historic literature review usa

7/28/2019 Historic Literature Review USA

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BIBLIOGRAPHYON LOAD DISTRIBUTION

IN BEAM-SLAB HIGHWAY BRIDGES

byZiya A'ktas

David A. VanHorn

This work was conducted as par t of the project enti t led"Latera l Dis tr ibu t ion of Load for Bridges Construc tedWith P.restressed Concre, te I -Beams fT , sponsored ,by thePennsylvania Department of Highways; the U.S. Departmentof Transportation, Bureau of Public Roads; and the Reinforced Concre te Research CaUDeLl'. The opinion's, findings,and conclusions express,ed in t h i s repoI't are those of theauthQrs, and not necessarily those o f t he sponsor s.

Fritz Engineering L a b o r ~ t o r yDepartme'nt of Civi l El1gineering

Lehigh UniversityBethlehem, P ~ n n s y l v a n i a

September 1968

Fri tz Engineering Laboratory Repor t No. 349.1


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TABLE-OF CONTENTS

ABSTRACT

INTRODUCTION

CLASSIFICATION OF REFERENCES

ANNOTATED REFERENCES

ACKNOWLEDGMENTS

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ABSTRACT

The p r i n c i p a l o bje ctiv es o f t h i s r e p o r t wepe toi n v e s t i g a t e th e a va i l a bl e l i t e ra ture on f ie ld t e s t s , a n a l y t -

\i c a ~ methods, model s t u d i e s r e l a t e d t o lo a d d is tr ib u ti on inbeam-slab highway b r i d g e s ut i l iz ing p r e s t r e s s e d c o n c r e t e 1 -beams a s th e main beams. During t h e p r o g r e s s o f th e i n v e s -t igat ion , however, t he -c o n te nt o f th i s work was ,e nla rge d t oi nc lu de b ri dg es support ed by o t h e r a r o s s - s e c t i o n a l shapes o fp r e s t r e s s e d c o n c r e t e b e ~ m s , as w e l l as some s tee l members.

A t o t a l o f 118 r e f e r e n c e s i s included. The re fe r -e n c e s a re c at eg or iz ed accordi ng t o ty p e o f coverage.


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INTRODUCTIONSince prestressed concrete was f i r s t ut i l ized in

bridge construction in the United States , there have been manydevelopments in prestressed concrete techniques for bridge construct ion. One of the most important developments was in beam-slab type highway bridge construction ut i l iz ing precast, prestressed concrete girders , together with a cast-In-place conc rete slah .

For several years, two of the most common shapes usedfor 'prestressed concrete girders have been the I-beam and thebox beam. According to the current design procedures uti l izedby the Pennsylvania Department of Highways in the design of prestressed concrete br idges , the in te r ior g irde rs of t he p rest re ss :edbridges are designed using a l ive load dis t r ibut ion factor of8/5.5 where S i s the average girder s p ~ c i n g in fee t . This facto r is ident ical to the load dis t r ibut ion factor given in theAASHO Specif icat ions governing the design of a beam-slab bridge

s ~ p p o r t e d by s t ee l I-shaped girders.The val id i ty of th is value of the 10ad distribution

fac tor for box-beam bridges has been the subject of an inves t i -gation a t Lehigh Universi ty , Bethlehem, Pennsylvania involvingf ie ld te sts on var ious b ri dges (see report Nos. 18, 30, 114, 115,116, 117, and .118). T0 date, the resul ts obtained have indicated

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tha t the actual dis t r ibut ion of l ive load differs f ~ o m the designassumption. Therefore, the 'val idi ty of the assumed factor forprestressed concrete I-beam bridges has also been opened to quest ion. As a , f i r s t stage of an invest igat ion, previous analyt icalwork, f ield t e s t s , and model stud ies of load dis t r ibut ion in prestressed concrete I ~ b e a m bridges are reported. Also, as aby-product of th is survey, the b rid ge s w ith other cross-sect ionalshapes of beams, and also with s tee l beams, a re included andgrouped accordingly.

All of the available reports are grouped. in two partsas Part I : Load Distr ibut ion for Bridges, Part II : Field Testsfo r Bridges.

The f i r s t par t i s sub-divided in to three parts as fo l -lows:

1. Analytical Methods2. Model Studies3. OthersAnalytical methods inclu des b rid ges w ith 'both general

and part icular types of beams. In the l a t t e r , the theories arederived fo r bridges with a cer ta ip type of girder , while in theformer, a theory i s derived for a ,general cross-section whichwould be applicable to any type of beam. Therefore, the formulat ion i s mainly a.function of the fl exura l and torsional r ig idi t i es of the gi rder , instead of the speci f ic shape.

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Model studies are grouped accordingto the materialsof the investigated models. Each group i s fur ther sub-dividedaccording to the shape of the girders of the model bridge.Those in which the girder types are not specified in the ' repor tare included in the item TTnot specified Tt .,

In the l a s t group of the f i rs t part , books, tables,and surveys related to the subject are put und er t he t i t l eTTothers""

Field t e s t s , as Par t I I , are presented in two groupsas Destructive Tests and Non-destructive Tests. They are furthersub-divided according to the material and shape of the 'gi rder ofthe t e s t bridgeo The load type, tha t i s , truck load or pointload, and load condit ion, tha t i s , s ta t ic or dynamic load, areemphasized in the summary of the reports whenever possible.

After the classif ica t ion of data referr ing to reportnumbers, the reports are l is ted essent ia l ly in alphabeticalorder by author 's name, or t i t l e i f a u th o r is n ot l is te d .Several la te additions .were made, beginning a t No. 114.

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CLASSIFICATION OF REFERENCES

Par t I . Load Di st ri bu ti on f or BridgesA. Analytical Methods

1. General Types of Beams1.1 Beam-slab system: 2, 3, 4, 12, 16, 19,22, 31 , 33, 35, 44, 52, G2, 65, 66,67, 75, 80, 85, 86, 91, 92, 99, 100,101, 103, 1.091 .2 Slab bridge: g, 72, 93, '95, 102

2. Part icular Types of Beams2.1 Prestressed concrete beams: 61, 6 8 ~ 69,70, 71, 1112.2 Reinforced concrete beams: 28, 49, 51,63, 76, 832.3 Pseudo-slab: 15

2.4 Stee l beams: 61, 78, 79, 1052.5 Timber: 8

B. Model Studies1 . Plexiglas or Other Plas t ics

1.1 I-beam: 131 .2 T-beam: 601.3 Box beam: 37, 57, 60, 90, 117, 1181.4 Not specif ied: 107, 112

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1.3 Others and not s p e c i ~ i e d : 2, 9, 10, 11,14, 17, 34, 35, 39, 42, 47, 48, 53,54 , 56 , 59, 61, 73, 96, 97, 1022. Reinforced Concrete Beams: 24, 27, 43, 77

Steel Composite or Non-composite Beams: 1, 2,7, 16, 20, 21, ~ 3 , ~ 4 , 25, 26, 27,41, 43, 77, 84, 113

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ANNOTATED' REFERENCES'

1. Arya, A. S. and Surana, C. S.DISTRIBUTION OF IRe STANDARD LOAD$ IN SLAB-ANDGIRDER BRIDGES, Indian Concrete Journal, Vol. 39,No. 12, pp. 466-73, December 1965The method derived by A. N. Hendry and L. Jaeger

was applied to find the load distr ibut ion_under Indian RoadsCongress wheel load so Two-lane bridges con si st in g o f threeor four beams were tested in the f ie ld . The tes t resul tswere used to compute the distr ibuted load as the fractionsof wheel loads 0 The tables prepared can be used to designreinforced concrete slab and girder bridges o r Qompositebridges.

2. Baldwin, J . W.IMPACT STUDY OF A,STEEL I-BEAM HIGHWAY BRIDGE, TheUniversity of Missouri (Columbia) "Bul le t in , Engineering Experiment Stat ion, Series No. 58, October 1964The purpose of the ' t es t s e r i e ~ reported was to inves

t igate the impact factoroThe t e s t structure was a t h r e e ~ s p a n , c o n t i n u o u s bridge

in Missouri. The bridge was .spbjec ted to rive ser ies oftestso The. f i r s t three series ,were used to investigate ,the'e',ff-e,ct,s 'o f the l at e ra l posi tion of t he 'tru ck ' lane on thebridge 0 The remaining two were designed to study the in duced roughness effect on,the impact factor . Each 'serieshad several s ta t ic and dynamic ' t es t runs.

In the f i r s t par t of the repor t , the s t r u c ~ u r e , t e s tvehicle , instrumentation, and t e s t cprocedure are described.

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Next, the t e s t resul ts are analyzed; theoret ical andperimental moments and deflections are-compared, Thecomposite action, frequency of vibra t ion, and amplitude ofvibration are invest igated, and the ,effect of speed onmoment and deflection is discussed.

A .comparison of the continuous span with a s implespan i s given in the l a s t par t of the repor t .

3. Bares, R.COMPLEMENT A'LAMETHODE GUYON-MASSONNET DE,CALCUL DESFONTS A'POUTRES MULTIPLES, Annales des Travoux Publicsde Belgique, Vol. 1, pp. 7-69, January 1965, pp. 14771, April 1965 (In FrenCh)As the t i t l e implies, this paper is a_complement to

the Guyon-Massonnet method in the design, of multiple beambridges & The author uses an analogy between a.beam,systemand an orthotropic plateo 'For an,easyand more accurateapplication, prac t ica l relat ionships are 'given, and coeff ic ients are-computed and l i s ted in 80 tables , for thepurpose of quick, complete, and accura te de te rmina tion ofshearing s t resses , reactions, bending 'moments deflect ions over a wide range of 'beams used in:pract ice .

4. Berkelder, Ao Go J.LASTVERTEILUNG BE! EINFELDRIGEN BRUCKEN ,MIT ZWEITORSIONSSTEIFEN HAUPTTRAGERN, Stahlbau, Vol. 35,No.6 , ppo 180-7, June 1966 (In German)Load distr ibut ion in single span bridges withtwo

tors ional ly rigid main,g irders . i s discussed. I t is assumed that (1) cross-t ies (diaphragms) are-close one toanother, and can betreated. as o n e c o n t i n u o u s . c r o s s ~ t i e ,and (2) both girder.ends are restrained from torsion byone common end t i e . To det ermine load dis t r ibut ion factors for ,symmetric and asymmetric loads, formulas are deriv ed. T heeffects 'o f ,end t i e deformation, l oc al s tr es se s

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due to tr an sv er se roadway r ibs , and sett lement of the subs t ructure are taken into consideration.

