By

Thomas Schaffer

David A. Van Horn

Prestressed Concrete Box-Beam Bridges

Progress Report No. 3

Fritz Engineering Laboratory Report No. 315.5

STRU T l N45° SKEW ES

BO -GIRDER ISUBJECTED T HI Ul liNG

BR KillE B 10 E

STRUCTURAL RESPONSE OF A

45° SKEW PRESTRESSED CONCRETE

BOX-GIRDER HIGHWAY BRIDGE

SUBJECTED TO VEHICULAR LOADING

BROOKVILLE BRIDGE

by

Thomas Schaffer

David A. VanHorn

This work was conducted as part of the project Lateral Dis­tribution of Loads in Bridges Constructed With PrestressedConcrete BOX-Beams, sponsored by the Pennsylvania Departmentof Highways, the U. S. Bureau of Public Roads, and the Rein­forced Concrete Research Council. The opinions, .findings, andconclusions express'ed in this report are those of the authors,and not necessarily, those of the sponsors.

Fritz -Engineer'ing Labor~tory

Department of Civil Engineering

Lehigh University

Bethlehem, Pennsylvania,

October 1967

Fritz Engineering Laboratory Report No. 315.5

PREFACE

During the summers of 1964, 1965, and 1966, a series of

field tests were conducted on five prestressed concrete box-beam

highway bridg~s located in the Commonwealth of Pennsylvania.

Four of the bridges were right bridges while one, located at

Brookville, was constructed on a 45° skew. In the field tests,

each bridge was subjected to vehicular loading consisting of a

3-axle truck which was a close simulation of the AASHO HS20

design vehicle.

This report, ba~ed on the test of the Brookville Bridge,

contains a (1) detailed description of the field test procedure

and equipment, (2) a complete outline and flow chart of the com­

puter ~rogram used in the processing and analysis of the data,

and (3) a summary of the measured structural response of the

bridge, including a comparison with a right bridge having nearly

identical overall dimensions and member sizes.

Initially, separate reports are being prepared on the

behavior of each of the test structures. The primary intent of

these reports is to present a detailed description of the be­

havior of-each of the bridges. After all of the separate-reports

have been completed, a summary report will be prepared.

ii

1.

2.

3.

TABLE OF CONTENTS

INTRODUCTION

1.1 Background

1.2 Object and Scope

1.3 Previous Research

TESTING

2.1 Test Bridge and Site

2.2 Gage Sections and Locations

2.3 Instrumentation

2.4 Test Vehicle

2.5 Test Runs

2.6 Loading Lanes

2.7 Longitudinal Position and Timing

DATA REDUCTION AND EVALUATION

1

1

3

4

6

6

7

8

9

10

10

11

12

3.1 Oscillograph Trace Reading 12

3.2 Evaluation of Oscillograph Data 13

3.2.l Strain Calculation 13

3.2.2 Strain Tabulation and. Plotting 15

3.2.3 Moment Calculations 15

4. PRESENTATION OF TEST RESULTS 19

4.1 Maximum Moment Coefficients 19

4.2 Deflections at Midspan 20

4.3 Maximum Strain at Bottom Girder Surfaces 20

4.4 Effective Width of Slab, Curb,-and 21Parapet Wall

4.5 Neutral Axis Location 21

iii

5. DISCUSSION OF TEST RESULTS 22

5.l Vehicle Position at Maximum Response 22

5.2 Maximum Moment Coefficients 22

5.3 Deflection and Rotation at Midspan 24

5.4 Maximum Strain at Bottom Girder Surfaces 26

5.5 Effective Width of Slab, Curb, and 27Parapet Wall

6. SUMMARY AND CONCLUSIONS ' 28

6.1 Summary 28

6.2 Conclusions 30

7. ACKNCMLEDGMENTS 34

8. APPENDIX 35

9. TABLES 59

10. FIGURES 80

11. REFERENCES 113

12. VITA 115

iv

1. INTRODUCTION

1.1 Background

Early prestressed concrete highway bridges in the

United States were generally constructed either with the longi­

tudinal girders in direct contact, or with very small lateral

spacing. This adjacent girder configuration was utilized as a

means of gaining positive interaction between beams in the lat­

eral distribution of live load. Transverse post-tensioning was

often employed, along with shear keys between the beams, to pro­

vide significant resistance to bending in the lateral direction.

As a result, the adjacent girder bridge could be analyzed as an

orthotropic plate structure, since longitudinal bending resist­

ance was greater in magnitude than that in the lateral direction. 1

A number of girder cross-sections were used, including I-shaped,

box-shaped, upright or inverted tee, and channel-shaped, with

most forms having some means of developing positive lateral in­

teraction. 2

In Pennsylvania, most of the adjacent girder bridges

have used the box-shaped cross-section. In these bridges, the

girders are placed with their faces nearly touching, and the

small space between is occupied by a cast-in-place concrete shear

key. With this configuration, there is no need to depend on a

rigid deck slab for any structural purpose, and the tops of the

beams provide an unbroken surface. Therefore, only a thin wear­

ing course need be applied for the structure to be ready for

traffic.

Recent design practice has led to the use of prestressed

concrete girders in a spread configuration, parallel to that in

a beam-slab bridge utilizing steel stringers. Load transmission

between beams is accomplished by means of a reinforced concrete

deck slab cast to act compositely with the beams. Diaphragms are

normally cast-in-place between beams at intervals along the span

to aid in a more uniform distribution of live load to the beams.

Both I-shaped and box-shaped cross-sections have been used "in the

spread beam configuration, with the utilization of the boX-section

being the most recent development in Pennsylvania. The box girder

differs in structural behavior over the I-shape in that it has

more resistance to torsion. It is believed that the box section,

by virtue of this torsional stiffness, may be superior. to the

other shapes in developing a·more uniform lateral distribution of

applied loads. Since this additional rigidity has not been taken

into account, it is felt that previous designs may be somewhat

conservative.

As a result, in 1964, the Structural Concrete Division.

of the Department of Civil Engineering initiated a research project

with the purpose of evaluating the structural behavior of spread

prestressed concrete box girder bridges. The foremost purpose of

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the project is to determine the actual lateral distribution of

vehicular loads in this type of bridge.

Initial tests were conducted on an existing highway

bridge near Drehersville, Pennsylvania. This test series served

as a. pilot for following tests, and provided insight into the

effects of certain design factors on the behavior of the bridge.

Two load vehicles, closely simulating AASHO H20-S16-44 loading,

were run across the test span, both singly and in combination.

Instrumentation was arranged to measure strains in beams, slab,

curb, and parapet, and to measure deflections. The pilot tests

indicated principally tDat (1) positive composite action "exists

between the beams and deck, including the curb and parapet wall,

(2) that the effect of multiple vehicle loads can be evaluated

by superimposing single vehicle effects, (3) that only half of

the beams in a bridge need be gaged to evaluate the behavior of

the entire bridge, and (4) that actual ~ive load distribution is

significantly different from that assumed in present design. 3

It was decided that subsequent tests be planned to

evaluate the effects of several f~ctors on live load distribution

in the spread-box bridge type. These are primarily (1) degree of

skew angle between the crossing routes, (2) width of beam section,

and (3) the effect of midspan diaphragms. One bridge, having no

significant degree of skew, was selected as the standard for the

tests, and three others of similar dimensions, but with desired

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variations from the standard, were chosen for the purpose of com­

parison. The characteristics of the four bridges are given in

Table 1.

1.2 Object and Scope

In the phase of the project reported herein, the pri­

mary purpose is to evaluate the effect of a 45° skew on the lat­

eral distribution of live load in one of the bridges tested.

Spread-box girder bridges existing at present in Pennsylvania

have been designed using a live load distribution factor of 8/5.5

for interior girders, where S is the lateral girder spacing,

center-to-center. The distribution factor determines the portion

of the standard design wheel load to be applied to each interior

girder in design. The factor in use is equal to the largest fac­

tor specified for any beam-slab bridge type currently listed in

the design standards of either the Pennsylvania Department of

Highways4 or American Association of State Highway Officials. 6

It is beli~ved 'that, due to the torsional characteristic of the

box section, this factor could be changed to more accurately re­

flect the behavior of the section. Data gathered from the test­

ing of a right bridge at Berwick, Pennsylvania, which is the

standard bridge for these tests, indicated maximum loads for in­

terior and exterior girders which differed significantly from the

design loads. 6 In this report, data is analyzed to compare the

distribution in the skew bridge with that of the ~ight bridge.

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The analysis performed in this phase of the project is

of experimental strain data only. In the processing of data from

the bridges tested which had no appreciable skew, the determina­

tion of externally applied moments was a simple matter. However,

with a skewed bridge, the analysis is considerably more complex.

The skew has the effect of creating an eccentric distribution of

beam end reactions which cannot be accurately determined.

1.3 Previous Research

In March of 1946, the University of Illinois published

the first of a series of reports on the extensive testing of slab

and beam bridge models. 7 The models utilized steel stringers of

I-shaped.section, with five beams in each model. The first re­

port covers simple span right bridges which were thoroughly in­

strumented to observe behavior in the beams and slab. Later tests

included studies of models with 30° and 600 skew angles. 8 Speci­

mens were loaded to failure, and influence charts compiled for

beam strain, beam deflection, and slab reinforcement strain.

The study considered the effect of skew on beam strain and deflec­

tion, slab reinforcement strain, ultimate strength, and dead load

moments in the test bridges. A later report published as part of

this same series presents a theoretical analysis of the same type

of bridge, comparing the behavior of bridges with 30°, 45° ~ and

600 skew to that of a right bridge. 9 The analysis consists basi­

cally of the simultaneous solution of difference equations, using

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symmetrical and anti-symmetrical load components on a grid con­

forming to the skew of the slab. The principal parameters used

in the analysis are beam spacing-span ratio, and the ratio of

slab stiffness to beam stiffness. Tables of coefficients are

compiled which may be used to compute quantitatively the effects

of single concentrated loads, or AASHO standard H-loading. A

formula is given for approximate conversion to H-S type loading,

so that the effects of this ,configuration may be evaluated.

Little published material is available on field test­

ing of skew bridges. A recent report from the University of

California1o describes the experimental evaluation of a theoret­

ical solution performed on a steel orthotropic plate skew struc­

ture. Tests were run on a bridge constructed for experimental

purposes on a California highway, with the main objective being

to determine the accuracy of the analysis. No comparison is

made of the behavior of the skew structure to a similar right

structure.

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2. TESTING

2.1 Test Bridge and Site

The test bridge, details of which are shown in Figs. 1

through 4, carries Legislative Route 701 over the eastbound lanes

of Int~rstate Route 80 (L.R. 1009-3) two miles north.of Brook­

ville, Jefferson County, Pennsylvania. Dimensions closely match

those of the Berwick Bridge, with a simply-supported span of

64 feet 10-1/2 inches, and a roadway width of 28 feet. The four

identical longitudinal girders are of precast, . pre-tensioned con­

crete, with a hollow box cross-section nominally 48 inches wide

and 36 inches deep, and laterally spaced at 8 feet 10 inches

center-td-center. The bridge was chosen because its only signif­

icant difference from the Berwick Bridge is the skew angle of 45° •

Interaction between the slab and beams is provided by extending .

the girder shear reinforcement through the top of the girder into

the slab. The curbs and p~rapet walls are linked to the s~ab by

reinforcing steel in much the same manner, but are not assumed in

design to form part of the load-bearing structure.

The bridge is located on a section of tangent roadway,

with a 3.1% grade falling toward the south~ The approach from

either end of the bridge is clear, with slight curvature and rising

grade on the road to the south, while a similar bridge spanning the

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westbound lanes of Interstate Route 80, slight curvature, and

gently rising.grade lie to the north. There is no super-elevation

or extreme crown in the immediate vicinity of the test span.

2.2 Gage Sections and Locations

It was concluded in Fritz Engineering Laboratory Report

No. 315.1 that only half of the beams in a bridge of this type

need be gaged thoroughly to give an accurate picture of its be­

havior. Therefore, only the two girders toward the east side of

the bridge were extensively instrumented. Gaged sections were

located at midspan on Girders A (exterior) and B (interior), and

a third section was located on Girder A on a line running perpen­

dicular to the girders from the interior gage section, as shown

in Fig. 5.

The two gaged sections on the exterior girder have been

designated as El (midspan) and E2, and the interior section is re­

ferred to as Section I.. Each section was mounted with four strain

gages per girder face; two gages were mounted on the bottom sur-.

face of the girder, with others placed nominally at 6 inches, 15

inches, and 34 inches-above the bottom surface, for a total of

eight gages per girder. Single gages were placed on the bottom

surfaces of Girders C and D in locations corresponding antisymmet­

rically to the main sections on Girders A and B to serve as a check

system. Single deflection gages were placed at midspan of each

-7-

girder. These gages are a type devised by the Bureau of Public

Roads, called a deflectometer. The deflectometer is described in

the following section.

2.3 Instrumentation

All strain gages used in testing were of the SR-4 elec­

trical resistance type manufactured by the Baldwin-Lima-Hamilton

Corpo~ation. The gages were mounted using a cement supplied by

Baldwin for the purpose, after the gage locations were ground

smooth and sealed with a prior coat of cement. Gages exposed to

weather were proteqted with Gagekote, an epoxy compound which is

applied after the gage cement has cured.

Following mounting, each gage was wired into a conven­

tional Wheatstone bridge circuit with three inactive gages placed

nearby such that all were at ambient temperature conditions.

Strain data was recorded using a mobile instrument unit owned by

the U. S. Bureau of Public Roads. The equipment is housed in a

trailer and consists mainly of an oscillator, 48 gage circuit am­

plification"channels, and three variable speed recording oscillo­

graphs. The oscillator transmits a reference signal to the bank

of amplifiers, where each amplifier is connected into a gage cir­

cuit as described above. During a test run, the transmitted sig­

nal will be altered by gage activity, magnified by the amplifier,

and transmitted to an oscillograph galvanometer, where the

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galvanometer movement is permanently recorded on photographic

paper. A flow-chart diagram of the circuitry in the testing

trailer is shown in Fig. 7.

Deflections are measured with the BPR deflectometer,

shown in Fig. Sb. The deflectometer is essentially a small can­

tilever beam of rectangular cross-section in which the width

tapers uniformly from the support end to the tip. The depth of

the small beam remains constant through its length, so that the

cross-section has a uniform, linear decrease in moment of in­

ertia from the support end to the free end. Four SR-4 strain

gages are bonded to the beam near -the support" end, which is

clamped rigidly to the bridge girder at the point where1deflec­

tion is to be measured. A wire is connected between the free

end of the cantilever and a weight resting on the ground, in or­

der to impose a downward deflection on the cantilever. When the

bridge girder deflects under load, .the forced deflection in the

canti~ever decreases, and the change is registered by the record­

ing equipment in the same manner as with the other strain gages •.

