Slab behavior of a prestressed concrete i-beam bridge ...

Lehigh UniversityLehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1971

Slab behavior of a prestressed concrete i-beambridge lehighton bridge, July 1971Chiou-Horng Chen

David A. VanHorn

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Recommended CitationChen, Chiou-Horng and VanHorn, David A., "Slab behavior of a prestressed concrete i-beam bridge lehighton bridge, July 1971"(1971). Fritz Laboratory Reports. Paper 1973.http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1973

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COMMONWEALTH OF PENNSYLVANIA

Department of Transportation

Bureau of Materials, Testing and Research

Leo D. Sandvig - DirectorWade L. Gramling - Research Engineer

Kenneth L. Heilman - Research Coordinator

Project 67-12: Lateral Distribution of Load for Bridgesconstructed with

Prestressed Concrete I-Beams

SLAB BEHAVIOR

of a

PRESTRESSED CONCRETE I-BEAM BRIDGE

LEHIGHTON BRIDGE

by

Chiou-Horng ChenDavid A. VanHorn

This work was sponsored by the Pennsylvania Department ofTransportation; U. S. Department of Transportation, FederalHighway Administration; and the Reinforced Concrete ResearchCouncil. The opinions, findings, and conclusions expressedin this publication are those of the authors, and not necessarily those of the sponsors.

LEHIGH UNIVERSITY

Office of Research

Bethlehem, Pennsylvania

July, 1971

Fritz Engineering Laboratory Report No. 349.5

DATA REDUCTION AND EVALUATION

INTRODUCTION

TABLE OF CONTENTS

ABSTRACT

8

8

8

6

4

4

5

5

1

20

17

17

11

15

17

11

8

10

3.2.3.1 Formulation of the Experimental Slab Bending Moment

3.2.3.2 Design Moments for Slab

Transverse and Longitudinal Strains

Transverse and Longitudinal BendingStresses

Experimental and Design SlabBending Moments

3.2.3

3.2.1

3.2.2

4.1.1 Influence Lines for TransverseBending Moments

4.1.2 Comparisons of Experimental TransverseBending Moments with'Design Values

3.1 Oscillograph Tracing Readings

3.2 Evaluation of Experimental Data

4.1 Transverse Bending Moments'

2.1 Test Bridge

2.2 Strain Gage Locations

2.3 Position Indicators, Timing, andInstrumentation

2.4 Test Vehicle, Loading Lanes, and Test Runs

GENERAL TESTING PROCEDURE

PRESENTATION AND DISCUSSION OF TEST RESULTS

2.

4.

3.

1.

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4.1.3 The Effect of the Corrugated Steeland the Depth of Concrete

4.2 Slab Strains

4.3 Slab Stresses

4.3.1 Influence Lines for TransverseSlab Stresses

4.3.2 Influence Lines for LongitudinalSlab Stresses

5. SUMMARY AND CONCLUSIONS

5.1 Summary

5.2 Conclusions

6 . ACKNOWLEDGMENTS

7. TABLES

8. FIGURES

9 . REFERENCES

21·

22

25

25

27

29

29

31

34

36

40

112

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ABSTRACT

This report presents the experimental results from the

field test of the deck slab of a prestressed concrete I-beam slab

sup~rstructure. In the test program, SR-4 strain gages were at

tached to the top and bottom surfaces of the deck slab, along a

superstructure cross-section near midspan. Measurements were made

of the strains produced by the passage of an HS 20-44 load vehicle

passing across the structure in each of nine load test lanes.

Tests were conducted with the vehicle moving at speeds ranging

from 2 mph to 60 mph, and moving across a midspan ramp at a speed

of 10 mph. Information on strains, stresses, and bending moments

is presented in the form of tables and influence lines. Experi

mental values of stresses were compared with the corresponding

typical allowable stresses, and experimentally determined bending

moments were compared with values used in the design of the slab.

The effects of the midspan diaphragm, the corrugated steel stay-'

in-place forms, and the local stresses produced by the wheel loads

are discussed. It was found that, under the static loading of the

bridge, the tensile and compressive strains and stresses on the

concret~ slab surfaces were small, and the experimental slab

bending moments were considerably less than the value used in the

design. Under the impact loading, the maximum tensile stress at

one gage location reached the vicinity of the ultimate tensile

strength of the concrete. However, it is concluded that in

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general, there is very little cracking of the slab under typical

live load design conditions.

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1. INTRODUCTION

In 1964, Lehigh University initiated a research inves

tigation of the overall structural response of prestressed con

crete beam-slab bridge superstructures to design vehicle loading

conditions. A major thrust of the investigation was a field test

program involving the testing of eight in-service superstructures.

Six of the test bridges were of the spread box-beam type, and two

were of the typical I-beam type. The principal objective of all

of the field tests was the development of extensive inform~tion

on the lateral distribution of a design vehicle load to the- longi

tudinal beams. Extensive testing programs were conducted on each

of the structures, yielding a large bank of experimental informa

tion on load distribution, as well as on a number of other aspects

of structural behavior.

In 1968, the last of the spread box-beam bridges Was

tested. One of the phases of the test program for this bridge

involved the measurement of slab strains at a number of locations,

not only on the surface of the concrete, but also on-some of the

lateral reinforcing bars. Later, two I-beam bridges were tested,

and in both cases, a part of the field test program was devoted

to the measurement of slab-strains. This report is devoted to a

description of the slab behavior of the last test bridge, and

I-beam superstructure.

The objectives of the slab investigation were (1) to

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develop information on strains and stresses produced on the slab

surface by a design load vehicle, (2) to develop information on

the bending moments produced at several locations on the slab,

(3) to compare the experimental results with values used i~ the

design of the slab, based on the AASHO specifications, and (4) to

form a bank of data for future comparison with the results from

analytical methods.

Historically, following the completion of KelleyT s work1

2in 1926, and the publication of WestergaardVs theory in 1930, a

simplified method for the design of reinforced concrete bridge

slabs was established and set forth in the AASHO specifications.

With the passage of time, a number of the provisions of the AASHO

specifications were modified and improved. However, the method

for determining live load bending moments in slabs 'changed very

little3,4,s. Over the years, a number of analytical studies,

4 6laboratory investigations, and field tests have been conducted' ,

for the purpose of confirming or improving the methods which are

currently being used in slab design. One of the general conclu

sions of the earlier researchwork7

was that the current procedure

is very conservative. However, since all of the analyses and test

programs were based on specific bridges, a more general formula

tion of the design provisions has not been possible, to date.

Basically, the study reported herein is an experimental

investigation of a single in-service superstructure. The overall

intent is to assess the actual structural response to vehicular

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loading, and to sense the possible need for additional investiga

tions which. would ultimately lead to the development of more re

fined specification provisions for the design of concrete bridge

deck slabs ,for beam-slab type superstructures.

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2. GENERAL TESTING PROCEDURE

2.1 Test Bridge

The test bridge (Fig. 1) is located near Lehighton,

Pennsylvania, and carries L.R. 164-8 over Pohopoco Creek. The

bridge consists of three simply supported spans, each 71 feet

o6 inches center-to-center of bearings, with a skew of 90 .

The cross-section of the bridge (Fig. 2) is composed

of six identical 24/45 prestressed concrete I-beams8

, with a

center-to-center spacing of 6 feet 9 inches. The slab (Fig. 3),

with minimum nominal thickness of 7-1/2 inches, was cast in

place on the top of the girders, utilizing corrugated steel,

stay-in-place construction forms. On the south side of the

i bridge, a· safety curb· was constructed on top' of the slab (Fig. 2),

with construction joints spaced at 18 feet 3 inches along the

bridge. Diaphragms were located at the ends of the spans above

the supports, and at midspan. The specified 28-day minimum

compressive strength of the bridge deck was 3000 psi.

The slab provided a roadway width of 35 feet 11-1/2

inches. The bridge was designed as a three-lane bridge 3, al

though the actual usage is for two·,lanes of traffic. Additional

detailed dimensions are given in the PennDOT Standards for Pre-e

stressed Concrete Bridges .

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2.2 Strain Gage Locations

Section M-(Fig. 1), which is a superstructure cross

section 3.55 feet east of midspan, was selected as the test sec

tion. Along Section M both longitudinal and transverse gages were

mounted to measure surface strains. Theoretically, the maximum

bending moment produced by the test vehicle was developed at this

section when the drive axle of the test vehicle passed eastward

over the bridge.

For the slab study, gages were applied on the top and

bottom surfaces of three of the five panels of the bridge deck

(Fig. 4). In each panel, transverse gages were applied near the

edges of the top flanges of the beams, and at the centers of the

panels. Longitudinal gages were mounted at the center of each

panel.

2.3 Position Indicators, Timing Indicators, and Instrumentation

Three lateral hoses were used as the position indi

cators for the test vehicle. One hose was located at Section M,

while the other two were located 40 feet east and west of Sec

tion M. As the wheels of the test vehicle passed over the hoses,

offsets were produced to indicate the location of the truck at

three points on the oscillograph records. Two additional hoses,

installed at approximately 90 feet east and west of Section M,

were used to actuate the timer which recorded the average speed

of the test truck.

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All gages applied were type A-9-3, except gages 608,

614, and 620 (Fig. 4), which were type A-3. The procedures for

installing the gages, including grinding and cleaning of the con

crete surface, waterproofing and mounting of the gages, as well as

the setup of other instruments, were described in previous Lehigh

•• 9 ... l.4Unlverslty reports .

2.4 Test Vehicle, Loading Lanes, and Test Runs

The test vehicle consisted of a diesel-powered tractor

and semi-trailer unit, provided by the Federal Highway Administra

tion, and operated by personnel from that organization. The3

vehicle was located with crushed stone to approximate the AASHO

HS 20-44 design loading. The actual loading and dimensions of

the vehicle are shown in Fig. 5.

In the test, the roadway of the bridge was divided into

nine loading lanes (Fig. 6). Lanes 2, 4, 6, and 8 were located

along the centerlines of the girders. Lanes 1, 3, 5, and 7 were

located midway between the girders, while lane 9 was situated 4

feet 9 inches from the face of the safety curb.

A total of 98 test runs were conducted in the test of

the bridge (Table 1). These runs consisted of crawl runs, speed

runs and impact runs.

The bridge was tested first with midspan diaphragms in

place, and then with midspan diaphragms removed. The crawl runs

were conducted at a nominal speed of 2 - 3 mph to investigate the

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static behavior of the deck slab. The speed in the speed runs

was varied from 15 mph to 60 mph. In the controlled impact runs,

all conducted at a speed of 10 mph, a wooden ramp was located

near Section M to produce a 2-inch drop of the axles of the test

vehicle.

This report contains the results from the crawl runs

and the controlled impact runs, since it was found that in the

speed runs, the amplification of static effects in the slab was

relatively small, as compared to amplification from the impact

loading.

