STRUCTURAL RESPONSE OF A 45° SKEW PRESTRESSED. …

STRUCTURAL RESPONSE OF A 45° SKEW

PRESTRESSED. CONCRETE BOX~GIRDER

HIGHWAY BRIDGE SUBJECTED TO

VEHICULAR LOADING

BROOKVILLE BRIDGE

by

Thomas Schaffer

FRITZ ENGINEERINGLABORATORY LIBRARY

STRUCTURAL RESPONSE OF A

45~ SKEW PRESTRESSED CONCRETE

BOX-GIRDER HIGHWAY BRIDGE

SUBJECTED TO VEHICULAR LOADING

BROOKVILLE BRIDGE

by

Thomas Schaffer

A THESIS

Presented to the Graduate Faculty

of Lehigh University

in Candidacy for the Degree of

Master of Science

FRITZ Ej\JGlr~EERIj\JG

LABORfiTOR'y' LJBR/~fr(

Lehigh University

1967

CERTIFICATE OF APPROVAL

This thesis is accepted and approved in partial

fulfillment of the requirements for the degree of Master of

Science in Civil Engineering.

(Date)

Professor D. A. VanHornProfessor in Charg~, and Chairman,Department of Civil Engineering

i

STRUCTURAL RESPONSE OF A 45° SKEW PRESTRESSED CONCRETE i-~ tpBOX-GIRDER HIGHWAY BRIDGE SUBJECTED TO VEHICULAR LOADING

BROOKVILLE BRIDGE

by Thomas Schaffer

.Durirlg t11e sumrners of 196 L)" 1965, a:nd .1'966, a series of

field tests were conducted on five prestressed concre'te box-beam

11:Lg-llVJtS,y bridg'es located ill the Cornm011tJJealth of Pen11sylvania_

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

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

each bridge was subjected to vehicular loading consisting of a

3-axle truel\. vvhich was a close sirnulatioll of tIle AASHO f"lS20 de-

sign vellicle.

This report, based on the test of the Brookville Bridge,

cO!1taiI1S (1) cl det'a:Lled deSC1~iptiorl of tile ld test procedure

c!nd equipfnent, (2) ;;1 cOJnplete outline and flow CflcU:,t of tr\6 eOl'n-

puter prog'rarH used iXl the pl"oCessirig arlel arlalysis of t:he data,

( 3) a s u-mmary of tlle rnea.sured s'tructural I"es pons e the

, irlc~luding a, cornpa,risori witll aright bridge having ne~lrly

identiccil overall dimensions and member sizes"

Initially, separate reports are being prepared on the

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

reports is to present a detailed ption of the

havior each of all se

:t:1eport vvill

ABSTRACT

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

field tests were conducted on five prestressed concrete box-beam

highway bridges 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 de

sign vehicle.

This report, based on the test of the Brookville Bridge,

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

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

puter program 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

3.2.1 Strain Calculation l3

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

5.1 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 Sununary 28

6.2 Conclusions 30

7., ACKNONLEDGMENTS 34

8. APPENDIX 35

9. TABLES 59

10. .FIGURES 80

11. REFERENCES 113

12. VITA lIS

iv

LIST OF TABLES

Table

1 Test Bridge Characteristics 60

2 Maximum Moment Coefficients, Crawl Run Loading 61

3 Maximum Moment Coefficients at Midspan for 62Berwick Bridge, Crawl Run Loading

4 Comparison of Maximum Moment Coefficients 63at Midspan



7 Effect of Skew on Maximum Moments at Midspan 66of Beams

8 Midspan Girder Deflections - Brookville Bridge 67

9 Girder Deflections at Midspan in Berwick Bridge 68

10 Comparison of Girder Deflections 69



13 Maximum Strain at Bottom Surface of Girder - 72Brookville Bridge

14 Maximum Strain at Bottom Surface of Girder - 73Berwick Bridge



17 Maximum Strain at Bottom Sllrface of Girder - 76Berwick Bridge

18 Comparison of Averaged Maximum Strains at 77Bottom Surface of Girder

19 Effective Slab Width 78

20 Neutral Axis Location 79

v

Figure

1

2

3

4

.5

6

7

8a

8b

9

10

11

12

13

14

15

16

17

18

19

20

21

LIST OF FIGURES

Test Bridge

Cross-Section of Brookville Bridge

Plan View of Bridge Deck

Composite Girder Cross-Section

Underside Detail Showing Gaged Sections

Cross-Section Showing SR-4 Gages Consideredin Evaluation for Moment Coefficients

Instrumentation Flow Chart

. Underside of Test Bridge, Showing Skewand Instrumentation

Detail of Instrumentation, Showing ·SR-4Gages and Deflectometer

Test Vehicle

Typical Strain Data Tabulation

Maximum Moment Coefficients at Section El

Maximum Moment Coefficients at Section E2

Maximum Moment Coefficients at Section I

Superimposed Moment Coefficients (Average)

Vehicle Location in Each Lane to ProduceMaximum Response at Section £1

Vehicle Location in Each Lane to ProduceMaximum Response at Section El

Vehicle Location in Each Lane to ProduceMaximum Response at Section E1


Vehicle Location in Each Lane to ProduceMaximum Response at Section £2

Vehicle Location in Each Lane to ProduceMaximum Response at Section E2.


vi-

81

82

83

84

85

86

87

88

88

89

90

91

92

93

94

95

96

97

98

99

100

101

Figure

22

23

24

25

26

27

28

29

30

31

32


Vehicle Location in Each Lane to ProduceMaximum Response at Section I




Deflection Due to Indicated Lane Loading

Deflection Due to Indicated Lane Loading

Deflections With Two Lanes Loaded

Deflections With Two Lanes Loaded

Maximum Strain at Bottom of Beam

Maximum Bottom Strain With Two Load Vehicles

vii

102

103

104

105

106

107

108

109

110

III

112

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 combinatione

Instrumentation was arranged to measure strains in beams, slab,

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

indicated principally t~at~ (1) positive composite action ~xists

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 believed 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 60° skew angles. a 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 theoretic~l analysis of the same type

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

60° 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 whi.ch 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

California10 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-supporte~ 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-tb-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 parapet walls are linked to the s~ab by

reinforcing steel in much the sam~ 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 curvatur~ 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

in~hes, 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 antisymrnet

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

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girder. These gages are a type devised by ~he 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

Corporation. 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 where deflec

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

cantilever 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-Sl6-44 de

sign loading,5 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 ~pecified 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 stud.ied in preparati..on 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 ~ach 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 Ollt 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 give? 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.