5. Best , Bo Co and Rowe, Ro EoABNORMAL LOADING ON COMPOSITE SLAB BRIDGES (1) TESTSON A BRIDGE WITHOUT TRANSVERSE REINFORCEMENT, Cementand Concrete Associat ion Technical Report TRA/301,London, October .1958Tests on the f i r s t of a "series of composite slab

b rid ge s a re d es cribe d and the resu l t s analyzed. The bridgetes ted had no t ransverse r e i n f o ~ c e m e n t and comprised onlyprecast pres t ressed inverted T ~ b e a m s and high-strength ins i tu concreteo

The tests:showed tha t the bridg e behaved sa t i s fac tor i lyunder ,both ,the design and the u lt ima te l oadi ng 'c ondi ti on s f orabnormal loading provided tha t the individual beams were designed on the basis of the Ministry of Transpor t increasedstandard loading 0 The dis t r ibut ion propert ies were not satisfactory 0

6. Best, Bo Co and Rowe, Ro EoABNORMAL.LOADING ON COMPOSITE SLAB BRIDGES (3) TESTSON A BRIDGE WITH SOME TRANSVERSE.REINFORCING STEEL,Cement and Concrete Assoc ia tion Technica l Report

T R A / 3 0 9 ~ London, January 1959Tests on.the third of aser ies of c o ~ p o s i t e slab

bridges are described and the resul ts analyzed 0 The bridgeincorporated p r e c ~ s t inverted T-beams,. in ,s i tu .concrete, andmild-s teel t ransverse reinforcement.

The bridge behaved sa t i s fac tor i ly under ,both the designand ult imate loading -conditions fo r abnormal lo ad in g, p ro vided that the individual beams were designed on the basisof th e M in is tr y of Transport increased standard loading.The dis t r ibut ion ,propert ies were poorer , than those of a simi l a r i so t ropic slab under , the abnormal load.

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7. Biggs, M. J . and Suer, H. S.VIBRATION MEASUREMENTS ON SIMPLE SPAN BRIDGES, Highway Research Board Bulletin 124, 19568. Boomsliter, G. P ., e t a lDISTRIBUTION OF WHEEL:LOADS ON TIMBER BRIDGE FLOOR,

W ~ s t Virginia,. Universi ty Engineering Experiment Stat ion , Research Bullet in No. 24 , 1951Tests were carried out to determine s t r inger load due

to wheel loadso Deflections caused by.dif ferent load placements ar e given. The effect of two rear ,wheels of a ,trucki s discussed. Stresses , as calculated from deflect ions arecompared with those determined from s t ra in readings.

9. Bouwkamp, Jack GoBEHAVIOR OF A SKEW STEEL-DECK BRIDGE'UNDERSTATIC.ANDDYNAMIC LOADS, University of California (Berkeley),Structures and Materials Report No. SESM 65-2, June1965The primary objective of the:studies described in th is

repor t was to evaluate the s t ructural response of askewly' s t i f fened skew s tee l deck pla te under,concentrated s ta t icloads. The load distr ibut ion ,in the ,deck under 'single andcombined concentrated s ta t i c loads -was ,the object ive of theexperimental phase of the program. An analyt ica l programwas also developed to predict the behavior'of such a deckunder wheel loads. The behavior of ,the pro to type sub jec tedto heavy dynamic t ra ff ic loadswas also ,studied ~ x p e r i m e n -t a l ly .

In the report , loading and instrumentation are givenf i rs to Next follows the 'analyt ical solutions-of -the 'skewpla te in a.closed form. A , f ini te difference method was alsoused to get an analyt ical solution. ,Later analyt ica l and experimental resul ts under ' s ta t ic and dynamic load are p ~ e s e n t e d .

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10. Bouwkamp, J . G., Brown, Co B., Scheffey, C. F ., andYaghmai, S.BEHAVIOR OF SINGLE SPAN COMPOSITE GIRDER BRIDGE,University o f Cal if ornia (Berkeley),. Structures andMaterials Research Report No. SESM 6 5 ~ 5 , August 1965The measurements obtained from the Webber Cl?eek Bridge

under a slowly moving vehicle were used to s tudy :th e behaviorof a-bridge of this type, and to develop an accurate mathematical model. The bridge 'was of asingle-span, compositegirder ,construction.

The report has three p a ~ s . In the f i r s t par t , f ie ldt e s t data and i t s reduction:is given. Using the experimentaldata, moment dis t r ibut ion to the four girders i s determined.Theoretical and computer analyses form the second par t . Thebridge was analyzed by.dividing the b ridge in to a.g rid systemand ut i l iz ing a dig i ta l computer.

In the l a s t par t of the report, the ,experimental resul tsare compared to those obtained analyt ical ly , and the accuracyof the prediction by the proposed analyt ical method i s dis-cussed.

11. Bramer, Co R., e t a lPRESTRESSED CONCRETE.CHANNEL BRIDGES FOR-SECONDARY ROADSAn Investigation of the Elastic Load Distribution UnderLive Loading , North Carolina State U n i v e r s ~ t y " E n g i n e e r -ing'Research Department, June 196212. Brooks, D. S.DESIGN OF INTERCONNECTED BRIDGE GIRDERS, Civil Engineering, (London), Vol. 53, No. 623,.pp. 535-8, May1958,and pp. 6 8 2 - ~ , June 1958

The manner in which a concentrated load or asystem ofloads is .carr ied by a-main beam with ' regard to interconnect ion with transverse beams is studied. A n ~ w , m e t h o d of analysis found a t th e Univ er si ty of Adelaide i s explained. In

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this method, operators.computed from simple beam theoryare used. Symmetrical and ant i- symme tr ic al oper ator s a re

d i s c u s s e d ~ I t i s the aut ho r' s f ee li ng tha t a relaxationmethod o f s olu tio n has the advantage of rapid closure, andenables a d esig ne r to solve a l l the redundancies in a s t ruc-

t u r e ~

Carpenter, Jo Ea and Magura, Do D.STRUCTURAL ,MODEL ,TESTING--LOAD DISTRIBUTION IN CONCRETE I-BEAM BRIDGES, Portland Cement Association Bull e t in D - 9 ~ , September 1965Tests on a.few s m a l l ~ s c a l e P l e x ~ g l a s models of pre

stressed concrete highway bridges con tinuous ove r two spansa-re reI>orted. Concentrated load dist r ibut ion --Tor ,diferentwidth- to-span ra t ios and several arrangements of in ter iordiaphragms was measured 0 The 'resul ts were found to,conformclosely to those predicted by .e lastic t h e o r y ~ Excellentagreement was found between the behavior of one of the smallscale :models and tha t of a.geometrically,similar half -scaleprestressed bridge tes ted ear l i e r in the laboratory.

T hee ffe ct o f p lac in g ,the AASHO loading HS-20 on thevarious t e s t bridges, as ,calculated from model t e s t data ,i s compared with the AASHO Specif icat ions and caleulationsbased onthe Guyon-Massonnet elas t ic theory.

There three appendicesgiven in the paper. InAppendix A ,brief descriptions are given of the constructionof the model, suppo rt appar atus , t es t methods, 'and inst ru-mentation. Appendix B includes a .br ie f description of the

~ u y o n - M a s s o n n e t theory, the Mat tock-Kaar ,correction Tor the. effect of concentrated loads, and the computer 'program forobtaining numerica l values from these th eo rieso Additionalvesults a re obta in ed analyt ica l ly for a .wider range of width

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to 'span ra t ios and diaphragm arrangements than-were invest igated experimentally. These ~ e s u l t s are given in Appendix C.

14. Caughey, R. A. and Senne, J . HoDISTRIBUTION ,OF LOADS IN BEAM AND SLAB BRIDGE FLOORS,Final Report to Iowa Highway Research Board, Iowa StateUniversi ty, Iowa Engineering Experimental Stat ion,September ,195915. Cusens, Ao R. and Pama, R. P.DESIGN OF CONCRETE MULTIBEAM BRIDGE DECKS, Journal ofStructura l Division, Proceedings of ASeE, Vol. 91 ,pp. 255-78, October ,1965

The composite slab is one made o f s ep arate precast beams(with 'or ,without some form of shear-key) , with a continuouscovering ,of cast- in-place concrete. The pseudo-slab, on theother ,hand, i s ,composed of separate beams, and transverseload distr ibut ion i s obtained by means of concrete shear 'keysand m ild s t ee l shear ,connectors or t ransverse prestre-ssing.The composite slab thus possesses more i nhe ren t t ransve rses t i f fness than the -pseudo-slab.

The s t ruc tura l performance of concrete pseudo-slabs-with 'shear 'keys and with transverse prestressing is theprimary concern of this paper 0 Recent t e s t s a re descr ibedand a method of design is s u g g ~ s t e d o

16. Davis, R. Eo, Kozak, J . J . , and Scheffey, C. F.STRUCTURAL BEHAVIOR OF A BOX GIRDER BRIDGE, CaliforniaState Highways Bridge Department, May 1965The primary objec tiv e o f the 'program was the study of

the 'manner ,in which l ive loads are distr ibuted t ransverselyin a-box girder bridge. Dead load distr ibut ion, inf luenceof intermediate diaphragms on l ive load distr ibut ion, andinfluence of curbs and ra i l ings on, l ive load distribution

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were the other objectives of the program. Besides f ie ldt es t s , model s tudies , i n c l u d i ~ g a small plas t ic model anda q u a r t e r ~ s c a l e : c o n c r e t e model of the prototype, were conductedo

A 'study of analyt ical methods was a l ~ o included in theprogram to compare with the experimental behavior of thes t r u c t u r e ~

In the f i r s t par t of the report , th e p ro to type s t ructure , . instrumentation, t e s t vehicle and materia l controltes ts used in the f ie ld tes t ing are described, and t es t re -sul ts are presented. Next, analyt ical methods are given.The f i r s t of the three analytical m ~ t h o d s discussed i s adis t r ibut ion procedure developed by Newmark for slabs on

. s tee l I - b e a m s ~ Due to the change of the "crass-sect ion,some modifications of the method noted. The secondmethod is the application of folded plate equations developed by Goldberg and Leve* using matrix algebra to t h e ~box girder bridges. The third method is a combina tion ofthe two methods such that the transverse r ig id i ty i s t reatedby NewmarkTs method, and the longitudinal r ig id i ty by foldedpla te e q u a t i o n s ~ I t i s aLso noted ~ h a t , in ,spite of thed iffe re nc e o f the mathematical approach between ,the secondand th i rd methods, the resul ts are essent ia l ly the same.

The experimental resul ts arethep.compared with resultsfrom the three analyt ical methods. Model tes ts a re p re sent eda t the end of the report .

* Goldberg, J. E. and Leve, H. L ., TTTheory, of Prismatic FoldedP la te S truc tu re s TT , Publications, Internat ional Association ofBridge and Structura l Engineer, Vol. 17, 1957

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point on the multi-beam b rid ge, are d'erived. The methoddeveloped is applied in ca lcu la ti ng the 'ver t ical moments inbeam elements of so lid square sect ion.const i tut ing a multibeam bridge. Influence l ines , for 'ver t ic le moment in multi-.beam bridges having two, three, and ten beam elements ofsol id square section are developed.

I t is assumed tha t the b ridge c onsists of beam e l e m ~ n t splaced s i d e ~ b y - s i d e and connected to each other along thespan by hinges a t the corners of the cross-sect ion a t thelevel of the top f iber.