The deflectometer is calibrated when it is fabricated, so that

the bridge girder deflection is easily evaluated.

2.4 Test Vehicle

The vehicle used for testing is a diesel-powered trac­

tor and.semi-trailer owned by the Bureau of Public Roads. The

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dimensions of the vehicle conform well to AASHO H20-S16-44 de­

sign loading,S measuring 13.0 feet from the front axle to the

drive axle, and 20.4 feet from the drive axle to the trailer

axle. The trailer was loaded with gravel distributed to produce

axle loads quite close to those specified in the design code, as

shown in Fig. 9. Between the start and finish of testing, there

was some change in the loads, due to change in the moisture con­

tent of the gravel.

2.5 Test Runs

Runs studied in preparation for this -report are of a

static nature, with the vehicle moving across the span at a crawl

speed of two to three miles per hour. Hand signals· were used to

guide the vehicle in the desired lateral position during all runs.

A total of twenty static runs were made, with two runs in each of

five northbound lanes, and two runs in each southbound- lane. Ex­

tensive dynamic testing was conducted, and is being evaluated by

the- Bureau of Public Roads.

2.6 Loading Lanes

The loading lanes, shown in Fig. 2, were laid out'so

that the load vehicle is laterally positioned either over a gir­

der centerline or over a line midway between girder centerlines.

On the Brookville Bridge, this scheme gives five loading lanes,

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spaced uniformly at 53 inches. When the vehicle is in the out­

side lanes, numbered 1 and 5,' the centerline of the outside wheel

is 17.5 inches from the curb face, which meets the AASHO specifi­

cation calling for placement 24 inches or less from the curb in

design. 5

2.7 Longitudinal Position and Timing

Vehicle position was indicated on oscillograph records

through the use of air hoses placed transversely across the road­

way in the path of the vehicle. As each axle crossed an air hose,

a pressure switc~ was activated, causing a sharp break in a ref­

erence trace on the oscillograph records. One hose was placed at

midspan, with two others 50 feet to the north and south of the

midspan hose, as shown in Fig. 3.

In addition to the air hoses indicating longitudinal

position, hoses were employed to determine vehi~le speed during

dynamic runs. These hoses were placed 165 feet apart, and served

to actuate a digital timing device, which allowed easy computa­

tion of average vehicle speed across the span.

-ll-

3. DATA REDUCTION AND EVALUATION

3.1 Oscillograph Trace Reading

The first step in data reduction was the editing of

oscillograph records to correlate the galvanometer traces with

the gage circuits of which they are a part. Following editi~g,

calibration records were evaluated~ Calibration of the galva­

nometers was required periodically during testing to ensure ac­

curacy of results. To calibrate, a large resistance was shunted

into each gage circuit in place of the strain gage, and the gal­

vanometer de-flection was noted. This provided an index to trace

deflection for a known_ resistance, and in turn allowed calcula­

tion of resistance change from trace deflection magnitude.

With preliminary information organized, the evaluation

of test run data was begun. When stra~.n occurred in a partic­

ular gage, the galvanometer to which the gage was connected de­

flected in proportion to the strain. By measuring any-trace

amplitude for.a given loading condition, the" strain- in the gage

associated with that trace was found by applying several factors

which will be described in the following section·. In previous

testing, strain data was studied for particular longitudinal ve­

hicle locations, since externally applied moments could be deter­

mined. Since the skew bridge did not allow accurate calculation

of applied moments, the strain data was interpreted on the basis

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of maximum respons_e. Noting the gages which reflected bending

at a particular section, the maximum trace ~mplitudes for those

gages were found on a test run record. At this location on the

record, the amplitudes of the traces under consideration were

measured to an accuracy of 0.01 inch, and the longitudinal- posi­

tion of the load vehicle. was determined by proportioning the

distance between axles on the vehicle to the distance between

reference marks on the oscillograph record (see Sec. 2.7). In

most ·cases, the maximum amplitude was located easily by eye.

However, when the, vehicle was placed in the westerly lanes on

the span, gage activity in the beams on the east side of the

structure was slight, making the location of the maximum ampli­

tude more difficult.

3.2 Evaluation of Oscillograph Data

3.2.1 Strain Calculation

After load trace amplitudes were measured and tabUlated,

they were entered as input in a computer program which calculated

strains and beam deflections in the test structure.' The conversion

of oscillogr~ph trace amplitudes to strain and deflection values

was a relatively simple matter, involving mUltiplication of the

load trace amplitude measurement by one variable and several con­

stant quantities which were dependent on electrical resistances.

-13-

The apparent strain in any gage is given by

~L

L

where R = gage resistanceg

R = calibrating resistancec

F = gage factor

The only variation from normal calculations involving

electric resistance strain gages is CL, which is a resistance

correction factor for the length of cable from the amplifier to

the gages. These lengths sometimes ranged as high as 300 feet.

The other values for Rg , Rc ' and F are known prior to testing,

and are constant. Calibrating attenuation and operating attenu-

ation, which are resistance adjustments in the amplifiers which

control the sensitivity of the oscillograph galvanometers, are

held constant for the static test series. For each gage circuit,

all constant factors can be combined as

K = ~L17""

operating attenuationX'calibrating attenuation

.Finally, the experimental values, which are the load

trace amplitude and the calibration trace deflection, are combined

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with K as

e = K x load trace amplitudecalibration trace d~flection

where € = experimental value for strain at a given location

on the structure

3.2.2 Strain Tabulation and Plotting

After strain values were obtained in the form of com-

puter output, they were tabulated on a schematic cross-secti~n

view of the test bridge, with each strain value written, in micro-

inches per inch, at the approximate location where the strain was

measured. A typical strain tabulation is found in Fig. 10.

Following tabulation, girder web strain values were

plotted by the computer, permitting easy location of unreasonable

values which did not fall within approximately 5% of a straight

line strain distribution through the depth of the girder. Strain

values which seemed unreasonable were dropped from consideration-

in subsequent calculations.

3.2.3 Moment Calculations

It was not possible to calculate moments directly from

the test data, because a dependable modulus of elasticity value

for the'girder concrete was not available. Instead, bending was

-15~

evaluated on the basis of a quantity termed the moment coeffi­

cient. The moment coefficient is simply the experimental moment

value as a function of the modulus of elasticity, having a unit

of ft-in2 if the moment is to be expressed in ft-lb and the modu­

lus in psi. MUltiplication of the moment coefficient by the mod­

ulus of elasticity, if known, would give the experimental moment

value.

After unreasonable girder strain values were eliminated

from the initial data, the remaining values were used as input for

the principal computer program. The program begins by determin­

ing the most probable straight line strain distribution by the

method of least squares, and calculates the distance from the bot­

tom surface of the girder to the experimental neutral axis for

each girder face. Taking the neutral axis location as determined,

along with various properties of the girder cross-section, the

program then calculates effective area of deck slab, and, for the

exterior girder, effective curb and parapet wall area by balancing

area-moments of concrete above and below the neutral axis. With

the ef~ective concrete area known, it is possible to compute the

properties of the composite cross-section in bending, and by

utilizing the previously computed strains, the moment coefficient

can be determined. For an exterior girder, the computer output

lists the following:

1. effective width of slab

2. effective width of curb

3. effective width of parapet wall

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4. x-x moment of inertia (composite section)

5. y-y moment of inertia (composite section)

6. 'product of inertia (composite section)

7. moment coefficient

Output from interior beam calculations contains the same informa­

tion except for curb and parapet figures. In calculating slab

widths, the program limits the width of slab available to the ex­

terior girder to half the distance between girder centerlines.

This condition is not imposed on the interior girder calcUlations,

in order that sufficient slab will be available in any case to

balance the area-moments.

When the program was first used, calculations were per­

formed giving consideration to transformed reinforcing steel area

in the deck slab, assuming a modular ratio of 6. In the bridges

studied, the deck reinforceme.nt does not follow a dimensionally

consistent pattern, and it was nece~sary to devote considerable

time and attention to altering the "program for each bridge studied .

.Therefore, it was decided to evaluate the effect of neglecting slab

steel on the moment. coefficient value, and found that the computed

value varies by less than· 1%. From that time, therefore, calcula­

tions have been made without considering deck slab reinforcement.

A more detailed description of the computer program is

included as an appendix to thjs report. The program was written

in the General Electric-Lehigh University LEWIZ compiler language.ll

A flow chart is included, so that th~ program logic may be studied

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in detail. Other contents in the appen~ix are a printout of the

LEWIZ program, a sample of the program input format" and a sample

output sheet.

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4. PRESENTATlON OF TEST RESULTS

4.1 Maximum Moment Coefficients

All moment coefficients listed in Tables 2 through 6,

and plotted in Figs. 11 through 14, represent maximum response

obtained in the structures tested. The position indicated in

Table 2 is the distance in feet from the load vehicle drive axle

to perpendicular midspan at the time when maximum response oc­

curred, and is presented graphically in Figs. 15 through 26.

Moment coefficients were computed for single vehicle loading in

each of the five l~nes, (Tables 2 and 4) and superimposed in four

combinations of vehicle direction (Tables 5 and 6) to produce re­

sults for two vehicle loading.

A compari~on of moment coefficients ,at midspan with those

determined in a similar right bridge is presented in the form of

ratios of skew bridge moment to right bridge moment in the columns

labeled ttBrookville/~erwickn (Tables 4 thrc;:>ugh 6). This comparison

is based on the assumption that elastic moduli for .the gi·rder con­

crete in both bridges -are equal.

Table 7 gives a. part of the results of an extensive study

of skew bridges conducted over a period of several years at the

Unjversity of Illinois, and is present~d to provide a comparison

with similar research. Values given are the degree of moment

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reduction in a variety of skew bridges when compared with a right

bridge of similar characteristics. The reduction percentages will

be discussed and compared with results obtained on this pr9ject in

Chapter 5.

4.2 Deflections at Midspan

In the calculation of deflections at midspan, longitu­

dinal vehicle position has been given primary consideration, with

deflections computed when the vehicle drive axle is located at skew

midspan on the structure. This condition was imposed in order to

provide a qualitative comparison of behavior as vehicle position

varies~ In Tables 8-through 12, deflection values for all four

girders have been compiled in a manner similar to that in the case

of moment coefficients, including values listed for both one and

two vehicle loads, and a numerical comparison between skew and

right bridges. Graphic presentation of deflection data, is given

in Figs. 27 through 30.

4.3 Maximum Strain at Bottom Girder Surfaces

Strain data is compiled for one and two vehicle loadings,

with comparison of midspan strain magnitude, in Tables 13 through

18. The strain values were computed at the same identical load

vehicle positions as were the moment coefficients. Strain data is

plotted in Figs. 31 and 32, to provide observation of strain trends

at the gaged sections.

-20-

4.4 Effective Width of Slab, Curb, and Parapet Wall

In Table 19 are listed the effective widths of slab,

curb, and parapet walls for exterior sections, and the effective

width of slab for interior sections. These widths were calcu­

lated to balance area-moments about the experimentally determined

location of the neutral axis. For the interior girder, as much

slab width as was theoretically required was made available. For

the exterior girder, the available slab width was terminated at

95 inches, the midway point to·the adjacent interior girder. More

concrete area was often required in exterior girder bending, and

was allotted as necessary from the curb and parapet wall. The

data given is for single vehicle loading only.

4.5 Neutral Axis Location

The calculated height of the experimentally determined

neutral axis above the bottom surface for left· an~ right girder

faces is listed in Table 20 .. The values listed are for ·single

vehicle loading, and provide for a qualitative look at girder ro­

tation. In calculating ~oment coefficients, neutral axis heights

were averaged for each section, and composite beam section proper­

ties were computed with respect to the horizontal axis. Neutral

axis locations are included for each gage section, considering

all test runs, for single vehicle loading.

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5. DISCUSSION OF TEST RESULTS

5.~ Vehicle Position at Maximum Response

In general, the test structure responded predictably

to lateral variation in load vehicle position. The largest mo­

ment in any gaged section occurred when the load vehicle passed

in the loading lane closest to the section, and the moment de­

creased as the vehicle was run in lanes at greater lateral dis­

tances from the section under consideration.

Response was not so predictable, however, with respect

to longitudinal vehicle position. In all cases, the vehicle was

placed so that skew midspan was within its length when maximum

occurred, but otherwise no general statement can be made. The

drive axle fell within 10 feet of skew midspan in almost all in­

stances, and considerably closer in sOLthbound runs. The general

trend of position shown in Figs. 15 through 26 follows the skew

midspan line, and seems to indicate that positioning with the

vehicle drive wheels at midspan would have yielded response very

close to maximum at the sections considered.

5.2 Maximum Moment Coefficients

It is notable that moment coefficients determined at

sections E1 and E2 are very close in magnitude. This is a probable

-22-

indication that the moment curve is rather flat near its peak,

and that values comparable to those at the gaged sections might

be found over a considerable length of the exterior girder. In

the University of Illinois reportS on similar research in steel

I-beam bridges, it is stated that, in a skew bridge, absolute

maximum moment in an exterior'girder occurs at some distance from

.midspan, with this distance increasing as the skew angle becomes

more extreme. In view of this, gaging of a third section on the

exterior girder might have been helpful in more exactly locating

the section and in determining the magnitude of absolute maximum

moment.