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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 deflection 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 response. 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 ~tructure" 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.

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The apparent strain in any gage is given by

where R = gag~ 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 = tiLL

operating attenuationX'ca~ibrating 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 deflection

where e = 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 corn-

puter output, they were tabulated on a schematic· cross-sectiqn

view of the test bridge, with each ~train 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 unr~asonable 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

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evaluated on the basis of a quantity termed the moment coeffi

clent. 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 effective 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 reinforcement 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 th~s report. The program was written

in the General Electric-Lehigh University LEWIZ compiler language.11

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

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in detail. Other contents in the append,ix are a printout of the

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

output sheet.

-18-

4. PRESENTATION 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 positiori 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 comparis.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 through 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

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

with similar research. Values given are the degree of moment

-l9-

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

mid~pan on the structure. This condition was imposed in o'rder to

provide a qualitative comparisQn 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 sla~ 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· and 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.

-21-

5. DISCUSSION OF TEST RESULTS

5.l 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 predicta.ble, 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 sOhthbound 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 El 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 report9 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 vehicle 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

30° 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

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 varying 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. "All deflections 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 lJy 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

composi~e section properties, which art 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

elastic moduli between the bridges. The disagreement is also, no

doubt influenced by 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 oscil~o

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 d~als 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 six

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

only to a structure of 45° skew, as it was·

previously established that the moment re

duction varies with the degree of skew.s,s

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

bri~ge 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

-31-

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 ~valuation 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

compa~able to those in the right bridge,

and in. general, the magnitudes were

sl'ightly 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 Roads.

The Lehigh University staff was represented in testing

by Mr. A. A. Guilford, Principal Investigator, and- by Messrs. W. J.

Douglas and R. J. Dietz. Data reduction and computer programming

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.

-34a-

The author wishes to extend gratitude to Professor D. A.

VanHorn for guidance and assistance rendered during all phases of

work leading up to, and particularly including, preparation of this

thesis.

-34b-

8. APPENDIX

The computer program used- ~n 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 valuesrequire.d for least ~....- .....

squares fit

Read (N) numberof good strain

values, runnumber

-37-

Read coordinatesof next strain

loc.ation

Add coordinatesof point in

L8 series

compute fittedvalues for

NA location,strain at bottom

es

no

1

Read bridge constants, number of

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

Initialize ·subscriptsstrains left and right,

and moment valuestorage location

Print column headingsfor interior beam

moment values

Interior Beam Program

-38-

. Take appropriate strainandNA values from L8 fit

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

Compute ef activeslab width by

bal.ancing areasabout NA

Compute Ix ofsegments, thencombine to get

total Ix

Compute I y ofsegmentS' and

combine to gettotal I y-

symmetrical section

Rl

compute I aboutinclined axis (1M)

Produc t (IMN),angle of loadapplication ct'

compute verticalmoment component

MX

R2

-39-

Increase subscriptsfor strain, NA,moment values

to denote nextinterior storage

location

Initialize subscriptswhich denote exterior

beam locations

no

no

Exterior Beam Program

ApprOX~lHate slabwidth taken to betrue effective width

Reaq. sectionvalues--beam depth,

slab thicknessnumber-r'Uns 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~adjacent beam

compute approximateslab width by balancingarea moments about NAx

Isapproximateslab width

greater thanmaximumllowed?

Maximum slab widthtaken to be trueeffective width

R3

-40-

R4

L1

Curb widthcalculatedtaken to beeffectivecurb width

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 anns,

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 (qJ)

. R3

R3

R4

R4

-41-

compute verticalmoment component

MXE

Print valueseffective slab, curb,

arapet width MXE,

Increase subscriptsfor strain, NA,

moment values todenote next exterior

storage location

Read number of setsf runs to be combined

for distributioncoefficients

Print explanatoryinformation

Read number runswithin followinget--Print colu

headings

R3

no

Distribution CoefficientProgram

RS

R4

no

-42-

-43-

Read Lane, Speed,Position, and

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

Locate necessarymoments and combineto get percentage

values

no

noPrint values forane, speed, position

and momentpercentages

END

NOTATION IN DISTRIBUTION COEFFICIENTS PROGRAM

Least Squares Program

NAS

T,0T

sx,sxxSY,SXyD,A,BN

RXyS(J)

NA(J)

neutral axis--averaged horizontalstrain determined by least squares fit at bottom

of beam ,total number of sets of strain readings to be

considered in-Ieast 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 ~eft and right of boxgirder (in.)

-44-

NUM

NAL , NAR

SL,SR

YNA

,T~D

IlliEG

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 tToverlapu 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 of composite section about

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

weWPHC,HP¢H

DXC

DXP

CWPiiJHNDN

DYS

Dye

DYP

MSW

BSASW

swCWPiiJISLX

IBEX

lex

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) (ino)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 centroid

of overlapwidth of additional slab thickness outside of

exterior beamx-distance from centerline of-girder to centroid

of additional slab thickness area

-46-

DXS

ANACAPAT¢TMA

DX

IY

IY

DXDXSDXNDXPADCXDPXIXY

MXE(J)

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

MLANE8PDA,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 describeeIfect 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 TtNEGn refer tothis area

@

®- ---~----+-~-------~........"""""""'-

OH

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

1. effective slab width limited by adjacent-interior 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-