20. No author l i s tedDYNAMIC TESTS OF TWO CANTILEVER TYPE STEEL GIRDERBRIDGES, Nebraska, Department of Roads, Bridge Divis ion , August 1961.21. No author l i s tedDYNAMIC TESTS ON A ROLLED BEAM COMPOSITE CONTINUOUSSPAN BRIDGE -PART 2, South Dakota Highway Commission,Impact and Vibration Study , October 195522 . Dziewolski, RoCOEFFICIENT DE REPARTITION TRANSVERSALE DANS,LES FONTS,

Construction Metall ique , No.2 , pp. 18-32, June 1965( In F rench)Transverse dist r ibut ion facto rs fo r bending momentsin

bridges i s the subject of this papero Using the the ory ofnon-uniform torsion for long thin-walled members, a methodto compute the t ransverse distr ibut ion factors is developedfor loads 'imposed on long bridges of doubly unsymmetr ic open,closed, and compound cross-sections. By means of a numericalexample, the'proposed method is.compared with the 'c lass ica lmethod for l a t t ice frame-works, and w ~ t h the method developedbyCourbon. The advantages of the proposed method are alsomentioned.

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280 Gifford, Fo WoTEST"'ON PRESTRESSED CONCRETE HOLLOW-:-BOX BRIDGE DECK,Magazine of Concrete Research, Vol. 13, No. 39, PP. 149156, November 1961Investigations proved that for bridges of spans from

30 to 90 fee t , t he p re -t ensioned prestressed concrete beamswould give the most economical solution. Inverted T-pretensioned beams placed s i d e ~ b y ~ s i d e ~ o r ' h o l l o w ~ b o x pretensioned beams placed s i d e ~ b y - s i d e and held together byprestress or other means appeared to be par t icular ly sui table .However, the comparison of the-character is t ics of these twobeams proved tha t the hollow-box beams were more advantageous.

In the paper a series of t es t s , purpose of which-was toverify the requirements for the transverse prestressing of

h o l l o w ~ b o x decks, is reported. The t e s t deta i l s , and loadingcondi tions a re given. l At the end of the tes ts it is concludedtha t the shear ' key between the h o l l o w ~ b o x ' - u n i ts provided anexcellent t r ansfe r of load.

In Appendices of the repor t , the d esig n character is t icsof 50 f t . span h o l l o w ~ b o x and inverted T units are comparedand design data for the t e s t deck, is presented.

290 Granholm, Co Ao and Rowe, R. EoTHE ULTIMATE LOAD OF SIMPLY SUPPORTED SKEW SLAB BRIDGES,Cement and Concrete Association, Research Repor t Nao 12,London, June 1961The yield- l ine theory for ,calculating the ultimate loads

of veinforced o r p re st re ss ed concrete slabs is applied toskew slab bridges subjected to the Ministry of Transport 'sAbnormal Loading 0 Equations are derived which enable thedesigner to , ob ta in th e ultimate load simply by taking accountof both the dead and the l ive loading.

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Experimental work on.eleven prestressed and reinfovcedconcrete slabs is described, and t he exper imen ta l ultimateloads are,compared with the theoret ical loads.

Final ly , a design procedure, combining elas t ic and ul t i mate load methods, is:suggested for'skew slab bridges subjected to abnormal loading.

30. Guilford, A. A. apd VanHorn, D. A.LATERAL DISTRIBUTION OF DYNAMIC LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE, Lehigh Universi ty, Fri tz Engineering ,Laboratory Report No. 315.2, February 1967'This is a.continuation of the study with the objectives

given in th e p rev ious paper (see No. 18) 0 In-this paper theef fec t o f v eh ic le speed on l a t e ra l dist r ibut ion of l ive loadsi s shown and the resul ts are compared with those in crawlrun tes ts p ~ e s e n t e d in tpe previous papero

The f ield t e s t data was evaluated to obtain moment coeff icients and dist r ibut ion,coeff ic ients . Ratios o dynamicmoment coeff ic ients to c r a w l ~ r u n coeff ic ients were :computedand.compared to the designvalue. Also, loaded and trnloadednatural frequencies were determined experimentally and com-

- ~ a r e d ~ w i t h , t h e o r e t i c a l values.310 Guyon, Mo Y.CALCUL DES FONTS LARGE A POUTRES MULTIPLES SOLIDARIEESPAR DES ENTRETOISES, Annales Des Ponts .e t Choussees,

~ n P o S 5 3 ~ 6 1 2 , 1946 (In French)In this paper, the theory, which is often referred to

as Guyon's load dist r ibut ion theory, i s presented. A,transla t ion of this paper i s given in the Journal of the PCA,Research and Development Laboratories, Vol. 3, No. 3, p p ~ 3070, September ,1961.

One of t he impo rta nt a s s ~ p t i o n s of Guyon is tha t notors ional resistance i s assumed in the analysis. A Fourier

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Series is used fo r so lu tio n o f the par t i a l dif ferent ia lequations 0

32. Hayes, J . M. and Sbarounis, J . A.VIBRATION STUDY OF A THREE-SPAN CONTINUOUS I-BEAM BRIDGE,Highway Research Board B u l l e t ~ n No. 124, pp. 47-78, 1956

330 Hendry, A. W. and Jaeger , L. G.THE LOAD DISTRIBUTION IN HIGHWAY BRIDGE DECKS, Journalof Struc tu ra l Division, Proceedings of ASeE, Vol. 82,Paper No. 1023, July 1956The paper presents a ~ g e n e r a l method fo r ,calcula ting

the dis t r ibut ion o f l ong it ud in al moments, deflect ions , etc .in bridge decks. I t i s assumed that the transverse system. can be replaced by a uniform 'medium of the same to ta l f lexura l r ig id i ty . Distr ibut ion.coeff ic ients are determinedfor the to ta l b e n d ~ n g moments or deflection of ~ h e span.The derivat ion of these coeff ic ients i s i l lus t ra ted for thegeneral case of beams with a r b ~ t r a r y to rs iona l r ig id i ty ,but in design, it i s ' su f f i c ien t ly accurate to in te rp ol atebetween zero and inf in i te tors ional r ig id i ty by means of asui table interpolat ion function. It i s shown tha t a.bridge,having a large number of longitudinal members can be replacedby an, equivalent f iv e l ong itud in al member structure for thepurpose of determining defleotions and dis t r ibut ion.coef-f ic ients fo r the longi tudina l members. Graphs of dis t r i -bution coeff ic ients fo r a - f i v e ~ g i r d e r b r i d g e are thereforeinCluded in the paper . Also, applicat ion to slabs i s cons idered. Theoret ical and experimental resul ts are-comparedfo r (1) an encased I-beam bridge with ,concrete deck', (2) as tee l beam and jack arch br idge , (3) a beam and slah;bridge,

a . f i l l e r j o i s t bridge deck, and (5) a reinforced concre te slab br idge .

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34. H i n d m a n ~ w. and Vandegrift , L. E,LOAD DISTRIBUTION OVER CONTINUOUS DECK TYPE aRIDGEFLOORSYSTEMS, The Ohio State University Engineering Experimental Stat ion, B u l ~ e t i n 122, May 1945In The paper, the diff iculty in theoret ical evaluation

of the di--stri,bution of concentrated loads over the f loors ofhighway bridges-is pointed out. influence of non-uniformtemperature dis t r ibu t ion on def lec t ion readings was' shown.The t heore t i ca l methods were modified to include the effec tsof non-uniform temperature distr ibut ion.

35. Holcomb, Robert M.DISTRIBUTION OF LOADS IN BEAM AND SLAB BRIDGES, I o w ~Highway Research Board Bul le t in No, 12-Simple-span highway bridges composed of lo I )g i tud ina l

s t e e l beams, or s t : r ingers , carrying a' reinforced cone-reteslab are considered. A new procedure fo r predict ing thestra ins and -deflections of the'be-arns in ' simple-span beams lab .br idges of the u s u ~ l propo'rtions wp,sdeveloped. Fourbridges, two in-service s t ~ u c t u r e ~ and ,two laboratory: models,were tested to compare the actual behavior (1) withpredictions by , the proposed procedure , (2) with the 19S3AASHO Spec i f ica t ions , and (3) with the t en ta t ive revisions(T-lS-50) .

Some-af the conclusions are: (a ) a n imp roved 'procedurefor the a nalys is o f the beams in simple-span and slap,bridgeshave been developed, and (b) the proposed method i s e-speciallysuperior-in p re d ic ti ng th e maximum e f fec t s of s ingle t rucks.

Theollowing recommendations fo r f u t u ~ e re se arc h a realso given: (1) t es t s to determine the ac tua l proper t ies ofthe beams in place , (2) mOt'e d e ta il ed s tu d ie s of the e f fec t sof diaphragms, including:efforts to arrive a t the equivalent

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propert ies of the diaphragms, (3) tes ts to check the d i s t r i bution of the loads to the beams, and along the beams, whenthey are-prevented from def lect ing. I f temporary supportsalong the beams are used, they should be placed that theyintroduce l i t t l e or no resistance to the rotat ion of thebeams, because this rota t ion 'affects the distr ibut ion,(4) fu rther inves tigat ion of the effects of t he varyingaross-section of the beams, (5) studies of bridges havingmore than four beams, (6) i nvest iga ti ons o f the possibi l i t ies of extending the proposed method to the analysis of cont inuous b e a m ~ b r i d g e s , and (7) th e extens ion of the analysisto the determ ination of moments in the s lab .

36. Hamberg, H.LASTVERTEILUNGSZAHLEN FUR BRUCKEN I . Band, SpringerVerlag-, 1967 (In German)Transverse load dis t r ibut ion coeff ic ients f or r or sio n

a l ly s t i f f girders were -,given by' Hamberg and Trenks in TTDrehs te i fe Kreuzwerken TT < For tors ional ly weak girders TTE-influssf lachen fur Kreuzwerken T1 by Hamberg and Weinmeistergave thesec o e f f i c ~ e n t s . In this book, the load dis t r ibut ion factorsfor th e b rid ges ,with arbi t ra ry :c ross-sec t ionare discussedo

Mainly there are three systems to be discussed asfollows: (a ) bridges with tors ional ly :s t i f f girders wherethe outside girders may, be s tro ng er o r weaker than the in terior"ones,- (b) skew bridges ,with different s t i f fness ofgirders , and (c) axial ly 'symmetrical bridges with variables t i f fness of girders . Resu lts are tabulated for design purposes.

37. Hamberg, He, Marx, W. R., and Zahlten, N.MODELLUNTERSUCHUNG AN EINEM SCHIEFEN KASTEN, Bautechnik,Vol. 38, No . 4 , pp. 118-123, Apri l 1961. (In German)This paper discusses model study of an oblique b o x ~ b e a m .

