STUDIES OF SLAB AND BEAM HIGHWAY BRIDGES
PART II
TESTS OF SIMPLESPAN SKEW IBEAM BRIDGES
I. INTRODUCTION
1. Object of Tests.Laboratory tests were made on five Ibeam
bridges having angles of skew of 30 and 60 deg. The structures tested
were quarterscale models of simplespan bridges and, except for the
skew, were similar to the longspan right Ibeam bridges described in
Bulletin 363.1 The purpose of these tests was to determine the effect
of skew on the behavior of Ibeam bridges. Since no analysis of the
skew bridge was available, the tests were so planned as to permit
direct comparison with the results from previous tests of right bridges.
In this bulletin the results of strain measurements at various points
on skew bridges are compared with the corresponding data for right
bridges. These comparisons furnish the basis for conclusions regarding
the effect of angle of skew on the behavior of Ibeam bridges.
2. Outline of Test Program.The structures tested may be divided
into two groups, depending on the angle of skew. Three bridges having
skews of 30 deg. were tested. They are designated 30N15, 30S15, and
30C15, and correspond to the right bridges designated N15, S15, and
C15 respectively in Bulletin 363. Two bridges having skews of 60 deg.
were tested. They are designated 60N15 and 60C15 and correspond
to right bridges N15 and C15. In addition to the angle of skew the
designations given above indicate differences in the nature of the bond
between the slab and the beams as described in Section 10.
The tests on the bridges were in most respects similar to those made
on the longspan right bridges of Series III of Bulletin 363. They may
be divided into two classes:
(1) Influence line tests in which the strain or deflection at a par
ticular point was determined for a single load placed at various loca
tions on the bridge. Influence lines were determined in this manner
for strains in the beams, for deflections of the beams, and for strains
in the slab reinforcement.
1 N. M. Newmark, C. P. Siess, and R. R. Penman, "Studies of Slab and Beam Highway
Bridges: Part ITests of SimpleSpan Right IBeam Bridges," Univ. of 111. Eng. Exp. Sta.
Bul. 363. 1946.
ILLINOIS ENGINEERING EXPERIMENT STATION
(2) Tests with simulated wheel loads in which the bridge was
loaded with either one or two pair of concentrated loads simulating
the rear wheels of a truck, and strains and deflections were measured
at various locations.
All tests except the influence line tests for beam strains were made
after the slab had been systematically cracked by the application of
a pair of loads at various points on the bridge. Influence line tests for
beam strains were made both before and after cracking the slab. At
the conclusion of the tests mentioned above, each bridge was tested to
failure under one pair of loads.
3. Acknowledgments.The tests described herein were made as
part of an investigation of the effect of concentrated loads on rein
forced concrete bridge slabs, conducted by the Engineering Experi
ment Station of the University of Illinois in cooperation with the
Illinois Division of Highways and the Public Roads Administration
of the Federal Works Agency.
The program of the investigation is guided by an Advisory Com
mittee having the following personnel:
Representing the Illinois Division of Highways:
G. F. BURCH, Bridge Engineer
L. E. PHILBROOK, Assistant Bridge Engineer.
Representing the Public Roads Administration:
E. F. KELLEY, Chief, Division of Physical Research
RAYMOND ARCHIBALD, Chief, Bridge Division.
Representing the University of Illinois:
F. E. RICHART, Research Professor of Engineering Materials
N. M. NEWMARK, Research Professor of Structural Engineering.
Consultants to the Committee, from the University of Illinois:
W. M. WILSON, Research Professor of Structural Engineering
T. C. SHEDD, Professor of Structural Engineering.
The tests of bridges 30N15, 30S15, and 60N15 were made by
W. M. PECKHAM as a thesis2 under the direction of N. M. NEWMARK.
The remaining tests were planned at the same time but were carried
to completion by J. C. HOUBOLT, Special Research Graduate Assistant,
who also assisted in the other tests.
The data were coordinated and this bulletin was prepared by
PROFESSORS C. P. SIESS and N. M. NEWMARK.
2 W. M. Peckham, "Tests of Skew IBeam Bridges," thesis submitted in partial fulfillment
of the requirements for the degree of Master of Science in Theoretical and Applied Mechanics in
the Graduate School of the University of Illinois, 1941.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
II. FUNDAMENTAL CONSIDERATIONS
4. Scale Relations.All specimens tested were quarterscale models.
In order to obtain equal stresses in the model and in the correspond
ing fullsized structure, or prototype, the loads on the two structures
must be related as follows:
(a) Concentrated loads should be %e as large for the model as
for the prototype.
(b) Loads distributed over a length, such as the weight of a beam
per foot of length, should be % as large for the model as for the
prototype.
(c) Loads distributed over an area, such as the weight of the slab
per square foot of area, should have the same magnitude per unit of
area for the model as for the prototype.
5. Definition of Terms.The following terms are frequently used
throughout this bulletin and are therefore defined here.
The span of the bridge is measured in the direction parallel to the
beams.
The angle of skew is the angle between the direction of the beams
and a line perpendicular to the abutments.
The transverse reinforcement of the slab is in the direction per
pendicular to the beams, and perpendicular to the direction of traffic.
The longitudinal reinforcement of the slab is in the direction paral
lel to the beams.
The relative stiffness of the beam and slab is denoted by the letter
H, and is defined by the equation
H Ebb
H
aEI
wherein a is the span of the beams, and EbIb and El are the products of
the modulus of elasticity and the moment of inertia of a beam and of
a unit width of the slab respectively. For composite bridges, EbIb is
computed for the transformed section of a composite Tbeam consisting
of the steel beam and a width of slab equal to the beam spacing.
A shear connector is a device which acts to transfer horizontal
shear across the plane between the beam and the slab.
Composite action is the interaction between beam and slab which
results from the transfer of shear between these two elements.
ILLINOIS ENGINEERING EXPERIMENT STATION
III. DESCRIPTION OF TEST SPECIMENS AND APPARATUS
6. Description of Bridges.Except for the skew the structures
tested were similar in all respects to the right bridges of Series III,
Bulletin 363. The design details for all the test specimens are given in
Table 1, and typical plans are shown in Fig. 1. For design details and
dimensions of fullsized bridges most nearly corresponding to the
various test specimens, reference is made to Bulletin 363, Table 2.
Five bridges were tested, three with a skew of 30 deg. and two
with a skew of 60 deg. Bridges 30N15 and 60N15, with skews of 30
and 60 deg. respectively, were constructed without shear connectors,
with only natural bond between the slab and beams. Bridge 30S15
was similar to bridge 30N15 except that composite action was pro
vided by means of shear connectors. Bridges 30C15 and 60C15 were
provided with shear connectors, but composite action was considered
in the design and a somewhat lighter structure was obtained.
TABLE 1
DESIGN DETAILS FOR MODEL BRIDGES
Bridge No. 30N15 30C15 30815
60N15 60C15
Span, feet 15 15 15
Spacing of beams, feet 1.5 1.5 1.5
Size of beams 10in., 9.0lb. 8in., 6.5lb. 10in., 9.0lb.
Junior Beam Junior Beam Junior Beam
Shear Connectors: Type None Channel* Channel*
Width, in. . ... 1% 1
Spacing, in. .... 6Y4 6.0
Diaphragms: End 4in., 5.4lb. Channels
Intermediate 3in. X 2in. X iesin. Angles
Nominal Depth of Slab, in. 1.75 1.75 1.75
Slab Reinforcement: All bars Ysin. square
Bottom Spacing, in. 1 1 X 1
p,tpercent 1.09 0.87 1.09
Transverse
Top Spacing, in. 1A 1% 1%
p, t percent 0.72 0.58 0.72
Bottom Spacing, in. 1 N 2 1%
p,tpercent 0.95 0.59 0.95
Longitudinal
Top Spacing, in. 6 % 6 6Y4
p,tpercent 0.19 0.20 0.19
Relative stiffness, H 3.88 5.01 9.41
* 1in. X %in. X Ysin. bar channel.
t p is the ratio of the area of reinforcement to the product of the width of the slab by the effec
tive depth of the particular bars considered.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
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FIG. 1. PLANS OF MODEL BRIDGES
7. Materials.The physical properties of the steel in the beams
were obtained from tension tests on coupons cut from the flanges. The
results of the tests are given in Table 2, together with corresponding
data from the tests of right bridges.
The slab reinforcement consisted of %in. square c'oldfinished
bars of SAE 1112 steel. These bars were normalized to lower their
strength and rusted to improve their bond, in the same manner as the
bars used in the right bridge tests. The tensile properties of the bars in
both the skew and right bridges are given in Table 3.
The slabs were made from a sandcement mortar similar in all re
spects to that used in the right bridges. The proportion of cement to
TABLE 2
PHYSICAL PROPERTIES OF STEEL IN BEAMS
Size and Weight ofNumber
of Beam Tests
10J.B.9.0 9
10J.B.9.0 3
8J.B.6.5 5
Yield Point
p.s.i.
40 800
43 200
41 000
Ultimate Per Cent
Smte Elonga
trenth tion in
p.S.i. 2 in.
64 900 35
70 700 33
64 900 36
* From Bulletin 363, Table 3, Series III.
Type of
Bridge
Skew Bridges
Right Bridges*
Right Bridges*
b
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 3
PHYSICAL PROPERTIES OF hINCH SQUARE REINFORCING BARS
Type of Bridge Number of Yield Point Ultimate Strength Per Cent
Tests p.s.i. P.S.i, in 2 in.
Skew Bridges 8 45 200 59 200 29
Right Bridges* 6 45 000 62 100 32
* From Bulletin 363, Table 4, Series III.
sand was 1:6.5 by weight, and the watercement ratio was 0.82 by
weight. The sand used was an artificially graded mixture of Wabash
River Valley torpedo sand and fine Lake Michigan beach sand.
The properties of the mortar are given in Table 4. Values for the
right bridges are also included to permit comparison. The "coated"
cylinders were coated with paraffin in the same manner as the slabs
on the test structures. The control cylinders were tested at the con
clusion of all the tests on each bridge. Tests were begun on the bridges
at ages ranging from 28 to 38 days. The control beams, from which
modulus of rupture values were obtained, were tested at the beginning
of the cracking tests.
There is relatively poor agreement between the compressive
strengths given in Table 4 for the right and skew bridges. This is not
important, however, since the compressive strength of the slab has little
or no effect on the behavior of the bridge except at loads producing
punching. Comparisons of the values of modulus of elasticity indicate
relatively good agreement between the right and skew bridges N15
and S15, but appreciably higher values for the skew bridges C15.
Although this difference in modulus may be significant, it has been
neglected in the calculation of H, and a value of the modular ratio,
n = 8, has been used for all bridges. This value is the same as that
used in the calculations for the right bridges.
8. Construction of Test Specimens.The procedure followed in
the construction of the test specimens was similar in all respects to that
described in Bulletin 363 in connection with the longspan right
bridges of Series III.
