input data and run number for checking and later
identification. Lists some computed member properties
(identified on output). Lists 201 points on the M-0-P
plot for the given panel.
Lists values of axial load P and lateral load Q.
Lists length, lateral midheight deflection, vertical
movement of ends, fixed end moment, and end slope for
a given midheight curvature. For each value of mid
height curvature, this information is produced twice,
once for the fixed condition and once for the pinned
end condition.
As a peak of L is passed in each of the plots of PHC vs.
L, (fixed end and pinned end) the peak value of L and the
corresponding values of other quantities are computed
and printed.
Summary of results for each combination of axial and
lateral load.
4. Symbol List and Definitions:
•
A
AF
AFF
Total area of section divided by area of plate
Area of flange divided by area of plate
Area of stiffener flange divided by area of stiffener
oJCDepending on amount of output
FI Curvature array for the M - 0 - P plot
FIC Increment of curvature in the integration subroutine
FlO Curvature at point zero (see EPSO)
..
248.16
AI
AMPN
AST
AW
B
BC
BRC
BRT
CM
CMO
COSF
D
Dl
D3
DSI
EPS
EPSO
EY
-8
Moment of inertia of the section (Nondimensional)
Negative plastic moment capacity of the section(Nondimensional)
Stiffener cross sectional area divided by area ofplate
Area of web divided by area of plate
Matrix which stores the results obtained by the integration subroutine for later printing in the summaryof results
Function which establishes equilibrium and compatibility for each length increment
Total width of compressive residual stress zone in theplate divided by the total plate width
Width of tensile residual stress zone in plate dividedby total plate width
Moment array for the M - 0 - P Plot
Moment at point zero (see EPSO)
Cosine function
Depth of stiffener divided by plate thickness
Total section depth divided by plate thickness
Distance from elastic neutral axis to the extreme fiberin the stiffener flange divided by the plate thickness
Increment of length ~sed in the integration subroutine
Strain in the extreme fiber of the plate'
In the original language used for this program, dimensi
oning an array for 200 locations reserved 201 machine
locations (0-200 inclusive). In Fortran II, dimensioning
for 200 locations reserves exactly 200 locations (1-200
inclusive). Therefore in the Fortran II translation, it
was necessary to create the variable EPSO to correspond
to the location EPS(O) in the original version.
Yield strain
248.16
GFC
GFT
GRC
GST
H
I
I RUN
ISW
ISWA
ISWB
ISWC
ISWD
JA
JB
K
N
P
PHC
Q
...,9
Compressive residual stress in the stiffener flange
(Ofc) divided by the yield stress of the plqte (Oyp)*
Tensile residual stress in the stiffener flange (aft)
divided by the yield stress of the plate*
Compressive residual stress in the plate (0 ) dividedrcby the yield stress of the plate*
Yield point in the stiffener divided by the yield
point in the plate
Resultant force acting on the cross sect,ion in the
z-direction
Counter
Run number or data set number
Switching parameter
Switching parameter
Switching parameter
Switching parameter
Switching parameter
Counter
Counter
Counter
Counter
Nondimensional axial load as a fraction of the yield
axial load (P/Py )**, where Py = (yield point of plate)
x (total panel area)
Curvature at the midheight of the section
Lateral load (Nondimensional) (Q=(q)(E)(b)(d)/(yield
point of plate)2 (total area) where:
q = Hydrostatic pressure on section
E = Modulus of elasticity
b = Stiffener spacing
d = Distance from elastic neutral axis to extreme•fiber in stiffener flange)
See Fig. 2oJd: Note that this quantity can reach a value greater than 1.0 f()r
some sections.
..248.16
QI
QIC
QMAX
S
SINF
SQRTF
VAL
W
Initial lateral load value to be run
Increment of lateral load in the integration sub
routine
Maximum lateral load value to be run
Section modulus (Nondimensional)
Sine Function
Square root function
Function for parabolic interpolation of curve peaks
Thickness of the stiffener web divided by the plate
thickness
-10
The following variables and arrays are intermediate and have no
general definition:
..
~':
Array
AU"
Cl
C2
C3
Cll
C12
Cl3
C14
F
• •
...._ _._-- ----------------------------------_ ..__._-------
C
.CCCCCC
(;
CCCC
CCCC
ccCC
.1HlS 15 THE EE.GllltbtlN!i._Or TWI' lUI .. pAMpA" .... ZCN COMII"U THEMOME~T - CU~vAT~RE • THRLST CUAVf rOR THE GIYIN SICTION.
..._----_ .._--_._----------ALL r.UANTITIfS ARE PLAcer IN CO~~ON SO THAT THEY WILL BE AVAILABLETO nE SUI:lROlT I~E AIIII) THEF".u~T~S-.lLIUU ARE REDUIRED,
COhMO" lLl\I.~. E£S•. 8RT' X, !Iwe. fl. el, liST' EPID. Elu. gl. [ •.a.lP. 1i1::L.. l,wA, ISWB, ISWC. ISWD. IS", AI.. DII. CM. CMU. "'1.1. JI:l.2C1. C2, CJ; REY. Cll, c:.12L~U--e.u.~CR. AM'N • .c.5..--.CA. ct!. K.3£lr, l~, OMA., OIC, IRUN
20U FOINTS wILL 4F COMPUTED ON THe M •. PHI. P CUAveHENCE. 200 lCCA[ICJl/S_U,nl"ENSION~1l rcR MOM& .. T leMI. CURYATuRE( FI I. ~N" STRAI~ I~ THF oUTER rlRER or THe PLATE I EPS I.
