WE LDED TIE PIATES by Donald P. Erb - Lehigh University · Donald P. Erb FRITZ ENGINEERING...
Transcript of WE LDED TIE PIATES by Donald P. Erb - Lehigh University · Donald P. Erb FRITZ ENGINEERING...
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FAtIGUE STRENGTH OF rACKWE LDED TIE PIATES
by
Donald P. Erb
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FATIGUE STRENGTH OF
TACK WELDED TIE PLATES
by
Donald P. Erb
FRITZ ENGINEERINGLABORATORY LIBRARY
A THESIS
Presented to the Graduate Committee
of Lehigh University
in Candidacy for the Degree of
Master of Science
in
Civil Engineering
Lehigh University
September 1975
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This thesis is accepted and approved in partial fulfillment
of the requirements for the degree of Master of Science.
w.w. Fisher
Professor David A. VanHornChairman, Department of Civil Engineering
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ACKNOWLEDGMENTS
This investigation was part of PennDOT Research Project 72-3,
. High Cycle Fatigue of Welded Bridge Details. The testing progr~
was conducted at Fritz Engineering Laboratory, Lehigh University.
Dr. Lynn S. Beedle is the Director of Fritz Engineering Laboratory
and Dr. David A. VanHorn is the Chairman of the Civil Engineering
Department.
The specimens were fabricated in the machine shop of Fritz
Engineering Laboratory. Mr. Richard N. Sopko prepared the photo-
graphs. The manuscript was typed by Mrs. Ruth Grimes.
Thanks are also due Dr. John W. Fisher for his s~pervision
and suggestions during the preparations of this manuscript and
Mr. Nicholas Zettlemoyer for his assistance in the finite element
phase of the investigation.
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TABLE OF CONTENTS
AESTRACT
1. INTRODUCTION
2. DESCRIPTION OF TEST SPECIMEN
3. TESTING APPARATUS AND TECHNIQUES
3.1 Installation of Tie Plates
3.2 Comparison of Test Setup to Bridge
3.3 Testing Procedure
4. TEST RESULTS
4.1 Observed Stress Distribution in the Tie Plates
4.2 Results of Tie Plate Fatigue Tests
5. EVALUATION OF STRESS CONCENTRATION CONDITION ATTACK WELD TOE
6. FRACTURE MECHANICS ANALYSIS OF CRACK GROWTH INTHE, TIE PLATE
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5
7
7
7
8
11
11
11
13
15
7. SUMMARY AND CONCLUSIONS 21
TABLE 23
FIGURES 24
REFERENCES 42
APPENDIX A: CRACK DOCUMENTATION 45
APPENDIX B: FATIGUE CRACKING OF THE UNWELDED TIE PLATE 70
VITA 78
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Table
1
Figure
la
Ib
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
LIST OF TABLE AND FIGURES;
Summary of Tie Plate Data
Cross-Section of Le~igh Canal Bridge
Tie Plate Detail at Floor Beam Bracket Connection
Typical Lehigh Canal Bridge Tie Plate
Test Specimen
Tie Plate Test Setup
Strain Gages on TPC-la and TPC-lb
Strain Measurements of First Stress Distribution Test
Strain Measurements on TPC-3
Strain Measurements on TPC-5
Summary of Test Results
Schematic of Finite Element Model
Corner Crack in Tie Plate TPC-2b
Schematic of First Analytical Model'sThree Stage Integration
Comparison of First Analytical Model toTest Results - K = 2.80
Comparison of First Analytical Model toTest Results - K = 2.52
Comparison of First Analytical Model toTest Results - K = 3.08
Comparison of Second Analytical Model toTest Results - K = 2.80
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24
24
25
26
27
28
29
30
31
33
34
35
36
37
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Figure
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18
Comparison of Second~Anal·yticalModel toTest Results - K = 2.52
Comparison of Second Analytical Model toTest Results - K = 3.08
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ABSTRACT
Fatigue cracks have been discovered in tie plates on several
bridges. These plates connect the outrigger bracket to the longitudi-
nal girder and floor beam. On the Lehigh Canal Bridge the cracks were
observed to grow from the ends of tack welds placed on the tie plate
edges adjacent to the cantilever bracket. Since fatigue test data for
this type of geometrical configuration was not available, a series of
tie plates were tested to acquire the needed data. From this data it
was found that AASHTO Category D provides a reaonable estimate of the
lower bound fatigue strength of this detail.
In conjunction with the physical testing, an analytical
study of crack growth in the tie plates was undertaken to confirm the
~ experimental results. A finite- element analysis was used to calculate
the stress concentration factor at the end of the weld. Two different
stress concentration decay functions were used in the fracture mechan-
ics analysis of crack growth and estimation of detail life under
cyclic loading. Both functions gave reasonable estimates of the
detail's lower bound fatigue strength.
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1. INTRODUCTION
Tie plates on several bridges, including the Lehigh Canal
Bridge, have developed fatigue cracks In the Lehigh Canal Bridge
these cracks have grown from the end of tack welds (approximately
2 in. long) placed between the tie plate and the top flange of the
outrigger bracket during construction of the bridge. The tack weld,
in addition to providing the initial flaw from which the crack propa-
gation, introduces a concentration of stress at the flaw location,
thereby accelerating crack growth.
A complex interaction of several bridge members produces the
cyclic stresses which drives the crack. The concrete slab, curb and
parapet provide a relatively stiff in-plane system supported by the
stringers (see Fig. 1). The stringers rest on the floor'beams and
outrigger bracket, with the outside stringer attached 6-1/4 in. from
the end of the bracket. The outrigger bracket is attached to the
longitudinal girder by the tie plate and a simple web angle connec-
tion, which offers little lateral restraint. The ti"e plates are con-
tinuous over the longitudinal girder, being connected to the floor
beam, longitudinal girder and outrigger bracket with' 7/8 in. rivets.
This provides a relatively rigid connection at the girder.
As vehicles pass over the bridge, bending stresses develop
in the longitudinal girders. Compressive stresses in the top flange
of the girder in positive moment regions cause the top flange to
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shorten when the vehicle is in the span. Smaller tensile stresses
occur in the top flange when the vehicle is in the adjacent span.
Since the bracket is attached by the outside stringer, to the rela-
tively stiff deck slab, the cross-sectional rotation of the longitudi-
nal girder at each floor beam - outrigger bracket during passage of
vehicles over the bridge causes a relative displacement to develop
between the top flange of the girder and the end of the outrigger
bracket. This relative displacement produces in-plane bending mO?1ent
stresses in the tie plate and top flange of the bracket thereby devel-
oping the cyclic stresses which result in fatigue crack growth.
Since the longitudinal girder 'is continuous over three
spans, the girder is subjected to both positive and negative bending
moments. Hence the tie plates experience various degrees of stress
reversals as the top flange of the girder shortens or lengthens de-
pending on the vehicle location along the bridge and the position of
the tie plate1 •
Because of the cracked tie plates on the Lehigh Canal
Bridge, it was desirable to have a laboratory definit~on of the
fatigue strength of the tie plate. Fatigue test data were not avail-
able for the geometrical configuration that existed. To assist in de-
fining the applicable stress range - cycle life"relationship, a series
of twenty tie plates were tested at various. stress ranges on the
dynamic test bed of Fritz Engineering Laboratory.