The five Ibeams were assembled into a single frame by means of
the end diaphragm channels, which were welded to the beams. A view
of the beams for a bridge with 60deg. skew is shown at the left in
SLAB AND BEAM HIGHWAY BRIDGES PART II
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ILLINOIS ENGINEERING EXPERIMENT STATION
Fig. 2. Welding was also used to connect the interior diaphragm angles
to the webs of the beams, and to attach the channel shear connectors
to the top flange of the beams.
Plywood bottom forms and steel side forms were used as before.
A view of the forms in place for one of the bridges withshear con
nectors is shown in Fig. 3.
The slab reinforcement was fabricated and placed in exactly the
same manner as in the previous tests. A view of the reinforcement for
a bridge with 60deg. skew is given in Fig. 4. The procedure followed
in mixing, placing, and curing the mortar slab was identical with that
used for the bridges of Series III in Bulletin 363.
When the forms were removed at the end of seven days, the exposed
surfaces of the slab were coated with paraffin in an attempt to retard
drying and reduce the accompanying shrinkage. This procedure was
not entirely successful; an appreciable amount of shinkage occurred,
as evidenced by marked curling of the slab in bridges N15 without
shear connectors. On bridge 30N15, the slab warped to such an
extent that at the conclusion of testing it had lifted clear of the edge
beams and end diaphragms around its entire perimeter. The warping
on bridge 60N15 was somewhat greater; the corners of the slab had
lifted off the supports when the tests were begun, and the slab was free
of the beams around its entire periphery at the time the influence line
tests for strains in the reinforcement were begun.
FIG. 2. BEAMS FOR 60DEGREE BRIDGE AND COMPLETED 30DEGREE BRIDGE
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
FIG. 3. SLAB FORMS FOR 30DEGREE BRIDGE PRIOR TO SETTING REINFORCEMENT
FIG. 4. REINFORCEMENT FOR 60DEGREE BRIDGE
ILLINOIS ENGINEERING EXPERIMENT STATION
No shoring was used to support the beams at intermediate points
while the slab was being placed, and the entire weight of the forms
and slab was carried by the Ibeams acting alone without benefit of
composite action.
9. Testing Apparatus.The apparatus for applying and measuring
load, and the instruments for measuring strain, deflection, and slip,
were the same in all respects as those used in the previous tests of
right bridges described in Bulletin 363.
Load was applied by means of a screwjack bearing against a
steel frame anchored to the floor of the laboratory, and was measured
by the aid of elastic ring dynamometers with capacities of 10,000,
20,000, and 50,000 lb. Loading disks 3% in. in diameter were used,
bearing on sponge rubber on the slab.
Strains in the slab reinforcement in all tests and strains in the
beams in the influence line tests were measured with Huggenberger
Tensometers of 2in. gage length. Beam strains in the tests under
simulated wheel loads were measured with a Berry strain gage of 2in.
gage length. Deflections were measured by means of deflectometers
equipped with 0.001in. dial gages. Slip between the slab and the center
beam was measured at each end of the beam by means of 0.001in.
dial gages.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
IV. TESTS OF BRIDGES WITH 30DEGREE SKEW
10. Description of Tests.Three bridges having skews of 30 deg.
were tested. They differed principally in the nature of the bond be
tween the slab and beams, as follows:
Bridge 30N15Natural bond between slab and beams.
Bridge 30S15Same design as bridge 30N15 but with shear con
nectors provided.
Bridge 30C15Composite action provided by shear connectors
and allowed for in design.
Details of the bridges are given in Table 1. The beams for bridge
30C15 were smaller than those for the other bridges, and the amount
of reinforcement in the slab was less.
Reference is made to Fig. 5, in which the coordinate system for
the location of points on the bridges is illustrated. The longitudinal
location of a point on the bridge is indicated by reference to the trans
verse lines drawn normal to the beams at intervals of 12 in. Line 0
is located at midspan and the lines on the east or west half of the
bridge are designated le, 2e, 3e, etc. and 1w, 2w, 3w, etc. respectively.
The transverse location of a point on the bridge is given with refer
ence to the beams, designated A, B, C, D, E, and to the panels, desig
nated AB, BC, CD, DE. Specifically, the panel designation refers
to a point at the middle of the panel.
Substantially the same tests were made on all of the bridges with
30deg. skew. They are described briefly on following pages.
e Se 4e e3e Ze /e 0 /w tw 3w 4w Sw 6w
Sfra.n'ag# line on beam .5w Center/ine
I 3fralngage 1ne on /ransverse reinforcemeVn
 Sfranqgage line on /ongI/ud/la/ reinforceament
FIG. 5. COORDINATE SYSTEM AND LOCATIONS OF STRAINGAGE
LINES FOR BRIDGES WITH 30DEGREE SKEW
ILLINOIS ENGINEERING EXPERIMENT STATION
Cracking Test. The slab of each bridge was systematically cracked
by the application of a pair of loads at the centers of two adjacent
panels at 24 locations on each bridge. Loads were applied in panels
AB and BC on lines 6e to 5w inclusive, and in panels CD and DE
on lines 5e to 6w inclusive. The magnitude of the cracking load was
4000 lb. per panel for bridges 30N15 and 30C15, and 4500 lb. per
panel for bridge 30S15. Strains were measured in the transverse slab
reinforcement under the loads during the application of the loads
on line 0.
Influence Lines for Strains in Beams. Strains in the beams were
measured at the gage lines indicated on Fig. 5 for a single load placed
at various locations on the bridge, both before and after cracking.
Before cracking, a load of 700 lb. was used for bridges 30N15 and
30C15, and a load of 1000 lb. was used for bridge 30S15. After crack
ing, two magnitudes of load, 1000 and 2000 lb., were used on all bridges.
Strains were measured on three gage lines for each beam  on the
bottom flange on the centerline of the beam, and on the underside of
the top flange near each edge.
Influence Lines for Deflections of Beams. Deflections of the beams
were measured after cracking at several locations for a single load
placed at various positions on the bridge. For bridges 30C15 and
30S15, loads of 1500 and 3000 lb. were used. For bridge 30N15, loads
of 1500, 3000, and 4500 lb. were used, the first increment serving
merely to bring the warped slab back into contact with the beams.
Influence Lines for Strains in Slab Reinforcement. Strains were
measured in the transverse and longitudinal reinforcement at the loca
tions indicated on Fig. 5, for a single load moving across the trans
verse lines in the neighborhood of the gage lines. The magnitudes of
load were similar to those used in determining the influence lines for
deflection of the beams. Strains were measured on one gage line on
the bottom longitudinal reinforcement at the center of each panel, and
on one gage line on the top transverse reinforcement over each interior
beam.
Tests with Uniform Load. At the conclusion of the influence line
tests, each bridge was loaded with sand and castiron weights in
amounts sufficient to increase the dead load on the models to an amount
bearing the proper scale relation to the dead weight of the prototype
structures. The manner of applying this added load was identical in
all respects to that described in Bulletin 363, Section 28, in connection
with the tests of right Ibeam bridges. Beam strains and deflections
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
FIG. 6. 30DEGREE BRIDGE WITH ADDED DEAD LOAD IN PLACE
were measured for the superposed dead load. A view of one of the
bridges with the sand in place is shown in Fig. 6.
Strains in Slab Reinforcement for Tests with Simulated Wheel
Loads. These tests may be divided into three parts, as follows:
(1) Strains were measured in the transverse reinforcement under the
loads and over the beam between the loads, for a pair of loads applied
at AB and BC on line 0, at CD and DE on line 0, and at CD and DE
on line 4w. (2) Strains were measured in the longitudinal reinforce
ment at the centers of the panels and in the top transverse reinforce
ment over the interior beams, for four loads on line 0, one at the
center of each panel. (3) After the test to yielding of the beams de
scribed in the following paragraph, the slab was tested to failure under
a pair of loads applied at BC and CD on line 0 for 30N15 and 30S15,
and at AB and BC on line 0 for 30C15. Strains were measured in the
transverse reinforcement under the loads and over the beam between
the loads. The test was continued until punching of the slab was
produced.
Strains in Beams for Tests with Simulated Wheel Loads. There
were two tests of this type: (1) Two pair of loads were placed on
line 0 and strains were measured in all beams on line 0. (2) Two pair
of loads were placed on line 1w and strains were measured in beam C
at 0, in beam D at 1w, and in beam E at 1w and 2w. The transverse
spacing of the loads in these tests was as shown in Fig. 8, and was the
ILLINOIS ENGINEERING EXPERIMENT STATION
same as that used previously in the tests of right bridges. The load
was increased in increments of 500 lb. per single load until yielding of
the beams occurred, and strains were measured for each increment of
load. Beam strains were also measured in the bottom flanges of the
most highly stressed beams during the tests for strains in the slab re
inforcement described in the preceding paragraph.
Deflections of Beams in Tests with Simulated Wheel Loads. De
flections of all beams were measured on line 0 in all tests under simu
lated wheel loads in which loads were applied on line 0. For bridges
30C15 and 30S15, deflections on line 0 were also measured in the
test for beam strains with two pairs of loads on line 1w. In a few
instances, deflections were measured at locations other than those on
line 0.
Punching Tests. At the conclusion of the tests described above,
the slab was loaded with one pair of loads at three or four locations,
and the load was increased until failure by punching was produced.
Only the maximum load was recorded in these tests.
11. Cracking Test.The coating of paraffin on the slabs made it
impossible to observe the pattern of cracking in these tests.
Strains were measured in the reinforcement for loads producing
first cracking on line 0. The loadstrain curves thus obtained were
very similar to those for the right bridges given in Bulletin 363,
Fig. 34. The curves for strains in the bottom transverse reinforcement
at the center of a panel exhibited the typical break indicative of
cracking at a strain of 0.00010 to 0.00020. No break was observed
in the curves for transverse strains over the beam at the maximum
loads applied in this test, and it may be concluded that cracking of
the slab was not produced at those locations.
12. Influence Lines for Strains in Beams.The influence values for
strains in the beams both before and after cracking the slab were
not significantly different from those for the right bridges in Bulletin
363, Fig. 35, and are consequently not presented here.
For bridge 30N15 the top flange strains were appreciably smaller
than the bottom flange strains before cracking and more nearly equal
to them after cracking. This results from the existence of partial com
posite action, which is greater before cracking than after. The same
phenomenon was observed in the tests of right bridges and is discussed
in Bulletin 363, Section 30. That discussion is generally applicable to
the results obtained for the 30deg. skew bridges.
For bridges 30C15 and 30S15 with composite action, the meas
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGEL  PART 11
ured strains for both the top and bottom flanges were in good agree
ment with the measured and computed values for the right bridges.
There was little change in magnitude of the measured strains as a
result of cracking.