UI~~NSIUN CM[200J. FI12UOI.EPS[200J, 'lI301, X12'1
~CAU IN THE "AlA SET NUM~ER AND P~INT IT ON THE Top or THE ~-IHSTPAGE nF CUTPl. T• ~_. .___ _ .. .__.__._ ....
1 READ' 33. fRUN3~ £OPMAT [ 10; )
PRINT 200. IRUIII20n £ORM~T [ 9HIDATA SET, 15 1
....... ---_...... ---_.--=-:--::----,------.,.:-::------RcAU THI:: NI::Ci::SSASY INPUT DATA '~D PRINT IT OUT ON THE OUTPUT SHEI::TSO nAT INPU! CAN liE CORAELATtD wITH H.ESULTS. .
PAINT ?Ul201 FOFM~T [114UINPUT OATAII)
READ ~ G, AS T, a.UE .I1RC.G..S.J .G$C.ll£.I.I'-_ • g I. Q 1C, gMU. OS 1. f1 C2U ~UPMAr 17fl0.4J
PH I II: T 31 ....31 FOPMAT [ 140, IX, 3HAST, lX, IHD, IX, 3HArF, 6X, JHGHC. 61(.
1 3I-GST. 6X, 3H'iEC, 6X, JHGrr. 1X•.1HP. 1X•.~L... 6X~ .3Hr.ilC-L5.x,_? 4"'OMA" ex. 31;051, 6X, ,3HFrc, III
FRI/IlT ~O. AST,.O, Af'E •..~_~T....Gr.c.... GrT. , •.....Q..l.........o.t.4.. Q''14X. DSI.1 E I e
3n £O"MAT [ 1~E9.51
CC CO~PcTE ~ErT'ON PROPERTr~S.
CEY = 1.3344595E-,3REy = ~.~5~0~54E-2
Cl = U + 1.8A! • "He I (1. + GACIBRe • 1•• 8ATAf = An • AS!AW • AST • A£W = ~W I CA=I.+A5TD2=U+C1CM~ = .5 • [ 02 + AW • UIEL = C~M I AOJ = U! • FL
c
Z of 13C6 • cl I 1)3C7 • 1:'1. I "1AI • A • cL • 1)3 •• 5 .10 • 1./3. • AW • D.r 1•• D/J,JlS.AI/F.lRR • SnRTF I Al I A IREl = fI~ I ELCR . 0:1 I ~R
Cl • A • ~
C2 = .~ +r 1. + r.Sl • AST • r.llCJ • Cj + ~L
A~FN .!.5.rGST+A~.r+021-2 •• r.2./D1 •• '.C21.CJI/9cC PRI~T OUT TMf5E SECTION PROP~HTleS IN A TABLE.C
PrilH .~2
J, FO~~AT rl~~OSEr.TION PHnpl:'RTIFS IPRINT 166
lb~ FOFMAT [1~n.8K.3HA~T.1~X.1Hn.l~x.JHAFr.12X.3HQRC.1JX.2HRR.13X.cHFL1 • 12A. 4~A~PN. lJ~. l~H, III
PRINT 107. AST. n. A~F. GHC.RH. ~L. AMPh, ~
16/ FO~~AT I 8'15.11l;
C 'O~ A~y HYfl~ID S~CTI~N. ~IGH AXIAL LoAnS "ILL CAUSE THE HOM~~T •C GUHVAT~~E LU~V~ TO LIE ALL O~ O~E ~IDe OF TH~ CURVATuRE Axis.C ~e~C~, T~~ ~~LLC,lNG CHErK IS NeC~SSARY.CC 5EI: IF T~E:Re; IS A NEljAT IVE LHi Dill THE' ~O"'t;NT • CURvATURIi CUR v!:.C IF ""'T. r.O 0' TC TIoII; ""Xl SeT OF l)AU.C
I, r A'PN 1 H. 35, 3')J~ PH'~T ,~e-
Je fO~MAT l ~H~~A~IAL LOAD TOC HIGH [SeCTION CANNOT HAINTAIN ~wulLlhR11 U~ l I
GO TI1 1cC Sid I P HE H~AUI"'GS "OR 1101., (>uTPUr OF TH~ "'lIMENT • CUHVATUkE •C ST~AIH R~L.TtONS.
C34 PRINT 1bH
Ib,l FOI;i'1AT [ 1"o. 7K. 1~~. 9X. o;Hnl~l. 11)(. 5HCM!"l/. 11X. 6HI:F";[NJ.t 1f'X. 1HN. ~X. r;Hr, [1'\1. 11)1. 5HC .. !IH. 11)1. 6~epS!NI. II/I
cC CO~PlTE THE 'EQ~r~~D 200 POI~TS. O~ T~E CURVE.C
X [1 I • -BHX/ ~ I HRIx [ ;<] -0;(;x[4 I = BRCXI Ii / • -wXUI • IIALl171 = C1AL!lQI = :l1ALf1fl1 = ,;AL!201 = 'JALf 211 = J
..
......_--------_ ..._---_._. -----
C
•
PAGE
AL!221 0 O.CA • Ar I rG>"c + G>"TI'Ir901 0 P • GST • Gf"TClolI.-GRC·P I+C6C20 11 •• GRC' GST + lIf"CI + (',71f"1 >"1190J - Cll 2. 100.100
1 0 0 f"I r90 I : C1.
