~i-2-against web buckling, since this occurrence does not cause immediate failure of the girder....
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2. ~j--I-'II
IN o EDU:?: 0
I
KO'NRAD BASLER
BUNC-TSENC YEN ·
JO'HN A. MUELLER
BRUNO THURLIMANN
VVELDED P TE GIRDERS
REP RT NO. 251~ 11
I
OVERALL INTRODUCTIO'N AND
PART 1: THE TEST CIRDERS
--~~~.------------- ._-------_._----- --------
L\~~\i\i\lI\\1\~I~~\~~\ii~\\~\i[\~\ili\'\~i3 9151 00897581 1
Welded plate Girders, Report No. 251-11
submitted to theWelded Plate Girder Project Committee
for approval as a publication
WEB BUCKLING TESTS ON WELDEDPLATE GIRDERS
including
Foreword, Acknowledgement, Table of Contents,Nomenclature, Literature Survey and References,
Part 1: The Test Girders
by
Basler, K., Yen, B.T., Mueller, J.A.) and ThUrlimann, B.
Fritz Engineering LaboratoryLehigh University
Bethlehem, pennsylvaniaMay 1960
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FOREWORD
An extensive experimental and theoretical investigation
was carried out at Lehigh University with the purpose of
determining the carrying capacity of plate girders whose web
slenderness ratios were beyond the limits stipulated by
present specifications. While the theoretical study will
soon appear in the Proceedings of the ASeE, a complete
report on the experimen~al work will be published in this
Journal in four parts:
Part 1: IfThe Test Girders"
Part 2: "Tests on Plate Girders Subjected to Bending"
Part 3: flTests, on plate Girders Subjected to Shear"
Part 4: "Tests on plate Girders Subjected toCombi~ed Bending and Shearo "
The objective of this investigation was to determine
the postbuckling strength of thin web plate girders. The
design of transversely stiffened plate girders presently is
limited to girders whose web depth to web thickness ratios
do not exceed the value of 170. This limit was derived
from the web buckling theory 0 But in discussing the appli-
cation of the theoretical buckling formulae, Ref. 253, po 415,
Timo~henko suggests using a Jfactor of safety of only 1$5
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against web buckling, since this occurrence does not cause
immediate failure of the girder. Also, similar consider
ations are advanced by many foreign plate girder specifi
cations to justify their factors of safety against web
buckling. For instance, the German specifications, Ref. 52,
require no more than 1.35 or 1.25 as a factor of safety
under principal loading, and principal and secondary loading
respectively. The corresponding Swiss specifications
recommend values of 1.3, 1.5, and 1.8 for plate girders used
in buildings, highway bridges, and railroad bridges respec
tively. In Belgium~ Massonnet suggests a factor of $afey of
1.35 against buckling due to shear and 1.15 against buckling
due to bending, Ref. 162, p. 81. Thus, not only the safety
factors differ but they also seem to depend on loading
conditions and other factors. In order to clarify this
uncertainty, this plate Girder Project was started.
Sponsored jointly by the American Institute of Steel
Construction, the u.s. Department of Commerce Bureau of
Public Roads, the pennsylvania Department of Highways, and
the Welding. Research Council, the research project at
Lehigh University was guided by its I1Welded p·late Girder
Committee" whose members were:
-3-
E. L."Erickson, u.s. Bureau of Public Roads, Chairman
A. Amirikian, Bureau of Yards and Docks, U.S. Navy
L. S. Beedle, Lehigh university
Karl de Vries, Bethlehem Steel Company
F. H. i.D:f-ll, American Bridge Div., U.S. Steel Corp.
Neil van Eenam, UeS. Bureau of Public Roads
E. R. Estes, American Institute of Steel Construction
LaMotte Grover, Air ,Reduction Sales Company
T,. R. Higgins, American Institute of Steel Construction
W. H. Jameson, Bethlehem Steel Company
C. D. Jensen, pennsylvania Department of Highways
Knut Jensen, pennsylvania Department of Highways
Bruce G. Johnston, University of Michigan
K. H. Koopman, welding Research Council, Secretary
George W. Lamb,
w. B. McLean,
N. w. Morgan,
w. H. Munse,
Eo J. Ruble,
J. E. South,
R. M. Stuchell,
Bruno ThUrlimann,
George Winter,
W. Spraragen,
Consulting Bridge and Struct. Engr. (deceased)
Dravo Corpo~ation
DoS. Bureau of Public Roads
University of Illinois
Association of American Railroads
pennsylvania Railroad Company
Pittsburgh-Des Moines Steel Company
Federal lost. of Technology, Switzerland
Cornell University
welding Research Council
-4-
ACKNOWLEDGEMENTS
This investigation has been carried out at Fritz
Engineering Laboratory of Lehigh University, Bethlehem,
pennsylvania. Wm. J. Eney is Director of the Laboratory
and Head of the Civil Engineering Department. The chairman
of the Structural Metals Division is Lynn S. Beedle. Thanks
are due to both for the support which they have given to
this plate girder investigation.
T~e project is jointly sponsored by the American
Institute of Steel Construction, the pennsylvania Department
of Highways, the u.s. Department of Commerce Bureau of Public
Roads) and the welding Research Council. It is supervised
by the Welded plate ,Girder project Committee. The financial
support of the Sponsers and the continued interest and
gui.dance which the members of the Committee have given to
the project is gratefully acknowledged.
Sincere appreciation is expressed to the Engineering
and Weldment Department of the Bethlehem Steel Company and
in particular to Mr. K. de Vries for supervision and
faprication of the test girders. At Fritz Engineering
Laboratory, Ken Harpel and his staff of technicians built
-5-
the test rig and gave constant cooperation. Special thanks
are due to finer Taysi and Jin Tah for their assistance in
testing, data reduction, and in the preparat~on of the
figures; also to pete Cooper for proof reading the report.
Part 1:
Part 2:
-6-
Table of Contents
WEB BUCKLING TESTS ON WELDED PLATE GIRDERS
ForewordAcknowledgementTable of ContentsNomenclatureLiterature Survey and References
THE TEST GIRDERS
1.1 Introduction1.2 Girder Dimensions1.3 Steel properties1.4 Cross Sectional Constants1.5 Reference Moments and Loads1.6 Web Buckling Stresses1.7 Deflections
TESTS ON PLATE GIRDERS SUBJECTED TO BENDING
201 Introduction2.2 Design of Girders and Test Setup2.3 Basic Test Observations2.4 Ultimate Loads2.5 Failure Modes2.6 Discussion
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Part 3:
.Part 4:
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TESTS ON PLATE GIRDERS SUBJECTED TO SHEAR
301 Introduction3.2 Design of Girders and Test Setup3.3 Ultimate Loads and Web Deflections3.4 SR-4 Strain Gage Measurements3.5 Additional Strain Measurements3.6 Discussion
TESTS ON PLATE GIRDERS SUBJECTED TOCOMBINED BENDING· AND SHEAR
4.1 Introduction4.2 Test Setup4.3 Test Results4.4 Discussion
-+
-8-
NOMENCLATURE
1. capital Letters - preferably used for quantitieswhich do not have linear dimensions
A Area of cross section
E Modulus of elasticity, 30,000 ksi
G Girder, used with a number, for example, G2 refersto girder Noo 2; also shear modulus, 11,530 ksi
I Moment of inertia
M Bending moment
NA Neutral axis
P Applied load
Q Statical moment of area
S Section modulus
T Test, used with a number, for example, TI refersto the first test on a girder
vX,Y,Z
Shear force
Cartesian coordinates (in inches) having theirorigin in the middle of the girder
~9-
2. Small Le~ters - preferably used for linear dimensions
a Panel length
b Web depth, b = 50" for all girders
c One-half the flange width
d Flange thickness
e : Distance from NA to the extreme fiber of the flange
h : .. Distance between the centroids of the flanges
k Buckling constant
1 Buckling length of a column
r Radius of gyration
t Web thickness
u,v,w Displacements in the X,Y,Z directions
x Longitudinal coordinate with origins at eitherend of a girder's span
3. Greek Letters - used for nondimensional parametersand stresses
a=a/b Aspect ratio, panel length to web depth
~=b/t Web slenderness ratio, web depth to web thickness
E : Strain
v Poisson's ratio (= O~3)
cr Normal stress
1: Shear stress
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4. S~bscripts Examples
a Above Sa Section modulus above NA
b Below eb Distance from NA toextreme fiber of bottomflange
cr Critical ocr Critical normal st,ress
t Centerline v~ Centerline deflection
e · End Ie Moment of inertia of· end sections
f Flange Mf Moment contributed byflanges
i Ideal 'Lcri Ideal critical shearing,stress before inelasticreductions
m · Middle 1m Moment of inertia of· middle or test section'
n .. Neutral axis In Moment of inertia about· NA
p · plastic Pp Load causing the· plastic moment
u Ultimate Pu Ultimate load
v Combined aver Critical stress undercombined loading
w Web Aw Area of the web
y Yield ayw Yield stress of web
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LITERATURE SURVEY AND REFERENCES
An extensive study of the pertinent literature
preceded the investigation. This study led to a survey
of literature on plate ~tability of plate girders. Although
this study was conducted in 1957, any additional references
appearing since then in the technical literature have been
inserted at their proper lo'cation. Figure 1 graphically
summarizes this survey, indicating place, time and 'nature
of the various papers.
This section contains first the abbreviations, as they
are found in the English, French, and German literature.
Then follows the literature survey, with a translation of the
title if in a foreign language. The references are listed
alphabetically by authors. Finally, some addit·ional
references, Ref. 269 to 276,complete this section & These
are papers to which referen~e· is made in this report but do
not necessarily belong in the literature survey which is
concerned with plate stability only.
Publications by:
Abbrevia,tionAbbreviation Full Title
Type of Their publications:
Meaning ofAbbreviation
Abbreviation
JO\Lrnals
Full Title
I.V.B.H.
A.l.P .. C.
I.A.B.S.E.
N.A.C.A"..
A.S.C.E.
Internationale Vereinigung fUr Brllk.kenbau und Hochbau
Association Internationale des Pantsec Charpentes
International Association for Bridgeand Structural"Engineering
N~tional AdvisaryCommittee o~ Aeronautics
American Society ofCivil Engineers
Vorb.Schl.Ber ..Abh.
Publ.p"rel.
Rap. f.Mem.
Prel.Rep ..
F .. Rep ..Publ.
T.N.T.M.~v .. R.
Proc.Trans.
VarberichtSchlussberichtAbhandlungen
PublicationpreliminaireRapport finalMemoires
Preliminary·ReportFinal ReportPublication
Technical NoteTechnical Memor,\Tartime R~port
ProceedingsTransactions
Bauing..
Stahlbau
Ing~ ArchLy
J~ Aero. Sci.
Nat.Aero.Res.lnst.
Weld. & Met. Fabrn.
Der Bauingeni.eur
Der Stahlbau
Ingenieur Archiv
Journal of AeronauticalScience
National AeronauticalResearch Institute
Welding and Metal Fabrication
BJ-I[\)I
Inscicut f~r BauInst.f.Baust. sta~ik an der Eida.d. E.T.H. genossischen Tech
nischen HochschuleZ~rich
Mitt" Nr .. Mitteilung Nr~
Luft£ .. Forsch~
Z~Flugtechn.u.Motorluftsch.
Luftfahrt-Forschung
Zeitschrift ftir Flugtechnikund Motorluftschiffahrt
T.K.V.S.B.
Technische Kommissian des VerbandesSchweizerischerBrUckenbau- undStahlhochbauunternehmungen. Changed1956 into: Schweizer Stahlbauverband
Mitt. Nr. Mitteilung Nr.
z~angew.Math.u~Mech.11
Zeitschrift fur angewandteMathematik und Mechanik
LITERATURE SURVEY
1 .. Back;, G. and Schumann ~_ L.nStrength of Rec-tangular Flat plates Under EdgeCompressi9n"N.A .. C.A.~· Rep. No. 356, 1930.
2. Ballerstedt, w. und Wagner~ H.'Ueber Zugfelder in ursprUnglich gekrllmmten, dUnnenBlechen- bei Beanspruchung __durch -Schubkr¥~te'fLuftf. Forsch.~ _vol. 12, 1935., S. 70. -I
"On the Tension Fields of Initially CUrved, ThinSheets Under Shear"
3. Ban, S."Knickung der rechceckigen platten bei verHnderlicher Randbelastung"I.V.B.H., Abh.~ Vol. 3, zUrich, 1935, S. 1.
"Buckling of Rectangular plates Under VariousLoading Conditions"
4. Barbre, R."Beulspannungen von Rechteckplatten mit I1ingssteifen bei gleichm~ssiger Druckbeanspruchung 'f
Bauing.~ Vol. 17, 1936, S. 268.
"Critical Stresses of Rectangular'Plates withLongitudinal Stiffeners Under Uniform Compression"Has been translated into English:Translation 78 of Navy Dept .. David Taylor ModelBasin, Washington~ D.C., 1943.
5. Barbre~.R..rtStabilitllt gleichmHssig gedrUckter Rechteckplattenmi.t LHngs- oder Quersteifen1l
Ing~ Arcbiv, Vo~. 8~ 1937, s. 1~7;
"The Stability of UnuQrinly Loaded RectangularPlates with Longitudinal or Transverse Stiffeners"Translated into English:
_ "N.A ... C.A:. ~ T.M. No. 904;, 1939.'
6. Barth~ W.~ BBrsch-supan~w. und Scheer~ J.. f~eu15icherheit ausgesteifter Ree~teekplattenbei
zusammengesetzter Beanspruchung fL
Stahlbau, Vol. 28~ 1959, S. 68.
"Safety Against Buckling of Stiffened RectangularPlates Subjected t.O Combined Loading Cases"
7 _ Basler, K."Strength of Plate Girders"Ph.Dc Dissertation~ Lehigh University~ Bethlehem~
pennsylvania~ October 1959.Reprints or Microfilms available through:Hie. 59-6958~ University Microfilms, Inc·. ~
313 N. First Street, Ann·Arbor~ Michigan.
8.. Basler, K. ~nd Thllr1imann, B."Plate Girder Researchlf
A.I.S.C. National Engineering Conference,Proceedings 1959, .American Institute of SteelConstruction, New York.
9 . Basler, K. and Thllrlimann , B."Buckling Tests on Plate Girders ff
International Association for Bridge and Structural Engineering, preliminary Report, 6th Congress,Stockholm ~ 1960. . "
10. Batdorf, S.B."Theories of Plastic Buckling ll
J. Aero. Sci.~ Vol. 16~ No.8, 1954, p. 543
,f-'W
(
, j.
11" Bergmann~ St. und Reissner~ H. ."Ueber die Knickung vou'Wellblechstteifen bei
SchubbeanspruchUr.."'1.g iT
Z~ Flugtechn. u. Motorluftsch., Vo16 20, 1929,s. 475 und Vol .. 2.1 07 1930, 5 .. 306.
nan the Buckling. of Corrogated Panels Due to Shearn
17" Bijlaard, P .. P ..rtGrundlegende Betrachtungen zum Ausbeulen derPlatten und Sehaien im plastischen Bereich1f
lust .. f ... Baust6- a.a. R.T.H.:; Hitt. Nr" 21,Verlag Leemann, Zllrich, 1948.
ITFundamental Considerations on the Stability ofPlates and Shells in the Plast.i.c. Regionll
12. Bergmann, St.HUeber Schubknickung von isotropen und anisocropenPlattenU
3rd Int. Congr. for Applied Mechanics, Proe.,Vol. III, Stockholm, 1930, p. 82.
nOn the Bllckling of Isotropic and AnisotropicPlates Due to ShearTl
13. Bergmann, St. und Reissner, H."Ueber die Knickung von rechteckigen Platten beiSchubbeansprucnung 11
z. Flugtechn .. u. Motorluftsch., Vol.23, 1932, s. 6.
HOn the Buckling of Rectangula.r Plates Under ShearnGets k value for a = 2, under pure shear ..
14. Bergmann, St."Be~..avior-of Buckled Rectangular plates Under theAction of Shearing Forces"Institution of Structural Engineering and BridgeBuilding, Rep., Stockholm, 1948.
lS~ BLjlaard, P.P~
J~heory of Local Plastic Deformations ~ Theory ofthe Elastic Stability of Thin Plates Tt
I .. A B.S.E., Pub1 4 , Vol .. 6 y 1940-41, pp. 27-69.
16. Bijlaard, P .. P.nSome Contributions to the.Theory of Elastic andplastic StabilityUI.A.B.S .. E., Publ., Vol. 8, Zurich, 1947, pp. 17-80.
L8~ Bijlaard, P.P.tITheory and Tests on the Plastic Stability ofplates and Shells"J. Aero. Sci., Vol. 16, No. 9~ 1949, pp. 529-54l~
19 .. Bij1aard, P.P., Kollbrunner, CoOF .. und Stussi, F"ttTheorie und Versuche tiber das plastische Ausbeulen von Rechteckplatten unter gleichmassig verteiltem LangsdruckJf
I V.B .. H., Vorb., 3. Kongress, Luttich, 1948,8.119 ..
"Theory and Experiment.s on the: Plastic Buckling ofRectangl..11ar plates Under Uniform Compre~sionlf
20~ Bleich, F .."Die Stabilitat dlinner l-Jartde gedrUckter Stl{be fT
I.V .. B.li .. , Vorbe, 1. Kongress, Paris, 1932~ s. 130.