A second objective of this study was to confirm the experi-
mental results with an analytical study of crack growth in the tie
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plates. Since the origin of the fatigue crack was at the end of the
tack weld, it was necessary to determine the stress concentration
factor in order to calculate the stress intens"ity factor range experi-
enced by the crack2 ,s. A finite element solution was used to estimate
the stress concentration factor at the tack weld toe. Then the
principles of fracture mechanics were used to analyze the growth of
the crack.
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2. DESCRIPTION OF TEST SPECIMEN
It was desirable to have the experimental tie plates dupli-
cate the tie plates installed on the Lehigh Canal Bridge as much as
possible. Two sizes of the plates are used on the bridge. Only six-
teen 12 in. wide plates (12" x 3' -8" x 1/2") were used over the
interior piers of the bridge. Two hundred 10 in. wide plates are
used at other floor beam locations. Hence, the tie plate tested in
the laboratory was modeled after the narrower plate, which is shown in
Fig. 2.
Figure 3 shows the dimensions of the test specimens. By
comparing with Fig. 2, it can be seen that the 10 in. width and 0.5 in.
thickness of the test specimen was the same as the narrower bridge tie
plate. Since the fatigue cracks grew from construction tack welds on
the outrigger bracket side of the tie plate, it was .not necessary to
include the floor beam portion of the tie plate in the test specimen.
Hence the test specimen was shortened from 3ft.-8 in. to 2 ft.-O in.
The hole pattern used for the tie plate - outrigger bracket
connection was maintained. But; the hole pattern corresponding to the
longitudinal girder - tie plate connection had to be altered to match. .
the dynamic test bed's W12 x 85 column holes, ,to which the specimens
were to be bolted. Fritz Engineering Laboratory did not have the
equipment to drive 7/8 in. rivets, therefore bolts had to be used.
One inch bolts were used as they were readily available'and the
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increased hole diameter did not appreciably alter the net area of the
tie plate. The necessary 1-1/16 in. holes for the bolts were drilled
instead of being punched as the 15/16 in. holes of the tie plates
were. This change was not considered significant for two reasons.
First, the fat~gue cracks did not grow through the holes. Second, the
end of the tack weld, where the fatigue crack originates, is just out-
side of the bolted connection between the tie plate and loading beam.
Because of the availability of plate material, plates were
taken from the laboratory's stock. A total of thirteen specimens,./'~
~-marked as TPG-x were made out of mild steel. Six of these were cut
from 1/2 in. plate that ha~ been removed from a highway bridge.
Another ten specimens were cut from 1/2 in. A514 steel plate. These
are marked as TPC-x.
One other detail of the specimen fabrication should be men-
tioned. All edges were saw cut to ensure that there would be compar-
able discontinuities along the specimen's edges after the tack welds
were placed.
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3 • TESTING APPARATUS AND TECHNIQUES
3.1 Installation of Tie Plates
Figure 4 shows the test setup used for the tie plate experi-
ments. One end of the tie plate was bolted to the W12 x 85 column,
while the other end was bolted to the W12 x 120 beam flange. The beam
was loaded by a 22 kip Amsler hydraulic jack connected to an Amsler
pulsator.
The tie plates were installed using the following procedure:
the bolted connections were pl~ced in bearing and the bolts were then
torqued to develop between 20 - 25 kips preload, i.e. between 1/3· -
1/2 of specified preload. This was to simulate. the clamping force in
.the rivets. Then the construction tack weld was placed.
The 3/16 in. construction tack welds were placed on both
sides of the tie plate and varied in length and location. A field
inspection of these welds indicated that they started about 1/2 in.
from the end of the outrigger bracket top flange and had an average
length of 2 in. Therefore, the laboratory tack weld was standardized
in the test as a 3/16 in. weld starting 1/2 in. in from the end of
the beam and extending 2 in. as shown in Fig. 4. This weld was placed
on both sides of the tie plate as observed on the bridge structure.
3.2 Comparison of Test Setup to Bridge
Figures Ib and 4 provide a comparison between the test setup
and the Lehigh Canal Bridge. The W12 x 85 column simulated one of the
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bridge's longitudinal girders, while the flange of the W12 x 120 beam
simulated the top flange of the outrigger bracket. In addition the
1/2 in. gap that existed between the longitudinal girder flange and
t~e outrigger bracket top flange was duplicated as a 1/2 in gap be-
tween the column flange and the beam flange in the test setup.
On the bridge a stringer is attached to the end of the .out-
rigger bracket at a distance of 2 ft.-6 in. from the edge of the
longitudinal girder's top flange. Corresponding to the stringer,. at
2 ft.-6 in. from the column flange of the test setup, a jack intro-
duced a cyclic displacement of the end of the beam. This provided.
the same moment gradient in the tie plate as existed in the bridge
due to the relative displacement of the .longitudinal girder's top
flange and the end of the outrigger bracket.
3.3 Testing Procedures
The stress in the tie plates was controlled by electrical
strain gages attached to the plates. For the first set of the plates
tested, TPC-la and TPC-lb, the strain gages were placed on the face of
the tie plates as shown in Fig. 5. There proximity to the bolted con-
nection resulted in jack loads which were twice as large as was pre-
dicted from bending theory~ As a result, an additional gage was
attached to the tie plate edge 1 in. from the tack weld, in line with
the column flange edge on all other plates. The predicted strain at
the edge gage based on the applied jack load was in agreement with the
measured strain. Hence, in all subsequent tests the stresses at the
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tack welds were controlled by strain gages attached to the tie plate
edge, 1 in. from the end of the tack weld.
Because of the inconsistencies with bending theory found
above, extra strain gages were placed on several tie plates to investi-
gate the stress distribution. The results are reported in Chapter 4.
The stress range at the tack weld for the first set of tie plates was
estimated from these measurements.
Initially the tie plates were tested in pairs, one bolted
to each flange of the loading beam. Those tie plates marked with sub-
script "a" were bolted to the east side and those with subscript lib"
were bolted to the west side. A problem with torsion was encountered
and this twisting was minimized by adjusting the hydraulic jack's posi-
tion under the beam until the deviation of stresses between the two
tie plates was a minimum. For the third tie plate set, TPA-3a and
TPA-3b, the W12 x 120 loading beam was split down the web to minimize
the unequal distribution of force to each plate.
When one of the tie plates in the set developed a 1-1/2 in.
or greater length crack, a steel strap was bolted over the plate so
that the second plate test could be continued. But the crack continued
to grow under the steel strap. As the crack grew in one of the tie
plates, ~edistribution of load was observed to occur between the two
plates. Therefore after TPA-3a and TPA-3b tie plates were tested the
procedure was changed and the remaining tie plates were tested one at
a time. The test tie plate was attached to the west side of the
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set~p. The east side tie plate was only bolted to the column and beam
and no tack welds were placed. In addition a strain gage was placed
on the bottom edge of the unwelded tie plate to monitor the load dis-
tribution between the two tie plates~ All tie plates with specimen
numbers lacking subscripts "a" or "btl were tested individually.
