Lehigh University P~oject 3~5

Li\TERAL IJISTRIBU]lION OF LOADIN PRESTRESSED CONCRETE BOX·... BEAf\1 BRIDGES

Reports Completed to Date

LATERAL DISTRIBUTION OF STATIC LOADS IN A PRE­STI~ESSED CONCRETE BOX·~BEAf.\1 BRIDGE .- DREJ-IE1<.SVILLEBl\IDGE Q DOLlglas, ~"! ~ J Q arld \lanHoT'n, D" A!I'F~ L~ Report 31501, August 1966

l~TERAL DIsrfRIBUTIO~l ()F DYNM'lIC LOADS IN A PRE--­S 'flzESSED CONCREI1E BO)(--BEAM BRIDGE - DREJ-IERSVI LLEBRIDGEo Guilford, A.. A9 and VanHorn, Do A.,~Fo L,) Re:po'rt 315,,2, Febr1 ua.ry 1967

STlllJCTlJRP.\L RESPOlJSE OF A qSQ SI<EVJ F'RESTRESSEDCOtTCl1.ETE BOX~GIRDER }Il Gl-{vvAY I3RID(~E SUBJECTED TO\lEl{I ClJLl\P, LOADI1~G ,"" IlROOI(VI l~LE BRIDGE ~

Sctlaffel'9 Tholna.s a'nd Va11}-{oI1n 9 D., AQ' F" I,,)Report 31SG5, October 1967

U1TET(AL DISTRIBUTION OF VEJ-IICUL1\R LOADS IN A PRE.,..STRESSED CONCRETE BOX-BEAM BRIDGE - BERWICK BRIDGE.Guilf'ord, A" A. arId Vanrlorn, D~ A .. , F .. L" Re)?ort31504, October 1967

T}fE EfFECT OF ~'IIDSP111\1 DIAPlfHllGt1S ON TJOAD DIS'rRIBlJ­TION IN A PRESTRESSED CONCRETE BOX-BEAM BRIDGE ­Pj-llLADELPHI.A BRIDGE., Lin, Chertg-shung a11dVanHor11) D~ A", F" IJ4 Report 315,,6, \Jutle 1968

I1ArrEILl\I~ DISTRIB1JTION OF VEJ-IICULi"\R LOADS IN A PRE~

STRESSED CONCRETE BOX~BEAM BRIDGE ~ WHITE HAVENBRIDGE. Guilford, A~ A" and VanHorn, D# A", F. LoReport 315.7, August 1968

srrRUCTlJRL~rJ BE1-{AVIOR CI-iARACTERISTICS OF PRESTI.zESSEDC01\JCRE11E BOX~BEAM DRIDGF~S~ VaXlJ-I0 T1n, D l' A .. ~ F .. L.'Report 31568, December 1969

THEORETICAL Al'lALYSIS OF LOAD DIS'IRIBlJTION IN PRE~-.

STRJ::SSED CfJNCR.ETE BOX-·Bf=I\~j BRIDGES <t Motarjf:~ITli, D <)

and VanHorn, D~ A~, F~ L~ Report 315~9, October 1969

COMMONWEALTH OF PENNSYLVANIA

Department of Highways

Bureau of Materials, Testing a~d Research

Leo D. Sandvig - Director~ivade L. Gramling - Research Engineer

Foster C. Sankey:- Research Coordinator

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Project No. 64-6: Lateral Distribution of Loadfor Br'idges Constructed withPrestressed Concrete Box Beams

STRUCTURAL BEHAVIOR CHARACTERISTICS'

of

PRESTRESSEp CONCRETE BOX-BEAM BRIDGES

by

. David A. VanHorn

This work was sponsored by the Pennsylvania Department ofHighways;U.S.Department of Transportation, Federal HighwayAdministration, Bureau of Public Roads; and the ReinforcedConcrete Research Council. The opinions, findings, and con­clusions expressed in this publication are those of theauthor, and not necessarily those of the. sp,onso!s.

LEHIGH UNIVERSITY

Office of Research

Bethlehem, Pennsylvania

December, 1969 .

Fritz Engineering Laboratory Report' No. 315.8

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~ABLE OF CONTENTS

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--1,i

;.ABSTRACT

1. INTRODUCTION

2. TEST STRUCTURES

2.1 General Description of Superstructure

2.2 Design for Vehicular Loads

3 • EXPERIMENTAL PROCEDURE

3.1 Conduct' of Te$ts

3.2 ,Instrumentation

3.3 Data Reduction

4. RESULTS

4.1 Load Distribution

4.2 Beam Deflections

4.3 Other Results

4.3.1 Effect of Midspan Diaphragms

4.3.2 Effect of Skew

4.3.3 Modulus of Elasticity

4.3.4 Effective Slab Widths

4.3.5' Behavior of Midspan Diaphragms

4.3.6 Effect of Deflection Joints

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. J± .. 3. 7 Use of Super-Position inDeveloping Test Results

5. DISCUSSION OF RESULTS

5.1 Load Distribution Factors

5.2 Beam Deflections

5.3 Other Results

5.3.1 Effect of Midspan Diaphragms

5 .3. 2 Modulus. of Elasticity

6. RECOMMENDATIO~S

6:1 Load Distribution

6.2 Deflections

6.3 Ef.fe,ctive Slab Width

7 • ACKNq,WLEDGMENTS

8. TABLES

9. FIGURES

10 • REFERENCES

16

18

18

20

21·

21

22

23

23

·26

27

28

3.0

34

91.

ABSTRACT

. This report summarizes the results from the field-

testing o-f five in-service spread box-beam bridges.. The sup.er--

structures are of the beam-slab type, and are composed of a

number of precast, prestressed concrete' box-beams, equally

spaced and spread apart, along with a cast-in-place composite

slab. The main emphasis is placed on the lateral distribution

of vehicular loa4s, and on beam deflections.

Experimentally-based load distribution factors are

compared with values used in the design, and with values derived

from a procedure recently recommended by Sanders and Elleby.

Based tin all facets of this investigation, it is recommended

that consideration be given to revision of the current AASHO and

PDH procedures for load distribution in spread box-beam bridges.

Although new design values are presented, which are based on the

field tests, it is emphasized that these experimentally-based.

values have been superseded by a more extensive analytically-

based procedure, as presented in a recent Lehigh University

report, No. 315 .. 9.

1.; INTRODUCTION

Since the early development of construction techniques

for fabrica-tion of prestressed concrete beams in the United States,

there have been a number of cross-sec"tional shapes which have been

utilized. One of -the shapes which has be~n used extens:Lvely, par-

(

ticularly in the Commonwealth of Pennsylvania, is the box shape.

In highway bridge construction, these box-shaped beams were first

. used in a superstructure design which consisted basically of beams

placed adjacent to one another, with longitudinal shear-keys to

assure lateral .interaction. The beams were then covered with ·an

asphalt roadway surface. Later, the adjacent configuration was

modified, by replacing the flexible sur"face material with a

cast-in-place reinforced concrete slab, constructed to act com­

positely·with the beams. More recently, the box beams we~e in­

corporated into a b~am-slab type superstructure design, with t~e

beams spread apart, as· in typical I-beam bridges.

To date, the spread box-beam bridges have been designed

for vehicular loads, in' accordance with standards which closely

parallel the procedure outlined in Section -1.3.1 of the AASHO

Specifications for-"Highway Bridges.1 However, in 1964,·a research

program was initiated at.Lehigh University (1) to develop experi-

"mental data which would yield the information on structural be­

havior needed to evaluate the design.procedure, and (2) to develop

a mathematical analysis which would.accurately represent the

structural response to vehicular loads.

rn the period 1964-8, five in-service bridges in Penn-

gylvania were field tested in the investigation. The first bridger

at Drehersville, served as a pilot structure-. In addition to the

development of basic information on structural behavior, several

experimental techniques were evaluated. The second, third, and

fourth structures, located at Brookville, Berwick, and White Haven,

had nearly identical span lengths, beam spacings, and' general. cross­

sectional dimensions. A comparison of the Brookville (450 skew)

and Berwic'k (900 skew) Bridges revealed the effects of skew, and a

comparison of the Berwick (beam size - 48u x 39 TT ) and the \qhite

Haven (beam.size - 36 Tf x 42 Tt) Bridges enable determination of the

effects of beam width on behavior characteristics. The fifth

bridge, near Philadelphia, ·was used to determine the effects of

midspan diaphragms. This bridge was constructed with diaphragms

in placeo After one series of tests had been completed, the

diaphragms were removed, and a second series was conducted. Six

2 a 6 6 7 11reports' , , " have been-developed to. describe the struc-

turaL behavior of the individual structures.

A theoretical analysis12

of the structural response

has been,co~pleted. The analysis, which is highly complex and

therefore not appropriate for direct use in design, has been

developed to utilize computer solu·tion techniques 0 The major

factors which influence the lateral distribution of loads have

been systematically varied in the program in developing usable

~2-

~expressions for distribution factors. These expressions represen~

a range of cross-sectional dimensions and beam sizes which are

typical of current design standards.

A separate investigation, devoted to a structural model ]

study of "the spread box-beam superst'ructures, was conduc·ted in the

period 1965-8. Model beam, slab, curb, and parapet sections were

prefabricated in Plexiglas units for the experimental investigation

of the effects of several parameters on the lateral distribution of

vehicular loads in the sp~ead box-beam bridges. Two repo'rt~,4 ~8

have been developed on this investigation.

; ,~

r-

This report has been developed (1) .to summarize the sig-

nificant findings which resulted from the field test phase of the

investigation, and (2) to recommend the consideration of revisions

in the currently used design procedures. A table of suggested

distribution factors is·preiented. To supplement" the'material and

recommendat,ions presented, a comparison of the experimentally-

based, proposed distribution factors is made with values developed

from expressions presented in the recently completed"~CHRP project10

report by Sanders and Elleby. At this point it·should be

I-I

emphasized that the suggested experimentally-based distribution

factors have now been superseded by the more extensive recommenda­

tions included in Report No. 315.9.12

The material in this report is arranged in the following

order. The first two sections are devoted to general descriptions

:(1) of the cros~-section, individual structural elements, alld

'-3-

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~onstruction of the spread box-beam type superstructure, and

(2) of the experimental procedures used in the field tests. The

next section is devoted to a presentation of the major results

derived from the five field tests, followed by a section centered

on discussion of the results. F,inally, recommendations for design

are presented, based on the results from the field tests.