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3. DATA REDUCTION AND EVALUATION

3.1 Oscillograph Tracing Readings

In the data reduction process, editing or identification

of the oscillograph traces was the first step. After the identi

fication was made, calibration and vertical excursions were

measured. As shown in Fig. 7, the local effect of the wheels

produced a sharp offset at the point where the tracing reached

its maximum amplitude. Therefore, two vertical excursions,

vex (1) and vex (2) , were measured. Vex (1) represents the

smooth vertical excursion without the local effect, and vex (2)

the vertical excursion which includes consideration of the local

perturbation produced by the wheel load. Details of the oscillo

graph trace readings and measurements were explained in refer

ences 12 and 17.

3.2 Evaluation of Experimental Data

3.2.1 Transverse and Longitudinal Strains

After the excursions vex (1) and vex (2) had been mea

sured, a computer program for the CDC 6400 computer was developed

to convert the vertical excursions of the gages into corresponding

strains and stresses. For easy identification, the strain e . in. Xl

the transverse direction was defined as e or e • The subscriptX·l Xa

i denotes the strain developed without the local effect, whereas

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the subscript a corresponds to the net strain, including the

local disturbance. The strains in the longitudinal direction e .yl

were specified similarly as e or e . For the development ofYl ya

stresses in the computer program, details will be presented in

the next section.

In addition to the aforementioned vertical excursions,

the input data for the development of the strain values consisted

of the attenuation of the vertical excursions, equivalent cali

bration values, gage numbers, connecting cable lengths, gage

resistances, gage factors, run numbers, lane numbers, and speeds

of the test vehicle. Since the slab acted compositely with the

girders, the longitudinal strain near the top flanges of the

girders could be evaluated from the results in the lateral dis-17

tribution of load in this bridge. The additional input data

included the thicknesses of the slab surfaces near the flanges,

locations of the neutral axes of the girders, and the strain

values at the bottom of the girders.

The output of this program included the reprints of the

input data, corresponding transverse and longitudinal strains, as

well as punched cards which recorded the strain values. The re

prints of the input data were for confirmation of the original

data. The punched strain cards served as the input data cards in

the development of slab bending moments, which will be covered in

Section 3.2.3.

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modulus of elasticity and Poisson's ratio of the concrete. The

Section 3.2.1). The added input data included the values of

and M ., which will be covered in the next section.Xl

(2)'

(1)

i = 1,2

i = 1,2

the theory of elasticityl6,

17problem can be defined·

[€.+V€.Jyl XlE= --a-

l-v

O'.=~ [€ .+v€.JXl l-v Xl yl

0' •yl

O'xi = bending stress in transverse direction

0'yi = bending stress in longitudinal direction

E = modulus of elasticity

v = Poisson's ratio

3.2.2 Transverse and Longitudinal Bending Stresses

In the following analysis, the concrete was assumed as

€ • = strain in transverse directionXl

€ • = strain in longitudinal directionyl

In order to obtain the stresses 0' • and 0' ., a com-Xl yl

puter program segment was inserted into the strain program (see

the local effect.

the bending stress for a two dimensional

0' represents the stress with local disturxa

bance. O'Yl and O'ya are defined similarly as O'Xl and O'xa' The

index notation is similarly applied to other variables w., B.,1 1

0' (index i = l) denotes that the stress was developed withoutXl

a homogeneous, isotropic material. From

as

where:

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Where z was the coordinate across the depth of the slab (Fig. 8),

and d was the actual thickness' of the slab where gages were in-

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(6)

(4)

(5)

(3)

2o W.= -z __1

0/e •yl

e .Xl

20 W. exib - e

xit1 =OX

:a d

:a0 w. e - eyit1 xib

a = doy

the curvatures in the transverse and longitudi-

e 'b and e 't were the strains (Fig. 8) at the bottomXl Xl

2Ow.

1--2- wereoy

It was assumed that the strain.was linear across the

3.2.3.1 Formulation of the Experimental

3.2.3 Experimental and Design Slab Bending Moments

Slab Bending Moment

2o W.1 and2

OX

stalled.

nal directions, defined as

,

strain and displacement relationships were:

slab section (Fig. 8). Considering the bending effect, the

output of the program were values of cr . and cr ..Xl yl

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The area of the reinforcing steel in the concrete and the corru-

gated steel on the bottom of the concrete were first transformeda

into concrete. The total area (in) of the concrete section

(9)

(8)

(7)

(11)

(10)

= _(EB~) zl-v

e .b and e ·tYl Yl

From the theory of elasticity18 the

f a . dA = aA Xl

a .Xl

aX1

• =~ [e . + v e . ]1 Xl Yl-v

Ez C·w. c·w.)axi = - --2

__1 + V __1

2 .. 2l-V ax oy

2 2a w. a w.

B. 1 + V 1 then=--1 2 2 ,

ax oy

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~A - 5d - 5. 476 + O. 476 n + 7. 21 t ns

having a width of 5 inches (Fig. 8) was

From the equilibrium of the forces on the section (Fig. 8),

and top of the slab in the transverse direction.

were similarly defined.

Substi tuting Equations (3) and (4) into (7)

stress and strain relationships were derived as

If

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3Z - 2) ]c- (d -

4

- Z - 2)c+ 1.25 [0.25 (d

and negative bending moment denotes concave downward.

For a better understanding of the contribution of each

5 ( )3 () _ Z _ 1) a+ 12 d - 2 + 5 d - 2 (0.5 d c

a 3+ 0.238 (n - 1) [ (d - Zc - 3) + (zc - 2) ]

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the concrete, and t was the thickness of the corrugated steel.s

Positive bending moment indicates curvature which is concave upward,

where nwas the ratio of modulus of elasticity of steel to that of

the bending moment, per foot width of slab, is defined as

established as

19Following the definition from the theory of plates and shells

From equations (9), (10), and (11), the neutral axis can be

... 1 :3Zc ::c L:A [2.5 (d - 2) + 5.0 (d - 1.167) + 0.238 (n·- 1) (d - 1)

+ 2.5 t n (d - 1) + 4.71 t n (d - 1) ] (12)s s

EB. ~ aM . = - --~~:3- 1. 25 t s n [(d - zc) + (d - ~c - 2) a ]

Xl 5 (1-\1 )

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Case III. Solid Slab - Full Depth: Corrugated steel and re-

element in the slab section, several cases were considered in

These cases are shown in Fig. 9.

evaluating the experimentally-based values of slab bending moment.

(15)

17 18 19as ' ,

Hence, the thickness (t )s

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a a ')Ed3 (0 Wi 0wi

= 2 --2- + --2-

12 (l-v) ox oyM .

Xl

Solid Slab - Equivalent Depth: Case IV was

with a total depth d. The bending moment

under the section1and therefor~ an isotropic,

homogeneous solid rectangular section was assumed

inforcing steel are replaced by the extra concrete

of the corrugated steel in equation (14) was in-

cluded as t = 0.0280 inches.s

(ft.-lb./ft.) was computed

tribute to the slab stiffness. Therefore, the

with the bridge deck.

corrugated steel was assumed to act compositively

Considering Corrugated Steel: In this case, the

Neglecting Corrugated Steel: Since the cast-in-

slab bending moment evaluated in this case can be

place corrugated steel was primarily used as a

construction form, it was not considered to con-

simply achieved by setting t s = 0 in equation (14).

Case IV.

Case II.

Case I.

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-15-

section is one inch less than that of Case III,

the reprints of input strains.

moment for simple spans with main reinforcement perpendicular to

(16)(S + 2)32 PaoM

traffic, and under HS 20-44 truck loading, was computed as:

over three or more beam supports, then a continuity factor of 0.8

per foot width of slab, S is the clear span between girders, and

to approximate the average value of the depth.

of this program consisted of the bending moments (4 cases), and

similar to Case III, except that the depth of

In computing the bending moments, a fortran IV computer

3.2.3.2 Design Moments for Slab

The slab of the bridge was designed according to the

AASHO Specifications, 1961 Edition. Accordingly, the live load

where M is the positive or negative bending moment in foot-pounds

program was developed. The input data included strains (from data.y

cards in the strain program), the ratio of the modulus of elastic~

ity of steel to that of the concrete (n), the actual thickness of

slab at gage locations, and the test run information. The output

Pao is the HS 20-44 wheel load (16,000 pounds). The development

of the slab design equation was essentially based on work bya aO_23

Westergaard and others Equation 16 represents a simply

supported slab with single span2

• If the slabs are conti~uous

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Finally, it would be appropriate to note that in the

was applied to amplify values of M computed from Equation (17).

actual design of the slab, the total effective depth was taken

as 7 in. The top ~ in. was considered to be ineffective, as

well as the steel form and the concrete below the top of the

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is applied and equation (16) becomes:

M = + (0.80) (8 + 2) p.... 32 20

3In considering the impact effect, the impact formula

- 50 ~'O 30I - L + 125 •

form.

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(17)

(18)

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4. PRESENTATION AND DISCUSSION OF TEST RESULTS

4.1 Transverse Bending Moments

4.1.1 Influence Lines for Transverse Bending Moments

In the computation of transverse bending moments, equa

tions (5 -15) were applied. The moduli of elasticity of steel and

concrete were taken as 29,000 ksi and 5,000 ksi, respectively. The

Poisson's ratio of the concrete was assumed as 0.18. Four cases

(I -IV) were considered in computing bending moments. The re

sults of Case I will be presented in this Section, and Cases

II -IV will be discussed in Section 4.1.3.

The bending moments obtained are interpreted with influ

ence lines as shown in Figs. 10-16. The upper part in the figures

represents the results with midspan diaphragms in place, and the

results with the midspan diaphragms removed are shown in the

lower part of the figures. Solid lines show the behavior of the

bridge under static loads. Each value is the average result from

two identical runs. The results from the impact runs are shown by

the dashed lines. Each impact value was obtained from one test

run. In both crawl and impact cases, the local effect is excluded.

With the use of the influence lines, the value of the

transverse bending moment can be determined, with the bridge under

single or multi-lane loading. Since the bridge was designed for

more than one load lane, the superposition method can be applied

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to find the maximum slab bending moment as long as the slab is

not cracked.

An examination of the influence values indicates that

the magnitude of the bending moment in the slab is greatest when

a wheel load is positioned nearest the gage location. It can also

be seen that the bending moment becomes smaller and sometimes

changes in sign, when the wheel is located farther away from the

gage location. In general, when the test results indicate that the

truck load is located near the designated gages in the bridge, a

positive bending moment is produced in the slab. Conversely, when

the truck is positioned farther away, the bending moment is negative.

The determination of bending moments was based on the

curvature of the slab in both transverse and longitudinal direc

tions. It was found that both the stiffnesses and spans of the

prestressed girders and slab affected the curvatures of the slab.

From Figs. 11 and 13, when the truck was positioned over gage lo

cations C and G (in lanes 3 and 7), with the wheels of the truck

directly over the girders, positive bending moments were produced

at the two locations.