OU5 2095 SCHAFFER--SOLUTION rOR LOAD DISTRI8UTION FACTORSS~p 1( 67 12 02.0

PAGE 1. SEP 12 67

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002. J:sl [

OU3. C~DTOT [U04. 51- COUNTER RUN NEUTRAL,. AXIS C

STRESS AT BOTTOH FIBER [ ] [ ) ( ) t J I005. 1 S(IlSXX~SY=SXYJIlO [ ] ( ) t i [ ) t0\16. fIXN.R.P"K [ ] ( J t J [ 1 [007. CRDN.R SNUM Of DATA POINTS AND RUN NUM [ ] [ ] [ ] [ ] [008. N~.N [ J t ] [ i [ ] [OQ9. 010 2 N'l=NN.1 [ ] [ J [ ] [99 1 tO~O. CRDX,Y $ ON~ DATA flOOINT [ ] t ] ( J [ ) [all. Sl(·SX.X,SY=SY·Y [ J [ ] [ i [ 1 [Ui2. S(X.SXX+X-X,SXY.SXY+X-Y [ ] [ J [ ] ( ] [2013, 99 O"SXX*N.SX*SX [ ] t 1 ( ] [ ] [Oi4, A:S[SXY*N~SY*SX]/D [ ] t ) [ ] ( J [U15. B~[SXX·SY·SXY*SX]/D ( ] t J [ ) ( ] [01,6. StJ]=C"'BJ/A [ ] t J [ J t J t01.7. N~[JJ=8 ( ) [ ) [ ] ( , tU~8, PV JiR,NAtJJ,SrJl ( ] [ ] [ ] t ] [019, PL ( ] t 1 ( 1 [ 1 [U20. [)-J+1)·TOT {1 ] [ ] ( 1 (1 ] t021. 001 CRDA~M.YBM.H8M,I8MX.IBMy,W.SEC { ] ( ] [ J ( ] [022, 00.5 C:a1 [ ] [ 1 ( J t J tOc3, r I XN'jM [ ] t ] [ 1 t 1 r0,4. 47 CRDD~.DR,TL,TR,N ( 1 [ J [ J t ] [0,5. 30 NIJM:1 { ] t ] [ ] [ ] [0~6. R"3,rc4,J~2 [ 1 t ] ( J [ ] [

Ot7. s~ I~TERI0R BEAM CALCU~AT!ON~ ( ] t ] [ 1 [ J [028. PI. EFr, WIDTH HOMENT/E.10**~6 LB.FT R-RUN C

. IX ty PHI { ] t J [ ] [ J [O~9. 55 N~L.NA[R"NAR.NA[r, ( ] [ ] [ j t ] [030. SLastR],SRl;s[r] [ ] t 1 [ ] [ l [O~l. 70 S COMPUTE EFFECTIVe WIoTH BY AREA MOMENTS [ ] [ 1 [ 1 ( 1 t032. 80 Yl\fA.CNAL+NARl/2 [ 1 t ] ( i t ) tO~3. 90 T;t[TL·TR]/2 ( ) [ 1 [ i [ ] [0~4. :;00 D~[DL+DR]/2 [ ] [ ] [ J [ , [O~5. 110 H~EG~HBH·D [ ] t ] [ ) [ ] [036. 120 NSG.HNEG*W [ ] [ ] t J [ 1 (

O~7. 130 A~D.YNA [ ) [ J [ ) [ ] [0~8. 140 D'iEGaA"HNEG/2 [ ] [ . 1 r ] [ J [O~9. 150 D3LA8~A+T/2 [ 1 t ) ( J [ J [O~O. ~60 D9M.VNA.YBM [ ] [ ] t i [ ] [041. E~[Jl~[ABM*DBM"NEG.DNE&J/t'.DSLABJ [ ] [ 1 [ J [ J [042. 210 S COMPUTE MOMENTS Of t~eRTIA ABOUT x, V, AND ( ] [ 1 [ ] [ J [043. 220 S INC~lNED M AXES [ ] [ 1 [ J t 1 [044. ISLAB.tEW[J].T••3J/12·EW[~'·T.DSLA8.*2 [ ] [ J ( J [ ] t045. 240 I~EG~rW*HNEG.HNeG.HNEG!/la.. W.HNEG*ONEG*DNeG [ ) [ ] ( J [ ] r046. 250 J9M_XBMX·ABM*08H*OBH [ ] [ ] [ ] t , [

047. 290 13 IX·IS~AB·INEG·JBM [ ] t ] 1 J [ J [O.8~ 300 K:t2 [ ] [ ] t i t 1 -r049. IY~18MY.[T·EwtJ]·*3]/12·{HNEG*W••3'/12 [ 1 t ] ( ] [ ] [

0'0. 8E~cATAN.t[NAL~NAR]/W' [ ] t ] t j [48 1 [49O~l. 48 BETAIJ.SETA [ ] r J ( j [ ] [

i . I0'2. 49 I~.[tX·IYJ/2·t[IX·IY]/2J.COS.[2.8ETAJ [ ] [ ) [ ] [ ] [

~O!)3-. .50 I~N=[[lX·IY]/2J*SIN.t2.BET·J ( J [ l [ J [ J [ ]

LOI

PAGE 2, SriP 12 67

SEQ LABL TYP STATEMENT C ZERO NOT 0 PLUS MINUS ELSE

054. 460 STRAIN;:rSL"'SR~/2 [ ] [ ] [ 1 ( ] [055. 470 IIaSQRT,[IMN*IMN+IM*IM' [ ] [ ] [ i [ ] [056. 510 L4M8ATAN,tIH/IMN] [ ) t 1 [ ] [50 1 [51057, 50 L~M •• \..AH ( ) t ] [ ] [ ] (

0;8, 51 P~I.BETA·LAH-J,1415927/2 [ ) [ ] [ ] t52 ] [530~9, 52 P~l.~P,",I [ ] t ] [ ) [ ] [060, 53 M~[Jl~[Il*STRAlN·COS,[PHI)'/[YNA.12.COS,[ C

BETA) ) [ ) [ ] [ ] ( ] (Obl, PI. [ ] [ J t j t ] [U62, PV E~(J,,~X[JJ,NUM.IX~Iy,PHI [ ] ( ] [ J [ ) [063. R~R ... 4,F"=F'+4 r ] [ ) [ 1 [ ] [064, [J:rJ·2J [ ) [ J [ j [ ] [065. 600 r~UMcNUM*1'-N [ ) [ ) [54 1 ( ) [55O~6, 54 [C=C+1J·SEC [ ] ( ] [854 i ( ] [47O~7. 000010854 CRDA~M,YBM,HBH.I8MX,I8MY,W,WC,WP,HC,HP,OH,DXC.C

, 020 D~~,BS,SEC [

Ob8, R=1,K=2 [

069, J21 [

DID, 000030 5=1 [

071, A49 CRDD~,OR.TL,TR,NUM [

072. OOOD50 N:;1 [

073, S~ EXTeRIOR BEAM CALCULATIONS [

0/4, 000051 P1.. ErF, SLAB I ErF", CURs I EFF, PARAPET/ C000052 ~OMENT/E.10.'.6, ~B·rT / N IX C

IV IXV [ ] ( ] [ 1 t J C ]

075, 001660 Pi.. [ ] [ ) t J t 1 [ J076, A50 N4~aNA(R].NAR.NA(K' r J [ J ( 1 1 J t ]

077, P01J.1 [ ] [ ] [ ) t ) ( )

078, Sl.=SCRJ .. SRpSrKl [ ] ( ] t ) t J [ ]