? 1.1 rill/OJ· C2J 101. 101. 31 01 f" I 19 0 I 0 • 0 t
~ ALI301 0 -p • CACl = P - G5T + GrCIr! AL!301 - Cl) 102. 102, 4
10;; AU 30 1 oCt4 I.' ALf30) • Cll 5. 10~, 103
103 AL1301 = -.01>; N • 91
151; = 1 I>15~C 0 I>DliP ••• OU~
JA 0 10GO TO 24
AN. 90IS\;C = 7ALr301 o'IIQOIDEp = .005GO Tn <,4X[25] = .O?15~ 0 14ISI;A • 16151;8 0 1815WC : 815,10 = 9I : 3
·~.N·l
IrfNI 21. 104, 104104 AMLT • [ALf261 - ALl2511/lALf2111 - ALf28))
II ALI301 : AI.r21l1.+xl2-5J.GO TO to
21 N : 9115~A • 11>15;:8 : 1815,C • 22IS~D • 23XI?5) •• 02olU29l • F 1(91)olLIZ8l • FIIIIO]DEI' ••• 00'5olLr261 • CM[lIllALlZ5l • Ct1ti.aJ.ALrZ31 • EP511111
22 N • N • 1IF!N - ZOOI 10'5. 1~5, 21
lU5 olMLT • IAIo[Z61.- ALl2"11t olLoIZ.1f1 -.AI..H1UIZ3 olLor301 • olLr21l 1 - x125)
GO T010
3
.J.QF __IJ__.__
~. AL(23) = F • ALr3n)1 C61~ IFl ALI3011 <~. ln~. ~~
1l1- ALl30J = .~nt~, ~ = A~(JOJ I EL
CO; = C~ • FCg • P + F • OJco 107 K • 1. ~
101 AUKl = O.~(71 = .~~
~l~l = (;';~[~I = -~.
~rlOl = .F·2.~(11) = G';C • t.~(12) = ~111J - FUO 10~ ~ = 17. cO
lU~ ~l~l = )[~.~) +~.
X(13) = -F-GHX[14) = X[IJl • F • tJX[15l = ~[14l • GrcXl161 = XI'41 - 11FTCO 10~ K • 21. 24
10Q ~I~I = ~(~-Al + ' •• usrCO 12 • = 1. '"IFf ALf?3J > XJK_All 11. 111. 111
111 AUKI = XI~1
AUK>"" = X[~_HI
GO TO 1211 IF! AL!231 > ~fK>16I) 112, 112. 12
11;; AUK) = X[qALrK>a, = '1~-161
1;: CO~TI"'l'i:
A~r15)=ALr'5) - ~rr
AU16J • Alr161 - ClrrCl • O.C2 • A • FC3 • -, •• r~ - CqCl1 = ALII) • GFCCt,. I\Lr~, • llrTC13 • r11 • C12C2 • P - "1,'C3 = c~ - ,.-[Clt*AL[151 • C12* ALI1611-IC11.QFC-C1Z* ~rTI
CO ltD ~ • 1. '. 2Cl1 •• LI~l - ALIK_l1C14 = 'L[~I • AUK_IIICl: • AL[~-11 • ALrK-91Cl? • rt4 - 1:1-;Cl~ • ct4 • ALlK-S I - C15 * 'UK-,91Cl • Cl - ~1 tC2 • C2 > C12
11~ C3 = C1 - rl~Ir(C2 • C2 • C1 * 031 26, 113, 113
lU C2 • 2•• r.zALfZ4)' ~C[Cl, C', C3, ALl2311IrfABSFI1 •• ALI241/ALI2311 •• 000001 I 13. 114. 114
114 JA • JA • 1
•
""IoFI3
,
.. •
........._~ ..._---------------------------I ....; c PARE ,
._-_._-------------
--- ._----- .._---
~ I I
. £0" I J. _. .. -1F: L.a.-l.-llH'!3L..~t.1.1 S.S....~lUtUSL- ._-IIL-.!LL-~.E- _
115 ALI231 • ALI241GO TO 10
26 ALI23J • ALl231 .. DEPGO TO 10
13 ALl27] • O.·00 t 16 K • 1, '5. aJB • K + 1C3 • O.00 117 JJ • 1. 2Cl • AL 1241 "ALtJlh81· -. -- ..---- ------ --- --.--.---._ _ .._ -.-..--.--C2 • AllJ81 .. C1 .. C1 .. IALIJS.,(,J • 01 I 13 ••C3 .• C3 +..t'~--_.-..---------- --'__. _
11 7 JB • JF' • 1116 ALl271 = AL.127.J. ...l:3 _ ...- .. _ .... _... ~_
JA c H_.... -_._._-~_.._,-- -.--- -----------_._---_..
THE ~EXT STATEMENT IS SE~SITIVF. To AXIAL LOAD I serTION MODULUS S'PPRCACHI::S ZI::RO lAblD_lIAY_.CAIISEc DI \! I 5 I 0.' By 2UD Fgp HIGH \tALliES orAXIAL LOAD P,
1.31
13f,
13~
._-------,---_._----...