Actually, the bridge deck is a form of one~way slab on

elastic supports, and the magnitudes of the bending moments are

greater at the center of the slab span than near the edges of the

beams. The test section (M) was near the midspan diaphragm which,

when in place, provided a partial restraint and reduced the bending

moments at the test section. The removal of the midspan diaphragm

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provided the release of the restraint and increased the bending

moments at the test section. This behavior without diaphragms

should parallel the behavior at a cross-section which is located

away from the end and midspan diaphragms, for instance, at the

quarter point of the longitudinal span where the effects of the

diaphragms are minimal. It is quite ~lear that in the vicinity

of the midspan diaphragm, the magnitudes of the transverse bend

ing moments are greater with the midspan diaphragms removed.

The general shape of the influence lines for the impact·

runs are similar to those for the crawl runs. However the magni

tudes of the bending moments under impact loads were, in all of

the cases, greater. than those produced in the crawl runs, both in

the positive and negative regions. Since the bending moments with

the midspan diaphragms removed were greater, the following discus

sion is mainly focused on this case. In the impact runs, lanes 1

and 9 were not included in the test program. Therefore, the bend

ing moments at locations A and I did not reach the possible maxi

mum magnitudes.

In the static behavior of the bridge, the maximum posi

tive bending moment produced was 1645 ft.-lb./ft. (at location E),

and the maximum negative bending moment was 400 ft.-lb./ft. (at

location H). In the impact runs, the maximum bending moment was

4600 ft.-lb./ft. (at location E), and the maximum negative moment

was 1350 ft.-lb./ft. (at position I). It is interesting to note

that the maximum positive bending moment always occurred at location

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E, and the maximum negative moment always occurred in panel GHI,

under both static and impact loading. The occurrence of greater

negative bending moments in panel GHI is probably due to the ef

fect of the heavy edge parapet in increasing the resistance to

transverse rotation at the outer edge of the panel. Finally, it

is also significant to note that in all slab panels (ABC, DEF,

GHI) , moment reversal was observed, both at midpanel locations B,

E, and H, and at panel support locations A, C, D, F, G, and I.

4.1.2 Comparisons of Experimental Transverse

Bending Moments With Design Values

Since the slab is supported by more than three flexible

supports in this bridge, the design bending moments, both posi

tive and negative, were evaluated from equation (17). The span

of the slab, center-to-center of girders, was 6 feet 9 inches.

Deducting the width of the top flange of the girder, 18 inches,

the clear span of the slab was 5 feet 3 inches. Equation (17)

renders M = 2900 ft.-lb./ft.

In considering the amplification due to impact, the im

pact fraction was computed from equation (18), yielding I = 0.38.

Since the impact fraction actually used must be less than, or

equal to, 0.30, the value 0.30 was used. Therefore, the design

value for maximum positive and negative bending moment in the

slab was ±. M = 3770 ft. -lb ./ft.

As shown in the last section, the maximum experimental

-20-

IIIIIIIIIIIIIIIII

II

I

slab bending moment under static loading was 1645 ft.-lb./ft.

Comparing this result with the design value of 2900 ft.-lb./ft.,

it is apparent that for this superstructure, the design of slab21

bending moment is rather conservative However, in considering

the impact behavior, the experimental slab bending moment, 4600

ft.-lb./ft., was greater than the design value, 3770 ft.-lb./ft.

Based on this result, it appears that an increase in the impact

factor used in the design of the bridge deck should be given con

sideration in future studies.

4.1.3 The Effect of the Corrugated Steel

and the Depth of Concrete

As described in Section 3.2.3.1, four different assump

tions (Fig. 9) were used in computing experimental values of the

slab bending moments, based on measured surface strains. A com~

parison of values from the four cases indicates the range of a

variation.

In the previous two sections, the values presented were

from Case I, where it was assumed that the corrugated steel did

not participate in resisting deformation from the loading. When

the corrugated steel was considered to be acting compositely with

the bridge deck concrete (Case II), the computations yielded an

additional 7 -~Ia to the computed experimental bending moments.

Actually, the slab moment values probably lie between the values

computed for Cases I and II. That is, the actual experimental

-21-

IIIIIIIIIIIIIIIIIII

bending moments would be between 1.00 and 1.08 times the values

presented in Sections 4.1.1 and 4.1.2, depending on the effective

bond between the corrugated steel forms and the reinforced con-

crete slab. For a better understanding of the composite behavior,

additional tests would be needed, in which extra gages should be

applied directly to the surface of the corrugated steel, as well

as on the concrete surface, in order to compare the strains at

the interface.

Since the development of bending moment values is rather

complicated when the reinforcing steel and corrugated steel are

considered (Cases I and II), equation (15) was utilized to com-

pute values in Cases III and IV, in which it was assumed that the

. . h d l' 1 1 t' 9,lO,J.l.material was lsotroplc, omogeneous, an lnear yeas lC .

In comparing the results from several test runs, it was

found that the slab bending moments in Case III were 25 - 30%

greater than those computed in Case I. After the depth of the

slab. was reduced by one inch (Case IV), the slab bending moments

were approximately 9% less than those in Case I. Since the slab

bending moment is roughly proportional to the cube of the depth

of the concrete, it is estimated that if 3/4 inch was deducted

from the total depth of the concrete slab, then the results from

Case IV would be nearly equal to the values found in Case I.

4.2 Slab Strains

All of the strains from all of the gages were computed

-22-

IIIIIIIIIIIIIIIIIII

and printed in the computer program output, with the superstruc

ture under the various loading conditions. The maximum measured

tensile and compressive strains at each gage location were then

selected from a comparison of values for the crawl runs in all

nine loading lanes, and under the two test conditions, with and

without the midspan diaphragms. For the impact runs, the same

procedure was followed except that the results represent only

the seven loading lanes which were used for the impact runs.

These maximum strain values from both crawl and impact runs are

listed in Table 2. At this point, it should be noted that all

gage numbers listed in Table 2 represent transverse gages. How

ever, longitudinal strains, e and e , are also listed oppositeyl ya

the transverse gage numbers. These longitudinal strains repre-

sent values obtained either from longitudinal gages at these

locations, or from extrapolations of strains from longitudinal

gages mounted along the sides of the beams.

It was found that each gage mounted on the slab was

subjected to both tensile and compressive strains, depending on

the location of the concentrated wheel loads during the various

test runs. Gages 1014, 1008, and 1002 (Fig. 4), located on the

bottom surfaces at the midspan points of three of the slab panels,

were subjected to higher tensile strains than compressive strains.

Conversely, gages 1015, 1009, 1003, located on the top side of

the slab directly above gages 1014, 1008, and 1002, yielded

larger compressive strains than tensile strains. The magnitudes

-23-

IIIIIIIIIIIIIIIIIII

and signs of strains from the other gages, all located near the

top flanges of the girders, varied considerably.

The maximum tensile strain, neglecting the local effect,

was 30.4 micro.-in./in. in the crawl runs, and 95.0 micro.-in./in.

in the impact runs. Both values were measured at gage 1008.

When the local effect was included, the maximum tensile strain

was 58.5 micro.-in./in. in the crawl runs, and 95.0 micro.-in./in.

in the impact runs. Again, both values were measured at gage

1008. The maximum compressive strain, neglecting the local

effect, was 22.2 micro.-in./in. in the crawl runs, and 54.3

micro.-in./in. in the impact runs. These values were measured

at gages 1011 and 1009, respectively. When the local effect was

considered, the maximum values were 41.3 micro.-in./in. in the

crawl runs, and 54.3 micro.-in./in. in the impact runs.

At this point, it would be appropriate to describe the

measurement of the longitudinal compressive strains. At the mid

points of the gaged slab panels (Fig. 4), longitudinal gages were

used to directly measure the longitudinal strains. However, the

longitudinal strains at the ends of the gaged slab panels,

directly above the edges of the supporting girders were evaluated

using the extrapolation of strain values measured along the verti

cal surfaces of the girders. This procedure was used to yield

the maximum information from the limited number of available re

cording channels.

Nearly all of the gages were subjected to local

-24-

IIIIIIIIIIIIIIIIIII

disturbance when a concentrated wheel load was located near the

gage. In the crawl runs, the local disturbance produced a magni

fication of strain values, with few exceptions. However, even

though the amplification percentage was large, the resulting maxi

mum strains were relatively low in. magnitude (-58.5 micro.-in./in.,

and 41.3 micro.-inA/in.). These values were measured at the

bottom and top surfaces at the midpoint of the middle slab test

panel.

In evaluating the results from the impact runs, the

vigorous vibration of the bridge made it possible to distinguish

the effect of the local disturbance from the oscillation due to

the impact load. Therefore, it should be noted that in Table 2,

the values listed ~ith subscripts 1 and 2 were the same.

4.3 Slab Stresses

The slab stresses are presented in the form of influ

ence lines, both in transverse and longitudinal directions. To

illustrate the variation in the magnitude of· the slab stresses

under different locations of the load vehicle, the maximum values

of the slab stresses are presented in Table 3. Listings in

Table 3 parallel the strain values listed in Table 2, as described

in Section 4.2.

4.3.1 Influence Lines for Transverse Slab Stresses

The slab stresses in the lateral direction, perpendicular

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IIIIIIIIIIIIIIIIIII

to the direction of traffic, are presented in the form of influ

ence lines, (Figs. 16 - 42). In these figures, the solid lines

denote the slab stresses which were evaluated without considera

tion of the local effect of the concentrated wheel load. In con

trast, the dashed lines represent the stresses with the local

effect included. Positive values indicate compression on the

slab surface, while negative values indicate tension. Near the

bottom of the figures, the stress distribution across the thick

ness of the slab is indicated for the various positions of the

load vehicle, assuming a linear distribution from top to bottom.

In the crawl runs, including the local effect, the maxi

mum tensile stress was 310 psi, produced at gage 1008, and the

maximum compressive stress was 344 psi, at gage 1007.

In the crawl runs, neglecting the local effect, the

maximum tensile stress was 160 psi, produced at gage 1008, while

the maximum compressive stress was 167 psi, at gage 1007. In the

impact runs, the maximum stresses were 513 psi tension, at gage

1008, and 281 psi compression, at gage 1009.

For the behavior under static loading, the Influence

lines are presented in Figs. 16 - 30, where Figs. 16 - 21 indicate

values with midspan diaphragms in place, and Figs. 22 - 30, with

diaphragms removed. For response to impact loading, the influence

lines are given in Figs. 31 - 42, with Figs. 31 - 36 representing

behavior with midspan diaphragms in place, and Figs. 37 - 42 with

diaphragms removed.

-26-

IIIIIIIIIIIIIIIIIII

4.3.2 Influence Lines for Longitudinal Slab Stresses

The development of influence lines for longitudinal

stresses in the deck slab was similar to the development of in

formation on transverse stresses. Figures 43 -50 describe the

variation in these stresses under crawl run conditions with the

midspan diaphragms in place. Figures 51 - 58 represent a similar

series of crawl runs, both with midspan diaphragms removed. The

response to the impact runs, with midspan diaphragms in place, is

indicated in Figs. 59 - 65, and with midspan diaphragms removed,

in Figs. 66 - 72.

