slab behavior of a prestressed concrete i-beam bridge
TRANSCRIPT
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
Follow this and additional works at: http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports
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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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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
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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
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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.
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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
.,
--- Crawl Run - Local Effect Excluded
--- 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
--- Crawl Run - Local Effect Excluded
-- - 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
--- Crawl Run - Local Effect Excluded
- - - 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
- - - Local Effect Included
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
--- Local Effect Excluded
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.
- - - Local Effect Included
--- Local Effect Excluded
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
- - - Local Effect Included
--- Local Effect Excluded
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
Fig. 23 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1015 and 1014
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
- - - Local Effect Included
~ 0wa::~ -200
-63-
--- Local Effect Excluded
(J)(J)wa::~ -200
-"Ci) 200Q.-
enQ.-
IIIIIIIIIIIIIIIIIII
Fig. 24 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1013 and 1012
--- Local Effect Excluded
- -- 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
Fig. 25 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1011 and 1010
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-
--- Local Effect Excluded
- - - Local Effect Included
~ 0wa:~ -200
~ 0wa:~ -200
ena.-
IIIIIIIIIIIIIIIIIII
-66-
- - - Local Effect Included
--- Local Effect Excluded
Fig. 26 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1009 and 1008
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
Fig. 27 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1005 and 1004
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
Fig. 28 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1003 and 1002
- -- Local Effect Included
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-
--- Local Effect Excluded
~ 200
~ 0wa::~ -200
enenwa::~en
-
'[-
-
IIIIIIIIIIIIIIIIIII
-69-
--- Local Effect Excluded
- - - Local Effect Included
-~-
Fig. 29 Influence Lines for Transverse Stress Crawl Runs Diaphragm Removed - Gages 1001 and 1000
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
--- Local Effect Excluded
- - - Local Effect Included
enenwcr~en
.(i) 100Q.
en aenwcr~ -100
Variatioin Stres
Acrossthe Dept
IIIIIIIIIIIIIIIIIII
Fig. 31 Influence Lines for Transverse Stress Impact Runs Diaphragm in Place - Gages 1013 and 1012
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)
--- Local Effect Excluded
-~-IOI3_~
- -- Local Effect Included
-71-
Variationin Stresses
Acrossthe Depth
IIIIIIIIIIIIIIIIIII
-72-
--- Local Effect Excluded
-{}-
- - - Local Effect Included
Fig. 32 Influence Lines for Transverse Stress Impact Runs Diaphragm in Place - Gages 1009 and 1008
Variationin Stresses
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
Fig. 33 Influence Lines for Transverse Stress Impact Runs Diaphragm in Place - Gages 1005 and 1004
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
Fig. 34 Influence Lines for Transverse Stress Impact Runs Diaphragm in Place - Gages 1003 and 1002
---- Local Effect Excluded
- - - Local Effect Included
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
- - - Local Effect Included
-75-
Fig. 35 Influence Lines for Transverse Stress Impact Runs Diaphragm in Place - Gages 1001 and 1000
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)
Variationin Stresses
Acrossthe Depth
IIIIIIIIIIIIIIIIIII
Fig. 36 Influence Lines for Transverse Stress Impact Runs Diaphragm Removed - Gages 1017 and 1016
--- Local Effect Excluded
- - - Local Effect Included
-76-
-~-
Variationin Stresses
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
Fig. 37 Influence Lines for Transverse Stress Impact Runs Diaphragm Removed - Gages 1013 and 1012
--- Local Effect Excluded
- - - Local Effect Included
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
Fig. 38 Influence Lines for Transverse Stress Impact Runs Diaphragm Removed - Gages 1009 and 1008
- - - Local Effect Included
8 9765432
-78-
--- Local Effect Excluded
Test Lones
-(/) 2000-
Gageen 1009enw 0a::~en -200
200Gage
(/)
10080-0
enenw -200a::~en
-400
Variationin Stresses
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-
-~-
Fig. 41 Influence Lines for Transverse Stress Impact Runs Diaphragm Removed - Gages 1001 and 1000
Variationin Stresses
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
- - - Local Effect Included
-82-
Local Effect Excluded
Long. Stress at Gage 1016
Fig. 42 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1017 and 1016
Variationin Stresses
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
--- Local Effect Excluded
- - - Local Effect Included
-{}-
Variationin Stresses
Acrossthe Depth
Fig. 43 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1013 and 1012
'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
Long. Stress at Gage 1011
Long. Stress at Gage 1010
--- Local Effect Excluded
- - - Local Effect Included
Variationin Stresses
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
Fig. 45 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1009 and 1008
- - - Local Effect Included
-85-
8 9765432
Local Effect Excluded
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 Excluded
--- Local Effect Included
Fig. 46 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1007 and 1006
-86-
Fig. 47 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1005 and 1004
8 97
-
65432
Long. Stress at Gage 1005
Long. Stress at Gage 1004
200--ena.