-4-

2. TEST STRUCTURES

2.1 General Description of Superstructure

The test structures were of general beam-slab, simple

span construction, utili~ing prestressed concrete box-beams as

the main longitudinal beams .. The general cross-section, along

with the main dimensions of the five test structures, is shown

in Fig. 1. In this type of con$tructi6n~ after piers and abut~ents

have been completed, the beams are set in place as the first major

step in tIle construction of the superstructure. Forms are then

erected for the slab, and for the end and midspan diaphragms be­

tween the beams. The slab' and diaphragm concrete is then placed,

with a finished surface over the roadway portion of the bridge,

and a raked finish along the edge portion to provide a construction

joint between the slab and the curb sections. In addition to the

raked surface, the joint is strengthened by three No. 5 reinforcing

bars which extend vertically from the slab up into the curb section,

at a spacing not exceeding 15 inches. Two of these bars extend on

into the parapet section. The next step involves forming. and cast­

ing the curb and parapet sections. The curb section is cdhstructed

continuously over the length of the slab, while·l/2-inch, open, de­

flection joints are placed in the parapet section at intervals of

approximately.15 feet.

The box beams are pre-cast, prestressed concrete members~

A view of the cross-section is shown in Fig. 2. In Penn~ylvania,

two standard widths (wb), 36 and 48 ,inches, are used. The beams

-5-

are manufactured in a number of depths (hb

) , ranging from

~l inches to 48 inches, in 3-inch increments. For all members,

the wall thicknesses are 5 inches, the bottom flange thickness

I~ ,

is 5 inches, and' the top flange thic'kness is 3 inches. End

blocks are utilized in the anchorage zone regions as shown in

Fig. 2. In addition, an interior diaphragm, 10 inches in thick-

ness, is located at mid-length of the member.

There are three sets of reinforced Cbncrete diaphragms

cast-in-place between the beams in this type of superstructure.

All of the diaphragms are cast integrally with the slab.' The

first set is located at one end of the span, and consists of

is-inch thic'k sections which extend from the bo~ttom of' the sl'ab

to the; bottom surface of the beams. The second set is located a~t

the other end of the span, and consists of 12-inch thick sections

which extend downward 21 inches from the top of the slab. The

third set is located at midspan, and consists of lO-inch thick

sections which extend from the bottom of the slab to within

9 inches of the bottom surface of the beams.

The reinforced concrete slab is designed essentially as

a one-way slab, with main reinforcement in the· transverse di-

reci:ion. The transverse reinforcement consists .of upper and

lower layers of straight bars, with size and spacing bf bars

identical in both layers. In the longitudinal djrection, nomi-

nal reinforcement is placed in an, upper .layer which extends' a-

cross the entire width 'of the slab, and a lower layer which

-6-

extends across the clear .spans of the slab between beams.

The general design and construction details for bridges

of this type are given in Standards for Prestressed Concrete

Bridges .9

2.2 Design for Vehicular Loads

All of the test structures were designed essentially in

accordance with t~e AASHO ~tandard Specifications for Highway

Bridges, with some modifications a? set forth in the Standards for

Prestressed Concrete Bridgeso9 The design highway live loading

was HS20-44 in all cases, and the AAS~O impact formula was used.

The procedures for .distributing vehicular loads were generally in.

line with the provisions of Section 1.3.1 of the AASHO specifi­

cations. See Fig. 3. All interior beams were designed utilizing

a distribution factor of S/5.5. All fascia beams were designed

by assuming simple support action between the exterior and first

interior beam, ~s shown in Fig. 3, with the center of the exterior

wheel load lo'cated 2 feet from the face of the curb.

-7-

3. EXPERIMENTAL PROCEDURE

3.1 CGnd~ct of Tests

The prime, overall obje6tive of the investigation was

to evaluate the lateral distribution of vehicular loads to the

longitudinal beams. In line with that objective, the general test

procedure consisted of driving a test vehicle ,over the te~t

structure in a set of prescribed lanes, measuring the response of

the bridge through use of SR-4 electrical strain gages, and record~

.ing the various responses through continuously recording equip~

ment. The main test vehicle used throughout the, investigation was

a three-axle vehicle, closely simulating the HS20-44 design vehicle.

See Fig. 4. With the, continuously recording equipment, the basic

static effect was evaluated by moving the test vehicle across the

structure at crawl speed (approxima·tely 2 mph). In addition, on

all structures, passes of the test vehicle were conducted at higher

speeds. Although one report~ was devoted to a description of the

effects of vehicular speed on the respons~ of the Drehersville

Bridge, the effects of moving l'oads are not included in this summa-

ry report. Reports on.structural respon~e as related to the speeds

of moving test vehicles on the Philadelphia, Berwick, and. White

Haven Bridges are being developed by the U. S. ,Bureau of Public

Roads.

3.2 Instrumentation

On all structures, the primary instrumentation consisted

-8-

I

-I

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of strain gages mounted around the periphery of the longitudinal

beams at various cross~sections. In.additi~n, gages wer~ mounted

on the curb and parapet sections. Deflection gages were mounted

at a section near midspan. ,The remaining gages were used to measur~

slab strains ano diaphragm strains, and the pattern, for these latter

gages was varied from structure to structure. The longitudinal 10-

cations of the sections at which the primary beam, slab, curb~ and

parapet gages were located "are-shown in Fig. 5. For more detailed

information qil the particular gaging pattern for-each individual

structure, the reader is r"eferred to the individual reports. 2 ,5 ,6'-;7

3.3 Data Reduction

Detailed" information on data reduction is presented in

.

.'·.·..·'.·.·.1..·'~

'"'1

each of the individual reports. However~ it would be appropriate

to describe the general philosophy in the derivation of information

used to develop distribution factors. The gages were located on

the main beams in such a way that the longitudinal strain distri-

bution on each vertical face of the beam CQuld' be determined. ·With

these distributions, the internal bending. moment in the composite

section was determined, based on the assumption that axial force in

the memb~ers reslllting from the vehicular loads "t'Jas negligible.

Since the "moduli of elastici-ty for the beam, slab, curb, and para-

pet concretes were not known, only moment' coefficients were direct-

ly developed from the datao Then, the distribution of load to the

individual beams was determined by .dividing the moment coefficien~

for each beam by the sum of the moment coefficients for all"beams

-9-

at that cross-section~ These distribution coefficients formed the

basis for the influence lines presented in Figs. 6-29.

An average value for the modulus of elasticity of the

beam concrete in each bridge was derived by ,equating the total

vehicle moment produced across the gaged cross-section in the super-

structure, to the sum of the moment coefficients for the· individual

beams, multiplied by the modulus of elasticity of the beam concrete..

This computation was made for each crawl run of the test vehicle.

The average values for each bridge'",. developed from a number of· crawl

runs, are shown in the table· in Fig. S4 .....

The results from data obtained from other str~in and de-

flection gages were reported· individually in the separate reports.

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4. RESULTS

4.1 Load Distribution

Since the main objective of the investigation was to

evaluate the' distribution factors to the individual beams, and

to compare, the factors developed for the different test structures,

sets of influence lines were developed for the individual beams in '

each of the bridges. See Figs. 6-2g~ These influence lines reflect

the percentage of the total bending moment in each beam' at the gaged

cross-section, produced by the load vehicle at some specific lateral

and Longitudinal position on the test structure. The base line of

the diagram represents the lateral location of the center of" the

test vehicle on the bridge roadway, pictured below in each case."

The longitudinal location of the test vehicle is shown at the top

of the diagram .for each case.

To utilize these influence lines to develop experimental

distribution factors, two vehicles (for the Drehersville , Berwic'k,

and White Haven Bridges) and" three vehicles (for the Philadelphia

Brid&e) were placed on the roadway in accordance with the lane

provisions outlined in Section 1.2.6 of the AASHO specifications.

In this regard, the trucks were positioned in the defined lanes so

as to produce the maximum moment in the particular beam under con-

sideratioh.

In Figs. 30-36, a comparison is made between the distri-

bution factors used, .in the design of the diffe,rent beams in the

four bridges, and, the experimentally developed distribution factors

-·11-

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derived from th~ in~luence lines presented i~ Figs~ 6-29. 'For

instance, in Fig .. 30, the. experimentally developed distribution

factors from two di~ferent longitudinal locations of the test

vehicle are compared with the design values for each of the three

beams in the bridge. The experimental factors were developed from

the influence lines given in Figs. 6 and 7. Likew~se~ Fig .. 31

represents' a comparison of expe~imental and design. values of distri-

bution factors as derived from ·the influence lines given in Figs. 8

through 11. Similarly; the comparisons in figs. 32 through 34 are

based on influenoe lines presented in, Figs. 12 through 21, and the

. com~arisons giv~n in Figs. 35 and 36, a~e deri~~d from influence

lines p~~sented' in Fi~s. 22 through·29.: The development·.ofthe

experimental distribution factors given' in Figs. 30~36 is given in

Table 1.

To facilitate discussion later in. this report, a series

of figures. was prepared to illustrate the effects of slab thickness

(t) and the modular ratio between beam concre·te ma·terial and

cast-in-:-place concrete material (k), on. the moment of inertia (Ina)

and the section modulus (Zb) of the exterior and interior beams.

The idealized composite cross-sections are shown in Fig. 37. In

Fig. 38, the variations in I and Zb are shown for an interiorna

girder in the Drehersville Bridge. Figs. 39 and ~O represent the

I and Zb' , respectively, for the exterior girder of the Drehers­na

ville Bridge. Figs. 41-49 represent similar quantities in the

Philadelphia, Berwick, and White Haven Bridges~

--12-

4.2 Beam Deflections

To enable an evaluation of the vertical deflection

characteristics of the individual beams for the four bridges, four

series of influence lines are developed in Figs. 50-53~ In these

figures, the ordina.te repre~ents' the vertical deflection of a par-

ticular beam, while t~e base, line represents the lateral location

of the test vehicle on the ~oadway. The longitudina~ location of

the test vehicle is shown in a diagram at the' top of each figure.

