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

-lm=

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

-2-

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 plate 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

P-tQ)

~H~

C\Jr-f1

rlLf\C\J

P-!

Part 3:

.Part 4:

-7-

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

-10-

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 deflectione End Ie Moment of inertia of end sectionsf Flange Mf Moment contributed by

flanges

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 NAp plastic Pp Load causing the plastic momentu 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

-11-

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 additional

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 Ver-einigung fUr Brllk-.kenbau und Hochbau

Association Inter-nationale des Pantsec Charpentes

International Asso-ciation for Bridgeand Structural"Engineering

N~tional AdvisaryCommittee o~ Aero-nautics

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

PreliminaryReportFinal 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 Bau-Inst.f.Baust. sta~ik an der Eid-a.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 Kommis-sian des VerbandesSchweizerischerBrUckenbau- undStahlhochbauunter-nehmungen. Changed1956 into: Schwei-zer 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 verHnderli-cher 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 I1ings-steifen bei gleichm~ssiger Druckbeanspruchung 'fBauing.~ 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 Quersteifen1lIng~ 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 fLStahlbau, 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, AnnArbor~ Michigan.

8.. Basler, K. ~nd Thllr1imann, B."Plate Girder ResearchlfA.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 ffInternational Association for Bridge and Struc-tural Engineering, preliminary Report, 6th Congress,Stockholm ~ 1960. . "

10. Batdorf, S.B."Theories of Plastic Buckling llJ. 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 iTZ~ 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 11z. 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 TtI .. 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 Ausbeu-len von Rechteckplatten unter gleichmassig ver-teiltem 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 11Stahlbau, 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' Flat

Plates in'Shear"N.A.C ..A.'- T~N . 15Sg., 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 Stresses-of Clamped Plat-esrlN.A:C"A", T.N" 848, 1946"

-3'2. Budi.aIi.s1

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 Rein-forced by'Angles Along rts Edges"

38. Chwalla, E."Die Beme-ssung --der waagrecht ausgesteften -Steg-bleche 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 flSolves the case of a longitudinally stiffenedplate under pure bending.

40. Chwalla;, E."Die Bemessung des Stegbleches im Endfeld vo11wan-diger 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~tHtstheorie des Stahlbaus JtStahlbau, 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 ftErganzung ~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 Mindeststeiigkeit T1Stahlbau;, 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~ionan 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 CompressionnAeron .. 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.Normblattent-wurfes"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 1954, p. 543 ..

I......-..]I

.51 ..

52.

nenke, P.H.1JAnalysis and Des~gn of Stiffened Sheart...rebs 1TJ", Aero ... Sci-., -Vol. 17, 1950 ~ p. 217 ..

Deutscher Normenausschuss"DIN 4114, Blatt 1 und 2 ftBeuth-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 Bucklingffpart 1 contains the specifications, Part 2 givesaddLtional recommendations.

?7 .

58.

Dubas, Ch ..rrContribution a l'etude du voilement des tolesradiesnA.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~tesnDerives 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 ltEngineer, 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 frEngineer, 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 gedrticktenRecht-eckplatte 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 nForsch. 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 LoadtTN.A.C.A., T.N ... 962, 1945.

65.- Friedrichs, K.O .. and Stoker, J .. J.ffThe Non-Linear Boundary Value Problem of theBuckled Plate tTNat".. 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 J1N.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~1IN.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. Heck, 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 Dutton, 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 tlSoc. 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 l1N.A.C .A.) T .,N. 2163, 1950 ..

89. Houbotte, M."Versuche {{her die 'Festigkeit blecherner TrllgerHDer 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-~lN.A~C.A.. , T.N. 1124, 1946.

91. Iguchi, S ..I1Allgemeine L8sung der Knickaufgabe fur recht-eckige 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 P1ateslfN.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 rtThe 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 rTStahlbau-Abh., Heft 12, 1952!i S... 92 ..