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4. TEST RESULTS
4.1 Observed Stress Distribution in the Tie Plates
Because of the discrepancy between the measured strain and
predicted jack load on the first test setup, several tie plates were
extensively gaged to determine the stress distribution in the tie
plate at the critical cross-section. Figure 6 shows the location of
the strain gages used in the first study. Also shown is the predicted
and measured strain distribution for a, nominal plate bending stress of
10 ksi at the end of the tack weld. Tests were also run on TPC-3 and
TPC-5. On TPC-5 the column bolts were only hand tightened. Figures 7
and 8 show the location of the strain gages and compares the measured
and predicted strains for a stress of 10 ksi. All of the tests
showed that the strains on the face of the tie plate were smaller
than expected based on bending theory. Apparently ~he bolted connec-
tion between the tie plate and loading beam flange interacted because
of the shear forces developed on the plate-beam flange faying surface.
H~nce there was a decrease in the estimated bending stress away from
the plate edge.
4.2 Results of Tie Plate Fatigue'Tests
~7enty tie plates 'were tested at stress ranges which varied
between 7.3 and 30 ksi. Shown schematically in Appendix A are the
fatigue cracks that formed in the tie plates. Because of the high
residual stresses at the tack weld, a number of tIle tie plates
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developed fatigue cracks at the tack weld on the tie plate's compres-
sian edge. These are -marked with a subscript nett after the tie
plate's number. Ot;1ly in one case, TPA-!ac, did this crack grow
through the tie plate ~hickness. Even in 'this case the tie plateI
failed on the tension side. A tie plate was considered to have failed
when the crack reached a length of 1-1/2 in. Table 3 sunnnarized the
results for each tie plate. Those cracks which developed on the
compression edge are also included in Table 1 since they would have
grown much larger when subjected to the stress reversals experienced
by the tie plates in the bridge.
The results of the tie plate tests are also summarized in
Fi.gure 9. This figure shows the stress range as a function of cycle
life. The test data are compared with the AASHTO Category n4 which
provides a ~ reasonabI.e, estimate of; th~ lower bound. fatigue. strel1gth of
this detail.
In addition to the fatigue failures which originated at the
tack weld, the unwelded plate used on the east side of the test setup
for the individual testing of the tie plates developed an 8-1/8 in.
fatigue crack. This fatigue failure is discussed in Appendix B.
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5. EVALUATION OF STRESS CONCENTRATION CONDITION
AT TACK WELD TOE
In order to evaluate crack growth in the tie plate, the
stress concentration at the tack weld termination was needed2 ,s. A
finite element analysis of the plate using the three dimensional solid
element (eight node brick) of the SAP IV s finite element program was
performed to estimate the stress concentration factor. The model-used
for the analysis consisted of the tie plate and bracket flange in the
immediate vicinity of the bolted connection between these two members
as shown schematically in ,Fig. 10.
The bracket flange and tie plate are connected by two 2 in.
long tack welds and eight bolts. In the finite element model the tack
weld was represented by a 2 in. long triangular wedge attached to the
edge of the tie plate and the face of the flange. The adjacent faces
of the tie plate and flange were unattached except at the bolt loca-
tions. Here the two faces shared four nodes, one at each corner of a
one inch square centered on the bolt hole center line. Though this
is not the same as the bolted joi~t, it does provide a relatively
stiff joint as do the bolts, torqued to one-half of the required tor-
qued, under the low shear stresses experienced by the tie plate. In
addition the bolts are far enough away from the point of interest, the
tack weld termination, that any errors introduced by the modeling of
the bo·1 ts will not significantly effect the results of the finite
element analysis.
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Appropriate forces from the bending moment and shear were
applied to the right-hand end of the bracket flange and the left-hand
end of the tie plate. The resulting stresses in the region where the
stress distribution was investigated agreed with bending theory and
th~refore not with the measured stresses. This could be expected since
the bolt clamping force was not modeled and therefore the faying sur-
face interaction was not included, except at the common node points.
Using the nodal displacements from this analysis as boundary
conditions; a second much finer mesh analysis of the region in the
immediate vicinity of the tack weld termination was performed. The
element stresses at the base of the tack weld termination obtained
from the analysis were then utilized in a least square fit using a
complete second order polynominal to approximate the stress concentra-
tion at the weld termination.
The above analysis was performed for the extreme case of the
tack weld having a vertical termination and also for the case of the
tack weld·termination having a slope of 1 to 3.75, which was typical
for the tie plate specimens. For the vertical tack weld termination
the stress concentration factor was estimated to be 2.82, whereas the
sloping tack weld termination provided a value of 2.80. As can be
seen the slope has little effect on the stress concentration, there-
fore in all calculations involving the stress concentration factor a
value of 2.80 was used.
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6. FRACTURE MECHANICS ANALYSIS OF CRACK GROWTH
IN THE TIE PLATES
An analytical study of the c~ack growth in tie plates was
undertaken to assist in evauating the experimental results. The dif-
ferential equation of crack growth proposed by Paris I1 was used for
this analysis. This -equation states
da ndN = C (11K) (1)
where ~~ is the rate of crack propagation, 6K is the stress intensity
range, and C and n are material constants. C and n were assumed to be
constant over the full range of 11K and were taken to be 2 x 10-1 0 and
3 respectively. These are rounded values of those found by Hirt and
Fisher12 and used in Ref. 3 to evaluate crack growth at stiffener and
attachment details. The stress intensity range is dependent on a
number of variables and therefore must be evaluated for each configu-
ration encountered.
The number of cycles to failure (N) can be obtained by
integrating Eq. 1 from the initial crack size (a.) to the final crack~
size (af). The result of this integration is:··
aN = .! f f
C a.1.
1---da(.6K)n
(2)
In order to perform the integration an estimate of the ini-
tial' crack size is needed. Th~ range of initial weld flaw sizes at
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the toe of fillet welds was reported to vary from a low of 0.00075 in•
. to a maximum of 0.02 in."with an average of 0.003 .in. S ,9. Reasonable
agreement with these observations was provided in subsequent studies
at Lehigh University2,lO. Flaws from tack welds would in all proba-
bility have larger sizes. Therefore the initial crack size used in
the analysis was varied from 0.001 to ·0.003 in. A crack length of
1.5 in. was used to define failure of the tie plate.
For each initial crack size used in the integration of
Eq. 2, a threshold stress range was also calculated. The threshold
stress intensity range of 3.3 ksi lin. found by Klingerman1l along
with the assumed initial crack size was substituted into the stress
intensity function to obtain the threshold stress range.
Two models were used to estimate ~ in the analytical inves-
t.igation of the tie plate crack propagation. Each involved the use of
a dec~y function for the stress concentration at the tack weld
termination.
In both models it was assumed that the initial crack was a
corner crack, since the tie plate cracks were observed to start as
corner cracks fram visual inspection of the crack surface. This cor-
~er crack can be seen in the phtograph of the p'late TPC-2b '8 crack
surface shown in Fig. 11.
The first model consisted of a three stage integration of
Eq. 2 shown schematically in Fig. 12. For the first stage the stress
intensity factor (K) was defined as
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(3)
where (J is the stress, a is the crack size and K.r ( ~) is the stressconcentration decay function 3 • The decay function was taken as
(4)
where KT is the stress concentration factor and w is the weld sizeS.