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38. Hondros, G. and Marsh, J . G.LOAD DISTRIBUTION IN COMPOSITE G I R D E R ~ S L A B BRIDGES,Jo urn al of Struc tu ra l Division, Proceed:ngs of ASeE,Vol. 86, No. STll, pp. 7 9 ~ 1 0 9 , November.1960For t he 'confi rma t ion of cer ta in assumptions made in thedesign of a prototype bridge, a-ser ies of simply-supported

composite girder-s lab systems were tes ted . Actual and theor e t i c a l behavior are compared, and the effects of skew angleof the bridge and tors ional s t i f fness of the girders arediscussed 0 I t 'was .concluded tha t the neu t ra l planes of thegirders are nei ther \co-planar ,nor s tat ionary arid th is factwas explained considering the induced dis t r ibuted longitudi na l forces in the s lab , which undoubtedly, occur in theses t ruc tu ra l memberso The primary obje ctiv e o f the work wasthe assssment of assumptions made 'with regard to dis t r ibut ion of loads, and the e f fec t of a.30o skew angle on a tengi rder , 130 f t . long composite s tee l gi rde r and concrete deckbridge s p a n ~ ' Following the, examination of the "f i rs t model,two addit ional types w e ~ e tested in which a l l propert iesweve re ta ined , except tha t in the second model the tors ionals t iffness of the beams,wasreduced by 50%, and in the th i rdmodel, the span was not skewed4 From ,each of these mainmodels, two 5 ~ g i r d e r ' s y s t e m s , craCked and uncracked, wereobtained by. cut t ing the frames along the i r lOJ:;lgi tud,inalcenterl ine ..

-" --39. Houston, N. Do and Schriever, Wo RoLOAD DISTRIBUTION;TEST, SUSSEX'STREET BRIDGE, OTTAWA,CANADA, Proceedings of th e World Conference on Pres t ressed Concrete, Part I I , Section V, Paper No. 20-1,July 1957In th i s paper , a . fu l l -sca le loading t e s t on a three-. span b-ridge-wi th 18, p o s ' t ~ t e n s i o n e d prestressed conClJete 1

beams is reported. One s imply-suppor ted span of the bridgewastested under s t a t i c loading to determine the t ransverseload dis t r ibut ion character is t ics . This span had a length

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4-0

of 86 f t . 7 ino and the loading consisted of two heavilyloaded t rucks. The t e s t resul ts forsymmetrical loading a tthe center of the bridge had shownfair ly good agreementwith the theoret ical values 0 However, under o f f - c ~ n t e rloading, the actual dis t r ibut ion obtained by the t e s t wass igni f icant ly less than that obtained by the theoret icalmethods 4Hulsbos, C. L.LATERAL DISTRIBUTION OF LOAD IN MULTI-BEAM BRIDGES,

H ~ g h w a y Research Board Bulletin No. 339, pp. 67-79,1962This paperpresents asummary of the research,conducted

since 1954 a t Fri tz Engineering Laboratory, Lehigh Univers i ty , on the l a t e ra l load dis t r ibut ion of multi-beam bridges.This type of bridge i s constructed from precas t rectangularbeams'made of e i ther r e i n f o ~ c e d or 'prestressed concrete.These beams are placed s i d e ~ b y - s i d e on the abutments andthe l a t e ra l in terac t ion between the beams i s developed by

,continuous longitudinal shear keys and l a t e ra l bolts thatmayor may not be pres t ressed .

The invest igat ion included: (a ) f ie ld t e s t , (b) theo. re t ica l study, and (c) ser ies of t e s t s on a larg e s ca le modelbridge.Hulsbos, C. Lo and Linger, D. A.DYNAMIC TESTS OF A THREE SPAN CONTINUOUS I ~ B E A M HIGHWAYBRIDGE, Highway Research Board Bulle t in No. 279, pp.4-6, 1961

42. Hulsbos, C. L. and Linger, D. A.DYNAMICS OF HIGHWAY BRIDGES, (Part I and Part II) , ~ I o w aState Highway Commission, I,owa Highway ,Research BoardBullet in No. 17, November ,196'0The report i s composed of two parts . In the f i r s t par t

of the r epo rt , c o rr el at ion between the actual response of a

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of a continuous highway bridges under moving load with thevibrat ion theorywas investigated. The parameters affectingth e b rid ge vibration.were determined using experimental data.The t es t bridges a re described in th is par t of the report.They a re three 'cont inuous highway bridges and one simple spanhighway bridge of the ' in ters tate highway s y ~ t e m around DesMoines, Iowao The simple span consis ted o f six p o s t ~ t e n s i o n e dprestressed concrete beams and had a span of 100 feet . Oneof the cont inuous bridges-was a 220 f t . continuous four-spanbr idge 'with four aluminum stringeJ:1s,,;and a composite reinforcedconcrete deck. The second bvidge was ident ical to the f i r s texcept that the str ingers were s tee l rather than a l u m i n u m ~The third continuous bridge was a ,part ial ly continuous fourspan prestressed concrete bridge. I t had a to ta l span lengthof 198G75 feetG In each of the four 's pans th er e were six

p r e ~ t e n s i o n e d prestressed concrete I ~ b e a m s oIn the second par t , the aim was the d e t e ~ m i n a t i o n of

experimental l ive load dis t r ibut ion, and p repa ra tion o finfluence l ines for the load carr ied by th e variou s ~ t r i n g e r s .The degree of composite action between the reinforced concreteslab and the longitudinal s t r ingers was also investigated.

Graphs of s ta t ic load dis t r ibut ion for the t e s t bridgeswere given a t the end of the reportG

43. I l l ino is , Univer sity o f (S . J. Fenves and A. S. Veletsos)DYNAMIC STUDIES OF BRIDGES ON THE AASHO ROAD TEST,National Academy of Sciences-National Research Council ,Highway Research Board, Special Report 71, Washington,D. C ., June 1962The program to study the dynamic effects produced in

the tes ts bridges of the AASHO Road Test undermoving vehicles was ,described. Sp ecial at tent ion was given for the purpose of obtaining re l iable , carefully ,controlled data on thebehavior of the t e s t bridges under actual f ield conditionso

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4 ~ ~ ' Jaeger, L. Go and Hendry, A. W.THE ANALYSIS OF INTERCONNECTED BRIDGE GIRDERS BY THEDISTRIBUTION OF HARMONICS, Structural Engineer, Vol. 34,Noo 7, pp. 2 4 - 1 ~ 6 6 , July.19S6In th is paper, a new method is proposed fo r the analysis

of s i m p l y ~ s u p p o r t e d interconnected bridge girders . The t ransverse system is considered to be a-uniform medium of , totalmoment of iner t ia equal to that of the actual transverse system,and a dif ferent ia l equa tion inc luding terms due to rota t ionand twist is writte n fo r ,each longitudinal member. Theseequations are solved by Fourier Series , and distributioncoeff ic ients are determined fo r the bending moment or deflect ion of each girdero The theory presented allows anydegree of torsional s t i f fness of the longitudinal members,and in the most general c ase, the dis t r ibut ion coefficients 'are ,ftll1ctions of three dimensionless parameters; the f i r s tis ameasure of the transverse s t i f fness of the bridge, thesecond is a measure of the torsional s t i f fness , and the thirdexpresses the rat io of the inert ias of the outer to the innerlongi tudinal members ,0

A number of comparisons with experimental resul ts arequoted, and the application to the design of s tee l and reinforced concrete bridges ' is demonstratedoJanney, Jo and Eney, Wo JqFULL SCALE TEST OF BRIDGE ON NORTHERN:"I;LLINOrS 'TO,LL

HIGHWAY, World Conference on Prestressed Concrete, BaperA-12, 1957A number of precast prestressed units were incorporated

into the design of many of the g ~ a d e sepa ra ti on s tructu res onthe I l l ino is Toll Highway. They are namely p re ca st p re stressed pi les , p recast p rest re ssed dedk slabs, precast prest! 'essed I ~ b e - a m girders , and precast diaphragms.


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box-beam type. The fourth bridge had box beams made ofprecast prestressed concrete I ~ b e a m and cast-in-place con

. c ~ e t e o The f i f th one was a prestressed concrete platebridge 'with a frame type stuctureo

In the p ap er, influence l ines of deflections for dif -ferent p oints are given and compared to theoret ical valuesf or l ongi tu di na l and transverse direc t ions.

47. Kinnier, H o L.A ,DYNAMIC STRESS STUDY OF THE WEYER'S CAVE BRIDGE,Progress Report No. 2- Vibration Survey of CompositeBridges, Virginia Council of Highway I n v ~ s t i g a t i o nand Research, August 1963The purpose of the f ie ld t e s t measurements was to

determine the following character is t ics of a typica l compos-. i t:e.: s tee l girder ,bridge: (a) t ransverse l ive load d i s t r i -bution, (b) posi t ion ,of the n ~ u t r a l axis in the girders ,(c) natural frequency of the vibration, Cd) logarithmicdecrement of bridge osc i l la t ion , (e ) amplitudes of thevibra t ion result ing from the dynamic load, and (f) impactfactors based on s t resses and def lec t ions.

In the repor t , instrumentation and t e s t p r o c e d u ~ e swere followed by, tes t resul ts and.conclusions.

48. Kinnier, H. Lo and McKeel, Wo ToA DYNAMICSTRESS STUDY OF THp ALUMINUM BRIDGE OVER THEAPPOMATTOX RIVER AT PETERSBURG, ~ r o g r e s s Report No. 4-Vibration Survey of Composite Bridges, Virginia Councilof Highway Investigation and Research, 1965

49. Kloeppel, Ko Ke and Thiele, F.ANALYTISCHE UND EXPERlMENTELLE ERMITTLUNG DER SPANNUNGS-VERTEILUNG IN KASTENFOERMIGEN BIEGEQUERSCHNITTEN MITKONSOLEN BEl OERTLICHER,KRAFTEINLEITUNG, Stahlbau, Vol ..35, Noo 5, ppo 1 5 2 ~ 6 , May 1966 (In German)

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This p a p e r ' p ~ e s e n t s th e ana+y tic al methods to determinethe s tre ss d is tr ib utio n in s tee l box girders.with.canti levers,under bending due to local introduction of f o ~ c e s . Usingthin plate theory and expressing t he int roduced loads byFourier Series, problem i s s o l v e d ~ Later this approach.issimplif ied u s i ~ g some assumptions of flexural theory.

The analyt ical solution was ,verified by model tes tsand it was shown that the resul ts of both analyt ical methodswere in good agreement wi,th the experimental data.

so. Kmita, J .o BADANIACH MODELOWYCH MOSTOW PLYTOWYCH, ArchiwumInzynier l i i ~ a d o w e j , Vol. 10, No.1 , pp. 57-70, 1964,(In Russian) ,An investigation of experimental models of plate bridges

i s d escribed . R esults of s t ress -s t ra in measurements on freely. supported p le xig la s, c as t plas ter , and aluminum"models ofplate bridge spans are report'ed. The tests were aimed a tdetermining transverse load distr ibut ion in isotropic andorthotropic plates and at ,determining moment influence surfaces in skew pla tes . Strains were measured using dialgages, a u t o ~ c o l l i m a t i n g telescope, and electric extensometer.Formulas are given to obtain moments and o rd in ate s o f influence surfaces from measured quanti t ies .

51. Kumar, B.EFFECTS OF TRANSVERSALS IN T-BEAM AND SLAB BRIDGES,Journal of Inst i tut ion of Engineers (India), Vol. 46,No.3 , pp. 132-40, November 1965After,a study of optimization in la te ra l load dist r i

bution in reinforced concrete T-beam and slab bridges, i twas shown that among various factors, number and size oftransversals (diaphragms) p l aya most important role . I t

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was. also concluded t ha t a .c en tr al ly located transversal wasmost effec t ive for l a te ra l load dis t r ibut ion.