"The Stability of Thin Halls in Compression Members f'
21. Bleich, F.tTBuckling Strength of Metal Structures" (Book)McGraw-Hill Company, New York, London, andToronto, 1952.
22. Boley, B."The Shearing Rigidity of Buckled Sheet Panels"J. Aero. Sci., Vol. 17, No~ 6, 1950~
!----2i--t-
~
, 2~" .Bollenrath, F""Ausbeulerscheinungen an ebenen,_ auf Schuh bean-spruchten Platten" '.Luftf" Forsch., Vol ~ 6~ 1929, S':> _1, (auch ThesisTechn. Hochschufe, Aachen" 1928) ,,'7
"Buckling Phenom~na on Flat plates Subjected toShear l
'
24. Bornscheuer j F .. W' " ,,'1~indeststeifigkeiten von Plattenaussteifungenbei berUcksichtigter Verdrehsteifigkeit"MAN-Forschungs-Heft, 1 .. Halbjahr, 1952.
'~he Optimum Rigidity of Plate Stiffeners Takinginto Consideration Their Torsional Rigidityfl
25". Brci~, V"''Ueber versteifungen einer auf Schub beanspruchtenrechteckigen Platte 11
Stahlbau, Vol. 25~ .1956, S. 88.
"On the Stiffener Rigidity of a Rectangular PlateUnder Shearn
-·26. Bridget, F.J .. , Jerome, C C .. , andVoseller, A"B."Some New Experiments on Buckling of ThinwallConstructions"A.S.M .. E., Trans., Vol. 56,1934, p" 569.
27 • Bryan, G"H.nOn the Stability of a plane Plate Under Thrustsin Its Own Plane, With Applications to theBuckling of the Sides of a Ship" ~
Math." Soc .. , Proc", Vol .. 22j1 London, l891~ p. 54-.
28.. Bryan~ G"R""On the Buck1ing and Wrink~ing of Plating whenSupported on Parallel~ Ribs or on a RectangularFramework"Math. Soc., proc ... ~ Vol" 25, London, 1894, p. 141.
29'~ Budiansky, B. and Connor:p- R ...W~
. . "Buckling Stresses· of Clamped Rectangular' ·FlatPlates in'Shear"N.A.C ..A.·'- T~N •. 15S·g., 1948.
30. Budiansky; B", Connor, R~W"., and, Stein, M' .."Buckling in Shear' of Continuous Flat Plates"N"A ...C.A~, T~N~ 1565, 1948"
31.. Budiansky, B. and Hu, P .. C.."The Lagrangian Multiplier Method of FindingUpper-and Lower Limits to Critical Stressesof Clamped Plat-esrlN.A:C"A", T.N" 848, 1946"
-3'2. Budi.aIi.s1<y, -Be-, Hu,. P ,,'C.• , andConnor,.R .. t-f..''Notes on the Lagrangian· Multiplier .Method 'inElastic Stability- Analysi.s tl
N.A.C"A", T·~N .. 1558~ 1947,,-
33n Budiansky, B. and Seide, P."Compressive Buckling, of Simply Supported 'Plateswith Transverse Stiffeners" -N..A..C ...A., T.N. 1557., 1948~
34. Burchard, W."Beulspannungen~der quadratischen Platte mitSchrHgsteife under Druck bz.w.~ Schuh"Dig. ~~chi.v, Vole- ~8-, 1.937, SO. 332.
"Buckling of a Square plate With a DiagonalStiffener Under Compression or Shear"
35.. Chapman, J.C ..."Behavior in' Pure· Bending of Box Gi.rders"Engineer, 1954, pp. 198 (514), 252~ 253-257"
Ij--J
\Jl.I
36.. Chapman, J .. c .. and Sparkes, S.R .."Structural Investigation on Box--Girders"Brit .. Shipbldo- Res .. Assn .. , Part i &~2,
Report Nos. 122, 127, and 160 ..
37 .. Chwalla, E."Das allgemeine StabilitHtsproblem der gedrUckten,-durch.Randwinkel verstHrkten Platte"lng. Archiv, Vol. 5, 1934, s. 54.
r~he General Stability Problem of a plate Reinforced by'Angles Along rts Edges"
38. Chwalla, E."Die Beme-ssung --der waagrecht ausgeste±ften -Stegbleche vollwandJ..ger Trager"I.V.B.H., Vorb., 2. Kongress;, Berlin-MUnchen,1936, S .. 957.
HThe Design of Longitudinally Stiffened Webs ofplate Girders 'I
39Q Chwalla 7 E."Beitrag Lur 'StabilitHtstheorie des Stegblechesvollwandiger TrMger"Stah1bau, Vol .. 9;, 1936;, ~. 161.
"Contribution to the Buckling Theory of Webs ofPlat~__ Gi-rder fl
Solves the case of a longitudinally stiffenedplate under pure bending.
40. Chwalla;, E."Die Bemessung des Stegbleches im Endfeld vo11wandiger Trager"Bauing., Vol. 17, 1936, s. 81.
'~he Design of a Web Located in the End Panel of aPlate Girder ll
41. Chwa11a, E .."ueber die probleme und L8sungen der StaQil~tHts
theorie des Stahlbaus Jt
Stahlbau, 1939, S. 1.
"On the probJems and solutions of the Stability_of Steel Structures"
42~ Chwalla, E.flErlHuterungen zu den Knick- und Beulvorschrift-enfiir Baustahl, DIN E 4114, 1940 ft
Erganzung ~ur Bautechnik, Vol". 17, 1939;, Nr. 51/52und Vol. 18;, 1940;, Nr. 2/3.
nExp1~nations to the Buckling Specifications forSt-ructural-Steel"
43. Chwalla, E.'TIeber die Biegebeulung der IMngsversteiftenPlatten und ~sproblem der Mindeststei£igkeit T1
Stahlbau;, Nr. 18/20, 1944, s. 84.
"On the Buckling Problem of a LongitudinallyStiffened Place Under Bending Moments and theProblem of Optimum Stiffness"
44. Chwalla;, E."Aussprache und Vortrag anlasslich der Ehrenpromo~ion
an der Techn. UniversitMt Berlin-Charlottenburg"Stahlbau-Abh .. , Heft 3, KBln, 1954.
J'Lecture of -the Technical University Berlin on theoccasion of His Promotion to a- Honorary Ph.D. Degree1f
45. Chwalla;, E. und Novak, A.tlTheorie der einseitig angeordneten Stegblechsteife"Stahlbau, Vol. 10, 1937, s. 72 und 92, oderBauing.;, Vol. 10;, 1937.
rtTheory of Unsymmetric web Stiffeners"
If-.I0'I
46. Coan, J.M."Large Deflect~on Th~ory for, Plates with SmallInitial Curvature, Loaded in Edge Compression"Jour .. Applied Mechanics,- Vol. 18, No.2, June 1957 ..
47. Cornfield, G..M-. and Sparkes, S.R."Buckling of t;he Webs of Plate Girders" .Jour .. of -the Inst.,_of Civ .. Eng .. , Vol.24, 1945, p.59.
48. Cox, H.L.lIsummary of the Present State of Knowledge RegardingSheet-Metal Construction"Aerori.Res.Comm.Rep .. and Mem .. , No .. 1553; London, 1933 ..
49.. Cox, H.L.fTBuckling of Thin-Plates in Compressionn
Aeron .. Res.Comm.Rep. and Mem., No .. 1554, London, 1933.
50. Cox, H.L .. and Gough, H.. J .."Some Tests on the Stability of Thin-Strip MaterialUnder SJ:1.earing Forces in the Plane of the StripllRoy. Soc .. , Froe .. , Ser .. A, Vol. 137, London, 1932,p. 145.
53. Deutscher Normenausschuss und Deutscher StahlbauverbandTlErlHuterungen zur Begrl:lndung des.Normblattentwurfes"Beuth-Vertrieb G.m.b ..H.. , Berlin W 15 und K8ln~
S .. 6-18 ..
"Commentary on the Provisions of the Standar4Specificat.ion$"Gives an excellentexplanatiop. of the. German"Specif~cations by E .. Chwalla.
54. j Deutscher StahlbauverbandI r'Stahlbau"
Stahlba~-VerIags-G.. m.. b .. H., KBln,· Banc;i 1, 1956.
ltSteel -Struc tures'" (B-ook)
55. Donnell, L.H .. , Karman, T.H., and Se<:;hler, E .. E.TfStrength of Thin Plates in Compression"A.S.M.E .. , T~ans., Vol. 54, 1932, p. 53.
56.. Drucker) D.C: and Onat, E ..T.aOn the Concept of Stability of Inelastic sys-tems"J. Aero .. SGi., Vol. 21, No. &> 1954, p. 543 ..
I......-..]I
.51 ..
52.
nenke, P.H.·1JAnalysis and Des~gn of Stiffened Sheart...rebs 1T
J", Aero ... Sci-., -Vol. 17, 1950 ~ p. 217 ..
Deutscher Normenausschuss"DIN 4114, Blatt 1 und 2 ft
Beuth-Vertrieb G.m'.b.H., Berlin W 15 und KHln,1952 una 1953.
l~he-German Standard Specifications CoveringScability Problems in Steel Structures: ColumnBuckling, Lateral Buckling, and Plate· Bucklingff
part 1 contains the specifications, Part 2 givesaddLtional recommendations.
?7 .
58.
Dubas, Ch ..rrContribution a l'etude du voilement des tolesradiesn
A.I.P.C .. , Publ .. prel .. , 3e congr .. Liege, 1948 etlnst .. f .. Baust .. a.d. E.T.H., Mitt. Hr. 23,Verlag LeemaDn', ZUrich, 1949.
IlContrihutions to the Problem of Buckling ofStiffened Pl~tesn
Derives locati.on of- most efficient longitudinalstiffener ..
Erickson~ E ..L.. and van Eenam;) N.ttApplication and Development of A.A.S.H.O.Specifications to Bridge Design" .A.S~C.E ~ Froe., Vol. 83) ~957, p. 1320-10/12.
61. Falconer, B.H. and Chapman, J.C."Compressive Buckling of Stiffened Plates lt
Engineer, Vol. 195,. 1953, pp. 789, 882.
59.
60 ..
62.
Fairbairn, w."Conway and Britannia Tubular Bridges ll
184-9
Falconer,- B.H."Post Buckling Behaviour of Long Square BoxesUnder Torsion fr
Engineer, Vol. 196, 1953, p. 690.
Faxen, O.H.'rnie Knickfestigkeit rechteckiger PlattenH
z. angew. Math. u. Mech., Vol. 15, 1935, S. 268.
-'The Buckling 'Strength of Rectangular Plates fT
66.
67..
_08 ..
Friedrichs,. K.O. and Stoker,. J.J.- "Buckling of the Circular .. Plate Beyond the
critl-cal Thrust" >
Jour. of Applied Mechanics, March 1942, p".. A7 __
Frbhlich-,. H.nStabilitHt der gleichmassig gedrtickten·Rechteckplatte mit Steifenkreuz 1J
Thesis Tech. Hochschule Hannover, 1937 undBauing., Vol. 18, 1937, S .. 673.
i1Stability of uniformly Compressed RectangularPlate with Crossing Stiffeners ' !
Gaber, ~.
"Beulversuche an Modelltragern aus Stahl I'Bautechnik, Vol .. 22, 1944, s. 6.
"Buckling Tests~_on Model Girders in Steel'f
63. Federhofer, K.l'TragfMhigkeit der tiber die Beulgrenze belastetenKreisplatte n
Forsch. auf d. Gebiet d. Ingenieurwesens> Vol. 11,1940, s. 97.
f1Tne Ultimate Load of the Circular plate LoadedBeyond BuckliQgrr
64. Fienup, K.L., Levy, s.> and walley, R.M.'lAnalysis of Square Shear Web Above Buckling LoadtT
N.A.C.A.·, T.N ... 962, 1945.
65.- Friedrichs, K.O .. and Stoker, J .. J.ffThe Non-Linear Boundary Value Problem of theBuckled Plate tT
Nat".. Acad .. of Sciences, Proc .. > Vol .. 25, 1939,p .. 535.
69. Gaber, E.1tUeber die Aussteifung von Vollwandtr~gern ausStahlTf •
Stahlbau, Heft 1 und 2, 1944.
nOn the Stiffening of Plate Girders t1
70 . Gall, H. ~7 .."Compressive Strength of Stiffened Sheet panels'TReporeed by Newell> J.S. ItStrength of AluminumAlloy Sheets q
, Airway Age, 1930.
71. _Gerard, G. .l'Secant Modulus Method for Determining plateInstability Above the proportional Limit fT
J. Aero. Sci., Vol .. 13, 1946, p. 38.
II--'CDI
72. Gerard~' G."Critical Shear Stress of Pl.ates Above theProportional Limit1f
Jour. of Applied Mechanics, Vol. 15 ~ No. l"1948~ pp. 7-12.
73. Gerard~ G. and Becker" H."Handbook of Structural Stability J1
N.A.C.A.;r T.N. 3781 to 3785~ 1957.
74. Girkmann~ K~
f'FIMchentragwerke t!
Springer~ Wien, 1956.
JlTheory of Disks~ Plates, and ShellsH (Book)
75.. Godfrey, H.J. and Lyse, I.-:Investigation of fNeb Buckling in Steel Beams lf
A.S.C.E., 'Trans.~ Vol. lOO~ 1935~ p. 675.
76. Green, G.G.~ Winter, G., and Cuykendall, T .. R.'fLight Gage Steel Columns in Wall-&aced panels rf
Cornell Univ. Engng. Exp. Station Bull. No. 35,Part 2, 1947.
77. Greenman, s. and,Levy, s."Bending \flith Large Deflection of ClampedRect~ular Plate with -Lengtl1.-_Width Ratioof 1.5 Under Normal Pressur~1I
N.A.C.A.~ T.N. 853, 1942.
78. Hampl~ M.TJEin B~itrag ~ur Stabilitat des horizontalangesteiften Stegbleches' f
Stahlbau) Vol. lO~ 1937) s. 16 und 21.
UA Contribution to the Stability of LongitudinallyStiffened Web PlatesU .
19. Hartmann;r F."Knickung - Kippung - BeulungTJ
Leip4ig und Wien~ 1937" VIII Absatz ..
"Column Buckling - Lateral and Plate-Buckling"(Book)
80. Hartmann~ F."StahlbrUckenIJ
herausgegeben von E. Melan, Wien~ 1953 ..
"Bridges in Steel'l (Book)
81. Hec·k, O.S. and Ebner~ H."Methods and Formulas for calculating theStrength of Plate and Shell Structures asu'sed in Aircraft DesignTJN.A.C.A.~ T.M. 785~ 1936.
82. Heimerl, G.J~
ItDetermination of Plate Compressive Strength"N.A.C.A., T.N. 1480~ 1947.
83. Heyman, J. and Du·tton, V.L."Plastic Design of plate Girders ~>Jith UnstiffenedWebs"Weld. & Met. Fab.~ Vol. 22, July 1954, p. 265.
84. -Hill, H.N.;"Chart for Critical Compressive Stress of FlatRectangular plates 1f
-
N.A.C.A.~ T.N. 773, 1940.
85. Hoff, N.J.~fNote on Inelastic Buckling lT
J. Aero. sci., Vol. 11, 1944~ p. 163.
It-''-D
I
86. Hoff, N.J., Boley, B.A. 3 and Coan, J.MoIf The Development of a Techniqu~ for Tes,tingStiff Panels in Edgewise Compression tl
Soc. of Exp. Stress Analysis, Proc., Vol. 5,No.2, 1948, pp. 14-24.
87. Hotchkiss, J.G."New Ways to Cut Bridge weight Lead to RecordSpans"Engineer~g News-Record, Nov. 7, 1957, pp. 36-51.
Gives some excellent examples on German plateg'irder bridges.
:0808. -'"11oUbo1t, J.C. and Stowell, E.2."Critical Stress ,of, Plate Columns l1
N.A.C .A.) T .,N. 2163, 1950 ..
89. Houbotte, M."Versuche {{her die 'Festigkeit blecherner TrllgerH
Der Civilingenieur,. Vol. 4:1 18;5'8, S. 98.
tfTests on the Strength of Plate, Girders lt
90. Hu, p.e.) Lundquist, E.E., a;nd Batdorf, S .. B.rTEffect pi Small Deviations from Flatness on theEffective Width .and,Buckl.ing ,o.f Plat.-es in
"Compres SiOn-~l
N.A~C.A.. , T.N. 1124, 1946.
91. Iguchi, S ..I1Allgemeine L8sung der Knickaufgabe fur rechteckige Platten"lng. Archiv, Vol. 7, 1936, S. 207.
"General Solution for the Buckling Problem of thctRectangular Platen
9-2. Iguchi., -5 •- "Die Knickung der rechteckigen.Plattedurch
SchubkrH.ft~n
lng. Archiv, Vol. 9,' 1938, 5.''1-12.
T1Buckl.ing of RectangUlar Plate Due to Shear"
'3. Ilyushin, A.A.TtThe EJ.asto-plastic Stability of P1ateslf
N.A.C'.A'., T.M. 1188., Dec. 1947.
94.. Johnson, 'J.H. and Noel"R.G.f'Critical Buckling' -Stress for. Flat' RectangularPlates' -Supporte"d-:Along All--Edges and ElasticallyRestrained Against Rotation Along the UnloadedCompression Edge'~,
J. Aero. Sci., Vol. 20, No.8, 1953" pp. 535-540.
95. Karman von, Th."EPcyklopHdie der Mathematisclien Wissenschaftenn
Vol. 15/4, 1910, S. 34~.
Derived the 'differential equations for the platewLth 'large deflect~ons.