When the maximum moment coefficient values at midspan

for the skew bridge are compared to maximum values obtained in

testing the right bridge at Berwick, assuming the two bridges

have nearly equal mod~li of elasticity in girder concrete, it is

found that the skew bridge yields values of substantially smaller

magnitude. On the average, reductions of 13% in the exterior

girder and 19% in the interior girder were experienced. This re­

duction was. found to be fairly consistent with the .results of the

University of Illinois work. 9 The most probable reason for the

reduction is that vehicle loading on a skew bridge, if the struq­

ture is viewed along a section parallel to the supports, becomes

a series of concentrated wheel loads, double the number of loads

in a right bridge, where the configuration can be viewed as axle

loads. 'Using a three axle vehicle, then, will effectively place

-23-

six individual concentrated loads on, a skew bridge, and three

concentrated loads on a right bridge. It can be seen that, on

the skew bridge, some wheel loads will lie closer to the end

supports than on a comparable right bridge, resulting in a re­

duction in the moment at any section. Data from this project

shows an overall average moment reduction of 16% for,single ve­

hicle loading. In a rough comparison, figures from University

of Illinois data, converted to use with AASHO H-S loading, show

an average reduction of 21% for a bridge of 45° skew. Disagree­

ment in the reduction figures could indicate some effect of the

difference in bending properties between the concrete box-shaped

section and the steel I-shaped section studied in Illinois r~-

search. This cannot be discussed at present as there has been

no work done specifically in this area. The Illinois reportsS,s ~

have provided conclusive evidence that I-beam bridges of up to

3if skew show no appreciable reduction in moment, but that.the~

reduction becomes considerable, and increases with degree of

skew, in bridges with skew greater than 30°. In view of these Vi

findings, it appears that valuable information might be gained

by investigating box girder bridges of other than 45° skew in

future testing, in order to' determine the magn~tude of moment re­

duction with ~arying skew in box girder bridges.

5.3 Deflection and Rotation at Midspan

Deflections experienced in this phase of testing are

quite consistent in magnitude with those in bridges tested

-24-

previously. .AII defl"ec.tions were measured at midspan, with the

load vehicle drive axle centered over the skew midspan line. Be­

havior was predictable with respect to lateral vehicle position­

ing, with the largest deflections occurring in girders most direct­

ly under the load vehicle, as can be seen in Figs. 27 through 30.

Deflections were small in all cases, as has been found in previous

testing. When skew bridge deflections are compared to those in the

right bridge, it is interesting to note that deflections are some­

what ·larger in the skew bridge in the beams most directly loaded,

and considerably smaller in the beams 'at greater lateral distance

from the load vehicle. These differences point to the desirability

of additional deflection gages in future testing.

The girders were not gaged for the measurement of rota­

tion in the testing of this bridge, but some idea of rotation be­

havior c'an be gained by observing the location and inclination of

the neutral axis (Table 20) for each loading situation. Rotations

seem to correspond well to the external loading conditions in terms

of direction. The girders show rotation in the direction which

would be expected in all cases, but no means is ava"ilable for num­

erical evaluation. A marked indication of rotational restraint be­

comes apparent, also, from the lateral bending behavior of the deck

slab, for which strain data is not listed in this report. Lateral

action in both the slab and midspan diaphragms demonstrated some

degree of flexure similar to that in a fixed-end beam when one

-25-

bridge girder deflected with respec~ to another. Slab bending

in the lateral direction has not been investigated at present,

and more intense study sho~ld provide further insight to the ro­

tational behavior of the box girder in a bridge of this type.

5.4 Maximum Strain at Bottom Girder 'Surfaces

All strain values listed in Tables 13 through 17 repre­

sent maximum response of the structure, and were used along with

computed composite section properties to determine moment coef­

ficient values. Comparison with right bridge strain values shows

'that there are average reductions of strain magnitude in the skew

bridge of 24% in the exterior girder and 12% in the interior gird­

er. These reductions do not parallel those found for moment coef­

ficients, but a comparison in this vein is heavily dependent 'of

the fact that the moment coefficient values are results of the

composite section properties, which ar~ based on several behavioral

assumptions. Reduction in strain is greater, on the average, than

reduction in moment coefficient, but the difference is not large.

Such a disagreement could be attributed to some difference in

elas~ic moduli between the bridges. The disagreement is also· no

doubt influenced py differences in the bending characteristics of

each bridge as a unit, especially with respect to the effect of

torsion.

-26-

5.5 Effective Width of Slab, Curb, and Parapet Wall

In most instances, effective concrete area seems to

appear as would be expected. In the exterior girder, some width

of curb and parapet wall were required to balance the section in

all cases where the load vehicle was most directly over the girder.

There are a few figures which fall somewhat out of line when the

load vehicle was in the west curb lane. The reason for this is

not apparent, except for the. fact that interpretation of oscillo­

graph records was more difficult when the vehicle was run in Lanes

4 and 5, due to the smaller magnitudes of the strains.

-27-

6. SUMMARY AND CONCLUSIONS

6.1 Summary

The main objective in this report is the evaluation

of data collected in the field testing of a prestressed con-

crete box girder highway bridge of 45° skew, and the comparison

of its structural behavior with that of a right bridge of simi­

lar characteristics. The bridge tested was a beam-slab structure

utilizing four precast, pre-tensioned girders of hollow box cross­

section, topped by a composite reinforced concrete deck slab.

The main instrumentation for field testing was devoted

to the measurement of fiber strains at three girder cross-sections.

Two of the sections were located on one of the exterior gird~rs,

and one on the adjacent interior girder, for the evaluation of in­

ternal bending moments produced by the rest loading. Additional

instrumentation was arranged to measure girder deflections, slab

strains, and midspan diaphragm strains.

Tests were conducted using a load vehicle closely con­

forming to AASHO HS20-44 loading, along with a mobile instrumen­

tation unit owned by the U. S. Bureau of Public Roads. All test

runs were made with the load vehicle moving at crawl speed, in

five loading lanes established for testing purposes.

-28-

The measured bending moments are presented as moment

coefficients, which take the dimensional form of bending moments

divided by the modulus of elasticity of the girder concrete, and

are expressed in the units ft-in. 2 This was done because no re­

liable value was available for the modulus of elasticity in this

bridge. A comparison of the internal bending moments produced in

the skew bridge with those in the right bridge is, therefore, based

on the assumption that the elastic moduli in both bridges are equal,

and deals solely with maximum response of the structure.

Moment coefficients were determined with the aid of a

computer program designed to perform calculations for any girder

.cross-section. The program calculates the area of the composite

section from strain data by balancing area moments about the neu­

tral axis determined for a specific loading situation, and calcu­

lates properties for tpe section which, when combined with ideal­

ized strai~ values for the bottom girder surface, yield the mo­

ment coefficient value. The logic of the program is described in

an appendix to this report.

In comparing moment coefficient values for the skew

bridge to those for the right bridge, it was found that the values

for the skew-bridge were generally lower. This reduction in mo­

ment is probably due to the geometry of the skew bridge, in that

the effect of the skew is to more uniformly distribute the ~ix

wheel loads over the span length.

-29-

Previous research conducted at the University of Ill­

inois established that the degree of moment .reduction in a skew

bridge varies with the degree of skew, increasing as the skew

becomes more extreme. The, Illinois report is discussed in this

text, with a rough comparison made between moment reductions in

a 45° skew steel I-beam bridge, and those in the structure upon

which this report is based.

The girder deflection" data for the Brookville ·Bridge

shows a reduction of similar magnitud~ to that experienced with

'moment coefficients, but without the same pattern in reductions.

The reason for the difference cannot be determined at present

because deflection instrumentation was not "sufficient to allow

a thorough analysis.

Also considered to a lesser degree were strains at the

bottom girder surface, calculated effective concrete areas in the

composite beam sections, and calculated locations of the neutral

axis in each section for all test runs.

6.2 Conclusions

From the crawl-run testing of the skew bridge -at Brook­

ville, the following conclusions can be drawn:

1. There was a reduction in moment coeffi­

cients in the skew bridge in all cases

-30-

compared with similar values from the

right bridge. The magnitude of the re-

duction, however, can be assumed to apply

oonly to a structure of 45 skew, as it was·

previously established that the moment re­

duction varies with the degree of skew. s,9

This suggests that consideration of bridges

with different skew angles is in order, if

a relationship between skew angle and mo-

ment reduction is to be established. There-

fore, it is apparent that girders in a skew

bridge, designed on the basis of provisions

specified for right bridges, will actually

be stressed to lower levels than their right

bridge counterparts.

2. On the basis of the data ana~yzed, it appears

that the maximum live-load moment·envelope

in the exterior girder has a nearly constant

v~lue near absolute maximum over a consider-

able length of girder. The exact location

and value of the maximum moment coefficient

cannot be estimated from available data, but

it is likely that the maximum occurs at some

distance from midspan, as was found in earlier

-3l-

studies at the University ,of Illinois. 8 ,~

Additional girder instrumentation in future

testing would help to provide useful infor­

mation toward this end.

3. For maximum response in either exterior or

interior girders, the longitudinal vehicle

was usually with the drive axle in close

prOXimity to the skew midspan line. It is

felt that data evaluation with the drive

wheels located at skew midspan would yield

nearly the same experimental results as were

found with the more exact location of the

positions which'produced absolute maximum

responses.

4. Deflections in the skew bridge were generally

smaller than those in the right bridge, but

there was a marked tendency for the girder

most directly loaded to deflect considerably

more than the other girders, and in some

cases, more than the corresponding girder in

the right bridge. The reason for this dif­

ferent distribution of deflections is not

apparent, and additional instrume~tation

would be required for a more complete evalu­

ation.

-32-

5. The magnitudes and distributions of

strains in the skew bridge 'were quite

comparable to those in the right bridge,

and in general, the magnitudes were

slightly smaller. The differences in

magnitude can be attributed primarily

to the more uniform longitudinal dis­

tribution of load in the skew bridge,

and to some difference in the effective

modulus of elasticity.

-33-

-~

7. ACKNOWLEDGMENTS

This study, which forms a part of an overall investi­

gation of load distribution in prestressed concrete box-beam

bridges, was conducted in the Department of Civil Engineering at

Lehigh University, under the auspices of the Lehigh University

Institute of Research. The program is being sponsored by the

Pennsylvania Department of Highways, the U. S. Bureau of Public

Roads, and the Reinforced Concrete Research Council.

The field testing was accomplished with equipment owned

by the U. S. Bureau of Public Roads, and made available through

the cooperation of Mr. C. F. Scheffey, Chief, Structures and

Applied Mechanics Division, Office of Research and Development.

The instrumentation and operation of test equipment were under

the supervision of Mr. R. F. Varney, assisted by Messrs. W. Arm­

strong, C. Ballinger, and H. Laatz, of the Bureau of Public Road~.

The basic planning in the investigation was in cooper­

ation with Mr.- K. H. Jens.en, Bridge Engineer, and Mr. H. P. Kor­

etzky, both from the Bridge Engineering Division, Pennsylvania

Department of Highways. The conduct and coordination of the

field testing were made possible through the efforts of Mr. W. S.

Stevens, District Engineer, and Mr. John Ralson, Bridge Engineer,

both from the District 10 Office.

-34a-

The Lehigh University staff was represented in test­

ing py Mr. A., ·A. Guilford, Principa~ Investigator, and by Messrs.

W. J. Douglas and R. J. Dietz. Data reduction and computer pro­

gramming were accomplished with the aid of Messrs. GUilford,

R. ,H. Kilmer, and C. S. Lin. The efforts of Mr. R. Sopko,

Miss Sharon Gubich, and Mr. J. Gera in drafting, and Mrs. Carol.

Kostenbader in typing the manuscript are appreciated.

-34b-

8 _ APPENDIX

The computer program used in the major portion of

data reduction is a combination of four independent programs,

each of which, with small modifications, can be used separately

when expedient-_ The program contains (1) a least squares fit­

ting routine which idealizes strain distribution through the

depth of the girder, (2) a program to calculate moment coe·ffi­

cients in interior girders, (3) a similar program for exterio~

girders, and (4) a routine to calculate lateral distribution

coefficients, not used in data reduction for the skew bridge.

The LEWIZ compiler language, unlike the more common

FORTRAN, requires no input format. Input data is entered in a

pre-determined sequential order as specified by' "card read"

(CRD) statements in the program. All LEWIZ arithmetic is carried

out in floating point form, unless otherwise specified. All al­

gebraic statements are written in exactly the same form used with

FORTRAN, and should be readily understood by ,anyone with· a general

knowledge of programming.

In the following pages are (1) a program flow chart"in

verbal form, (2) a list of all program variable names, each with

a description of the quantity it represents, and (3) a printout

of the program as written, with a sample output. The LEWIZ program

-35-

may be used by entering the values called for in CRD statements,

in exactly the order given in the printout. The only format re­

quired in input data is a space left after each value on the

punched cards.

-36-

Least Squares Fit Program

Start

Dimension for values1. NA location 4~ Interior moments2. Strain 5. Exterior3, Effective slab width

Initialize valuesrequired for least ..~ ~

squares fit

-37-

Add coordinatesof point in1S series

Compute fittedvalues for

NA location,strain at bottom

es

no

1

Read bridge con­stants, number of

.....------------.. sections to beconsidered

Initializesection

cou~" C

Initialize subscriptsstrains left and right,

and moment valuestorage location

Interior Beam Program

-38-

. Take appropriate strainand NA values from LS fit

storage and compute moment ~~---­arms to area segments

compute ef ect1veslab width by

bal.ancing areasabout NA

compute Ix ofsegments, thencombine to get

total Ix

compute I y ofsegmentSi and

combine to gettotal I y -­

symmetrical section

Rl R2

Compute I aboutinclined axis (1M)

Product (IMN),angle of loadapplication ct'

Compute verticalmoment component

MX

Increase subscriptsfor strain, NA,moment values

to denote nextinterior storage

location

Initialize subscriptswhich denote exterior

beam locations

no

no

Exterior Beam Program

-39-

-40-

Reaq. sectionvalues--beam depth,

slab thicknessnumberrllns forthis section

Print columnheadings forexterior beam

values

Take NA and strainvalues from

appropriate loca­tions in L8 fit

Initialize curband parapet width

to zero

ompute moment armsto area segments for

Ix--compute maximumslab width allowed-SY-adjacent beam

Compute approximateslab width by balancingarea moments about MAx

pprOX1JUate slabwidth taken to betrue effective width

Maximum slab widthtaken to be trueeffective width

R3 R4

Ll

Curb widthcalculatedtaken to beeffectivecurb width

4

Compute curbwidth, using slab

width determined, bybalancing area moments

Iscurb width

greater thanmaximum

llowed?

yes

Maximum allowablecurb widthtaken to be

effective curb width

Compute effectiveparapet widthby balancingarea moments

about NAx

Taking effectivewidths computed,

find Ix for all areasegments and combineto get Ix of section

Compute areas,moment arms,

area moments, I yfor all segmentsinvolved--combine

to get I y for entiresection, and location

of NAy

compute I xy for allsegments and combineto get I xy for entire

section

Compute I aboutinclined axis M,(1M), Product, (IMN)and angle of loadapplication (cp)

R4

-41-

R3 R4

5

compute verticalmoment component

MXE

Print valueseffective slab, curb,

arapet width MXE,

Increase subscriptsfor strain, NA,

moment values todenote next exterior

storage location

Allruns com­

plete for thisheam sectionQ

Read number of setsf runs to be combined

for distributioncoefficients

R3

no

Distribution CoefficientProgram

R4

no

-42-

Print explanatoryinformation

Read number runswithin followinget--Print colu

headings

RS

Read Lane, Speed,Position, and

locations of valuesto be combined ~.......------,

Locate necessarymoments and combineto get percentage

values

Print values forane, speed, position

and momentpercentages

Allruns in

this setcompleted?