079, 000061 C·~;:PW~O [ ] [ ] [ ] t ] [ )

060, 000070 NJ\Jl[NAL+NAR]/2 [ ] [ J ( j t l [ JU81, 000080 T2[TL·TRJ/2 [ ) [ ) [ ] t ) [ )

062, 000090 D~tDL·DRJ/2 [ ) [ ] [ j t J ( ]

083, 000100 H\jaHBM"D [ ] [ ) [ J t J ( ]

U~4, 000110 A~D-NA l ] [ ) [ ) t 1 [ ]

O~5, 000+20 D-3M:NA-yBH [ ) t J t J t , [ ]

Oa6. 000130 D~wA·HN/2 [ ) [ J [ j t ] [ ]

067, 000140 DYSaA.T/2 [ ] t ) [ ] t ] [ ']

068. 000150 D'(C:A*T.HC/2 '[ 1 [ ] [ J [ J [ J089, 000160 DYP:zA.T.HC"HP/2 [ ] [ ) [ 1 t ] [ )

O~O, MSW.OH·W/2·8S·EW[P]/2,~SW·tO~+W/2·9S/2] [ ) ( J lA99 J t 1 tA98 IU~l, A99 HSW.OI-l*W/2*BS/2 r ] [ ] [ J t ] [ ]

O~2, A98 ASW.CABM*DBM1/[T*DYS-HN*QNf [ J [ ) ( J [ ] [ )

Oii3. 000231 ASW-MSW r ) [ ) [ A!5] t ] [ A97)O~4, 000240 A97 ASW-W/2 [ ] [ ] [Ai 1 t ] tA04 JO~5, 000250 A1 ASWs(ABM.OBM+(W/2J*tHN*ON*A ft O,5])1 C

, 000260 tT·OYS"A-0,51 [ 1 [ I ( ) ( J [6, 000270 ASW.tW/2·0H) [ ) [ ] [A2 i [ ] [.047. 000280 .2 ASW.tA8M·DBM-OH.[HN.DN*A-O.~))/[T*OYS.HN·ON) [ l t ] [ l [ ] [

8, 000300 ASW-CW·O,,",] r l [ ] rA3 t ( 1 [A49. 43 ASWatABM*OBM+W*CHN*ON).OH*lA.O,51JI C

000320 rT*OYS, t ] [ 1 [ ] t .1 t ]

100, A4 S,"ASW [ ] [ ] [ j [ J t ]

101. 000340 S';·HSW [ ] [ ] [A5 J [ , [A18 ].102. A5 Sii~M5W [ ) [ J [ l [ J t r103, 000360 S"'-rW/2.0HJ [ ] [ ) [ J tA6 J lA' ] I

Ul0I

PAGE 3, SEP 12 67

11 SEQ LABL TYP ST4TEMENT C ZERO NOT 0 PLUS MINUS ELS~--,

lU4. A6 C~.[A8M*D8M~S~.T.OY~+[~/2].HN*DN+[SW-W/2J. COOO~BO [~·o,5J]/{HC*OYC] [ ] [ J [ J [ J [,6,10 J

105. 147 Sol/.[W .. OHl [ 1 [ J [ J [048 ] [A9 ]

106. 400 AS C~=[ABM*D8M.SW.[T·DVS~~N*ON'-O~.[HN*DN+A·a.5]C

410 J/[HC*DVCJ [ J [ J [ J [ ] r Al~}107. A9 C~=[A8M.08M.SW.T.OYS+W.~N·ON-OH.[A~O.5]l/ C

000440 {..,C.OYC] [ ] [ 1 [ ] [ J [A10 ]1P8. 1410 C.oj-..wc [ 1 t 1 [A11 1 ( ] tA18 J1U9. All C..j·WC ( ) [ } [ J [ J [ ]

110. 000470 S.oj-rw/2.0Hl ( ] t 1 [ J [A12 f [ Al,jJ111. A12 P~=[A8M*D8M-CW.HC.DYC·S~.[A~O.5}+t~/2J.[A·O.5C

000500 +~N.ON)]/rMp.OYP) [ ] t 1 [ ] [ ] [.416112. A13 S~,[W~OHJ [ 1 [ ] [ j (0414 J [A1S11.3. A14 P~c[A8M.DBM·Cw·HC*DYC·SW*(T*DYS~HN*DN1-OH. C

000540 [~·o.5·HN.DNJJ/[HP.DYPJ [ ] [ ] r J [ ] [A16114. 1415 P~3[ABM.DBM.Cw*HC*OYC-SW·r·DYS.W*HN*DN-OH. C

000570 {~·O.5l1/[HP*DYP] ( ] [ ) [ J t 1 [ ]115. A16 p·~·wP [ ] r ) (A17 J t 1 rA18 1116. 1417 p~ P4RAPET WIDTH EXCEEDS. ~AXIMUM ( ) [ ] [ J [ ) r ]117. AlB S"'''[~/2+0HJ [ 1 r ) [ J (.19 1 [.42D . J118. A19 I5LX=Sw*[T**3/12+T.DYS··2J+tSW~W/2'*(1/12· C

000630 [~·O.5J.·2J·[W/2J.fH~··3/12+HN*DN*·2J [ ) [ ) [ ) [ , tA23119. A20 S..j-rW+OHl [ ] t ) [ J [.421 ) CA22120. A21 ISLX=sw·tT··3/12+T*DYS·*2J+o~·r1/12+[A-D.'j C

000670 **2j-C SW·OH1*(HN**3/1Z.HN*ON*.21 [ J t J [ J [ , [A23 ]121. A22 ISLX=SW.(T··3/12+T*OYS·*21+0H*[1/12+(A-Q,5] C

, 000700 **2]~w·[HN**3/12+HN*DN.·2l [ ] t ] [ J [ 1 [122. A23 I3EX=IBHX+ABM*OBM·.2 [ ] [ J [ j [ ] [lc3. 720 ICX=C~*[HC·.3/12+HC·OVC.*21 [ ] [ J [ J [ ] [124. 730 IPX=P~·[HP·.3/12+HP·DYP·.2J [ 1 [ J [ ] ( 1 [1.::5. 000740 IX=IBEX.ISLX+!CX+IPX t J t 1 [ J [ ) (1~6. 000750 AS=SW*T t ] [ ] [ ]- [ J t1e7. 000760 S.o/-[W/2+0H] [ ] t ] [ ) [042<4 J [A251,a. A24 W\j:W/2 [ ] t ] [ ) [ ) [1~9. 000780 D(N:-\ol / 4 [ ] t ] r J ( ] [