96. Karman vori, Th .. , sechler, E .. E .. , and Donnell,. L.H.J~he Strength of Thin. Plate ' in -.Compre'ssion,t.A.S.M.E., Trans. 54, 1932. '
97. Kaufmann, W'.i1ueber ·unelastisches Knicken rechteckiger Platten"Ing. Archiv, Vol. 7, 1936, s. 156.
"On Inelastic~Buckling of Rectangular Plates"
98 ... Kerensky, O.A., Flint, A.,R., and~own', W.Ch.''The Basi.s for Dengn of Beams and plate Girders"in the 'Revi.sedBritish Standard 153 rt
The Insti.tution o£.Ci.vi.l Engineers, Great GeorgeStreet, westminster,. London S.W.l~ Struct. paperNo. 48~1956, pp. 427-440. ,
If\)oI
99-.,. KIBppel, K.IIZur EinftIhrung derneuen. StabilitHts-Vorschriften rT
Stahlbau-Abh., Heft 12, 1952!i S... 92 ..
11commentary to the New German Standard Specifications"
100~ Kloppel, K. und Lie, K.H."Das hinreichende Kriteriwn ftir den Verzweiguugs-·punkt des elastischen Gleichgewichts"Stahlbau, 1943, S. 17.
'~he Sufficient Criterion for the Point of Bifurcation of the Elastic Equi1ibrium"
101 .. KlHppel, K. und Scheer, J."Das praktische Aufstellen von Beuldeterminantenfur Rechteckplatten mit randparallelen Steifenbei Navierschen Randb~dingungen"-
Stahlbau, Vol. 25, 19s6~ s. 117.
"The Derivation of Buckling Determinants ofRectangUlar Plate~ ~o1ith Stiffeners" the plateBeing Simply Supported and the. StiffenersParallel to the_ Edges U
1.02..Kloppel, K. und Scheer, J.'1Beulwerte del:' durcb. ",wei_gleic~e LMngssteifen inden Drittelspunkten der Feldbreite ausgesteiftenRechteckplatte bei Navierschen Randbedingungen l
,'
Stahlbau!iNr. 11', 1956, s . .265/7.4 und Stahlbau,Nr. 9, 1957, S. 246/52.
IrBuckl-ing Values of ·a Simply Supported RectangularPlate with Two Lungitudinal Stiffeners Subdividingthe Panel into Three Equal parts"
103. K18ppel, K. und Scheer, J."Beulwerte der durch eine rllngssteife im Drittelspunkt der Fel~breite ausgesteiftenRechteckplattebei Navierschen Randbedingungen" -Stahlbau,~Vol. 26, 1957, S. 364.
'1Buckling Values of a Simply Supported RectangularPlate with One Longitudinal Stiffener Located atthe Third-point. of the panel Depth"
104. Kl8ppel, K. und Scheer, J."Beulwerte der durch eine LJ:lngssteife im Viertelspunkt der Feldbreite ausgesteiften Rechteckplattebei Navierschen Randbedingungen TT
Stahlbau, Vol. 27, 1958-, S .. 206.
"Buckling_Values of a Simply Supported RectangularPlate with One Longitudinal Stiffener Located atthe Quarter-point of the panel Depth"
105. Knipp, G._. 'HUeber die Stabilitlit der gleichmHssig ged~cktenRechteckplatte mit Steifenrost~J -Bauing., Vol. 22,1941, 'S. 257.
110n the Stability of the Uniformly CompressedRectangular Plate Stiffened by a GrillageSystem"
106. Kollbrunner, C.F.>'Das Ausbeulen des auf Druck beanspruchtenfreis tehenden r.vinkels:TInst. f. Ba~st. a.d. E.T.H.:J Mitt. Nr. 4,verlag Lee~ann, .Zllrich, 1935.
~ "Th'e Buckling of Compre~ssed Angles"About 500 steel and aluminum'alloy angles weretested. The author used angles for his teststo simulate buckling of plates being simply.supported along one edge and free along the other.
If\)J--II
107 .. " Kollbrunner, C.F.. _"IfStabilitHt der auf Druck lieanspruchten plattenim elastischen urid plastischen·Bereichl1
'. Jf.I.V.B.H., Abh .. , Band 7, verlag Leemann, Zurich,1943/44, S. 215. -
111..- Kollbrunner,. C.F. mid Herrmanri., G.t'El-astischeBeulung von" auf .einseitigen" 'unglei.ch-mH'ssigen Druckbeanspruehten Plattenll
•
T.K .. V .. S.B., MLtt_ Nr. 1, verlag Leemann, zUrich,1948.. .
'-rhe 'Stability of Compressed Plates in the. Elastic·and Inelastic Region"Experimental Investigation ..
"Elastic Stability of Non~Uniformiy CompressedPlates tr
-
108. Kollbrunner,- C .. F .."Das Ausbeulen der auf einseitig.en, gleichmHssigverteilten Druck beanspruchten Platten 1melastischen _und plastischen _Bereich"In~t .. f .. Baust .. a.d. E.T .. H., Mitt... · Nr. 17,verlag .Leemann ,. Z&ich, 1946.
''l'he Buckling of Uniformly Compressed Plates inthe· Elastic and Inelastic Rangeff
Experimental Investigation .. ,
109. Kollbrunner,C .. F.. "Versuche {{ber das Ausbeulen- von Rechteckplatten
unter dreieckf8rmig vertei1tem Ilngsdruckrf
I.V .. B.H .. , Schl'OBer.) 3. Kongress, LHttich, 1948,s. 301 ..
112.. Kollbrunner,. C ..Y. und Hen:m-ann~ G."Reine Biegungsbeulung rechteckiger Platten ime1astischen Bereichfl
T.K.V ..S .. B .. , Mitt. Nr .. 2, verlag Leemann,. ZHrich,1949.. -
t'Elastic Stabili.tY of- Rectangular Plates underPure Bending'J
113. Ko1lbrunner, C .. F. und Herrmann, G."Der Einfluss der" Poi.ss-on" schen Zah1 auf die Stab:LlitHt rechteckiger ,'PlattenU
T .. K.V.S.B., Mitt. Nr. 4, verlag Leemann, zllri.c~,1951.
''The Influence of Poisson's Rati.o on the ·Stabilityof Rectangular~PlatesH
If\)f\)I
/y/
"The Influence of Shear on the Stabili.ty of Plat.esin the Elastic Rangeff
Usually, the shear distributionover the thickness of the plateis neglected· in calculating thestrain energy. The authors showthat this simplification generally results in a negligibleerror.. Note that the publ~ca-
t:ion dea1s o~ -t:xz and ·";yz> noton 1:xy
114 ~ . Kollbrunner, C.F ~ und Herrmann,. G'O"Einfluss des Schubes auf cl:Le' S-tabi.LLtlit der' Plattenim elastischen Bereich"T.K.V .. S.B., Mitt .. Nr. 14,. Verlag VSB, ZHri.ch,1956 ..
"Buckling 'Tests of Rectangular plates UnderCompression with Triangular Distribution"
''The Stability of Plates in the plastic Range"The theory of A.A. Ilyushin is compared withtest results. .
110.. Kollbrunner, C .. F. und Herrmann, G.. .-IJStabilitHt der Platten im p1astischen Bereichu
Inst .. f .. Baust. a.d .. E .. T.H., Mitt. Nr .. 20,.Verlag Leemann, Zllrich, 1947 ..
115 • - Kollbruniler, C..F.. und Hernnann, G... ."plattenbeulung-im plastischen-Bereich mitBerUcksich.tigung der Schubverzerrungt'T.K.V'.S-~B ... , Mit-t. Nr. 19, verlag VSB,Zllrich, 1959~ -
'~late Buckltng.in the plastic Range byConsidering Shear H
As in the previous re£er~nce, shear refersto.'t XL and 't yz.' not 't xy.
116 ..Kol1brunner, C.F. und Meister, M.'IAusbeulen1
' (Book)Springer-ve~lagBerlin, GSttingen und He1delberg.
_~te ,.Buck] jog"
117. Kondo~ K. and yamamoto,' M. __11Buckling and- Failure of Thin Rec"tangular platesin Co~pression" .Aeron. Res. lnst.,. Rep .. No. 119,. Tokyo, Imp._ Univ.,.1935.
118. Krabbe, F.W."Beitrag ~ur Berechnung der Stegblechaussteifungenvol+wandiger B1echtrager 1f
Stahlbau, Vol. lO~ 1937, s. 65.
"Contribution - to the calcu1~_t.ion of Web Stiffenersof Plate Girders"
119. Krabbe, F.W.o~rundsHtzliche"BemerkungenLur Frage der Beulsicherhei-t der Stegbleche vollwandiger Blechtrlig.er n
. Stahlba~, Vol. 10, 1937, SO. 97.
"Fundamental Considerations on the Problem ofBuckling safety of plate Girders"
12.0. Kroll', W.D. "TlTables of Stiffness and carry-Over Factor forFlat Rectangular Plates-Under Compressionn
N ..A. C.A., W...R. t.-39-8" 1943.. "
121. Kroll, tV.D., Fisher, G.P .. ," and Heimerl., G..J.TtCharts for Calculati..on_of -the Cri.tical"Stressfor Local InstabilitY of Columns wLth r-, Z-,Channel-, and _Rectangular-Tube SectionsTl
N ..A.C.A .. ,W..R .. L~42?, 1943.
122_. Kromm,. A.tlZur Frage der Mindests~eifigkei.tenvon rlattec..-aussteifungenTl .
Stahlbau,. Heft 18/20,. 1944, S ... 8l-84"~
nOn- the prob-lem of Optimum Rigidi_ty of Sti£fenedPlates"Contains fundamental- considerat:lons .. -
123. Kromm., AoO und Marguerre, K.I1Verhalten eines von S_chub-. und DruckkrHften be..anspnichten Plattenstreifens oberhalb- ·der- BeUlgrenzell
Luftf'. Forsch., 1937.
"Behavior of a Plate Strip Und.er Shear and Compression. Beyond the Buckling Load"Translated into English:- N.A.C ..A., T.M. 870, 19.38.
124. Krupen, ph.. ~~d Levy, s."Large-Deflection Theory for End Compressi.on o£Long Rectangular Plates Rigidly Clamped AlongTwo- Edges H
N.A.C.A.. , T .. N. 884:> 1943 ..
125. Kuhn,_P. and. Peterson, J.P ...rrStrengthAna~ysi.s of Stiffened Beam.-WebsH
N ...A.. C.A .... :) T .M... 1364~ 1947.:-
If\)WI
126 ..Kuhn, p.~ peterson, J.P. and Levin,-L.R.fJA Summary of Diagonal Tension ff Part I and II.N.A,.C.A., T.N. 2661 and 2662, May 1952.
,127. Lahde, R. und wagner, R."Versuche zur Ermitt1ung des Spannungszustandesin Zugfe1dern"Luftf. Forsch., 'Nr. 13, 1936, S. 262.
See translation N.A.C.A., 'f.·,.M. 814, 1936:"Experimental Studies of the" Effective Width ofBu'ckled She'ets It
128. ""Leggel:t:., "1);-M.A."On the Elastic Stability of a Rectangular Platewilen'Subjec.ted to Variable Edge Thrust lt
Proceedings of the Cambridge Phil. Soc., Vol. 31,1935, P: 368.
129. Leggett, D.M.A."The Buckling of a Squar~ Panel Under Shear ~-Jhen
One Pair· of Opposite Edges isClamped lJ
R. & M. No. 1991, 1941. . .
130. Levin, L~R. and Sandlin, C.W., Jr."Strength Analysis. of Stiffened Thick Beam ~"ebslf
N'.-A.C.A. ,7~N. 1'820, 194.e,.
131. Levy, S. ,"Bending of Rectangular plates \vith LargeDefLections"N.A.C.A., T.N. 840, 1942.
132. Levy, S'.,"Square plate With Clamped Edges Under .NormalPressure producing Large Deflections" .N.A.C.A4, T ..N .. 847" 1942 ..
133-.. Levy, s.ffBuckling of Rectangular, Plates wi.th BUilt-InEdges." 'A.S .M.E.:t Trans. > VoL .. -64,. 1942, p ... A 171. ..
134. Levy, s. ."Large-Deflection Theory of Curved Sheet"N.A.C.A., T.N. 895, 1943.
135.' Levy, S., Fienup, K.L., and Woolley, R.M.lTAnalysis of Square Shear Web Above Buckling Loadff
N.A.C.A., T.N. 962, 1945.
'136. Li, Y.;S."Theoretical and ExPerimental Study of ' the Behaviour of Thin· Flanged Box Girders in Pure Bending lf
Thesis for degree of Ph.D. £n Univ. of'London, 1948.
l37~ Lungbottom, E. and Heyman, J.;.'~xperimental Verification of'the Strengths ofPlate Girders Designed in Accordance with theRevised British Standard IS3: Tests on Full S~eand on Model Plate Girders1f
The Institution of Civil Engineers, Great .. GeorgeStreet, tVestminster,cLondon s .. toJ.l, Struct. paperNo. 49, 1956, pp. 463-486.
138. Lundquist, E.-E.ifComparisoD, of Three Methods for. Calculating theCompressive Strength of Flat and Slightly CurvedSheets and Stiffener CombinationH
N A.C.A., T .N. 455.
139. Lundquist, E.E."Local .Instability of Symmetrical RectangularTubes Under Axial Compression"N A.C.A., T ..N. 686, Feb. L93S.
If\)
~I
140"
141.
142.
Lundquist 3 E .. E ..IfLocal Instability of Centrally Loaded Columnsof Channel-section and z-section tt
N~A .. C~A~, T .. N. 722, 1939.
Lundquist, E.E .. and Stowell, E.Z .."Critical Compressive Stress for Flat Rectangularplates Supported Along All Edges and ElasticallyRestrained Against Rotation Along the UnloadedEdges t1
N.A .. C.A .. , T~N. 733, 1942.
Lundquist, E.. E. and Stowell, E.Z."Critical Compressive Stress for OutstandingFlanges 11
N.. A .. C.A .. , T .. N.. 734, 1942.
147 .. Mackey,. S .. and Brotton, DeM ..HAn Investigation of the Behavior of a RivetedPlate Girder Under Load tf
Structural Engineer~ Vol. 30, No.4, 1952, p.73.
1480 Madsen, 10;ttReport on Crane Girder Tests"Iron and Steel Engineer, Vol .. 11, Nov~ 1941~
pp.47-97.
149. Mayers, . J. and Budiansky, B.tfAnalysis of Behavior of Simply Supported FlatPlat~s Compressed Beyond the Buckling Load intothe plastic Range"N A.. C.A., T.N. 3368, 1955.
143. Lundquist, E~E .. and Stowell, E.Z.tlRestraint Provided a Flat Rectangular plate bySturdy Stiffener Along the Edges of the Plate"N.A.C .. A., T.N. 735, 1942.
-144 .. Lundquist, E .. E., Stowell, E.Z., and Schuette, E.H.IIPrinciples of Moment Distribution Applied toStability of Structure~ Composed of Bars orplates U
N.A .. C.. A., W.. R. L-326, 1943.
145. Lurie, H..riLateral Vibrations as Related to StructuralStabilityHCa~if. Inst. TechnO', Guggenheim Aeron. Lab.,Rep~ No .. 2, 1950.
146 . Lyse, I.. and GodfreY:J H.."Investigation of Web Buckling in Steel Beams:!A.S.C.E .. , Trans., 1935, po 675.
150. Marguerre, K.TtDie {{ber die Ausbeulgrenz.e belastete platte Energieansatz und Differentia1g1eichungen1f
Z.A.M.M., Vol. 16, 1936, s. 353.
I1Plate Loaded Beyond the Buckling Load Potential Energy and Differential Equations"
151. Marguerre, K.flDie mittragende Breite der gedrllckten Platte"Luftf. Forsch., Vol. 14, 1937~ S. 121.
"The Apparent Width of the Plate in Compression lt
Translated into English: N.A .. C.A':l T.N. 833" 1937.
152. Marguerre, K.Hueber die Behandlung von St:abilitMtsproblemenmit Hil£e der energetischen Methode H
z.angew. Math. u~ Mech. 7 Vol 0 18) 1938, s~ 57.
nOn the solution of Stability Problems byEnergy Methods"
IJ\)\..rlI
153. Marguerre ~ K.TlZ.ur Theorie' der gekrUmmten Platte mit grosserFormHnderungU
Proe. 5th Int. Congr. for Applied Mech.~ Vol. 5,cambridge, Mass .. ~ 1939, - p. 93.
"On the Theory" of the CurYed, Plate. with LargeDisplacements fl·
158. "Massonnet, Ch."Le.- voilement des ,plaques planes'solliei.tees'
dans, leur plan" ~
A. I..P .C., Rap. f., 3e congres, Liege, Belgique,·septembre 1948, pp.• 291-30Q.
liThe Buckling of Plates"
154.. Marguerre, K. und ~effz, E.'~eber die TragfMhigkeit eines IHngsbelastetenPlattenstreif.ens nach ueberschreiten der Beullast fl
z. angew. Math. u. Mech.• ,Vol. 17, 1937> S. 85.
Tl.Qn . .the Load-ca:rrying-Gapac.i-ty -,of-----a- .Wagi.tudinallyLoaded plate Strip in the post Buckling Rangelt
155. Massonnet, Cn.riLes relations entre lesmodes normaux de vibrationet La stabilite de_s systemes elas"tiques"Bull. C.E.R.E.S., Liege, Tome I, Nos.1-2,. 1940.