--- Local Effect Excluded
Local Effect Included
-87-
~ oL--k=:b=d:=d:::::::::::::t==t=j::::'l-I'"":--~--wa:: f-
t; -200f-
Test Lanes
Variationin Stresses
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
Local Effect Excluded
Long. Stress at Gage 1003
Test Lanes
-88-
- - - Local Effect Included
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--
Variationin Stresses
Acrossthe Depth
--- Local Effect Excluded
- - - Local Effect Included
Fig. 49 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm in Place - Gages 1001 and 1000
-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-
Variationin Stresses
Aerossthe 0 epth W
""""
--- Local Effect Excluded
- - - Local Effect Incl uded
Fig. 50 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1017 and 1016
-90-
-91-
- - - Local Effect Included
/71/
I
~/ IIi
-<}-
--- Local Effect Excluded
Variationin Stresses
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 1013
Long. Stress at Gage 1012oL---C:t::t=±=±=±=::bdd-
Test Lanes
Variationin Stresses
Acrossthe Depth
--- Local Effect Excluded
-92-
- - - Local Effect Included
Fig. 52 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1013 and 1012
enenwa::~
en -100
en 100Q.-
'c;;..9- 100 -enf3a::~en
IIIIIIIIIIIIIIIIIII
---- Local Effect Excluded
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
- - - Local Effect Included
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
Fig. 54 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1009 and 1008
-94-
- - - Local Effect Included
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
--- Local Effect Excluded
(/)
c.
(/)c.
~ 0wa::~ -200
~ 0wa::~ -200
-
IIIIIIIIIIIIIIIIIII
8 9
-
765432
Long. Stress at Gage 1007
Long. Stress at Gage 1006
-~-
ol-----1f-~---+--+--_+_-_+_-_+--+_-_r___jr_--
200~
I"" ~ t-
Varia tionin Stresses
Acrossthe Depth
~ - f-'
Test Lanes
- - - Local Effect Included
Fig. 55 Influence Lines for Longitudinal Stress Crawl Runs _Diaphragm Removed - Gages 1007 and 1006
---- Local Effect Excluded
-95-
(f)(f)wa::t; -200~
·Cii 200 ~a.--
If)
a.--
IIIIIIIIIIIIIIIIIII
Fig. 56 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1005 and 1004
8 9765432
Long. Stress at Gage 1004
Long. Stress at Gage 1005
200'-
Test Lanes
--- Local Effect Excluded
-96-
Variationin Stresses
Acrossthe Depth
- - - Local Effect Included
~ 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
Fig. 57 Influence Lines for Longitudinal Stress Crawl Runs Diaphragm Removed - Gages 1001 and 1000
- l-
IIVaria tionin Stresses
JAcro55
the Depth f-I
o~-~-4---I-===*=:t==~===t===+:::::+--
8 9
...----
765432
Long, Stress at Gage 1001
-~-
Long. Stress at Gage 1000
-- - Local Effect Included
--- Local Effect Excluded
-
-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-'
--- Local Effect Excluded
- - - Local Effect Included
Fig. 58 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1017 and 1016
-98-
-99-
- - - Local Effect Included
.Ju.J
Long. Stress at Gage 1012
-~--
---- Local Effect Excluded
Variationin Stresses
Acrossthe Depth
Fig. 59 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1013 and 1012
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
Long, Stress at Gage 1011
Long, Stress at Gage 1010
-~-
Test Lanes
-100-
Fig. 60 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1011 and 1010
Cf)Cf)W
~Cf)
Variationin Stresses