Since this decay function was derived for a different detail, w had to
be modified. The stress concentration effect was taken into account
until a crack length of 0.26 in. was obtained. This corresponded to
12 times the weld size at the end of the weld toe as shown in Fig. 12
Equation 2 was integrated from the initial crack sizes of 0.001, 0.003,
0.02, and 0.03 in. to the final crack size of 0.26 in. considering the
stress concentration factor to be 2.80 as derived from the finite
element analysis.
For the second crack growth stage, Eq. 2 was integrated
from 0.26 in. to the plate thickness (t) of D.5-in. The stress inten-
sity function used the secant correction for a free surface and there-
fore was defined as 3
c- ~aK = cr vTIa {sec 2t (5)
The shaded reg ion shovm in Fig. 12 was not included in th e
analysis, as the number of cycles required to propagate the crack
though this region was small.
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During the first two stages of growth, the crack was not
appreciably affected by the moment gradient in the tie plate. But in
the third stage, the crack was growing in a region of moment gradient
and therefore the following stress intensity factor~2 was used:
K = /2W tan1fa
TIa
2w x0.923 + 0.199 (1 - sin ~ )
1facos 2w
(6)
where W is the plate width. Equation 2 was then integrated from a
crack size of 0.5 in. to 1.5 in.
In addition to varying the initial crack size, the stress
concentration factor of 2.80 was varied by ±lO%, i.e. 2.52 to 3.08.
This was done to evaluate the effect of a deviation of the stress con-
centration factor from the value derived from the finite element
analysis.
The results of the first analytical model used in the analy-
sis of crack propagation in the tie plate are shown in Fig. 13 for the
three initial cr,ack sizes, 0.001, 0.003, 0.02 and 0.03 in., and a stress
concentration factor of 2.80. Also shown are the threshold stress
range for each initial crack. Design Category D and the test data are
plotted in Fig. 13 for comparison. It can be seen that the lower life
estimate for this model is just above Category D, with all but three
of the test data points between the outer two prediction lines. Two
of these points fall just below the lower life estimate and suggest
a slightly larger initial crack size than'assumed. The third point,
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at 30 ksi, is tie plate TPC-lb. The stress range was estimated for
this tie plate. In addition the crack was only 3/4 in. long when the
test was stopped. Integrating the third stage of growth from 3/4 in.
to 1-1/2 in. at a 30 ksi stress range, adds 20,000 cycles to its life
and provides better agreement with the lower bound life estimate. By
comparing Fig. 13 with Figs. 14 and 15, the results of using stress
concentration factors of 2.52 and 3.08 respectively in the first ana-
lytical model, it can be seen that variations in the stress concentra-
tion factor has little effect on the predicted life. The first ana-
lytical m0del provides a threshold stress range of 4 ksi based on an
initial crack size of 0.03 in. and stress concentration of 3.08 and a
reasonable lower bound estimate of the tie plate's fatigue life.
In the second analytical model, stages I and II were com-·
bined. For this combined stage the stress intensity factor was
expressed as
'ITa - -
2t
where
rs: [1- 3.215 ~+ 7.897(~)2 - 9.288(~)3 + 4.086(~)"J(8)
is the decay function with a ~ t, the plate thickness 3 • With this
formulation of the stress intensity, Eq. 2 was integrated from the
initial crack sizes of 0.001, 0.003 and 0.03 in. to a crack size of
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0.5 in. The second stage of crack growth was identical to the third
stage of growth used for the first model.
The results of using model II are summarized in Figs. 16,
17 and 18 along with Category D and th~ test data. Figure 16 is for
the stress concentration factor equal to 2.80. As can be seen in
this figure the lower bound estimate of the stress range-cycle life
relationship is closer to Category D than the first model and all
test data falls between the lower and upper bound estimates of life.
Figures 17 and 18 are the results obtained using a stress concentra-
tion of 2.52 and 3.08 respectively. Changing the stress concentra-
tion factor had little effect on the predicted life. About the same
crack growth threshold stress range (4 ksi) was predicted for an
initial crack size of 0.03 in. and stress concentration factor of 3.08.
Figures 13 through 18 demonstrate that Category Dis a rea-
sonable lower bound life estimate for the tie plate with tack welds.
Only an extreme condition would cause the crack growth threshold to
fall below the fatigue limit for Category D. It also can be seen
that all the test data fall above Category D.
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7. SUMMARY AND CONCLUSIONS
The following summary and conclusions are from the labora-
tory tie plate tests and the analytical studies of the tie plates.
1. The stresses on the face of the tie plate at the critical
section were smaller than expected based on bending theory.
The stresses on the plate edge did conform to bending theory.
Apparently the bolted connection between the tie plate and
loading beam interacted because of shear forces developed on
the plate-beam flange faying surface. Hence there was a de-
crease i~ the estimated bending stresses away from the tie
plate edge. This decrease had no influence on crack growth
from the tack weld on the tie plate edge.
2. The fatigue cracks originated at the toe of the tack weld
termination, at the corner where the tie plate edge and face
meet. From here the crack grew through the thickness and up
the face of the tie plate.
3. A finite element analysis of the stress concentrations at the
tack weld termination revealed that the stress concentration
was not sensitive to variations in the slope of the weld
termination. A stress concentrat~on factor equal to 2.80 was
found for the typical slope on the test specimens.
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4. Two different analytical models, using different decay.func-
tions for the stress concentration, were used in the fracture
mechanics analysis of crack growth in the tie plates. Even
with a ±10% variation of the stress concentration factor both
models provided a reasonable lower bound estimate of the tie
plate fatigue life; with failure defined as a 1-1/2 in. or
longer fatigue crack.
5. With failure of a tie plate defined as a fatigue crack of
1-1/2 in. or more, Category D of the AASHTO specifications
provides a reasonable lower bound for the fatigue life data
obtained from the twenty tie plates tested and is in agree-
ment with the lower 'bounds found from the two analytical
models use. Therefore Category D can be used to define the
fatigue strength of these tie plates.
-22-
-
TABLE 1 SUMMARY OF TIE PLATE DATA
Tie PlateS Ranage S Minimum N Failure
(ksi) (ksi)
TPA-la 13.8 2.0 1,281,800-lac 18.2 -2.3 1,281,800-lb 15.6 2.1 1,018,500
TPA-2a 12.3 2.0 3,363,200-2b 11.8 2.0 3,363,200
TPA-3a . ~7 ~·8 .' 1.9 7,466,700-3b 8.2 2.3 26,354,200*
TPA-4 20.0 2'.0 452,000-4c 21.4 2.0 481,500
TPA-5 20.0 2.0 552,000-5c 20.2 2.4 600,000
TPA-6 10.0 2.0 3,366,400-6c 9.9 2.0 3,670,500
TPA-7 10.0 2.0 4.947,000
TPC-la 30.0 3.8 71,800**-lb 30.0 3.8 71,800
TPC-2a ( 13 .. 4 1.6 1,046,600-2b 12.3 1.5 15,936,700
TPC-3 8.0 2.0 20,522,400*-3c 7.3 1.9 12,619,700
TPC-5 16.0 2.0 3,314,600-5c 11.7 1.9 2,283,700
TPC-6 16.0 2.0 628,500-6c 16.8 2.3 628,500
TPC-7 24.0 2.0 211,000
TPC-8 24.0 2.0 252,000
* No detectable crack** Test stopped before failure, see crack documentation
.-23-
-
81_0~12
IO'-3J.!'8
(At Hunch)
41-0" 12'-0"
ct Rdwy~
12'- 0" 1r21- 011Tie ff..