'~he Relations Between the Normal Modes of Vibration and the Stability of Elastic Systems H
159. -Massonnet , Ch."Recherches experimentales sur Ie "0ilement, del'ame des poutres a "be pleine ff
Bulletin duCentre d'Etudes, TomeS, 1951,pp. 67-240, au A.I.P.C., ~~bl.prel., "4e congrescambridge-Londres, .1952" pp. 539-555.
t1Experimental Investigations -of ·t'1eb Buckling ofPlate Gird~rsll
160. Massonnet, Ch."Recherches sur le dimensionnement et le raidissagerationnels de l'ame des poutres a ame pleine, entenant compte du danger ·-de voilement U
. Annales de l'Institute Technique du Batiment ~t
des Travaux Publics, NO- 71, nov. 1953,7 pp. 1062-1080.
If\)0'I
157; Massonnet, Ch.IIEssais de voilement sur·poutres a ame·raidie"tse' congres Int-ernational des Centres d r Informationde l'Acier. (~ee Ref.' 161)
"Buckling Tests of Stiffened Plate Girders"
-162. Massonnet , Ch."Stability Considerations in· the Design of SteelPlate Girders"A.S.C.E., Proc. -Vol. 86, No. ST1, paper .No. 2350,January 1960.
156. Massonnet, Ch."La stabilite dellame des poutres munies de.xa.i.disseur.s horizontaux .e.t so.Llic..i.tees-par. ,flexion.purerl
A.I.P.C., Mem., Vol. 6, Zurich, 1940-41, pp. 234-246.
liThe Web Stability of Longitudinally StiffenedPlate Girders Subjected to Pure Bendingtr
161.
I1Invest.igations·on the Design and the EfficientStiffening of l~ebs in Plate Girders, Taking inAccount Web Buckling"
Massonnet, Ch •.f1Essais de voilement sur poutres a ame raidierl
A.I.P.C., .Man., Vol. 14, Zurich, 1954) pp. 125~186)oU4cier~ ·NO· 2, ~eV:ier 1955, pp. 3-12.
HBuck~ing Tests of Stiffened plate Girders rl
163. Massonnet, Ch. et Greisch, R.flAlbaques permettant Ie choix rapide de 1 J epais,seur
de ll ame d i une poutre a moe p1eine et de11ecartement des raidisseurs vert~caux en tenantcompte du danger de voilement"A.I.P.C., Rap. f •. , 4e congre.s, Cambridge~ondres"1,952; pp. 299-308, ainsi que'Notes techniques publiees par 1a C.E.C.M.,Bruxelles, 1953, editeur Fabrimetal.
'.'Charts for a Plate Girder, E~,etermining the Webthickness and the Spacing of Vertical StiffenerTaking into Account the' Factor of safety AgainstBuckling;' -
168., Milosavljevitch, M.IfSur 1a stabilite des plaques"rectangulairesrenforcees par des, raid~sseurs',et, s'ollicitees,it' 1a flexion et au,cisaillementU
A.I.,P_C.,- Mem~ ,Vol·.. 8,.l947,. pp,. 141-160.
Han the Stability of Rectangular plates Reinforcedby Stiffeners and Subjected to Bending and Shear"
169. Moheit" w."schubbeulung rechteckiger Platten mi.t' ei.nge-spannten RMndern fT ~
'Thesis Techn. Hochschule, Darmstadc y Leipz~g~ 1939,oder Stahlbau, '19.40, S. 39.
(~.~
lb4-~ _' Maulbe~t.sc~ ,J_.L...."Buckling of Compressed Rectangular plates withBuilt-In-Edges"A.. S.M .. E., APM, Vol. 4> 1937, p. A59"
165. Melan, E.HUeber die StabilitHt von St,;{ben> welche aus einemmit'Randwinkeln verstirkten Blech bestehenf1
3 .. Int. Kongress, ftlr'angew. Mechanik, Vol. 3,1930,s. 59.
flori, the Stability of Members Consisting, of a Web,and Edge Angles" .
166 . Meyerding"Knickung von lHngs- und querversteiften ebenen .Blechen"Techn. Berichte der Luftfahrtforschung, Bd. II,1944. '
f~he Buckling of Longitudinally and TransversallyStiffened Sheets"
1670 Miles, A.J."Stabi..lity of Rectangular plates ElasticallySupported at the Edges"Jour.Applied Mechanics, Vol. 3, 1936, p. A-47~
'I'Buckling of Rectangular Plates with.Clamped Edges'Due 'to'-Shear't
170.. Moisseiff, L.S. and Lienhard, F.tTTheory of Elastic Stability Applied to StructuraLDesign" .A..S.C.E., .Trans., Vo~. 106, 1941, p. ) ..052.
171. Moore, R.L."An Investigation' of the Effectiveness of'Stiffeners on Shear-Resistant, Plate Girder Webs T1
N.A.C.A.,- T.N. 862, 1942.
172. Moore, R.L~
.TlObservati'3ns on the Behavior of, AluminumA110yTest.Girders"A.S.C.E., Trans., Vol. No ... 112~ 1947, pp __ : 901-920.
173. MUller-Magyar:L _TlBeitrag, ZUID' Uberkritischen Verhalten eines dlinn~,
wandigen, verstei£ten Plattenstreifens unter Druck1,
Federhofer-Girkmann-Festschrift, Verlag Deuticke,Wien, 1950. '
I1Behavior ,of' a Thin Stiffened Platestrip underCompression in the ·post Buckling Region"
If\)-J
I
174. Nadai', A."ElaStische Plattenl~
spr~ger-verlag,."Berlin,. 1925.
"Theory of Elastic' Plates" (Book)
1,80. P£lHger,. A."StabilitHtsproblem.e der Elastostatik~'
Springer-Verlag,. Berlin,. G8ttingen,:. Hei.delberg,1950,.•
"Elastic Stabili.ty~f" (Book)-
183,. Reimtzhuber, F.UBeitrag zur Berechnung gedrUckter, dlInnwandigerProfile oberhalb der Beulgrenze"Luftf. Forsch., Vol. 19, 1942, S. 240.
175.
176.
Nagel, H."gtabilitHt gedrUckter Rechteckpl?tten mitstreifenweiser konstanter DickeTt
Diss. T.R. Hannover, 1942.
"The Stahi·lity of' a Compressed Rectangular Platewith Piecewise constant Thicknessll
N81ke, K.·'·£i-egangsbeahmg·-tier'·"1~eCh1:eC1q11Q.'tte':m1't--e1.nge-spamiten,LlingsrHnciern" '.Bauing •. , Vol. 17, 1936, S. 111, Und· .lng'. 'Archiv, yol. 8, 1937, s. 403.
"Buckling strength of Rectangular Plates withClamped Edges 11.
181.
182.
Pippard, A.J.S., Sparkes, S.R •. , and Chapman, J.C.'''Experiments on Flexure of Rectangular Box
Girders .on Thin Steel Plating"Colston papers, Symposium on Engineering..Struc~es, Bristol, 1949.
pride, R.A. and Heimerl, .G.J ..llPlast'ic Buckling of Simply 'Supported Compressedl'lat'eS"uN.A:C~A., T.N. 1817, 1949.
If\)CDI
177. anat, E.T. and Drucker, D.C."Inelastic Instability ~d Incremental Theory ofplasticity II ,_ ,o--_r. __.,
J. Aero. Sci)~ Vol. 20'j 'No. 3, March 1953, p.181.
17,g .; .·.p..eters,,,'~.-G.;.
"Buckling Tests of. Flat. Rectangular Plates UnderCombined Shear and .Longitudinal 'Compress~onn
N.A.C.A.. , T .N.· 750, 1.948. .
179.- PflUger, A.flZum Beulprob1em.der anisotropen Rech-teckplatte"Ing. Archiv, Vol. 16,1947,.5.111/20.
"an th.e Buckling of the Anisotropi.c Rectangularpiatell
"Contribution to the-problem of Compressed, Thinp+ofiles Beyond Bucklingtf
184. Reissner" 'E.IlBucklingof· Plates with Intermediate RigidSupper,tst' "-J. Aero~. Sci. ,Vo.l.. 12, 1945:1 p. 375.
185. Reissner, H."Ueber die Kni.cksicherheit ebener Bleche"zentralblatt derBauverwa~tung, 19-09, s. 93.
"Qn the Buckling of Plane Plates"
• ~ 1 ...... ~
186. Rendulic, L~
HUeber die StabilitHt von StHben" welche auseinem mit-Randwinkeln verstHrkten Blech bestehen"Ing. Archiv, Vol. 3, 1932, s. 447.
"On the Stability of Members Consisting of a'WebPlate and Angles"
187. Ritz, w.ttueber eine neue Methode zut~ LHsung gewisserVariationsprobleme der mathematischen Physik"Journ. f.d. reine U'. angew. Math .. , Vol. 135"1909, s. 1.
nOn.a N~w Meth.od for Solving Certain Variationaliroblems'-' in the :Fie1.cl'6E~atnemati:ea:1''Phy'Si'C~-U
188. Rockey, K.C. .... "The Design of Intermediate' Vertical Stiffeners
on ~'1eb Plates Subjected to ShearnAluminum Development Assocn., Tech. Memo No~ 295C,(British) .
189. Rockey, K.C."Shear Buckling of a Heb Reinforced by VerticalStiffeners and a Gentral Horizontal Stiffener"I.A.B~S.E., Publ .. Vol. 17, 1957") p .. 161.
190~ Rockey, K.C. and Jenkins, F.:rThe Behav'ior of Web Plates of Plate GirdersSubjected·to Pure Bending"Structural Engineer, Vol. 35, No.5, 1957, .
..pp .. 176-189~
191. Rockey, K.C."t..Jeb Buckling and plate Girder Design"Engineering (36 Bedford St., London, W.C. 2),Vol. 185, No. ~800, p. 312, March 7, 1958.
192. Rockey" K~.C.
"web Buckling and the Design of Web Plates'"The Structural Engineer" February,. 1958Discussion on the paper:The Strtic tural Engineer, september, ~958 •.
193.· Rode, H.H~
ffBeitrag ZI..lr Theorie der KnickerscheinungenJT
Eisenbau, Vol. 7, 1916, s. 121,. 157, 210, 239und 295 ..
"Contribution to the Theory of (Plate) Buckling lt
For that time a very advanced paper written bya man with wide experience in designing plategirders.
194. RoS,· M. and Eichinger, A.On inelastic plate buckling.I.A.B.S.E., F. Rep." 1st Congress, Paris, 1932,p. 144.
195. Sattler, K."Beitrag zur Knicktheorie dllnner Plattenr!Forschungsanstalt Gutehoffnungshlltte,Mitt~, Vol. 3, 1934/35, S. 257.
"Contribution to the Buckling 'Theory of ThinPlates"
196•.Sazawa, K. arLd Watanabe, ~.
"Buckling of a Rectangular Plate with FourClamped Edges-·-Re-Examined with Improved Theory"Repts. Tokyo Imp.Univ .. Aeronaut. Research Inst.,Vol. 11, No. 143, 1936.
197. Schapitz, E~
'~eitrMge zur Theorie des unvollstRndingen Zugfeldes"Luftf. Forsch., Nr. l4~ 1937, S .. 129.
"Contributions to the Theory of. th,e Incom"pleteTension Field"
I£\)
'"t
203. Schleicher, F.-"Stab:i?-~:cH.tsprobleme-vo~lwandi.ger Stahltragwerke ..
Uebersicht und Ausblicklt
Bauing-., Vol. 15,. 1934, S. 205.
198. Schapitz, E."F_estigkeitslehre fUr Leichtbaun
Deutscher I~g. Verlag G.m.b.H.; DUsseldorf.
"Strength of Materials for Light Gages Steeland Aluminum Structures" (Book)
199. Scheer., J."Neue -Beulwerte ausgesteifter Rechteckplatten"Stahlbau, Vol. 22, 1953.
"New Buckling Values of Stiffened RectangularPlates ll
~2'9<3.. SClleer,~ ;;l•.HZum Problem der 'GesamtstahilitHt von einfachsymmetrischen I-TrHgernJI
Stahlbau, Vol. 28, 1959, S. 113, S .. 165 ..
"an the Problem of the Complete-Stability*of Simply Symmetric Girders with I-Sections"
* How does _web buckiingaffect lateral bucklingof the beam and vice versa? In a Doctor_f~;
dissertation the author investigates theinteraction of these two stability cases.
f.04.
. 205.•
"Stability ,Problems of Plate Structures .-, Surveyand butlook" .Contains.smal1. tabula of optimum st~ffneS5 forstiffeners ..
Schleicher, F .."Einfluss der Querdehnungauf di.e Stabilitlit vonStahlplatten fl
Stahlbau, Vol. 8, 1935, S. 7.
"The Influence of Poisson's Ratio on the Stabilityof Steel Plates"
Schleicher, F •"Einfluss der StabilitMt· der Stegbleche auf dieGestaltung vollw3Ildiger BalkenbrUckentt
I.V.B.H .. , Vorb., 2. Kongress, Berlin-MUnchen,1936" S. 1391.
IJThe Influence of the Web Stab.ility on'the Design,of Plate Girder .Bridges U
IWoI
201. Schleicher, F.. .'~-eK-ni-ckspa.nnUng:en-von ::ei:rrgespannten, 'recllteckigen Platten"Mitteilungen ·derForschungsanstalten Gutehoff-".nungshlltte, Konzern 1, Heft 8, 1931.
,".-.-
UBuckling Stresses of Rect~gular Plates withClamped·EdgesH -
202. SChleicher~ F.UStabilitHt leicht gekrl:lmmter RechteckplattenH
I.V.B-.H.,·Abh., Vol. 1, zHrich; 1932, S .. 433.
"The Stahil:ity o£-Sl:ightly Curved RectangularPlatesn
206 • Schleicher, F •. und Barbre, B.nStabilttHt·versteifterRechteckplatten mitanfHnglicher Ausbiegung"Bauing. Nr. 18, 1937, s. 665.
nOn the Stability of Stiffened Rectangular Plates~aving Initial Deflections"
207. Schleicher~ F."Unelastische Beulung versteifter Stegbleche'·Bauing .. ~ Vol. 20, 1939, S. 217.
nlnelasticBuc~lingof Stiffened I-lebs n
208. Schleicher, F.flU~ber die B2ulungvQn Re"chteckplatten mitanfHng1icher AusbiegungnForschungsh .. aus do Gebiete do Stahlbaues, Nr. 6,1943,. s. ,146.
nOn the Buckling of Rectangular Plates withInitial-Deflections"
209. Schleicher, F.1'Taschenbuch fllr Bauingenieure, Erster Band,tSpringer-Verlag, Berlin, G8ttingen, Heidelberg,1955.
"Handbook for Civil Engineers"
210. Schmi~den, C."nas Ausknicken versteifter Bleche unter
Schubbeanspruchungt t
z. F1ugtec~. u. Motorluftsch .. , Vol. 2:1, 1930,s. 61. .
"The Buckling of Stiffened Sheets in-Shear"Translated into English by U.S~ Experim.entalModel Basin,NC? .. 31, 1936.
211. Schnadel, G."Die ueberschreitung.derKnickgrenze bei
diinnen .platt-en"3. rnt. Kongress. fUr angewandte Mechanik,publ., Vol. 3;.Stockholm,1930, s. 73.
"Post. Buckling Behavior on Thin Sheets"
212.- Schuette, E.H. and McCulloch, J.C~
"Charts for the Minimum weight Design ofMultiweb Wings in Bending"N.A.C.A., T~N. 1323, 1947 ..
213. Sc~, T.E."Die quadratische Plat;te- bei Schubbelastimg.·oberhalb der BeuIgrenzen
rng. Arcbiv', Vo~. 1], 1949, S. IIi•.
liThe Square plate Under She~ Beyond BucklingJT
214. Schwerin, E.'"ueber die Knicksicherheit ebener Bleche beL.,exzentrischer Randbelastungr•
z. angew. Math. -u. Meeh. ,.-Vol. 3', ..1923, S. ~22 ..
"On Buckling of. Eccentrically Loaded> Plane Sheets"
'215. Scott,. M.. and. Weber, R..L."Requirements for 'Auxiliary stiffeners Attachedto Panels Under Combined Compression. and Shear: tr
N.A.C.A , T.N~ 921, 1943.
216. sechler', E.E.f~he Ultimate Strength of Thin Flat sheets in. Compression" .
Guggenheim Aeron. Lab., Calif. lnst. of. Teehn.,.Publ.· 27, 1933.
'217. Sechler, E.E."Stress 'Distributi.on in Stiffened panels· UnderCompressionfl
J .. Aero .. ~ci., Vol. 4, "1937, p. 320.
218. seide,p. and Stein~ M~
"Compressive Buckling of. Simply Supported placeswith Longitudinal Stiffeners"N.A.C.A., T.N .. 1825, L949.
219 • .Se'ide ,. P."The Effect.of .Longitudinal Stiffeners Locatedon One Side of a plate on the Compressive Buck1irigStresso£ the Plat~-StiffenerCombinations"N.A.C.A., T.N. 2873, 1953. "
.~~~-
I\....aJI--'I
220. Seydel, E. .HUeber das Ausbeu1en eines orthotropen Plattenstreifens (einer sehr langen, rechteckigen,versteiften Platt"e) bei Schubbeanspruchung"Proc .. of 3d Int. Congr. for Applied Mechanics,Vol .. 3, Stockholm, 1930.
"On the Buckling of an orthotropic Plate (BeingExtremely Long, Stif-fened and of RectangularShape) Due to Shear"
221. seydel, E."Be{trag zur Frage des Ausbeulens versteifterPlatten unter Schubbeanspruchung"Jahrbuch, Deutscher Verein fUr Luftf. Forsch.,19~0.~ s. 235 ..