11commentary to the New German Standard Specifi-cations"

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 Bifur-cation 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 Drittels-punkt 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 Viertels-punkt der Feldbreite ausgesteiften Rechteckplattebei Navierschen Randbedingungen TTStahlbau, 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 plastischenBereichl1

'. 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. Elasticand 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 RangeffExperimental Investigation .. ,

109. Kollbrunner,C .. F.. "Versuche {{ber das Ausbeulen- von Rechteckplatten

unter dreieckf8rmig vertei1tem IlngsdruckrfI.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:L-litHt 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 gener-ally 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 BereichuInst .. 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 reer~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 Beul-sicherhei-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 StifenedPlates"Contains fundamental- considerat:lons .. -

123. Kromm., AoO und Marguerre, K.I1Verhalten eines von S_chub-. und DruckkrHften be..an-spnichten Plattenstreifens oberhalb- der- BeUlgrenzellLuftf'. Forsch., 1937.

"Behavior of a Plate Strip Und.er Shear and Com-pression. 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 oLong 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 ltProceedings of the Cambridge Phil. Soc., Vol. 31,1935, P: 368.

129. Leggett, D.M.A."The Buckling of a Squar~ Panel Under Shear ~-JhenOne Pair of Opposite Edges isClamped lJR. & M. No. 1991, 1941. . .

130. Levin, L~R. and Sandlin, C.W., Jr."Strength Analysis. of Stiffened Thick Beam ~"ebslfN'.-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 LoadffN.A.C.A., T.N. 962, 1945.

'136. Li, Y.;S."Theoretical and ExPerimental Study of ' the Behav-iour of Thin Flanged Box Girders in Pure Bending lfThesis 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 Girders1fThe 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 CombinationHN 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 tfStructural 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 ltTranslated into English: N.A .. C.A':l T.N. 833" 1937.

152. Marguerre, K.Hueber die Behandlung von St:abilitMtsproblemenmit Hile der energetischen Methode Hz.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 flz. 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 Vibra-tion and the Stability of Elastic Systems H

159. -Massonnet , Ch."Recherches experimentales sur Ie "0ilement, del'ame des poutres a "be pleine ffBulletin 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 ~tdes Travaux Publics, NO- 71, nov. 1953,7 pp. 1062-1080.

If\)0'I

157; Massonnet, Ch.IIEssais de voilement surpoutres a ameraidie"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.igationson the Design and the EfficientStiffening of l~ebs in Plate Girders, Taking inAccount Web Buckling"

Massonnet, Ch .f1Essais de voilement sur poutres a ame raidierlA.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 Web-thickness 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,cisaillementUA.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 bestehenf13 .. 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 T1N.A.C.A.,- T.N. 862, 1942.

172. Moore, R.L~.TlObservati'3ns on the Behavior of, AluminumA110y

Test.Girders"A.S.C.E., Trans., Vol. No ... 112~ 1947, pp __ : 901-920.

173. MUller-Magyar:L _TlBeitrag, ZUID' Uberkritischen Verhalten eines dlinn~,wandigen, versteiten 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. PlHger,. 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 DickeTtDiss. T.R. Hannover, 1942.

"The Stahility 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~onnN.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 GirdersSubjectedto 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 KnickerscheinungenJTEisenbau, Vol. 7, 1916, s. 121,. 157, 210, 239und 295 ..

"Contribution to the Theory of (Plate) Buckling ltFor 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 Four

Clamped 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 LeichtbaunDeutscher 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

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 tz. 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 BeuIgrenzenrng. Arcbiv', Vo~. 1], 1949, S. IIi.

liThe Square plate Under She~ Beyond BucklingJT

214. Schwerin, E.'"ueber die Knicksicherheit ebener Bleche beL.,exzentrischer Randbelastungrz. 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: trN.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 Platten-streifens (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 (Zahlen-beispiele 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 Longi-tudinal 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 Walz-werkprofilen"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

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~gitudinalStiffeners 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 ein-seitigen, gleicbmHssig und ungleichmMssig ver-teilten 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 Non-Uniformly Compressed"Plates"

u .'24"6. Stussi, F., Kollbrunner, C.. F.. und ~.;ranzenried., W*

, "Ausbeulen rechteckigerplatten 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 UniformCompression, 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 ffrT ..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 sciffenedPlatesTJ

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.