3'-91.114
5'-911
Fig. la Cross-Section at Lehigh Canal Bridge
. III642'- 6"
LongitudinalGirder
Flange ofBracket
3'-311....------....~2'-3"FloorBeam
SECTION A-A
: Fig. lb Tie Plate Detail at Floor Beam Bracket
-24-
-
FLOOR BEAM,CON NE,C'TION
~~
LONGJTUDJNALG tRDER
COf\JNE'CTION
r-~
BRAe Kt.T\CONNECTION
I
NOTES .l, ALL 1-l0LEs 'o/jt' ¢2. PLATE !/Zll THIC K
Fig. 2 Typical Lehigh Canal Bridge Tie Plate
-25-
-
2' - 0 II
1I%," 5 ~6' 3" 3/1 3/1If6// IYz
2/1 2 k,'13/1 . 2~/I
fOI' - ED -I,311 .-J 2. xt2JJ l~/J
NoTESJ; ALL 'HOl'ES ) 1611 ¢2~ALL EDGES SAW cur3,~ PLATE YZ'I TH/
-
%'1 FILL ER ·Ft
3 I{~b TACK WELD
, TACK \AlE LD DETAIL
W12xl20
TJEPLATE
22. Kt P, AM SLER~-JYDRAULJC JACr\
Fig. 4 Tie Plate Test Setup
-27-
-
1m - STRAIN GAGE
Fig. 5 Strain Gages on TPC-la and TPC-lb
-28-
-
ooo
1-/70I'
/I
/I
+5 II
. I
. ~ ~
4- "2./I
//
I
I
f.204.. CD rT\J -\.0
MEASURED
1-- -325
-I8b
+32S'G)-CD
COM PUTE.D
o 00'
000
.- STRAIN GAGE.
,-30
I
I
,I,I
It
·52@-CY
ST RA I l\f CjJ. - ,'NI JN )
... 3 17 ------I
-
... - STRAIN GAGE
o 0
o 0
· 'l..,1JIf-~ ~"I
'1~1 7 !~-+---------IJJJ~l""---8,).. S-f"·-9
o I t8-04"04---. fO .
ooo
GAGE 'LOCATIONS
7 -3rOb 1/-2045 ,-152-
I/
I4 1_ 8
B -)879 1':'/86
'/III
10 -12.
II
+144 / :a+21.6 / 2-
+-345./ Q)-'(D
M EA-S UR E- D
II
II
+'51 I II:#-J90 / 12
@-CVSTR AJ N ().J. - IN/IN)
7 r__-_ -345" -3105 ... 276
89
-30B-274
.. 276 3+ 3/0 Z.
~345 -·-(i)--'0
COMPUTED
+ 274 II+308 J2-
@-G>STRAIN (J't-IN/'N)
Fig. 7 Strain Measurements on TPC-3
-30-
-
o 0
o 0
.. - STRAIN GAGE
LOCATJONS
~/~ep2.~'1
~~2." 7 jr---"'1'--------_1/ 6 " 8
~ ---5-=1=-=:=9o ! III-CB-O
4 11
04-- 11-/0 .4'1 Io -C±)-O
'1;/~1-- .:=-~~
ooo
7 ./ - 2476 ,"=-/'2.55 / -85
III
+/0IIII
"'25 I 3~/6S. .... I 2-
1345 CD--cD IMEASURED
, -. J 001- 78IJIIII-6
III
I""30'
-+173 I
®-@STRAIN (}A-IN/IN)
.., _----..t-3 4 S6 -3105 -276
a9
+216 3"'3'0 2
~ 345 "--Q)-,-_CD--I 1
CO'MPUTED
+2.74 II+ 306 J~
®-@5T RA1J'\j ( ;..t - tNil N )
Fig. 8 Strain Measurements on TPC-5
-31-
-
IWNJ
30~"I
25"
20
15STRESSRANGE. .
(KSI)
fO9.
87
6
5
o 0
CAT E. GORY '-D
oocP
8o
oo 0
o
·0
8c:o 0
oo
o
~o---
4'
3[ I I I I 'I I I I I i I I 'I I I I I I I I I I I I·6 105 10 6 107 5
CYGLE..S TO FA1LlJRE
Fig. 9 Summary of Test Results
-
16//
r 1I " i_':~
8ol~1 _....:.-.l__, ---!- _I r..... ,
,I ' .....,JJ-~~tlSHAl
-
Fig. 11 'Corner C~ack in Tie Plate TPC-2b
-34-
-
STAGE ill
I }'z.1I
Y/'
1
1/
~b STAGE IIf
Fig. 12 Schmnatic of First Analytical Model'sThree Stage Integration
-35~
-
5
OJ- 0-..o
'""'"" II.........., A" =0.02-'~ 5"'" "'"5.2. ks,_~"'" - L_ _ II
'""'"" n· =O.03~''-''\..,J... __Sr::: 4,.5 ksJ
o
'0 6
CYCLES TO FAILURE
................... " .................., ...........,~ ...........
"~, ..... , ""'"" ",..... ',"","" a; ::: 0.00 1 .-~Q. ">-... --- ------------S:-:-211 ks,"'-,,- 'v...... - ". .".......... O~....... ,-.{").........., ~.
"'-....'" 0~ ""~ "'"''0~ ,
~O'''" 0,
~ ...................., ..,"............. ........ 0"" 'n- = 0 OO~0' .......... . , ~ .. _ ..
CATEGORY D '~, "'-""":"--G---- - --'. -e-S
-:;- ~2_3 kSI"'-...."""- 0 0 ....
''-'""~~~Oo' 0~
~~
"'~ 0~
IDS
20
30
25
15STRESSRAtvGE(k~~J)
1098
I 7w0'\I
6
5
4
3 -6
Fig. 13 Comparison of First Analytical Model to Test Results - K = 2.80
-
51- =4.Cf ks I
~ ct;.,;' ~ 0,1 02. '1~~~ =s.aksl __
" ct..z :: 0.0311
-----...
~o---
o
'D-
~~ " ""'= ,~* " "-~ ~ """ . ct.;: ':. a.oot ll~ '" '-_._--------------------------....~ ~~ SI'" ": 23.5 kSI~&~ .
'--::::~" . 0~~ "~,~~" 0~~"'_. ~-t. =o.oo~
~ .8 0 51-" ::. 13.7 kSI~" \"~. -0
~~~~o
'.~,""
CATEGORY
20
30~,
25
J5
STRESSRAj\lG E(ks, )
10
98
J 7VJ""'-JJ
6
5
4
5":J '-----I • , , " I , , I I , I ,!" I , I I ' " I ,
6 lOS J0 6
eye L ES TO FA J L U R E'\..