13. Influence Lines for Deflections of Beams.The influence lines
for deflections of the beams for the 30deg. skew bridges were in
general quite similar to those for the right bridges, presented in
Bulletin 363, Fig. 37. In some instances there were differenices between
the results for skew and right bridges which could be attributed to the
presence of skew. These differences, however, were neither consistent
nor particularly enlightening, and no conclusions regarding the effect
of skew could be drawn from them.
The influence lines for beam deflections for the 30deg. skew bridges
were generally in fair agreement with the theoretical influence lines
for the corresponding right bridge.
14. Influence Lines for Strains in Slab Reinforcement.The in
fluence values for strain in the bottom transverse reinforcement of the
A B C D E
50  easred
_  Computed for Right__
QBri/dge, H=3.88
30
0 // 'i ~ Center of Panel AB
I^ O          
0
FIG. 7. INFLUENCE ORDINATES FOR STRAIN IN LONGITUDINAL
REINFORCEMENT AT LINE 0; BRIDGE 30N15
ILLINOIS ENGINEERING EXPERIMENT STATION
30deg. skew bridges were somewhat greater than the values obtained
for the corresponding right bridges. The greatest differences occurred
for bridge 30N15 without shear connectors; the agreement for the
bridges with composite action was somewhat better.
Influence values for strain in the top transverse reinforcement over
the beams were usually quite small and agreed very closely with the
measured right bridge strains for corresponding bridges, and also
with the right bridge strains computed for the uncracked section.
Influence lines for strains in the longitudinal reinforcement at the
center of a panel were also obtained in these tests. No corresponding
experimental data are available for the right bridges. The influence
lines for bridge 30N15 are given in Fig. 7, and computed values for
the corresponding right bridge are included for comparison. The agree
ment is poor, as would be expected from the data obtained previously
in loadstrain tests of right bridges. The curves for bridge 30C15 and
30S15 are not given, but were similar in shape to those of Fig. 7.
However, because of the existence of composite action in these bridges,
TABLE 5
STRAINS AND DEFLECTIONS OF BEAMS DuE TO ADDED DEAD LOAD FOR BRIDGES
WITH 30DEGREE SKEW
Beams Beams Beam Ar Relative
A and E B and D C Average Values
Average Bottom Flange Strain on Skew Centerline, X 105
Skew Bridge 30N15 15.5 10.9 15.5 13.7 0.88
Right Bridge N15* 11.5 14.8 15.5 13.6 0.88
Right Bridge: Computed* .. . .... .... 15.5 1.00
Skew Bridge 30C15 10.9 12.8 15.5 12.6 0.77
Right Bridge C15 14.3 16.2 18.0 15.8 0.96
Right Bridge: Computed .... .... .... 16.4 1.00
Skew Bridge 30815 10.0 12.8 9.1 10.9 1.00
Right Bridge 815 8.8 11.0 13.5 10.6 0.97
Right Bridge: Computed .... .... .... 10.9 1.00
Average Deflections on Line 0, in 0.01 in.
Skew Bridge 30N15 7.5 9.7 10.1 8.9 0.85
Right Bridge N15 7.9 9.3 9.3 8.7 0.83
Right Bridge: Computed .. . .. . .... 10.5 1.00
Skew Bridge 30C15 6.6 7.4 7.6 7.1 0.93
Right Bridge C15 7.5 7.9 8.1 7.8 1.02
Right Bridge: Computed .. . .. . .... 7.6 1, 00
Skew Bridge 30815 4.7 6.0 5.7 5.4 1.25
Right Bridge S15 4.3 4.7 4.9 4.6 1.07
RightBridge: Computed .... ... .... 4.3 1.00
* All right bridge values from Bulletin 363, Table 8.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
the resultant longitudinal strains at the bottom of the slab were nega
tive except for a load in the neighborhood of the gage line.
15. Tests with Uniform Load.Strains and deflections of the beams
resulting from the added sand load are given in Table 5, together with
both measured and average computed strains for the corresponding
right bridges. The strains given for the skew bridges are the maximum
observed along the length of each beam and usually occurred at the
skew centerline. (See Fig. 5.) The deflections are those measured on
line 0, normal to the beams at midspan, and are not necessarily the
maximum values. Average computed strains for the right bridges are
based on the assumption that the load is distributed equally to all
beams, and quantitative comparisons should be made only with the
average of the measured values.
The average strain and deflection for bridge 30N15 were approxi
mately equal to those for right bridge N15, although both sets of
measured strains were somewhat less than the computed values as the
result of partial composite action produced by friction between the
slab and beams. The presence of such action was indicated also by
the fact that the top flange strains were smaller than the bottom
flange strains.
The agreement between values for the composite skew and right
bridges was not consistently good. However, considering the relatively
small magnitude of the quantities observed, the discrepancies cannot
be considered significant.
Attention is called to the fact that the manner of adding dead load
to the model bridges did not exactly duplicate the conditions in a full
sized structure. In an actual bridge, the weight of the slab is carried
entirely by the beams acting independently without benefit of the
distributing effect of the slab or of composite action. In these tests,
the added dead load was applied to a completed Ibeam bridge and
was carried by the beams and slab acting together as a unit, and by a
structure with full composite action in those bridges provided with
shear connectors.
16. Strains in Beams for Tests with Simulated Wheel Loads.The
strains in the beams measured in the tests with two pair of loads on
the bridge are plotted in Fig. 8. Two tests were made on each bridge,
one with the loads on line 0 and one with the loads on line lw.* The
* The transverse position of the loads on line 1w was the reverse of that for loads on line 0.
However, the results of this test will be discussed as if the loads were reversed about the skew
centerline and were applied on line le at the same transverse locations as the loads on line 0.
Thus, the strain measured in beam E at 1w for loads on 1w will be referred to as the strain in
beam A at le for loads at le, beam D at 1w will become beam B at le, etc.
ILLINOIS ENGINEERING EXPERIMENT STATION
I II  Afasured, Ri'ht Bridge
\  feasrd, 30o Skew Bridtage
I \ II ~/8 X~ 
 / jv _  "b1
\co ^.s.. \f . f HI %AI 
 rfo7 0^^W~
I / ý I
I  4 ~~¶ 14 ~'{ ~4~l ~4  ~LX 4! 414
2'i
A'.amA Beam Beam C , ea, , il s Iam F
f a IIe oT, f~ le/ of/0 aO Ifr at
rao t 17 roa t o a4 a/ V0oad 01 0 L7eoacd af 0 t oad 0#
20 40 0O 2 40 2040 0 40 0 2040 60
bBridges S. 5I
Composite /
/,I / I
Be r A Beam  , em C / 0Bemr fe eVm 8
J/' I 1, I J.
Ir'~"'s T7'f ~"k iT1 ~. §1t~7 a'~ fV117 of 0
jfLoaa~atJe JI'i~Oud5at U fLoods O~ 0 J__fLOuds ~9 4
0 40 40 0 40 0 40 d 40 O 80 20 40
ct. o,, . 2r \A \I\ S
Compositeyt 41 U r
llA*f'on I% "/." /.' "A"./,
I I 4 444 1 I ,4'.ie I  I ~A.4~ L. 44 II 44,1I
I  I Il I  + J~4 I ~ I  il  44I ~4   I
, I I \ \ "I I ! i I l I
0 0B.amA\ A Belam B oeam C /oeam 0 em
/ at/C I at le \~ at 01,1 a/O [0 at 0
/ aI/ld atle V17ad at 0 VLoada/0 at 0{a
0 ZO 40 60
FIG. 8. LOADSTrAIN CURVES FOR BEAMS; 30DEGREE SKEw BRIDGES
0 RO 40 0 FO 40 0 20 40 O 30 40 60 80
Averoge Bo//om F/onge Strod? 7 /O'
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
transverse location of the loads was similar in both tests and is indi
cated on the figure. The maximum strains in beams A and B for all
bridges occurred at le for loads on line le, while the maximum strain
for beam C occurred at 0 for loads on line 0. The strains obtained for
beams D and E were, of course, not maxima for the loads on either
line because of the transverse location of the loads.
The measured and computed right bridge strains from Bulletin 363,
Fig. 40 are also given in Fig. 8 to facilitate comparison.
For purposes of comparison, strains were taken from the load
strain curves of Fig. 8 at a load of 3000 lb. per panel. At this load,
the strains in beams A, B, and C of bridge 30N15 are from 2 to 10 per
cent less than the measured strains in the correspondinghbeamaof right
bridge N15. The maximum beam strain in the skew bridge at 3000 lb.
was 9 per cent less than the maximum measured strain in the right
bridge, and about 5 per cent less than the maximum computed strain
for the right bridge. These differences are about as expected since the
moments in the skew bridge for loads placed as in the tests are some
what less than those in the right bridge.
The relation between strains in the beams for the skew and right
bridges with composite action are different from those for bridge
30N15. For bridge 30C15, which is a typical composite design, the
strains in beams A, B, and C were 2 to 10 per cent greater in the
skew bridge than in the corresponding right bridge C15. The maximum
strain at 3000 pounds per panel was 5 per cent greater than the maxi
mum measured strain in the right bridge, but was about equal to the
maximum computed strain in the right bridge.
For bridge 30S15, the strains in beams A, B, and C ranged from
33 per cent less to 5 per cent greater than the corresponding strains
in the right bridge. The maximum strain in the skew bridge at 3000
lb. per panel, however, was 5 per cent greater than the maximum
measured in the right bridge, and 9 per cent greater than the maximum
computed for the right bridge.
Strains in the top flanges are not shown on Fig. 8. For bridge
30N15 without composite action, the top flange strains were generally
equal to or slightly less than the bottom flange strains. For the bridges
with composite action, the top flange strains were quite small and in
dicated that complete composite action was obtained.
Strains were measured in all of the beams on line 0 for loads on
line 0, and an opportunity was thus afforded to compare the distri
bution of moment to the beams in the skew and right bridges. In
ILLINOIS ENGINEERING EXPERIMENT STATION
general, the distribution was slightly less uniform for the skew bridges
than for the right, but the differences were not significantly large.
It may be noted from Fig. 8 that the bend in the loadstrain curves,
which is usually taken as an indication of yielding, occurs at an unusu
ally small strain, from 0.00050 to 0.00070, whereas the theoretical
yieldpoint strain corrected for the effects of dead load is approxi
mately 0.00110. Careful study of the data has led to the conclusion
that there were residual tensile stresses in the flanges of the beams
used in these tests. Investigation of a different lot of similar beams
revealed residual tensile stresses in the flanges on the order of 18,000
p.s.i. This would correspond to a reduction in apparent yieldpoint
strain of about 0.00060, and is in agreement with the observed be
havior of the bridges in these tests. The presence of residual stresses
was also indicated by the nature of the loadstrain curves for the top
flanges on bridge 30N15. These curves showed no break for loads
appreciably higher than those producing yielding in the bottom flanges.
This phenomenon follows naturally from the fact that the applied
stress in the top flange is opposite in sign to the residual stress.