In each of the' four cases, the'influence lines' represent the effect

of the load vehicle positioned longitudirtally to produce maximum

moment in the test structure. The idealized'deflection of ~n en­

tire bridge -cross-section' is 'shown in rig,.' 54"., In the ",table i"n.'

this figure, factors are listed which we~e used to compute an

idealized uniform deflection of all.beams "under the center axle

of the v~hicle, indicated"as 6 in this figure. A"comparison of

-these computed uniform v~lueswith actual beam d"eflectiollrS can be

m~de in Figs. 55-and 56. In these figures, beam deflectian profiles

are shown, as d~veloped from the influence lines for vertical de- .

flection presented in Figs,; 50-53. The idealized values presented

in Fig. 54 are found to be closely related to the aver~ge de-

flection of the beams as shown in Figs. 55-and 56.

4.3 Other Results

4.3.1" Effect of Midspan Diaphragms

Although a complete report' is devoted to the effect of

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midspan rliaphragms on lateral load distribution in one of the test

bridges, it would be appropriate to mention the significant find­

ings. First of all, it can be seen from Fig. 31 that there was

very little variation in ~aximGm moment produced in the individual

beams at the maximum moment section. The results shown were de­

veloped both with midspan diaphragms in place, and with midspan

diaphragms removed. Therefore, since load distribution factors

usea in design represent the combined effects of'~everal vehicles,

the midspan diaphragms have very little effect on the design

factors. However, it should be emphasiz€9 that even though there

was very little difference in the combined effects, there was a

definite difference in the response of the bridge to a single load

vehicle. For instance, for a test vehicle located directly over

th~ center beam, the center beam developed 32.5 percent of the

total moment,~ith diaphragms removed. On the other hand, under

the- same load condition, the center beam carried 27.5 percent of

the total momen4 with diaphragms in place. Another comparison of,

the effects of the midspan diaphragm can be made in Fig. 55 1 ' which

il1ust~ates the deflection profile at the maximum moment section

under a particular loading condition, both with diaphragms in place

and with diaphragms removed. For a more complete comparison, the

reader is referred to .the individual -report. 7

4.3.2 Effect,of:8kew

The fifth bridge 'tested in this investigation was a 45°

skew bridge having cross-sectional characteristics nearly identical

-14-

to those of the Berwick Bridge. A separate report11 was devoted

to describing the behavior of this particular bridge. Although

no further information on the results from the ,test of the skew

. bridge is presented in this report, it would be appropriate to .

mention the significant conclusions. It was found that beam moments

measured in the center region of the skew bridge were consistently

less than those measured at the maximum moment ,section in the

".::",.:.-.,•

Berwick Bridge. ~,Likewise, beam deflections m~asured along the

skew at midspan were "similarly less t~a~ values measured in the

Berwick Bridge. Further comparisons and additional information

are given in the individual report.

4.3.3 Modulus of Elasticity

As mentioned in Section 343, the effective modulus of

elasticity of the peam concrete was computed based on data col-

lect~d from ea6h crawl run of·the test'vehicle on each.of the test

bridges 4 These individually c~mputed values are reported in the

separate reports .. Average values are,given in Fig4 54.

4.3".4 Effective Slab Widths

In t~e procedure for computing internal beam moments,

determinations were made of effective 'slab widths. Each of the

indiviual reports contains information on transformed effective

slab widths at the gaged cro~s-sections.

4.3.5 Behavior of Midspan Diaphragms

"

Although no detailed analy~is was made of midspan diaphragm

--15-

Jl

behavior~ several strain gages were used to measure concrete

surface strains on the diaphragms in both the Berwick and White

Haven Bridges.

4.3.6 Effect of Deflection Joints

To evaluate the effect of the parapet deflection joints

on the load distribution at a particular cross-section, both the

Berwick and White Haven Bridges' were gaged at a cross-seqtion

which,p~ssed through one of the joints. Moment and distribution

coefficients were developed for these sections~ and compared with

,similar values obtained at the section of the maximum moment in

each case.' The comparisons can b,e, made in the influence lines

presented in Figs'., 12-17 and Figs.' 22-29, and 'in the experimentally

develop~d distribution factors presented in Figs. 32, 33, 35 and 36.

Ip'the latter comparison, it is apparent that'the parapet deflection

joints have little effect on the distribution factors.

4.3.7 Use of Super-Position in Developing Test Results

In the te~t-of the D~~hersville Bridge, two concepts were

used to check the accuracy of using the principle of super-position

in combining the results obtained from single vehicle runs to re­

flect the effects of more- than one vehicle on the structure. First

of all, al~ fivebeam$ were gaged at one cross-sectio~ of the super~

,_structure. A-single truck' was then'driven across the structure in

each of seven prescribed lanes. Computations of moment and distri­

,bution coefficients w~re made directly, baied on data from all gages.

-16-

Comparisons were then made utilizing data from only three of the

five beams, and using the principle of super~position~

In a second check, two load vehicles were used. Each

was driven across the test structure separately, and the computed

combined effects were compared with those developed in running the

two trucks across the span simultaneously. In general, the re­

sults from both methods indicated a very favorable comparison.

For· more detailed information, the reader i 9 referred to the indi­

vidual report. 2

!

-17-

5. DISCUSSION OF RESULTS

·5.1 Load Distribution Factors

Based on the compar'isons of experimentally developed

distribution factors with the calculated design values, as illus-

trated in Figs. 3~-36, a general behavior characteri~tic is very

apparent. Specifically, in all of the test structures, the ex-

. perimental value$ for all interior girders are significantly

less than design values. Corr~spondingly,. the experimental values

for all exterior 'girders are somewhat larger than design values.

This ~ehavior clearly ~mphasizes the fact that the curb and para­

,.pet sections definitely and significantly ~ontribute to the longi-

tudinal flexural stiffness of the bridge superstructure.

The strain measurements on the curb and parapet sections,

when aligned with those on the slab and extebl0r beam, consistently

indicate a full composite behavior between the exterior beam, slab,

and curb sections. In addition; the full composite. behavior ex-

tended to the top of the parapet section in three of the bridges.

In the fo~rth bridge,- although the straight line behavior did not

extend through the parapet, there was partial participation.' The

full participation of' the curb section was not unexpected, prima-

rily because the curb is continuous over the entire length of the

st~ucture, and because the construction joint was sufficient to

provide complete composite action at the curb-slab interface.

However, .the participation of the parapet sections was not as con-

sistent, mainly due to the incidence of the discontinuities provided

-18-

by the deflection joints.

With the additional stiffness resulting from th~ inter­

action of the curb and parapet sections wi th the' slab, the exterior

girder consistently carries more load than-is computed in the de­

sign method. With the increase in load carried by the exterior

girders, the interior girders then carry less of the total load,

and· the maximum magnitudes are considerably'less than the design

lo~d values. This curb-parapet effect was particularly sign~fi­

cant in the three 2~lane bridges (Drehersville, Berwic'k 1 and White

Haven). In the 3-1ane bridge (Philadelphia) the effect was ~light­

ly r.educed, which· is not' surprising ~ since the· sizes of the curb

and parapet -sections were ,the same in' all test structures.· There'­

fore, with ,the greater width of the Philadelphia Bridge, the

. contribution of- curb and parapet sections to -total superstructure

-stiffness was less than the contributions in the thr~e narrower

2-1ane bridges. It is obvious that the contribution would continue

to diminish with increasing roadway width.

At this point, it is appropriate to point out that al­

though the experimental resul'ts indicated maximum loads greater

than.design values for exte~ior beams, the exterior beams were

definitely not overstressed. Th~ participation of the ·curb and

parapet sections se~ved to increase the flexural stiffness to the

extent that the maximum flexural stresses produced in the exterior

girders were proportionately reduced, generally to a level approxi­

mately·equal to, or below, the-maximum values produced in the in­

teri6~ girders.

-19-

5,.-2 Beam Deflections

In comparing measured deflections with the computed

values, which were based.on the idealized assumption that the

deflection.is the same for all beams, se~eral point? should be

no·ted. First of all, the computed values given in Fig. 54 are(

based on values of E measured ~n the load distribution phase of

the study, and on a moment of inertia for the entire cross-section

of the supers~ructure. For thes~ computations, (1) the moment of

inertia was taken as the sum of the individual values for each of

the interior and exterior beams, (2) a modular ratio of 0.7 was

used for all bridges, and (3) the curb arid parapet sections were

asswned to be fully effective. For -the Drehersville and Whi'te

Haven Bridges, the computed values closely approximate the aver-

age deflection of the beams, as indicated in Figs. 55 and,56.,

For the Berwic'k Bridge, the computed value is slightly less than

the average deflection measured ,experimentally while in the Phila-

delphia Bridge, ,the computed value is slightly greater than the

measured average. It is certain that th~ parapet was not fully

effective QV e.r--. the.. entir~e."le.llg-th .of.-the s.tructures ... If thi,s

factor could be taken into acc.ount, al,l computed values would be

slightLy ~,g.reate.rthan the· values. indicated, in. Eig. 54. '. However, .