"Contribution on the problem of Buckling ofStiffened Plates Due to Shear"Translation into English: N A.C.A., T.M. 602, 1931.
222. seydel, E."Ausbeul-Schublast rechceckiger platten (Zahlenbeispiele und Versuchsergebnisse)" .z. Flugtechn. u. Motorluftsch., Vol. 24, 1933,s. 78~ .
"Buckling of Rectangular Plates Under Shear ..It~erical Examples and Test ResultsI'
223.,._~ydel, E."Das Ausbeulen von rechteckigen'ib orthogonalanisotropen platten bei_Schubbeanspruch~g"
Ing~ Archiv, Vol. 4, 1933, s. 169~
"On the Buckling of erthogonal AnisotropicPlates Under Shear"
224. Sezawa, K."Das- Ausknicken vonallseitig befestigten undgedrUckten Rechteckplatten"z .. angew ... Math. u ... Mech., Vol .. 12, 1932, S .. 227 ...
"The Buckling of Compressed Rectangular plates"
225.. Shibuya, I."A Method of Estimating the Theeiretical BucklingLoad from Experiments on Rectangular Plates"Proe .. 2nd Nat .. Congress for Applied Mechanics,Japan, 1952, p. 139.
226. Sievers, H. und Bornscheuer, E.- '"Ueber dis Beulstabilicllt durchlaufender Plattenmit drehsteifen LHngssteifen"Stahlb~u, Volo 22, 1953, s. 149.
liOn the Stability of Continuous Plates with Longitudinal Stiffeners Having Torsional Rigidity"
227. Skan, s.w. and Southwell, R.V .."On the Stabili.ty under Shearing Forces of- aFlat Elastic Strip"Froc .. Roy. Soc., Series A, Vol. 105, London,1924, p .. 582.,
228. Sommerfeld, A."Ueber die Knicksicherheit der Stege von Walzwerkprofilen"z. f. Math. _u. Phys., Vol .. 54, 1906., S .. 113.
"On the Buckling Safety of webs of Rolled Beams"
229. Sparkes, S ..R~tiThe Behaviour of the webs of Plate Girders"Welding Research, Dec. f947, p. 4.
ILvI\)I
230. Sparkes, S.R., Chapman, J .. C.. , and Pippard, A.J .. S."Experiments on the Flexure of Rectangular BoxGirders of Thin Steel Plating".Research, Eng. Struct. Suppt., 1949, p. 61.
231. Stein, M. and Fralich, R.W."Critical Shear· Stress of Infinitely Long, SimplySupported Plate with Transverse Stiffeners"N.A.C.A., T.N.' 1851, 1949~
232. Stein, M. and Neff, J.'TBuckling Stresses of Simply Supported -Rectangularplates in Shear"N.A.C.A., T.N. 1222, 1947.
233. Stein, O."Die StabilitHt ,der BlechtrHgerstehbleche imzweiachsigen SpannungszustandT'
Stahlbau, Nr. 7, 1934, S. 57.
"The Web Stability· of Plate-Girders Under aTwo-Dimensional State of Stress"
234. Stein, o.I1StabilitHt ebener Rechteckb-leche unter Biegungund Schub"Bauing. Vol. 17, 1936, S. 308.
t~The_St-ability<)f-Plane Rec'tangular ·Sheets UnderBending and Shear'"
235. Stiffel, R."Biegungsbeulung versteifter Rechteckplatten"Bauing-., Vol. 22, 1941, 5. 367.
"Buckling. of Stiffened Rectangular Plates UnderBending"Gives design chart for a longitudinally stiffened plate" with stiffener at a quarter of theplate depth.
236. StowelL, E..Z."Critical Shear Stres of an. Infini.tel.y Long- Flat Plate with. Equal Elasti.c RestraintsAgainst Rotation Along the. Parallel Edges tT
N.A.C.A., W.R. L-476, 1943.
237. Stowell, E.Z.TtA Unified Theory of Plastic Buckling of Columsand Plates"N-A.C.A., T.N. 155&,1948.
238. Stowell, E.Z."Critical Shear Stress of an Infinitely LongPlate in the Plastic Regi.onTl
N.A.C.A., T.N. 1681, 1948.
239. Stowell, -E.Z. and Lundquist, E.E-.nLocal Instability of Columns with Channel andRectangular Tube sections"N.A.C.A., -T.N. 743) 1939.
240. Stowell, E.Z., Heimerl, G.J., Libove, Ch .. and.Lundquist, E.E.
HBuckling Stresses for Flat plates and· Sections"A.S.C.E. Proc. Vol. 77, July 1951 (Separate.No. 77)
241. Stllssi, F."Berechnung der Beulspannungen gedrUckterRechteckplatten"I.V.B.H.I; Abh., Band 8, Verlag Leemann, ZUrich"1947, S. 237.
"The Calculation of Cr:iti.cal Stresses of CompressedRectangular Plates lf
24-2. St{lssi, F.I'Zur Bemessung von Leichtbauten aus Stahl r ,
I.V.B.H., 5. Kongress, Schlussbericht, Portugal,1957.
"Design of Light Steel Structures"
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I
243~ Sttlssi., F' .. , -Dubas,.~ ch .. etoubas, P ... "Le voilement de 1-' ama__ de-s poutresflechies,
avecraid~sseurau c'inqui~e' superieur"A ... I .. p.C .. Mem.7 vol.• , Zurich, 195T..
"Web Buckling of' plate Girders with LongitudinalStiffeners in the Upper Fifth Poi.Q.t of the Web"
244. Stllssi, F", Duba:s, Ch. et Dubas, P ..TILe voilement del'ame 'des RPutres fl~chies,avec raidisseur au cinquieme superieur.Rtude complementaire"A.. I ..p .. C.Mem"" 8 vol .. , Zurich, 1958.
"Web Buckling of Plate-Girders with .Lo~gitudinal
Stiffeners in the upper Fifth Point of the Web ..Further SJ:udy'"
245. Stllssi, F·.. , Ko'llbrunner, C..F. und Walt, M.."Versuchsbericht {{ber das Ausbeulen der auf einseitigen, gleicbmHssig und ungleichmMssig verteilten Druck beanspruchten PlattenT
'
lnst. f. Baust. a.d. E.T.H .. , Mitt. Nr. 25,:Verlag Leemann, Zllrich, 1951.
TlTest Report on Buckling of Uniformly and NonUniformly Compressed"Plates"
u .'24"6. Stussi, F., Kollbrunner, C.. F.. und ~.;ranzenried., W*
, "Ausbeulen rechteckiger·platten unter Druck,Biegung und Druck mit Biegung"lnst.• f. Baust .. a.d .. E.T.H .. , Mitt. Nr. 26,verlag Leemann, zllrich, 1953 ..
"The Stability 0'£ Rectangular Plates Under Uniform·Compression, Pure Bending,. and'Compression andBending" . - .,ContaiI;l5 calculations which check and improvevarious k-values obtai.ned until 195'~" They areconsidered. to be the, most accurat'e bucklingvalues. In connection wi.th this numerical datais a folder containing a chart with k-values(see next reference).
247 • stUssi, F., Ko.llbrunner,. C.F·... und wanzem:i.ed, .R_llTabellen der Beu1.werte." k ff
rT ..K.V.S.B .. ,zllri.ch, ~ ·1953.
trTables of' Buctling jTalues k"
248. Taylor, G.I ..."The Buckling Load for a Rectangular Plate. wi.thFour Clamped Edges"Z .. angew .. Math .. u .. Mech., .. VoL.... 1.3, 1933, p.147 ..
249. ThUrlimann, B."Strength of Plate,Girders."A.I.S.C .. National Engineering Conference,.'proceedings 1958, American Inst:ltute. of SteelConstruction,.. New York.
250. Timoshenko, S. _"Einige StabilitM.csprobleme der E1astizi.tMtstheori.e"zeitschrift f& Mathematik und Physik, Vol. 58,1910, S. 337.
·"Some Problems of Elastic Stabi.li.ty1t
251. Timoshenko, s .."ueber -die S'tabilitlit versteifter Platten"Eis~nbau7 Vol. 12, 1921, s~. 147.
Hon the Stability of sciffenedPlate·sTJ
252. Timoshenko, s."Stabili.ty of the Webs-of plate Girders Tt
Engineering, Vol. 238, 1935, p. 207 ....
253. Tlmoshenko, S'."Theory of Elastic Stabi1.ityfl (Book)McGraw-Hill Book Company, .New York and London,1936.
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I
254.. Torre, K."Vorschlag filr die praktische Beulberechnungversteifcer Rechteckplatten ll
Stah1bau, Heft 10/11, 1944 ..
"Suggestions-for the practical Calculation ofCritical Loads of Rectanguiar Plates lf
255... Trefftz, E ..HEin Gegenstllck zum Ritzschen verfahren"
2 ... Kongress fllr angew ... Mech ... , Abh., ZUrich,1927, S~ 131-137.. -
'fA Method Opposite to the Ritz Procedure"
256. Tref~tz, E... >
t1Zur Theorie der StabilitMt des elastischenGleichgewichtes ll
z. angew .. Math .. u. Mech ... , .'la.l. 13, 1933, 5 .. 160 ..
"On the Elastic Stability of Equilibrium Canfigurations 1t
257. Trefftz, E .. and Willers, F .. A."Die Bestimmung der Schubbeanspruchung beimAusbeulen rechteckiger Platten"z. angew .. Math. u. Mech~, Vol.16, 1936, s. 336.
"The Determination of the Shear Strength ofRectangular plates in the Moment of Buckling"
258. Wagner, H.. ."Ebe:D.e BlechwandtrHger mit sehr dilnnem StegblechT1
Z .. Flugtechn. u. Motorluftsch., Vol. 20, 1929,s. 200, 227, 256,279 u. 306.
"plate Girders with Extremely Slender webs fl
25 9 • i.J'ang , C .. T .."Nonlinear- Large-Deflection Boundary-Valueproblems of Rectangular Plates:'N.A.C.A., T.N. 1425, 1948.
260.· Wang, C.T. and zuckerberg, H.rtInvestigatiolJ, of. S'tress Distribution in Rectangular plates with Longitudinal Stiffeners UnderAxial Compression after Buckl.ingtl
N.A.C.A., T.N. 2671, ,1952.
261. Wang, T.K."Buckling of Transverse Sti.ffened plates Under ShearnJourn. of Appl. Mechanics, Vol. 14, No.4,Dec. 1947, p. A-269.
262. WHstlund, G. and Bergman, St."Buckling of Webs in,Deep,Stee1 I-Girders rt
Report of the Institution of Structural Engineeringand Briqge Building, Stockholm, 1947, p. 206 orr.A.B .. S.E-., Publ., Vol. 8" -1947 ,p. 291.
263. Way, S .."Stability of Rectangular plates Under Shear andBending Forces"Journ. of App1. Mechan'ics, Dec. 1935, andA.I.P.C., Rap. f., 1936, pp .. 631-638. '
264.. Weidlinger, P."Aluminum in Modern Architecture"Reynolds Metals Company, Louisville, Kentucky.,Vol. 2, 1956.
265. Windenburg, D.. F."The Elastic Stability of Tee Stiffeners H
U.S .. Experiinental Model Basin, Rep. 457" 1938.
266. Winter, G."performance of Thin Steel Compression Flanges!lr.A ... B.S.E. Pre1. Publ. 3rd Congress, Liege, 1948.
267. Winter, G."Post-Buckling Strength of Plates in Steel Design"I.A.B.S.E., F. Rep.,.l952, p. 268.
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I
2680 Young, J ..M. and Landau, R.E.- "A Rationa~ Approach to the Design of Deep
Plate Girders"Instn; Civ. Engrs., Prac., Pt. 1, Vol. 4,1955, p. 299. -
274. Tall-, L. and Ketter,- R.L."On -the Yi.eld Properties of Structural. SteelShapes"Fritz Engineering Laborat:ory Report No. 220A..33,Lehigh University, 1-958 ..
ADDITIONAL REFERENCES
* *- * 275. Thllrlimann, B. and Eney, W.J.'Modern Installation for Testing of LargeAssemblies Under Stati.c and Fatigue Loading"'Society for Experimental Stress Analysis,proceedings, Vol. XVI,- No.2.
269. Conyers; A_L. and Ozell, A.M.~...RepDrJ:~ . Tr.ansf.er- .of -Stre&SeS--in---Wel4edCover Plates tl
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270. Dill, F.H."A Report on Transfer of Stresses in Welded
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JW0'I
Graphical Summary of ReferencesCountry
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Part 1:
-1-
THE TEST GIRDERS
1.1 Introduction
The purpose of part 1 is to describe the test girders
and the physical properties of materials used. Then, based
on this information, standard reference values such as
"yield loads", "plastic loads", "critical loads", and com-
puted deflections will be established. The organization
of the test ,program must first be, described.
A girder section can be subjected to bending, shear, or
a combination of· both these loadings. In this research pro
ject all three conditions were investigated. Consequently,
three different test setups were used as shown in Figs. 1.1,
1.2, and 1.3. This cla.ssifies the thirteen..plate girders
into the following three groups:
Grou.p shown in subjected Girders,.
to
1 Fig. 1.1 bending GI, G2, G3, G4, G5
2 Fig. 1.2 shear G6, G7
3 Fig. 1.3 combined El, E2, E4, E5, G8, G9
Throughout the entire project the girders are termed as given
in the last column of this table.
--2-
The cross' section of some girders changed wi·thin their
lengths _. ,~he.,reason for th~s design was· to confine failure" .
t9: ac.ertain'reg1on whose loading eondi tiona were well
defined. Thi's region was the test .section proper as indi
ca'ted ·in Figs.l~l an<l1.2. The el:1d sections, flanking the test
see~'ion, onl-y diff'ered in web :thickness for the 'first· group,
.whereas in', t~e second group cover plates .. were also added. over
a. ,por'ti'on 'of their length. In the third grou.p the cross
se~tion did cnot change and the entire girder was the test
section proper. The rour girde~s termed El, E2, E4, and E5
w~re fabricated by splicing the undamaged end sections of
~.he ·corresp'ondingly numbere'd girders Gl, G2, G4 and G5.'· an'd
.reinforcing .them with cover plates-.
Each girder was subjected to at least two ultimate load
tests. After caus~ng failure in a particular panel) the
'load was remo~ed'and the panel reinfo~eed. All bending
girder' fail.urea, occurred in the compressio,n flange and thus
reinforcement consisted of welding small steel plates to
this flange. Diagonal ~nd transverse stiffeners were used
to s,trengthen the girders of the other two groups. Since
no major deformati6ns were caused in panels adjacent to the
one which failed in th~ first test, referr.ed to as. Tl, a
second test, T2, could be conducted. In some cases this
process waf3 repea.ted and additional tests', such as' T3 and
T4, were carried out.
-3'"
'Of all the po~sibl~·parametGr~ influencing the ca~rying
capaoity of,plate girde~s, the investigatio~ was reBtric~ed
to the ,.following four:
'1. Loa.ding ootidi t1on: ~ ::; '7:/0 -shear stressnormal stress
'2,. Type of cross section': various shapes of eompr. flanges
3. Web s'lenderness: ~ = bit = web depthweb thickness
4. stiffener s,pacing: a == alp = panel lengthweb depth
The first parameter was, taken care,of by choosing the three
t'est setu,ps ,pr,eviously mentioned. The. second ,parameter' was
of special import,ance to the bending girders, wherefore
three, ,different shapes of the co~pressi~n f~angeswere
chosen as illustrated with cross sections t, II, and III
shown in Fig. 1.4. Denoting with na,n the stiffener spacing,
"b" the web d.epth, and nt" the web thickness, the third and
fourth parameters completely defined the, shape of a web
panel. In the test 'program, the third parameter was varied
by b~ilding pairs of girders which only differed in the web
slenderness, such as G2 and G4, or G3 and G5. Finally, the
fourth parameter was accounted for by subdividing the test
section into panels with different lengths. After failure
occurred in a longer panel, it was reinforced and thus
failure could be, forced to occur in a shorter panel.
-4-
The parametric values of all the girders 1 test sections
are listed in Table 1.1. The added sketches indicate where
each girder failed, how the obtained tests were designated,
and where reinforcement plates were welded to the flanges
or webs. Taking as an example girder E4, the sketches give
the following information: The first test of this girder,
Tl, caused failure in the left-hand end panel whose stiff-\
ener spacing was 1.5 times the web depth. The girder was
then reinforced by subdividing each of the two larger
panels with new transverse stiffeners. Thus failure was
roread ,to occur in the right-half of the girder where the
spacing of the stiffeners was 0.75 of the depth4 This
happened in the panel adjacent to the loading stiffener
and furnished the second test, T2. Welding a reinforcing
stiffener across this damaged panel allowed for a third
test T3 in a panel whose aspect ratio was a = 0.,.
In the following sections the evaluation of girder
plate dimepsions is given first, followed by the determi
nation of steel properties, and finally, the detailed
computation of specific reference values.
1.2 Girder Dimensions
-5-
After the general survey of the girders given in
Sec. 1.1, it is the purpose of this section to establish
the accurate dimensions of each girder. The overall
dimensions, as ordered, are given in Figs. 1.1, 1.2, and
1.3; for all practical purposes they can also be considered
to be the actual ones. However, this situation can not be
expected to apply to the size of the component plates and
measurements must be taken to determine their true dimen
sions.