END

no

no

-43-

NOTATION IN DISTRIBUTION COEFFICIENTS PROGRAM

Least Squares Program

NAS

T,0T

SX,SXXSY,SXYD,A,BN

RXyS(J)

NA(J)

neutral axis--averaged horizontalst~ain determined by least squares fit at bottom

of beamtotal number of sets of strain readings to be

considered i~ast squares routine--amultiple of 4 since there are four beamsides (two exterior and two interior) for anyone run

intermediate values in least squares fit procedure

number of strain values to be considered for onebeam side

run numberstrain valuestrain gage location; inches from bottom of beamstrain at bottom of beam as calculated in least

squares routineneutral axis location as calculated in least

squares routine

Interior Beam Moment Program

ABMYBM

HBMIBMX

IBMY

WSEC

DL,DR

TL,TR

area of nominal box girder section (ina)centroidal distance from bottom of beam for box

girder section (in.)nominal depth of box girder (in.)moment of inertia of box girder" about its

centroidal axis x-x (in4)"

moment of inertia of box girder about itscentroidal axis y-y (centerline of section)(in4

)

nominal width of box girder (in.)number of beam sections to be considered in a

set of computations (composite section variesdue to change in slab thickness)

measured depth of beam with slab in place, leftand right, respectively (in.)

measured slab-thickness to left and right of boxgirder (in.)

-44-

NUM

NAL , NAR

SL,SR

YNA

.TDHNEG

NEGA

DNEG

DSLAB

DBM

EW(J)

ISLAB

INEG

JBM

IX

IY

BETA1M

IMNSTRAINIILAM

PHIMX(J)

number of computation runs for'a given beamsection

neutral axis location, left and right, for a. given .loading case

strain at bottom of beam, left and right, for agiven loading case

distance from bottom of beam to horizontalneutral axis'

average slab thicknessaverage beam depth with slab in placeheight of ttoverlapn i.e. distance which girder

protrudes into slabarea of overlapdistance from horizontal neutral axis to bottom

of slabdistance from horizontal neutral axis to centroid

of overlapdistance from horizontal neutral axis to centroid

of slabdistance from horizontal neutral axis to centroid

of box girdercalculated effective width of slab for a given

loading case (in.)moment of inertia of effective slab about

horizontal neutral axismoment of inertia of overlap about horizontal

neutral axismoment of inertia of box girder section about

horizontal neutral axismoment of inertia bf composite section abdut

neutral horizontal neutral axis~oment of inertia of composite section about

girder centerlineangle of inclination of experimental neutral axismoment of inertia of composite section about

experimental neutral axisproduct of inertia of composite sectionaverage strain at bottom of beamdirected -moment of inertiaangle between plane of loading and experimental

neutral axisangle between plane of loading and verticalmoment coefficient value in interior beam for a

given loading case

-45-

Exterior Beam Moment Program

we

WPHC,HP¢H

DXC

DXP

CWPvJHNDN

DYS

Dye

DYP

MSW

BSASW

SWCWPvJISLX

IBEX

rex

IPX

IX

ASWNDXN

WPA

DXPA

width of curb on the bridge (from edge ofroadway to outside of parapet) (in.)

width of parapet wall on the bridge (in.)height of curb and parapet, respectively (in.)width of overhang (from outside of exterior

beam to outside of parapet) (in.)x-distance from centerline of girder to centroid

of curb (in.)x-distance from centerline of girder to centroid

of parapet wall (in.)calculated effective curb widthcalculated effective parapet wall widthheight of overlapy-distance from horizontal neutral axis to

centroid of overlapy-distance from horizontal neutral axis to

centroid of slaby-distance from horizontal neutral axis to

centroid of curby-distance from horizontal neutral axis to

centroid of parapetmaximum width of effective slab--determined by

slab width required by adjacent interior orbeam

c-c girder spacing (in.)approximate effective slab width--intermediate

valuecalculated effective slab widthcalculated effective curb widthcalculated effective parapet wall widthmoment of inertia of effective slab about

horizontal neutral axismoment of inertia of girder about horizontal

neutral axismoment of inertia of effective curb about

. horizontal neutral axismoment of inertia of effective parapet wall

about horizontal neutral axismoment of inertia of composite section about

horizontal neutral axisarea of effective slabwidth of overlapx-distance from centerline of girder to cen"troid

of overlapwidth of additional slab thickness outside of

exterior beamx-distance from centerline of girder to centroid

of additional slab thickness area

-46~

x-distance from centerline of girder to centroidof effective slab

area of overlaparea of effective curbarea of effective parapet wallarea of effective composite sectionarea-moment of all segments about girder

centerlinex-distance from girder centerline to y-y centroidal

axis of composite sectionmoment of inertia of effective composite section

about girder centerlinere-defined as moment of inertia of effective

composite section about its y-y centroidalaxis

re-defined to comply with transfer of referencefrom centerline of girder to y-y centroidalaxis of composite section

product of inertia of effective composite sectionwith reference to its own centroidal axesx-x and y-y

vertical component of moment for a given loadingcase

Distribution Coefficients Program

MPA,MPB,MPC,MPD

Note:

N

MLANE8mA,B,C,D

POGSMD,MC

MT

number of sets of runs to be considered (varieswith position, section, speed, direction:set consists of sufficient runs to describeerIect of anyone position, section, speed,direction combination)

number of runs within set to follow instructionlane in which test run took placespeed of test vehiclestorage locations of proper moment·values to

be combinedcombined expression for position and sectionmoments in beams D,C,B,A respectively for a

given loading casesum of internal moment in all beams for a given

loading casepercentage of total moment carried by beams

A,B,C,D respectively

where variable names in interior beam program areused again in exterior beam program, they are de­scribed in the explanation of interior beam namesonly. Variable names not described here are thoseof index counters and subscripts.

-47-

INTERIOR GIRDER

EW

experimentalneutral axis

horizontalneutral axis

EXTERIOR GIRDER

variable names usingletters TtNEG ff refer tothis area

@

.@- ---......._----+--~----------.q---

OH

Section is considered to have curb and parapet wall atleft in all cases

1. effective slab width limited by adjacentinterior beam requirements

2. curb considered constant height and variablewidth, so that x-distance to centroid is constant

3. parapet considered constant height and variablewidth.

-48-

005 2095 SCHAFFER--SOLUrION ~OR LOAD DISTRIBUTION FACTORSS~p 1~ 67 12 D2~Q

PAGE i. SEP 12 67

SEQ LABL TYP STATeMENT C ZERO NOT D PI..US M!NUS ELoSE:

U01. U N~[160],S[160',Ewt40],~X[2D],MXE[20] r002. J::I1 {

OU3. CJ;tDTOT [

004. 51. COUNTER "lUN NEUTRAL AXIS CSTRESS AT 80TTOM rIsER [ ] [ ] ( ] [ ] t

005. i SX~SXX·sY=SXY.o [ ] t ] [ ] [ ) tOU6. F"lXN,R,P"K [ ] t ] t ] [ 1 [007. C~ON ..-R $NUH Or DAT~ POINTS AND RUN NUM [ ] [ ] [ ] [ ) t008, N~IIN [ ] [ ] [ i [ 1 [009. 010 2 N'4=NN.1 ( ] t ) [ ] [99 ] [010. CRDX,Y $ ONe DATA POOINT [ ] [ 1 [ J [ ) tOil. sx-sx.x,SY=Sy... y { ] [ ] [ i [ ] [ui2. sxx.Sxx+x.x,SXY=SXY+x-Y ( ] [ ] [ 1 [ ] £2013. 99 D~SXX*N.S)(·SX ( ) [ J [ 1 [ ] [Oi4. Aa[SXY*N-SV*SX1/D [ ] ( 1 [ ] ( , [0).5. 8~[SXX*SY·SXY·SX]/D [ ] t J [ J ( 1 t01,6. S[J]=[""Sl/A [ ] [ ] [ ] t ] [017. N~[Jl=B [ ] t 1 t J t ] tU~8. PV J;R,NA(JJ,S[J] [ ] [ 1 [ 1 ( J t019. Pl. ( ] [ 1 [ 1 [ ] [u~o. [;-J+l,·TOT (1 J [ ] [ 1 (1 J [

0,,1. 001 C~DA~M,VBM,H8H,I8MX.IBMYIW,SEC [ J [ ] [ I t J [0,2. DOS C~1 [ ] [ 1 [ J [ J [

023. F I XN·jH [ ] t 1 [ J [ J [024. 47 CRDDL,DR,TL,TR,N [ 1 [ ) ( ) [ ) [01::5. 30 N,JM=1 [ ) t ] [ J t , [

Oi6. R~3,F'~4,J=2 r ] [ ] [ ) [ ] t0,7. Sl. I~TERtOR BEAM CALCU~ATIONS [ ] [ ] [ ) t ] [

Ut8. PLo EFF'. WIDTH MOMENT/e.l0*.~6 L8erT R-RUN CIX IV PHI ( 1 t ) ( ] [ ] t

0,9. 55 N~LKNA(RJINAR~NAtF' [ J t ] [ 1 t ) [0;50. SI.-StRl,SR=S[F] [ ] t I [ ) [ , tOSl. 70 S COMPUTE EFrECTIVE WIDTH BY AREA MOMENTS ( ] [ I t ] [ ) [032. 80 Y"iAc[NAL+NARJ/2 [ ] [ ] [ j [ ] [U~3. 90 T:a[TL .... TR]/2 ( ] [ ) [ j t ) t034. 100 D~rDL ... DR'/2 [ I [ I [ J [ ) [

O~5. 110 H~EG;;~BM·D [ ] t ) [ ] [ ) [

036. 120 NEG.HNEG*W [ ] [ 1 [ ] [ ] [

OJ? 130 A~D.YNA [ J [ J [ J t ] [038. 140 D"4EG_AlIoHNEG/2 [ ] [ . 1 [ J t J [O~9, 150 DSLAB;.;A.T/2 [ ) [ 1 [ ] [ J [

040. ~60 09M.YNA·YBM [ ) t J [ i t J [0.1, EACJJ.CA8M*DBM+NEG.DNES]/t'.OSLABJ ( ] [ ] [ 1 t ] [0~2. 210 S COMPUTE MOMENTS Of I~eRTIA ABOUT x~ V, AND [ ] t ] [ ) [ ) [043. 220 $ INC~INEO H A~ES [ ] [ ] [ J t J [044. ISLAS-tEW[J]*T.*3J/12+eWtJ,*T*DSLAB.*2 r ] [ ] ( ) [ ] [045. 240 I~EG~rW.~NEG.HNeG.HNEG'/12.W*HNEG.ONEG*DN=G [ 1 [ 1 [ 1 t J [046. 250 J9M_IBMX"'ABH*D8H*DBM [ ] [ ] t ] [ ] r047, 290 13 IX·IS~AS·INEG·JBM [ ) t J [ J [ ) I048 .. 300 K~2 [ ] [ ] r j t 1 -r049. IY~IBHY.tT*EW[Jl.*3)/1t·[HNeG·W**JJ/12 [ 1 I 1 [ 1 [ 1 [

o'o. 8ETAcATAN.trNAL-NARJ/Wl [ ] r ] [ ~ t48 ) 1490,1, 46 BETAP.BETA ( ] [ 1 ( J t ] t I0~2. 49 I~-[IX·IY]/2·t[IX·IY]/2)*COS,[2.BETA] [ ] [ ] [ ] t 1 [ )

-J:::::.0~3-. .50 I~N:f[lX·IY)/2J*SJN.[2~BeTA~ [ ] t J [ ] t ] [ 1 ill

I

PAGE 2. SEP 12 67

seQ LABL TYP STA.TEMENT C ZERO NOT 0 PLuS MINuS ELSe

o 4. 460 STRAIN!=[SL+SRJ/2 ( 1 [ ] [ 1 t , [o 5. 470 II-SQRT.tIHN*lMN+IH*tM, [ ] [ ] t 1 [ 1 [o 6. 510 L4M=ATAN,[IM/IMNl [ ) t ] [ J t50 ] [51o 7. 50 L~M.·LAM [ ] t ] [ ] [ , [U 8. 51 P~I.8ETA·LAM~~.1415927/2 [ 1 [ ] [ 1 (52 1 [53o 9. 52 pion _"pH I [ 1 [ ] t ] [ , [o O. 53 M~tJl~[Il*STRAlN·COS.tPHt'J/[YNA*12*COS.( C

8ETA)] [ 1 [ 1 [ ] t ] [061. Pl.. ( J [ J [ 1 ( ] [U62. PV E1[J'.~X[J!.NUM.IX,IY.PHI [ J t 1 [ ] t ) [Ob3. R=R+4,F=F+4 ( 1 t ) [ ] [ J [Ob4. [J=J"'2] [ J { ] [ j [ ] {065. 600 [ '~UMcNUM ...11 .. N [ ] ( ] [54 j [ ) [55066. 54 [C=C·1J·SEC ( ] [ ] [854 ] [ ) [47O~7. 000010854 CRDA~H.YBM.HBM.IaMx,IBMy,W.WC.WP.HC,HP..OH#DXC,c

020 D~P.8S,SEC [

068. A:1.K~2 [

069, J=1 [

010. 000030 5=1 {

011. A49 CRODL.OR.TL.TR~NUM t012. 000050 N~1 (

073.-- Sl.. EXTERIOR BEAM CALCULATIONS [

0/4. 000051 PL EFF. SLAB I EFF', CURB I EFF. PARAPETI C000052 ~OMENT/E*10**~6, LB~FT I N IX C

IY tXy ( 1 [ ] [ 1 t I t J075. 001660 PL [ ] [ ] t J [ ] { ]

076. A50 N4L=NA[Rl.NAR-NA[K, [ 1 [ 1 [ ] c ) f 1077, P~J ... 1 [ ] [ J [ ] f ] ( J078. SL=S[RJ .. SRpSrK) [ ] t ] t J t 1 f J0/9. 000061 C-"=PWc:O [ ] { 1 [ ) [ ) [ 1060. 000070 N4:1[NAL+NAR)/2 [ ) [ 1 [ j f 1 t ]