In general, the longitudinal stresses were found to be

compressive, except for a few values measured at the ends of the

slab test panels. In these exceptions, the gages indicated small

values of tensile stresses when the truck was located on the oppo

site side of the bridge. It is also interesting to note that all

of the longitudinal stresses measured at the midpoint; of the slab

test panels were very small, no matter where the load vehicle was

located. This indicates that the primary bending at the midpoint

of the slab panels occurs in the transverse direction. However,

it was found that for the locations at the ends of the slab test

panels, the values of the compressive stresses in both longi

tudinal and transverse directions were of approximately the same

magnitude.

Since the longitudinal strains at the ends of the slab

test panels were computed from measurements taken on beam gages,

-27-

IIIIIIIIIIIIIIIIIII

there was no way to evaluate the local effect in the longitudinal

direction. It was only possible to evaluate the local effect in

the transverse direction in these regions. On the other hand,

the influence lines for the midpoints of the'slab test panels,

with local effect included, were evaluated based on direct strain

measurements. The maximum compressive stress with the local

effect included was 296 psi in the crawl run series, and 426 psi

in the impact series. Both measurements were obtained at gage 1015.

-28-

IIIIIIIIIIIIIIIIIII

5. SUMMARY AND CONCLUSIONS

5.1 Summary

This investigation of slab behavior is one part of an

overall investigation of the behavior of ~he superstructure of a

prestressed concrete I-beam bridge. The principal objective of

the overall investigation was to obtain information on the dis

tribution of vehicular loads to the longitudinal beams. The main

objectives of the investigation of the slab were (~) to develop

information on stresses on the surface of the slab, (2) to develop

information on the bending moments produced by both static and

dynamic loading, (3) to compare the experimental results with de

sign values yielded by the AASHO specifications, and (4) to estab

lish a bank of experimental test results to form a base for com

parison with analytical procedures to be developed in the future.

The superstructure of the test bridge was basically com

posed of six identical prestressed concrete I-beams, topped-with a

composite cast-in-place reinforced concrete slab. A reinforced

concrete safety curb section was cast along one edge of the slab.

This superstructure was designed according to PennDOT Bridge Divi

sion standards8

•

The test section for the structue was selected as the

cross-section at which the maximum bending moment was produced by

the load-vehicle. At this cross-section, located 3.55 feet from

midspan, the first, third, and fifth panels of the slab were

-29-

IIIIIIIIIIIIIIIIIII

instrumented with SR-4 strain gages. Nine loading lanes were es

tablished across the width of the slab. A diesel-powered tractor

and semi-trailer unit, loaded with crushed stone to approximate

AASHO HS 20-44 design loading, was used to load the test structure.

Basically, the test series included passes of the load vehicle in

the nine test lanes at speeds ranging from 2 mph to 60 mph, along

with a series of controlled impact tests produced by driving the

load vehicle over a small ramp located near the test cross-section.

A series of tests was conducted first with the midspan

diaphragms in place, as originally constructed. After the first

series had been completed, the midspan diaphragms were completely

removed, and a second series of tests was conducted. A total of

98 passes of the load vehicle comprised the entire load test pro

gram for this superstructure.

The results from this investigation of the slab are pre

sented in the form of tables which list the maximum measured

strains and the maximum computed stresses developed from measure

ments made at selected locations on the top and bottom surfaces of

the slab. In addition, influence lines are presented to illus

trate the variation in stresses at the various gage locations, and

to show the variation in the bending moments in the slab at nine

different locations in the three slab test panels. These influ

ence lines are based on positions of the load vehicle which re

sult in wheels either directly at the midpoints of the slab spans

or directly over the girders. Other positions were not included

-30-

IIIIIIIIIIIIIIIIIII

because of time limitations dictated by the availability of the

field test equipment. Although it is possible that other posi

tions of the wheels might have resulted in larger experimental

values in a few cases, the shapes of the influence lines do not

indicate the probability of maximum values greater than those

measured. Finally, a comparison is made between experimentally

developed bending moments produced during the load test program

and the computed design bending moment.

5.2 Conclusions

The following conclusions can be drawn from the investi

gation of the structural response of the slab.

1. Under static loading conditions, the maximum bending

moment derived from strain measurements at all gage

locations in the slab was considerably less than the

value computed according to the AASHO specifications.

2. Under impact loading, the bending moment exceeded the

design value at only one location. However, it should

be emphasized that the value of the modulus of elastic

ity for the concrete was assumed to be 5000 ksi in

evaluating the experimentally based bending moments.

This value was selected as an absolute upper bound for

the slab concrete. For the concrete actually used in

the slab (fT = 3000 psi), the value for the modulus ofc

elasticity would more probably be in the range 3500 -4000

-31-

IIIIIIIIIIIIIIIIIII

ksi. For the more realistic value of modulus of elas

ticity, the experimentally based maximum bending moment

under the impact loading condition would not have ex

ceeded the design value.

It should also be emphasized that the controlled impact

test was not of a type normally taken into account by

design specifications. Instead, the impact factor

yielded by the AASHO equation is to account for the typi

cal vertical motion of the load vehicle developed at

normal speeds.

3. The transverse negative bending moments were considerably

smaller in magnitude than the maximum positive values.

These maximum negative values were produced in the slab

panel nearest the side of the bridge where the safety

curb section was located. It is concluded that the ef

fect of the safety curb was to restrain the torsional

displacement of the exterior girder, thereby providing

greater rotational restraint to the slab in the exterior

panel.

4. The effect of the midspan diaphragm is to reduce the

strains, stresses, and bending moments in the slab, at

the near midspan cross-section. With the diaphragms in

place, the local effect of the concentrated wheel load

provides a larger component to the total stress than in

-32-

IIIIIIIIIIIIIIIIIII

the case when the diaphragms are not present.

5. Based on a comparison of values computed from test re

sults, the experimentally based bending moments produced

in the slab were increased by approximately ~/a in the

case when the corrugated steel forms were considered to

act fully compositely with the cast-in-place slab. Con

versely, this would mean that full composite action be

tween the form and the slab would result in a reduction

of approximately ~/a in stresses produced by the load ve

hicle. The maximum transverse and longitudinal compres

sive stresses were found to be much less than the allow

able stress permitted in the concrete slab, both in the

static and in the impact loading series. The maximum

tensile stress produced in the static tests was less

than the tensile strength of the slab concrete. At one

of the nine gaged cross-sections, the tensile stress in

the impact series was near to the tensile strength of

the material. This would indicate that very little

cracking would normally be produced in the bridge slab

by vehicular loading.

6. As a result of the testing program on this superstruc

ture, it is obvious that additional theoretical and ex

perimental work is needed to more clearly consider and

formulate the many factors which effect slab behavior

-33a-

IIIIIIIIIIIIIIIIIII

under vehicular loading conditions. Some of the factors

which need to be considered are slab thickness, slab re

inforcement, slab cracking, torsional stiffness of the

beams, and local stresses produced by the wheels.

7. The findings from this investigation of slab behavior

are the third series reported in the current overall re

search investigation of beam-slab type bridge behavior

conducted at Lehigh University. Therefore, at this time,

the results will serve as a representation of the slab

behavior at three different transverse slab spans in a

typical prestressed concrete I-beam superstructure.

Similar results from another I-beam bridge (Bartonsville)

and a spread box-beam bridge (Hazleton) will form a

basis for comparison of field test results, and will

provide a useful data base for the future analytical

work required to develop possible revisions in specifi

cations and procedures for deck slab design.

-33b-

IIIIIIIIIIIIIIIIIII

6. ACKNOWLEDGMENTS

This study was conducted in the Department of Civil

Engineering and Fritz Engineering Laboratory, under the auspices

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

search investigation sponsored by the Pennsylvania Department of

Transportation; the U. S. Department of Transportation, Federal

Highway Administration; and the Reinforced Concrete Research

Council.

The field test equipment was made available through

Mr. C. F. Scheffey, now Director, Office of Research, Federal

Highway Administration. The instrumentation of the test struc

ture, and operation of the test equipment, were supervised by

Messrs. R. F. Varney and H. Laatz, both from the Federal Highway

Administration.

The basic research planning and administrative coordi

nation in this investigation were in cooperation with the follow

ing individuals representing the Pennsylvania Department of Trans

portation: Mr. B. F. Kotalik, Bridge Engineer; Mr. H. P. Koretzky,

and Mr. Hans Streibel, all from the Bridge Engineering Division;

and Messrs. Leo D. Sandvig, Director; Wade L. Gramling, Research

Engineer; and Foster C. Sankey and Kenneth L. Heilman, Research

Coordinators, all from the Bureau of Materials, Testing, and

Research.

The following members of the faculty and staff at

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IIIIIIIIIIIIIIIIIII

Lehigh University made major contributions in the conduct of the

field tests and in the reduction and processing of the test data:

Dr. C. N. Kostem, Prof. J. o. Liebig, Jr., Felix Barda, Yan-Liang

Chen, and Anton Wegmuller. The manuscript was typed by Mrs. Ruth

Grimes, and the figures were prepared by John M. Gera and Mrs.

Sharon Balogh.

-35-

IIIIIIIIIIIIIIIIIII

7. TABLES

-36-

-------------------TABLE 1 LIST OF TEST RUNS

IUJ-....JI

Nominal With Without

Description Speed Midspan Diaphragms Midspan Diaphragms

(mph) Lanes No . Lanes No..•....~.~._ .. ..... .. ~._~ ..-...... ~. ...~= .~",..~::- ....,-_....__. .- ......., .'~'- -.. - - '. -.. -.-.... ".'" - .. -- ---- - .-' . - ~._ .. ._, . --.-' -. _....

'._~ . .....- ....~ .....__..... _""_. _.-Crawl 2.0-3.0 1,2,3,4,5,6,7,8,9 18 1,2,3,4,5,6,7,8,9 18

Speed 15.0 2,6 2 2,6 2

17.5 2,6 2 2,6 2

20.0 2,6 2 2,6 2

22.5 2,6 2 2,6 2

25.0 '.J 2,6 2 2,6 2

27.5 2,6 2 2,6 2

30.0 2,6 2 2,6 2

32.5 2,6 2 2,6 2

35.0 2,6 2 2,6 2

55.0 2,6 2 2,6 2

57.5 2,6 2 2,6 2

60.0 2,6 2 2,6 2-.• <.-

Impact 10.0 2,3,4,5,6,7,8 7 2,3,4,5,6,7,8 7

Sum 49 49..

Total 98

-------------------TABLE 2 MAXIMUM MEASURED SLAB STRAINS

U ·t 10-6• I·nl : In. In.

ILA)

<XlI

.. --~~'-'" ."-"_... _.............._~-_.-_.-

Crawl Runs Impact Runs.. r ...._~-- ...,....~_ ....~----._ .....-Gage Tensile Compressive Tensile Compressive

Strain Strain , Strain Straini

No.