AL127] c ALE30] +IA .. tL .. IALI241~CSI ... ' .. ALI271/F:I/SLil = lSI<GO TO 11~
1A .Cl • Assr LlALt.C:6.Jd.lll.! .. _12'] L' AI (27! •IF [ Cl - .001l 15. 130. 130I • 1 • 1IFfl1 16,'16. 131Lil • I~I<A
GO Tn I1HIH (,;1 •• nnOll151132...1~_._( • I • 1IFfll 16. 16. 133LI3 • l~WH
GO Tn 118IFIN] 137. 138, 137Flc • AL(30)CHC • nlt7lEPSO • ALC;>.]GO TO 13t>rllNl • ALf301CHINl • AL (27]EPSIN] • AL[~4]
I • 300 134 K I 2~, 29ALIKI • ALfK+llL8 • UWCGO TO 118
17 X1251 •• 0215\00•• 111
ISI/S • 18GO TO 135
18 XI:!'l •• 1ISWA • 17151018 • 19
13C
137
H138
CCCCC
c
GO TO 135l' XII''' •• ~
ISwB • 16IS~A·111·
135 Lfl • ISIIDGO TO 111l
cC PRINT OUT THF r.CMFUT~D PCI~TS AFT~R CHECKI~G TO SEe IF T~ERE IS AC POSITIvE 8PA~CH ON T~E HCHENT • CURVAT~R~ CURVE, I T~IS CHeCK ISC SIMILAR TO r~AT ~EHFDRMEt AFTER THE PHIN! UUT or SECTION PHO~EHT.C IES .BOVE,Ie
21 N • 0IF CCMOI ~7. 37. 1~9
37 PRINT ~6
GO TO 113Q PRINT 169, ~, FlO, CMO, EFSO16Q FOR~AT [el7X. 13, ~F16.7JJ
CO 1 4 2 N I 1. 100NN • N + lno~RINT lbO, ~. FICNI. C~(NJ, EPS(~J, ~N, rJIN~I, CHINNJ, EPSINNI
14~ CO~TI"lJ~
C
e ONce THE 2nD POINT~ ~~VE b~E~ eCH~UTED, ijU TO THE I~TEGRATION ST~Pe
CAI.L I~H-~ee IIPON RElI:R'" FHn~ Tf'E INUGRATI0~ nEP, GO ~ACK A~D SEE IF THEHE ISe .NOT~ER S~T rF [ATA.e
GO TOeC THE 'EXT S~HIE~ OF STATE~ENT~ IS A ROUTI~E TO ~ETERMINE WHERE TMEe PRDU~.~ SHnUt D EP.~C~ TO NEXT. GIVEN THE VALUE OF T~E SWITCHINGe PAkA~ETER IS". IS~A, ISWF, IS~e, ISWO, THE ROUTINE PICKS THEe STATF~ENT NlJ'R~~ TO (0 Tr NEXT.e
PAGE 6
,O~ ,~
(;
ece
11" IFrLH-l0J 11Y. ~R. 12011" LEi • U' - Ii
GO TO r b. 7. F·. 9 1. LE120 IF ILf'-;' 01 121, 9/1, 122121 Ld : LE • 13
GO TO (11- 9U, H, n, 111, 19), Lb12'; LEi : U - /1
c; a T'.1 1;.0 ':. ;> 3 1. l F1
SHOllLlJ A~ I~Jrl~ r~ s(·~~ IF S~~TE~H.T 0,1 (IUT UF bCUIIJDS, Hq~
srAT~"FNT WILL H CALI f'D A~Jl) lH~ PROC:"~M ~lLL T"~MIN~TF.
9" f'RINT ~I
~7 'ORHAT (uf;"lrF'l9" CAlL ... If
~ ~Jr
I
•
~ROM STATEME~TS ~ AND ~j R~LD~, iT CAN BE SEEN T~i. SOHE CURVATU~E
"il ;4- ·t ESS na~'-- T" AT O~TFII~ TNED ABOVF TS USED AS A 'HA"TlNG PO I NTTO I~SUR~ THAT 1HE P~AII 0, THE CURVE WILL BE PASSED THROUQH,
~G.n"'-.4
GO tn ~
1_0JN.N~1IfrNT1~?-;-m
N .-901 O~ iF' Tl'p~ i ~il :1 • i ij 0;,jj0;10 ii ---------..-..10~ IF IFP~[~IJ.RRT·~ii11.BRC,;,991 '50, !to, 'H
"'-5" IF IFP~INl-F'IIN1/C'.GSTI '1, U1. 101
!·W·I~:;g;h~:~hti.aRc-·:9.'-~-;T; ,-------3 I' [FP~O·FIO/C7.r.STl ,; 101, 101_. "_._- ,"._--- . - _._-
1PAGF
... __ , __ _ _ - _..,-----_ _._---
-- "
SlJJJAov-r'rtc INT'"SUPROUTINE INTEG
~UBR~UT1~F INTEG IS A PRrGRA~ w~ic~ WHFN GiYEN t~F MOMENT r.UFii(A TURF PEn ti I'l~ rOil A SFC" j M;~ wilL DEtER",j NETwE MAX jMUHrl~Er AND PINNF[ LFNGT~ THAT THe ~~CTION CAN SUSTiiN UND!R A GIYENU.THAL AND A~IAL LOAD. - ------ ...-
T~E 'OLLl'lwINr. O~ANTIT'FS ARE PLACED IN COMMON SO THEv WILL BE4"A1LAsLE-rRt-" T~;: "diN PRoilRiM,-- .....