081. OOOOBO T=[TL+TR1/2 t ] [ 1 [ J t , r ]

Ob2, 000090 D=-[DL~DR1/2 [ 1 [ 1 [ j t ] t J063. 000100 H~=H8M"'D [ ] t ] ( ) [ ] [ ]

O~4. 000110 A~D .. NA [ ] { J [ 1 [ J [ 1085. OOO~20 D03M:NA-yBH [ ) t ] [ ) t ] [ ]

086. 000130 D~;ilA·HN/2 [ ] [ 1 t j t ] [ ]

067. 000140 DYS.A.T/2 t ] [ J [ ] ( ] t ']

066. 000j,50 Dl'C:A.T.HC/2 '[ ] [ 1 [ ) [ J [ J089. 000160 DYP.A.T",HC"'HP/2 [ ] [ ] r ) t ] r ]

0i'0. MS~.OH·W/2·BS·EW[P'/2,~SW·fO~·W/2·8S/2] r ] { 1 [A99 1 t J [A98 1U~l. A99 HSWaOH·W/2"'BS/2 f 1 [ ] [ ] [ ] [ J0~2, "98 ASW.tABM*OBH1/[T-OYS.HN-ONJ [ 1 { 1 t ) [ 1 [ ]

Oi3. 000231 ASW .. HSW [ 1 [ J [ A5] [ ] t .l97]0~4. 000240 A97 ASW-W/2 ( ] [ 1 [41 ) t J fA. JU~5. 000250 Ai ASWa[ABH·DBH+[W/21·(~N*DN.A"0,5)]/ C. 000260 [r*OYS"'A·O.51 [ J [ J [ 1 [ , t0~6. 000270 ASW .. CW/2·01-l) [ ] { ) fA2 j [ ) tA<4U~7. OOO~80 .42 ASW&~ABM*DSM-OH*[HN*DN.A~Of?)l/{T·DYS·HN*DN] [ J t J [ ] [ ) tO~8. 000300 ASW.tW·OH) [ ) [ 1 rA3 ~ [ ] [A<4O~9. A3 ASW.CABM*OBM+W*[HN-ONJ.OH*rA.O.51}1 c

000320 [T*oYS' [ ] t ] [ ] [ . ] t 1lUO. A4 S-,;jI:ASPl [ 1 t ] [ i [ J t ]

101. 000340 SAj"MSIJJ [ ) r 1 [A5 J [ ) (A1S J ~

102. A5 SW~MSW t 1 [ J [ ] [ J [ l103. 000360 S~·tW/2+0Hl [ ) ( ] [ ) tA6 , tA' ] I

Ul0I

--~......-..-.....~~ _. --_.~_...::..-.- ~-- ...,._------ --""'-------'--~-- - - .. -

PAGE ~, SiP 12 67

II- SEQ LABL TYP ST4TEMENT C ZERO NOT 0 PLUS MINUS ELS~- "

lU4, A6 C~.[A8M*DBM.sw.T*DYS+[W/2].MN.DN.(SW-W/2]* COOOJ80 [4-0,5'1/[HC*DYCl [ ] r ] [ ] [ 1 (A10 J

105, .,7 S~ .. [\tI'''OH) I ] [ J [ ] [A8 ) EA9 ]

106. 400 A8 C~=[A8M*D8M_SW.[T.DYS~~N*DN1·0H*[HN.DN·A·O.5]C

410 ]/CHe-DyC] [ ] t ] [ ] [ ] [ AlgJ107. A9 C~.(A8M*DBM.SW.T*OYS.W.HN*DN.OH.[A~O.5)]/ C

000440 ('1C.DY Cl [ ) [ ) [ ] [ ] [AiD JIPS, Al0 C..j .. wc ( ] [ ) (A11 ] ( 1 tA18 JIU9, All C.o/:;wC [ ] [ J [ ] [ J [ J110, 000470 S,,·[W/2+0H] [ ] [ ] [ J (A12 1 t Al,sl111, A12 P~=[A8M.DBM.CW.HC.DYC-SW*(A~O.5]·tW/2]*[A·O.5C

000500 +~N.DN]]/[HP*DYP] [ ] t ) [ ] [ ) [A16112, A13 S";-[W;.°H) ( ] [ ) [ j (A14 ) [A15113, 414 P~.[ABM*DBM.CW·HC.OYC·SW*(T*OYS·HN.DN]·OH. C

000540 [~·o,5·HN*DN)]/[H~*DYP' [ ] [ ] [ 1 [ 1 [A16114, A15 P~~[ABM*D8M.CW*HC.OYC·SW*T·DYS.W.HN.DN·OH. C

000570 [~·O.5)1/[HP.DYPl { ] [ ] ( 1 t ) [ )

115. A16 P-1"'WP [ ] [ J [A17 J [ 1 CA18 )116, A17 PL P4RAPET WIDTH EXCEEDS ~AXIMU~ ( ] [ ] [ 1 [ ) [ J117, A18 S.,j.[W/2.0H] [ ) [ 1 [ J (.19 1 [A20 . J118. A19 I5LX:Sw.[T**3/12+T*DYS·*21+tSW~W/2).[1/12. C

000630 (~·0.5]**2].[W/2].[H~·.3/12·~N·DN·*2] [ J I ) ( J ( 4 IA23119. A20 S.,·rW+OHJ r ] [ ] [ J [A21 J [A22120. A21 ISLX=Sw·[T**3/12+T*DYS**2l·0"*{1/12+[A·O.~J C

000670 .*2J-[SW·OH)*tHN**3/12+HN*DN.*21 { ] [ ] [ ] [ 1 [A231,1. A22 ISLX=SW*[T**3/12+T.DYS**21·0~.[1/12+[A·D.5J C

000700 *.2]~N·[HN*.3/12.HN·DN.·2J ( ] [ ] [ J [ 1 [1,2. 11.23 13EX=I8MX+ABM*DBM**2 [ ] [ ] [ J [ ) [.123. -720 ICX=Cw*rHC**3/12+HC*DYO**2J ( ] [ J [ J [ ] [IZ-4. 730 I~X:Ph*rHp**3/12+HP·DYP**2J [ J t ) [ ] [ 1 [1~5. 000740 I~=IBEX+ISLX+ICX+IPX [ ] [ J [ J [ J [li:6, 000750 AS=SW*T [ ] t ] [ J- I J [1.e7. 000760 S.o/·rw/2.0H] [ ] t ] r ] (A24 1 [A251,8, 424 W~=W/2 I ] [ ) [ 1 t 1 [1,,9, 000780 D(N= .. \IJ/4 [ ] [ ] [ J [ 1 [1,$0, WPA=S,,"W/2 ( ] [ ) [ J [ ] IIS1. D"(PA:ltIl[SW+W/2J/2 ( ] [ ) [ ] ( ] [1..52. 000810 D)(St;"sw/2 r ] [ 1 [ j [ ) [A291.s3, A25 S~"'[W·OH' [ 1 t 1 [ 1 [A26 ] (A271~4. A26 W1\l-SW .. OH [ ] t. ) [ 1 t ] [1.:15, 000840 DXNc[wN.Wl/2 [ ) [ ] [ 1 t J [A28136. 427 W~:W [ ] [ ] ( J [ ] [lJ7, 000860 D(N=O [ ) [ } t J I 1 t1J8. A28 W~A=OH [ ) [ ] [ J ( ] t1~9. 000880 D)(PAa.,[W+OI1]/2 ( ) t J [ 1 [ ] [140. 000890 OX:S=[SW.W]/2 ... 0H { ] [ 1 [ ] [ ] [141. A29 A".~N·~N ( ] [ ) [ ) [ ] [1_2. 001200 ACGCW*HC [ ] [ ] [ J ( ] [

1.3. 001270 APapW*Hp ( ] [ ] t ) ( ] [1~-4. 440 ATOT-ABM+AS.AN+WPA.Ac·AP [ ] [ ] t J [ J [

145. 1320 M4.AS*DXS~AN·OXN.WPA*DXPA.A~*DXC.AP.DXP [ ] t ) [ j [ 1 [146. 001340 DX.MA/ATOT [ ) t J t ] ( ] [

147. 00135U IY=IBMY.T.SW··3/12.AS*DXS**~·HN*WN*.3/12 C1360 -4N_OXN_*2·WPA*tWPA·*2/12·0XPA C1370 *.2].HC*CW*.3/12+AC*DXC·.2.~P.PW••3 C I13BO 112+AP*nXP**2 [ ) [ J [ ] t ] [ J V1

_~ _ ~ _... ~ _ __~ .~ r·.j---J

~ _I _~.... ~~ ....... ___ ~ ...... _

I

PAGE 4, SEP 12 67

IU1l\.)

I

EL.Stt

[r[[CA44[

(A46[

[[[[

[

IA50(A49[

r[

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(

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MINUSPLUS

{

[[[(['

[

{[[[

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(A47["48(

[

t

NOTC ZEROSTATEMENT

IYfl,IY~ATOT*DX"'*2

O<-·DXO(S:sDXS.OXO.;N=OXN+DXD(PA=PXPA+OXDCX:aDXC ... OXDPXcDXP.OXI(Y3ABM*OX*r·OBM]+AS*OXS*OYS-AN*DXN.ON+WPA*O(PA*rA-0.5]+AC*OCX*OYC+AP*OPX*DYP86TAsATAN.[[NA~-NAR1/Wl

I~·!tX·IYl/2·t[IX·IY]/2l·CoS.t2·BETA]wIXY*

SIN,[2*BETA]I~Nc[[IX·IY]/2]*SlN,[2.8ETAl+IXY·CDS.[2.BETA]

II=SQRT.[IMN*IMN+tM*IM~

STRAIN~[SL·SRl/2

L~M=ATAN.[IH/IMN)

L4Ha"'i,.AMP~I=BETA·LAM·3,1415927/2

Pl-olI3 w PHIM~E[J)=[II.STRAIN.CDS,[PHI]]/[NA.12.COS,[

<3ET4!]Pv S~,CW,PW,MXE[JJ,N,lX,I¥'IXY

Pl,.

PLL=1

CRD~~NE.SPD.A,B.C.D,POOS

M)aMXE(AJMCaMX{8]Mq-HX[C)M~lilMXE[O]

MTcMD.MC·MB.MAMPA.ttolA/MTl-100MPB=[MB/MT1*100MPCc{MC/MT)*100M~Dz[MD/MT)*100

PV L~NE.SPD,POOS.MPDIHPC.MP8,MPA,MT

PI.

[

[

[[[[[

C[

tC

t[

[

[[

{

r[

c[[

[

J~J.2 [R2R+4,KcK+4 [[~=N+1]·NUM [[S~S·1]·SEC [

rIXL~NE,SPD,POOS rCRDN SNUMSER OF SETS OF RUNS [

K21 rSLPERCENTAGE OF TOTAL MO~ENT C~RRIED BY EAC~ BEC

A~ [PL [PLI~ LANE COLUMN, SECOND DIGIT INDICATES OIREC

CTION, 1 FOR ~, OR E" AND 2 FOR S. OR ~. (p~ I~ POSITION AND SECTIO~ COl.U~N, 1=~OSITION oRe

S6CTIO~ A, 2=POSITIO~ OR SECTION B, ETC, [CRDM sNUMeER OF RUNS WIT~IN rOL~OWING SeT [

PL (PL LANE/DIR. SPEED POSt/SEC, C

BEAM 0 BEAM C BEAM B CBEAM A TOTAL MOMeNT [

- [

{[

[

r(

r((

[(

I[

t

00009U000100

SEQ LABL TV?"

001390001400001410001420001430001450001460001480001500001510001530 A42001540001550001551001560001610001620 A43001630 A44001640 A45

A46

001700001710 A47

A48000020000030Ooa040Cl000050000060000070OOOOBO

000140000150

C2

00019U000200000210000220

OOO~5U

156.1:)],

148.149.180.1~1.

1~2.

1'3.l;A.1:;'5.

1/6.177.

178.

179.IbO.1"1.

1'8.1'9.lbO.1~1.162.Ib3.164.165.

166.167.1~8.

169.170.1/1.1/2.1/3.1,4,1/5.

162.183.18~.1~5,186.187.188.169.190.1~1.1~2.

1~3.1~4.195,

PAGE 5. SiP: 12 67

~ SeQ LABL TYP STA.TEHENT C ZERO NOT 0 pL,:us MINUS ELSE

196. 000260 tl.IL.,.)·.H [ ] r l [ C3] [ J [ C2ll1i7. C3 [!(IJK·1J~N [ ] t ] tEND ] t 1 tCl l·i~8. 000280 END ENO- l ] [ ] [ i [ ] [ ]

·~ ••*SYMBOL TABLE._•••A AeM ATANA49 -.!SO .1998 gETA 85-48S '98 ASWC cos CWAS 1.97 .110 DL DRDNEG OSLAB DBMEW exc gxpDN DYS DyeF DYP ••A2 '3 A18A6 &7 Al0A8 A9 AllHBM !-tNEG HeHP HN A12I8MX IBMY ISLASINEG IX IV1M IMN 11Al~ A16 A14A15 A17 A19A20 ISLX .123A21 '22 IBEXlex fPX ASA24 '25 DXNDX". DXS A29A26 '27 JJS"'- "28 ANAC 'P K

*A40 "rOT DxLAM ccx DPXIXY MX MXEHSW MA *.42A4;5 NA NNN NUM HAL.NAR NEG OHA44 ... 5 .146A047 P PWIPW ....8 L.ANEp~gs 01 M

IL 02 MD Ul-He iii "8 LN

I

MTMPCENDSXXSECTRTSQRTWWNY

MPAMPDSsyfOTSL.SINswwe~PA

YBM

PAGE 6. SEP 12 67

MPBC3sxSXYTL.SRSTRAINSPDWP)(

YNA

IUl~I

CO~NTER RUN NEUTRAl. AXIS STRESS,AT ~OTTOM rISER1.0000060.00 261 3,1394546+01 4,4193216+01

2.00000UO+OO 261 3,6422619+01 5.1304983.01.

3,0000000+00 261 3,4l101660+D1 4.156.961~Ot.

4.0000090.00 261 3,3868373+01 3,6123233+01

5-. 0 l) 000fJ 0,. 00 262 :3 _.2666.89+01- ;J.1591087+01

6.00000~O+OO 262 3,4828998+0; 3.2638524.0!