52 . Lin, To Y.LOAD FACTORS FOR PRESTRESSED CONCRETE BRIDGES, JournalOT Structura l Division, Proceedings of ASeE, V o l ~ 83,Paper No. 1315, July 1957Load factor may be defined as the ra t io of the 'collapse

l o ~ d for a structure to i t s working load.The size of load factors in ultimate design for pre

stressed concrete bridges is-compared to the e las t ic theoryand allowable s t ress method. Variables affecting ' the loadfac tor of bridge sect ions are analyzed, indicating the widedivergence when designed on the basis of no tension in con

c r e t e ~ In a dd itio n to the load factors for f lexura l s t rength. of simple and continuous spans, factors fo r , s t reng th .. at t ransfe r , for ' shear , and for tension and compression members, arediscussed.

The significance of load dis t r ibut ion, load repet i t ion ,and the meaning of yield point and usable s t rengths , arebrought Quto

53. Lin, To Yq and Hronjef f , RoLOAD DISTRIBUTION BETWEEN GIRDERS ON SAN LEANDRO CREEKBRIDGE, Highway Research Board Research Repor t No. 1 4 ~ B ,1952

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existing between the reinforced concrete slab and girderswas also investigated.

In the report , af ter discussing the b rid ge s t ructures ,loading, and i n s t ~ u m e n t a t i o n , t es t resul ts were given. Theconclusions are: (a ) the exterior and interior girders hadusual ly .di fferent values of composite action than those predicted by specif icat ions , (b ) composite action was existingat the in ter ior supports, (c ) s ta t ic and dynamic loadingconditio ns y ield ed th e same type of l a t e ra l load dis t r ibut ion,and (e ) experimental wheel load factors were less thanthose predicted by AASHO Specifications.

56. Linger, D. A. and Hulsbos, C. L.FORCED VIBRATION OF CONTINUOUS HIGHWAY BRIDGES,Highway Research Board Bulletin 339, pp. 1-22, 1962In this paper, a.correlat ion of forced v ib :rat ion theory

with dynamic impact tes ts for three continuous highway bridgesand one simple span highway bridge i s p r e s e n t e d ~ The t es tbridges were the same bridges described in paper No. ofthis bibliography.

The experimental impact 'was determined in the outerand innerspans and at the in ter ior supports of the continuous:four-span highway bridges, and a t thecenterl ine ofthe single span highway bridge. The ef fec t of the vehiclewas taken as an osci l la t ing forcing funotion. The fOFce ofthis function is the osci l la t ing load effec t o f a .con stantforce t raversing a beam, and i t s frequency is the frequencyof axle repet i t ion.

At the end of t e s t s , the correlation of the theoret icaland experimental impact values showed tha t the experimentalvehicle speeds used, and assumptions made in the effect of

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The t e s t s on a scale model of a 15 skewed prestressedbridge formed by twenty precas t beams prestressed togetherto form a-slab have yielded resul ts which are comparablewith-- those found for the f ul l- si zed s tr uc tu r e.

The dis t r ibut ion of load as measured by deflect ionsand bending moments was control led by the t ransverse momentof res is tance and deteriorated when this moment had been exceeded.

For ,loads less than the c r i t i c a l load ~ e l e v a n t tot ransverse bending the dis t r ibut ion of load is explained bythe methods of Guyon and Massonnet i f modifications are madein the parameters of f lexura l and tors ional resistance foran isotropic slab a

60. Li t t l e , G. and Rowe, R, E.LOAD DISTRIBUTION IN MULTI-WEBBED BRIDGE STRUCTURESFROM TEST ON PLASTIC MODELS, Cement and ConcreteAssociation, Technical Report TRA/185, London, May1955A 'multi-webbed bridge structure is defined as one

which i s intermediate between the two extreme cases, i . e . ano-.torsion gri l lage and a f u l l ~ t o r s i o n slab, considered inthe load dis t r ibut ion analyses.

The theoret ical in terpola t ion formula which gives thedis t r ibut ion factors for this type of construct ion makesuse of a torsion parameter. Tests have been made on Perspexbridge models to determine the correct value of this parameterto be- consistent with the assumptions of the a n a l y s i s ~

The manner in which th e par amet er is determined for aT-beam and s la b b rid ge , and a box-section bridge is i l l u s t ra ted , and the theoret ical and experimental dis t r ibut ionfactors are compared for ,each type of bridge.

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Lount, A. MoDISTRIBUTION OF LOADS ON BRIDGE DECKS, Journal ofStructural Division, Proceedings of ASCE, Paper1303, July 1957This ,.pcwer "examines recent developments in computation

techniques as applied to the determination of load dis t r ibut ion between longitudinal members of bridges .

There are two basic approaches to the problem of c o m ~putation of load dis t r ibut ion in a bridge deck. The f i r s tof th ese p uts major.emphasis on the action of thedeck s lab ,whereas the second, on the ac tio n of the diaphragms.

The analyzed bridgedeck has structural s tee l girderswhich have l i t t l e tors ional r ig id i ty . The elas t ic analysisused assumed no-' torsional s t i f fness .

A ser ies of tes ts were conducted on a prestressed concrete g i rder bridge, to show the-effec t of tors ional s t i f f -ness on load dis t r ibut ion.

The Guyon approximate method and the elas t ic analysisboth neglect the ' e f fects of torsion. The Massonnet approximate method, whieh'is an .e laborat ion o f the Guyon method,considers torsiono Comparing the-estimated with the actual,it may be seen tha t the ef fec t of torsion is considerable 0I t may also be seen that it has the-effec t .o f reducing themaximum moments, both posit ive and negat ive, for which thestructure has to be designedo I f an estimate of tors ionalr ig id i ty made by comparing the Guyon and Massonnet resu l t s , and the resul t ing estimated r igidi ty is ,applied tothe elas t ic analys is p re sent ed , then it may be seen tha tthe calculated resul ts are remarkably:close to the ac tua lload distributiollo

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62. Malter, HenryNUMERICAL SOLUTIONS FOR INTERCONNECTED BRIDGE GIRDERS,Journal of Structura l Division, Pro,ceedings of ASCE,Vol. Paper No. 1815, October1958The numerical methods ,for the s olu tio n o f the problem

of th e in te rc onne cte d b ridge girder are considered for thepart icular case ;involving inf in i te tors ional r igidi ty of themain longitudinal members. Formulas are developed for bothdeflection and moment for a t w o ~ g i r d e r and four-gi rder ' s t ructu re , and resul ts from bothcases are compared with those o b ~tained by using rigorous formulas. Tables are included tocompare solutions for various values of r el at iv e s ti ff n es s .The possibi l i ty of replacing the ent i re c r o s s ~ f r a m i n g by asingle center diaphragm for analysis purposes is clearlyindicated.

63. Marsh, J . G., Hondros, G ., and Michael, K. C.STIFFNESS ANALYSIS OF INTER-CONNECTED T ~ B E A M BRIDGESYSTEMS BY DIGITAL COMPUTER, Australian Road ResearchBoard Proceedings, Vol. 2, Part 2, pp. 1370-99, 1964I t has been known tha t load dis t r ibut ion in T-beam

bridge systems occurs by f lexural action and i s lnfluencedby.direc t forces induced by'slab t ransfer . The purpose ofthis paper i s to investigate th ee xte nt o f th i s influenceeThe Guyon-Massonnet theory for T-beam systems was used tocompare resu l t s of t he ana ly sis ., The method of solutionpermits var ia t ion o f important parameters.

In ,the analysis , the structure is decomposed into a. ser ies of i nd iv idua l s lab and aeam elements, and the loadis expressed as a F o u r i e r S e r i e s ~ Using st i ffness coeff i cients , a program is prepared for , and processed by a BendixG-1S computer.

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64. Marten, G.MODELLVERSUCHEUBER DEN ElNFLUSS DER TORSlONSTElFIGKEITBEl EINER PLATTENBALKEN B R U C ~ E , Wilhelm Ernst u. Sohn,Verlag , .Ber l in, 1952 (In German)The a nalys is of resul ts of model tes ts to determine the

influence of torsional r igidity in a r ig id frame br idge isgiven. Tests performed on a three-span reinforced concreterigid frame bridge model were mentioned.

65 . Massonnet, C.COMPLEMENTS ALAMETHODE DE CALCUL DES FONTS A POUTRESMULTIPLES, Inst i tute Technique du Batiment e t de Travaux Public, Annales, Vol. 15, No. 169, pp. 1-36, J a n ~uary 1962 (In French)This i s an addi t ion to the method fo r ,calculation of

multi-beam bridges. The paper p r es en ts a.generalization ofthe method developed-by M. Y. Guyon, to thecase where thetors ional r ig id i ty of the elements of t he bridgecanno t beneglected. After.analysis of the torsion parameter and thebrac ing paramete r, factors o f tr an sv er se dis t r ibut ion of loadsare determined 0

Multiplying the mean bending moment by the dis t r ibut ionfactor , one can obtain the b e n d ~ n g moment existing in a.givenbeam. Calculations of the bending moments'in st iffeninggirders and to rs iona l moments in bridges are also shown ..Massonnet, CharlesCONTRIBUTION AU CALCUL DES FONTS AJ?QUTRES MULTIPLES,Annales des Travaux Publicsde Belgique, Vol, 103,3, pp. 377-422, June 1950, and pp. 7 ~ 9 - 9 6 , O c t o ~ber 1950 (In Erench)

Calculation of multiple beam bridges i s discussed further . The paper had a comment on ~ x i s t i n g methods of calcula t ions. Engesser 's approximate method and comparison withother 'methods, Leonhardt's approximate method, influence l ines ,

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theory of stresses and s t rains are the bas ic poin ts discussedin the paper.