In illustrating the procedure used to obtain the dimen
sions and the differences between ordered and actual dimen
sions, the test section of girder Gl is used. The top
flange, web, and bottom flange of this girder are shown in
Fig. 1.5. Here, it is seen that at the ends of each plate,
a piece was cut off and used for coupons. These end pieces
were also used to obtain the width and thickness of the
corresponding plates. The dots in these portions are points
at which thicknesses were measured and the results are
recorded beside them. The averages of all the measurements
recorded were considered to be the true dimensions. Meas
ured at 20 different locations, the web presented an
interesting finding. As readings were taken from the upper
edge to the lower, the thickness was found to increase, exceeding
the ordered quarter inch thickness anywhere from 1 to 10%_
-6-
This variation is due to the fact that the web was originally
cut from a plate whose width was 100 inches and the lower
edge of the web was located at the midspan of the rolls
during the rolling o,peration. The slight flexibility of the
rolls gave this increase of two hundredths of an in,ch.
Using the same procedure and layout of observation
points, the other girders' dimensions were determined and
are presented in Table 1.2. All subsequent computations
are based on these values and other data given in Figs. 1.1,
1.2 and 1.3.
-7-
1.3 steel Properties
A great amount of time and effort was spent in evalu
ating the properties of the girders t component steel plates.
Because the property of paramount importance to this
research program was the yield str~ss, the major part of
this section is devoted to its definition and determination.
It will be seen that, although mild steel was specified for
all girder components and care was taken to obtain a uniform
yield level, a con~iderable scatter of results is unavoid
able.
Tests on tension coupons made from the material under
consideration were conducted to determine the yield level.
At least one coupon was cut from each flange plate, unless
two or more flanges came from the same slab. In this case,
a single coupon was considered sufficient for the entire
slab. This s~me principle applied to the web plates and,
in addition, a limited number of coupons were cut trans
versely to the platets longitudinal direction. The relative
location of both flange and web coupons in their respective
plates is shown in Fig. 1.5.
In Table 1.3 all coupons tested for the plates com
prising girders Gl through G7 are listed.. The additional
coupons, needed to complete the yield stress evaluation in
the group of girders under combined bendin.g and shear, are
recorded in Table 1.4. The first columns of these tables
-8-
describe the location of the plates from which the corre-
sponding coupons were cut. Although the exact dimensions
of these plates already appear in Table 1.2, for the
~onvenience, the nominal plate thicknesses are tabulated
again. Each coupon is assigned a number as shown in the
third column. Besides its number, a coupon. is designated
further by listing its steel quality according to ASTM
specifications and its heat and slab numbers provided by
the steel manufacturer. It may be observed that, if two
or more coupons have the same slab number, they originate
from one and the same rolled piece. A common heat number
indicates that the steel of these coupons were taken from
the same furnace charge, therefore they must have the same
chemical composition.
Further listed in Tables 1.3 and 1.4 is the chemical
analysis procured from the mill, showing the carbon,
ma~ganese, phosphorus, and sulfur content of the steel.
In the following columns of the, tables are the yield stresses,
ultima4e stresses and elongations, all determined by the
mill according to standard practice. Finally, in the last
five columns are tabulated the results of the coupon tests
conducted at Fritz Engineering Laboratory~ The three
characteristic values of yield stress, ultimate stress and
elongation are listed here, together with the area reduction
at the fractured section and the rupture stress cr occuringr
over the reduced area. To -compare the laboratory results
~ ......'. ~
-9-
with those obtained by the mill, the former results need
further explanation.
Each coupon was machined to the dimensions given in
Fig. 1.6. These coupons conform with ASTM requirements
for plates over three-sixteenths of an inch in thickness.
(For plates below this value, specifications call for a
smaller coupon with a two inch gage length rather than the
eight inch length used.) Figure 1.6 is a typical data
sheet illustrating in detail the evaluation of pertinent
data of the coupon. Figure 1.7 is the corresponding load-
strain curve for this coupon. An extensometer was used to
obtain the strain for this figure and an electronic
recorder automatically plotted the resulting curve. The
abscissa is the average strain in inches per inch gage .
length, while the ordinate is the tension force applied to
the coupon. By converting load to stress, this d.iagram
could be considered as a stress-strain curve extending to
about thirty times the yield strain, only about one-eighth
of the complete diagram up to· the rupture point. Charac
teristic of this diagram would be the straight-lined
elastic part, the yield level and the inception of strain
hardening. Also included in this graph are: the upper
yield point; immediately ~ollowing the lower yield point;
the dynamic yield level about which the load fluctuates
during yielding; and, finally, the static yield level which
shall be discussed further.
-10-
The static yield" level is the yield stress obtained
under a zero strain rate. This strain rate could easily
,be imposed by the 120,000 pound Tinius Olsen machine used;
a screw-powered type machine which allowed complete control
of the speed of the movable crosshead. When pronounced
yielding was apparent, the movement of this crosshead was
stopped after which the load settled to the static yield
level, Fig. 1.7. After about five minutes, the speed of the
crosshead was <again set at its former value of 0.10 inches
per minute. As seen, the resulting dynamic yield level
coincided with its previous value. This procedure was
repea~ed a second time in the yield zone where another
typical V-notch in the recorded load-strain curve occUrred.
It is generally known that the yield stress level does
depend o~ the speed used to test a coupon and increases
with higher testing speeds. However, the signifioant
research work carried out in Fritz Engineering Laboratory,
Ref. 274, correlates the dynamic yield levels obtained at
various strain rates and points out that this static yield
level is a material constant which. can be obtained more
accurately than the fluctuating dynamic yield level. Since
it is impossible to maintain any constant strain rate on a
steel element such as a plate girder, it is obvious that
the static yield level must be adopted as the significant
level in the testing of structural members. Only with zero
strain rate can complete correlation between both structure
-11-
and coupon be attained. Therefore, the yield stresses cry
hencefor~h mentioned in these reports will always be the
static yield stresses. As a consequence, the ultimate load
must be defined as the highest load which the structure can
statically maintain.
The results of these carefully conducted coupon tests
can certainly be used as added data to be collated for
statistical purposes. Of the many conclusions which may be
drawn from the two summary tables, o~ly the following are
mentioned. From Table 1.3 the seven t'hres-quarter inch
coupons show the scatter of yield level which mu~t be ex-
pected when plates of equal dimensions are rolled, even
though they origin.ated from the SaPI8 ingot. The one-half
inch,an~ ~hree-eighth inch web material also came from a
common ingot but differed in thickness and, thus, in the
extent o~ rolling. This resulted in a marked difference
in the static yield levels. Furthermore, the 'static yield
levels of the three-quarter inch plates were about 10%
lower than the yield stresses determined by the mill.
However, this percentage chang~s considera~ly with the
plate thickness and the chemical composition. For plate
thicknesses greater than three-quarter of an inch, this
reduction may well be as much as 25%, as seen from Table
Contrary to the aforementioned, it was found that for
the coupons cut from the one-eighth inch plates, CF 23 and
-12-
CP 47, the relation was reversed. Static yield levels as
much as 15% higher than the dynamic ones furnished by the
mill were observed. This was then believed to be a mistake
and additional coupons adjacent to the previous ones were
cut from the plate specimen and tested by both the fabri
cator and the investigator. It can be seen from Table 1.3
that the results of these duplicate coupons, termed OF 23B
and OP 47B,were just about the same as previously obtained.
As stated before, the gage length of the mill and laboratory
coupons w~re two and eight inches respectively; the mill
coupons conformed to ASTM standards. It is interesting to
speculate as to whether the size causes such effects.
In summary, it must be emphasized again that the impor
tant material property called "yield stress", as determined
by standard practice in the mills, is not adequate for
strength predictions in research work where structures are
subjected to static loads.
For the tubular compression flanges of girders G3 and
G5, a co~pression test was conducted on a short section of
the pipe rather than tension coupon test. Reference should
be made to Fig. 1.8 where the size of this stub column, th~,to.
load-deformation record, and the computed stress-stra.in
diagram are all shown. Also the wide scattering of wall
thickness in the tested pipe can be seen. The yield stress
was evaluated from the evident yield level.
-13-
Finally, the yield stresses of all co~ponent plates
are summarized in Table 1.5, grouped according to the
respective girders. The computation of all girder reference
values is based on the data tabulated here.
-14-
1.,4 Cross Sectional Constants
In this section will be presented the moments of
inertia for all girders with their corresponding section
moduli. To compute these values, it is necessa~y to
know the cross sectional shapes and dimensions. The former
can be found in Fig. 1.4, while the latter are summarized"'1-10
in Table 1.2.
A typical computation of the cross sectional constants
is carried out below. The procedure was first to find the
moment or inertia '1 about the Z-axis which was located at. z
the mid-depth of the web. Then, after determining the
actual centroid of the section, the moment of inertia about
the neutral ax~s was found by means of the parallel axis
theorem. Finally, dividing this value by the drstance to
the extreme fibers sa and eb , the s~ction moduli Sa and Sb
were 'obta.ined. The indices "a." and "b" distinguish between
quantities above and below the neutral axis respectively.
". ..
·-15-
Computation of Section Moduli of Gl·-Tl t Test Section
12.2.' )t' 0,160
AY = Qz/A = -15.0/31.59, ~ -O~47 in
!m = I z-(Ay)2A = 14,390 - 0·472x31.59
Sa = 25 + 0.47 + 0.43 25.90 in
eb = 25 0.47 + 0.76 =25.29 in
Sa = Inlea = 14,380/25.90
Sb = In/eb = 14,380/25.29
= 555 in:;'
== 568' in),
Following the above procedure, all.necessary cross
'sectiona'l constants were COnl.puted for the girders and are·
pre,sented in Tab'le 1.6. In the. first th~ee columns of this
'table ar~ 'givan the properties of the test '~ection, namely,
the moment of inertia 'lm and the corresponding section
moduli S~ and Sb. Next, the moments.of inertia of the
bending and shear girders' end sections~ Ie, a~e added.
Finally, some special moments of inertia are given in the
last column which will now be explained for each girder:
....16-
Gl. After the first test on this girder was completed,
its top flange width was reduced by flame cutting to
13.56 inches. Thus, for computations involving GI-T2
(second test of girder Gl) this new width must be used,
resulting in I = 12,210 in4 and a neutral axis at
y = -3.158 in.
G2, G3, G4, G.5. After completion of the first tes'ts of
these bending girders, a steel plate was welded on each
side of the top flange. Each of these two plates had an
area of one square inch, had the same distance from the
neutral axis as the centroid of the unreinforced flange,
and extended over the longest panel of 75 inches. Where
from this new I-value is computed.
G6, G7. These values are the moments of inertia of the
sections under the reactions where cover plates were
a.dded, that is, re D shown in Fig. 1.2.
El. The outside cover plates of girder El were termi
nated 75 inches from its ends and, therefore, two moments
of inertia are needed to compute deflections. The value
shown in the last column applies to the end portions of
the girder. Since the third test produced failure within
this region, the values without cover plates must be used
for calculations concerning EI-T3.
-17-
1.5 Reference Moments and Loads
This section is devoted to the computat ion of ,the fla.nge
moment, yield moment, and plastic moment with the correspon
ding loads of the latter two. These moments are defined in
Ref. 7, p. 34. Their de~initions are repeated below with
the modifications needed to take into account the different
yield stresses of ~he component plates.
The flange moment, Mf
, is defined as the moment carried
by the flanges alone when the stresses over the flanges are
equal to the yield st~ess. For a symmetrical girder whose
yield stresses are the same for both flanges, this would
simply be computed as Mf =Afcryfh, where Af and cryf are the
area and yield stress of one flange and h is th~. distance
between the centroids of the rlanges. The actual girders
tested exhibited a certain degree of dissymmetry in shape
and yield stress. Therefore, the area and yield stress or
the compression flange are selected to be used for the com
putation. Incidentally, the alternate use of the tension
flange properties would not lead to any great differences.
Computations show that their use could only give a value
lower by 2.5%. When more than one plate comprises a ~lange,
a weighted yield stress of the compression rlange was used.
This weighted stress, d , will be defined as (J =J:.Acr /r.!y y y
where A and cry are the areas and yield stresses of the com-
ponent plates and L indicates the-ir summat ion.
-18-
The yield moment, M , is the moment which initiatesy
nominal yielding in the most extreme fiber. In the case
where' the yield stresses of the flanges would be the same,
it would be computed as MY = crys, where the smaller value
of the section modulus, S, would be used. Since the yield
stresses of the flanges differed, the definition that
MY= cryasa is adopted, where crya and Sa are the yield stress
and section modulus of the compression flange. As in the
case of the flange moment, the value of the yield moment,
when computed using bottom flange properties, could be lower
than the defined value by only 2.5%. In accordance with the
procedure adopted previously, a weighted yield stress was
used when the flange.was composed of a number of plates.
The plastic moment, MP' is the limiting value of the
moment which would be reached upon applying an infinite
curvature to a section, neglecting the effect o~ strain
hardening. Usually it is calculated as the product of the
girder 1 s yield stress and plastic modulus, Z. This method
assumes a section whose yield stress is constant for all its
elements. As such, it can not be used in computations in-
volving th~ test girders since most of their component parts
yielded at different stress levels. This moment will be
evaluated from the relation that MP = r..AcryyP' where the A
and cry are the area and yield stress of a section's elements
and yp is the distance from the plastic neutral axis, NAp,
to the centroid of each element.
-19-
COMPUTATION OF· PLA'STICMOMENT OFE2. ,
NA' ,.r F, '50 x 0.507
"'4.9 KsJ
Ya = 24.8 in .
,.[~Acry] a - [LAcry] b = 0
,474 + 362 + 17.69Y~ - (885 +17.69Ya} -355 -474 = 0 '
16.00 J( 1.00729.4k~i, ",
12,'(9. x 0,'769.,3S·6'ksi
l2 .19 x Oa77437~G ksi .
. IG~OO ~ 1,00729. 4.-.kS i .
Mp =2:: (Acry)yp
= 474 x26~07 +' 362 x 2$.19 + ~39 x 12.4 +
446 x' 12.6 + 355 x 25059 + 474 x 26.4~
M~ = 54,lOO'~-ih
This plastic neutral axis is found f~om the equilibrium con
dition that ~he ,sum 'of the normal .forces over the entire
cross section mUB.t vanish. USing the subsc,~i.pts a and b
mentioned before , ,t,hi~ condition is "ex:pressed as
[tAcrYJ a . - !l=AcryJ b= o. As a sample computation, the plastic
moment of E2 has been calculated apove. All necessary'
static' yield stresses are listed in Table 1.5.
To calculate the yield and plas~ic loads, ,the spans Of
the girder~ enter.. Again, due to' t:pe' different· test setu,ps,
three groups are distinguished: 'bendi~g, shear, and combined
loading.
-20-
The bending group has a constant moment over the test
section, M = 150P. Thus the yield and plastic loads are
simply computed' as Py = My/150 and Pp = Mp/150, ,where the
moments are expressed in kip-inches and the loads in kips.
The shear group, although subjected to a relatively
small variable moment, was considered to be under pure
shear. Therefore, the yield load is the load that initiates
nominal yielding at the neutral axis in the web and is com
puted from Vy = 't'yw1t/Q where Vy is the shear force at first
nominal yielding, ~yw the shear 'yield stress of the web, Q
and I are the static moment and moment, of inertia about the
neutral axis, and t is the thickness of the web. From
Fig.L2 it can be seen that V = P. Substituting this value
in the preceding equation and using the Mises yield con-
dltioh that cryw = 13' 'T:yw, the yield load will be evaluatedcr It
as p = yw where cryw is the yield stress of the web. TheY ITQ
plastic load is defined as the load which causes the web to
yield completely due to shear,- Pp :: aywAw/n, Aw being the
area of the web, Aw = bt.
The combined grou,p was subjected to both shear and
moment. Since the moment varied throughout the girderts
length, e' cross section in the failed panel was selected
at which the reference loads for each. test were to be
evaluated. This section was chosen to be at a distance of
one-half the web depth a~ay from·the maximum moment in the
panel or at the middle of ,the panel when its l'ength is less
-21-
than its depth. It is realized that this method of evalu
ating the yield and plastic loads differs from the usual
procedures used for a beam. Thus, the "yield load is defined
as the load which initiates yielding in the critical cross
section of a girder. In general, yielding first occurs at
the intersection of the web and flange where th~ yield con-
dition, o =/0 2 + 3 2/ is used to evaluate the yield load.yw 't' ,
Substituting the values of (j =MY = 12..s2 and 't'_ VQ _ PQ-- .....
I 2 I It 2Itinto the equation above, where M = Px/2 and V = P/2 from
Fig. 1.3, the yield load for the girders under combined
loading will be
= crywJ(2,5x/2I)2 + 3(Qj2It)Z'
x being the distance from the end of the girder span to the
critical cross section. If yielding does not begin at the
aforementioned point, the bending or shear case discussed
before applies.
The plastic load of any single test on a girder is
de~ined as the load producing plastification at the critical
cross section of the failed panel,. The presence of shear
in the combined bending and shear group of girders reduced
their full plastic moments MP. For these girders, an ex
pression for a modified plastic moment MPs was developed
from the following considerations. The stress condition
sketched on next page is the basis for evaluat ing MPs' (Ref'. 272).
It will be assumed that the flanges have fully yielded,
...........