Acrossthe Depth
--- Local Effect Included or Excluded (Coincident)
~ O~--!--J:::::::;===t:===t=~~~==+----I---wa::t; -200
-enC1-
-'Ci) 200C1-
IIIIIIIIIIIIIIIIIII
--- Local Effect Included or Excluded (Coincident)
Fig. 61 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1007 and 1006
J
t-JI
8 9765
J
432
Long. Stress at Gage 1006
Long, Stress at Gage 1007
200f-
Test Lones
Variationin Stresses
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
Fig. 62 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1005 and 1004
1l
J
Long. Stress at Gage 1004
-~-
200~
- - - Local Effect Included
--- Local Effect Excluded
Variationin Stresses
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-
--- Local Effect Excluded
-- - Local Effect Included
Variationin Stresses
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/)
Fig. 63 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1003 and 1002
IIIIIIIIIIIIIIIIIII
8 9765432
Long. Stress at Gage 1000
Ol-----+---+-~f---+---+--+----+---+---+--
Long. Stress at Gage 1001-100
100
Test Lanes
200II)
a.
Variationin Stresses
Acrossthe Depth
--- Local Effect Included
Fig. 64 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1001 and 1000
-104-
--- Local Effect Excluded
enenwa::tn
~ Ol------l.....---+--_t_-~-__+-___lr__-_t_-__+-+_--wa::t; -100
-II) 100a.-
IIIIIIIIIIIIIIIIIII
-105-
--- Local Effect Excluded
Long. Stress at Gage 1016oLLCt=t=~:::::dd-L-
200~
--- Local Effect Included
Variationin Stresses
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
-106-
--- Local Effect Excluded
-- - Local Effect Included
Long. Stress at Gage 1015
Variationin Stresses
Acrossthe Depth
Fig. 66 Influence Lines for Longitudinal Stress Impact Runs Diaphragm Removed - Gages 1015 and 1014
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---+---+--+--~
Long. Stress at Gage 1012
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
--- Local Effect Excluded
enenw~
t; -200f-
lJ) 200 ......a.-
Fig. 67 Influence Lines for Longitudinal Stress Impact Runs Diaphragm Removed - Gages 1013 and 1012
IIIIIIIIIIIIIIIIIII
Fig. 68 Influence Lines for Longitudinal Stress Impact Runs Diaphragm Removed - Gages 1011 and 1010
-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-
Long. Stress at Gage 1011
200~
2001-
-200~
Test Lanes
en0.
Variationin Stresses
Acrossthe Depth
en(f)wa::~ -2001-
enenwa:::~en
-
-
en0.-
-
IIIIIIIIIIIIIIIIIII
-109-
Fig. 69 Influence Lines for Longitudinal Stress Impact Runs Diaphragm Removed - Gages 1007 and 1006
J
I-
With or Without Local Effect
Long. Stress at Gage 1006
Variationin Stresses
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--
Variationin Stresses
Acrossthe Depth
With or Without Local Effect
Fig. 70 Influence Lines for Longitudinal Stress Impact Runs Diaphragm Removed - Gages 1005 and 1004
-110-
Fig. 71 Influence Lines for Longitudinal Stress Impact Runs Diaphragm in Place - Gages 1001 and 1000
·en 200~0.-en
0enwa:: ~
~ -200 !o-Long. Stress at Gage 1000
en
I- ~
Varia tionin Stresses
Aerossthe Depth .... ....
8 9765432
-111-
With or Without Local Effect
Long. Stress at Gage 1001
-~-
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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IIIIIIIIIIIIIIIIIII
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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