1~0. WPA=S~"W/2 ( ] t ] t 1 [ , [1~1. D~PA="'(SW+\ll/2J/2 ( ] t ] [ 1 ( ) tlS2. 000810 D:<Sr:;-S\ol/2 [ ) [ ] [ j t ) [A29133. A25 S"j .. rW+OHl [ ] [ 1 [ J [.426 ] [A271~4. A26 ~P'4I1SW.OH r ] [ ] [ J t ] [lJ5. 000840 DXN-[wN.Wl/2 r 1 [ ] [ ] t J [A28136. A27 W'I='" [ ] [ J [ ) [ J [1~7. 000860 D)(N=O [ ) t ) [ ] [ ) r1~8. A28 WPA.OH r ) r ) [ J ( ] t1~9. 0008BO O)(PAD,.[W+OH]/2 [ ) [ } ( ] [ ) (

140. 000890 D:<S=[SW-Wl/2-0H [ ] t ] [ ) [ ) [141. A29 o4-4-HN.WN [ 1 r J [ J [ ) [

1.2. 001200 ACaCW*HC [ ] [ ] [ J t ] t143. 001270 AP-PW*HP [ ] [ ] [ J [ ] [14 .... A40 ATOTaA8M+AS-AN·WPA.AC·AP [ ] [ } t J [ ] r145. 1~20 H~·AS*DXS.AN·OXN+WPA.DXPA• .4q.DXC.AP.DXP ( ] t J [ j [ ] t146. 001340 DXilMA/ArOT [ J r ) ( J t ] [

147. 001350 I1 D IBMV.T*SW*·3/12.4S-0XS*.Z·HN*WN**3/12 C1360 -4N*OXN.*2+WPA·tWPA••2/~2·0XPA C1370 .*2].HC*CW.*3/12+o4C.DXC.*2.~P*PW.*3 C I1380 112+AP*OXP**2 [ ] t ) t J t ] t J V1

-> --~---~.~~-~------,

__ ~____ r .~. ~ ~ _ r _.~ ... _~ .. _ ~ ~J--II

PAGE 4. SEP 12 61

II SEQ LABL TYP, STATEMENT C ZERO NOT 0 p~US MINUS ELSt:

·1~8. 001390 IYc!YI'ATOT*OX··2 [ ] [ ] [

149, 001400 D~II-DX [ ) t ] [150. 001410 Dl(SaDXS.OX ( ] [ J [

1~1. 001420 O(N=DXN ... OX [ ] t ] [

152. 001430 O"PA=DXPA+OX [ ] r ) [

1'3. 001450 DCX:rOXC.OX [ ] [ ] r1'4. 00146U DPXcDXP.OX ( ] [ ] [

1'5, 001480 Il(YaABM.DX·[·08M]·AS*OXS*DYS~AN*DXN.DN·WPA*C001500 O<PA*r A·O,5]+AC*DCX*DYC+AP*OPX*DYP [

1,6. 001510 BETAsATAN.[[NAL-NAR1/W' [

1~7, 001530 A42 I~·[lX·IY]/2·t(IX-IY]/2l*CoS.t2·BE'A]·IXY. C001540 SIN.[2*BETA] [ ] [ ] [ J [ J [

1'8. 001550 I~Nc[{lX·IY]/21*SJN,[2*BETAl+IXY·COS.[2.BeTAl[ J [ ] [ ] [ ] [159. 001551 It=SCRT,CIMN*IMN+IM*IH, [ ] [ J r J [ ) [

1~0. 00156U STRAIN!;[SL+SRJ/2 [ ] t ] [ J [ J [

1~1. 001610 L~MI:ATAN,[IM/IMNJ [ ) [ J [ J [A43 1 [A44162. 001620 A43 L~M."LAH [ 1 [ J [ ] [ J (

lb3. 001630 A44 P~1=8ETA+LAH·3.1415927/2 [ ] [ J [ j [ ••5 ] [A46164. 001640 A45 P~I ... PHI [ J [ 1 [ 1 [ ] [

165. A46 MXE[Jl~[II*STRAIN.COS.fPHlJ'/~NA.12.COS,[ C03ETAJ] [ ] [ ) ( 1 [ ] [

166. Pv S~,CW,PW,MXE[J],N.IX,I~'IXY ( ] [ ] ( J [ ] [

1~7. PL [ ] [ ] t J [ J [

158. J;lJ+2 [ ] t ] [ ] t ) [

169. R2R.4 f K:cK"'4 [ J [ J [ ] [ 1 t170. 001700 [~=N+l]-NUM ( ] { 1 [A47 J [ 1 (A50111. 001710 A47 ('SJlS·1)·SEC [ ] [ ] [A48 ] [ ) 1A49112. A48 F'IXLl\NE,SPD,POOS [ 1 [ ] t J [ 1 [

1/3. 00002U CRDN SNUM8ER Or SETS OF RUNS [ ] [ ] [ ] [ ) [

114. 000030 K21 [ ] [ ) [ 1 [ ] t11'5. 000040Cl S~PERCENTAGE OF TOTA~ MOMENT C~RRIED BY EACH BEC

000050 A~ [ ] { ) [ 1 "[

1/6, 000060 PL [ ] [ ] [ J [

177, 000070 PLIIl ~ANE COLUMN f SEcOND DIGIT INDICATES DIREC000080 eTION, 1 VoR ~, OR E., AND 2 FOR S. OR W. [

178. p~ I~ POSITION AND seCTIO~ CO~U~N, 1~~OSITION oReSECTIO~ A, 2=POSITIO~ OR SECTION 8, ETC. [

179. 000090 CRDM SNuMBER OF RUNS WIT~lN rUL~OWING SeT [

leO. 000100 PL (

ltsl. PL LANE/DIR, SPEEO pOS./SEC, CBEAM D BEAM C BEAM B C

BEAM A TOTAL MOME:NT ( 1 ( 1182. 000140 PL [ 1 [ ]

183. 000150 L=1 t ] [ ]

184. C2 CRDL~NE.SPD.A,B.C,D,POOS [ ] [ 1185. M1.MXE[AJ [ ) [ ]

186. MC-MX[B] [ ] [ 1lB7. MIi-MXtCl ( ] [ ]

188. M4crMXE[Ol [ ] [ ]

169. MTsHO.MC·MB+HA [ ] t ]

190. 000190 MPA. (t'1A/HT] -100 [ 1 [ ).