Fig. 14 Comparison of First Analytical Model to Test Results - K = 2.52
-
0-. 04'-
oCATEGORY
"~
~ 'I'~, a..: 0.02-~, A =4-.8 k,s/·~~.SY__~
. "'""'- .........._~
5 -::.4~1 ks,r I)0..1 ~ 0,03
" .........,~~ " """ ......... """~ , , u~~, ...... a.' =0,001~ ...... ~ -~~u, '-..... _~~ .......... , ~ --------------- 51" -::=f9.. 2ksl~ t::'l . _"~~ ---
,,~ ''''-. 0
'~Q"""""'" 0~", "'~-Q.~ II
~_u, 0 Q. =0.003V"'~" 8 A --.....~ ' .........a - - -- -- -- --5 _ t J 2. kSf~ ~----- r- ~~
'~~O 0-- ~~
'''~ 0"",....
• I I I I I : LJ I r I II " I L, I III I I I I·10 6 f0 7 5
eye LES OF -FAl LURE
30~,
25
20
IIS L
STRESSRANGE(1~51)
JO9
8I
W 700!
6
5
4
3 ..6
Fig. 15 Comparison of First Analytical Model to Test .Results - K = 3.08
-
a-.....~
o
"-~ .. ~ 0.02'~~ CL,Ai 3 kSI'""'~ . S ... =5. __..__ ~ +~'~ _.- 3
'1""~. a.... ::: O.~ __' '---
o
5
25
20
~"- ~ "-30 J---=~~~ ................"- "-
~. ~~ ........ ............ 1/
0:", ........ '- 0.. ... =0.001~~ O~ ~ ~"--~~'-.J r..::;~ ............ 212l
..
~~:--..... ,. '0..--- - - -- - - Sr:: , "51~~ "0 cfJ~"" 0~", "'-
~~ 0"-..~---o "-0
~~ ......... II~ b- Q,c : 0.003. ~ "- -----......CATEGORY 0 -I R, '---G---------C-s
-1-2-3ksl~'-...::::--.. 0 0 ... _ .~~
~0-...~~ Go 0~~~
~" 0~~.........
15
STRESSRAt~GE
(k5\)
1098
7
6
1w\0I
4St"'=- 4~6 kSI
510 7')0 6
CYCLES TO FAILURE
}053. , ! , , '.! I I , I! ! "" I , "! I I , ,
6
Fig. 16 Comparison of Second Analytical Model to Test Results - K = 2.80
-
5J0 7
~ a...: =0,02#~__5 I- = 5_~ ks.!..-.-
~' Q...A, ==. 0,03 11'------~
Sr::' 5#1 kSl
J0 6
CYCLES TO FAJLURE
10 5
~~ "'-- ~~~ "'--""- ""- .
~~~""-~ ,, . ~ "a.;. = O. 001~........ ~",,- ~'-O - Sr =23.5 kSI
~OC3P .~ "-.. ""- 0~ a- 0 .~ "--." . - a.-t. =0.003/1
CATEGORY D ---I ~....._-------- ---- -- S).-:: 13,,7 kS'-+-~~o 8 0~~~Oo -0
~~ ~~~~ 0--
~~ 0
20
30
25
15
STRESSRANGE(ks~ )
1098
I 7.:::--0I
6
5
4
36
Fig. 17 Comparison of Second Analytical Model to Test Results - K = 2.52
-
'SI"": 4 ... 2 kSl
0+- Q-t--
CATEGORY 0
.......... ..........
" "-~ ............ ""-~ " "-, .................................
.........~. ~O"~ ............ " ., 0 H~.~ "-,,---Ci-~ Q;'::'o.o~~
""'~ ",,- 0 . sr : 19.'2. kSJ~ ~~ 0 0
~ " 0~~ "--- . 8~~ ........... 0 . 0 {LA. =0.003/1~ '---.------. -.-------------~~ 5 r:' \ L2. KS I. 00 0~
~~
~ 0 0~~~~ , , -a...~ = O.02.,J
~........... 5)-:: 4-... 8~,----.....-"""- ....... a...... = 0.03"-----..,...
20
4 ~-
5~-
6
"
25
15
STRESSRAI'J GE
(ksJ)JO9
. 8J
+' 7rr
3! ! , I I " I , , , , I I I" I , , I I' " I IG 105 10 6 fO' 5
CYCLES TO FAILURE.
Fig. 18 Comparison of Second Analytical Model to Test Results - K = 3.08
-
REFERENCES
1. Fisher, J. W., Yen, B. T. and Marchica, N. V.'FATIGUE DA:MAGE IN THE LEHIGH CANAL BRIDGE, Fritz EngineeringLaboratory Report No. 386.1, .Lehigh University,November 1974.
2. Fisher, J. W., Albrecht, P. A., Yen, B. T., Klingerman, D. J.and McNamee, B. M.
FATIGUE STRENGTH OF STEEL BEAMS WITH WELDED STIFFENERS ANDATTACHMENTS, NCHRP Report No. 147, Transportation ResearchBoard, National Research Council, Washington, D.C., 1974.
3. Albrecht, P. and Fisher, J. W.AN ENGINEERING ANALYSIS OF CRACK GROWTH AT TRANSVERSESTIFFENERS, International Association for Bridge andStructural Engineering, Zurich, Switzerland, 1975
4. Amer-ican Association of State Higllway Transportation OfficialsI~TER_IM SPECIFICATIONS BRIDGES, 1974.
5. Bathe, K., Wilson, E. L. and Peterson, F. E.SAPIV: A STRUCTURAL ANALYSIS PROGRAM FOR STATIC AND DYNAMICRESPONSE OF LINEAR SYSTEMS, University of California atBerkeley, April 1974.
6. Paris, P. D., Gomez, M. P., and Anderson, W. E.. A RA-TIONAL ANALYTICAL THEORY OF FATIGUE, The Trend inEngineering, University of Washington, Vol. 13, No.1,January 1961.
7. Hirt, M. A. and Fisher, J. W.FATIGUE CRACK GROWTH IN WELDED BEAMS, Engineering FractureMechanics, Vol. 5, pp. 415-429, 1973.
8. Signes, E. G., Baker, R. G., Harrison, J. D. and Burdekin, F. M.FACTORS AFFECTING THE FATIGUE STRENGTH OF WELDED RIGlISTRENGTH STEELS, British Welding Journal, pp. 108-116,February 1967.
--42-
-
9..Watkinson, F., Bodger, P. H. and Harrison, J. D.THE FATIGUE STRENGTH OF WELDED JOINTS IN HIGH STRENGTHSTEELS AND METHODS FOR ITS IMPROVEMENT, Proceedings,Fatigue of Welded Structures Conference, The WeldingInstitute, Brighton, England, July 1970.
10. Fisher, J. W., Sullivan, M. D. and Pense, A. W.IMPROVING FATIGUE STRENGTH AND REPAIRING FATIGUE DAMAGE,Fritz Engineering Laboratory Report No. 385.3,Lehigh University, December 1974.
11. Klingerman, D. J. and Fisher, J. W.THRESHOLD CRACK GROWTH IN A36 STEEL, Fritz EngineeringLaboratory Report No. 386.2, Lehigh University,September 1973.
12. Tada, H. and Irwin, G. R.K-VALUE ANALYSIS FOR CRACKS IN BRIDGE STRUCTURES, FritzEngineering Laboratory Report No. 399.1, Lehigh University,(in preparation).