!,

I..

, ~

e e e e e e i e e e e ! e eXl. Xa Xl xa yl ya ~ Xl xa Xl xa yl ya

i I..._... .. ·..··"·-"· .. 1..·· . _.... ."' .. ~.",- ............ ,.. -, --...._......,...........'" _.....--..~._- - ,,,.--- -_.- ~--.".'" ., ,.. , . ..................._-c.. ,....1'

1017 -6.9 -11.8 5.0 9.9 31.4 31.4 -12.9 -16'.2 5.6 9.6 149.1 1 49 •11016 -11.1 -18.5 4.7 11.8 15.2 15.2 -15.8 -15.8 10.2 10.2 j 26.0 I 26.01015 -'-4.6 -4.6 10.3 31.5 33.2 51. 7 --- --- --- --- : 82.5 I 82.51014 -20.8 -47.2 4.7 4.7 2.4 2.4 -32.2 -78.6 12.2 12.2 ; 3.2 I 3.2i I1013 -5.3 -54.6 11.8 10 ;2 25.6 25.6 i -14.8 -14.8 31.0 31.0 l 43.4 I 43.4I

I1012 -19.6 -19.7 3.8 3.8 13.9 13.9

!-37.8 -37.8 13.1 13.1 I 22.8 I 22.8I,

1011 -11.4 -37.0 22.2 12.7 16.9 16.9 --- --- --- --- ! 32.7 j 32.71010 -18.6 -21. 7 6.7 6.8 8.3 8.3 -34.0 -34.0 9.3 9.3 ! 14.3

,14.3, ,

$ i

1009 -11.8 -26.5 19.9 41.3 15.4 I15.4 ! -16.7 -43.2 54.3 54.3~ ;

~ --- : ---1008 -30.4 -58.5 12.6 12.6 1.2 1.2 ~

-95.0 -95.0 12.2 12.2 1.2 ! 1.2! I1007 -9.6 -9.6 5.1 5.1 17.3 17.3 ! --- --- --- --- 32.4 32.41006 -22.8 -26.7 10.8 10.8 6.9 6.9 -47.6 -47.6 15.6 15.6 13.2 i 13.21005 -6.7 .. -6.7 7.5 7.5 18.9 18.9 -20.9 -20.9 30.2 30.2 31.4 i 31.41004 -16.4 -13.8 4.8 4.8 7.7 7.7 -29.4 -29.4 12.5 12.5 13.0 I 13.01003 I -8.6 -13.0 11.0 33.2 19.4 38.8 -14.0 -24.2 35.8 35.8 39.8j39.81002 -11.3 -34.3 4.4 4.4 2.9 10.0 -45.2 -45.2 10.3 10.3 11.4 11.41001 I -7.9 -7.9 4.6 5.1 22.2 22.2 -29.7 -29.7 14.5 14.5 38.1 38.1

IL

1000 -12.1 -22.2 4.3 4.3 9.2 9.211

-16.0 -16.0 12.1 12.1 16 • ~_ _:~ ..~_... .._"-- ...

-------------------TABLE 3 MAXIMUM COMPUTED SLAB STRESSES

Unit: psi

IW1.0I

Crawl Runs Impact RunsGage

Tensile Stress Compressive Stress Tensile Stress Compressive StressNo.

0: (J (J (J (J (J (J (J (J (J cr crXl xa Xl xa yl ya Xl xa Xl xa yl ya

1017 -23.9 -37.8 54.4 80.6 165.4 171.3 -45.2 -45.2 74.4 74.4 259.0 243.4

1016 -44.7 -81.6 30.2 72.8 69.5 77.7 -57.8 -57.8 62.8 71.0 119.4 126.3

1015 -36.4 -36.4 74.6 210.8 146.2 296.3 ---- ---- --- --- 426.4 426.4

1014 -105.2 -241. 7 24.3 24.3 4.4 4.4 -169.1 -409.2 61.3 61.3 6.0 4.7

1013 -22.0 -258.3 79.4 72.4 135.0 118.5 -62.8 -62.8 194.5 194.5 239.3 219.4

1012 -89.4 -89.1 22.7 22.7 62.7 54.1 -178.0 -178.0 75.7 75.7 95.4 95.4

1011 -74.2 -181.3 129.5 81.4 103.4 99.1 ---- ---- --- --- 169.0 169.0

1010 -89.7 -106.4 40.6 40.6 47.1 47.1 -163.9 -163.9 56.2 56.2 71. 2 71.2

1009 -56.6 -165.0 114.0 243.4 96.5 205.9 -86.2 -223.2 280.8 280.8 --- ---1008 -160.2 -309.9 64.6 64.6 10.0 10.0 -512.7 -512.7 60.6 60.6 16.0 16.0

1007 -87.4 -87.4 167.2 344.0 100.5 114.3 ---- ---- --- --- 167.4 167.4

1006 -112.2 -132.3 60.3 60.3 38.7 38.7 -233.6 -233.6 89.0 89.0 61.8 61.8

1005 -28.6 -28.6 55.0 55.0 104.7 96.1 -94.8 -94.8 184.2 184.2 187.1 187.1

1004 -77.8 -64.6 25.5 25.5 30.1 33.0 -139.7 -139.7 71.1 71.1 55.9 55.9

1003 -42.3 -65.1 57.1 171.3 101.7 210.8 -72.3 -87.7 191.0 184.9 233.7 183.5

1002 -55.9 -168.2 20.7 20.7 4.2 19.8 -223.0 -223.0 50.6 50.6 17.1 17.1

1001 -31.6 -31.6 42.1 38.0 114.9 115.5 -135.0 -135.0 110.3 110.3 210.5 210.5

1000 -54.2 -106.2 26.0 26.0 40.6 43.1 -67.4 -67.4 66.1 66.1 79.2 79.2

IIII·IIIIIIIIIIIIIII

8. FIGURES

-40-

- - - - - - - - - - - .. - - - - - - -

1'_6" 1'_6"

71'-6" Clc Brg.

-3.80%

'~

3.55' It 32.20'

Test Section M

71'-6" Clc Brg.71'-6" Cf'c Brg.

I+:".....I

Fig. 1 Elevation of Test Bridge

-----------~-------

37 1-11 ~211

~I

10 1- 011

~81 per ft. =v---- .::>LO

121-0

11

-I ItYa per ft.

Profi Ie Grade

121- 011

1,1; IIa per Ft. Point of-1

-1=I\..l1

21-1 11 6- 24/45 Pis I-Beams @61-g11 clc=331-9 11 21-1 ~21

H~------------HFig. 2 Cross-Section of Test Bridge

-------------------

Strain Gages

-C\I

I-l=wI

o Transverse Gage

- Longitudina I Gage

CorrugatedSteel

I

1- 5"I

-I

=

Fig. 3 Transverse Cross-Section of Slab

- - - - - - - - - - - - - --- - - -, -

I++I

0--.o (7)- I\)~ 0

8'-3"

<? <p0

(7) 00 0 0

<D UI .....~-..

0--.0 (7)

0 ~CD

o Longitudinal Gages

Transverse Gages

51-3"

Fig. 4 Location of SR-4 Gages

Rear

t32.340k (I)

32.67Sk (2)

Drive

t32.32S k

32.200k

Axle Loads

Axle and Wheel Spacing

Fig. 5 Test Vehicle

-45-

(I) Load: July /S -24, 1969

(2) Load: July 2S, 1969

Front

t10.42Sk

10.200k

1- 13.01

--1-- 20.41

--II I I I

l' I

c:Ito b -LO (\J

to ~ Iri to..:I I II I I I

IIIIIIIIIIIIIIIIIII

-------------------

CD ® ® ® ® ® 0 ®®I I" I I II I II If I II II I IJ' II I IJ' II I II II I II 4' 9 II .

1~-41'~1~-4~1~-4'.:1~-4'.:1~-4';.1~-4'1~-4::1~.. - _I.::;:;:;:;..........................:.:-:.:.:.: :.:.:.:.:.:.: :.:.:.:.:.:.: :.:.:.:.:.:.:.: :.:.:.:.:.:.: :.:.:.:.: :: ~ ~ ~ ~ ~ ~ ~ ~ ~j'

I~enI

Fig. 6 Loading Lanes

-- ':"-.--

IIIIIIIIIIIIIIIIIII

-,.-----------xw>

---- Local Effect Included

- - - - Local Effect Excluded

Fig. 7 Typical Oscillograph Record - Crawl Run

-47-

-C\J-XW>

o

=

€ xit

t =0.0280 II

A~=0.238 in2

C\J

.As =0.238in2

-.--~--= y = IIL6 (- z +d +1- Zc)

5 " I"Ya I ~4

UIN

-48-

Longitudinal Gage

o Transverse Gage

Fig. 8 Distribution of Strains

qC\J

I

UIN

I"'0

N.A.y----t-----+--+----+-----+---

IIIIIIIIIIIIIIIIIII

-49-

Fig. 9 Assumptions in Development of ExperimentalSlab Bending Moments

C\J

Case Dr

Case n

- l--'-J

-C\J

Case m

Case I

• Reinforcing Steel

= Corrugated Steel

IIIIIIIIIIIIIIIIIII

Fig. 10 Influence Lines for Transverse Bending Moment - Location A

-50-

8 9765432

,

--- Crawl Run - Local Effect Excluded

-- - Impact Run - Local Effect Excluded

I I

WithoutDiaphragm

I

II--

With~ Diaphragm

--- ~

1----f----1----~- --~

t--

.....zw~ -2~

-

.....zw~ -2o~

....., 2.0

-I~

If) 0o

-+-= 2,.0

Test Lanes

IIIIIIIIIIIIIIIIIII

8 97654

.,


--- Impact Run - Local Effect Excluded

WithoutDiaphragm

I I

-51-

.....z~ -2o:E

.....zw:E -2o~

-I..:....

'0 0 t--t----jr----t--r~+__;;:::~==~=1=:;_--

-

Test Lanes I 2 3

=- 2 With I,.J:i Diaphragm

Fig. 11 Influence Lines for Transverse Bending Moment - Location C

IIIIIIIIIIIIIIIIIII

8 97

,

65

,

4

I

32

I IWithout

Diaphragm

---- Crawl Run - Local Effect Excluded

----- Impact Run - Local Effect Excluded

2With

Diaphragm

oL-i----i~=f::::t=t=t~bLL-

~zw -2~o~

~

zw~ -2o~

-52-

-

-..:~ 2.0

I

.a=If)

o Ot--__r---:::::::::J~,e-+_-_+_-+_-+_-+_~~=t_--

~........ri'.~

It)

o

Test Lanes

Fig. 12 Influence Lines for Transverse Bending Moment - Location E

IIIIIIIIIIIIIIIIIII

987

,

65

..