(:0"f'40'" j,N: EP~'; pilT; li~ iiiii',ri. C7~ jj!iT,'F"SO~ riO, QI, r; Ji,1P, REL', ISWA.lsIoIe, ISIoIC, iSWD~ isw, A~, aRi, &P~ CHO, A"LT, Je,;>Ci. c2. c3. REV. C11. r.12, c13, C14, E, C, A , c!l, c1, CB, II,3,IC, L~. 'f'4AX, CIC, IRuN
iJ i ,.eNs ION r~ i 20Q'~ f i i 20 oj ~--Ej:is12iillr-;-.Lnrr;-j(Un~·-B 114]
STARliNG wiTi' rio" ORIGiN'; tHF-pofNTso~-tHI-ponfivrBRiNcH OF THE~9ME~~I~VAT!:.~E CURve. ARE CHEell:Fa FOR A POSSIBL~ STARTING n. __CURVATUR~. I, ~('l TRAN~VFRSE LOAD IS ArTING ON THP SEcTION, THISWILLUSU~L.!Y ~.F: c.. nSf-N AT T~FORIGIN. L~QINT 9iiL_,.~
ccCCC
CCCCCi:
-c'CCCCCCCCC
cC ir Nr suiTABl E~r'liNt'CAN 'RE 'roU~il: GO O~To-liii!'ijFiTDifi nr,'C
RETURN51 G. nlN) - .4-IIQ-.---ol '- --. -- .
cc THE ~FXTSTATEMEN.S AIIF THE nilES WHir.H CHOOSETME'r.URYATURE AT THEc r'lIIIGIN A~ A ~TARTING ponT IF' LA.ERAL LOAD I_S ..z_ERO~_~_c
Ir [O} 60, 103, liD1O~·T.fn90 r---;·-;T------------
GO TO ~1
6" F • G6' PHC • F'
JAoi 2"c ._--------'-------_ .._- -_._- .__..
cccccccc
PAGE 2
~El I P HF. llTU.~ rop TW~ IN+.EGRATIO~"ANn ll!l;T TWF' VALliE or TwElOAD~ AT TwE 'Tn~ cr l~F ~HFET, " ,Ir JX~ OR JX~ A~E 1, THIS INDICATES THATCONve.OENCE HAS NOT BEENnAlAINEn Y!'T ro~ EITHFP tHF rlllEn nR PiNNEll END CASE ,.nR TWePR~S~NT UA1U~ or Q. ~WE' rO~VFAGF~C~ ,s oeTAINEn~ ,THEY ~ILL BE~F.T TO Z~Rn ANI1 T~IS ~Ill rAllSF TW~ IIBULTS TO AE PRINTEIl ON TWE~1J,",t1H1Y cWFET,
PRINT 'Oll.o~ rO_,",AT (1~1 !
PRINT 1n., P , Q10' rO"J"AT I 17Hnu ,iL 10AI' IPI ., "',4, 4X, 1/lwi ATF.llAl LoAD IOJ .,
1 n .• IQ = ".~EL
Jl(A = 1JX- = 1PRINT 100;
1n~ rO~,",A-T I l"n, n, CWCURVATlIPF, 8y, 6HLF.NnTW,' 9X, 7WLATERAL, 9x,1 /l~VFRTIr:AI, 9X,,,':' FNII , 1U, ~HF.ND, 11 x', 11110
PRINT 10
1~ roc,",AT (11Y. '~At~ ,~x, 10WnF,.lEftroN, ~ll, "WMOVEHENT, 9X, "HMO~EN1T, lnx', o;H~IOPf 1
PRINT 11 "1.1 rO_~AT ( ey, 9"~IIl':'F1GIolT~ '1V" bHAT MIDHEln':''i' I
IS"A a 1IS." a 7f>IS.r: • 1r.nH6K.1~~0
10~ AUK! a n.6' IS. • 1
IS.O a 1X 1171 • PX(1 '11 • 115'ost • rSIno 1n7 I< • 1. 11'0
107 xr~1 a 0.SN • n,CS • 1.~ • ?on
10= N • N ; 130n IF' r~] 76, '00, 1011HQ Ir IF'! PN] ~ PHt'1 tr,~~ 110, 110?on Ir Irl"- FW¢l 10AI_?~~' ?01 ' ,201 AMI T • Irln-PHr:,/lrIO-rlllll
Xll11 ~ c~n-AMlT.lt'MIl-r~tll~GO TO ~02
11" AMLT • (rlrNI - PHfl/lF'II~I~"ltN~lllXll11 D, C~INI -AMLT.[CM[NI.CH[N+lll
202 Ir [lClUII 111,1:1.1, 6~ ,111 pwr D IIHC •• 1
GO tn :tOO6~ IF' INI 203: 204, 2;'3
20' XI211 D EF~~-AMit.jFPsn-~P!l~JIGO tn '"05
20~ X[~lJ • FFSINI.AHLT.[EPSthl.~PStN.111
•
PAGE 3
205 xl231 • P~~
JIl • 5;'131 JI3 • J= - 1
IF" lJR.' 11', 90, 9;'11' ALr21.. 1.