7.00000uo.00 262 3,4299859+01 -4.610'2425+0!

8.0000000+00 262 3.4;'15861-+01 -4.3474118+01

9.0000000+00 264 3.6798125+01- 2.3139396+01

1., OOOOO~O+O1 264 3,3879962+01 2.0277993+01

1.100QOtJO.01 264 3,4'084046+61 ;S.5856991.0(

1.20000UO+01 264 3.4503349+01 a.7252619+0t

1.30000UO .. 01 265 3,6978561+01 .2..6202891+01

1,4000060+01 265 3,3248865+01 1.36691'2.01

1,5000000.01 265 J.4872999+0~ 2.7680619+0t

1-. 60 0 0 000• 01 265 3.0721863+01 2.6970.89.01

1.7000000.01 266 3,4523597·01 8.8931408";08

1.800006,0+01 266 2.7671484+01 7.2145000.0"

1.90000UO+01 266 3.120~392·D~ -2.1427516.01

2.0000000+01 26 6 2,7236820·01 ,~. 9832048+Q!IVlVlI

INTERIOR BEAM CALCVLATIONSEF"F. WI~TH MO~ENT/E.10·.·6 L8·~T R~RUN I~ IY "~J

1.0969444+02 4.02331 59.04 1 4.1912182.05 8.7978574+05 6.4167380;04

1-.1526155+02 4,6273079·04 2 4.2534247+0!i 1.0013044.06 1,-5724450-04

1,15011_27+02 3.7771154·04 3 ~.2506968+05 9.9558097+05 3~9798543.D~

9.14390Q3+01 2.~78i6102·04 4 3, 9632eDl+0~' -5.6042555+05 6,797~780;O2

5.1443512+-01 1,93018 5 5+04 5 ~.2808153+05 1.9910248.05 6 .,6816460: 02

IlJl(j)

I

EXTERIOR SEAM CA~CULATIONS

EFF. SLAB I err, ~URB I EFP. PARAPETI MOMENT/E.10*.-6, L8.rr I N tx ty IXY9.215~7~O+01 3~30000oo.oi 1.8128213+QO 5.8014886+0. 1 5~25640~O~05 B.4~i3~~i+D5 ·'1.0'00041.0~

8.93692~3.01 1.0854j60*01 0.0000000.00 3.3439342.04 2 ·•• 2210284~65 6,3839389.05 -7.1133839.03

8.949~3~7+01 2,4004726.01 0.0000000+00 2.4911886.04 3 4~6917266.ri5 7,1099465+05 85,-9361933+04

9,30060uo+01 2104865~O.ol 0.0000000.00 1.688~840+0~ 4 4.602806J.o§ ~.6~66j~9.05 .3.196'832~O~

7.5049324*01 0.0000000*00 O,QOOOOOO.OO 7.95037l1+0~ 5 3f564054~~ri5 3.8~~52~8.05 ~1.?8~3645.04

ILn-...JI

PERCENTAGi OF TOTAC' MOMENT tARRiED BY EACH SEAM

IN LANE COLUMN, $E~ONri DIGIT INDtCAT6S Ot~E9TION, _1 rbR Nt OR ~~t. AND ~ "rOR_S, OR_W,IN POSITION AND SecTION COLUMN, 1-POSITJON A :OR SiCTJOM M, -2: POSITION B OR -SECTION N, 3.P0s t TtON C• .. ! P0S l t l' 0 N" -D

~ANe/DIR. SpEeD POSt/sEC. SEAM .f'

12 1 11 6,3349434+08

22 1 11 1.,3575038+01

32 1 11 1.9871123:"'Q1,

BEAM C -BEAM B eEAM A 'OTA~ MOMENT

l~SJ79931.01 3,2058225~rii 4,6226901.01 1,2550027.05

2.2356910.01 3.71915i9~~1 2.68j6~33.01 ~i24~i836~05

3.01288".01 -3.D1288~7.hi l.9S+1123.oi 1~2536728~D5

TYPE #END' STATeMeNT EXECUTED,J\JN 22· 61' 1'-- 57.9RUN TIME 0001.4 ~lN.

IU1coI

9. TABLES

-59-

Table 1 Test Bridge Characteristics

Test Span C-C Clear Beam Size Skew MidspanSpacing Spacing Diaphragms

Pilot 61 f 6 Tf 7 f 2 Tt 3 1 2 Tt 48 ft X 33 TT 90° yes

Berwick 65 f 3Tf 8 f 9-3/8 Tf 4 f 9-3/8 TT 48 Tt X 39 ft7 90° yes

Brookville 64 f 10-1/2 tT 8 1 lOTf 4 f Ion 48 TT X 36 Tf 45° yes

White Haven 64 1 8 TY 9 1 OTT 6 f OTT 36 TT X 42 TT 82° yes

Philadelphia 71 T 9 TT 9 f 6 Tf 5 T 6 TT 48 Tf X 42 ft 87° yes

Philadelphia 71 f 9 TT 9 ' 6 Tf 5 T 6 TT 48 TT X 42 TT 87° no

IOloI

Table 2 Maximum Moment Coefficients, Crawl Run Loa9ing

Position indicates distance of drive wheelsfrom midspan

(lO-6 ft-in2)

Lane Direction Section Position Section Position Section PositionEl E2 I

1 NB 48,857 14.9 N 46,838 5.5 N 26 667"-'--, 5.1 N'". ,

2 NB 25,471 14.4 N 28,455 9.0 N 32,950 5.3 N3 _ NB 20,284 16.3 N 20,730 8.3 N 31,278/ 5.2 N4 NB 10,201 6.7 N 10,250 3.0 N 19,066 5.4 N --)

-5 NB 5,536 6.7 N 5,562 0 11,713 3 . 6 N -c-+"~)

1 NB 46,768 14.4 N 41,498 6.2 N 28,770- 5.4 N2 NB 31,933 14.1 N 21,112 6.3 N 33,665 5.2 N3 NB 19,780 9.8 N 20,122 9.7 N 29, 735 -/ 5.6 N d~/'-'

4 NB 10,631 9.2 N 12,119 7.9 N 18,818 5 . 8 N :.?:-~)

5 NB 5,649 0 6,900 6.2 N 12,059 o•8 N ~--,~',"1-)

1 BB 43,979 10.0 N 43,113 3.6 N 30,063 4.0 N2 BB 30,120 0.3 N 28,505 0 33,028 4.0 N3 BB 21,420 2.4 S 20,847 3.6 S 27,980 3.8 N4 BE 11,482 3.0 S 8,934 5.5 S 11,224 2.9 S5 SB 7,717 7.2 S 6,046 5.9 S 11,421 11.0 S

1 SE 46,537 0 46,292 4.0 N 28,949 3.4 N2 BE 30,264 4.7 N 29,058 3.1 N 33,268 3.8 N3 SE 21,645 2.0 S 20,888 4.8 S 27,128 3.4 N4 SB 12,081 3.0 S 12,720 6.7 S 15,813 7.6 S5 BB 6,735 2.9 S 7,427 8.6 S 11,387 12.1 S I

01j--JI

Table 3 Maximum Moment Coefficients at Midspanfor Berwick Bridge, Crawl Run Loading

(10-6 ft-in2 )

Lane

1

2

3

1

2

3

Direction

North

North

North

South

South

South

A

49,512

37,997

23,373

49,337

34,922

24,304

Girder

B

34,970

35,776

31,900

35,329

35,987

30,429

c

16,982

24, 036

31,900

14,578

20,770

30,429

D

11,539

17,410

23,373

14,570

16,206

24,304

x

ImJ\..)

I

Table 4 Comparison of Maximum Moment Coefficients at Midspan

Brookville Bridge - 45° skewBerwick Bridge - 9if skew

(Elastic Moduli assumed equal)

Lane Direction Brookville Berwick Exterior InteriorExterior Interior A B Brookville/Berwick Brookville/Berwick

1 North 48,857 26,667 49,512 34,970 0.99 0.76

1 North 46,768 28,770 -- -- 0.94 0.82

2 North 25,471 32,950 37,997 35,776 0.67 0.92

2 North 31,-933 33,665 -- -- 0.84 0.94_,·V'-

....-~--....-

3 North 20,284 31,278 23,373 ,,31 900) 0.87 0.98~~-.?_--_.,-,_/--

3 North 19,780 29,735 -- -- 0.85 0.93

1 South 43,979 30,063 49,337 35,329 0.89 0.85

1 South 46,537 28,949 -- -- 0.94 0.81

2 South 30,120 33,028 34,922 35,987 0.86 0.92

2 South 30,264 33,268 -- -- 0.87 '0.92

3 South 21,420 27,980 24,304 30,429 0.88 0.92

3 South 21,645 27,128 -- -- 0.89 0.89

I(j)LNI

Table 6 Comparison of Maximum Moment Coefficients at Midspan

(Two Load Vehicles Traveling in Opposite Directions)

Maximum Moment Coefficient, ft-in2 Ratio

Lane Direction Brookville Berwick Brookville/BerwickA B A B Exterior Interior Exterior Interior Exterior Interior

1 4 North South 60,339 37,891 65,718 55,740 0.77 0.682 5 North South 33,188 44,371 52,567 50,354 0.63 0.88

1 4 North South 60,938 42,480 65,718 55,740 0.93 0.762 5 North South 32,206 44,337 52,567 50,354 0.61 0.88

1 4 North South 58,250 39,994 65,718 55,740 0.89 0.722 5 North South 39,650 45,086 52,567 50,354 0.75 0.90

1 4 North South 58,849 44,583 65,718 55,740 0.90 0.802 5 North South 38,668 45,052 52,567 50,354 0.74 0.89

1 4 South North 54,180 49,129 66,747 59,365 0.81 0.832 5 South North 35,656 44,741 46,461 52,969 0.77 0.84

1 4 South North 54,610 48,881 66,747 59,365 0.82 0.822 5 South North 35,769 45,087 46,461 52,969 0.77 0.85

1 4 South North 56,738 48,015 66,747 59,365 0.85 0.812 5 South North 35,800 44,981 46,461 52,969 0.77 0.85

1 4 South No'rth 57,168 47,767 66,747 59,365 0.86 0.812 5 South North 35,913 45,327 46,461 52,969 0.77 0.86

I01U1I

Table 7 Effect of Skew on Maximum Moments at Midspan of Beams

(Reproduced from Illinois Engineering Experiment Station - Bulletin No. 439)

Percentage reduction in moments in corresponding right bridges

Span Spacing Relative c.p = 30° cp = 45° cp = 60°, of Bridge of Beams Stiffness Rear Combined Rear Combined Rear Combined

a b of Beams Wheels Rear and Wheels Rear and Wheels Rear andft ft H Front Front Front

Wheels Wheels

2 23.4 21.7 30.6 28.9 33.5 32.480 8 5 16.3 16.8 23.8 23.6 30.0 28.1

10 8.3 16.2 25.7

2 26.0 24.6 32.7 31.8 36.6 35.670 7 5 16.6 17.1 26.4 27.5 31.0 ,29.7

10 11.1 17.2 25.3

2 28.6 28.0 33.8 34.3 37.8 37.460 6 5 18.3 19.1 24;6 25.8 32.5 31.4

10 8.7 14.1 20.9

2 28.3 29.5 35.8 37.2 42.9 43.250 5 5 16.7 18.3 23.7 24.6 32.5 33.3

10 5.2 11.3 20.9

Immr

Table 8 Midspan Girder Deflections - Brookville Bridge

Load vehicle positioned ~ith drive wheelson midspan line

(Deflection in inches)

Girder

Lane Direction A B C D

1 NB 0.075 0.073 0.035 0.014

2 NB 0.048 0.078 0.047 0.020

3 NB 0.032 0.066 0.064 0.040

4 NB 0.017 0.046 0.070 0.062

5 NB 0.009 0.030 0.062 0.089

1 NB 0.077 0.075 0.035 0.012

2 NB 0.049 0.080 0.050 0.022

3 NB 0.032 0.066 0.062 0.036

4 NB 0.017 0.046 0.070 0.065

5 NB 0.009 0.030 0.061 0.092

1 SB 0.084 0.071 0.030 0.009

2 SB 0.058 0.082 0.044 0.015

3 SB 0.037 0.073 0.060 0.033

4 SB 0.020 0.051 0.070 0.056

5 BB 0.011 0.036 0.066 0.084

1 SB 0.084 0.072 0.030 0.009

2 SB 0.059 0.084 0.046 0.019

3 BE 0.036 0.072 0.060 0.033

4 BB 0.018 0.042 0.052 0.040

5 BE 0.010 0.033 0.063 0.080

-67-

Table 9 Girder Deflections at Midspan in Berwick Bridge

(Deflections in inches)

GirderLane Direction

A B C D

1 North 0.0800 O.07l0 0.0504 0.0273

2 North 0.0612 0.0718 0.0529 0.0291

3 North 0.0461 0.0682 0.0715 0.0455

4 North 0.0331 0.0538 0.0752 0.0609

5 North 0.0243 0.0428 0.0723 0.0810

1 South 0.0728 0.0649 0.0610 0.0204

2 South 0.0546 0.0677 0.0800 0.0296

3 South 0.0381 0.0617 0.1114 0.0398

4 South 0.0258 0.0478 0.1016 0.0524

5 South 0.0188 0.0372 0.0974 0.0745

IOJOJI

Table 10 Comparison of Girder Deflections

(Load vehicle positioned with drive wheels at midspan)

Deflection, lO-3 inches Ratio

Lane Direction Brookville Berwick Brookville/BerwickA B C D A B C D A B C D

1 North 075 073 035 014 080 071 050 027 0.94 1.03 0.70 0.521 North 077 075 035 012 -- -- -- - -- 0.96 1.06 0.70 0.442 North 048 078 047 020 061 072 053 029 0.79 1.08 0.89 0.692 North 049 080 050 022 -- -- -- -- 0.80 1.11 0.94 0.763 North 032 066 064 040 046 068 072 046 0.70 0.97 0.89 0.-873 North 032 066 062 036 -- -- -- -- 0.70 0.97 0.86 0.784 North 017 046 070 062 033 054 075 061 0.52 0.85 0.93 1.024 North 017 046 070 065 -- -- -- -- 0.52 0.85 0.93 1.065 North 009 030 062 089 024 043 072 081 0.38 0.70 0.86 1.105 North 009 030 061 092 -- -- -- -- 0.38 0.70 0.85 1.14