--22-
I
----r--+------t-.~ -I-T " "~o'-i
~f-i
th,ere,by 'pI'o~1d,:tng the .'flange moment" Nr,' and' that a con-
stant normal stress' (j is present ,.,over the web accotrl:panied,
by the eonst~nt ~hearlng.,stres~~. From the sketoh, the
modified moment is : Mps. = Mi' + a~b ~.~. An expression
for ais obtained from the yield criterion ayw = la 2 + 3~2~
V Mpawhere 't = b,t =btx.. Substi tut1ng the value of C1 in tl;le,
.first equation gives Mps ;:: Mf + ~ tb 2 :Ja.;w- 3 (Mps/btX)2' •
After solving for Mps and.observing that Mps = Ppx/2,
2 -L j' 2 27JPp = xa Mf + aMw -(a-l)Mr
where .. the constant a = 1 + -ft(~) 2, and Mw is the portion
o·f the full plastic' momen,t M,p cont~ibuted by the web,
Mw = aywtb 2 /4. When a negative number results under the
radl~al sign, the shear case e~plained before must be used
to obtain Pp ,. Physic~lly this result'implies that the web
yi~lds due to shea!' befo:re 'the yielQ. stress is .reached in
the ~langes.
In Table 1.7 ar·e sUITJInarized the reference moments and
lo~ds for all test girder~. Unlike the bending and shear
gr6ups, which ha.d constant moments and shear's over their,.
test section's, the combined grou:p had a var'lable moment
over 1 ts test sections whlc"h re·sults in two or more yield
and plas,tic loads for' each girder.
-23-
1.6 Web Buckling Stresses
An additional reference value with which the obtained
ultimate load can be compared is the conventionally computed
web buckling stress or load. It is the objective of this
section to establish these stresses and loads for all the
girders ~
The general equation for the ideal critical stress of an"f
isolated web panel is
= krr2 E I----..-
12(1-,,2) /32
where 0cri and ~cri are the ideal critical normal and shearing1I2 Estresses, respectively. The ractor is a qonstant
12 (1- \12 )
dependent only on the material properties,'.that is, the
modulus of elasticity E and Poisson's ratio v, while ~ = bit
is the slenderness ratio of the web. Finally, the buckling
coefricient k is a variable depending on the loading and
boundary conditions and, in general, also on the panel's
aspect ratio a = alb. Values for this coefficient can be
:found in such literature as Ref. 73, ..,116, and 247.
Some detail information must be specified in order that
the web buckling stresses of the actual girders can be com~
puted. In general, the procedures of Ref. 21 and 52 have
been adopted for the details which follow:
-24-
1I 2 EThe constant, l2(1-v2 )' for steel plates is equal to
26,750 ksi.
Web panels are considered pin ended on all sides.
The proportional limit 'of the web material is taken as
a.8oy • If the ideal critical stress 0cri is less thanI
this value, it'is equal to the critical stress ocr,
0cri = ocr" Whenever it exceeds this value, the critical
stress ocr is found from a reduction procedure,
ocr = Gy(l - a.16~y), a relation derived from Eq. (64),cr or 1.
'Ref. 21. Similar ly 't cr = 't' (1 - a •16't"y) , where 't is they ~cri
shear stress.
When a moment gradient exists in a panel, the critical
section is considered to be at a distance of one-half the
web depth from the maximum moment in the panel. In the
case where the panel l s length is smaller than its depth,
this section is at the middle of the panel.,
The critical shear force of a panel subjected to pure
shear is computed as the product of the critical shear
stress and the area o~ the web, Vcr = ~crAw.
In all cases, the unsupported web depth "b 1t is taken as
the clear web depth, which is 50 inches for all girders.
Finally, when the neutral axis is 1/2 inch or less away
from the web's geometric center, it is assumed to
coincide with the centerline,
The general cases of bending, shear, and combined
loading are presented next,
-25-
F~r.bendl:pg, the general formula for the normal criti
cal stress Ocr! applies. The k-value is the only remaining
unknown. Since all the girders except GI-T2 had their
neutral axes less than 1/2 inch away from the web's geometrio
center, the k-value is k = 23.9. In GI-T2 the neutral axis
shifted 3.62 inches down from the web's centerline and thus
the co~pressive stresses a~e higher than the tensile stresses.
In accordance with Ref.52, this leads to a k-value of
k =18.6. The critical load Per is determined from the re~
lation tha.t o·cr = MerY/I, where Mcr = Pcrx/2, see Fig. 1.1.
For.shear, the general formula for the critical shear-
ing stress ~crl.app11e8. The buckling coefficient of
k = 4.00 +~ is used when the panel's aspect ratio aa
is equal to or less than unity, and k = 5.34 + 4.go is used. a
when a. ;:"1. In .this ease, Per 1s evaluated from 1;cr = Vcr/bt,
where Vcr = Per, see Fig. 1.2.
For combined bending and shear,
where overi is the equivalent ideal critical stress for com
bined loading according to Ref. 52, cr the extreme bending
stre'ss of the web, (j ::: MY/I, and 't the a,verage shearing stress
~ =·V/bt. M and V are the applied moment and sh~ar respec
tively :Ln the..conside:red qross ,s·eetion o The formula above is
only applicable to girders whose neutral axes coincide with
their web's 'geometric centers and as such ap.plies to a.ll the
-26-
girders of the combined group whose axes were all less than
1/2" away from the centerline of the web. After reducing
the ideal stress for inelastic action, if necessary, .t~e
cr it ieal loadPer is obtained from the equation 0vcr=!o2+3't'2',
where cr and't' are both functions of 'P, the applied load.
As an example, the critical load of the first test of
E2, a girder under combined loading, shall be computed.
From the tables and figures of previous sections the proper-'
ties of E2-Tl are as follows: a = 3.0, ~ = 99, Aw = 25.3
I = 39,620 in4 and 0yw d 34.9 ksL From Table 1.1 it is seen
that the long panel failed iti this first test. Since a
the critical stresses due to moment and shear are evaluated
moment gradient exists in this panel, the critical cross
= 37.5 ksiJ(O.0394P)2+ 3(O.0198P)2! = O.0522P
,(0.0 394p 2+ (9 •0198p\ 2 0 •00 139 P65.2 \ 15.8 7
°vcri =
The proportional limit ,is 0.80y = 0.8x34.9 = 27.9 ksi.
section is at a distance of 25" to the left of the center
bearing stiffener or x = 125" from the end of the girder.
Knowing this data and using ka = 23.9 and k~ = 5.79 (a>l),
as 0cri = 65.2 ksi and ~cri = 15.8 ksi. The stress at the
compressive edge of the web is a = MY = P.125 25 = O.0394pI 2.39,620
~s~ , and the average shearing stress over the section is
't' = :!- = P = 0.0198P [}rs~. Substituting these valuesAw 2.25.3
into the equation for the combined crfuical stress,
-27-
Since Over! /' O.8oy ,the reduction for the inelastic range
sl?plies. as follows ~
: ~vc~ :: 34.9(1'- 0.16 j~:§)= 29.~ ksi
Since aver:: JaJ.+3n;21
:; 0.05'22Pcr , Pcr = 29.8/0.05'22, or
Per = 570 kips
In Table 1.8 and 1.9 are surrnnarized the. or! tical stresses
and lo~ds for ·all girders., The bend1ngand shear groups
never exceed the elastic limit and thus 0cr1 = ocr and
~cri = ~cr. The eente~ panel of E5-Tl was sUbjec~ed to pure
moment and therefore no' entries are made' under the' qolumns
for shear.
-28-
1.7 Deflections
In order to check on the elastic behavior of the
girders, their predicted deflections are evaluated in this
section. Again three groups exist': bending, shear, and
combined loading girders. The centerline deflections are
obtained for the bending and combined groups while the end
deflections are given for the shear girders.
The method of Virtual Work is used to obtain all
deflections. In this method a unit load is applied to
the girder at the point where the deflection is desired
origin of the x-axis is taken at the end of each girder.
integrals extend over the entire girder length where the
In this expression M and V are the moment and shear due to
J~ dx + J Vv dxEI GAw
v =
computed as the sum of the bending and shear contributions:
the actual loading, E = 30,000 ksi is the modulus of elas
ticity, and G = 11,530 ksi is the shearing modulus. All
and its resulting moment, m, and shear, v, diagrams drawn.
Then the deflection directly under this "dummy" load is
-29-
The units for all quantities and dimensions are kips and
inches.
To illustrate the procedure followed in calculating
deflections, the expression for the centerline deflections
of the bending girders is developed now. In the example
shown on the next page, the loading is first pictured, to
gether with sketches of the areas and moments of inertia of
the girders. Then the moment and shear diagrams, both for
the real and dummy loadings, are drawn. Below these diagrams,
the integrals are written, the first three representing the
moment component and the last one inclUding the shear con
tribution. Observing the symmetry of the loading and cross
sectional properties, the integrals need only be evaluated
over half the length of the girder and then doubled to obtain
the final value.
SUbstituting the properties of GI-Tl into the resulting
equation (a), where Ie' I m, and Ae equal 15,550 in4 ,
14,380 in4 , and 19.10 in2 respectively, the centerline
deflection for the applied load of cP = 100 kips would be
1.172 inches. In this case the shear component i85.8% of
the total deflection.
Using the same procedure as above, the equations needed
to evaluate all required deflections are obtained. These
expressions are listed on page 31 together with the cases to
which they apply.
-30-
C~nterllne Deflection Qf'Bend1ng"Girde~~
V-diagram
v~.diagram.
Loading
m~diagram
Mom~ of" Inertia
M-diagram.
k " p p , "
,"150-, 'w~ , '33J~~~ ~~
540"
AeA,rn
Ie 1m
r~~ llSOP /~~~
+P .. '
+1/2 . 11
V~ - J: dx +.. J~~w dx .
150 . 183·'·. :::: 2 J<PX) (xL2)dX + J(150P) (xL2) dx
EIe . < EIeo " 150 . .
270'·" 150'
+ J(150~i(x!2) dx + r<Pl~~!2)183 . m... ~
= 2xl0.3 [562.~P + 412.1P + 1418p + O.0750Pj. EIe·· EI EI·' Aw'G,6 m .
, ;
. Vt = p[64.97/Ie.+ 98. 53/Iiri+ O.OI301/Ae] (a)
-31-
All bending girders, ~xcept Gl)" were reinforced with
ste~l ~lates "afte~ their first test. With a new cross
B~oti,on' 'pre,sent, . whose moment of inerti'a I 'is' 'listed in
th.~: "sp'eclal s<?ct'i.ons" of· Table 1.6 the expres~ion for the
centerline deflection,in the second test is:
Vet = P(64.97/Ie.·+ 54.~3/Im + 43.59!I + O.01301/Ae ) (b)
The shear girders have a maximum deflection at their
ends. Obse'rving t,p-at the'sa girders ,bav-6 cover plates at
their reaction points " thus having' specia.l moments of
inertia I, the equation 'for' end deflections is:
Va = P(5.689/Ie + 7.316/Im + 25.39/1 + O.0132/Ae,
+.O.0075/Am) (0)
Girder El, the first of the girder,s' under combined
loading,had its second cover plates term~nated 75 inches
frol11; 1 ts ends. ' ·Let~ing the moments' of ~nert1a of the
se,ction wi th and without the second cover plates be Im and
I, the relation for centerline deflect~oh is:
All other girders. under combined loading had constant
cross sections throughout their lengths. As such, the
centerline" deflection's can be found ,from Eq. (d) by sub
stituting I = lrn.' The resultin'g e'quation is:
Vt = P(22.23/Im + O.00689/Aw)
A summary of girde:r def~ections, co~puted from the
above equations,' ,is given in Table 1.1011 Here, the bending, .
and shear componen'ts o;r the total deflection are listed,
together with the equation that is applied to determine
( d)
(e)
them. The centerline deflection ·18 given for the bending
and combined groups while the end deflection is' listed for
the shear girders. As ~ m~tter of interest, the percentage
of the shear contribution to the total deflection is in
cluded. All deflections are eva~uated for ~ = 100 kips.
, --33-. I
Table 1.1'- summa~y o~ .. ~G:t:rder Pa,rameters
beH ~Q).' . tM
'rrj .' ."0H. .. 'g;t
.,....,., 0,o 'H
.'. '1,
S ....:: ~~tI) -n .. "d ',",rn 4-). "':~ tJio 0, t) ~Q) 01~ .Q) Q)" rl (I)
t.,) rJ)" :;: tf) .f=I .
stiffener Location· of ·Failure ~" Spacing: C1 . 'arid Reinforcements'.Tl· " ,T2'· Tl ' " 'T2T3 T4'," T3 " .,T4
Gl I. 185 .,1.50' 0.75 .CrCJ r::r:cJG2
,bO ·.'II 185 1.50 0.75 ITO crrJ~.1'4ro
G3',$:I .
III 185 1'.5° 0.75 rrr:::J m=J(J)
~
G4 <DII 388 1.50 0.7,5 ITO r:tDH
~,
P-t
05 I·II 388 1.,,50 0.75 ITCJ ITO
'1.50' 0.75 ~J !ZIJII]G6 I'I 259 .
I.
H 0.50 ~ai ',I ~ I I,
<D,dCIl ~ ITJZJ [Z[]S]G7 ,'II' 255 1.00 1.00
Table 1.2
Summary of Or-css ,Sectional 'Dimensions'in inches
Top Flange Bottom Flange Web ThiqknessGir- 'Cross Width 'Thick- 'Width Th1ck- Test End·dar· ' Sect.• ness, ness
20 d 2c d t' t
Gl-" I 20.56 0·427 12.25 0.760 0.270 0 .. 38,2
G2 II 12.,19 0.769 12.19 ,0.774 0.,270 0.507
G3 III 8.62 0,.328 12.19 0.770 0.270 0·492
G4 II 12.16 0··-774 12.19 0.765 0.129 . O. 392
G5 III' 8.62 0.328 12.25 0.• 767 0.,129 0.392
G6 II 12.13 0.778 12.13 0.778 O.I?3 0.)69
G7 II 12.19 0.769 12.19 0'.766 0.196 o. 38'1
El IV 20.56 0.427 12.25 . ',' 0.760' 0 •. 382'- .:
E2 V 12.i9 0.769 ' 12.19 '0.774 o~'507
E4 VI 12.16 0.,774 12.19 0.765 0.392
E5 III. 8.62 0.328 12.25 0.767 0.392
G8 II 12.00 0.752 ',12.00 0.747. 0.197
G9 II 12.00 0.755 12.00 0.745 o.i31
'{'PL A: 15.04 x 0.882,Cover Pl'ates
PL B: 18.00 x 0.750,
PL c: 16.00 x 1.007
PL D: 11.19 x 0.510
"
TABLE 1.3
Summary of r-1a.terial Properties (Gl to G7) .
Des i g nat ion Che~ica1 Analysis Mill Tests Fritz Lab. Tests
LocationThick-
CouponSpecif'i- Heat Slab C Mh P S CJy _ (Jult El~ng CJyst o-ult Elong Ared 0;
ness cation No. No. % ::t % " % ,(ksi) (ks i) 15/ (ksi) (ksi) % % (ksi)..r~ /0,.
B attorn Gl CP 9 40572 -., . 40.2 65.8 30.0 35.8 61.8 33.5 '63.9 127.9_
Top G2 CP 17 40569 42·0 66.4 29.0 38.6 63.7 27.1 61'.9 120.7([) Top G4 OF 27 r-I 40511 40.5 66.4 30.0 37.6 63.8 31.5 60.9 125.3r-co B attom G3 3/4n OF 40 C\I 40569 .17 .70 .016 .026 42.0 - 66.4 29.0 38.1 63.7 32.1 61.1 125.9
G5 . c'p 51 ~ 40570 40·4 65.1 30.0 '37.0 63.0 "32.6 61 . .5 123.3B attorn ....0
~ Top G6 CF 54 0::> 40561' h1.9 66 .. 0 30.0 37.9" 63.8 31.4- .59.0 121.4cd Top G7 Op 62 -.. 40568 41.7 65.8 29.0 37.0 63 .. 1 31.6 . 59.6 '122.3
M ~
fx.t Top Gl 7/16:T CF 7 >-I 87K270 40833 .22 .59 .011 .029 40.8 66.5 29.0 3.5.2 6~ .5 28.2 59.4 -Top Gl CF 8 "r""I 35.5 62.2 30.0 58.-1 -
0)
~
Top Cov. G6 1/2" CF 53 0 87K254 ,(4°859) .22 .59' .008 .023 38.1 63.2 29.0 33.6 60.8 29.3 61.5 129.2Top Cov. G7 CP 63 E-t . 33.3 60.1 31~e 62.4 -....0 0
G2 CP 12 'U'\ ...::t 40671 40.5 66.3 29.0 35.4 63.2 29.9 59.4~ I. -0 G2 1/2 fT CP 12A CV'\ ~ 4067l 40.5 66.3 29.0 34·3 62.7 24.0. 51.6 -...-i r- ed~ G3 OP 35 ('1"'\ 0 41200 40.2 67.8 26.0 37.3 67.4 2E.7 60 .. 0 137.00 "d r- .22 .59 .Oll .029Q) ~
~{\J
t1 G1 OF 2 E-i ~ 39809 40.9 67.7 28.0 41 69.2 24·9 51.4 -rt.1 ..-f r-'"0 Gl 3/8" CP 2A « ctS co 39809 40.9 67.7 28.0 42·4 68.4 21.8 32.0' -~~ G4 OF 22
'0'" 398.08 42.,0 67.6 29.0 40.0 67.0 28.2 63.3 105.6'Q)
G1 CP "3 .I"'i 32.9 55.8 35.1 62.2~ -.D' G1 1/4,i CP~ 3A ..,..; 84K24l > 53268 .13 ,.49 .009 .026 39.1 60.9 28.0 33.0 54.4 34·6 58.2 . -"dtD G2 CF 13 0 35.3 60.0 31.1 63.3 -
Q :E:~ 0
G6 OF 57 ...-40.7 64.5 23.5 62.4 28.6 53.5 112.0...-i -
~ G6 3/16" OF 57A 59K346 83483 .22 .50 .008 .020 40.7 64.5 23.5 36.8~ 63.3 30.0 49.3 108.2. 0Q) G7 CP 66 40.8 66.3 24.5 - 36.6 64.2 28.4 52.7 113.4et.l
~ G:4 CF 23 40.6 62.9 28.5 43.5 60.7 28·4 .51.4 104.7tr.ICD G4
1/8 l1OF 236 ASTM-A 40.6 62.9 28.5 43.2 60.9 25.4 63.3 -133.38 GS CP 47 245-57T 9%198 - .18 .82 .010 ~022 40.2, 62.3 26.0 46.6 62.'8 27.1 59.9 129.9
G5 CP 47B 40.2 62.3 26.0 44 .. 8 63.5 24.2 ,57.9 126.8-
r-f 8" pipe G3 O.322 n CF 3i A-53 - - - - .017 - 40.2 60.4 42.5 35.5' (,51.5)Jii Grada.p!- - - -~
Note: A ref'ers to call,pon taken in transv~rse dir~ction.