GO TO 059 ~ I = 1
xI,OI • nSTxl,5) • x['~1
113 C1 • 1-1,3"3. +Krj51/6,lo~ELoxljOlC2 = [rS-S~o~loRE,'oxl'OI
C3 • (c:N/"FY+C!i+C1 ,oxi,olCil • =E'*CRC13 = v [ i 5" :.. 0 * ;c,-:" ia, * !IN'Cl' • " * FYC14 • -(17, + C1; • it~ ; eR * C~JxrI21·vl11'-rC?rC13·.~.D*C".C3.1C14-.5.C120C311/REL
11~ ~ = III • 1IF" rill) 64, j~6. in
?O~ IF" rrM~-X[1,11 115~ 11~, 116114 IF" reM'NI - ~ll'l) 115, 11~, 1161H IF" IXl12J - C"'IN+1JI 117, 66, 66117 III = III + 1
IF" 1 N_200, 11~. tiR' llR11" C1 • x'lll - AMp~
IF" rCl' 11~~ i'9; 1';'12" GO TO '6~, ~71, is~n11~ Cl • x'111 - AMP~
X(,Ol • ,5.xr201*c1/rXll11-xrl,,1GO Tn 43
64 Cl • C~U • xrl11N = 1X[?OI = ,2 * xr,n, • C1Ilxi1?I~Xr1iJlGO Tn 43
6~ XI'"' = ,l.xr,OI4 ~ I. = 1 + 1
IF" rl - 151113.1.13. A96' IF" r ~I J 207. "0 R. ? n7
20. AMIT = Ir~n-Xrl,lIIlCM"-CMil11XI,41= F"1~;AMLT*;rio~F"I;ll'xln,- = FFc:(1~AMI r.rFPSn-FP5rl1'GO TO A8
'07 AMIT = [c~r~1 - Xl,"lIrCMiNl-C,.,iN+lIJXI,4' • FlrNI-AMiT.iF"liNl~r,iN+l1JXlnl ,; FFc:rNl -AMI T • lFP!'!rN' - EPSlN*11 JGO Tn '8
67 C4 • [rMl2nnl - AMPNI/CIC5 • C4.Cl/r~Mrlo9'-CMr20011
Xl'41 = le1 + 1,1*F"P?nOI- C rllHF"IABSF"IF"1!20nl- *rrtI2001-F"I119Clll*C5111
Xlt'2) =IC4+1,J.EPSI2001-SCRTFIABSFIEPSI2001*JEPS[20Ul-EPSI1 9911*lC51)
6e IF" IA~c:F[l,-)(r?~J/)(['411-,nnnOl) 69. 121, 121121 I • I + 1
1F"'1-1·] 1?2. 12'. ~o
,-~--'-~----
701211
12471
12~
12'1n
13"
lQ 0/&:- 13 __122 X12'1 • XI'41GO --"To H3 ... - ..... -- --.-.---.---------..--.--.-----------..- ..-------....
6'1 Cl • xI231 + XI241Xt141 io iil\31 .~;.iieYiojjEi..iH.wi2li1SN • SINrlWl1411CS • ctlsrlrii41J~a~1 ~~D~g!~H~ _XI181 • r,14.C12eCRecSXI" • XI8' + CJXI",' • XI'I + 2. e C~ ---._.XI~I • XI21 • 4.exl?DI/I2 •• FVeix;Z11.XI221;eie.,LeC.11C5 • XI241 - XI2JI - - .---.CA • xr191CB • Xi201GO TO "D. 711. i!l~ir iX(j211 123, 710 71Cl • (~1121~XllilleXI191C2 • (r(lD'-XI111IeXIZDIC4 • 1llI191!~i~gJleXI19IeXJ201_C3 • lr~l + C~I/C4.. _ _C4 • lrl • XI191-C'eXI2011/C4C1 • BrIC;S: C4, Xi1tl~ 0.1ALI291 • ."31 +lxij31+.5.t~eC"XI201~eREY.REL.ClALi~31 • O. - -- - -IS~' • ,,-15"'0 • 2nSf •• 2.[~i~ • 0;
no 124 I • " 7~ 3ALi~l • vALlxrll. jij~il~ xii.jl~ Cll~ • ~ • i-Ir [)cr'4l] ;;ii. 72"; 72C1 •• ~*c~*AeY*AFL/XI2nl
C2 • X'2~I*AEY.AFL
C3 • -llI20,*rc5.lll;~1/C"C1 = BrrC1; r.2, xri3', C~IAU3"1 = O.~ . ,.,no 1'6 I • 1. 1n. ~
AL'~I io vAlixijl~ llij+il~ xii.jl: Cll~ '" I( • 6I( = MPRINT 127, PIolC. AL;K-2.1. AI ;1(;;11'1, ALlIe-t21. ALlIe;'61, ALllqror:;MAT r1l-n~ ;r1;'.~1K = K • 1Ir (K ;; 28' 129, 1;9, ,2BGO Tn 'n. 7~1. iS~Ano 130 I • 1. 23)t(1I '" xrl+llI • 1GO Tn '31Iri AI ("'] - AI. III IIi;,3• 13:1 ~ ;-J'GO TO 175, 771. is~c
ISIoJA = "K....
121'9S;
12~
127
.. .. •
.. ..
ISPl • IS." ~ I7~ C1 • AI 1~-41 - AI r~l
C? • AI {~1 • 2.-H;~-21.ALf~-~'C3 •• ~ • ~Ir. - r.l/r.?CA = F"ICCll = CAALIKI • ALrK-21~.5-r.I-rl/C'
K • K • '"134 ALfKI • VAI,IALlK~4'. AI.IK*'I. AL;KI. C31
K = K + '"IF" rK-~1J 13~, 1~5. 13~
13" AAA • ~Mr ~ FIr _ r~
5
11 of 13
CC ~RIN' CliT wHnHE" TMf PI~NFn Hie r:'ASF nR TME FllCl'n F.ND CASE MASC "EEN FOU~D. rAr.C~R"I~G Tr WMFTHER TMF ~Nn ~O~EN' j~ lEAO OR NOT.C
IF ( AL (K-6)) 13. 12. 1312 pRINT ,414 FOP~AT ( I~HnFIXFO END CASE
JX • ~
JX A • nGO TO '5
P PRINT 161~ FORMAT ( 1~~nPI~~E~ FNO r:A~E I
JX • 1JXF • n
1~ PRINT 127. AAARIJXl • lAAAAA • ~ • a-l'y*iALrK*le,+;r.osrIALIK*611-1.I*eRIRrJX + 11 • ALI~~3nl"'1,!X+?l AL rK-;i'~1
R[.'X+3'. ALrK-illl8rJX+4. AlrK-j"8 ( J X.~ I ' AL (1\ - II 18[JX."" AlA
14n
137
7 II!141
PRINT 1.3t>. Alf~~M". AI [1l-'~1. AI [II-tel. AL iii*121. AL [K-61. AUFaRHAT (l~n. l11X~ ~~i6.elIFrl~wP-/\5' i37~ 1~7~ 138L!l • I ~Wfl :.: 59GO Tn '60. !H. ~:l~,.6~. 6~L~ijl. ISIF "sw8 • 70J 1~9. 139. 1~n
LB. I~wP ~ 115GOT n ; 6't>. 1\ 7. 6~ '; IIll. 70]'. i BL" • IcWR ; 70GO TO 171. 72. n~ 74. 75. 7111'; isIF, r~Lt51 ~ ALI3" 1.1. 77~ 77~ • 5IS~B • I~." • 1ISwC • 2GO TO 7.