191. 000200 MFB&:[HB/MT1*lQO ( ] t ]

192. 000210 MPCc(MC/MT1*100 [ J [ )

1~3. 000220 MFJOarMD/HT1*100 ( ] [ l194. PV L4NE,SPD,POOS.MPD,MPC,~PB,MP~,MT [ ] [ ] \ . \ , \ ,li5. 000250 PI. [ ] t ] [ J t J t ]

U1I\)

I

PAGE 5. SiP 12 67

~ SeQ LABL TVP STATEMENT C ZERO NOT 0 -PLus MINUS ELSE-. + _ •• ~

1~6. 000260 [L.IL+S.J·H [ ] r 1 [ C3J [ ] [ C2l1~7. C:5 [1<.K·11~N-- [ ] [ J [END J t 1 rei J"~~8. OOD28~ END END [ ) t J t i [ J [ )

*~.**SYMBOL TABLE•••••A AeM ATAN••9 'A50 199B BETA B5-4BS '98 ASWC COS CWA5 A97 AtD DL DRDNea DSLA8 DB"EW DXC DXPON Dys DyeF DYP ••A2 A3 A18A6 ., Al0A8 .9 A11HBM WNEG HeHP ~N A12I8MX IBMY ISLASINE13 IX ty1M IMN ItA13 '-16 A14Ai5 A17 419A20 ISLX A43A21 '22 IBexlex tPX ASA24 A25 DXNDX'" DXS A29A26 '-27 JJ8f't" A28 ANAC AP K

*A40 ATOT DXLAM DCX DPXIXY MX "XEHSW MA *.. -42A4~ NA- NNN NUM NAL.NAR NEG OM

"4" ... 5 ••6A47 p PHIPW ...8 L.ANEpoos C1

'" IL C2 MD Ln--He ----- R JIl8 LN

I

MTMPCENDSXXSECTRTSQRiWWNY

MPAMPDSSVfOTSLSINswweWPAYBM

PAGE 6. SEP 12 61

MPBC3sxSXyTLSRSTRAINSPDWPXYNA

IlJl..j::::=.I

INTERIOR SEAM CALCULATIONSEFF. WleTH MOMENT/E.10·.~6 L8~rT R~RUN I~ IV P~I

1. 09694~4+02· 4.02.331 5 9*04 1 4.1912-182.05 8.7978574+05 6,41673BO~04

1-.15261:>5+02 4.62730;9·04 2 4.2534247+0!J 1..0013044.06 1.5724450-04

1,1501127.02 3.7771754·04 3 4.2506968+05 9.9558097+05 3.9798543-03

9,1439003+01 2 -. 7 8161 02" 0 4 4 J.9632e01+0fS 5.6042555+05 6.-797~780;O2

5.1443512+-01 1,930185 5*04 5 3.2808153+05 !.9910248+05 6 e- 6816 46 0; 02

IUl(J)

I

EXTERIOR SEAM CALCULATIONSEFF. SLAB I EFF, ~URB I EFP. PARAPETI MOMENT/E-l0*.-6. LB~rT I N t~ tv IXY

9.215~7~O.01 3~~OOOOOO.Ol 1,8128213+00 5.8014886+04 1 5i25640~O~05 8.45j3j~i.05 '1.0'00047.0~

8.93692~3.01 1.0854160*01 0.0000000.00 ~.3439342+0~ 2 .-,2210284'05 6.3839389.05 -7.1133839.03

8.9494367+01 2.4004726*01 0,0000000+00 -2.4911886.04 3 4~6917266.ri5 7,1099465+05 .5.,9367933+0.

9.3000000+01 ,.04865~O.01 O.OOOOOOO.OQ 1.6889840+04 4 4,6028003.05 7.6206159.05 -3,196'832.04

7,5049324.01 O.oooOtiOO.OD 0.0000000.00 7.95037l1+0~ 5 3.5640541~ri5 !,8~852~8.05 '.1t?8~3645.0.

IlJl-....j

I

PERCENTAGi or TOTAL; MOMeNT CARRIED BY EACH BEAM

IN LANE COLUMN, ~E~ONti OIGlT iNDICATES Dl~E9TIONJ _, '~R ~t OR ~.~. AND ~ ",OR_S, OR_W,IN POSITION AND SiCTION COLUMN, 1~POSfTION A :QR SECTtOM M, .2: POSITIONs OR -SiOTION N, 3~PDSifjbN ~. 4,posrT10~ b

L.ANE/DIR. SpEeD POS,/sEc, BEAM D

12 1 11 6.3J494~4... 0e

22 1 11 1.3575038:"01

32 1 11 1.9871123+01.

BiAM C -BEAM B BeAM A 'OTA~ MOMENT-

!~5379931.01 3,2058225~ril 4,6226901.01 1,2550021.0'

2.2356910.01 3.71915i9.~1 2.'8j6~J3.01 ~i24~1836~OB

S.0128e".Cl !,01288~7.~i ~.98t1123.oi li2536728~OS

TYPE #ENO' STAffMi~T ExeCUTED.JUN 22- 67 i'- 51~9

RUN TIME 0001.4 ~lN.

IUlOJI

9. TABLES

-59-

Table 1 Test Bridge Characteristics

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

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

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

Brookville 64 f lO-1/2 TT 8 f Ion 4 f lOTT 48 TT X 36 ft 45° yes

White Haven 64' 8 TT 9 ' on 6 f OTT 36 TT X 42 ft 82° yes

Philadelphia 71 f 9 ft 9' 6 TT 5' 6 TT 48" x 42" 87° yes

Philadelphia 71' 9 TT 9 f 6 TT 5 f 6 TT 48 TT X 42 TT 87° no

IOJoI

Table 2 Maximum Moment Coefficients, Crawl Run Loading

Position indica~es distance of drive wheelsfrom midspan

(lO-6 ft-in2 )

Lane Direction Section Position Section Position Section PositionE1 E2 I

1 NB 48,857 14.9 N 46,838 5.5 N 26,667 5.1 N2 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 N5 NB 5,536 6.7 N 5,562 0 11,713 3.6 N

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 N4 NB 10,631 9.2 N 12,119 7.9 N 18,818 5.8 N5 NB 5,649 0 6,900 6.2 N 12,059 0.8 N

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

1 BB 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 BB 21,645 2.0 S 20,888 4.8 S 27,128 3.4 N4 BB 12,081 3.0 S 12,720 6.7 S 15,813 7.6 S5 BE 6,735 2.9 B 7,427 8.6 S 11,387 12.1 S I

ml-JI

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

(lO-6 ft-in2 )

Lane

1

2

3

1

2

3

Dire·ction

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

Ienf\..)