43I 2

I IWith

Diaphragm

I IWithout

Diaphragm


-- - Impact Run - Local Effect Excluded

-53-

.....zw~ -2o~

.....zw~ -2o~

-

-OOI-t::::::t:====1~~~=7P~I-I-II--

.;..;-'O°I~==::t==+===t===::{T:"""-II-I----'I-

Test Lones:? 2........ci

Fig. 13 Influence Lines for Transverse Bending Moment - Location G

IIIIIIIIIIIIIIIIIII

Fig. 14 Influence Lines for Transverse Bending Moment - Location H

8 9

,

765432

-Dr-

WithoutDiaphragm


- - - Impact Run - Local Effect Excluded

- IWith ,/

Diaphragm ----/'-- .........

--r-------....-~

'-"

~zw -2~o~

-54-

~zw~ -2o~

I~~

If)

o O~-+---+---+---+----:o'--+--:::i:::oo-'~-+---+---+--,

-

'-"

-;:........ 2.c

~ 2.........c

I..:~

'0 0

Test Lanes

IIIIIIIIIIIIIIIIIII

Fig. 15 Influence Lines for Transverse Bending Moment - Location I

8 97654

-

32

---- Crawl Run - Local Effect Excluded

---- Impact Run - Local Effect Excluded

r- I IWith

Diaphragm~

~

---~-------f-

r-

-55-

-....zw -2~o~

-.,: I I~ 2...... WithoutJ:iI Diaphragm-~

.." 00-....zw

-2~0~

-:: 2.......c

I.,:

;- 0o

Test Lanes

IIIIIIIIIIIIIIIIIII

Fig. 16 Influence Lines for Transverse Stress Crawl Runs Diaphragm in Place - Gages 1017 and 1016

-56-

- - - Local Effect Included

8 9765432

-Gage1017 -, - ..............

' ... ...----

-Gage

/11',...1016 / ' .....

l- V~

tV\ 7 , , I

ionsses ,

\ 155 I \pth Ll l __ ~ 1

a

a

100en0.

--Local Effect Excluded

Variatin Stre

Acrothe De

Test Lanes

- 100

enenwa:..... -100en

enenwa:..... -100en

-

-

IIIIIIIIIIIIIIIIIII

Fig. 17 Influence Lines for Transverse Stress Crawl Runs _Diaphragm in Place - Gages 1013 and 1012

---- Local Effect Included

--- Local Effect Excluded

8 97654:32

I-

Gage

/'~--

'"1013 ...1-,

/1---_1-

~ //

II-

......Gage1012

~" / ~I- ~ ......~/ -"..

~

r---

r~ :r 1 ,I

n \\

es \ ,I

\

~ lh ~ I J

a

a

-57-

-200

U)U)

w -1000:~U)

Test Lanes

100

U)U)W0:::~ -100U)

.iii 100a.-

fI)

a.-

-

-

Variatioin Stress

Acrossthe Dept

I-III,I

IIIIIIIIIIIIII

Fig. 18 Influence Lines for Transverse Stress Crawl Runs Diaphragm in Place - Gages 1009 and 1008

8 9765432~

~

Gage ./',

/'1",f-1009 ./ ,~

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

I--

l-

I--

f-Gage1008 .... --~ -7

~..../ ",

f-- ' .... ./ " v/

1 1 T7 11

W I { \n I'I I

A, \es

j d I I \

h 1

-58-

CJ) 0CJ)IJJ0:::~ -200


Test Lanes

-- Local Effect Excluded

CJ)

CJ) 0IJJ0:::

~ -200

~ 200-

-en 200Q.-

Variatioin Stress

Acrossthe Dept

IIIIIIIIIIIIIIIIIII

8 9765432

-~-

-59-

Influence Lines for Transverse Stress Crawl Runs Diaphragm in Place - Gages 1005 and 1004

I-Gage

./~1005 ""i;;;; ". ....................--

~

~

I-Gage

~

1004

~

I--

I r; ~ ~Ionssesspth 1 ~ ) I

o

Fig. 19


Variatin Stre

Acrosthe De

- Local Effect Included

enenlLJa=:I- -200en

en 0enlLJa=:I- -200en

Test Lanes

=:: 200en0.-

-en 2000.-

IIIIIIIIIIIIIIIIIII

8 9765432

-60-

Influence Lines for Transverse Stress Crawl Runs Diaphragm in Place - Gages 1003 and 1002

~

Gage ""1',1003 ,- -...

.--r-

~ .

~

Gage1002 -

~ -....1--

r--

I 1 1 I 7 ~t-l Vtion vsses I

ss lJ depth j

Fig. 20

Variain Stre

Aerothe 0

II) 200Q.

II)Q.



en 0enw~ -200en

~ 0wa::t; -200

Test Lones

- 200

-

--

IIIIIIIIIIIIIIIIIII

Fig. 21 Influence Lines for Transverse Stress Crawl RunsDiaphragm in Place - Gages 1001 and 1000



8 9765432,.....Gage1001 ".,- 7'"

--

~

~

Gage1000

-.......~ '"'"....-

1 ,~

,~ lr ~7ion It

ses I ~

s~ LLpth J ~ 1 L .

a

a

(f)enLLJ

~ -100en

-61-

enenLLJ

~ -100en

= -100ena.-

Test Lanes

·in 100a.

Variatin Stres

Acrosthe De

IIIIIIIIIIIIIIIIIII

Fig. 22 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1017 and 1016

--- Loco I Effect Excluded

- - - Loco I Effect IncIuded

8 9765432

~

~Goge ~~

1017....-,

""....-

~

f-

~Goge

1016 "-'- ----/' ~~

~'~

V7{ { I {

nses

I LI 1th iL J 1 ~ 1 j J

100enQ.

-62-

Test Lones

en 100Q.

~ 0wa::~ -100

-

--

-

CJ) 0CJ)w:= -100CJ)

Voriotioin Stres

Acrossthe Dep

IIIIIIIIIIIIIIIIIII


98765432

~ ,/'1',Gage " ~"1015 r-

Io-.

I-

~

~

Gage1-

1014

--- -7~I', "~ " v"

f rJ7 I I , Ion

Ises

lilsth I J 1 j J

o

Test Lanes

200

Variatiin Stres

Acrosthe Dep


~ 0wa::~ -200

-63-


(J)(J)wa::~ -200

-"Ci) 200Q.-

enQ.-

IIIIIIIIIIIIIIIIIII



- -- Local Effect Included

8 9765432

~

Gage~ /' '"1013 / i'-.

l- II-- I

//

I-- Il- IiI--

Gage1-'0 12

.J

VV

~ t><f". ...........~

I--

,---r fr r 7 I I I I,s',

1 L ~'\L l J ~ 1 J

a

a

-200

enenw -100a:~en

-200

III0.

-64-

Test Lanes

100

100

enenwa: -100~en

III0.-

Variationin Stresse

Acrossthe Depth

IIIIIIIIIIIIIIIIIII


8 9765432

-{>~

~'OII-

l-

I--

Gagei':.............1011 ./ I'C"...... ",'" I'-..........

~ ' ....-.....~

1'- ""'.......I-- --~--l-

I-

I--Gage1010 t--

--............-- r- -~' ..~ ....I--

,

~ ,r P\1 \ ~ ntion\ \

\sses

~\ \, \

55 1 ~I \

pth l I I 1

200

200

Test Lanes I

ena.

Variain Stre

Acrothe De

-65-



~ 0wa:~ -200

~ 0wa:~ -200

ena.-

IIIIIIIIIIIIIIIIIII

-66-




Test Lanes 2 3 4 5 6 7 8 9

400(/)c.- 200 ,en Gage ,en 1009wa::: 0l-en

-200

200Gage-.iii

c. 1008- 0enenw -200a:::l-en

-400

Variation,

\in Stresses \ \\ \

Across \the Depth

IIIIIIIIIIIIIIIIIII


8 9765432

-0 -

Gage-0

1005 .... -,-

0-

0 -Gage

01004

---- 1.0 ......

0 --

tion{ 7 7 rvr~

sse5, I

S5 L Llpth 1 1 j j l

Test Lanes

- Local Effect Included

Variain Stre

Acrothe De

--- Loca I Effect Excluded

-67-

CJ)CJ)w~ -20CJ)

CJ)CJ)wa::t; -20

- 208.-

-8. 20-

IIIIIIIIIIIIIIIIIII



8 9765432

-Gage /' r",

1003 ,,/~ ...

-,......

....-t"""f-

I--

f-

~

Gage1002

"/'' ..."r--

I , I ~ \ \ 7 Uionses ~

s

~ l Lpth ~ 1 ~

o

200

-200

Test Lanes

Variatin Stres

Acros

the De

-68-


~ 200

~ 0wa::~ -200

enenwa::~en

-

'[-

-

IIIIIIIIIIIIIIIIIII

-69-



-~-


Variationin Stresses

Acrossthe Depth

Test Lanes I 2 3 4 5 6 7 8 9

- 100en GageQ.

1001Cf) aCf)w0:

-100.-Cf)

- 100'Ci) GageQ.- 1000Cf) aCf)w0:

100.-Cf)

IIIIIIIIIIIIIIIIIII

Fig. 30 Influence Lines for Transverse Stress Impact Runs Diaphragm in Place - Gages 1017 and 1016

8 9765432

-~-

--Gage

1017 "---~-

-Gage ..........1016 ...... ,..,.--

-- ,-

7' '\ \ \ \ \n \

ses \\

~ ~h L~ J 1 ~ ~

a

100

-100

enQ.

-70-

1017

Test Lanes

200



enenwcr~en

.(i) 100Q.

en aenwcr~ -100

Variatioin Stres

Acrossthe Dept

IIIIIIIIIIIIIIIIIII


Test Lanes 2 3 4 5 6 7 8 9

III 100 Gagea.-Cf) a 1013Cf)wa:::~ -100Cf)

III 100Gagea.-

Cf) a 1012Cf)wa:::~ -100Cf)


-~-IOI3_~


-71-


Acrossthe Depth

IIIIIIIIIIIIIIIIIII

-72-


-{}-




Acrossthe Depth

Test Lanes 2 3 4 5 6 7 8 9

If) 200a. GageU> 1009U> 0wa::~U>

If) 0a.-U>U> -200w Gagea:: 1008~U> -400

IIIIIIIIIIIIIIIIIII


8 976

c ded

543

oco

2

Loco I Effect Included

-~-

~

Gage v---- I', -1005 ./ '" ....

roo

~

~

r-Gage1004

r-- -----...~

I I 7:rionssess I

pth 1 ~ L I

L I Effect Ex lu

o

200

Test Lanes200

-73-

Voriotin Stre

Acrosthe De

~ 0wa::t; -200

Cf)Cf)wa::.- -200en

enQ.-

enQ.-

IIIII'.1IIIIIIIIIIIII


---- Local Effect Excluded


8 9765432

-<}-

-VGage-

1003 ...- ........, ....

l-

f-

~

Gager-

1002

r- ...., .