17. Deflections of Beams for Tests with Simulated Wheel Loads.
Deflections of the beams on line 0 were measured in several of the
tests with simulated wheel loads. The maximum load applied ranged
from 3500 to 6000 lb. per panel, and in all cases the loaddeflection
curves were straight lines for their entire length. Deflections at a
load of 3000 lb. per panel were taken from these curves and are plotted
in Fig. 9 for three different loading conditions. For the tests with four
loads, measured deflections for the corresponding right bridges are also
given. For the tests with two loads, no deflections were measured for
the right bridges and computed deflections are given instead for com
parison with the skew bridge results.
The agreement between deflections for the skew and right com
posite bridges is generally good, although the deflections for the skew
bridges tend to be somewhat less uniform. This results from the fact
that the outer beams are relatively stiffer than the center beam because
the line on which the loads are applied does not intersect these beams
at midspan.
The nonuniformity of deflection appears to be greater for the non
composite skew bridge 30N15 than for the composite skew bridges
30S15 and 30C15. This condition probably results from the lower
value of H (the relative stiffness of the beam and slab) for the non
composite bridges.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
     feasured, 30 Degree Skew Bridges
* easured, Riqghf gBrdges
  Compufed, R/gh/ dr/dges
P P P P P P P P P P
p pp p p p p p ppJ^JL
#4 4i 1 j4 4 3 r i I
301/5
/
30C/S 30C/S
N.
FIG. 9. DEFLECTIONS OF BEAMS ON LINE 0 FOR LOADS
ON LINE 0; 30DEGREE SKEW BRIDGES
0
/0
* 20
zs
_ .
I
N
'C"
'3
'N
'Is
30
1 NJ
FIG. 9. "]')EFLECTIONS OF BEAMS ON LINE 0 FOR LOADS
ON LINE 0; 30I)EGREE SKEW BRIBGES
ILLINOIS ENGINEERING EXPERIMENT STATION
18. Strains in Slab Reinforcement for Tests with Simulated Wheel
Loads.Strains were measured in the transverse reinforcement under
the loads, and over the beam between the loads, for a pair of loads
placed in six positions on the bridge.
The positions are as follows:
(1) In panels AB and BC on line 0, for all bridges.
(2) In panels CD and DE on line 0, for all bridges.
(3) In panels CD and DE on line 1w, for 30C15 only.
(4) In panels CD and DE on line 4w, for all bridges.
(5) In panels AB and BC on line 4w, for 30C15 only.
(6) In panels BC and CD on line 0, for all bridges.
Loadstrain curves for the first five load positions are given in
Fig. 10, and those for the remaining position are given in Fig. 11.
In both figures the maximum strains measured in the comparable tests
of right bridges, and the computed strains for the right bridge loaded
at midspan, are also given for comparison. These data are taken from
Figs. 43 and 44 of Bulletin 363.
At the center of a panel, the measured strains in the skew bridges
were generally greater than the maximum strains measured in the
right bridges. The best agreement between skew and right bridges was
obtained for bridge 30C15 for which the average measured strain at
a load of 4000 lb. per panel was equal to 95 per cent of the maximum
rightbridge strain. For bridges 30N15 and 30S15 the ratios of
average skewbridge strain to maximum rightbridge strain were 119
and 108 per cent respectively at a load of 4000 lb. Of greater im
portance, however, is the ratio of maximum skewbridge strain to
maximum rightbridge strain. This ratio ranged from 123 to 136 per
cent for the 30deg. skew bridges.
Strains at the center of a panel for loads on line 4 were, on the
average, about 80 per cent of those for loads on line 0.
Over the beams, the maximum skewbridge strains at a load of
4000 lb. per panel were never more than about 85 per cent of the
maximum strains obtained for the right bridges. An exception to this
statement occurs for one of the tests on bridge 30C15 in which the
strain over beam B (Fig. 10) was quite large. The shape of the load
strain curve for this test, however, indicates that cracking of the slab
had been produced. In none of the other tests were there any indi
cations that cracking had occurred over the beams.
Strains in the top reinforcement over the beams were also measured
for four loads on line 0, one at the center of each panel. These strains
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
 Weosured, Skew Bri/d'e 7a Line 0
. .easured, Skew 8ridgae at/ L ne 4
  Maximum feasure,
for R1i0, 1r/8r1ge
. Compu/le Ri,/ Br/d4e a A/'dspan
8 8
30NI5 /
6   6 
Oufer Panel Beam
k 0 80 /60 0 80
30S/5
8 Outer Panel
80 /6
Pp
6
30 C/S
8
0 80 /60
2 O
0 80
S/roin X /0
Fia. 10. INDIVIDUAL LOADSTRAIN CURVES FOR TRANSVERSE REINFORCEMENT
FOR LOADS AT CENTERS OF INNER AND OuTER PANELS;
30DEGREE SKEW BRIDGES
were either equal to or slightly greater than those obtained for only
two loads on the bridge; any differences were not significant.
The reason for the differences between the strains in the skew and
right bridges may be perceived by reference to Fig. 9, in which the
deflections of the beams for two loads on the bridge are given. The
deflections of the skew bridges are such that there is a somewhat
greater curvature of the slab at the center of a panel and a smaller
IL
8
4
r Panel
7 /&
'Ni
Y
Q
c? ,
(
»
ILLINOIS ENGINEERING EXPERIMENT STATION
P P
A B C 0 E
 easured, Skew Br/ýiye a'1 L/Z' 0
 a/ i'm /easur'a IfIr Rghy/ r/'dge
Compu/fea, /'g9h Br/dge ao Aa'idspan
8
6
0
r

f
Over
Beam C
80
OU /O O V
Stra,, X /0
FIG. 11. INDIVIDUAL LOADSTRAIN CURVES FOR TRANSVERSE
REINFORCEMENT FOR LOADS AT CENTERS OF PANELS
BC AND CD; 30DEGREE SKEW BRIDGES
8
6
4
I'
6
%;
8
44
2
fr,
<
y
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
curvature over the beams as compared to the right bridges. Since
strain in the reinforcement is approximately proportional to curvature,
it becomes evident that the differences in strain result almost entirely
from differences in the deflections of the two types of bridges.
Loadstrain curves for the longitudinal reinforcement in the bot
tom of the slab at the centers of the panels are given in Fig. 12 for
four loads on line 0, one at the center of each panel. The maximum
measured strains from the corresponding tests on right bridges are
also given. Comparisons between the results for skew and right bridges
are not very conclusive. The skewbridge strains are greater for bridge
30N15, while for bridge 30C15 the strains in the outer panel are
appreciably less than the maximum rightbridge strains. The rather
peculiar results for bridge 30S15 cannot be explained. It is of interest
p p P P
A B C D E
  Measured, Skew Bridge at Line 0
 ax/mum Measured, R/'hl Bridce af a/Mdspan
. . Compufed, Rh/z't Bridge a." A".'dspan
6
$ 4
6
,4
0
Strain X /10
FIG. 12. INDIVIDUAL LOADSTRAIN CURVES FOR LONGITUDINAL
REINFORCEMENT IN SLAB; 30DEGREE SKEW BRIDGES
1ý
K
to
ILLINOIS ENGINEERING EXPERIMENT STATION
to note, however, that at the higher loads the curves for the skew
bridge appear to become parallel to those for the right bridge.
19. Effect of Interior Diaphragms.Interior diaphragms consisting
of 3 in. by 2 in. by %6 in. angles were located between the beams at
the onethird points of the span as shown in Fig. 1. In order to de
termine their effect on the quantities measured in the tests, the interior
diaphragms were omitted from bridge 30S15 when it was constructed
and were welded in place after certain of the tests under simulated
wheel loads had been made.
The tests with a pair of loads at the centers of panels CD and DE
on line 0 were made both before and after the diaphragms were
installed. The following measurements were made in both tests: trans
verse strains in the reinforcement at CD and DE and over beam D,
strains in beams C and D on line 0, and deflections of all beams on
line 0.
There were no significant differences between the strains or deflec
tions measured in the tests with and without diaphragms. These
results are similar to those obtained previously in the tests of right
bridges.3 However, as cautioned in discussing the result of those tests,
a different result might be obtained if considerably stiffer diaphragms
are used.
20. Slip Between Slab and Beam.Slip between the slab and the
center beam was measured in several of the tests with simulated wheel
loads. The results were similar to those previously obtained in the
tests of right bridges and presented in Bulletin 363, Fig. 46. The slip
for the bridges with composite action was negligible (from zero to
0.0007 in. for a load of 4000 lb. per panel), and it may be concluded
that complete composite action was obtained. Slips measured for
bridge 30N15 without composite action ranged from 0.0160 to 0.0337
in. at 4000 lb. per panel, and were comparable with those obtained for
the right bridges.
21. Tests to Failure.The tests to failure may be divided into
three parts:
(1) Tests to yielding of the beams with two pairs of loads. These
tests are the same as those discussed in Section 16, and the loadstrain
curves are given in Fig. 8.
3 Bulletin 363, Section 37.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
(2) Tests to failure of the slab with one pair of loads. The loads
were placed at BC and CD on line 0 for bridges 30N15 and 30S15,
and at AB and BC on line 0 for 30C15. The loadstrain curves for
these tests are included in Figs. 10 and 11.
(3) Tests to failure of the slab in which punching was produced by
the application of a pair of loads at four or five locations on the bridge.
The results of these tests are given in Table 6.
The results of the various tests to failure are discussed separately
in the following paragraphs.
Capacity of Beams
It has been pointed out in Section 16 that yielding of the beams
occurred at abnormally low strains, and consequently at abnormally
low loads, as a result of residual stresses in the flanges. This un
fortunate condition makes it impossible to draw conclusions regarding
the capacities of the beams from the loads producing yielding in the
tests to failure. However, the relative capacities of the right and skew
bridges and of the various skew bridges can probably be obtained
from the relative magnitudes of the beams strains at loads less than
those producing yielding. Based on the strains at a load of 3000 lb.
per panel, the capacity of the beams for the noncomposite skew
bridge 30N15 would be about 9 per cent greater than that for the
corresponding right bridge, and the capacities of the beams for the
composite skew bridges 30S15 and 30C15 would be about 5 per cent
less than those for the corresponding right bridges.
TABLE 6
SUMMARY OF PUNCHING LOADS FOR BRIDGES WITH 30DEGREE SKEW
Bridges loaded with a pair of equal loads at the centers of the panels unless otherwise indicated.
Bridge Loads at Loads on Punching Load, Punched at
Line lb. per panel
30N15 BCCD 0 11 935 CD
BCCD 4w 14 075 BC
ABBC 2e 11 540 AB
CD* 3e 9 570 D
BCt 2w 13 175 C
30C15 ABBC 0 13 870 AB
BCCD 0 13 800 BC
CDDE 2e 14 320 DE
CDDE 2w 13 700 DE
BCt 4w 15 730 B
30S15 BCCD 0 15 500 CD
CDDE 4w 14 250 DE
ABBC 0 14 650 AB
BCCD 2w 15 400 CD
* Loads placed 6 in. north of beam centerline.
t Loads placed tangent to south edge of beam flange.