I

Table 4 Comparison of Maximum Moment Coefficients at Midspan

Brookville Bridge - 45° skewBerwick Bridge - 90° 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

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

IOJLNI


(Two Load Vehicles Traveling in Same Direction)


(Two Load Vehicles Traveling in Opposite Directions)

Maximum Moment Coefficient, ft-in2Ratio

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 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 0.8.2 0.822 5 South North 35,769 45,087 46,461 52,969 0.77 0.85



ImUlI

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 cp = 30° ep = 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

I01OJI

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 NE 0.009 0.030 0.061 0.092

1 BE 0.084 0.071 0.030 0.009

2 SB 0.058 0.082 0.044 0.015

3 BB 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 8B 0.084 0.072 0.030 0.009

2 BB 0.059 0.084 0.046 0.019

3 BB 0.036 0.072 0.060 0.033

4 SB 0.018 0.042 0.052 0.040

5 8E 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 0.0710 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

IOJ0)

I

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 O.5l 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 I

01LDI



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 North 092 119 105 076 113 12~ l26 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 057 108 108 112 086 115 125 110 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 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


J'-J0I



f · -3 RatioDe lectlon, 10 inches

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 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 10l 118 100 074 lO6 119 l36 081 0.95 0.99 0.74 O.9l2 5 South North 068 114 107 III 079 110 152 III 0.86 1.04 0.70 l.OO

I-....j

f---JI

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

(One Load Vehicle)

(lO-6 in/in)

Section El 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 l4 Maximum Strain at Bottom Surfaceof Girder - Berwick Bridge

(lO-6 in/in)

Exterior InteriorTruck Location Left Right Left Right

Lane l 3.8.9 42.0 34.8 30.9

Lane 2 3l.4 30.l 34.0 34.2

Lane 3 23.2 19.5 29.5 32.2

Lane 4 l7.9 lS.O 23.6 23.7

Lane 5 ll.7 9.2 18.9 15.8

I-......Jl.NI

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


(10- 6 in/in)

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


(10- 6 in/in)

Lane Direction Section El 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 5·0.7 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



I-JUl1

Table l7 Maximum Strain at Bottom Surface of Girder Berwick Bridge

(Two Load Vehicles)

(lO-6 in/in)

Exterior InteriorTruck LocationLeft Right Left Right

56.4 (Avg)Lanes land 4

56.8 57.0

56.9 (Avg)

58.4 54.6

45.1 39.3 52.9 50.0Lanes 2 and 5

41.2 (Avg) 51.4 (Avg)

I-......j

mI

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 0 111.685 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 a 95.00 24.37 a 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 a 82.512 South 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.....JOJI

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 23.68 28.78 23.355 North 30.56 19.77 31.40 27.67 27.51 22.32

1 South 30.89 26.72 30.12 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 So'uth 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

'-JLOI

10. FIGURES

-80-

-81-

East

33' - 6 11

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

5

I234

I ~Iope ~41~Ft.~SIOpe Y4''112: I=(.\J-,o.N

3 1-6 11 3 Spaces @ al-IO" = 26 1-6" 3 1-611

Scole:II II 1 a../4 =1 -

Fig. 2 Cross-Section of Brookville BridgeI

OJf\..)

I

661-10" North

"50' -0"

~ ~Midspan~, Line

(Skew)

'\.

I Midspan Li ne~ (Perpendicular)"

II

AirHose~1II

50'-0"

II

~Air HoseII

Fig. 3 Plan View of Bridge Deck

IOJWI

-84-

hamferomer

~.<J

<f J> <1= 0' 4 <Q &\ , is 4 4LO 4 4 ArO -q 4r-: .(/ ,

" ;.f .a (]

, .. 4b

~",. ~~

~ ~ ./ A4.

~

I>

V

04

.. ,4

Vtf

q0 CO ,

~. (\JCDro

3 11 Chamfer,4 4

.4 /4Corners d.

~II"'-

C.G.S. . 4<t·~.28111 .r ~ iA

0 "'"d .0.• ,. • 4 JJ .. ~ 3/411 ClOt 4 "4

\..

5.0" 38.0" 501l~Bott- · Corn

48.0" - I

Fig. 4 Composite Girder Cross-Section

Legend:

o Def~ection GageI

: Fully Gaged SectionI

x Single SR-4 Gage

D', (18,36)

c

,

(17 ,35)

x (118)

North

.....

B, K ,Sec.I(goges9-16) '\: ;::::==~ ',II '

A

Sec. E2 (gages 101-108)

Sec. EI (gages 1-8) --

Fig. 5 Underside Detail Showing Gaged Sections

(viewed from top)

IcoV1I

1,1011 18,108 91 116

2,1021 A 17,107 101 B 115

3.1031 16,106 III 14

4,104 5,105 12 13 17

D

18,118

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

IOJOJI

"

VOLTAGE REGULATOR

95 - 130 v. INPUT

I 10 v. OUTPUT

"

OSCILLATOR

REFERENCE SIGNAL

-87 -

"-- SR-4

AMPLIFIER ---- AND-~GAGE CIRCUIT

1SIGNAL ALTERED .BY

GAG E ACTIVITY

+OSCILLOGRAPHGALVANOMETER

Fig. 7 Instrumentation Flow Chart

-88-

Fig. Sa Underside of Test Bridge, Showing Skewand Instrumentation

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

-89-

I. 13.0' .1_ 20.4'

-1I I

- -- C\Jto . en• r-- •,... V

I

AXLE AND TRACK SP.ACING

Front Drrve Rear

J t t·9,890 31,945 31,445

Before Testing

t t ~10,000 32,640 31,940

Aft.er Testing

AXLE LOADS (LBS.)

Fig. 9 Test Vehicle

2

i3 4 5

I ', I

-5.01 -3.4 -8.91 1-9.4

18.41A

19.9 13.31 t 14.5B C D

31.71 35.3 26.41 123.6- - -

37.7 l 41.2

0.0806 11

35.3 30.4

~0.0680"

114

~0.0465"

13.5

+0.0249"

Fig. 10 Typical Strain Data Tabulation

ILOoI

50,000

40,000

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

20,000

10,000

--Northbound

--- Southbound

2 3

LANE

4 5

Fig. 11 Maximum Moment Coefficients at Section ElI

1Dj--JI

50,000

40,000

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

20,000

10,000

- Northbound

--- Southbound

2 3

LANE

4 5

Fig. l2 Maximum Moment Coefficients at Section E2-Jto1'0I

50,000

401000

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

20,000

1-0,000

-- Northboun-d

--- Southbound

~~

....... ~"'''''~,

",'\'\.'