13. Polmear, I. J., Tuisk, U. U., Stephens, P. J. and Voruerg, P. R. B.FATIGUE CHARACTERISTICS OF A SIMPLE BOLTED JOINT, The CivilEngineering Transactions of the Institute of Engineers,Australia, October 1970.
14. Fisher, J. W. and Struik, J. H. A.GUIDE TO DESIGN CRITERIA FOR BOLTED AND RIVETED JOINTS,Wiley Interscience, 1974.
15. Kanazawa, T. and Kobayaski, A. S.SIGNIFICANCE OF DEFECTS IN WELDED STRUCTURES, Proceedings ofthe Japan - United States Seminar, Tokyo, Japan, 1973.
16. Swanson, S. R.RAMDOM LOAD FATIGUE TESTI~lG: A STATE OF THE ART SURVEY,ASTM, Materials Research and Standards, Vol. 8, No.4,April 1968.
17. Barsom, J. M.FATIGUE CRACK GROWTH UNDER VARIABLE AMPLITUDE LOADING INASTM AS14-B STEEL, ASTM STP536, 1973.
~ -43-
-
18. Fisher, J~ W., Frank, K. H., Hirt, M. A. and McNamee, B. M.EFFECT OF WELDMENTS ON THE FATIGUE STRENGTH OF STEEL BEAMS,NCRHP Report No. 102, Highway Research Board, NationalAcademy of Sciences - National Research Council,Washington, D.C., 1970.
19. Miner, M. A.CUMULATIVE DAMAGE IN FATIGUE, Journal of'the AppliedMechanics, Vol. 12, No.1, September 1945.
20. Schilling, C. G., Klippstein, K. H., Barsom, J. M. and Blake, G. T.FATIGUE OF WELDED STEEL BRIDGE MEMBERS UNDER VARIABLEAMPLITUDE LOADING, Research Results Digest No. 60,Highway Research Board, 1974.
-44-
-
APPENDIX A
CRACK DOCUMENTATION
-45-
-
o 0o 0 0 0
o 0 0
o
o
o
o
TPA- I Q5r= '3_8 KSJ
F.ig. A-I Tie Plate TPA-la
-46-
-
o 0
o 0
o 0 0 0
(
o
o
o
o
TPA-Ia..cSr == 18#2. KSJ
, IIVz
Fig. A-2 Tie Plate TPA-lac
-47-
-
o a
o
o
o
o
000 0
o 0
TPA- J bS~= 15,6K51
',ola.; 500'12Y32/1
Fig. A-3 Tie Plate TPA-lb
-48-
-
TPA-2o.. I 4"457;900S" ;:: /2.3
K5
4- 457. 9 0 0 . 13t II ~ '~ .Jr ,; 2. //6! I 2. /4 .
Fig. A-4 Tie Plate TPA-2a
-49-
-
a 0
o
o
o
o
000 0
4,1450900·-\"~#-i~ -I, . r 13;J6 II,I,,JfI,III
TPA- 2 bSr=Jl,8KSJ
Fig. A-5 Tie Plate TPA-2b
-50-
-
o 0
000 0
o 0 0
o
o
o
o
TPA- 3aS'y = 7#8 KS J
----\---4fFig. A-6 Tie Plate TPA-3a
-51-
-
o 0
o 0
o o 000 0
TPA-4S~ -::. 20.0 K51
l Jt y 32~OOO }Fig. A-7 Tie Plate TPA-4
-52-
-
o 0
o 0
o 0
_;__9_~_1_I-=--=-=4=8=,J=5=o=o===: ---J)
( .
TPA- 4cSr=- 21.4KSl
Fig. A-8 Tie Plate TPA~4c
-53-
-
o o 000 0o 0
o o o 0
TPA--5Sr = 20,0 KSJ
~ 409, 60~_1..L..-_~.:l_
Fig. A-9 Tie Plate TPA-5
-54-
-
o
o
o
o
o
o o 0 0 0'
TPA - 5 cSr= 20.2 KSJ
,\ i 3/8'
Fig. A-IO Tie Plate TPA-5c
-55-
-
o. o 000 0o 0
o 0
TPA- 6Sr=IO.OKSI
~ig~ A-I1- 'Tie Plate TPA-6
-56-
-
o
o
o
oo
o
TPA - 6 cSy= 9d9.KSJ
~-
7/'1i'IG
Fig. A-12 Tie Plate TPA-6c
-57-
-
o 0
o
o
o
o
000 0
TPA-7Sr=IO.OKSI
.~
Fig. A-13 Tie Plate TPA-7
-58-
-
o 0
o .0 0 0
000
o
o
o
o
TPC- J(LSr =30 K51
l\--__.o..--_::~_-_-_-_-_-_-_- 7='=J8==O=3~=IT~-l.j~r...--._%_1/_7_1
J_
6
----lt
Fig. A-14 Tie Plate TPC-la
-59-
-
o
o
o
o
o
o
o 0 0 0 ~
o 0 l
TPC -, bSt-=30KSI
---r--.....--- 71)800
. 3/'4-"
Fig. A-IS Tie Plate TPC-lb
-60-
-
o 0
o 0 0 0
o 0 0
o
o
o
o
/3I., 058.1 000
'/ 7(6
T pc- 2 ClSt =/3.4 KSI
\ 4_3
_7
J_q, DO 5/16
1/ t ~-~-411- 3 6 4~ 500
Fig. A-16 Tie Plate TPC-2a
--61-
-
o o o .0 0 0o 0
o o o 0
--------TPC - 2 bSr=J2.3KSI
-: t8/16'/ ISJ 936/700\----.r.--
~ )V4-""""'-11-.-t-....-l_-_-_'_5,_9_3_6_1 7_0_0__--'-~__--JJ
Fig. A-17 Tie Plate TPC-2b
-62-
-
oo
o
o
o
o
o 0
TPC-3cSr ~ --- .7•.3 KS J
Fig. A-18 Tie Plate TPC-3c
-63-
-
o 0
o
o
o
o
000 0
o 0 0
TPC-5Sr :: 16~O KS J
Fig; A-19 Tie Plate TPC-5
-64-
-
o 0o
o
o
o
o 0
o a
5 II
2'/96 OOO~6'J :J
TPC-ScSr=:' 11,7 '(\SI
Fig. A-20 Tie Plate TPC-5c
-65-
-
o a
o 0000 0oo
TPC-6Sy ::: J6,0 KS I
,1I\\
IIII
II
~628J500
~ 3 II \ ,
2·~· \ 628 500\ ..-\,
2 11 II "- .\ 116 ',\
J J
Fig. A-21 Tie Plate TPC-6
-66-
-
oo
o
o
o
o
2tf-----628.1 500
\\ I 5A,'1~62B500
~
T pc- 6 c5y=- '16~B KSJ
Fig. A-22 Tie Plate TPC-6c
-67-
-
o 0o
o
o
o
o 000
o 0
TPC-7Sr=24.0KSI
21'}OOO Ifa'i :, -~-2-'L--;-:1I 211} 000J /32I !