H a • O/"ELPRINT 401l. iRUN
CC ~RINT OUT TMF RE~uIREn I~FnRHATlr~.
C
40· FORMAT ( ~~jnAT' SFT. ix. i~ IPRINT 104. P. IIPRINT 400
400 FOFMAT ( 1ClHOSl'MMAFY OF RE!!lIi TS 1PRINT lO~
PRiNT 10PRINT 11p!iiNT 16IF rJX~ I -O~~ 4n1~ 40?
40' PRiNT 127. iRIJX1~ JX • " ;1GO Tn 405
402 PRHd' 40640~ FOPM,T ( l~HnN~ rO~VeRr.ENCe 14ij~ P!iiNT '4
Ir r JXA I 404. 40~. 4"4403 PRINT 127, IAIJX1~ JX ~ ~,i~1
GO Tn 407404 PRINT 40"
cc iNCR"MeNT tHF VAtU" or Q AND CHErli til !lEE iF'fM!iiiiIMUM YALUE HA!!C BEEN REACHED. IF IT HAS BEEN EXCEEDED, "ETURH TO THE "'IH PROGRAMC nTHEPWISF. RIIN T~E NExt CA!'lE:c
PAllE 6
JZ of 13
407
14~
II • II .. Olr,Ir In .. a~AXI 60. flO, 142...IlE'lJRNJA • J' • 1
PHr • "He + ricDO 143 K • 1. 21. ;Al;KI • AL;K + ;1AlIK+11 = ALIK+31GO TO 1\2ENr nr PRCr.R'M
..
FUNCTION·FUI\CTltN BcrBC1. Ill~2. IjC3. ac.,C3 • "rJC4 • ~(;4
till • l~
ltr4'O CJ· • BCl • C4 0 C.4.·.... IfCc ,.,. c;,,_. ~"C4=C 4- r J/ I2 • oBe loC4~H(;;21
KK'KK-t1~'KKJ~19U,PleO.R1PO
8l~1 1~IAHSF(C~l-O,QOOOQOlIA190.819D.8l40~11J1I AC=C4
RETUln;E"/C
YAL.FU~CTI(" vhL[A. fl. C. 111 .. __. _CU~Mr1N I. III, F~~. PRT. X. BRC. 1'1. C7. O!lT. FPSO. 1'10.
tR, tll:L. 1~I-JA, ISWB. ISwC. ISWO. 15W. AL. OBi •.CIl._ CHO.?Cl, (~". C~, ~EY. C11, Cl:? ra~. c14. EY. CFl. AHliN. C5.J Fie. Lh ~ I~ AA. 0 I C·OI~~NSION ~~(2VOI. ~lLcUOl. EPS[2UOI. AL130l. Xl25lAA = It-tlJ .c~
88 c~.r.P..rr.A+CHI
cc • (f.-I-' loCHCli (AA+fr.lIRFCC = [~A·C4-CC·CBI/B~
VAL = ru.c.r, + ceor + 8Hl:luHI,ENe
QI. r. JA.AMLT. JB.CA. CR. K.
.~ rA··~e~ ---;o--Ta-·.-S-I!l"r----g-e--'N--py-r--p-'A-n-----------I EX1s MPl..
'",PUT gUA
ASf c . AFF ARC GST arc GrT 01 "Ie os! Fie...._-------_._--_._--_._-_.__._----------
2.00000 U.300UO r.300UO 0.600~0 i.~oooo ~.OOoOO 3.00000 0.1AO~U 0.150000.30011U 10.00UOU U.4';1I0l O.
P
UoIHUOOOU
AI'4PN
li,/1153115
Flit.. )
GRC
U.
l:'PS l~'l
ArF
O,4~OOOU(
e~ r~ I
D
1U. vllOl 000
.....---t--_---3~~;L..AyCO~.2~.1J:ll~ll~.e.:---~~a.. ....':lJ~l.:~z.:;l!~l.;~~~L--·-~j-11~• .Q.5A."1.0ll-07J.P~0l--I-....:..,I-l..:'1~..I!~D.·1L.i..3.JrL.0.10~00~on'---JljL.A1,]."'2~7r.9-3-'91.t_z5'---J1JMr.Jl..0-;...:2~I:2]joLIl-5~~"+if['f." 1't,4fl!,,,t1t18 < .. flll??]<
J 13.9n(~~A8 2.40el~Q' 10.784~743 lU3 ·1.3400000 ·1.3101123__._. L~~..'_i:.Il!l.ll8.liIl.l!.e ....22.....!I1..uUJl5.!14Jl/lcJ3c!:i5'-- .1.IIWlVJ~~L-II__.....JUL!L..----'·~'L •..;J~6~[[jJ1OOJuUJQUJou...... ·~l....~S2.2<I~Ll.'i9~3~~__
~ 1 •• 9Ui:~a68 2.40471~6 10.0U86703 1~5 ·1.3liOOOOO ·1.3390161..' . .9. ._----.1.-":..,~4clili"i:..eIlLl:BLtIllJ!8L __-'WLa..lWW'___......JWl.2J1.8.;L1JL_I_-.:1...lLL---!:.L..u.aaaa.lL.__~.1.a...u.L2.5Jj"....