.if the compu,ted _values had been based on (1) values of E computed

as a funct~on of £1 in currently used expressions, and (2) valuesc

of' I based on the assumption that, the c.urb and .parapet sec-tions

,contribute .no~thing to the stiffness, the computed values would have

-20-

i···~·.·····'~

~

II

been significantly greater than the measured values. These com-

parisons further sub~tantiat~ the participation of the curb and

parapet in increasing the longitudinal stiffn~ss of the super-

structure, and in addition, confirm that the modulus of elasticity

of the beam concrete is definitely greater than values of E based

on the 28-day fT assumed in design.c

5.3· Other Results

5.3.1 Effect of Midspan Diaphragms

The intended function of the midspan diaphragms is to

distribute the vehicular loads more uniformly than 'if the dia-. .

phragms were not ~sed·. In the Philadelphia Bridge, this effect

was quantitatively evaluated. For a single vehicle on the

structure, there was a distinct difference in distribution of the

load to the individual beams. However, the maximum load conditions

for each of the girders ~lways i~olved the consideration of vehi-

cles in all load lanes. There~ore, the combined effects used to

develop the distribution factors resulted in nearly identical

values, either with.diaphragms in place or removed. This behavior

is n~t 'surprising, since the superst~ucture tends to exhibit· prima-

rily ·simple beam behavior with all lanes loaded. Therefore, it is

felt that th'e diaphragms really serve no purpose when the super-

structure is supjected to. design load conditions. On the other

hand, since· the midspan diaphragms do serve to more evenly ·distri-

bute the effects of a single vehicle, the effect of these diaphragms

-21-

~~d"~1itL~j~~~!'M~-:':'~{,·>s:...; ::G"""TI2~~:!~:~ji:..;.::i::5"~~~7£':'"..:.-::·~~~~~:~~V:1:;:;<".....:;:..·.:.::.':~:-~~~.:.t~- .....:.:.£;:.~/..-...:.:.... ......,~y.~.~~~.:.o.p;;...:_...,o:or.::r:::--=-:_. -: .. -:r......... . .....:.-=:•..,~..L.<.......- •..:...~ •• ..........~~~ _.~- _ •• - - _. _ ... - ....

;

would be far more significant in considering the effects produced

when a heavier-than-design vehicle is moved across the structure.

5.3.2 Modulus of Elasticity

It is felt that the E values, calculated as described

"earlier in Section 3.3, are definitely realistic, even though they

are greater than those normal~y used in design. This is not meant

to imply that empirical expressions for E, expressed as a function

of fT, do not yield reasonable values. Instead, it is felt thatc

the primary difference lies in the value of f~ uped in the calcu-

lation of E. That" is, the value" of- f"T after the superstructure isc

" in use is usually "significantly greater than the 28-day value used

in design. In fact, it is 'very common for beam concrete to reach

the specified 28-day value at, or "shortly after, release o~ the

pre-tensioning elements.

-22-

6. RECOMMENDATIONS, .

6.1 'Load Distribution

In initiating a discussion of recommendations relative

to vel1icular load distribution, it would be appropriate to note

that during the process of sponsors' review of this report, an

analytical 'procedure was completed and published as Report

1.2No. 315 .. 9 ,. I'n the development of the analysis, emphasis was

placed on correlation of results with the actual ,behavior of

field test structures. Based on all facets of the overall'

investigation, it is recommended that consideration' be given

to revision of the procedure for load distribution. Specific

recommendations are given in Report No. 315.9. Therefore, it

should be not~d that these recommendations s~persede the

recommended distribution factors listed in Table 2 on page 33

of this report, set forth for preliminary consideration prior

to the completion of Report N"o.· 315. g.

At this point it would be appro~riate to briefly

describe a recently distributed report by w. W.'S~ders, Jr. and

10H. A. Elleby. This is a final report entitled Distribution.of

Wheel Loads on Highway Bridges, resulting from a study ~ponsored

as a.part of the National Cooperative Highway Research,Program~

In this report, significant changes are suggested for determining

vehicular load "distribution factors to be utilized in design, to

-23-

First of all, it is suggested that for all beams, both interior

repla,ce the current Section 1.3.1 in the AASHO Specifica,tions.

and exteribr, the same distribution factor would be used for a

(3)

(2)

(1)s

== :B

L 2N C 2D ::: 5 + 10 + (3 7L) (1 3) £or C<3

D'= 5NL for C>3+ 10

Distribution Factor

specific bridge, namely:

where·D is expressed as:

In the above expressions,

S = average beam spacing, ft.

NL ·= total number of design traffic lanes

C = a.stiffness parameter which depends uponthe type of bridge, bridge and beam geometry,and material properties

For prelimina~y designs, C may be approximated as:

c K ':!- L (4)

. where

K = 1.8 for spread box-beams

W = overall ~.width D.f .br.idge' superstructure, ft.

,L ,=~span length, ft ..

-24-

Sanders and Elleby were developed from an analysis which does not

veloped from the proposed method, Table 3 has been prepared to

indicate the values for D as calculated from the proposed ~heory.

It ahould be noted (~ that the expressions' prop~~ed by

(5)

t b = thickness of bottom flange, in.

LAs an indication of the D factors which would be de-

L WC = 1 .. 2 L

where L

.Ib moment of inertia of the beam, .. 4= l.n.

b = external width of beam, in.

h =: external height of beam, in.

t = vertical wall thickness, in.w

- 1t = 2 (tt + t

b) , in ..

tt = thic'kness of top flange, in.

there ,is little variation in the values of D computed for the

include. the effects of curb and parapet sections, and (2) that

~ more exact expression for C is· given as

different bridges. It can also be seen that the D values are

slightly less than the values listed in Table 2. This would be

expected since the factors listed in Table 2 reflect behavior

resulting from complete interaction of the curb and partial

interaction of the parapet with the beam-slab system.~

.:;25-

,~--_.--... -.-.--..~----_:_---

Based on the consistently observed behavior of the field(

test structures, it is recommended that the construction joint

between the curb and the slab be revised to further insrire com-

posite interaction between the slab and exterior beam. Under the

present constructibn procedure, this interaction consistently

occurs. Even though it is also apparent that the parapet section

is at least partially effective, it 'is felt that it would be con-

servative and appropriate to ignore this participation in' design

calculations.

6.2 - Deflections

In the computation of deflections for design,purposes,

it .,is recommended tl1at consideration be given to the inclusion. of

the curb ,and parapet. sections as included in the computation of

idealized bridge deflections presented ~n Fig. 54. It is felt·

that the principle included in these computations will result in

a·more accur~te prediction of the deflection of the bridge in

service. If there is a possibility that curb and par~pet sections

would be removed at a later time to provide for the widening of

the structure or £or some other purpose, the d~flection of the

TTstripped downu superstructure can easily be calculated by

revising the I values computed for the exterior girders.. , na

In addition, it is also recommended that typical cylin-

der strength data be used to develop information on beam concrete

strengths to evaluate typicaL strengths during the usable life of

~26-

:hhe structure •. Use of the higher strengtns to. predict the

effective E values will also result in a·more accurate com-

putation of deflection.

6.3 -Effective Slab Width

Based on tIle mult,itude of computations of effective

slab widtl1 in ,the many ·determinations used to det.ermine distri-

bution factors, it is felt that the effective 'slab width may be

accurately assumed equal .to the center-to~center spacing of the

beams. For the typic~l dimensions found in the beam slab

structures of the spread box beam type, the effective slab·width,..' . . , 1

,c~ite~ia set forth in Section 1~7.99of the AASHO Spebifications

indicate that the center-to-center spacing would typically be

the governing factor in assuming an effective flange width for

design purposes.

,~27-

7. ACKNOWLEDGMENTS

This study was conducted in the Department of Civil

Engineering at Fritz, Engineeririg Laboratory, under the auspices

of the Lehigh University Institute of Research, as part of a re­

search investigation sponsored by the Pennsylvania Department of

Highways; the U. S. Department of Transpol'ltation, Federal IIighway

Administration, Bureau of Public Roads; and the Reinforced Concrete

Research Council.

The field test equipment was made available through

Mr. C. F. Scheffey, Chief, Structures and Applied Mechanics Di­

vision,. 9ffice 'of. Research and Development, Bureau of Public, Roads.

The instrumentation and operati"on, ,of the test equipment was managed

primarily by Mr. 'Robert F. Varney, assisted by Mr. Harry Laatz, both

from the BUI'eau of Public Roads.

The basic research planning and administrative coordi­

nation 'in this investigation were in cooperation with the following

individuals' representing the Pennsylvania Department of Highways:

Mr. 'K. H. Jensen, formerly Bridge Engineer, Mr. B. F. Kotali'k,

Bridge Engineer, and Mr. H. P. Koretzky, Engineer in Charge of Pre­

stressed Concrete Structures, all from the Bridge Engineering Di­

vision; and Mr. Leo D. Sandvig~ Director, Mr. Wade L. Gramling, Re­

search Engineer, and Mr. 'Foster C. San'key, Research Coordinator,

all, from the Bureau of Materials, Testing, and Research.

The following Lehigh Universi ty graduate stude.nts made

major contributions in the conduct of the field tests, reduction

-28--

and processing of data, and development of the individual" reports:

Albert A. Guilford, Walter J. Douglas~ Thomas Sbhaffer, and

Cheng-shung Lin.