1 South 084 071 030 009 073 065 061 020 1.15 1.09 0-.49 0.451 South 084 072 030 009 -- -- -- -- 1.15 1.11 0.49 0.452 South 058 082 044 015 055 068 080 030 1.05 1.20 0.55 0.502 South 059 084 046 019 -- -- -- -- 1.07 1.23 0.58 0.633 South 037 073 060 033 038 062 III 040 0.97 1.18 0.54 0.823 South 036 072 060 033 -- -- -- -- 0.95 1.16 0.54 0.824 South 020 051 070 056 026 048 102 052 0.77 1.06 0.69 1.084 South 018 042 052 040 -- -- -- -- 0.69 0.88 0.51 0.775 South 011 036 066 084 019 037 097 074 0.58 0.97 0.68 1.145 South 010 033 063 080 -- -- -- -- 0.53 0.89 0.65 1·.08

Im1OI

Table 11 Comparison of Girder Deflections

(Two Load Vehicles Traveling in Same Direction)

Deflection, 10-3 inches Ratio

Lane. Direction Brookville Berwick Brookville/BerwickA B A B A B C D A B C D A B C D

I 4 North North 092 119 105 076 113 125 126 088 0.81 0.95 0.83 0.862 5 North North 057 108 109 109 086 115 125 110 0.66 0.94 0.87 0.99

1 4 North North 092 119 105 079 113 125 126 088 0.81 0.95 0.83 0.902 5 North North 057 108 108 112 086 115 125 lID 0.66 0.94 0.86 1.02

1 4 North North 094 121 105 074 113 125 126 088 0.83 0.97 0.83 0.842 5 North North 058 110 112 III 086 115 126 110 0.67 0.96 0.90 1.01

1 4 North North 094 121 105 077 113 125 126 088 0.83 0.97 0.83 0.882 5 North North 058 110 III 114 086 115 125 110 0.67 0.96 0.89 1.04

1 4 South South 104 122 100 065 099 113 163 073 1.05 1.08 0.61 0.892 5 South South 069 118 110 099 073 105 177 104 0.94 1.12 0.62 0.95

1 4 South South 102 113 082 049 099 113 163 073 1.03 1.00 0.50 0.672 5 South South 068 115 107 100 073 105 177 104 0.93 1.10 0.60 0.96

1 4 South South 104 123 100 065 099 ·113 163 073 1.05 1.09 0.61 0.892 5 South South 070 ' 120 112 103 073 105 177 104 0.96 1.14 0.63 0.99

l 4 South South 094 114 082 049 099 113 163 073 0.95 l.Ol 0.50 0.672 5 South South 069 117 109 099 073 105 177 104 0.94 1.,11 0.62 0.95

J'J0I

Table 12 Comparison of Girder Deflections

(Two Load Vehicles Traveling in Opposite Directions)

Deflection, lO-3 inches Ratio

Lane Direction Brookville Berwick Brookville/BerwickA B A B A B C D A B C D A B C D

1 4 North South 095 124 105 070 106 119 152 080 0.90 1.04 0.69 0.882 5 North South 059 114 113 104 080 109 150 104 0.74 1.04 0.75 1.00

1 4 North South 093 115 087 054 106 119 152 080 0.88 0.97 0.57 0.682 5 North South 058 III 110 100 080 109 150 104 0.72 1.02 0.73 0.96

1 4 North South 097 126 105 068 106 119 152 080 0.92 1.0,6 0.69 0.852 5 North South 060 116 116 106 080 109 150 104 0.75 1.06 0.77 1.02

1 4 North South 095 117 087 052 106 119 152 080 0.90 0.98 0.57 0.652 5 North South 059 113 113 102 080 109 150 104 0.74 1.04 0.75 0.98

1 4 South North 101 117 100 071 106 119 136 081 0.95 0.98 0.74 0.882 5 South North 067 112 114 077 079 110 152 III 0.85 1.02 0.75 0.69

1 4 South North 101 117 100 074 106 119 136 081 0.95 0.98 0.74 0.912 5 South North 067 112 105 107 079 110 152 III 0.85 1.02 0.69 0.96

1 4 South North 101 118 100 071 106 119 136 081 0.95 0.99 0.74 0.882 5 South North 068 114 108 108 079 110 152 III 0.86 1.04 0.71 0.97

1 4 South North 101 118 100 074 106 119 136 081 0.95 0.99 0.74 0.912 5 South North 068 114 107 III 079 110 152 III 0.86 1.04 0.70 1.00

I....Jf---lI

Table 13 Maximum Strain at Bottom Surface of Girder - Brookville Bridge

(One Load Vehicle)

(lO-6 in/in)

Section £1 Section E2 Se.ction ILane Direction Left Right Left Right Left Right

1 North 36.7 43.7 33.9 40.2 31.0 25.82 North 28.5 28.3 26.6 27.5 36.3 32.73 North 18.4 15.8 19.7 19.1 27.8 34.84 North 11.7' 9.2 12.7 12.0 20.0 19.65 North 6.0 5.5 9.2 7.0 13.7 11.9

1 North 35.4 43.1 33.5 40.5 33.9 25.52 North 26.2 28.5 30.1 28.4 37.2 35.03 North 18.4 15.4 19.6 17.2 '26.2 33.44 North 11.0 8.7 12.3 10.4 19.8 19.25 North 6.9 4.3 7.4 4.6 14.0 11.9

1 South 37.2 41.5 35.8 43.6 36.0 27.22 South 26.8 24.6 26.9 28.6 36.5 34.73 South 18.'2 16.9 19.3 19.7 25.1 30.04 South 10.0 8.9 13.8 9.5 10.9 15.45 South 8.0 4.1 7.9 6.0 13.4 11.6

1 South 37.1 37.0 36.9 45.6 34.6 27.52 South 24.8 23.1 '26.5 27.7 38.4 34.23 South 19.3 15.5 19.5 19.4 24.4 31.54 South 11.1 8.0 12.3 11.3 19.0 15.75 South 7.9 5.0 7.0 7.1 12.1 11.8 I

.....,J1'0I

Table 14 Maximum Strain at Bottom Surfaceof Girder - Berwick Bridge

(lO-6 in/in)

Exterior InteriorTruck Location Left Right Left Right

Lane 1 38.9 42.0 34.8 3-0.9

Lane 2 31.4 30.1 34.0 34.2

Lane 3 23.2 19.5 29.5 32.2

Lane 4 17.9 15.0 23.6 23-.7

Lane 5 11.7 9.2 18.9 15.8

1......j

LNI

Table 15 Maximum Strain at Bottom Surface of Girder - Brookville Bridge

(Two Load Vehicles Traveling in Same Direction)

(10- 6 in/in)

Lane Direction Section E1 Section E2 Section I

A B A B Left Right Left Right Left Right

1 4 North North 48.4 52.8 46.6 52.3 51.0 45.42 5 North North 34.4 33.8 35.8 34.4 49.9 44.6

1 4 North North 47.7 52.4 46.2 50.6 50.8 45.02 5 North North 35.4 32.6 34.1 32.0 50.3 44.6

1 4 North North 47.1 52.3 46.2 52.6 53.8 45.12 5 North North 32.2 34.0 39.2 35.4 50.9 46.9

1 4 North North 46.3 51.8 45.8 50.9 53.7 44.72 5 North North 33.2 32.8 37.5 33.0 51.2 47.0

1 4 South South 47.2 50.4 49.6 53.1 46.9 42.62 5 South South 34.8 28.7 34.8 34.5 50.0 46.3

1 4 South South 48.3 49.5 48.1 54.9 55.0 42.92 5 South South 34.6 29.6 33.9 35.6 48.6 46.6

1 4 South South 47.1 45.9 50.8 55.1 45.5 42.92 5 South South 32.8 27.3 34.4 33.7 51.9 45.8

1 4 South South 48.2 45.0 49.3 56.9 53.6 43.22 5 South South 32.7 28.2 33.5 34.8 50.5 46.1

I-....j

~I

Table 16 Maximum Strain at Bottom Surface of Girder - Brookville Bridge

(Two Load Vehicles Traveling in Opposite Directions)

(10-6 in/in)

Lane Direction Section E1 Section E2 Section I

A B A B Left Right Left Right Left Right

1 4 North South 46.7 52.6 47.7 49.7 41.9 41.22 5 North South 36.5 32.5 34.6 33.4 49.7 48.1

1 4 North South 47.8 51.6 46.2 51.5 49.9 41.52 5 North South 36.4 33.4 33.7 34.5 48.4 44.6

1 4 North South 45.4 52.0 47.3 50.0 44.8 40.92 5 North South 34.3 32.6 38.0 34.4 50.6 46.7

1 4 North South 46.4 51.1 45.8 51.8 52.8 41.22 5 North South 34.2 33.6 37.1 35.5 49.3 46.9

1 4 South North 48.9 SO.7 48.6 55.6 56.0 46.82 5 South North 32.7 30.1 36.0 35.5 50.2 46.6

1 4 South North 48.2 50.2 48.2 54.0 55.8 46.52 5 South North 33.7 28.9 34.3 33.1 50.6 46.6

1 4 South North 48.8 46.2 49.7 57.7 54.6 47.12 5 South North 30.8 28.6 35.7 34.7 52.1 46.1

1 4 South North 48.1 45.7 49.3 56.0 54.4 46.82 5 South North 31.7 27.4 33.9 32.3 52.5 46.1

I-...JU1I

Table 17 Maximum Strain at Bottom Surface of Girder ­Berwick Bridge

(Two Load Vehicles)

(lO-6 in/in)

Exterior Interior

56.9 (Avg) 56.4 (Avg)

41.2 (Avg) 51.4 (Avg)

Truck Location

Lanes 1 and 4

Lanes 2 and 5

Left

56.8

45.1

Right

57.0

39.3

Left

58.4

52.9

Right

54.6

50.0

I-...j

enI

Table 18 Comparison of Averaged Maximum Strainsat Bottom Surface of Girder

-77 -

(Ratio of value from Brookville Bridge to value from Berwick Bridge)

One Vehicle

Lane Direction Exterior InteriorLeft Right Left Right

1 North 0.92 1.03 0.93 0.832 North 0.87 0.94 1.08 0.993 North 0.79 0.80 0.92 1.064 North 0.63 0.60 0.84 0.825 North 0.55 0.53 0.73 0.75

1 South 0.95 0.94 1.02 0.882 South 0.82 0.79 1.10 1.013 South 0.81 0.83 0.84 0.964 South 0.59 0.56 0.63 '0.665 South 0.68 0.50 0.68 0.74

Two Vehicles

Lane Direction Exterior InteriorA B A B Left Right Left Right

1 4 North North 0.84 0.92 0.90 0.822 5 North North 0.78 0.85 0.96 0.92

1 4 South South 0.84 0.84 0.86 0.782 5 South South 0.78 0.72 0.95 0.92

1 4 North South 0.82 0.91 0.81 0.752 5 North South 0.82 0.84 0.94 0.93

1 4 South North 0.85 0.84 0.94 0.862 5 South North 0.75 0.73 0.97 0.93

Table 19 Effective Slab Width

(inches)

Section El Section E2 Section ILane Direction Slab Curb Parapet Slab Curb Parapet Slab

1 North -95. 00 33.00 2.51 95.00 33.00 4.66 87.182 North 95.00 24.50 0 95.00 15.45 0 99.143 North 95.00 14.93 0 95.00 16.86 a 110.824 North 95.00 0.75 0 6.18 0 0 11l.685 North 61.57 0 0 12.49 0 0 69.13

1 North 95.00 33.00 2.98 95.00 25.69 0 111.952 North 95.00 24.76 0 49.28 0 0 84.353 North 95.00 25.53 0 95.00 17.97 0 106.414 North 95.00 9.25 0 95.00 11.15 0 90.845 North 83.26 0 0 95.00 31.99 0 74.26

1 South 95.00 24.38 0 95.00 24.37 0 97.532 South 95.00 33.00 0.12 95.00 14.36 0 81,.013 South 95.00 26.08 0 95.00 19.06 0 120.104 South 95.00 15.72 0 35.21 0 0 41.635 South 95.00 33.00 8.93 6.04 0 0 64.73

1 South 95.00 33.00 2.43 95.00 30.38 0 82.512 S_outh 95.00 33.00 3.60 95.00 16.48 0 72.763 South 95.00 33.00 0.73 95.00 16.62 0 101.104 South 95.00 27.21 0 95.00 15.18 0 65.515 South 73.71 0 0 95.00 7.15 0 82.09

I-Jco1

Table 20 Neutral Axis Location

[Location given as distance (inches) above bottom girder surface]

Section E1 Section E2 Section ILane Direction Left Right Left Right Left Right

1 North 31-.69 28.98 32.02 29.80 24.53 27.112 North 26.24 24.95 29.93 25.78 25.28 27.863 North 32.99 22.61 30.21 25.81 29.70 24.744 North 31.11 20.97 21.89 25.15 28.09 26.445 North 26.08 20.92 16.00 19.59 26.86 22.17

1 North 31.15 29.78 30.92 26.96 26.06 28.492 North 31.89 25.80 . 18.79 26.26 25.99 25.283 North 31.96 25.88 30.81 25.46 29.74 24.224 North 31.66 22.60 31.04 23.6-8 28.78 23.355 North 30.56 19.77 31.40 27.67 27.51 22.32

1 South 30.89 26.72 30.l2 27.49 25.48 27.472 South 31.72 27.61 29.27 26.20 25.42 25.393 South 32.79 25.16 30.06 26.44 30.13 25.254 South 33.44 22.33 19.40 22.62 23-. 03 20.825 South 31.68 32.29 23.27 23.55 27.06 21.25

1 South 32.34 28.28 30.77 28.00 24.49 26.532 South 32.18 29.07 30.37 25.57' 24.80 24.803 South 32.64 27.04 30.46 25.52 28.72 24.644 South 33.47 24.70 30.71 24.94 26.96 21.485 South 29.86 19.05 31.43 22.32 28.51 22.45 I

'-JillI

lO. FIGURES

-80-

-81-

.tn'n~

East

33'- 6"

21-9'~ 28'-0" 2 1-9 11

o

5

[

c

234

\ ~Iope Y411FtJSlope Y4"/12.\

BA

=(\1-,o.1

'"

3 1-6" 3 Spaces @ a'-Io" = 26'-6 11 3 1-6"

Scale:II" 1 0 tI/4 =1 -

Fig. 2 Cross-Section of Brookville BridgeIrorvI

661-10" North

.....