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 7
SUMMARY OF DATA FOR TESTS TO FAILURE OF BRIDGES
WITH 30DEGREE SKEW
Load per Panel in lb. at: Ratio: Skew/Right
Ratio
Bridge
First First Punching First First Punching Ult. (4)
Yielding Yielding of Yielding Yielding of Compr. (3)
of Beam of Reinf. Slab* of Beam of Reinf. Slab Str.t
(1) (2) (3) (4) (5) (6) (7) (8) (9)
30N15 3500 4700 12 520 0.67 0.73 1.22 1.34 2.66
N15 5250 6400 10 300 .... .... .... .... 1.61
30C15 3000 6000 13 920 0.57 0.92 1.13 1.56 2.32
C15 5250 6500 12 300 ... . . ... . .... 1.89
30815 5000 7000 14 950 0.67 0.88 1.05 0.95 2.14
S15 7500 8000 14 200 .... .... .... .... 1.78
Values for right bridges from Bulletin 363, Table 10.
* For loads at centers of panels only.
t From Table 4, for coated cylinders.
Capacity of Slab
Inasmuch as there was usually no wellmarked break in the load
strain curves for the slab reinforcement in Figs. 10 and 11, it was
assumed that yielding had occurred when a strain of 0.00150 had been
reached. This is the strain corresponding to the tensile yieldpoint
stress of 45,200 p.s.i. and is the same as that used in the tests of right
bridges. The loads producing this strain are given in Table 7, which
also includes similar data for the corresponding right bridges.
From the ratios in column 6 of Table 7 it can be seen that the
loads producing yielding in the skew bridges were from 8 to 27 per
cent less than those for the right bridges. The greatest decrease in
capacity occurred for bridge 30N15, the least for bridge 30C15. In
general, the relative capacities of the skew and right bridges were
consistent with the relative magnitudes of the strains produced at
low loads.
Though the capacities of the slabs were less than those for the
right bridges, they were still more than ample when considered in
terms of design loads. The loads given in column 3 of Table 7 may be
converted to live loads corresponding to a standard H20 truck by
dividing by 1300 lb. This results in capacities of 3.6, 5.4, and 4.6 live
loads respectively for 30N15, 30S15, and 30C15.
Punching Loads
The loads producing punching are given in Table 6. The average
values for loads at the centers of the panels are given in column 4 of
Table 7.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGESPART II 35
The punching loads for the skew bridges are from 5 to 22 per cent
greater than those for the corresponding right bridges. This increase is
probably due, at least in part, to the higher compressive strength of
the mortar in the skew bridges. However, the results for bridge 30S15
(5 per cent higher punching loads and 5 per cent lower compressive
strength) seem to indicate the presence of other factors.
The loads producing punching were on the average about 2.37
times as great as the loads producing first yielding of the reinforcement.
This ratio is considerably higher than the average value of about 1.80
for the right bridges.
ILLINOIS ENGINEERING EXPERIMENT STATION
V. TESTS OF BRIDGES WITH 60DEGREE SKEW
22. Description of Tests.Only two bridges having angles of skew
of 60 deg. were tested. They were designated 60N15 and 60C15, and,
except for angle of skew, were similar in all respects to the correspond
ing 30deg. skew bridges 30N15 and 30C15. Details of the bridges
are given in Table 1, and a plan view is shown on Fig. 1. The coordi
nate system for the location of points on these bridges is illustrated
in Fig. 13. The notation used is similar to that in Fig. 5.
The tests performed on the 60deg. bridges differed from those
made on the 30deg. bridges chiefly in the larger number of load posi
tions which were used. The various tests are described briefly in the
following paragraphs.
Cracking Test. The slab of each bridge was systematically cracked
by the application of a pair of loads at the centers of adjacent inner
and outer panels at 20 locations on each bridge. Loads of 4000 lb.
per panel were applied in panels AB and BC on lines 7e to 2w inclu
sive, and in panels CD and DE on lines 2e to 7w inclusive. Strains
were measured in the transverse slab reinforcement under the loads
during the first applications of the loads on line 0.
Influence Lines for Strains in Beams. Strains were measured in the
beams at the gage lines indicated on Fig. 13, for a single load moving
transversely across the bridge on the line through the gage line and
on one or two lines each side of the gage line. The load used was 700
lb. in the tests before cracking and 2000 lb. in the tests after cracking.
The locations of the strain gage lines on the crosssection of the beam
were the same as for the bridges with 30deg. skew.
e 5tranguage line on beam Snkew
I Strainqgae ine on transverse reintorcement Centerline
 Straingage e Ae on longiaud'in/ re/nforcement
FIG. 13. COORDINATE SYSTEM AND LOCATIONS OF STRAINGAGE
LINES FOR BRIDGES WITH 60DEGREE SKEW
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
Influence Lines for Deflections of Beams. Deflections of the
beams were measured after cracking, for a single load placed at
various positions on the bridge. Loads of 1500 and 3000 lb. were
used for bridge 60C15, while loads of 1500, 3000, and 4500 lb. were
used for bridge 60N15.
Influence Lines for Strains in Slab Reinforcement. Strains were
measured in the slab reinforcement at the locations indicated on Fig.
13, for a single load moving across the transverse lines through
and adjacent to the gage lines. Two magnitudes of load, 1500
and 3000 lb., were used. Strains were measured on a single gage line
at each location.
Tests with Uniform Load. The tests with uniform load were similar
in all respects to those described in Section 10 for the bridges with
30deg. skew.
Strains in Slab Reinforcement for Tests with Simulated Wheel
Loads. These tests may be divided into three parts:
(1) Strains were measured in the transverse reinforcement under
the loads and over the beam between the loads, for several positions
of a pair of loads: at CD and DE on line 3w, at CD and DE on line 0,
and at AB and BC on line 0. The load position last mentioned was
used only on bridge 60N15.
(2) In the next test, four loads were applied, one at the center of
each panel, at several lines on the structure. For the loads on line 2w,
strains were measured in the longitudinal reinforcement at DE on
line 2w for 60N15, and at DE on lines 2w and 3w for 60C15. For the
loads on line 1w, strains in the longitudinal reinforcement were meas
ured at CD on line 1w for both bridges. Strains were also measured in
the transverse reinforcement over beam C on line 2w for loads on 2w,
and on line 1w for loads on 1w.
(3) After the test to yielding of the beams, strains in the trans
verse reinforcement were again measured for a pair of loads on the
bridge. For 60N15, load was applied at BC and CD on line 1w and
strains were measured at CD under the load and at C over the beam
between the loads. This test was continued until the slab failed by
punching. For bridge 60C15, three tests were made. The bridge was
first loaded at BC and CD on 1w, and strains were measured at CD
and C. This test was similar to that just described for 60N15 except
that it was not carried to failure. The bridge was next loaded at BC
and CD on line 0, and strains were measured at CD and C. Finally
the slab was tested to failure by punching, with loads at CD and DE
on line 0, and strains were measured at CD, D, and DE.
ILLINOIS ENGINEERING EXPERIMENT STATION
Strains in Beams for Tests with Simulated Wheel Loads. The three
tests of this type described below in the order in which they were
made: (1) Two pair of loads were applied on line le, and strains were
measured in beam A on line le, in beam B on lines 0, le, and 2e, and
in beam C on line le. (2) Two pair of loads were applied on line 0,
and strains were measured in beam B on line 0 and le, in beam C on
line 0, and in beam D on lines 0 and 1w. (3) Twopair of loads were
applied on line 2w, and strains were measured in'beam D on lines 1w
and 2w, and in beam E on lines 1w, 2w and 3w. At the first load posi
tion, the transverse location of the loads was as shown on Fig. 17; at
the other positions, the transverse location of the loads was reversed
about beam C from the location shown on the figure. In all tests the
load was increased in increments of 1000 lb. per panel to 3000 lb., and
then in increments of 500 lb. per panel until yielding of the beams was
produced.
Deflections of Beams in Tests with Simulated Wheel Loads. Deflec
tions of all beams were measured on line 0 in all tests under simulated
wheel loads in which loads were applied on line 0. In addition, other
deflection measurements were made at various locations in the tests
with one or two pair of loads.
Punching Tests. At the conclusion of the tests described above,
the slab was tested to failure by punching under one pair of loads at
four locations in addition to the one already mentioned in the descrip
tion of the slab strain tests.
23. Cracking Test.For loads producing first cracking on line 0,
strains were measured in the transverse reinforcement. In all important
respects, the results obtained were similar to those for the 30deg.
bridges (Section 11) and for the right bridges of Bulletin 363.
24. Influence Lines for Strains in Beams.In the test before the
slab was cracked, the top flange strains for bridge 60N15 were appre
ciably smaller than those for the bottom flange. After cracking, the
agreement was much better but the top flange strains were still as
much as 10 per cent smaller. These conditions resulted from the
presence of some interaction due to frictional forces between the slab
and beams, and are typical of the results obtained in the other tests
of bridges without shear connectors.
Typical results from these tests are given in Figs. 14 and 15. The
influence surfaces in Fig. 14 are interesting in that they show the same
general shape for the bridges with and without composite action.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGESPART II
k
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K
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CQo «
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o
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ILLINOIS ENGINEERING EXPERIMENT STATION
Similar experimentally determined influence surfaces are not available
for the corresponding right bridges. However, theoretical values may
be obtained from Bulletin 336,4 and a comparison with influence
surfaces plotted from those values indicates a relatively small effect
of skew on the shape of the surface.
The influence surfaces in Fig. 14 may be used to determine the posi
tions of the two pair of loads which will produce maximum effects at
the center of beam C. If this is done for bridge 60N15, it is found
that maximum strain in beam C on line 0 is obtained with both pairs of
loads on line 0. For 60C15, the maximum occurs for one pair of loads
on line 0, and for the other pair only a short distance away.
In order that comparisons may be made with measured values for
the .right bridges, representative influence lines are given in Fig. 15 for
bridge 60N15. These influence lines are for the points on each beam
at which the greatest strains were measured. Values for the correspond
ing right bridge, N15, are for strains at midspan; they are taken from
Fig. 35a, Bulletin 363. The most significant difference between the
influence lines for the right and skew bridges is the greater rate at
which the strains for the skew bridge decrease as the load is moved
away from the point in question. This is characteristic of the skew
.bridge and results from the fact that as the load moves away from
the beam in question, it generally moves nearer to the support. Conse
quently, more load is carried to the support by other beams and less
by the beam for which the influence values are being determined.
Comparisons similar to those discussed above may also be made
between the composite skew and right bridges, 60C15 and C15. For
these bridges, the rate of decrease in strain as the load moved away
from the gage line was again somewhat greater for the skew bridge.