67. Massonnet, CharlesMETHODE DE CALCUL DES FONTS A POUTRES MULTIPLES TENANTCOMPTE DE LEUR RESISTANCE A-LA T O R S I O ~ , InternationalAssociation for Bridge and Structural Engineering, Publ icat ions pp. 147-82, 1950 (In French)This paper is covered in the Journal of the peA Research

and Development Laboratories, Vol. 3, No.3 , pp. 30-70 , September 1961. I t is also discussed by Rowe in his book "Con-crete Bridge Design TT - Chapter 3. The author g e n e r a l i z ~ sGuyonts method, which is oase.d on the assumption o f a con."t inuous gri-d o'f longi tudina,l and t ransverse beams, to :Lnclude,t h e e f fec t of the torsional resistance of these s t ructuralparts . Numerical values are gi,ven for the t r a n sve r s ed i s t r i -bution coefficients of the loads for a l l bracing parameters,and for a l l values of the torsional s t i f fness of the beams.In addit ion, tables a re p re sent ed which make it possible tocalculate the character is t ic ,coeff ic ients of the fuending moments ,i n the t ransverse beamso

The use of the Fourier Series allows an accurate deter-,m in ation o f the influence of any load system. The method notonly furnishes more accurate resul ts ',than the c l a s s i ca l methodsfor bridges of typical construct ion, -but can also be adoptedfor b ridge s w ith ,continuous longitudinal beams prestressedtransversely, and fo r slab bridge s-in r ein fo rc ed o r p re st re ss ed

c o n c r e t e ~

68 . Mattock, Alan H. and Kaar, Paul H.PRECAST PRESTRESSED CONCRETE BRIDGES, 3. FURTHER TESTSOF CONTINUOUS GIRDERS, Portland Cement AssociationBul le t jn D43, September 1960An-extensive l a b o r a t o r y , i n v e s t i g ~ t i o n of precast-pre

stressed concrete bridges is reported in th is series of papers. -

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The type of bridges under s tudy involve s I -shaped girderswith ,cas t - in-place deck s lab . Here, an experimental pro-.gram, designed to provide further ' information regarding thefeas ib i l i ty of establishing continuity between precast girdin adjacent spans, i s reported. I t was concluded tha t ,by placing deformed bar reinforcement longitudinally. in thedeck slab over the in te r ior supports , it i s possible to produce,oontinuity, and adequate negative support moment res is t -

. ance for both s t a t i c and dynamic loads. A br i e f investigat ion of two simple s t ruc tura l deta i ls , designed to providecontinuity between precast girders-when r ev ers al o f momentoccurs a t support sect ions , i s also reported. I t was concluded that the deta i ls described can provide an adequateresistance to posi t ive moments of the magnitude l ikely tooccur a t support sect ions of multi-span continuous precastprestressed concrete b r i d g e s ~

69. Mattock, Alan H. and Kaar, Paul H.PRECAST-PRESTRESSED CONCRETE BRIDGES, 6. TEST OFHALF-SCALE BRIDGE CONTINUOUS OVER TWO SPANS, Portland'Cement Association Bulletin D51, September 1961This report presents an experimental investigation of,the behavior of a half-scale highway bridge continuous over

two spans when subjected to loads a t and above se rv ic e loadl e v ~ l . The behavior of the b rid ge under both service loadsand considerable over-loads.conformed closely to calculat ionsbased on the elas t ic theory. The l a te ra l distribution of c o n ~centrated Loads was found to be in, close agreement with thedis t r ibut ion predicted by the Guyon-Massonnet theory. Addit ional data was also obtained on the punching shear strengthof reinforced concrete deck slabsQ

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The Guyon-Massonnet Load Distr ibution Theory, and anoutline of load distr ibut ion calculations for t e s t bridges,are also given as Appendix I and I I , respectively.

70 . Morice, P. B. and Li t t l e , G.LOAD DISTRIBUTION IN PRESTRESSED CONCRETE BRIDGE S Y S ~TEMS, Structural Engineer, pp. 83-110, M a ~ h 1954Methods ,which t rea t the problem through an elas t ica l ly

equivalent uniform 'system are studied in g re ate r deta i l , andthe methods of prac t ica l calculation using distr ibut ion coeff icients are-explained. For the use of pract ical ,design

-'-purposes, the resu l t s of computat ional work of Guyon andMassonnet for non-torsion and torsion structures are givenin the form of graphs. A.method of calculat,ion and the ef-fects of torsion are discussed.

A.description of tests of a number of interconnectedprestressed beam systems is included, and the resul ts ofthese tes ts show g ood agreement with theoret ical results .Tt i s in teres t ing to note that the effects of distr ibat i6nare virtually. ' ,eliminated by a simple support, and do not appear in the unloaded span of a c o n t ~ n u o u s specimen. Examplesof the method of calculation are given, two being tak en fromthe e x p e r ~ m e n t a l specimens, and one of amore pract ical nature.

The main conclusions from the tes ts were tha t the simplysupported gri l lages behaved as non-torsion gr i l lages , and ,thatthe. deflections and the bending moments were forecast withqgreeable accuracy bythe method of distr ibut ion coefficientsin i t ia ted by M. Y q Guyon.

The continuous gri l lage on the other hand showed goodagveement with tors ion qalculations based upon the analysisof Massonnet.

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7'1. M orice, P. B. and Li t t l e , G.LOAD DISTRIBUTION IN PRESTRESSED CONCRETE BRIDGE SySTEMS, Summary, Structural Engineer, pp. 21-34, 1955This is ' the discussion of the previous paper ,wri t ten

by the authors. The ef fec t of Poisson's ra t io i s one of thesubjects discussed.

72. Morice, P. B.MINIMUM TRANSVERSE STRENGTH OF SLAB BRIDGES, Cementand Concrete Association, Technical Report TRA/205,London, September 1955I t is known tha t the normal method of elas t ic analysis

leads-to a design in which-the tpansverse f l exural a trengthi s considerably greater than that re qu ire d to give a factorof safety in the structure as a whole ,equal to that of lon-

.gi tudinal elements considered alone. In the design of slabbridges, advantage of this can be taken by permitting moderate tens i le s t resses when ca lcu la t ing the degree of t r a n s ~verse prestressing required, and in reinforced slab bridgesthe amount o f tr an sv er se reinforcement can be appreciablyreduced l'

73. Morice, P. B, and Lit t le , GoLOAD TESTS ON ASMALL PRESTRESSED:CONCRETEHIGHWAYBRIDGE, Cement and Concrete Association, TechnicalReport TRA/153, London, September 1954This paper describes load tes ts on a small prestreesed

concrete bridge of 15 skew and a q u a r t e r ~ ~ c a l e model of thebridge. The resul ts of the an alysis of the structure by themethod of distr ibut ion coeff ic ients are compared with theexperimental performance. Certain difficul t ies in applyingthe analysis i in t hi s p ar ti cu la r ,case a re d is cu ss ed .

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74. Morice, P. B., L i t t l e , G., and Rowe, R. E.DESIGN CURVES FOR THE EFFECTS ON CONCENTRATED LOADSON CONCRETE BRIDGE DECKS, Cement and Concrete Association, Publication Db.lla, p. 36, 1956These prepared charts give the load distr ibut ion coef

f icients for the analysis of bridges underconcentrated loads .75. ,.Mor ic e, P . BetTHE ANALYSIS OF RIGHT BRIDGE DECKS SUBJECTED TO ABNORMALLOADING, C e m ~ n t and Concrete Association, London, July1956

A'method of analyzing the effects of heavy indivisibleloads on highway bridges using di st ribu tion coe ff ic ien ts , is

e ~ p l a i n e d . In par t icular , t he determinat ion o f longi tudina land t r a n s v e ~ s e bending moments i s considered and it is shownhow the tors ional s t r e ~ g t h , o f the structure can be allowedfor ,in design. I t is shoWn how the neglect o f to rs io na lstrength-in design,will overestimate the:moments which-willactually occur ,in a bridge.

76 . Nasser, K. N.DESIGN PROCEDURE FOR LATERAL LOAD DISTRI'BUTION IN MULTI-BEAM BRIDGES, P r ~ s t r e s s e d Concrete I n s t i t u t ~ Journal,Vol. 10, No. pp. 5 ~ - 6 8 , August 1965A 'sfmple:procedure i s presented for ,determining l a tera l

load distr ibut ion in m u l t i ~ b e a m b ridge s using pre-fabricatedc o n c ~ e ~ e members. The method is based upon a theoret icalstudy-and analysis of orthotropic pla tes . Experimental workis carried out on', model and prototype members of hollow corebeams. Graphs are presented which-can be used to directlyevaluate the percentage of axle loads carried by a singlebeam due to center and edge loadings on the bridge.

77 . National Academy of Sciences-National Research C.ouncilTHE AASHO ROAD TEST, R E P O R T ' ~ - B R I D G E RESEARCH, HighwayReseavch Board, Special Report 6ID, Washington, D. C.,1962

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An ' investigation of t he ce ff ec ts o f spe ci fi ed axle loadsand g'ross vehicle loads applied at, known , frequencies on bridgesof known characteristics was the'primary object ive of theset es t s .

In part icular , the investigation.was divided into twophases: (1) determination of the b e h a v i o ~ of certain shortspan highway bridges under repeated overstress, and (2) determination of the dypamic effects of moving v e h ~ c l e s on shortspan highway bridges.

Inconnection with the f i r s t phase, the primary quest ions were on the fat igue l i fe of structures subjected torepeated high. s t ress , and the maIUler" in which fa i lu re occurs .

The second phase was,conoerned with the behavior of individual t e s t bridges under a , r ~ n g e of loads, and correlationof o b s ~ r v e d dynamic effects with those 'predicted theoretically.

The tes t bridges ,were selected.considering the ,require-ments of the f i r s t phase of the invest igat ion. Eighteensimple span 'slab and beam bridges were tes ted. Each bridgehad three beams and a reinforced concrete slab. All bridgespans were 50 feet in ' length, and'the beams'incLuded threetypes of' wide-flange, rolled s tee l sections: n o n ~ c o m p o s i t ewithout coverplates, non-composite with.coverplates, and com-posite withcoverpIates; p ~ e - t e n s i o n e d and post-tensionedprecast pres t ressed conarete I-sect ions; and reinforced con-.cvete T ~ b e a m s cast monolithically with thes lab.

The 'principal variables for stresses were character- i s t ics of thecross-section and design,vehicle, and axleloadings and configurations.

Stat ic , crawl , and dynamic tes ts were conduoted. Thes t a t i c tes ts were c o n d u c ~ e d only a t the beginning of the

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invest igat ion. Temperature measurements were also takenusing t h e r m o - c o u p l e s ~

The following major t e s t conditions were investigated:(a) variationsin vehicle character is t ics , and (b) change ofbridge-characterist ics w ith time, and specia l tes ts included:

the ,effec ts o f the springs o f veh ic le s, (b) i n i t i a l o s ci l la t ions of the bridge, Cc) simulation of continuous t ra f f ic ,Cd) la te ra l posit ion of the vehicle on the bridge, and (e ) sudden braking ,on the bridge.

78. Newmark, N a t h a t i ' M ~DESIGN OF I-BEAM BRIDGES, ASCE Proceedings,'pp. 305331, March 194-8

R e c o m m e n d ~ t i o n s are p resented for the design of theslab and the beams of I-beam highway b r ~ d g e s . The'behaviorof the s l ab-and-s t r inge rbr idge having beams in the directionof t ra ff ic is discussed. The slab:may be mechanically bondedto the beams-by 'shear, connectors. The main reinforcement inthe "slab:is in the direc t ion tr an sv er se to the beams. There-

. fore , the long i tud ina l reinforcement is 'secondary.reinforcement.

In the p a p e r ~ a load dis t r ibu t ion factor-k, . , is :given bythe formula ,b-k = S'

~ w h e r e b - spacing of the beams andas = 4.6 + 0.04 IH

In , the la t ter ,express ion, a i s the span length and H i s re lat ive s t i f fness , defined by

H = _ _ --......_(:llo,..E_I""""""')_b _ e _ a , . . . ; . - m ~ _ - - _a (EI) slab per unit width

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The usual values of s are given in Table 2, as 5.5 to5.7 for n o n ~ c o m p o s i t e sect ions and 5.2 to 503 for I compositesect ions .