""'\ '---.. .........

" --.;:'\. ----'- -

2 3

LANE

4 5

Fig. l3 Maximum Moment Coefficients at Section I

ILOLNI

Sec. EI

-94~

0"'--------1...---------------......---Sec. I

Fig. 14 Superimposed Moment Coefficients (Average)

Load vehicles traveling in lanes anddirections indicated on plot

North

,

5 '\: I'b '< . 11' ~

,2 '< Il> I >( II> ID "

3'< I'b 'k 11' It>---"

4'< It: At I ID tD "

LaneNumber

......

Sec. EI

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

First Set of Northbound Runs

ILOV1I

North

,

5 ' rb > Ib Il> '< < -

"

"

2 '< ['b I)< I'b Ib '

3 '< Il> >l [l) It> '\

4 '< rt >, I It> If:) ' ..

LaneNumber

" Sec. E I

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

Second Set of Northbound Runs

IlO0)

I

North

"

5 " <1J > < < ,

'\.

4 '\: <1.1 >«11 I c1l ",

LaneNumber

3 "\: <1.l Q.1 'h: dl '"

"2 " <lI <II ) d1 "< < ""

,,-·~Sec. EI

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

First Set of Southbound Runs

I1.O-.......JI

/

North

5 '< <II > ( <Ill <.11 >

4 " ([]) c:n I <1' "< < ....

, I

LaneNumber

3 '< <11 (1\ >L <II >,.

2 '< <II I <0 en "'..

,Sec. EI

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

Second Set of Southbound Runs

IlDcoI

North

"

5 '< ~),< ID lD >,

"4 '< 1D > ,

LaneNumber

3 '< ID'k ID ID >,

"2'"'<---------.:.- I'D I'(ID ID-------~",

(--sec. E2

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


ILD1.OI

North

....

5 '" ID >< II' ID >,

....

3 '" ID 1< ID 1D >,

4 '< It> >,

LaneNumber

rsec. E2



IJ--IooI

North

,

5 "< <II > < a I I (II ' ..

,4 '< <11 (II >( I 01 ' ...

3 '"< <11 (II 1 en '

LaneNumber 2' <f1 'c: d1 >( dl '

I--- Sec. E2



I}--JoJ---II

North

"

5 '< <l1 aJ <11 ' ..

"4 ' ~ ~> ~ ,

< < "

LoneNumber

3 '< QJ QI 1< Ct., "...

"2 "< (JJ I C(J'{ OJ J\,

I---sec. E2



IJ--lol'0I

North

"

"4' In > I ID ID >

5 ....< ID >c I ID ID >

LaneNumber

3 ....< 10 'C::: tD ID > ...

Sec. I2 ' ID I YID ID > ..

"

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


II--'ol1'J1

North

"

,

4 >< In) 1 ID ID "'...

5 ' 10 '( ID ID >,.

Sec. 1

,2' ID----------II--=:~'D ID--------~\.

3 "'c ID II ID ID >

LaneNumber



If--!o~I

North

"

5 'c (J I Q I ] 

"



1f--..JolJlI

North

"5 '\L «J eu >,

4 >< (JJ ell >,

Sec. I2 '< ell I k <.11 >

" I3 "\L <tJ >k <l.J a:I "

LaneNumber

"



Ir-'omI

A

2

B

3 4

c

5

-107-

o

0.076 0.074 0.035 0.013

0.048 0.079 0.048 0.021

I!

I II

0.032 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-

Il-r I 2 3 4 5 ~A B C 0

0.084 0.07,2 0.030 0.009

0.058 0.083 0.045 0.018

lI I I I

0.036 0.072 0.060 0.033

I1 ' I 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

-109-

~ I 2 3 4 5 ~A B C 0

N N

0.093 0.120

N

0.105

N

0.076

0.058

S

0.109 0.110

S

0.112

0.101

0.069

0.118

S

0.091

O.tlO

s0.057

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

s

0.114 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

-lll-

IS-25

-----.. 3S..-

...... 45I---........ -

55 -----

50

40

30

20

10

°L RSECTION EI

Q fJ50

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30 25

20 35

4510 55

°L RSECTION E2

~ !J50

40

30

20 45

10 55

L- RSECTION I

[\ ~50

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30 2N

20 3N

104N

N

o L RSECTION EI

,....J:

~ J]uz""-(J)LLJ 50J:U

40zI

0 30 2Na:~ 20 3N:t 4N-........

z 10<t 5Na:: o L.... R(J)

SECTION E2

[' J]50

40 2NIN

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-

2S.5N

C' ~

I

~ !J

50

40

30

20

10

o L RSECTION I

20 ....

10 ....

aL

SECTION EI

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30

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:~tl 15,4N I

2N,5S

2N.5S

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~ ~

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40

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201

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30

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SECTION E2

50

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. 20

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o L RSECTION EI

IS,4S

~ f]

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40

30

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50

40

30

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50

40

30

20

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oL

SECTION E2

R

2N,5N

50 t-r-- 7=>

40

30

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4°11 2. N. 5N

30

20

10

o L RSECTION EI

,-.

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I 3000::0 20:E

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\Fig. 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

3 Douglas , 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

4Pennsy1vania Department of Highways, Bridge DivisionSTANDARDS FOR PRESTRESSED CONCRETE BRIDGES, 1960

5 American 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 IllinoisEngine~ring 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,Janqary 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

11Lehigh University, Computing LabWIZ COMPILER MANUAL, Bethlehem, Pennsylvania, September 1964

-114-

12. VITA

The author was born on June 3, 1942, the son of

William and Isabelle Tait Schaffer, in Philadelphia, Pennsyl

vania.

Basic education was taken in Philadelphia public

schools to graduation from Germantown High School in January of

1960. The author was enrolled at the Pennsylvania State Univer

sity from September 1960 to December 1964 at which time he re

ceived the Bachelor of Science Degree in Civil Engineering.

Following employment for a short time with Gannett,

Fleming, Corddry and Carpenter, Consulting Engineers, the author

joined the staff of the Department of Civil Engineering, Lehigh

University, as a research assistant in the Structural Concrete

Division of the Fritz Engineering Laboratory in July of 1965.

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STRUCTURAL RESPONSE OF A 45° SKEW PRESTRESSED. …