B refers to additional coup-on taken next to the original one, e. g., qP 23 and GP 238
IW\Jl..
I
"
...::.'.
TAB IE .. 1.4
Summary of -Material Properties (continued)
Des i g nat i' 0 n Chemical Analysis Mill Tests Fritz Lab. Tests. ~
Thick- Speciri- Heat Slab C Mn P S0:.
(j'ult Elong O"'yst O'~lt Elong Ared (JryLocation ness Coupon cation No. .No. % % % d1 ksi ks1 % ksi ksi % % ksi/0
Top Cov. E2 CP E5 - 60.7 32.2 61.5 122.6Top COV. E2 1" CP E5B p.., -1772 .17 .65 .010 .032. 38.5 62.3 28.0 28..6 60.9_ 31.6 61~9 119.3Bot.Cov. E2 CP E6 30.3 62.0· 30.3 60.4 119.8>tTou COV. El CP El ..,.; r-i 30.1 59-.8 31.9- 64.2 125.3Ul C""\
Q) Top- Cov. El 7/8" CP_E2 ~ i--i 1773 .17 .64 .008 .032 38_.7 62.8 29.0 30.2 60.2 32.2 62.6 121.1~w Top Coy. El CF. E2B
~co 30~1 60.8 33.4 62.5 120.4r--
s:l C"'"\O
Bot.Cov. El CP E3r-....::t
61.5 57.9as- f'I'\" - 31.0 113.2Bot.Cov. E1 CF E.3B +t
1771 .16 .65 .011 .031 38.7 63.0 29.0 29.6 60.9 32.0 62.1 119.7r-i < aslit Bot.Cov. El CP E4 :z."'C 30.0 62.2 30.2 60.0 121.6
3/4ft E-I CD •(/) E
Top G8 CPEG3<C .....
C'l""\ U\ 40.2 76.1 27.0 . 49.3 123.1asTop G8 CPEG4 0' r-f 42.4 76.7 24.5 53.7 132.2.... r-i -~ 45.1 75.5Top G9 .GP EG9 -0 ~ .26 -70 .022 .027 22.0 42.1 76.3 22.6 53.5 131.2co 0'Top ;_ G9 CP EGIO CD 41.5 76.6- 25.9 51.5 128.8 'n...... r- eo
It-I t"f"\-.....
(\J--0- '"G8 CP EGI 0 C"'\ r-f . 37.9 57.8 28.1. 58.4 -:E: t"'"\~G8 3/16 lf CP EGiA ~ .13 .52 .008 .028 39'.5 56.7 32.0 38·4 58.0 28.8 42.2 -en 0'
.0 .. G8 CP EG2 " r- a:> 38.4 57.4 29·4 62.3 -C"'\(D 8
G9- CP EG7 - roo-=:t ,l.-::j- 43.8 58.0 23.1 48.8 -;;: U\
G9 CP EG7A -:E: fa> C'l""\ ON . 42.6 '-57.1 21.7 47.2 -1/8" E-il.r\~ C"'\ 1.J\~._ ,.18 '-49 ,.-011 .0}2 39.6 56.7 29.0~
G9 . CP EGB rJ]~ cd ~ I 0' - 47.5 59.2 25.0 45.1 -<C\I H -::t ~("\'"\ .G9 CP EG8A _<0 0' 44.1 59.2 27.3 47.4 ---
Note: A refers to coupon tak~n -m transverse direct-ion
B re:rers to- ~<ldit1onal~oupontakeIl:-next to the -original one~ e-.g., CP E2 and_ CP E23
'"
IW0'I
Table 1.5
Summary of Static Yield stresses(kips per a'quare' inoh, ks1)
Girder Cr9ss B'langes WebsSect. To.p 'Bc)ttom T~st End
Gl I 35.4 35.8 ' 33.0 41.7
G2 I'I 38.6 37.6 35.3 34·9
G3 III 35.5 38.1 33.7 37.3.. G4 II 37.6 37.0 43·4 40.0
a5 III 35.5 37.0 r~5 9 7 40.0
G6
G7
II
II
37.9
37.6
36.7
36.7
El IV 35.4 35 .. 8 41.7
E2 V 38.6 37.6 34-9
E4 VI 37.6 37.0 40.0
E5 III 35.5 37.0 40.0
G8 II 41.3 41.3 38.2
G9 II 41.8 41.8 44·5
, {PL A: 30.1.,Cover Plates
PL B': 29.8,
PL c: 29.4
PL D: 33.5
, - .38~
Table 1.6'
'SUmmary. , .
Mo'ciuliof M9m~nts of Inertia "and Se'c.tion, '
,EQd $p~~ .•T. e ,s. 't, S e c t 1 0 n sect." Sect.
G;l.rder : '1m Sa " Sb ':Ie ' 'I. 1'n+ in) . ,in3 1n4 .in+
"
Gl 14,3'80 . 555 568 15,,550 12 210,
G2 14,940 578 581 17,400 16,170
G3 16,220 488 620 ,~8~530 17,'790"
. G4", 13,4,20 522 519 16,160 14, 6~.,O
G5 14,710 443 561 17,450 16,9$0
Gl?, G7
14,,180
14,,100
550$48 ,
550
'547
'16,010
16,030
23,750
23,.7'60
El 52,920 1,922 1,968 33,·6,70
E2 39,620 1,480 . 1,485
E4 '34,390 1,.292 1,28.7..__....
E5 17,480 $24 .' 672 "-"",,--G8 i3,640 531. 528
G9 12., 960 505' 501
..
-39-
. Tab'le 1 ..7
,Summary of Reference, Moment~ and Loads
Girder Test . M'f , My Mp , !?y l'pk-1n' k-in k-ln kips kips
Tl 15,700 19,600 ,21,900 1)1 148Gl
T2 1Q,400 15,100 18,700 ~Ol' , 118
G2 Tl,T2 '18,400 22,300 .' 24,200 149 167
G3 T~,T2 16',600 17,300 23,600 116 156
G4 Tl,T2 ' 18,000 19,600 '21, 200 130 139
G5 Tl,T2 16,500 15, '700 21,3'00 105 134
G6 Tl,T2,T3 18:,200 20,800 '2'2,600 193 205
G7 Tl,T2 17,900 20,600 22,300 196 208
Tl,T2',T4 .5'~, 000 60,000 ' 68, 600, 826 ,920El
T3 36,600 40 ,,700 47,100 905 920
E2 ~1,T2 43,400 48 ,$00 54, 1,00 716 855
Tl 880 905
E4 T2 '39,100 43,000 48,600 658 691
T3 639 666
Tl 248 367E5 16,500 18,600 27,500
T2 ..... 358 386
.Tl, T3, T4 280 368a8 18,900 21,900 23,600
T2 410 434
Tl,T3, 19,206
264 354G9 21,100 22,700
T2 324 336
Table 1.8
Summary Q·f Critical stress'as and Loads
. Bending Girders
Girder Test. on ~ k O'er Perksi kips
Tl 1'.50 23.9 ,18.7 70.1G1' 185
18.'6T2 0.75 14,.5 41.,9
Tl 1.50·G2 185 23 .. 9 18.7 74·1 .
, T2 0.75
Tl 1.50G3 185 23.9 18.7 82.1
T2 0.75
TI' 1.50G4 388 23.9" 4·25 15.3 0
T2 0.75
Tl 1.$0,G5 388 23.9 4,·,25' 17.0
T2 0.75
Shear Girders
Girder Te,st a (3 ,k 't" c'r Per
Tl ° 1.50 7.12 2.84 27.4
G6 T2 . ,0,.75 259 13.5 5.38 51.9
T3 0.50 2,5·4 10.1 97.6
Tl 1.00G7 255 9.34 '3.84 37.6
T2 1.00
Table 1.9
Summary of Critical Stresses and Loads
Girders under Combined Loadin,g
Ben~ing . Shear I CombinedGirder Test ~ (3 I k O'cri k (Jeri, .o-vcri .<rver I Per
ksi ks i 1 ksi ks-i kips
Tl 3.00 5.19 9.01 18.0 . 18.0 332T2 1.50 7.12 11.1 21.8- 21.8 402
El T3 1.50 ·131" 23.9 37.2 7 .12 l·l~ 1 20.3 20.3 415T4 1.00 9.34 14.6 27.4 27.4 S06
Tl 3.0065.2
5.79 15.8 37.5 29.8 570E2 T2 1.59 99 23.9 " 7 .12 19.4- 44.1 --JO.4 584 1
+:-.....Tl _.1.50 7'.12 11.6 21~3 21.3 445 1
~4 "T2 '0.75 128 -23.9' 39-.0 13.5 22.• 0 38.5' ' 33.4 513T3, 0.50 25.4 41.4- 46.9 34.5· 517
E5 Tl 0.36128 -- 39'.0 ·33.-4 - 314
'T2 ,0.75 23.9 39.0 13.5 22.0 38.-.8 33.4 322
Tl 3.00 5.79 2.40 5.99 5'.99 41.5T'2 1:..50
2547.12 2.96 5.59 5.59 56.4
G8 T3 ~.50 - 2).9 .9.91 .. 7.12 2.96 6.96 6.96 48'.3·T4 . . l~OO 9.34 3.88 8.26 ~.26' - 57.3
Tl 3.00 5·.79 1.06 ,2.32 . ·2.32 12.·9G9 '1'2 1.50 382 -23.9 .. 4-.38- 7.12 '1'.31 2.36 2.36 - 16.8
T3' 1.50 7."12 1.31 ' 2.78 2.__18 15-.5
. -42- .
Table 1.10
Summary of GirdC?r Deflect,ionskips)'(in inches and under nominal· lo~d P=lOO
Eq•. Deflections due to %ShearGirder ~est Used Bending Shear Total o Total
Tl (a) 1.1,°4 1.172 5.·8,Gl 0.068
T2 (a) 1.225 1.293 5. .3
Tl (al 1.033 1.,084 4.7G2 0.051
. T2 (b) 1.008 ,1.059 4.8
Tl ,(a) 0.958 '1.011 5.2G3 0,. 053
T2 (b) 0.931 .0.984 5-4
T'l (a) 1.136 1.202 5.5,G4 0.066
T2 (b.) 1.102 '1.168 5.6
Tl (a) 1.042 ,1.108 6.0G$ 0.066
T2 (b) 1.000 1.066 6.2
a6, All (cl 0.194 0.150 0.'344 43.6
G7 All (c ). 0.194 0.147 0.341 43.i
El (d) 0.045 0.034 0.079 43~1
E2 0) (e) 0.056 0.026 l 0.082 31,.7..J..)
E4 ta (e) O.O~4 0.033 , 0.097 34·0(1)E-i
E5 r-I ( e,) .0.127 0.033 0.160 20.6r-f
G8<
28 .. 8(e) 0.163 0.066 0.229
G9 .( e) 0.172 0.099 0.271 ·36.5
IO:'~3'-9'1-6'-3"+- 6'-3'~3~* Id-O'~~6"I.. - - - 40'-Cf' - J
. . j . . 1, 1
,---4~2U i-*-- :r;---~~.........L~~U-il
~ Test 1! Section
I y+
6h-jt= 12'-6,,-J 3'-9"~ 6·-3,l6~3·J3~9,L 12'-6'Y~6"t-- - , 45·-0"-----~
SHEARJVI
+--- v=-p
V= P
SHEAR, VI
v=-p
MOMENT,MJ - .
h Mmolt.=P·150"
MOMENT,MI
~ JI
~-Mmax:=P-120
-Fig. l.l~ Test Setup of Bend-ing Girders Fig. I. 2;: Te-st Setup or Shear Girders'
III J. b=5o"
Jd~2CP-
'p
~1 Iat= I !.~~t=12~S~.. -~.~-S" i2'-"6"==:jI-SII ... .. 26':-6"' ' ..
r-2c -j.df ~f-
b=50" ) I
L:.-d-r-
-.!2C 1-
-j 2c Gd
_
1jtlill 1:"~2C~
0.328 --L8'~8a
tl--- -. .
V=O.5P;. Gt G2,G4
G6 J G7.G8~G9
G3,G~
·E5
SHEAR,VI
'V:-O.5P
F"ig. l.>~ Test St?tup o:f G~iptl·erEf':·'Under
VI. I b=50"
---1..E.A
E4
F1ig o 1.Lr' Gi~der Cross Sections
ftAItS ~c
tlf t
b=50" IV V b=50"
LMmax_=P·7SH L ~.A1
-l12.8
-c IlCEI £2
MOMENT,M"I
Cornl:;lnec1 IJ{)ading
Thickness
Thickness
Width
0.431 OA31 0.430 0.425. O~425 O~424
[~ C~7~] ~~i:~2%'6 .[W>i2~?~??@:I.0.432 OA32 Q430 . 0.4230.423 0.422
20.5620456 20~56 20.56 20.56 20.56,
Girder GI
Average
0.427
0.427
2056 in
0.427 in
0.253
0.264enU1Q)
50c:~ 04268:c1-
0.274
0.277
· 0.257 0.259 • ·
·~I
• O~267 0.271 . ·
· • 0.271 Test WebO~275 •
JtSOxlj4
.rzz: w 0.274 (' 0.277 1Z2 U ????? ??22ZiJ-
CP3
~'CP4
· • 0.277 0.278 · ·
0~259 0.257
,O~270 O~268
O~274 O~272 r O.270in
O~277 0.276
0.278 0.276
'....
(AU dimensions are in inches)
~ ,
Thickness Q760 0759 0759 O~762 0762 0.761
I~ G~9 ~] ~o,t~~";~~,ongel~??c~io?@]Thickness 0.760 '0759 0758 0.761 0762 04761
Width 1225 1225 1225 12.25 1225 1~25
Fig 0 105 .. EVA.LUAT'ION OF PLATE DIMENSIONS AND COUPON LOCATIONS
0760}0.760 in
0476012425 in
Subject: Coupon Dimensions and Test Results
Specimen No: GP 27 IDate: July 5,1958
Note: Crosshend Spep.d 0.10 inches/minutel Tested by: STY, 80.
/" J_~Il
1
Thickness
0.769
0.770
0.767
0.769
0.768
0.769
0.768
0.7700.771
Width
1.500
1.500
1.500
1.500
1.500
1.500
1.499
1.499
1.499
Upper '(.F,> •••••• 48,60Qlb
Lower Y. F! '.' • • • •46,OOOIb
46,250 }Dynamic'f.F? 46,250 46,2001b
46.5-45.8
Static Y. P. :~:~~~ }43,4001b
Ult. Lood • • · • . • • 73,500lb
Rupture Load •••• ,56,4001b
Reduced Area . ~ . ~..• O.450j~
Elong. Gage Length. ',' 10,49 in
5"
Area 0.768 '1.50=1.152 in2
Static Yield Stress
Ultimate Stress
Elongation
Rupture 'Stress
~ - 43.4 37. 6 k ·y-~-: • SI
(j, - ~- 638k 'u - 1.152 - · S I
E= I0.4~9~98'IOO=31.5%
Fig. 106 - TYPICAL DATA SHEET FOR COUPON TESTS
Teat No., CP..2t Slze U50.0~~t(.Q\7.fi.I~Area l.leiZ.ti: ~.Yield Point Lbe. Sq. ID•......~f&.OQ •••.•.•U1tlm8te Str_LbL Sq_ In 6~............ •
I Elofll1ation l .. II .,-=:1' '!Iltt ~O.9°j' .tllIy'" ~ I:IlTV f.~ r rIn.....1.9.B.•,..Inchea.,........"".,f),,........Per CelJt. EloDlllldoll.......'......" ..Per Cent. Reduced Area...,..~........"Il....Date....K_••,,""...M .....'.... ,
:n\C.
en.....
"" ::0!?:
-t z-<"'Un· c:~ 2_.....V'l II-+
0....CD 0&It..,. 0I
~Vl-+ 3-..,~. "::s s-OI::..,<CD
Average Thickness = 0.323 in.
Average Diameter : 842 in.
Cross Sect- Area, A = 8.56 in2
Yield Load Py ;:: 300 kips
Yield Stress ay = 35.5k.s.i.
€=~h ~=~A
0.3100.32"3
-tp
8or i 1 [ . I I I I iii iIi i •
0.5 1.0 15in €li" i j iii iii i I I I I iii i •o 10 20 30 40 50 60 ~~·lo3
10
01
o due to loCOI
J .. jP,to
zoor! i .~2~ I j
o
100 .I
30
4
Fig. 1.8 - YIELD STRESS DETERMINATION OF TUBULAR F-LANGE
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