79. Newmark, Nathan Mi.'. and Siess , Chester P.MOMENTS IN I-BEAM BRIDGES, Universi ty of I l l i no i s ,Urbana, Engineering Experiment Station Bullet in SeriesNOe 336, 194-2The studies reported in th is bul le t in were undertaken

in an attempt-to obtain a bette r'unders tand ing of the behaviorof the type of structure commonly called the I-beam bridge,con si st in g o f a concre te s lab :cont inuous over ' s tee l beams.

The numer ical va lues of moment coeff ic ients are gen eral ly applicable to structures with.concrete instead of s tee lbeams, as ,well as to structures with ' s tee l beams anchored toth e con cre te slab ,by means of shear connectors. The anal y t i ca l work-on I ~ b e a m b r i d g ~ s has been supplemented by t e s t sof models of a number of bridgesG Influence values are givenfor-moments in the slab and in the beamso The f lex ib i l i ty ofthe beams is taken.into account.

_Using the resul ts of the analyses, empi ri ca l pe la tionsare derived upon which the design of the slab and the beamscan be based. Formulas for'maximum'moments in the slab , in thedirec t ion t ransverse to the beams, both a t the-center of a.panel and over a.beam, for-maximum longitudinal-moments in thes lab , and fo r 'maximum moments in the beams, are given in Chapters III and IV.

80. Nicolsky, V. A.REMARQUES SUR LE CALCUL DES FONTS LARGES, AlUlales desPonts e t Chaussees , pp. 613-29, September-October 1952This i s a d is cu ss ion o f the paper writ ten by M. Guyon

in 1946. Nicolsky points out mainly tha t (a) discrepancies

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in calculations of diaphragm moment can be reduced, (b) therei s some error introduced in the moment distr ibut ion,coeffi -cients for principal beams, and (c) i t might be preferable tot rea t the problem using a s ~ m p l e series instead of the doubleseries used by Guyon.

81. Olivares, Ao E., Goa, Co, Meiser, Me, and Sanobrich, J .LOAD DISTRIBUTION IN BEAM-GRILL BRIDGE, Indian ConcreteJournal , Vol. 37, Noo 4, pp. 138-40, April 1963Tests on a 1/5 s ca le p re st re ss ed concrete model in con

nection with an elevated expressway in Caracas, Venezuela, arereported 0 The bridge consists o f p r e ~ f a b r i c a t e d ~ r e s t r e s s e dconcrete main beams and s t i f fener beams forming a beam. gri l l_Model analysis was undertaken to study the behavior of theg r i l l under.concentrated t ra f f ic , especially.with regard toload distr ibutioDo A.comparison o f t he or eti ca l analysis following Guyon-Massonnet method with ,experimental resul ts showedfa i r agreement.

82. Plet ta , D. H. and Frederick,MODEL ANALYSIS OF A-SKEWED RIGID FRAME BRIDGE AND SLAB,Journal of ACI, Vol. 26, pp. 217-230, November 1954This paper presents the f i rs t par t of a t e s t ser ies

which-would include an aluminum and a reinforced concretemodel of askewed slab rigid frame bridge.

As a . f i r s t par t of the invest igat ion, model tes ts onthe aluminum 'model of askewed slab rigid frame bridge are

r e p o r t e d ~ The tes ts on'model reinforced concrete beams todevelop the technique of making.small models of reinforcedconcre te a re also given $

For , the .comparison of t he behav io r of a-reinTorced concrete model and i t s prototype, tes ts on a 1/8 ;scale reinforcedc o n c ~ e t e skew slab'were-conducted and the vesults are given inthe l a s t part of the paper.

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83. Pool, Ro A r y a ~ Ad and Robinson, Ao RoANALYSIS OF M U L T I ~ B E A M BRIDGES WITH BEAM ELEMENTS OFSLAB AND BOX SECTION, University of I l l i no i s , Urbana,Engineering Experiment Station Bul le t in No. ~ 8 3 ,93 pp . , 1965The analysis of single-span, r ight , m u l t i ~ b e a m bridges

having beam.elements of solid or hollow sect ion is given. A-method i s presented, based on the asymptotic behavior ofFourier ,coef fi ci en t s fo r accelerat ing convergence of FourierS eries for jo in t forceso This method i s ,computationallyprac t i ca l and leads to e x p l i c ~ t de te rmina tion of most import an t character is t ics of jo in t forces 0 The resu l t s for jo in tforce dis t r ibut ions , and shears and moments in beams, arepresented in tables fo r ' se lected, prac t i ca l multi-beam bridgescomposed of four and eight beamso

84. Prentzas , Eo G.DYNAMIC BEHAVIOR OF TWO CONTINUOUS I-BEAM BRIDGES,Iowa Highway Research Board Bulle t in No. 1 4 ~ . 1958In t h i s repor:t , - f ie ld t es t s on two continuous I ~ b e a m

bridges were reportedQ Test resul ts were compared to thet heo r e t i c a l values and the following conclusions were given:(a) the actual l ive load re sis ta nc e cap acity o f the bridgeswas higher than the ass'umed value in des ign, (b) composite

I ~ b e a m bridges behaved c loser to the assumed design,valuesthan non--composite s t ructures , (c) the-curb and the ent i rewid'th of the slab have had contr ibut ions in the load carrying capaci ty , Cd) the t e s t s t ructures ,were s t i f f e r thanassumed in ,design ,since ac tua l deflections-were less thanthe computed ones, (e ) the impact factors obtained for twobridges proved t ha t t hi s quant it y was very:var iable , (f) theave rage impact factors f ~ r an ent i re bridge span,was in mostcases less than AASHO impact values, and (g), individual im pact factors exceeded AASHO values in ,many,cases .

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8S. Rakshit, Ko SoLOAD DISTRIBUTION IN BRIDGE DECKS, Indian ConcreteJournal, V o l ~ 38, No. 6"pp . 214-218, 237, June 1964In this paper, the author discusses P. B. Morice's

theory of load distr ibut ion in bridge de6ks and outliries asimplified method based on this theory. Design.charts ~ r ealso provided so t ha t d is tr ibu ti on coefficients can be obtained direct ly at var ious reference s tat ions , with the loadat different positions on thedeck. The method proposed i sapplied to a prestressed concrete b ~ i d g e problem 0

86. Reil ly , Robert J . and Looney, Charles T. GoDYNAMIC BEHAVIOR OF HIGHWAY BRIDGES - FINAL REPORT,University of Maryland, Civil Engineering Department,April 1966In th is repor t , the f ina l re su l t, s of craw l runs and

dynamic tes, ts on th ree highway bridges located in Marylandare given.

The f ie ld t e s t of the b rid ge 's , th e r e d u c t l , ~ ] n , & ~ , : ~ , thedata . from th es e te sts " ._and the analys is of, the resu l t s arethe t hr ee phases of the project .

One of the bridges had' three simply-supported spansand it was composed of aluminum t r iangular box sections anda l ightweight c o n c ~ e t e deck. The t e s t span had a ~ e n g t h of94-05 feet .

The other two bridges ,were a:welded s t ee l girdercom.. posi te deck s t ructure a p o s t ~ t e n s i o n e d prestressed conc re te s tr u ct ur e both simply-supported with a span length of100 feeto

The post- tensioned prest ressed concrete gi rder ' s t ruc-ture was composed of equally;spaced and la tera l ly p o s t ~ t e n ~sioned nine T ~ b e a m s . The s tee l composite b ri,dge had equally:spaced seven girders .

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Test speeds varying from.crawl to amaximum of 50 mphwere used in the t e s t . For each tru ck ru n, (a ) the m a x i m ~fo r "each def lect ion gage, (b) the ' maximum fo r , each straingage, (c) the stra ins a t the t ime of maximum def lect ion,(d) the projected maximurnfor,each def lect ion gage , (e ) themaximum semi-amplitudefo.r,each,deflectiongage, and (f) thel ong itud ina l pos it ion of the truck for ,each of the above condit ions were measured and recorded.

In the repor t , t e s t resul ts are used to bfutain effect ive bridge s t i f fnesses , free vibrat ions , s t ra in-def lect ionr el at io n sh ip , n e ut ra l axis loca t ion , l a t e r a l d ' is t r ibut ion ofl ive load, bending stresses , and impact factors .During the t e s t s , xo obtain i nduced impact to thei rr egu la r it ie s i n a.bridge surface, board ramps were placedon the path of the t ruck.

The information about the gages and the'computer program followed by ,conclusions and suggestions fo r ,future bridgetes ts i s the l a s t pa r t of the report ..

87. Reynold$, G. :C 0THE STRENGTH OF PRESTRESSED CONCRETE GRILLAGE BRIDGES,Cement and Concrete Association, Technical ReportTRA/268, London, June 1957The members of a , t ransversely loaded gri l lage are sub

jected to bending, tors ion, and shear . To p r o v i d e : d a t a ~ f o rthe analyses of the grillq,ges tes ted in this invest igat ion,twelve beams have been tes ted in . combined bending and torsion.

A method, based on plas t ic theory and using some simplifying assumptions, is described for t he det ermina ti on ofthe col lapse load of gri l lage bridges. I t is shown tha t itis possible to obtain an indication of the rotat ions whichmust occur a t p la st ic hinges-for fu l l ,moment redis t r ibut ion

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For dynamic t es t s , a truck was driven a t a speed of25 mph and to get induced impact , a 2-i-n 0 t h i c ~ plank wasl a te r placed across the bridge a t midspan. The truck loadwas 57 kips distr ibuted on th re e ax les a t 13 f t . and 22 f t .spacingse

90. Roll , Fo and Aneja, I .MODEL TESTS OF BOX-BEAM HIGHWAY BRIDGES WITH CANTILEVEREDDECK SLABS, ASeE Transportation Conference, Philadelphia,Pennsylvania, Conference Reprint No. 395, October 1966The fabr ica t ion, instrumentation, and test ing of two

plas t ic models of simply-supported highway b o x ~ b e a m bridgeswith symmetrically cantilevered top decks a re descr ibed .One bridge is s t ra ight artd the other is curved in plan. Testresul ts are not reported.

The cross-section may cons i s t of a single ce l l , multiFleadjacent c e ~ l s o r m 1 1 1 t d ! . p l e , ~ separate ce l l s joined a t the deck.These s t ructures a re f requen tly/ const ruc ted by ~ r e ~ c a s t i n gre la t ively shor t lengths of a concrete box sect ion , and then

p o s t ~ t e n s i o n i n g the segments together fa form requiredbridge structure 0 Because of the s t ruc tura l e ff ic ie ncy o fsuch a .cross-sect ion, and the eff ic ient methods of construct ion, such s t ruc tures are becoming i n c ~ e a s i n g l y important.

In spi te of i t s simplic i ty , the response of such s t r u c ~t u re s t o. concent ra ted loads or par t i a l lane loads on the topdeck is not 'known,'and no sat is factory analysis is available.The methods of analysis normally used 'for t h i n ~ w a l l e d boxsections 'such as those used in a i rc ra f t structures may notapp ly because of the re la t ively thick webs required for thepassage of the prestressing tendonso I t becomes more com-pl ica ted when the bridge', i s .curved in plan .