However, this effect was obscured by the fact that the strains for the
skew bridge were consistently less than those for the right bridge. A
similar relation found in the influence lines for beam deflections is
discussed in more detail in the following section.
25. Influence Lines for Deflections of Beams.Typical influence
lines for deflections of the beams are given in Fig. 16. The values
plotted are averages of deflections at symmetrically located points on
the two halves of the bridge. The point on each beam for which the
influence lines are given is that at which the maximum deflection was
recorded. Except in the case of beam A on 60C15, the load was moved
across the bridge on the transverse line through the point at which
4N. M. Newmark and C. P. Siess, "Moments in IBeam Bridges," Univ. of Il. Eng. Exp.
Sta. Bul. 336. 1942.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
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ILLINOIS ENGINEERING EXPERIMENT STATION
deflection was measured. Slightly greater deflections for loads not at
the gage points would be obtained for a load moving across the bridge
on a diagonal line in a direction between that of the transverse line
(normal to the beams) and the skew centerline (at 30 deg. to the
beams).
Influence lines for the corresponding right bridges, N15 and C15,
are also given on Fig. 16. They represent deflections at midspan of the
beams for a load moving transversely across the bridge at midspan.
The curves were obtained from Fig. 37, Bulletin 363.
The influence lines for bridge 60N15 without composite action
show a decided effect of skew. The rate of decrease in deflection as the
load moves away from the gage point is much greater for the skew
bridge than for the right bridge. A similar effect was noted for the
influence lines for strains in the beam, and the reason for it has been
discussed in the preceding section. The greater deflection of beam A
of the skew bridge for a load over the beam is difficult to explain. It
is possible, however, that for a load in this position, some of the re
maining beams may have been lifted from the abutments at their ends,
and consequently did not carry their share of the load. For a load
over an edge beam near midspan, there is a tendency for the bridge
to rotate about a line connecting the obtuse corners.
The influence lines for bridge 60C15 with composite action lie an
almost constant distance below the influence lines for the correspond
ing right bridge, C15. This difference in magnitude tends to mask the
effects of skew, which are nevertheless present in the form of a more
rapid decrease in deflection as the load moves away from the gage
point. This effect, however, is less for the composite bridge than for
the noncomposite bridge, probably because of the greater relative
stiffness of the beams in the former.
There are at least two possible reasons why the deflections are
smaller for the composite skew bridge than for the corresponding right
bridge. One reason is that the beams in a composite skew bridge behave
as if they are partially restrained at the ends. Near the ends of the
bridge, the slab is constrained to remain horizontal along a line parallel
to the abutments, and is at least partially thus constrained along lines
making a small angle with the abutments. The beams make an angle
of only 30 deg. with the abutments, and are tied to the slab by means
of the shear connectors. Consequently, it seems probable that the slab
offers some restraint against rotation of the beams at the supports.
Such restraint would be negligible in the bridges without shear con
nectors, and in the bridges with small angles of skew.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
Another possible explanation of the smaller deflections for the
composite skew bridge lies in the increased torsional stiffness of the
composite beam as compared with that of the Ibeam alone. As a
result, there is an incrtase in the proportion of the moment resisted
by torsion in the plane normal to the axis of the beam, and a cor,
responding decrease in the moment carried by bending in the direction
parallel to the beam. This effect is probably important only for rela
tively large angles of skew.
26. Influence Lines for Strains in Slab Reinforcement.The influ
ence values for strains in the bottom transverse reinforcement were
generally greater than those for the bridges with 30deg. skew or for
the right bridges. The greatest increase in strain corresponding to an
increase in angle of skew from 30 to 60 deg. was found in the com
posite bridges, for which, however, there was practically no increase
in strain for the change in angle of skew from zero to 30 deg. On the
other hand, the noncomposite bridges, which had a fairly large in
crease in strain from zero to 30deg. skew, showed only a slight increase
from 30 to 60 deg. As a result, the increase in bottom transverse strain
for the 60deg. bridges as compared to the right bridges was about the
same for the structures with and without composite action. For the
noncomposite bridges, the increase in maximum strain under the load
ranged from 62 to 78 per cent, and was greatest for strain in an inner
panel. For the composite bridges, the corresponding increase was 18 to
53 per cent, and was greatest for strain in an outer panel.
Strains in the top transverse reinforcement over the beams were
small and were in reasonably good agreement with those for the bridges
with 30deg. skew and for the right bridges.
The maximum transverse strains in these tests occurred at points
on line 0 for the composite bridges, and at points on the skew center
line for the noncomposite bridges.
The influence lines for strains in the longitudinal reinforcement at
the center of a panel were similar in shape and magnitude to those
obtained for the bridges with 30deg. skew. The maximum strains
under the load were obtained at points on the skew centerline for both
the composite and the noncomposite bridges.
27. Tests with Uniform Load.Strains and deflections resulting
from the added dead load were not measured for all five beams on any
single transverse line or on the skew centerline. Sufficient measure
ments were obtained, however, to indicate that the maximum values of
ILLINOIS ENCINEEnrM' EXPE 'MENT TIOI
strain and deflection probably occurred on a diagonal line between the
skew centerline and transverse line 0, and that these values were in
general somewhat greater than those obtained for the bridges with
30deg. skew.
The maximum strains in the various beams ranged from 0.00012
to 0.00018 for bridge 60N15, and from 0.00011 to 0.00021 for bridge
60C15. The maximum value of deflection was 0.108 in. for 60N15
and 0.087 in. for 60C15.
Attention is again called to the fact that although strains and
deflections were measured, the test itself was not made to simulate the
effect of the dead load of an actual bridge. (See Section 15.)
28. Strains in Beams for Tests with Simulated Wheel Loads.
Strains were measured in the beams of both bridges with 60deg. skew
for two pair of loads on lines le, 0, and 2w, as described in Section 22.
The results of these tests are given in Fig. 17, together with measured
and computed rightbridge strains from Bulletin 363, Fig. 40. For con
venience in making comparisons with the results for the right bridges,
certain of the load positions shown on the sketch in Fig. 17 have been
reflected about a line of symmetry in a manner similar to that used in
connection with Fig. 8.
The strains plotted for beams A, B, and C for the skew bridges
are the maximum values obtained for any of the load positions used.
The strains given for beam D are the only ones measured in that beam,
and are not maxima for the transverse location of the loads shown. No
strains were measured in beam E.
Because of the presence of residual stresses in the beams of the
skew bridges, comparisons between strains for the skew and right
bridges will be confined to those portions of the loadstrain curves
below yielding. For bridge 60N15 without composite action, the
measured strains in the skew bridge at a load of 3000 lb. per panel
were about 78 per cent of those in the corresponding right bridge. For
bridge 60C15 with composite action the measured skewbridge strains
at the same load were about 86 per cent of the rightbridge strains.
For both bridges, the measured skewbridge strains were about 80
per cent of the computed strains for the corresponding right bridges.
Strains in the top flanges are not given on Fig. 17. Those for the
noncomposite bridge 60N15 were usually within 10 per cent of the
bottom flange strains; sometimes greater, sometimes less. The top
flange strains for the composite bridge 60C15 were quite small and
indicated the presence of complete composite action.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
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FIG. 17. LOADSTRAIN CURVES FOR BEAMS; 60DEGREE SKEW BRIDGES
The strains plotted on Fig. 17 are the maximum measured values
for any given beam. However, strains very nearly equal to these
maximum values were generally obtained for the loads at positions
other than those indicated as giving the maximum effects. In all of
these tests, the four loads were placed on the same transverse line,
normal to the direction of the beams. This arrangement was chosen,
primarily for convenience, after a study of influence surfaces such as
those in Fig. 14 indicated that little increase in maximum strain
would result from a staggered arrangement. However, on purely
ILLINOIS ENGINEERING EXPERIMENT STATION
theoretical grounds, there is some reason to believe that a greater
moment may have been produced in the 60deg. bridges by the use of
a staggered arrangement of the loads.
If it is assumed that there are no twisting moments on the section
of a beam normal to the axis, the total moment parallel to the beams
may be computed by statics for any section cut through the bridge
parallel to the abutments. For both pairs of loads on the same trans
verse line the maximum static moment on a skew section is equal to
only 71 per cent of the corresponding moment for a right bridge,
while for a staggered arrangement of the pairs of loads this figure may
be increased to 83 per cent. Thus the total moment in the 60deg.
bridges theoretically may have been increased by about 16 per cent
if the loads had been staggered. This increase, however, refers only to
the total moment and not to the moments in the individual beams,
which depend not only on the total moments but also on their distri
bution. It has been observed in these tests that the moments in the
beams for all loads on the same transverse line are less uniformly dis
tributed than those in a corresponding right bridge. Correspondingly,
it would seem logical to believe that as the loads are staggered, the
distribution on a skew section would become more uniform, approach
ing that for a right bridge.
It is seen, therefore, that although a staggered load arrangement
tends to produce a greater total moment, it also tends to produce a
more uniform distribution of load, and thus possibly a smaller maxi
mum moment in an individual beam. This behavior serves at least
in part to explain the apparent contradiction between the influence
surface data and the static moment calculations. In view of this argu
ment, it does not seem reasonable to assume that the maximum beam
moments would have been increased 16 per cent by the use of a stag
gered arrangement of loads, nor is it entirely on the safe side to accept
the evidence of the influence surfaces completely; the true condition
probably lies somewhere between these two.
29. Deflections of Beams for Tests with Simulated Wheel Loads.
Deflections of the beams were measured at various locations in several
of the tests with simulated wheel loads. The maximum load applied
ranged from 4000 to 6000 lb. per panel, and the loaddeflection curves
were usually straight lines for loads less than about 5000 lb. For
higher loads, there was a slight decrease in the slope of the curves.
Deflections of all five beams at the same line were obtained only
on line 0 for loads on line 0. For these cases, the deflections at a
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II 47
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ON LINE 0; 60DEGREE SKEW BRIDGES
load of 3000 lb. per panel have been taken from the loaddeflection
curves and are given in Fig. 18. Measured or computed deflections for
the corresponding right bridges with loads at midspan are also shown
on the figure.
As was pointed out in connection with the 30deg. skew bridges, the
effect of skew is to make the deflections more nonuniform than those
for a right bridge. This effect, however, is considerably greater for
the bridges with 60deg. skew than for the bridges with 30deg. skew,
as can easily be seen by comparing Figs. 9 and 18.
The deflections plotted in Fig. 18 are not necessarily the maximum
values obtained in the tests except for the center beam. However, the
maximum deflection for beams A and B for four loads on the bridge
at locations other than line 0 was only slightly greater than the
deflection of beam C on line 0 for loads on line 0.
4
ILLINOIS ENGINEERING EXPERIMENT STATION
The maximum deflection of the bridge for four loads was 15 to 20
per cent less for the 60deg. skew bridges than for the 30deg. skew
bridges.