,~

r--

I 1 7~!ion V

sses /Is~

Ipth ) l LLL

200

200

Test Lanes I

~ aw0::~ -200

Variatin Stre

Acrosthe De

-74-

~ aw0::~ -200

.~

-

II)Q.--

IIIIIIIIIIIIIIIIIII

Local Effect Excluded


-75-


Test Lanes 2 3 4 5 6 7 8 9

- 1008- Gage- 1001

CJ) aCJ)wa:

-100.....CJ)

"ii) 100Gagea.- 1000

CJ) aCJ)w~ -100CJ)


Acrossthe Depth

IIIIIIIIIIIIIIIIIII

Fig. 36 Influence Lines for Transverse Stress Impact Runs Diaphragm Removed - Gages 1017 and 1016



-76-

-~-


Acrossthe Depth

II) 100Gagea.

U> a 1016U>w0::t- -100U>

Test Lanes 2 3 4 5 6 7 8 9

- 100en Gagea.

U>1017

U> aw0::t- -100U>

IIIIIIIIIIIIIIIIIII




8 976542

-{>-

- V11\~I

Gage If-

1013I

'"Ii'\

t---

~

f--Gage

/'1012lor

V~

~

'"f--

,~ V1 , ,

tionsses

ss l L ~pth l j

a

-200

100

-77-

-100

a

Variain Stre

Aerothe De

CI)Q.

Test Lanes

200

enen~ -100~en

-

-

IIIIIIIIIIIIIIIIIII



8 9765432

-78-


Test Lones

-(/) 2000-

Gageen 1009enw 0a::~en -200

200Gage

(/)

10080-0

enenw -200a::~en

-400


Acrossthe Depth

IIIIIIIIIIIIIIIIIII

--- Local Effect Included or Excluded (Coincident)

Fig. 39 Influence Lines for Transverse Stress Impact Runs _Diaphragm Removed - Gages 1005 and 1004

8 9765432

-~-

~

~Gage

./V

1005- l/-"- 10'"

~

-Gage1004 - i"""'-o.....

~ --~

{ \ ~ 1 V7ionsses55

~ ~ L Lpth 1

200

Test Lanes

200

~ 0wa::~ -200

Variatin Stre

Acro

the De

-79-

en 0enwa::~ -200

ena.--

ena.-

IIIIIIIIIIIIIIIIIII

8 9765432

Locol Effect Included or Excluded (Coincident)

-80-

-<}-

Influence Lines for Transverse Stress Impact Runs Diaphragm Removed - Gages 1003 and 1002

l-

I--

VGage1003 /- ./

l-

I--

Gage1002 .........

....... ,... ...............I-

'"~

{ 1 ~~ 7tion

sses55

l Lpth ~ ) J I

Test Lanes

Fig. 40

~ 200

Variain Stre

Aerothe De

~ 0LLJa::t; -200

U>

~ 0a::~U>

en 200Q.-

IIIIIIIIIIIIIIIIIII

---- Local Effect Included or Excluded (Coincident)

-81-

-~-



Acrosst he Depth

(/) 100Gage0-

(J) a 1000(J)W0::::~ -100(J)

Test Lanes 2 3 4 5 6 7 8 9

100Gage(/)

0-

1001(J) 0(J)W0::::~ -100U>

IIIIIIIIIIIIIIIIIII


-82-


Long. Stress at Gage 1016

Fig. 42 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1017 and 1016


Acrossthe Depth

Test Lanes 2 3 4 5 6 7 8 9

.~ 200~~

(J)0(J)

wa: Long. Stress at Gage 1017..... -200 ---(J)

(J)(J)wa:~ -200---

.(i; 2001Q.-

IIIIIIIIIIIIIIIIIII

-83-

Long. Stress at 1012



-{}-


Acrossthe Depth


'iii 100Q.-(f) a(f)wa::..... -100(f)

Test Lanes 2 3 4 5 6 7 8 9

-(/) 100Q.-(f) a(f)w Long, Stress at 1013a::~ -100(f)

IIIIIIIIIIIIIIIIIII

8 976543

.c,-

2






Acrossthe Depth

-84-

Fig. 44 Influence Lines for Longitudinal Stress Crawl RunsDiaphragm in Place - Gages 1011 and 1010

enen Ol-----+-~--~--+---+---+---+--+-+--wa::~ -100

Test Lones

~ a....---+---+---+----t--+---;----+--I---t---Wa::~ -100

'(i; 100Co-

-.~ 100-

IIIIIIIIIIIIIIIIIII



-85-

8 9765432


f-- / 1',",'"1', ,/ "1£'" ......V --

Long. Stress at Gage 1009\

\

~

~

f-

--..~- -f- Long. Stress at Gage 1008~

T7 7 r7 I~,-

ion I I \I I \ses I I \

s I I \pth l I d l

o

o

-200

Test Lanes

(/) 2000.

enenwa::~en

200

Variatin Stres

Acros

the De

enf3a::t; -200

-

--

-

IIIIIIIIIIIIIIIIIII

IIIIIIIIIIIIIIIIIII

-{>-

Test Lanes 2 3 4 5 6 7 8 9

100r--enQ.- ,..-

Cf) aCf)LLJ f- Long. Stress at Gage 10070:I- -100~Cf)

-en 100-Q.- -Cf) aCf)LLJ Long. Stress at Gage 10060:I-

-100Cf) -f- f-

"""" "' 1 I I 'IVariation

in StressesAeross

jthe Depth .Al Uf.J f.I


--- Local Effect Included


-86-


8 97

-

65432



200--ena.


Local Effect Included

-87-

~ oL--k=:b=d:=d:::::::::::::t==t=j::::'l-I'"":--~--wa:: f-

t; -200f-

Test Lanes


Acrossthe Depth

enenw~en -200--

-'c;; 200 f-a.-

-

IIIIIIIIIIIIIIIIIII

Fig. 48 Influence Lines for Longitudinal Stress Crawl Runs _Diaphragm in Place - Gages 1003 and 1002

- 200~enQ.

I--C/)

0 --~--C/)w ~ Long. Stress at Gage 1002ll::I- -200I--C/)

~ '7~Varia tion I I

in Stresses I II I

Across I Ithe 0epth

8 9765432



Test Lanes

-88-


C/)C/)w~C/) -2001--

-enQ.-

IIII,IIIIIIIIIIIIIII

IIIIIIIIIIIIIIIIIII

Test Lanes 2 3 4 5 6 7 8 9

·en 100I--~--Q. L.----en a --~en --w

~ Long. Stress at Gage 1001a::~ -100 r--en

-'en 100 r--Q.- ~

enen awa:: Long. Stress at Gage 1000~en -100 I--


Acrossthe Depth




-89-

IIIIIIIIIIIIII;1

IIII

-~-

Test Lanes 2 3 4 5 6 7 8 9

- ~

en 100- ~~a. r---- ----en a I----

enw ~ Long. Stress at Gage 1017a::.... -100 I--en

en 100 -a.- -

en aenw Long. Stress at Gage 10 16a::.... -100 -en

f-- I-


Aerossthe 0 epth W

""""


- - - Local Effect Incl uded

Fig. 50 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1017 and 1016

-90-

-91-


/71/

I

~/ IIi

-<}-



Acrossthe Depth

Fig. 51 Influence Lines for Longitudinal Stress Crawl Runs _Diaphragm Removed - Gages 1015 and 1014

III 200 t--a.

I-C/)

0C/) --.....W0::: Long. Stress at Gage 1014~C/) -200r--

Test Lanes 2 3 4 5 6 7 8 9

- ,,'t'"200 r-- 1;-/ "III "'-- "a.- r0-

C/) 0C/)w Long. Stress at Gage 10150:::~ -200I--C/)

IIIIIIIIIIIII.IIIIII

8 9765432


Long. Stress at Gage 1012oL---C:t::t=±=±=±=::bdd-

Test Lanes


Acrossthe Depth


-92-



enenwa::~

en -100

en 100Q.-

'c;;..9- 100 -enf3a::~en

IIIIIIIIIIIIIIIIIII


Test Lanes 2 3 4 5 6 7 8 9

200~(/l

a.-- - -- ...._~----(J) a ~

(J)w ~ Long. Stress at Gage 1011a:::~ -200 I--(J)

-93-

-

Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1011 and 1010


Fig. 53

(/l 200 -a.

(J) a(J)w

Long. Stress at Gage 1010a::: I-

~ -200~(J)

~~ !l ~ , nVaria tion I I I I I

JIin Stre sses I I I

Aero ssJ ~ Jthe Depth .....J

IIIIIIIIIIIIIIIIIII


-94-


8 9765432

-{}-

I-- //1', //1\,L... /,

"'"\. -,

f- Long. Stress at Gage 1009 " /r'--,~ ' .... ,/

-

-~ ~I"'"'..... ,1- -- --.;;;~ .....

f--Long. Stress at Gage 1boa

tion 1 [7 /q rT7 \ ' r-- \\sses I

/ \ \ \IV \

\ \s \

J 1 \ \pth I J \

200

200

Test Lanes

Variain Stre

Acros

the De


(/)

c.

(/)c.

~ 0wa::~ -200

~ 0wa::~ -200

-

IIIIIIIIIIIIIIIIIII

8 9

-

765432



-~-

ol-----1f-~---+--+--_+_-_+_-_+--+_-_r___jr_--

200~

I"" ~ t-

Varia tionin Stresses

Acrossthe Depth

~ - f-'

Test Lanes


Fig. 55 Influence Lines for Longitudinal Stress Crawl Runs _Diaphragm Removed - Gages 1007 and 1006


-95-

(f)(f)wa::t; -200~

·Cii 200 ~a.--

If)

a.--

IIIIIIIIIIIIIIIIIII


8 9765432



200'-

Test Lanes


-96-


Acrossthe Depth


~ 01------f=='====t:==F==+:=~===F=+==t_-wQ:: l-t-00 -2001--

'iii 200~a.

- I-

'iiia.