IW+=-

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 llz. angew .. Math .. u. Mech ... , .'la.l. 13, 1933, 5 .. 160 ..

"On the Elastic Stability of Equilibrium Can-figurations 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 Rectan-gular 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 rtReport 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.

IW\.T\

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 -To be published in the Welding Journal, 1960.

270. Dill, F.H."A Report on Transfer of Stresses in Welded

Cover Plates"Appendix. - Application to Design.To be published in the Welding Jourhal, 1960.

2 71 ~ Haaijer, G. and Th{fr1imann> B."On Inelastic Buckling_in Steel"Proceedings of the ASCE, Paper No. 1581, April-1958.

272. Kusuda> T. and ThHrlimann, B.-"Strength of Wide Flange Beams Under Combined

Influence of Moment, Shear, and Axial Forcet.fFritz Laboratory Report No. 248-1, LehighUniversity, May 1958.

273.' Mueller, J.A."Stresses in Cover Plates and Bearing Stiffener-sri

To be published in ~he Welding Journal, ~960.

276. Timoshenko, S. and MacCUllough, G. H.TtElements of Strength of Mate.rialsH (Book)D. van Nostrand Com.p~Y_3 Inc-., New York andToronto, 1954. -

JW0'I

Graphical Summary of ReferencesCountry

cf ~o'0 6;'6 &o.c. df5"l$u. S. A. 0

0 Buckling, of Rectangular Plates 6 000 g$.~ 0 ens Bending, Compression 1 or Shear De 6 DO- $.6~i 6 e-ts DOd' Contai ni og Test Results c c 0 00-&= 6606g o0"6 n-e $ o. (Jrtl g-eQ c c. d c- c. c. 0[106_In. 6 110000Inelastic Buckling' DO OQOSQ (1000

01849 -e- Longitudinal Sfiffners rf [repc Q EJ 'So -Er &~ -q-e-Great Britain 01890 Transverse 5ti f1ners 0 s Cfo BC C o cf~ On a 44-01894 bJ Post Bu ckling' Beh avi or 0 0

Belgium Book s on Plate Buckling[J

France e.d'-e-flf -iboe 0-

~s -&

Switzerland 0 o ifB 'i:r ~ 0 EM'" f.I" tr ~ 0 ~ Ofre

0BoDO

1),

go

eto-0c

Germany ~D0'1858 fle- $-

4J !}~ -$rfJ 0 H. .. -$ -Ets eSC:

o lJ-e 0 0 -$ E-D OgODOD Qc EJ CJ 6 -g eta &C c ~ eo c- d D-$-a .$-DO OB-a Q gaD 0c0 0 0 0 0-06 DO Eto-e.O$ $--$- 0 gl3- 0 0g-e-$-ao ~e-fr~0 DO

~

Other S~ ~0Countries s c s0 0 DO .g a

1900 1910 1920

FigJ

1930 1940 1950 Year

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 within 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

-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 chemicalanalysis 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

-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. zthe 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 - 0472x31.59Sa = 25 + 0.47 + 0.43 25.90 ineb = 25 0.47 + 0.76 =25.29 inSa = Inlea = 14,380/25.90Sb = 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 aty = -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 momentsof 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 withthe 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 thearea 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 ywhere 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 initiatesynominal 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 valueof 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 stressand 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 theprocedure 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 themoment 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 Aand 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.,3S6'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 entirecross 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 aresimply 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 firstnominal 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