30. Strains in Slab Reinforcement for Tests with Simulated Wheel
Loads.Strains were measured in the transverse reinforcement under
the loads, and over the beam between the loads, for a pair of loads
placed in the following positions on the bridges:
(1) In panels CD and DE on line 0, for both bridges.
(2) In panels CD and DE on line 3w, for both bridges.
(3) In panels AB and BC on line 0, for 60N15 only.
(4) In panels BC and CD on line 1w, for both bridges.
(5) In panels BC and CD on line 2w, for 60C15 only.
Loadstrain curves for the tests listed above are given in Figs. 19
and 20, together with the maximum measured strains for the corre
sponding right bridges, and computed strains for the right bridges
loaded at midspan. The rightbridge strains in these figures are iden
tical with those given in Figs. 10 and 11.
The results for these tests were not greatly different from those
for the 30deg. skew bridges. The skewbridge strains at the center of
a panel were greatest for loads on line 0 and were usually greater than
the corresponding strains for the right bridges. The observed increase
was greatest for the noncomposite bridges. The ratio of maximum
skewbridge strain to maximum rightbridge strain at a load of 4000
lb. per panel was 165 per cent for 60N15, and 129 per cent for 60C15.
Corresponding values for the bridges with 30deg. skew were 136 per
cent for 30N15, and 123 per cent for 30C15. If the exceptionally high
strain in panel CD of bridge 60N15 is neglected, the maximum ratio
for that bridge becomes 138 per cent. In general, with the exception
of this one high value, the strains for the 60deg. bridges compare
favorably with those for the 30degree bridges.
Over the beams, the strains in the skew bridges for one pair of
loads were greatest at line 3w. At a load of 4000 lb. per panel, the
ratios of maximum skewbridge strains at line 3w to maximum right
bridge strains were 86 and 61 per cent for 60N15 and 60C15 re
spectively. These ratios are approximately the same as those for the
bridges with 30deg. skew. However, for loads on line 0, in positions
producing maximum strains at the center of a panel, the strains over
the beams were appreciably less than those obtained at line 3w. For
loads on line 0, the ratios of strains in the skew bridges to those in the
corresponding right bridges were 4459 per cent for 60N15 and 2047
per cent for 60C15.
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
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ILLINOIS ENGINEERING EXPERIMENT STATION
Strains in the top reinforcement over the center beam were also
measured for four loads, one at the center of each panel, on line 1w or
2w. For bridge 60N15, these strains were as much as twice as great as
those obtained with loads in only the center panels, and the maximum
value at a load of 4000 lb. per panel was 20 per cent greater than the
maximum rightbridge strains. It seems probable, however, that crack
ing of the slab occurred in these tests at a load of about 3000 lb. per lb.
For bridge 60C15, the strains for four loads were equal to those for
two loads shown on Fig. 20.
The difference between the transverse strains in the skew and
right bridges results from the more nonuniform deflections of the
beams for the skew bridge, and has been discussed in Section 18 in
connection with the 30deg. skew bridges. Some idea of the difference
in deflection of the beams and in curvature of the slab for the skew
and right bridges may be obtained from Fig. 18.
Loadstrain curves for the longitudinal reinforcement in the bottom
of the slab at the centers of the panels are given in Fig. 21, together
with maximum values obtained in similar tests on the right bridges.
The results are not significantly different from those given in Fig. 12
for the bridges with 30deg. skew. For the noncomposite skew bridge
60N15, the strains are somewhat greater than those for the right
bridge; for the composite bridge, 60C15, they are generally smaller.
31. Effect of Interior Diaphragms.The effect of light interior
diaphragms on the transverse strains in the reinforcement and on the
deflections of the beams was investigated for bridge 60N15. For this
bridge, tests with a pair of loads at AB and BC, and at CD and DE,
both on line 0, were made both before and after the diaphragms were
installed.
Strains in the transverse reinforcement and deflections of the
beams were measured in all tests. There were no significant differ
ences in either of these quantities for the tests with or without dia
phragms. This result is in agreement with that found in the tests of
both the right bridges and the bridges with 30deg. skew. Again it
must be recognized that heavier diaphragms may have more of an
effect on the structure.
32. Slip Between Slab and Beam.Slip between the slab and the
center beam was measured in several of the tests with simulated
wheel loads. The results were generally similar to those obtained for
the bridges with 30deg. skew. For bridge 60C15 the maximum slip
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
A B C D E
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  Aeasured, Skew Bridge at Line /w
 Maximum Measured, Right Bridge
 Computed, Right Bri/dge
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FIG. 21. INDIVIDUAL LOADSTRAIN CURVES FOR LONGITUDINAL
REINFORCEMENT IN SLAB; 60DEGREE SKEW BRIDGES
observed at a load of 4000 lb. per panel was 0.0002 in., which is
negligible and indicates the presence of full composite action. For
bridge 60N15 without composite action, the slip at 4000 lb. per panel
ranged from 0.0140 to 0.0230 in., which is somewhat smaller than was
obtained for the 30deg. skew bridge or for the right bridges.
33. Tests to Failure.The tests to failure may be divided into
three parts, as follows:
(1) Tests to yielding of the beams with two pair of loads. These
tests have been described in Section 22, and the significant loadstrain
curves are given in Fig. 17.
(2) Tests to failure of the slab with one pair of loads at BC and
CD on line 1w for 60N15, and at CD and DE on line 0 for 60C15.
The loadstrain curves for these tests are included in Figs. 19 and 20.
(3) Tests to failure of the slab in which punching was produced
by the application of a pair of loads at five locations on each bridge.
The results of these tests are given in Table 8, on the next page.
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 8
SUMMARY OF PUNCHING LOADS FOR BRIDGES WITH 60DEGREE SKEW
Bridge Loads at Loads on Punching Load, Punched at
Line lb. per panel
60N15 BCCD 1w 11 950 CD
BCCD le 12 500 BC
CDDE le 11 850 DE
DE* 2w 10 950 D
CDt 4w 13 400 C
60C15 CDDE 0 13 600 DE
BCCD 0 14 100 BC
ABBC 2e 13 750 AB
DE* 2w 12 625 E
CDt 4w 15 330 D
* Loads placed 6 in. south of beam centerline.
t Loads placed tangent to north edge of beam flange.
The capacities of the bridges as determined from the various tests
to failure are discussed below.
Capacity of Beams
The loads at which yielding of the beams first occurred are given
in Table 9. Unfortunately, these loads have little significance because
of the unusually large residual stresses in the beams. However, the
relative capacities of the beams in the various bridges can probably
be predicted from the relative magnitudes of the strains at loads less
than those producing yielding. Based on the strains at a load of 3000
lb. per panel, the capacity of the beams for bridge 60N15 would be
about 17 per cent greater than for bridge 30N15, and about 28 per
cent greater than for the right bridge N15. Similarly, the capacity
of the beams for bridge 60C15 would be about 22 per cent greater
than for bridge 30C15, and about 16 per cent greater than for bridge
C15. The excess in capacity of the 60deg. skew bridges might pos
sibly have been slightly reduced if a different arrangement of loading
had been used.
Capacity of Slab
Since there was usually no wellmarked break in the loadstrain
curves, it was assumed that yielding of the reinforcement occurred
at a strain of 0.00150. This criterion is the same as that used for the
right bridges and for the bridges with 30deg. skew. The loads produc
ing first yielding are given in Table 9, and the relative capacities of
the slabs, as measured by the load producing yielding, are given in
column 6 of Table 9.
The capacities for the 60deg. skew bridges are 10 to 17 per cent
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
TABLE 9
SUMMARY OF DATA FOR TESTS TO FAILURE OF BRIDGES
WITH 60DEGREE SKEW
Load per Panel in lb. at: Ratio: Skew/Right
Ratio
Bridge
First First Punching First First Punching Ult. (4)
Yielding Yielding of Yielding Yielding of Compr. (3)
of Beam of Reinf. Slab* of Beam of Reinf. Slab Str.t
(1) (2) (3) (4) (5) (6) (7) (8) (9)
60N15 4000 4200 12 100 0.76 0.66 1.18 1.08 2.88
30N15 3500 4700 12 520 0.67 0.73 1.22 1.34 2.66
N15 5250 6400 10 300 .... .... .... .... 1.61
60C15 3500 5000 13 800 0.67 0.77 1.12 1.48 2.76
30C15 3000 6000 13 920 0.57 0.92 1.13 1.56 2.32
C15 5250 6500 12 300 .... .... .... .... 1.89
Values for 30deg. skew bridge from Table 7.
Values for right bridge from Bulletin 363, Table 10.
* For loads at centers of panels only.
t From Table 4, for coated cylinders.
less than those for the 30deg. skew bridges, and 23 to 34 per cent less
than those for the right bridges. The capacities of the slab were
smaller for the noncomposite skew bridges than for the composite
skew bridges. This is in contrast to the results for the right bridges,
for which there was little difference between the composite and non
composite structures.
The number of design live loads may be obtained from Table 9 by
dividing the loads in column 3 by 1300 lb. The resulting capacities
are 3.2 and 3.8 live loads for 60N15 and 60C15 respectively.
Punching Loads
The loads producing punching are given in Table 8. The average
values for loads at the centers of the panels are given in column 4
of Table 9.
Although the punching loads for the skew bridges were consistently
higher than for the corresponding right bridges, there was no signifi
cant difference between the loads for the bridges with 60deg. or
with 30deg. skews. It seems probable, therefore, that a large propor
tion of the increase in punching loads for the skew bridges was due to
the greater compressive strength of the mortar in those bridges, as
indicated by the ratios in column 8 of Table 9.
ILLINOIS ENGINEERING EXPERIMENT STATION
VI. DISCUSSION OF RESULTS
34. Preliminary Remarks.Laboratory tests were made on five
skew Ibeam bridges, three with 30deg. skew and two with 60deg.
skew.
The effect of skew on the behavior of Ibeam bridges may be de
termined by comparing the strains and deflections measured in these
tests with the corresponding data from previous tests on right bridges.
Comparisons may also be made with the theoretical strains for right
bridges, obtained from Bulletin 336.
Comparisons of this sort have been made in the preceding portions
of this bulletin. The results are summarized in the following sections.
35. Effect of Skew on Strains in Beams.In general, the effect of
skew was to reduce the beam strains for the skew bridges as compared
to those for the corresponding right bridges. The relative values of the
maximum measured beam strains in the various bridges are given in
the following table.
Relative Values of Maximum
Angle of Measured Beam Strains
Skew,
degrees Noncomposite Composite
Bridges Bridges
0 100 100
30 91 105
60 78 86
The differences indicated above between the bridges with zerodegree
and 30degree skew are not believed to be significant, since in previous
tests of right bridges the measured beam strains for two companion
specimens varied by as much as 15 per cent from the average value.
The measured beam strains for the bridges with 60deg. skew were
78 to 86 per cent of the measured strains for the corresponding right
bridges, and about 80 per cent of the computed strains for the right
bridges. The ratio of beam strains in the 60deg. bridges to those in the
30deg. bridges was approximately 83 per cent, and was quite con
sistent for the various strains measured on each bridge.