50'-0"

~ ..,..---Midspan""<, Line(Skew)

"

I Midspan Li ne~ (Perpendicular)"

II

AirHose~lII

50'-0"

II

l"-Air HoseII

Fig. 3 Plan View of Bridge Deck

IOJLNI

-84-

homferomer

~.0' <I

<1 ,p.-4 <1= 4- .q 4. , d 4

LO .4 d A

r--: rO '<1 4 , 4, t4 <J P",

Q P'I>

4( 4'\ d .d

4. At\

•I> ,

4

'" A

V..

q0 CD ,

~.C\JCD

ro3 11 Chamfer,

4 -4

.I

/4Corners d.

~Ie.G.s. · 4<l

·~.28111 .1 - ;b

0 ,P .a• tJ , 4 11 . . / 3/4" C~ LO~ <4 <I

'"5.0" 38.0" 5 0 II ""'-Bot t

· - Corn48.0"- I

Fig. 4 Composite Girder Cross-Section

Legend:

o Deflection GageI

: Fully Gaged SectionI

x Single SR-4 Gage North

D" (18,36) x (118)

,(17,35)

Sec. E2 (gages 101-108)

Sec. EI (gages 1-8) ,.

A

c

B~"<----------Sec.I(goges 9-16) '< -

Fig. 5 Underside Detail Showing Gaged Sections

(viewed from top)

IcoLnI

o

18,118

1,1011 18.108 91

2,1021 A 17,107 101 l B

3,1031 16,106 ·111 14

4.104 5,105 12 13 . 17

Fig. 6 Cross-section Showing SR-4 Gages Consideredin Evaluation for Moment Coefficients

IcoOJI

VOLTAGE REGULATOR

95 - 130 v. INPUT

110 v. OUTPUT

"

OSCILLATOR

REFERENCE SIGNAL

-87 -

r.,-- SR-4

AMPLIFIER.......

AND-~GAGE CIRCUIT

1SIGNAL ALTERED .BY

GAGE ACTIVITY

+OSCILLOGRAPHGALVANOMETER

Fig. 7 Instrumentation Flow Chart

-88-

Fig. 8a Underside of Test Bridge, Showing Skewand Instrumentation

Fig. 8b Detail of Instrumentation, Showing SR-4 Gagesand Deflectometer

-89-

13.0'

o•LO

20.4'

AXLE AND TRACK SP,ACI NG

Front Drive Rear

i ~ t·9,890 31,945 31,445

Before Testing

~ t •10,000 32,640 31,940

After Testing

AXLE LOADS (LBS.)

Fig. 9 Test Vehicle

2<t.3 4 5

," I

-5.01 -3.4 -8.91 1-9.4

18.41 19.9 13.31 14.5A 8 C D

31.71 :35.3 26.41 23.6- - -

37.7 ~ 41.2

0.0806 11

35.3 30.4

~0.0680"

174

~0.0465 11

13.5

~0.0249"

Fig. lO Typical Strain Data Tabulation

Il.DoI

50,000

40,000·,

MOMENTCOEFFICIENT 30,000( FT. - IN. 2 )

20,000

10,000

-- Northbound

--- Southbound

2 3

LANE

4 5

Fig. II Maximum Moment Coefficients at Section ElI

LOl--'I

50,000

40,000

MOMENTCOEFFICIENT 30,000(FT.-IN.2)

20,000

10,000

-- Northbound

--- Southbound

2 3

LANE

4 5

Fig. 12 Maximum Moment Coefficients at Section E2I

1OrvI

50,000

40,000

MOMENTCOEFFICIENT 30 000 ~--~~--,._--,(FT.-IN.2)

20 000--,

10,000

'30 'l Cj

Northbound

--- Southbound

2 3

LANE

4

/>

\

5

\..

Fig. 13 Maximum Moment Coefficients at Section I~

Iill-LNI

Sec. EI

-94-

60,000 IN,4S........IN,4N-..15,45......IS,4N"""

........... 50,000C\J

Z ......-2S,5N. 2N,5S

~LL........... 40,000

~25,58-..

.' 2S,5N-..Z 2N,5~l1J 2N,5UlJ.. 30,000LLW0t)

I-ZlLJ 20,000~0::E N - Northbound

S - Southbound

10,000

o""""-------------------~--Sec. 1

Fig. 14 Superimposed Moment Coefficients (Average)

Load vehicles traveling in lanes anddirections indicated on plot

North

,

5 '< Ib A< • ID ~

'\.

4'< ID '< I ID ID" >,

LaneNumber

3'< ('b >k ID I~

"2 " 11> I >, ID ID >,

,Sec. EI

Fig. lS Vehicle Location in Each Lane to Produce MaximumResponse at Section El

First Set of Northbound Runs

IU)U1I

North

"

5 '< '1'> '< It> 11) "

,4'< 10: >( I ID rD ' ...

"2 '< If} I >c ID ID >

3 '< ID >L If) 1[:1 "Lone

Number

" Sec.E I

Fig. l6 Vehicle Location in Each Lane to Produce MaximumResponse at Section El

Second Set of. Northbound Runs

ILO01I

North

,

5 '" c::u)<Q.I I dl ' ..

"4 " <1.1 '<QI I c1l ' ..

,LaneNumber

3 '< <1.1 <II 'I dI ' ..

2"'<: . I<Il I<11 > ~---~~--~,...

" )I----Sec. EI

Fig. l7 Vehicle Location in Each Lane to Produce MaximumResponse at Section El

First Set of Southbound Runs

ILO'-JI

North

"5 "< ([I ) , <11 I a I >

4 "< ([I ),crl I c3l).

" I

LoneNumber

3 '< <11 ell 'l <[I "

2 "< <II I <11 <11 >.

" Sec. EI

Fig. 18 Vehicle Location in Each Lane to Produce MaximumResponse at Section El

Second Set of Southbound Runs

I1O00I

North

"

5 '< It> '< 11'> u:> ",

4 '< 11' >( I ID ID ' ...

"2',<------:.-...-.-11D------+-1-~)...<----lID-------'ID--------~>,

3 '< ID 'k ID 11;1 >,

LoneNumber

l--sec. E2

Fig. 19 Vehicle Location in Each Lane to Produce MaximumResponse at Section E2

First Set of Northbound Runs

I1O1...0I

North

"

5 '< ID '< I ID II>-~

,4 " It> ' < I 1D' ID >'1

"2 '< ID 1'< ID 11> "

3 '" ID 1< ID II:) ' ..

LaneNumber

I--sec. E2

Fig. 20 Vehicle Location in Each Lane to Produce MaximumResponse at Section E2

Second Set of Northbound Runs

IraooI

North

'\,

5 " CJ I )( Cli I <II '.

,4 'c Cli Cli >( I ell )L: ...

3 'c <J I Cli 1 01 >

LaneNumber

......

2' "c CJ I a I ell '

I--- Sec. E2

Fig. 21 Vehicle Location in Each Lane to Produce MaximumResponse at Section E2

First Set of Southbound Runs

Il-'oI--JI

North

......

5 '< QJ aJ 'Q 1 ' ...

......

4 " 01 al >. ctl > ....

3 c: <:II CIt 1 Cit '

LaneNumber

,2 " OJ I 0 I > c: CJ I > ...

l---sec. E2

Fig. 22 Vehicle Location in Each Lane to Produce MaximumResponse at Section E2

Second Set of Southbound Runs·

Il-'otvI

North

"

./"4 ", 10 > I In In '

5 'c ID ' I 10 ID >

.~

LoneNumber

3 'c ID )f ID ID ' ...

Sec. I2 " II:) I XID ID "'-

"

Fig. 23 Vehicle Location in Each Lane to Produce MaximumResponse at Section I

First Set of Northbound Runs

If--JoLNI

'\_._---,~-~~---~-

North

"5 '< Ie: >( olD 1[;) >~

"4 "'< le'< I ID ID ' ..

Sec. 12'< ID

________.1-1-~'lD

------....JID-----------..::~>",

3 '< ID )Ok ID ID >.

LaneNumber

"

Fig. 24 Vehicle Location in Each Lane to Produce MaximumResponse at Section I

Second Set of Northbound Runs

I}--Jo...p::..I

North

,

5 ' () I CJ I < I Q.I >",

"4 > al Cli I Cli >

3 "< a I lc a I QJ ' ..

Sec. I2 ' (J I I elll c a I ' ...

'"

Fig. 25 Vehicle Location in Each Lane to Produce MaximumResponse at Section I

First Set of Southbound Runs

Ij--JolJ1I

North

"5 " «J QJ > I e:u >< < ,

4 '< QJ c:J 1 > < I "lJ >,

Sec. I

" I3 >< <1.1 >l QJ QI "

LaneNumber

"

Fig. 26 Vehicle Location in Each Lane to Produce MaximumResponse at Section I

Second Set of Southbound Runs

It--JoenI

A

2

B

3 4

c

5

-107-

D

0.076 0.074 0.035 0.013

0.048 0.079 0.048 0.021

I I1

I I0.032 0.066 0.063 0.038

0.017 0.046 0.070 ·0.064

0.009 0.030 0.062 0.090

Fig. 27 Deflection Due to Indicated Lane Loading (inches)

Northbound runs

-108-

~ I 2 3 4 5 ~A B C 0

0.084 0.072 0.030 0.009

0.058 0.083 0.045 0.018

lI II I

0.036 0.072 0.060 0.033

l I1 I0.019 0.046 0.061 0.048

0.010 0.034 0.064 0.082

Fig. 28 Deflection Due to Indicated Lane Loading (inches)

Southbound runs

A

N

2

B

3 4

c

N

5

-109-

o

0.093 0.120

N

0.105

N

0.076

0.058

S

0.109 0.110

S

0.112

0.101 O~118

S

0.091

s0.057

0.069 0 .. 1-18 0.110 0.100

Fig. 29 Deflections With Two Lanes Loaded

Vehicles superimposed in same direction

A

N

2

B

3 4

c

s

5

-110-

o

0.095 0.120

N

0.096

s0.061

0.059

s0.114 0.113

N

0.103

0.101 0.113

s

0.100

N

0.072

0.068 0.113 0.108 0.101

Fig. 30 Deflections With Two Lanes Loaded

Vehicles superimposed ~n opposite direction

-111-

IS -r--

........ 2S

- 35-

45Iiooo-....

5S - -

l"----J]50

40

30

20

10

°L RSECTION EI

[\ J]50

40

30 28

20 35

4810 5S

°L RSECTION E2

[\ J]50

40

30

20 45

10 55

L- RSECTION I

~ ~50

40

30 2N

20 3N

104N

N

o L RSECTION EI

,....x

C' J](.)

z""'-enw 50J:()

40zI

0 30 2Ncr:g 20 ~N:e 4N...., .

z 10<t 5Na:: 0I- L Ren SECTION E2

[' !J50

40

30

204N

5N

10

L RSECTION I

Fig. 31 Maximum Strain at Bottom of Beam

Single vehicle loading - vehicle travelingin indicated lane and direction

-112-

C' ~ [' ~ [' :J:~tl

15,45

I

50 50 LT IS,4N

40 2N,5S 40~----- IL 2S,5N

30 30 30

20 20 20

10 10 10

o L 0 0R L R L R

SECTION EI SECTION EI SECTION EI

C' :J .C' ~ ~ J]I I IS,4N

50t 50t 50

40 40 2N,5S 40 rl 2S,5N

30 30 30

20 20 20

10 10 10

0 o L 0L R R L R

SECTION E2 SECTION E2 SECTION E2

.[' ~ r; J [' !J50 2S,5S 50 50

40 40 40

30 30 30

20 20 ' 20

10 10 10

o L o L o LR R R

SECTION I SECTION I SECTION IR

50r-r I

40 l-I - 2N ,5N

30

20

10

o L

SECTION I

~ J]50 11 IN,4N

4°11 2. N, 5N

30

20

10

o L RSECTION EI

,.....

[; ~J:UZ

""en 50IJJJ:U 40z,

3000::0 20:11....... 10z<C o L0::: RI-

SECTION E2en

IFig. 32 Maximum Bottom Strain With Two Load Vehicles

Vehicles traveling in indicated lanes and directions

11. REFERENCES

1 Walther, R. E.INVESTIGATION OF MULTI~BEAM BRIDGES, Fritz EngineeringLaboratory Report 223.14, August 1956

2 Ruudlett, J. C.PRESTRESSING PRACTICE IN BRIDGE BUILDING, ASCE Proceedings,July 1955, Vol. 81, No. 733

3Douglas, W. J. and VanHorn, D. A.LATERAL DISTRIBUTION OF STATIC LOADS IN A PRESTRESSED CON­CRETE BOX-BEAM BRIDGE, Fritz Engineering Laboratory Report315.1, August 1966

4Pennsylvania Department of Higt~ays, Bridge DivisionSTANDARDS FOR PRESTRESSED CONCRETE BRIDGES, 1960

5American Association of State Highway OfficialsSTANDARD SPECIFICATIONS FOR HIGHWAY BRIDGES, Washington,D. C., 1961

6 Guilford, A. A. and VanHorn, D. A.LATERAL DISTRIBUTION OF VEHICULAR LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE - BERWICK BRIDGE

7 Newmark, N. M., Siess, C. P., and Penman, R. R.STUDIES OF SLAB AND BEAM HIGHWAY BRIDGES, PART I - TESTSOF SIMPLE-SPAN RIGHT I-BEAM BRIDGES, University of IllinoisEngineering Experiment Station, Bulletin No. 363, March 1946

8 Newmark, N. M., Siess, C. P., and Peckham, W. M.STUDIES OF SLAB AND BEAM HIGHWAY BRIDGES, PART II - TESTSOF SIMPLE-SPAN SKEW I-BEAM BRIDGES, University of IllinoisEngineering Experiment Station, Bulletin No. 375, January1948

9 Chen, T. Y., Siess, C. P., and Newmark, N. M.STUDIES OF SLAB AND BEAM HIGHWAY BRIDGES, PART VI - MOMENTSIN SIMPLY-SUPPORTED SKEW I-BEAM BRIDGES, University ofIllinois Engineering Experiment Station, Bulletin No. 439,Jan~ary 1957

-113-

10 Bouwkamp, J. G.BEHAVIOR OF A SKEW STEEL-DECK BRIDGE UNDER STATIC ANDDYNAMIC LOADS, Report No. SESM-65--2, College of Engineering,Office of Research Services, University of California,Berkeley, April 1965

llLehigh University, Computing LabWIZ COMPILER MANUAL, Bethlehem, Pennsylvania, September 1964

-114-