-29-

I

· '8. TABLES

-30-

Table 1 Development of Experimental Distribution Factors

Values from Influence Lines Distribution

Load Lane Factors

Total Experi-Bridge l Beam Case Left Center Right ~L+C+R mental Design

Drehersville A D-l " 40.0 ...... ~...., ....... 12.4 52.4 1.05 0.81D-2 40.8 ... --- -- ... 11.4 52.2 1.04

B D-l 28.5 ............. ......., 14.0 '42.5 0.85 1.30D-2 28.6 .................. iIIIIIIII 13.7 42.3 0.85

C D-l 20.0 ................ -- 20.0 40.0 0.80 1.30D-2 20.5 ................... 20.5 41.0 0.82

PhiladelpI:-ia A P-l 46.0 17.1 6 ...2 69 0 3 1.39 1.16P-2 47.6 14.6 5.8 68.0 1.36P-3 43.0 16.4 6.4- 65.8 1.32

~ I ·P-4 44.6 14.2 5.7 64.5 1.29c,/'- , ,..,

I':f~ j~~ B P-l- 31.5' 23.4- 10.0 64. 9 1.30 1.73

P-2 34.1 24.0 7.9 66.0 1.32P-3 32.1 22.7 9.8 64.6 1.29p-y. 35.0 24.1 8.0 67.1 1.34

C P-l 17a2 27.5 17.2 61.9 1.24 1.73P-2 16.9 32.6 16.9 66 .. 4 1.33P-3 17.8 29.4- 17.8 65.0 1.30P-4 17.5 32~1 17.5 67.1 1.34

Berwic'k A B-1 43.8 ...... .",....".IIIIIIII! 1.4.3 58.1 1.16 1.05B-2 41.8 .15.8 57.6 1.15B-3 42.6 ~~~ ... 13.1 55.7 1.11B-4 43.9 - ...... ~ ... 11.6 55.5 1.11B-S 41.8 .................. 14.4 ·56.2 la12B-,6" 46.7 .................... ,... 14.0 60.7 1.21B-7 38.5 ................. ~ 15.1 53.6 1.07B-3 41.8 ....... ~.-: 13.1 54.9 1.10B-9 . 45.1 ...................... lO~4 55 0 5 1.11B-IO 4-0 .. 9 ....................... 13.0 53.9 1.08

B B-1 31.5 ...... ~1IIIIr,,;a ..... 20.1 51.6 1.03 1.60B-2 33.3 ............. --.~ 18.7 52.0 1.04B-3 35.2 --- ..... 20.5 55.7 1.11B-4 40.3 ...... ~.-.. ....... 19.6 59.9 1.20B-S 31.1 ~-- ......... 22.1 53.2 1.06B-6 32.7 ........................ 18.2 50.9 1.02B-7 3-1.7 ..... --... ......... 21.5 53.2 1.06B-8· 34.6 ........... ~ .... 21.0 55.6 1.11B-9 40.9 ~"""lIIIIIIIIJiIIooIiIIIII 19.8 60.7 1.21B-IO 33.6 ...-. ................ 21.4 55.0 1.10

-31-

Table 1 (continued)

Values from Influence Lines~ Distribution

Load Lane Factors

Total Experi-Bridge Beam Case Left Center Right EL+C+R mental Design

White Haven A W-l 48 .. 3 .............. iIIIIIIIIIIt 10.3 58.6 1.17 1.00W-2 46.8 ~ .................... 11.4 58.2 1.16W-3 48.0 .... __ 11III-. ...... 12.1 60.1 1.20W-4 4-5.3 ................ iIIIIIIIIIII 14.1 59.4 1.19w-s 49.3 ............. ...".,.. ....... 11.5 60.8 1.22W~6 49.8 .................. ~ 9.5 59.3 1.19W-7 47.6 ..... ~ ........ IIIIIIIIIII 10.2 57.8 1.16W-8 49.4- ...................... 9.5 58.9 1.18

B W-l 35.4 ... --~ ........... 20.0 55.4- 1.11 1.64W-2 31.0 .-._IIiIIIIIII- ..... 21.3 52.3 1.05W-3 36.8 .... ~ ........ 20.4 57.2 1.14-W-4 30.3 ...................... 22.0 52.3 1.05W-5 33.5 ...... :llMBiIIfIIIoIIlIIIIIIII 19.0 52 .. 5 1.05W-6 41.8 .............. .-.. 17.2 59.0 1.18W-7 36.3 ,.................... 20.1 56.4- 1.13W-8 40.4- ............... ..". 18.8 59.2 1.18

-;32-

'fable 2 Recommended Distributiol1. Factors

- .

Distribution Factor

4-beam 5 beam

Exterior Interior Exterior Il1.terior

2-1ane 8/6.5 8/6.5 8/6.0 8/7.5

3-1ane ............................ ..... ........................... 8/6.0 8/6.5

Table 3 Values of D (Sanders-Elleby)

BridgeN. W L D D

L ft'. f~t • (Eqs. 2,4) (Eqs. 2 ~S)

Drehersville 2 35.5 61.5 6.35 6.65

Philadelphia' 3 45.5 71.8 6.29 6.40

Berwicl< 2 33.5 65.2 6 .. 49 6.66

White Haven .2 33.5 64.7 6 .. 49 ' 6.50

-33-

'. g. "FIGURES

--34-

...:::::::::::Jii

······..····r:·········· s ········=r=··· s ~=........ s . . =1"":... s.·· ~ .

I­UJLnI

Roadway Beam Beam No. of BeamBridge Skew Width Size

SpacingBeams Span(W) (S)

Drehersville 90° 30 1-0" 41 x 3311 7 1 -211 5 61 1 -6 11

(S-425IA)

Berwick 90° 281 -0" 41 x39" 8'-93/s11 4 651-311

S-5357A)

White Haven 82° 28'-0:1 31x42u gl_O" 4 641

_ 8 11

(S-5767A)

Brookville 45° 28'-0" 41.x 36

11 S'-IO" 4 641-IO~n(S-4737A)

Philadelphia 87° 401-0" 4' x 4211 9'_6115 71'_911

(S-6624A)

Fig. 1 Cross-sectional Dimensions of Test Structures

~,,",,-~."- ......~.. ---_....., _._...,..--......,...,,-~-_.--.:-"'--j<O~~~'~~'~--r<.~J;~.y~.4~~~~~~~~~~~~~~~~~~"";~~':~~fftl*~1.~t~n}'ll!>~~l1~':J:"~~'~,~~If't~r.~!~~~:it:AA~»i"t~<';~';'·~!~!('i.:,,0't~~,',!i~yl:~I<~i..,..~"_f!fi

End Block21-0" Minimum

'-3" Chamfer

TYPICAL CROSS -SECTION

---j riO" Diaphragm

r-------.r-------.,I I I ' IL ~-__..J L ~__ -_-.J

LJ"'_IIi-' B_as_ic_c_r_o_ss_-_s_e_c_t_io_n ---.,__WEnd Block

21-0" Minimum

TYPICAL PLAN

Fig. 2 General Description of Prest.ressed Concrete Be~ms

-36-

~ s· ~._ S _1..5 _~ S _I.. Distribution Factor = ~

For Spread Box Beam Design, K Taken as 5.5

tNT.ERIOR BEAM

Assumed Hinge

R:: Load Transmitted to Exterior Beam

R

"EXTERIOR BEAM

Fig. 3 Distribution of Vehicular Loads Assumed "in Designof Spread Box-Beam Superstructures

-37-

t .8k

--~-

t32k

t32kAxle Loads:

r---------Il_...... - - - '-'-----..---w--.l~----.I/..-... 0'-)I... 30' (max.) 1__ 14' (min.>

~

H'g 20- 44 Design Load Vehicle

20.4- --1- 13.0· -I~

~i5.0[:7.5.1 j6:6'~

.~

t t32k 10k

o.~~-~........---~

---~

7.21 4.9[:-------~

tAxle Loads: 32 k

TEST VEHICLE

Fig. 4 Characteristics ot Design and Test Vehicles

-38-

SectionM

~II Deflection Joints (to top of curb)

3.55'

I

I<t.. Section

M

3.55'

Se,etlanL M

3.55' 3.00'

ft.'Section

M

3.55'

L/2 = 30.75'

DREHERSVI LLE

L/2 =35.88'

PHILADELPHIA

SectionN

9.76'L/2 = 32.62'

BERWICK

SectionN

L/2:: 32..381

WHITE HAVEN

-1

- Fig. 5 Locations of Instrumented Cross-sections.

-39-

A

c

'II!iI

'. B

CASE 0-150 r----1r----..,.---~- ---,.---.. 50

,.,..-·1--""""0_·_~~+ h ~

3 0 r----r-----------t~--+---_t__-__+----....__+__--_4___1 30

-:Ezol­e.>w 40 t--~r----t---+----,-----r-----.-----+----140en

ti......ZIJJ:Eo:aElJJ-I()

:I:IJJ>..J<tbl-

LLo

O---t-----+-----+-------I-----+------+---~---'O

:::0..· ···· .. ··::: ::0···············::

,..----II!L ..;II..----+II:.. J-.......-..............................

Span: 61 1- 6 11

Beam Spacing: . 7 1- 2!'

Roadway Width s 30'-0"

Fig. 6 Influence Lines for Bending Moments ~n BeamsDrehersville Bridge - Section M - Case D-l

-40-

50 CASE p-t 50~

S ~Ez A0

7PT~ M +uw 40 4·0(J)

~-I-Zw 30 30:E B0:Ew..J(,)

J: 20 20LtJ>..J C<Cf0-g 10 10IJ..0

~0

o ~--*+---","+-...--t---+-------t-----+----+--- 0

fA'! fli!!! if71i; !D!'~~~ft-----I:J~~~B----4:~:"'----'i!: , ;J---~:~~~:j

Span:Beam"Spacing:Roadway Width:

71 '-9"9'-611

40'-0"

Fig. 8 Influence Lines for Bending Moments in BeamsPhiladelphia Bridge (Midspan diaphragms 'in place)Section M ~ Case P-l

-42-

.111 ... l1li

.........IJII

:::;::..............::-:...:000.; ::

: ::, '.

::, .00' ••••• ;~;

--~--50CASE P-2

:00 :o~ C ~• 0· .· .. , ..

'0"".~ B Io ,. .. '4:. 111 ...