The differences in beam strains for the various angles of skew
are made up of two parts: (1) differences in the total static moment
on a given section and (2) differences in the distribution of that
moment to the various beams. In these tests, the two pair of loads
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
used to obtain maximum strains in the beams were always placed on
the same transverse line normal to the beams. For the skew bridges,
some of the loads are thus closer to the support than others, and the
total static moment on a given section is less than it would be for a
right bridge with all four loads at midspan. This is undoubtedly the
principal reason for the differences in beam strains for the skew and
right bridges. However, the results of computations indicate that the
measured reduction in beam strain was significantly less than the
theoretical reduction in total moment on a section. The explanation lies
in the different distribution of moment to the various beams in the
skew and right bridges. The results of the tests indicated that the
distribution of moment for the 30deg. skew bridges was not appre
ciably different from that for the right bridges. However, for the
60deg. bridges, with all of the loads on the same transverse line,
there were definite indications that the distribution of moment to the
various beams was considerably more nonuniform than in a similar
right bridge. Consequently, the reduction in total static moment is
partially offset by the fact that a greater proportion of that moment
is carried by the most heavily loaded beam. Similarly, the increase in
total static moment which would have resulted from the use of a
staggered arrangement of the loads would possibly have been counter
balanced in part by the relatively more uniform distribution of moment
to the various beams.
In summary, the following conclusions may be drawn concerning
the effect of skew on the behavior of the beams in an Ibeam bridge:
(1) For loads placed on a single transverse line at right angles to
the beams, the total static moment on a given section decreases as
the angle of skew increases.
(2) For loads thus placed, the distribution of moment to the vari
ous beams becomes more nonuniform as the angle of skew increases.
(3) The maximum strain in the beams decreases as the angle of
skew increases, but the decrease is not significant for angles of skew
up to about 30 deg.
(4) In the bridges tested, for a skew angle of 30 deg. the reduction
in maximum beam strain was negligible; for a skew angle of 60 deg. the
reduction in maximum beam strain was from 14 to 22 per cent. These
numerical values would be different for bridges of other span lengths,
and might have been slightly less for the 60deg. bridges if a staggered
arrangement of the loads had been used.
36. Effect of Skew on Deflections of Beams.The effects of skew
on the deflections of the beams were similar in all respects to the effects
ILLINOIS ENGINEERING EXPERIMENT STATION
on strains in the beams discussed in the preceding section. They are
best illustrated by the data given in Figs. 9 and 18.
The beam deflections were affected by skew in two ways: (1) a
more nonuniform deflection of the several beams was produced, and
(2) the maximum beam deflection was decreased. The increase in
nonuniformity of deflection for a given angle of skew appeared to be
appreciably greater than the corresponding increase in nonuniformity
of strain. The decrease in maximum deflection, however, was approxi
mately the same as in maximum strain (Section 35).
Quantitatively, the maximum beam deflections for the bridges
with 30deg. skew varied from 7 per cent less to 7 per cent more than
the maximum for the corresponding right bridges; for the bridges with
60deg. skew the maximum deflection was 22 per cent less than for
the right bridges.
37. Effect of Skew on Strains in Slab Reinforcement.In the fol
lowing subsections the effects of skew will be discussed separately for
the slab reinforcement at the following locations: (1) the bottom
transverse reinforcement at the center of a panel, (2) the top trans
verse reinforcement over a beam, and (3) the bottom longitudinal
reinforcement at the center of a panel.
Transverse Strains at Center of Panel
The effect of skew was to increase the transverse strains at the
center of a panel. The relative values of the maximum measured
strains in the bridges with various angles of skew are given in the
following table.
Relative Values of Maximum Measured
Strains in Transverse Reinforcement
Angle of at Center of a Panel
Skew,
Noncomposite Composite
degrees Bridges Bridges
0 100 100
30 136 123
60 165 129
The increase in strain accompanying an increase in angle of skew
is the direct result of the increase in relative beam deflection dis
cussed in the preceding section. An increase in relative deflection of
the type occurring in these tests causes a decrease in negative slab
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES PART II
moment over the beam, and a consequent increase in positive moment
at the center of a panel. However, the transverse strain at the center
of a panel cannot continue to increase indefinitely as the angle of
skew increases, since, for very large angles, the effective span of the
slab between abutments becomes smaller than the transverse span
between beams, and at a skew angle of 90 deg. the transverse strain
should be equal to zero.
Transverse Strains over Beams
In general, the effect of skew was to decrease the transverse strains
over the beams. The relative values of the maximum measured strains
for various angles of skew are tabulated below. The strains compared
include only those obtained with one pair of loads on the bridge.
Relative Values of Maximum Measured Strains
Angle of in Transverse Reinforcement over Beams
Skew,
degrees Noncomposite Composite Composite
Bridges "C" Bridges "S" Bridges
0 100 100 100
30 83 61 84
60 86 61
The decrease in transverse strain over the beams is consistent with
the increased strain at the centers of the panels; both changes result
from the more nonuniform beam deflections in the skew bridges.
The values in the table above indicate no tendency for further de
crease in maximum strain for angles of skew greater than 30 deg.
This is not unreasonable, for, in obtaining maximum transverse strain
over the beams, it is usually possible to place the loads at locations
for which the effects of nonuniform deflection are a minimum. Con
sequently, there is no reason to expect greater reductions in negative
slab moments than those indicated in the table, even for larger angles
of skew.
Except in one or two tests, there were no indications that cracks
were produced in the top of the slab over the beams. This, of course,
accounts for the low ratio of measured to computed strain in the
reinforcement, since the computed values were based on the assump
tion of a cracked section. The absence of cracks over the beams is an
abnormal condition, which, although it has consistently been observed
in laboratory tests of Ibeam bridges, cannot safely be assumed to
exist in actual structures.
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Longitudinal Strains at Center of Panel
The effect of skew on the strains in the longitudinal reinforcement
was considerably different for the bridges with and without composite
action. The relative values of the maximum measured strains in the
skew and right bridges are given in the following table.
Relative Values of Maximum Measured
Strains in Longitudinal Reinforcement
Angle of at Center of Panel
Skew,
degrees Noncomposite Composite
degrees Bridges Bridges
0 100 100
30 124 48
60 132 37
The strains in the longitudinal reinforcement of the noncomposite
bridges increased as the angle of skew was increased, and the maxi
mum values were about 80 per cent of the theoretical strains for a
right bridge. On the other hand, the strains for the composite bridges
decreased as the angle of skew increased, and were a very small pro
portion of the theoretical values.
38. Effect of Skew on Ultimate Strength of Bridge.Because of the
large residual stresses in the beams, the capacities of the beams, as
measured by the loads producing yielding, cannot be determined from
the results of these tests. However, since the effect of skew was to
decrease the maximum strains in the beams, it would seem reasonable
to assume that the load carried by the beams before normal yielding
would be increased in proportion. On this basis, the relative capacities
of the beams for various angles of skew are approximately as given
below. The capacities for bridges with 60deg. skew might have been
slightly reduced had a different arrangement of loads been used.
Relative Capacities of Beams Before
Yielding as Determined from Relative
Angle of Values of Beam Strains at Low Loads
Skew,
Noncomposite Composite
degrees Bridges Bridges
0 100 100
30 109 95
60 128 116
BUL. 375. SLAB AND BEAM HIGHWAY BRIDGES  PART II
The relative capacities of the slabs, as measured by the loads first
producing a strain of 0.00150 in the transverse reinforcement, are given
in the following table. The values in the table are in good agreement
Relative Capacities of Slabs as Measured by
Angle of First Yielding of the Reinforcement
Skew,
degrees Noncomposite Composite Composite
Bridges "C" Bridges "S" Bridges
0 100 100 100
30 73 92 88
60 66 77
with those predicted on the basis of the relative values of the maxi
mum measured strains in the transverse reinforcement.
The ultimate capacity of the slab may be taken as the load at
which the slab failed by punching. These loads were from 5 to 22 per
cent greater for the skew bridges than for the corresponding right
bridges. These increases, however, are believed to result primarily from
the greater compressive strength, and the consequent greater shear
strength, of the mortar used in the slabs of the skew bridges.
The effect of skew on the capacities of the various components of
an Ibeam bridge may be summarized as follows:
(1) The capacity of the beams as measured by first yielding in
creased as the angle of skew was increased.
(2) The capacity of the slab as measured by first yielding of the
reinforcement decreased as the angle of skew was increased.
(3) The ultimate capacity of the slab as measured by the load
producing punching is probably independent of angle of skew, at
least for angles not greater than 60 deg.
39. Effect of Skew on DeadLoad Moments in an IBeam Bridge.
The results of the test with uniform load described in Sections 15 and
27 are not applicable to a study of the deadload moments in the
beams of an actual Ibeam bridge, since the added uniform load
carried by the beams was affected by the distributing action of the
slab already in place. In an actual Ibeam bridge, constructed without
the use of temporary supports beneath the beams, the dead load of
the slab is carried by the beams acting independently, since the slab
concrete is incapable of any loaddistributing action when it is first
placed. Consequently, it seems reasonable to assume that each beam
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carries the dead load of one panel of the slab, just as in a right
bridge, since the skew can have little effect on a beam acting inde
pendently before the slab hardens.
If heavy diaphragms are used, or if temporary supports are placed
beneath the beams during construction, the angle of skew may have
some effect. However, it is on the safe side to compute the deadload
moments in the beams on the same basis as for a right bridge.
None of the tests reported in this bulletin yield any information
regarding the deadload moments in the slab, or the manner in which
they are affected by skew. However, since these moments are oply a
small proportion of the total moment, it is sufficiently accurate to
assume that they are unaffected by the angle of skew.
40. Conclusions.The results of the tests reported in this bulletin
indicate two principal effects of skew on the behavior of Ibeam
bridges. They are:
(1) The maximum moments in the beams are decreased slightly,
but only for the larger angles of skew.
(2) The controlling moments in the slab  the positive moments
at the center of a panel  are increased.
The decrease in maximum beam moments for large angles of skew
may be sufficiently large to be considered in the design of skew
Ibeam bridges. This can be done most conveniently by the use of a
reduction factor applied to the design moments recommended for the
beams of right bridges. There is no simple rational basis for the
evaluation of such a factor, and the test results do not permit a
precise evaluation by empirical means.
The increase in maximum slab moment is also sufficiently great to
require consideration in the formulation of design specifications. How
ever, the manner in which this is done will depend to a large extent
on the nature of the recommendations for right bridges. If, for
example, the design moments for right bridges are based exclusively
on the test results reported in Bulletin 363, they will be considerably
smaller than the theoretical moments obtained from Bulletin 336, and
provision will have to be made for the greater moments in a skew
bridge. On the other hand, if the moments for right bridges are
assigned more conservative values, it may be practicable to use them
without change for the design of skew bridges.