I 11.9u~~allb ~,4029371 Y.~3296~8 .1.36S116~3
b 1 4 ' 4
0.25~1943
0.2"61\664U.i4401~"
1I.2 404 ,J6U·. 2.l04 v06
Y lu.~O~~8H8 2.4U06439 b.4572609 ·1.3900267 0.2~~0'27
...A.!L .....1J!LJ~4UJL!'.:.1l.fUitL__~~~~WL.----I:l...JiI.6.!~~~-I_-U.L---!:.L..~.lI.L.~.lL.--~L.u.1Jl~J...---_~il4>I 5/11111 ~.9Ui:~bhb 2.~~76206 ·1.~000UOU ~1.4114634 0.icl~860
1t ~.4U~~bb8 ~,~Y57350 4 O.il1/iJ48·-1-:;-----t.YLJell~1I8 ~,J\l3o;.27 -1.4JOl~i6 0.?-140u61
1" t •• 11. ~~!I!1 C ~"U9l 9 4
l.l7 -2.0~00U01 ·1.~287517
v8 ·~.U400U01 ·1 ~ ~~8
1.lY ·2.U600001 ·1.~~J0838 v.l~2J349
1 ~ U - ~ • UII 0 U00l_..~~.AJL lLti..2ll~ __ ...-"l-;;-l·-·---'T~(io·GU01- -1. ~3li36~6 u 014 ~d 7J
__.1 ~~ -~ .12 U0 U01 .. __ ...._~L2~.kli4L._. ..Ji..114 O. 4121~.l -2.1400U01 ·1.~4i:8111 U.144eJ9~
1~4 -'.leODOU1 ·1.~449~J9 U.14cej26
·1.b200UU1 ·1.1991021.~__~~ ~b400001 ·1.0;029881
-1.6600001 -1.~061d11
,,,,,,~'-"-"'--II-_--''-''-''--'--- __~l, ~ JUlQ \1.J1. L___ ·1 • , 0 ~ l" 4 8-1.9000uUl -1.~12jOlj
·1.Y200001 5 41.l3 ·1.94UOOUl ·1.~180878
''-7'-,,-,,-~-=-,=-''''''--'_1~L. ~119600001 -1,~2086391~~ ·1.98UOOOI ·1,~2356~~
1~6 -~.00U0001 ·1,~20190j
.lIJ ?1u"~bYO 2.~4911~36 3.9O;817t-74 U :>~U O<~~_'I.J1._. .L...l4 721.?L ... J_1_!lJ!m.tl......
--~~l q.\luce~?o c.~444,,8i .l.80JO.l~9
4c 4.bU~Ilb<lU 2.J41463i .l.72546~4
. 4~ ;;:iu~i~~-~o~-=_.33l!2~41'----· .. J_;-647ilO75-·44 ~.bu<e~\lU ~.J341"05 J.56752~4
1::> 1.\lu"Il~!j8 c.~b77ic4 .1.H~Od~i ,).2Uo.ll91.._!.~ . __...!.""4-,-l,,-":..~,,-. ~:..t:..H,,--l ::.2.!..=-~::.:.1l::.3=-9::.b=-~::.~----~-'...:...=~-"-"----if---""'-"'-------"'-'-"'-"-''-''-''-''-''--- • 1 , 4 0; .l 0 0~ 0 . U• " U~ J6 40
17 j.3n.Ap~~ 2.~BJl~~O ·1.4o;9~163 o.202~J48
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248.16
'Longitudinal'Girder
~-+-LongitudinalBulkhead
,
1
TransverseRib
LongitudinalStiffener
..(a) . TYPICAL MID-SHIP CROSS SECTION
q
(b). LOADING ON THE SIUP BOTTOM PANEL DUE TO WAVEACTION-HOGGING
Fig. J.,QNGITUDINALLY ,STIFFENED PLATE PANELS IN THE SHIPBOTTOM' STRUCTURE.
-
•
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248.16
Fig. 2 Typical Cross Section With Simplified. Residual Stress Distribution
I
248.16
1.
REFERENCES
Kondo, J.ULTIMATE STRENGTH OF LONGITUDINALLY STIFFENED PLATEPANELS SUBJECTED TO COMBINED AXIAL AND LATERALLOADING, Fritz Engineering Laboratory Report No.248.13, Lehigh University, 1965
248.16
ACKNOWLEDGEMENTS
This study is part of a research project "Built-Up Members in
Plastic Design" currently being carried out at Fritz Engineering
Laboratory, Lehigh University, Bethlehem, Pennsylvania. Professor
William J. Eney is Head of the Laboratory, and Professor Lynn S.
Beedle is Director.
The research has been sponsored by the Department of the Navy
under the Bureau of Ships Contract NObs-94092. The study was ini
tiated by Mr. John Vasta of the Bureau of Ships. His interest in
the support of the project is gratefully acknowledged.
The task of translating the original program was greatly facili
tated by the cooperation of the staff of the Lehigh University
Computer Laboratory.
Messrs. J. Vojta and R. A. Strawbridge made significant contri
bution by offering general assistance. The report was typed by
Miss Marily L. Courtright. Her cooperation is appreciated.
Lehigh University
OCT 1 9 2010
Library
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