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As a means of observing the-e last ic response of suchbridges, and for experimental veri f ica t ion of proposed methodsof analys is , two mode ls were constructed and tes ted. Eachmodel was made of an acryl ic resin with , essent ia l ly s imi lardiJ11ensions and suppor t condi t ions . The d imens ions were s,elected to repvesent a scale f ac to r of approximately 1/30 ofthe dimensions of a typica l prototype s t ruc ture .

For the purpose of conve rt ing the measured' st ra ins tostresses unit loads and unit moments, a Fortran IV programfo r IBM 7040 has been writ ten ' ;and data ,processed.

91. Rose, E. A.DIE BERECHNUNG LANGSVERSCHIEBLICHER RACHMENBRUCKENUNTER BERUCKSICHTIGUNG DER S C H U B S T E I F H E ~ T DER FAHRBAHN-PLATTE, Bautechntk, Vol. 38, No.4 , pp. 136-8, April1961 (In German)The caloulation o f long itud ina ll y movable f r a m ~ bridges-,

taking into account the modul'us of shear of roadway s l ab , i spresented. I t is pointed 'out tha t th e impor tant effec t ofthe deck slab on load distr ibut ion has to be considered inthe design of prestressed frame system of bridges. Theoreti ca l and graphical analyses of load di 's t r ibut ion are alsogiven.

92. Rowe, R. E.A -LOAD DISTRIBUTI'ON THEORY FOR BRIDGE SLABS ALLOWINGFOR THE EFFECT OF POISSONTS RATIO, Magazine of ConcreteResearch, Vol. 7, No. 20, pp. 69-78, July 1955The use of the load dist r ibut ion t h e o r i ~ s presented by

Guyon and Massonnet has fac i l i ta ted the e st ima ti on o f the effects of heavy abnormal loads on bridge deck s t r ~ c t u r e s .Tests on laboratory- m o d e l s ~ as well as on actual bridges subjected to such loading, have establ ished the v ~ l i d i t y of the

t h e o r i e ~ , a t le as t as fa r as the determination of the defleot ions and longitudinal bending moments i s c o n c ~ r n e d . However,

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disorepancies between the actual and theoret ical t ransversebending moments have been noted, part icular ly , in the case ofan isotropic slab bridge s t ructure. I t was f e l t tha t theneglect of Poisson's ra t io in the load dis t r ibut ion theoriesled to the discrepancies, and tha t a consi de ra ti on o f thisfactor would lead to a more accurate evaluation of t ransversebending moments. For these reasons the analysis of bridgedecks presented by Guyon has been.extertded to allow forPoisson's r a t io .

The effect of the value ~ f Poisson's ra t io on the theor e t i ca l dis t r ibut ion factors for deflections and longi tudina l

b e n d i n g ~ m o m e n t s i s discussed. In the case of the transversebending moments, a ser ies of curves fo r ,the dis t r ibu t ion coef f ic ient , have been prepared from which more accurate mo--ment values can be computed. In these computations, Poisson'sra t io is taken as 0.15, which is the case for reinforced andprestressed concrete.

93 . Rowe, R. E.A NOTE ON THE TRANSVERSE MOMENTS IN A PRESTRESSED CONCRETE BRIDGE S L A B ~ Magazine of Concrete Research,Vol. 6, No. 18, pp. 149-50, December ,1954This ar t ic le deals wi th , the application of the theories

of MaSSolUlet and Guyon to a . ,flat slab bridge model. Part icu-lar 'mention i s made of the dis t r ibut ion and th e ab so lu te val--ues of the t ransverse moments in r ela tio n to the theore t ica lvalues. Only one slab had been ' tested a t the time of this

p a ~ e r , but fur ther tes ts on' slabs of di f fe ren t span/wirlthra t ios ,were reported to be in progress.

9 4- Rowe, R. E.CONCRETE BRIDGE DESIGN, John Wiley and Sons, New York,1962

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95. Rowe, R. E.LOAD DISTRIBUTION IN BRlDGE SLABS, Magq.zine of ConcreteReseavch, Vol. 9, No. 27, p. 151, November 1957Tests on three prestressed concrete slabs o f varying

span breadth ra t ios have given data concerning the load d i s ~t r ibut ion propert ies of such structural forms. The resul tsfor the dis t r ibut ion of deflections, longitudinal and transverse bending moments under one, two, or four equal loadsare given, and compared with resul ts , given by the t h e o r e t i c a ~analysis. The effect of considering Poisson's ratio in thetheoret ical analysis is discussed. The dis t r iput ion of trqnsverse bending moments, both in the transverse and longitudinaldirec t ions, i s considered in deta i l . The maximum value of thetransverse moment occurring under Ministry of Transportationabnormal load i s estimated, and the posi t ion of the wheelloads to give themaximum moment is considered. The variation in the t ransverse moment along the span due to such abnormal loading i s also discussed.

96. Rowe, Ret E.LOADING TESTS ON LANGSTONE BRIDGE, HAYLING ISLAND,HAMPSHIRE, Cement and Concrete A s s o c i a t i o n ~ TechnicalRepovt TRA/289, London, January 1958

. Loading tes ts on a prestressed concrete pseudo-slabbridge ( i .e . individual .prestressed concrete beams placedside by s ide, jointed and subsequently t ransversely stressed)using an abnormal loading-vehicle were carried out to d e t e r ~mine the d i st ri bu ti on charac te r is ti c s of the 'bridge.

The nesults were in good agreement 'with the theore t ica lassumptions except for the s o ~ c a l l e d "mean" deflections andmoments 0 Laboratory tes ts on beams s':Lmilar to those used inth e bridge 'were carried out to determine both Youngfs modulusand the loss of prestress .

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97 0 Rowe, RoE 0LOADING TESTS ON STo MARTINTS BRIDGE, STAMFORD, LINCOLN-SHIRE, Cement and Concrete Associat, ion, Technical ReportTRA/288, London, January 1958Tests on a short span composite-slab bridge are described

and the resul ts ,obtained presented. From these it is evidentthat the make-up concrete forming the road camber acted s t ructura l ly to a certain extent and that edge-st iffening effectswere introduced by the masonry parapet beam and the:concretef i l l under the sidewalkso

The overa l l behavior of th e b rid ge throughout the tes tswas consistent with the assumption that it was a beam and slabbridge in which cracks had formed between the precas t beams.

98 .. Rowe, RoE II.THE ANALYSIS AND TESTING OF A TYPE OF BRIDGE SUITABLEFOR MEDIUM RIGHT SPANS SUBJECTED TO ABNORMAL LOADING,Cement and Concrete Association, Technical Report

T R ~ / 2 g 2 , London, March 1958A type of bridge is analyzed that, is sui table for

medium r ight spans in the range from 20 to 60 f t . and possesses good d i st r ibu t ion cha rac t er i st ic s which enable it tosustainboth t he Min ist ry of Transport standard and abnormalloading . The bridge i s e s s en t i a l l y a b o x ~ b e a m constructionemployingprecast prestressed inverted T-beams, precas t diaphragms, and a top slab precas t o r ,c as t in 's i tuo

Two models of this type of bridge were constructed andtested to destruction in order to chgck both the val idi ty ofthe design and the methods of construct ion employedQ

99. Rowe, R. EoLOAD DISTRIBUTION THEORY FOR N O N ~ T O R S I O N BRIDGE GRIL-LAGES WITH VARIOUS SUPPORT CONDITIONS, Civil Engineering (London), Volo 53, pp .. 1271-72, November 1958;1405-7, December 1958; and V o l ~ 54, pp. 73-4,January 1959; pp. 7 3 ~ 4 , February 1959

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to any system4 To prove the v a l i d i t ~ of th e th eo ry , t e s t results on amodel of 304 meters long concrete highway bridgeoverseven spans with seven main girders and without tors ional,strength, are given. Calculations with specia l regard to tor -s iona l r es is tance of main and transverse beams and load dist r ibut ion are also shown.

102. Scordelis, A. C., Samarzich, W., and Pir tz , D.LOAD DISTRIBUTION ON PRESTRESSED CONCRETE SLAB BRIDGE,Prestressed Concrete Ins t i tu te Journal, Vol. 5, No.2,pp. 1 8 ~ 3 3 , June 1960Analytical and experimental stud;i:es for transverse dis-

t r ibut ion aT wheel loads on a simply-supported prestressedconcrete s lab bridge are pres 'entgd. The s lab .under considera-t ion was p o s t - t e n s i o n ~ d in two direc t ions. The t es t resu l t sproved that -existing empirical rules for t;he design of slabsof lo ng span s wi th large width had b'een, too conservative fromthe point of view of s t resses . I t was also noted that t ransverse prestressing had no ef fect on moments produced by wheelloads.

103. Siess , C. P. and Veletsos, A. SoDISTRIBUTION Or LOADS TO GIRDERS, IN SLAB AND GIRDERBRIDGES, Highway Research Board Bul le t in .14-B,. 1952

1040 Siess, C. P. and Viest , I . M.STUDIES OF SLAB AND BEAM HIGHWAY BRIDGES, TESTS OF CONTINUOUS RIGHT I-BEAM BRIDGES, Univer sity o f I l l i no i s ,Urbana, Engineering Experiment Station Bulle t in SeriesNo. 416, Vol. 51, No. 16, 30 pp. , October.1953Laboratory t es t s made on 1/4 scale models of bri9ges

con si sti ng o f s tee l be&rns supporting areinforced concreteslab are repor ted . The main object ive of the studies was todetermine in teract ion between beams and slabs in positive andnegative moment region, and also the effects of composite act ion on the 'behavior of continuous I-beam bridgeso

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105. Siess , Chester P.COMPOSITE CONSTRUCTION FOR I-BEAM BRIDGES, Journal ofStruc tural Divis ion , Proceedings of ASeE, pp. 331-353,March 1948The several problems associated w ith the design of com-posite I-beam highway bridges which a re d is cu ss ed in , this pa

per , may be divid'ed into t hree cat ego ri es : (1 ) comparativedesign studies of I-beam bridges to determine the savings inweight possible from the use of var ious types of compositebeams, (2) experimental and analyt ical studies of t he behav io rof composite beams and composite bridges, and (3) studies ofth e behav io r of shear connectors for use in composite I ~ b e a mbridges.

106 . Somerville, G. Roll, F., and Caldwell, J . A: D.TESTS ON AONE-TWELFTH SCALEMODEL OF THE MANCUNIANWAY, Cement and Concrete Association, Technical Repor t TRA/394, London, December 1965,A.description i s given of the building and tes t ing of

a one-twelfth' scale model, made of micvo-concrete, of a- typi ca l i n t e r io r span.of the proposed Mancunian Way. Data.havebeen obtained on the-diffusion of. prestress through the sect ion, th e behav io r of the structure under i t s design loadingand under the act ion of point loads on the cant i levers , andthe behavior of the structure a t ultimate load.

107. Stevens, L. K. and Gosbell, K. B.MODEL ANALYSIS OF COMPOSIT

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