J93J500j,f ". 189 400I :'b 7: " )
) :" 'I---....-'_~~~ 175) 600~ 151[(,' I67 4 0 0
O '.%," .J163)00 ' 2/ 11)2"r, 156 600I~ \1 II }
f5'J200~J_:. V32 148 400fl' ",)
1+5°00 sit: 9 138 6005/l:.4/
A-23 Tie Plate TPC-7Fig.
-68-
-
o 0 0 0
o
o
252)000 12%2 :
( !I
233~ 700 I"t/1
2/.5/200 1~6'f /252 000 1S?'Ti'
:/ '732 I l,".
Fig. ·A-24 Tie Plate TPC-8
-69-
-
APPENDIX B
FATIGUE CRACKING OF THE UNWELDED TIE PLATE
Near the end of the tie.plat~ test the unwe1ded tie plate on
the east side of the test set-up developed a fatigue crack. The crack
started at the bottom hole under a washer and was not discovered until
it had grown 8-1/8 in. This crack is shown schematically in Fig. B-1.
The bolted connection was not fully slip resistant since the
bolts were only preloaded between 20-25 kips, which is less than the
full clamping force of 1 in. A490 high strength bolts. Previous tests
have shown that reducing the clamping force lowers the fatigue life
of a bolted joint13s14. Therefore this failure was compared to
Category B of the L\ASHTO Specification* for a bearing-type joint.
Since the fatigue strength of bearing joints are governed by stresses
on the net section, all calculated stresses on the tinwelded tie plate
were based on bending stresses at the net section.
Category B was derived from fatigue data for welded details
and shown to provide a lower bound to the fatigue strength of bolted
bearing joints with fully preloaded joints14 • A lower bound estimate
of the fatigue crack growth thres~old for bolts with low clamping force
was made using a linear approximation of the stress intensity factor
for a small crack at the edge of a holelS. Since the tie plate holes
were drilled, a small initial crack (a.) of 0.005 in. was assumed.~
This resulted in the following approximation for the stress intensity
factor
-70-
-
K = 2.97 cr & (ksi lin ) (B-1)
where cr is the stress based on the gross area. Dividing this stress
by the ratio of net area to gross area gives the stress based on the
net section, which is needed for this analysis. By substituting a
rounded value of the stress intensity range threshold found by
Klingerman 1l of 3.0 ksi lin. into Eq. B-1 for K, along with 0.005 in.
for a and the correction for stress based on net section, a threshold
stress range of 10 ksi was estimated for the tie plate.
A strain gage had been placed on the tie plate's bottom edge
to check twisting of the beam. Therefore the stress range at the edge
of the hole could be estimated for each block of loading. The result-
ing ,stress ranges and cycle history is summarized in Table B-1.
The root-mean-square (RMS) method 1S ,17,l8 was one of two pro-
cedures used to determine an effective stress range so that the failure
could be compared with the constant cycle relationship. In this
method the root-mean-square stress range is defined as:
SrRMs = (2: a. 82 ) 1/2
1 r.J..
(B-2)
where cx. is the frequency of occurrence of stress range S1 r.
~
The second procedure consisted of combining the relationship
provided by constant cycle datal8 and Miner's cumula tive damage hypo-
thesis 19 to obtain an equivalent stress range SrMiner20 • This equiva-
lent stress range was estimated as
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S M" . = (E ct. S3 ) 1/3r 1Uer 1 r"
1
where a" is the frequency of occurrence of-stress range S~ r
i
In order to assess the most critical condition, several
(B-3)
effective stress range values were determined for the random block
loading sequence. Severa~ of the initial block loadings were below
the fatigue limit of 10 ksi. Hence the lower stress range blocks. were
eliminated from the effective stress range analysis one at a time.
The results of this analysis are tabulated in Table B-2 and plotted
along with Category B in ~ig. B-2. Since there may not be a fatigue
limit for random cyclic loading when some of the stress cycles exceed
the fatigue limit this figure shows the stress range-cycle life rela-'
tionship extended beyond the fatigue limit.
The first block loading (TPC-3) with a 6.5 ksi stress
range can logically be eliminated from the effective stress calcula-
tion, since it was well below the threshold. 111e second block eli-
minated was TPA-7 with a stress range of 7.1 ksi. Although some
crack growth may have occurred under earlier loading blocks, it is
probable that the crack size did not increase e110ugh to cause the
crack growth threshold to be exceeded at a 7.1 ksi stress range.
This same reasoning was used to eliminate the 7.8 ksi stress range of
the third block loading, TPA-6. The 11.3 and 13.3 ksi stress ranges
of TPC-5 and TPC-6 respectively were also eliminated to determine the
effects on the fatigue strength calculations.
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Figure .B-2 shows that removing up to three of the lower
stress range blocks provided approximately the same tie plate fatigue
strength. The test data fall at or above the stress range-cycle life
r~lationship for Category B indicating failure. When more stress
range blocks were truncated the effective stress range began to fall
below the fatigue strength line indicating that no failure should
occur. Therefore anyone of the first four effective stress ranges
calculated gives a "reasonable estimate of the tie plate's fatigue
strength.
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TABLE B-1 UNWELDED TIE PLATE STRESS RANGE
AND CYCLE HISTORY
Stress Range (8 ) at Hole,r
Specimen Cycles Base on Net Section (ksi)
TPC-3 20,522,400 6.5
TPC-5 3,314,600 11.3
TPA-6 3,670,500 7.8
TPC-6 628,500 13.3
TPA-7 4,947,000 7.1
TPA-4 481,500 16.9
TPC-7 211,,000 17.4
TPC-8 252,000 18.7
TPA-8 1,582,000 13.5
NOTE: 1. Specimens listed in order of testing
2. TPA... 8 not included in S-N curve as resultsquestionable because of crack in unwelded tie plate
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TABLE B-2 SUMMARY OF EFFECTIVE STRESS RANGES
SpecimensExcluded
None
TPC-3
TPC-3TPA-7
TPC-3TPA-7TPA-6
TPC-3TPA-7TPA-6TPC-5
TPC-3TPC-7TPA-6TPC-5TPC-6
Total Cycles
35,609,500
. 15,087,100
10,140,100
6,469,600
3,155,000
2,526,500
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s' ·(ksi)r RMS
8.3
10.3
11.5
13.1
14.8
15.1
S (ksi)r
MINER
8.8
10.8
12.2
13.3
14.9
15.3
-
o 0
000
ooo
Fig. B-1 Schematic of Fagiue Crack inUnwelded Tie Plate
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30
20
~;~ . ~~
CATEGORY ~B
"LOWER 4S~ EXCLU~ED
--
LOWEST S,.EXCLUDED'
8I
......r-......JJ
Sr(l
-
VITA
Donald P. Erb, the son of Katharine and Paul S. Erb, was
born on October 16, 1950 in Lancaster, .Pennsylvania. The author
attended Manheim Township High School in Lancaster •. He was a Dean's
List student at Drexel University in Philadelphia, Pennsylvania
where he received a Bachelor of Science degree in Civil Engineering
with highest honors in June, 1973. He was awarded a Research
Assistantship in Civil Engineering at Fritz Engineering Laboratory,
Lehigh University in October, 1973 and received his Master of Science
degree in Civil Engineering from Lehigh University in October, 1975.
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