~ otl---l~J===b==±=±=:±==t=!-:'-l--wQ::

t;; -2001--

IIIIIIIIIIIIIIIIIII


- l-

IIVaria tionin Stresses

JAcro55

the Depth f-I

o~-~-4---I-===*=:t==~===t===+:::::+--

8 9

...----

765432

Long, Stress at Gage 1001

-~-


-- - Local Effect Included


-

-97-

Test Lanes I

- 200 -'ina.-(f) 0(f)wa:::..... -200 -(f)

(f)(f)wa:::.....(f)

(/)

a. 200---

IIIIIIIIIIIIIIIIIII

IIIIIIIIIIIIIIIIIII

-~-

Test Lanes 2 3 4 5 6 7 8 9

- 200 ~'en I--

~ r--.-- I-

C/) 0 -enUJ P- Long. Stress at Gage 1017a::.... -200I--C/)

- 200'en fo-

~ Gage boo-- P-

C/) 0C/)UJ Long. Stress at Gage 1016a::.... -200 fo-C/)

~"I-- I-

Variationin St resses

Acrassthe 0epth J f-J I-'



Fig. 58 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1017 and 1016

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-99-


.Ju.J


-~--



Acrossthe Depth


Test Lanes 2 3 4 5 6 7 8 9

- 200~ -I/) ---a.~ t--

en 0enlLJ

~ Long. Stress at Gage 1013a::..... -200~en

8. 200""-

~ Ot-----t-.......,t---+---+---+.---t----j--t---+---~ ~~ -200~

IIIIIIIIIIIIIIIIIII

8 9765432



-~-

Test Lanes

-100-


Cf)Cf)W

~Cf)


Acrossthe Depth


~ O~--!--J:::::::;===t:===t=~~~==+----I---wa::t; -200

-enC1-

-'Ci) 200C1-

IIIIIIIIIIIIIIIIIII



J

t-JI

8 9765

J

432



200f-

Test Lones


Acrossthe Depth

-101-

~ oL--l-----!=::t==:i::=~=i:==:t:==:t_..t_-lLJa::t; -200~

CJ) 0"---+---1--~-+--+--+---+--+-+---CJ)

lLJ I-

~ -200...-CJ)

-'enQ.-

'en 200fQ.-

IIIIIIIIIIIIIIIIIII


1l

J


-~-

200~




Acrossthe Depth

-102-

Test Lanes 2 3 4 5 6 7 8 9

- 200.- -enQ. --- ,--(J) 0(J)w Long. Stress at Gage 1005Q:.... -200 -(J)

~ 01-----1--+--+---+--+---+--+---+---+--WQ: l-

t; -200~

~--

IIIIIIIIIIIIIIIIIII

-103-




Acrossthe Depth

Test Lanes 2 3 4 5 6 7 8 9

-enQ.

C/) 0C/)w Long. Stress at Gage 1003a:::..... -200C/)

en 200Q.-

C/)0C/)

wLong. Stress at Gage 1002a:::..... -200C/)


IIIIIIIIIIIIIIIIIII

8 9765432


Ol-----+---+-~f---+---+--+----+---+---+--

Long. Stress at Gage 1001-100

100

Test Lanes

200II)

a.


Acrossthe Depth



-104-


enenwa::tn

~ Ol------l.....---+--_t_-~-__+-___lr__-_t_-__+-+_--wa::t; -100

-II) 100a.-

IIIIIIIIIIIIIIIIIII

-105-


Long. Stress at Gage 1016oLLCt=t=~:::::dd-L-

200~



Acrossthe Depth

enf3a:::ti; -200~

Test Lanes 2 3 4 5 6 7 8 9

200--- ~r---(/)

0- r---- I--.

en 0enwI- Long. Stress at Gage 1017a:::

I- -200~en

(/)

0---

Fig. 65 Influence Lines for Longitudinal Stress Impact Runs Diaphragm Removed - Gages 1017 and 1016

IIIIIIIIIIIIIIIIIII

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Acrossthe Depth


Test Lanes 2 3 4 5 6 7 8 9

- 400(/)Q.-fJ) 200

fJ)wa::t; 0

-(/) 200Q.-

fJ)0fJ)

w .",..

a::Long. Stress at Gage 1014~ -200fJ)

IIIIIIIIIIIIIIIIIII

-107-

Local Effect Included

Ol-----t----t--;---+--+---t-----;-----t--t---

J

I--

j

I""-----'"t---r---+---+--+--~


Variation

in StressesAcross

the Depth

-{}-1013 {XF={][}-

Test Lanes 2 3 4 5 6 7 8 9

200~ - --..........lJ) r----a.~-en 0enw Long. Stress at Gage 1013

~~ -200~en


enenw~

t; -200f-

lJ) 200 ......a.-


IIIIIIIIIIIIIIIIIII


-108-

Ol-----+---If---+---+---+---t----+---If---t---

8 9

-

7

J

654

rJj

3

J

2

With or Without Local Effect

Long. Stress at Gage 1010I-

I-


200~

2001-

-200~

Test Lanes

en0.


Acrossthe Depth

en(f)wa::~ -2001-

enenwa:::~en

-

-

en0.-

-

IIIIIIIIIIIIIIIIIII

-109-


J

I-




Across

the Depth

~ O~--!-----t==t::::::!=~==*===i=:::t-!--wa::t; -200--

Test Lanes 2 3 4 5 6 7 8 9

- 200·en I--

c. -- -en 0enw Long. Stress at Gage 1007a::~ -200 I--en

-f1) 2001--C.-

IIIIIIIIIIIIIIIIIII

IIIIIIIIIIIIIIIIIII

-~-

Test Lanes 2 3 4 5 6 7 8 9

- 200~'en~Q. -- I-

CJ) 0CJ)wa:: Long. Stress at Gage 1005~en -200 I--

- 200'en I--

Q.- I-

CJ)0CJ)

w~a:: Long, Stress at Gage 1004

~CJ) -200 I-- I

I--


Acrossthe Depth



-110-


·en 200~0.-en

0enwa:: ~

~ -200 !o-Long. Stress at Gage 1000

en

I- ~

Varia tionin Stresses

Aerossthe Depth .... ....

8 9765432

-111-



-~-

Test Lanes

IIIIIIIIIIIIIIIIIII

IIIIIIIIIIIIIIIIIII

10. REFERENCES

1. Kelley, E. F.EFFECTIVE WIDTH OF CONCRETE BRIDGE SLABS SUPPORTINGCONCENTRATED LOADS, Public Roads, March, 1926.

2. Westergaard, H. M.COMPUTATION OF STRESSES IN BRIDGE SLABS DUETO WHEEL LOADS, Public Roads, March, 1930.

3. American Association of State Highway OfficialsSTANDARD SPECIFICATIONS FOR HIGHWAY BRIDGES,Tenth Edition, Washington, D.C., 1969.

4. Reese, R. T.LOAD DISTRIBUTION IN HIGHWAY BRIDGE FLOORS: A SUMMARYAND EXAMINATION OF EXISTING METHODS OF ANALYSIS ANDDESIGN OF LOAD DISTRIBUTION IN HIGHWAY BRIDGE FLOORS,M.S. Thesis, B~igham Young University, March, 1966.

5. Moorman, R. B. B.BENDING MOMENT~ETERMINATION IN HIGHWAY BRIDGE SLABS,Engineering News Record, 113, 3, July 19, 1954.

6. Aktas, Z. and VanHorn, D. A.BIBLIOGRAPHY ON LOAD DISTRIBUTION IN BEAM-SLAB HIGHWAYBRIDGES, Fritz Engineering Laboratory Report No. 349.1,September, 1968.

7. Newmark, N. M., Seiss, C. P., Perman, R. R.STUDIES OF SLAB AND BEAM HIGHWAY BRIDGES PART I, TESTSOF SIMPLE-SPAN RIGHT I-BEAM BRIDGES, University ofIllinois Engineering Experiment Station Bulletin No. 363,March 8, 1946.

8. Pennsylvania Department of Transportation, Bridge Division,STANDARDS FOR PRESTRESSED CONCRETE BRIDGES, 1960.

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9. Guilford, A. A. and VanHorn, D. A.LATERAL DISTRIBUTION OF DYNAMIC LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE - DREHERSVILLE BRIDGE, FritzEngineering Laboratory Report 315.2, February, 1967.

10. Guilford, A. A. and VanHorn, D. A.LATERAL DISTRIBUTION OF VEHICULAR LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE - BERWICK BRIDGE, FritzEngineering Laboratory Report 315.4, October, 1967.

11. Schaffer, T. and VanHorn, D. A. 0

STRUCTURAL RESPONSE OF A 45 SKEW PRESTRESSED CONCRETEBOX-GIRDER HIGHWAY BRIDGE SUBJECTED TO VEHICULAR LOADING - BROOKVILLE BRIDGE, Fritz Engineering LaboratoryReport 315.5, October, 1967.

12. Lin, Cheng-Shung and VanHorn, D. A.THE EFFECT OF MIDSPAN DIAPHRAGMS ON LOAD DISTRIBUTIONIN A PRESTRESSED CONCRETE BOX-BEAM BRIDGE PHILADELPHIA BRIDGE, Fritz Engineering LaboratoryReport 315.6, June, 1968.

13. Guilford, A. A. and VanHorn, D. A.LATERAL DISTRIBUTION OF VEHICULAR LOADS IN A PRESTRESSEDCONCRETE BOX-BEAM BRIDGE - WHITE HAVEN BRIDGE, FritzEngineering Laboratory Report 315.7, August, 1968.

14. VanHorn, D. A.STRUCTURAL BEHAVIOR CHARACTERISTICS OF PRESTRESSEDCONCRETE BOX-BEAM BRIDGES, Fritz Engineering LaboratoryReport 315.8, June, 1969.

15. Motarjemi, D. and VanBorn, D. A.THEORETICAL ANALYSIS OF LOAD DISTRIBUTION IN PRESTRESSEDCONCRETE BOX-BEAM BRIDGES, Fritz Engineering LaboratoryReport 315.9, October, 1969.

16. Chen, Chiou-Horng and VanHorn, D. A.STATIC AND DYNAMIC FLEXURAL BEHAVIOR OF A PRESTRESSEDCONCRETE I-BEAM BRIDGE - BARTONSVILLE BRIDGE, FritzEngineering Laboratory Report 349.2, December, 1970.

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17. Wegmuller, A. W. and VanHorn, D. A.SLAB BEHAVIOR OF A PRESTRESSED CONCRETE I-BEAM BRIDGE BARTONSVILLE BRIDGE, Fritz Engineering LaboratoryReport 349.3, May, 1971.

18. Timoshenko, S. P. and Goodier, J. N.THEORY OF ELASTICITY, McGraw-Hill Book Company,New York, 1951.

19. Timoshenko, S. P. and Woinowsky-Krieger, S.THEORY OF PLATES AND SHELLS, McGraw-Hill BookCompany, New York, 1959.

20. Jensen, V. P.SOLUTIONS FOR CERTAIN RECTANGULAR SLABS CONTINUOUS OVERFLEXIBLE SUPPORTS, University of Illinois BulletinNo. 303, June, 1938.

21. Newmark, N. M.A DISTRIBUTION PROCEDURE FOR THE ANALYSIS OF SLABSCONTINUOUS OVER FLEXIBLE BEAMS, University of IllinoisBulletin No. 304, June, 1938.

22. Jensen, V. P.MOMENTS IN SIMPLE SPAN BRIDGE SLABS WITH STIFFENEDEDGES, University of Illinois Bulletin No. 315,August, 1939.

23. Jensen, V. P., Kluge', R. W., and Williams, C. B.HIGHWAY SLAB BRIDGES WITH CURBS, LABORATORY TESTSAND PROPOSED DESIGN METHOD, University of IllinoisEngineering Experimentation Station BulletinNo. 346, 1943.

24. Ferguson, P. M.REINFORCED CONCRETE FUNDAMENTALS, Second Edition,John Wiley & Sons, Inc., New York, March, 1965.

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