A

I0 I----+---+------~---+--~--+------~--_t__--t 10

50----y-----y--------,r----

-~

LLo

zoI-trl 40 I--------If---lr---+----f------r----r-----r-------t-----f40(f)

....«t­z~ 30 t------~-~r-----""'--------fl:-__zF_-__+_____.JiIl~_+_--_i_----t--__'_i30o:Ew...J~~IJJ>..J

~oI-

Span:Beam Spacing:Roadway Width;

71 1- 9"

9' - 6"40'-0"

Fig. 9 Influence Lines for Bending Moments in BeamsPhiladelphia Bridge (Midspan diaphragms removed)Section M Case P-2

-43-

---..------ 50CASE P-3West....-

c

50 r-----r-'---,...-.-----..---

~

zQI- Afd 40 t------f--r----+----...4--- - __----..----a.----"40CI)

~'

«l-t] 30:¥Eo~

W..J~ 20t-----+--~-~~-~..____-..J__-~--__.:.___---J20:t:W>-I

~o .1 0 t----t----t----+----+---~--.-{-~---+---.--.+ 10J-IJ.o

........Jt

Span: 71'- g"Beam Spacing: 91-6t~

. Roadway Width: . 40'-0"

Fig. 10 Influence Lines for B~nding Moments in BeamsPhiladelphia Bridge (Midspan diaphragms in place)Section M Case 'P-3

-44-

'0'"f . Ii .: ~i

------+---_---::fI ~-__+_--__l20

CASE P-4' 50West

rcQ:S ~;;;M

40

c

A

B

o-...----r-----f----+---+----+----~-----J----.J 0

:Ezoi=

.()w(I)

~I­Zw:io:Ew-JUJ:

·IJJ>.J

~o...l.L..o

Span:Beam Spacing.:Roadway Width:

711-9'19 1

- 6 11

40'-0"

Fig. 11 Influence Lines for Bending Moments in BeamsPhiladelphia Bridge (Midspan diaphragms removed)Section M Case P-4

-45-

...J,ZoI­ulJJC/)

,~

}­zw~o~

W....JU::cw>...J

~ol-

LLo

CASE 8'-150 50

A P9TS ~NOr~

L ~40 40

:30 ~B=---+-_~---+-~----=---=:-+__-+__----+_--t 30

20 I-----J----------+-----+-~-~Itilt;:__--__t_-__I 20

101-------J-----------4-----r------i-----y.---t 10

0------+-------+-----+-----+-----1---0

t-

t

I

I

S '65'-3"pan:S · 8'- 9 3.r.a"Beam pacing: Il

Roadway Width: 28'-0"

Fig. 12 Influence Lines for Bending Moments in BeamsBerwick Bridge Section L - Case B-1

-46-

tII'

I

1

1"

.

•.=.".•.••...

t

r:

~.'.~.'.. '~_.

651-3"8 1-9 3/8

11

2-8 1-0"

Span:Beam Spacing:Roadway Width:

o ----+-------+-----+-----+-----1-- 0

Fig. 13 Influence Lines for Bending Moments in BeamsBerwick Bridge Section L Case B-2

50-'z0.- A(..)w 40enI-<J:

I-Zw 30~0 B:Ew..JU- -20J:

.W>-I

f!0 10I-

L!-a~0

-47-

It

~~~~~- ~~w .~u~._, b ~m~1__~~_ t

CASE B-350 50

~ '0 -~Nz0 779T M J77TJ-- Auw 40 p·40(J)

~

I....z BlJJ 30 30~0:Ew-JU

20 20:cw

I>.-Ig

10 10

Il-

LL0

I~ L0

0 0

.~.

t~ )~

Span:. Beam Spacing.:

Roadway Width :

65'-3"a'-9 3/s 11

281-0"

Fig. 14 Influence Lines for Bending Moments in BeamsBerwick ~ridge - Sectiori M - Case B-3

-48-

-------50

65'-3 11

8'-9~a"'

28'-0"

Span:Beam Spacing:Roadway Width:

I0 J--------f----+------+-----+----~~ 10

30

50----...-------

Fig. 15 Influence Lines for Bending Moments in· BeamsBerwick Bridge - Section M - Case B-4

-4-9-

CASE 8-4

::E i ~North'6 a _-fl-

l- A ft ~'~ 40 ....--~-~........---~----r----+-------&40en

~.1-­zW:Eo~

W-I~J:W>-.oJ

~oI-IJ..o

;:;:;:;:::;:;;:::;:;:;:;:::;::::::::::::::::::;:;::::::::;:::;:;:;::::::;:::;:;:::;:;::::;:;:::::;:;::::::;:::;:;:;:::;::::;:::;:;:::;::::::::::::::::::;::::::::::::;:::::;::;:::::::;::::::::::::;:;:::;:::;:::;::::::;:;:;:;:::;::::::;:::;:;:::;:;::::::::::::::::;:;::::::;:::;:;:;:;::::::;:;:::;:;:;::::,

-50-

!f!

I!.iIf

!lt

II

65.'-3al -93/s

11

28 1-0"

Span:Beam Spacing:Roadway Width I

Influence Lines for Bendirig Mo~ents in BeamsBerwick Bridge - Section M - Case B-5

'Fig. 16

____..__-- --,-- ----:---.....--.....--~.<OC~

65'-3"'8'-93/s"28'-0"

-51-

Span:Beam Spacing:Roadway Width:

Influence_Lines for Bending Moments in BeamsBerwick Bridge Section M Case B-6

Fig. 17

50 Case 8-6 50.:! South Q& 0

1z ~

0 rJJT I 7b-I*- M0 40 40w(f) A

~t-Z

30 B 30w~0:Ew-I~ 20 20:cw>...J«t-

100 10t-1J...0

~0

0 0

~

j. i

1

ItIi1

ilIt{

\i

I1,t

tt\t

1

65'-3"a'-93/s"28'-0 11

CASE B-7---"--"---r-_ 50

Span:Beam Spacing: ,Roadway. Width:

A

B

10t--------t-------.----+--~-+----4----+----IIO

50-------

20 t------+-----+---~--l---~~__-__I_-----__J 20

30t------t---+-+-----+-~-___+_--__I_~___J30

zzo-"t-uW(J)

!:i.t-­ZW::a:o:Ew..JU:I:W:..>..J«5l-

LL..o

Fig. 18 Influence Lines for Bending Moments in BeamsBerwick Br~dge - Section N - Case B-7

-52-

50CASE 8-8

50z10 ~NOr~z

07fjT..... . N 7hu Awen 40 40

~t-Z Bw:E 30 300-:I:w--JU:t: 20 20IJJ>...J<tI-0t- 10 10LL0

tfl

0 0

18.:.:.:.~.:.:.:.:.:.:I·;~---to .....----t'ID...---.-.-..ID.:.....·.·...:.:...:.:.:::.:!~~~~ 41~ • :t I111 • • .. ·."'.. 41 .

rt

I[I,I

-53-

Influence Lines for Bending.Moments in Beams. Berwick Bridge - Section N - Case B-8

Fig .. 19

Span: .. Beam Spac ing :

Roadway Width:

65'-3"S'-93/s"28'-0" I

It!!f

t

It

fl\

\l(

CASE 8-95050

z '0 ~O~z A ;JJT0l- N'U

40 40w(J)

~, BI-Z

30lJJ 30~0:t:w..JU 20 20'J:W>..J«b 10 .101-"LL0

~0

0 0

~.

I

Span:Beam Spacing s

Roadway Width:

651-3"a' -93/s"28'-0"

Fig. ·20 Influence Lines for Bending Moments in BeamsBerwi~k Bridge Section N -. Case B-9

-54- ,

-55-

Influence Lines for Bending Moments in BeamsBerwick Bridge - Section N - Case B-10

f l~i?it!I11tttl~

tri.~

\1

i\i

iIf

t

Iit\~

t-

t~

It:t1:

I

It~

tI

tr

~

Ill\

i!~

1

\I

t

IfI

I\f

\f

1

II1

651-3"8'- 9~'a"28'-0"

Span:Beam Spacing:Roadway Width:

Fig. ·21 .

CASE VI-I50 50

:2: A

IJ & Northz

?1fTL( ~

0 M :&I-<..) 4-0 40w(J)

~I-- Bzw 30 30:!:0:iEw-J

i(.) 20 20:r: .Iw>-I

f«g 10 10I

LL0

* 0 0

. ft

Span:Beam Spacing I

Roadway Width

64'-8"g'-O"2S'-Ou

Fig~ 22 Influence Lines for Bending Moments in BeamsWhite Haven Bridge - Section M - Case W-l

-56-

-------.----50

B1--~t----~---+-----+------I30

50----------.-­A

IJ..o

lJJ....JU 201----+---~----::~------+-.:IlIir----~---I20:cw>..J

~

O'"----+----f------+----~--..-~--10 !t

Span'Beam Spacing:Roadway Width I

641-8"9 1

- 0"28'-0"

Fig. 24 Influence Lines for Bending Moments in BeamsWhite Haven Bridge Section M - Case W-3

-58-

i ,

50 CASE W-4 50

A ~uth~ d&- ~1 /J9;

40 40

:Ezot­ULlJ(f)

~1­ZJJJ 30 8 n--_..---."..r-~----{~---4------..--4------I30

~o~

W-J

. ~ 2OI-----+----l----~--"\:I:---------+---:"""---4-------.l20W>-J«b I Or-----+----f--------+---------+----~--+------f~ 10

IJ..o

o o

Span I 64' -allBeam Spacing: 9' - a"Roadway Width t 28'-0"

Fig. 25 Influence Lines for Bending Moments in BeamsWhite Haven Bridge - Section M - Case W-4

-59-

50

64'-8"9'-.0"28&-0"-

CASE W-5

I~ ~North_J ~--.-

Nh

-60-

Span:Beam Spacing:Roadway Width:

Influence Lines for Bending Moments in BeamsWhite Haven Bridge Section N Case W-S

A-r--------

O""----t-----+-----+-----+------+-----J;Q

, Or--~----t-----+-·-----l-~-----I-------I t0

3 0 r---=B~---+-~-~-f----...,...--------..:....-----+------I-----I30

50

Fig. 26

.:i.l.::r:l..·.·.·.·.·.~.·.·..·..·.·...J·l..~~I~r;1~·~I. ID·····..····lll~.L:J J~.. :;: ;~~~~

zoi=uwen

~J­Zw:Eo:E

z

W..Jo-J:LaJ>..J

~'0l-lL.o

B

A-"'"--------- CAS E V~ - 6--.- , -----,.--......-----..,50

~~N~

10 t-------4-------f----+-------i'1-----..+--------I 10

50

201-----+----+---~--~--.....-...:...---+----I20

30 t----+---------(J-------f-....Jt----f-------4----I30

zz0t-&3(J)

j~

~::....4.~

t-ZuJ .~0~

W-IUJ:W>-I

~gLI-0

<f!.

I··. F.:._.-."

.,".~!.. ...~

O'--+-------t------t----4------t-------'Q

Span:Beam SpacingRoadway Width:

641-8"gl_O"

28'-0"

Fig. 27 "Influence Lines for Bending Moments in BeamsWhite Haven Bridge - SectionN. - Case W-6"

-61-

~

f~(Ii!!

~f~It

fI~I

IIIt

IIII'

itI

!II\

I'It

ljI!

I I64'-8"9'- au28' -0"

Span:Beam Spacing:Roadway Width:

'CASE W-750

S~uth~ oj 50::?: A

I 7fnz rJ};0 Nt-u 40 40w(J)

1-,« B1-'Z

30 30w,::E0:!:w-I(J 20 20J:IJJ>..J

~10 100

l-LL0

~0

0 0

.~

i~r:1ii !!:O·············!!

ii~i!,~, ~l J::r--.-t111:.. 411 "'".........0lil:.:11 ..: ........11: ...:. ..............~...,.,. ......~~

. Fig. 28 Influence Lines for Bending Moments in BeamsWhite Haven Bridge - Section N - Case W-7

-62-

t1-

IIt!ri

S/5

S/6

S/8

8/9

SIlO

...:.=:::.....................................................................::::*.- ....................................m~........­...:::...:::..­.-..-..-.0·.:::

Beam C0"----

Beam A Beam B

Design1::::::;:;::4 Case 0-1

~ Case D-2

.~ 1.00I-o~lL.

Zot-::>CD

a::I-(f) 0.50o

DREHERSVILLE BRIDGE

Fig. 30 Experimentally Developed Distribution Factors andDesign Values: Drehersville Bridge Section M

-64- .

It,

II

S/5

Beam CBeam B

DesignI::::::::;:) Case pwl~ Case P-2~ Case P"3~ Case P-4

-65-

PHILADELPHIA BRIDGE

Beam· A

Experimentally Developed Distribution Factors andDesign Values: Philadelphia B~idge - Section M

Fig. 31

2,00

1.500::0.-0

li:z0 1.00t-::>co0::I-(f)

·00.50

Design~ C B I~ ase -1.·:::1 Case B-2

Beam A Beam B

S/5

S/6

5/7

SIB

S/9SIlO

BERWICK BRIDGE

Fig. 32 Experimentally Developed Distribution Factors andDesign Values: Berwick Bridge Section L

-66-

" .

2.00

0"----

Design(:;:::;:;:::! Case B-3

~ CaseB-4. [Z2J Case 8-5~ Case 8-6

Beam A Beam B

S/5

5/6

5/7

S/8

S/9S/IO

BERWICf< BRIDGE

Fig. 33 Experimentally Developed Distribution Factors andDesign Values: Berwick Bridge Section M

2.00

Designffi] Case B-7o Case 8-8f?ZJ Case B- 9~ Case 8-10 5/5

-68-

Experimentally Developed Distribution Factors and.Design Values: Berwick Bridge Section.N

5/6

S/8

S/9S/IO

5/7

BBeamA

BERWICK BRIDGE

Beam

Fig. 34

1.50

·0.50

0::oI­(.)

~zo 1.00t-::>co0::t-(f)

Q

-69-

Fig .. 35 Experimentally Developed Distribution Factors andDesign Values: White H~ven Bridge - Section M

5/5

S/6

5/7

S/8

S/9

Beam B

WHITE HAVEN BRIDGE

't Designf:::::::::~~ Case W-Io Case VtJ-2~ Case \//-3~ Case W-4

Beam A0------

1.00

1.50-

0.50

2.00

WHITE HAVEN BRIDGE

2.,00

o~-

Design

I~~:;:;:~ Case W-5o Case W-6I2ZJ Case W-7&S1 Case W-8

Beam· A Beam B

S/5

Fig. 36 Experimentally Developed Distribution Factors andDesign Values: White Haven Bridge Section N

-70-

.EXTERIOR GIRDER

ks

k~c

r ks --IJtNA NA

hb Yb

35~~~~~~,...,....,....~

tNA ---4-----J---+~-__+__-~"d_-_t__r--___.__- NA

INTERIOR GIRDER

Fig. 37 Idealized Composite Cross-sections

30 30

12 12

1.0~k

0.9

10 . 20 0.8 20 fO .0.7

INAI.O=1t

8 0.9 80.8Zb INA Zb 0.7

in3 x "103 in~x 104

6 6

10 Drehersvil fe Bridge - Interior Girder 10wb=48 hb=33 5=86

4 4

(See Fig. 3-' for diagram)

2 2

-72- .

!I

I.

6060

50 50

1.0= k

0.9

40 0.840

Case I 0.7

INA

in~ x 104.

30 I.O=k 300.90.80.7Casell

I.O=k20 0.9

200.80.7Casem

Drehersville Bridge- Exterior Girder

wb= 48 hb= 33 S =8410 Case I: hp=r6 hc=9 he = IO-t 10

I'wp= 15 we= 33 we= 17Case E: Same as I, except that hp=O, wp'= 0 ICase m: Same as JI, except that hc=Ot we =0

t(See Fig. 37 for diagram).t0

6.0 0I

6.5 7:0 7.5 8.0

t. in.

Fig. 39 Moment-of-Inertia Exterior GirderDrehersville Bridge

-73-

16 16

14 14- 1.0=((--- - 0.9

~ - 0.8Case I - 0.7

12 r-- 12

10 1.0=k 10- 0.9Z-b - 0.8-

Cesen 0.7

in~x 103'~

b·O=k8 - .9 80.8

Casem - 0.1

6 Drehersville Bridge - Exterior Gir-der 6

wb= 48 hb= 33 S =84Case I: hp = 16 he=9 he=IO-t

4 4wp= 15 we= 33 we= 17

Case ]I: Same as I, except that hp=O, wp= 0Case ]]I: Same as TI, except that he =0, we =0

2 2(See Fig.37 for diagram)

oa..-_~-,,"------""''''---'-_--.&_-_-.-L_-_-...L._-----'O

6.0 6.5 7.0 7.5 8.0

t J in.

Fig. 40 Section Modulus - Exterior GirderDrehersville Bridge

-74-

~

!

II!

IIi

·1

401.0=k 400.90.8

0.714 14

INA

12 30 1.0:: k 30 120.90.8

,Zb 0.7

10 10Zb INA

1n~ x 103 in~ X 104

8 20 20 8

6 Philadelphia' Bridge - Interior Girder 6

wb=48 hb=42 5=114

4 10 (See Fig. 37 for diagram) 10 4

2

I[,

I6.56.0Ol.-..--------L-----......I..----L-.---_---L --'---~·---'0 0

7.0 7.5 8.0

2

o

Fig. 41 Cross-sectional PropertiesPhiladelphia Bridge

Interior Girder

-75-

10

60

Case I

50

Casel[40

'INA

in.4 x10 4

Casem30

1.-0:= it

0.9

0.8

0.7

1.0= k0.90.80.7

1.0= k0.90.80.7

Philadelphia Bridge - Exterior Girder

20

10

Wb= 48Case I:

-Case JI:Case m:

hb=425=102hp =., 6 he=9 he =10 - t

Yip= 15 wc=33 we:: 21

Same as I, except that hp=O, wp=OSame as 1(, except that he=0, we =0

(See Fig. 37 for diagram)

O~---",-----_.a--_-_.L---_--"'------"'-----'

Fig. 42 Moment-of-Inertia - Exterior Girder·Philadelphia Bridge

-76-

6.0 6.5 7.0

t, in.

1.5 8.0

II

Ii

Ii

18 18

- 1.0 =It

I16 -----.- 0.9 16------- ----- 0.8,-~1""'"

Case I - 0.7I-

i-

14 14

1.0= k- 0.9~ 0.8

Case II:- ~ 0.712

1-

121.0:: k

---",0.9==--+ 0.8

Cas.em -- .0.1=--10 10

Zb

in~x 103

8 Philadelphia Bridge - Exterior Girder 8

wb= 48 hb=42 S =102Case I: h - 16 hc= 9 he = 10- t

6 p- 6 i

wp=15 wc=33 we= 21fi

Case Jr: Same as It except that hp=O, wp=O- f-I

4Case :m:: Same aslI,excepf that hc=O, wc=O 4 I

!(See Fig. 37 for diagram)f

I2 2

r!

O"-------------~------"""'-----~O6.0 6.5 7.0 7.5 8.0

t I in.

Fig. 43 Section Modulus Exterior GirderPhiladelphia Bridge

-77-

Interior Gird'er

t. in.

oL.-__---'- ....I....-__---I --L- ..L..-_--.J0 06.0 6.5 7.0 7.5 8.0

Cross-sectional PropertiesBerwick Bridge

o

Fig. 44

35 35

LO=k

0.9

0.8

30 0.7 30

INA

25 2512 12

I.O=k0.9

to 20 Zb0.8 20 100.7

Zb INA

in.S'x 103 in~)( 104

8 815

Berwick Bridge - Interior Girder

wb=48 hb=39 5=1053/8 6

10 (See Fig. 37 for diagram) 10

4 4

5 ~

2 2

20

10

I.O=k0.9 400.80.7

I.O=k0.9 30o.s" ,0.7

hb =39 S = 95 5tahp= 16 he:: 9 he = IO-t

wp= 15 wc=33 we= 18

Same as I. except that hp=0, wp=OSame asIT,except that hc=O, we=0

Berwick Bridge - Exterior Girder

Case II:Case ill:10

20

60 601.0= k

0.9

0.8

0.750' Case I 50

40

I t4A Casellin~x 104

30

Casem

(See Fig. 37 for diagram)

O~----'"'----------~----'----------06.0 6.5 7.0 7.5 8.0

t 1 in.

Fig. 45 Moment-of-InertiaBerwiok Bridge"

Exterior' 'Gird,er

-79-

16

14

_..__.l----~---I I. 0 =k_____.J.-----------~-1 0.9

-'--'---~. -:=.J----....----t--_=_ ~__....L__---------. 0.8

=~l__----t---. - 0.1Case I =---~.l--------r""'----------

16

14

12 1.0:: k12- 0.9- 0.8

Case J1 0.7~

1.0= k-- 0.910 -~ 0.8 10

Zb Casem ....-- 0,'"~

.:3 103In. x

8 8

Berwick Bridge - Exterior Girder

w,b:: 48 hb=39-- S = 95 0/86 Case I: hp =16 he= 9 he =10- t

6

~p= 15 we=33 we= 18

Case ]I: Same as I, except that hp·=O, 'wp=O44 Case .TIr: Same asJI,excepf that hc==Ot wc=O

(See Fig. 37 for diagram)

2 2

o'---__--L--.__--..L- L--.-__~__..___ 06.0 6.5 7.0 7.5 8.0

t, in.

Fig. 46 Section Modulus - Exterior GirderBerwick Bridge

-80-

1225

35LO=k

0.9

0.8

0.7

30

25

30

35

12

10 20 I.O=k 20 100.90.8

Zb 1NA Zb 0.7

in.3 X 103 in.4 x104

8 815 15

6 White -Haven Bridge - Interior Girder 6

wb=:36 hb=42 S=I08i10 10

4(See Fig. 37 for diagram) 4

5 52 2

o O~-------------"--_-.l--_--""'--_--.JO 06.0 6.5 7.0 7.5'

t J in.

Fig-. 47 Cross-sectional Properties ~ Interior GirderWhite -Haven Bridge

-81-

LO=k0.9

400.80.7

1.0 =k0.90.8 300.7

60 . J.O=ft 600.9

0.8

Case I 0.7

50 50

40

INA CaseD·

i~4x 104

30

Casem

White Haven Bridge -Exterior Girder20-

10

Wb= 36Case I:

Case II:Case lJl::

hb=42 S =93

hp =J 6 he= 9 he =10 - t

wp= 15 we= 33 we =21

Same as I. except that hp=O, wp=OSame as II', except that he:: 0, we =0

20

10

(See Fig.37 for. diagrorrl)

O------"'------'--------lI.---~----4-----JO.6.0 6.5 7.0 1.5 8.0 -

t tin.

Fig. 48 Moment-of-Inertia Exterior GirderWhite Haven Bridge .

-82-

1.6 16

[f

It1

I

14

Case I

I -----+---------:=t:===-=t f. 0:: k

=::::::::t====::::j===:::t:====-=j 0.9

E====-:t~=====F===::t====-~ 0.8E....---====:t===i---r----l 0.7

14

12 121.0=«

- 0.9:::..-...-

- 0.8

n: ~ 0.7~

~

10 I.O=k .10:=: 0.9

Zb - 0.8

in~x 103 m ......---- ~~ 0.7.~

8 8

White Haven Bridge - Exterior Girder

6 6wb= 36 hb= 42 S =93

Case I: hp = 16 he=9 he. =10-t

4wp=.15 . we: 33 Ytle =21 4

Case II: Some as I, except that hp=0, wp=0Case m: Same as II, except that he =0, we =0

2 (See Fig. 37 . for diagram) 2

8.07.57.06.5. 0 '--- --" -'- ---&. ---1--_---' 0 .

6.0

t, in.

Fig _. 49 Section Modulus - Exterior GirderWhite Haven Bridge

-83-

:-:,

:,~

0.10 0.10en~ ~w

:r:pP; 7f7r()

z M...~ 0.08 0.08z A0

8I-uWU) 0.06 0.06LL..0

Z C0,

t- 0.04 0.04.~-.JLL"W0

-I 0.02 0.02«<...>l-~W>

0.00 0.00

~

Span:Beam Spacing':

Roadway Width:

61' - 6"71 -2"301-0"

Fig. 50 Influence Lines for Vertical Deflections of BeamsDrehersville Briqge - Section"M

-84-

II '

I

.;....)fIfif

71 1 -9 11

91

- 611

-40 1"0"

Span:

Beam Spacing:Roadway Width:

c

-0- With Diaphragms

- -lz-- Without Diaphragms

0.12 0.12

S. ~A;#; /737-M

0.10 0.10

B

0.08 0.08

O.021-------'------'----------'----+-------+---3Il~.,.-+---+-----iO.02

. O.OO'----------.-+--:.---<---f------il-----+---'"O~OO

Fig. 51 Influence Lines for Vertical Deflections of BeamsPhiladelphiaBridge - Section M

-85-

if:O··········.. ···t fl:O·········.. ·..}

t----·-~1 ; Jt------ItI 11~......................... .;......•..: ;.:..;..

Span: ' 65'-3"Beam Spacing:. 8 8

_ 9 3/e"Roadway Width: 28'- OU '

Fig. 52 Influence Lines for Vertical Deflections of BeamsBerwick Bridge - Section L

-86-

lI

O.021-----f-----.....-----+-----f--~--t------tO.02

0.10 0.10A

~) ~?hB

0,08 0.08

~

t.-

0',06 0.06

ft

:a:zot­(JW(f)

lL.'oZo.....~ O.04J----4---+-----+--~---+-----+----tO.04

-IlJ...Wo-I«()

t-o::W>

0.00""'"""'---+------+-----+-----+----+'---'0.00

,Span:

Beam S,pacing :Roadway Width

64'. aU9' .. 0"28'-0"

!t

I

\II

Fig. 53 Influence Lines for Vertical DefLections of BeamsWhite Haven Bridge - Section M

-87-

{

I\tI

}

20.4'

Deflected Shape

L

13.0'

i I 8.~3.55'

PL38=C--

EI

c P L E* I** IiBridge kips ft. ksi · 4 106 in.In. x

Drehersville 0.594 4 61.5 6800 1.33 0.106

Philadelphia 0.627 6 71.8 5400 2.19 0.203

Berwick 0.615 4 65.2 7300 1.58 0.102 .

White Haven 0.614 4 64.7 6000 1.60 0.120

*Measured in Flexural Investigation

**Assumed as ·Sum of Values for Individual CompositeBeams t = 7.5 i,n. , k =0.7 I Curb and Parapet Fully Effectiv~

See Figures 37 to 49

Fig .. 54 Idealized Bridge Deflections - Test Vehicle atSection of Maximum Moment

-88-

(-(

~'

',>,c'

i;'Af:'::':i,,<,":~

,{ .-t'{

/:\ ~'~:, t;', ;'~L"',~,

:'.,

'}'

·C.,

',,"'"

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PHILADELPHIA

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--t:r--Without Diaphragms

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0.15

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0.05

0.10

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Fig. 5S Beam Deflection Profiles (All lanes loaded)Drehersville and Philadelphia Bridges

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7' 7' 7' 7'

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BERWICK

WHITE HAVEN

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-90-

Fig. 56 Beam Deflection Profiles (All lanes loaded)Berwick and White Haven Bridges

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10. REFERENCES

1. American Association of State Highway OfficialsSTANDARD SPECIFICATIONS FOR HIGHWAY BRIDGES,Ninth Edition, AASHO, Washington, D. C., 1965

2. Douglas, W. J. and VanHorn, D. A.LATERAL DISTRIBUTION OF STATIC LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE, DREHERSVILLE BRIDGE, Lehigh·'University, Fritz Engineering Laboratory ReportNo. 315.1, August 1966

3. Guilford,' A. A. and VanHorn, D. A.LATERAL DISTRIBUTION OF DYNAMIC LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE, DREHERSVILLE BRIDGE, LehighUniversity, Fritz Engineering Laboratory ReportNo. 315.2, February 1967 .

4. Fang, Shu-jin, Macias-Rendon, M. A. and VanHorn, D. A. I

ESTIMATION OF BENDING MOMENTS IN BOX-BEAM BRIDGESUSING CROSS-SECTIONAL DEFLECTIONS, LeJ1igh Universi ty,Fritz Engineering Labor~tory Repo~t No. 322.2, June 1968

S. Guilford, A. A. and Variliorn, D. A.LATERAL DISTRIBUTION OF VEHICULAR LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE, BERWICK BRIDGE, Lehigh Uni­versity, Fritz Engineering Laboratory Report No. 315.4,-October 1967

6. Guilford, A. A. and VanHorn, D. A..IATERAL DISTRIBUTION OF VEHICULAR LOADS IN A' PRESTRESSEDCONCRETE BOX-BEAM BRIDGE, WHITE HAVEN BRIDGE, LehighUniversity, Fritz Engineering Laboratory Report No. 315.7,August 1968

7. Lin, Cheng-shung and VanHorn, D. A.THE EFFECT OF MIDSPAN DIAPHRAGMS ON LOAD DISTRIBUTIONIN A PRESTRESSED CONCRETE BOX-BEAM BRIDGE, PHILADELPHIABRIDGE, Lehigh University, Fritz Engineering LaboratoryReport No. 315.6, June 1968

8. Macias-Rendon, Miguel A. and VanHorn, D. A.A STRUCTURAL MODEL STUDY OF LOAD DISTRIBUTION INBOX-BEAM BRIDGES, Lehigh University, Fritz EngineeringLaboratory Report No. 322.1, May 1968

9. Penpsylvania Department of Highways - Bridge DivisionSTA~mARDS FOR PRESTRESSED CONCRETE BRIDGES, ST~200 ­ST-208, Harrisburg, Pennsylvania, August 17, 1964

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10. Sanders, W. W. and Elleby, H. A.DISTRIBUTION OF WHEEL LOADS ON HIGHWAY BRIDGES,Engineering Research Institute Report No. 361,Iowa ,State U~iversity, Ames, Iowa, December 1968

11. Schaffer, T. and VanHorn, D. A.STRUCTURAL RESPONSE OF A 45° SIffiW PRESTRESSEDCONCRETE BOX-GIRDER HIGHWAY BRIDGE SUBJECTED TOVEHICULAR LOADING - BROOKVILLE BRIDGE, LehighUniversity, Fritz Engineering Laboratory Report'No. 315.5, October 1967

12. Motarjemi, D. and VanHorn, D. A.THEORETICAL ANALYSIS OF LOAD DISTRIBUTION INPRESTRESSED CONCRETE BOX-BEAM BRIDGES, LehighUniversity Fritz Engineering Laboratory ReportNo. 315.9, October 1969

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