FAtIGUE STRENGTH OF rACKWE LDED TIE PIATES

by

Donald P. Erb

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

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

ii

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.

iii

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

1

2

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

iv

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

v

23

24

24

25

26

27

28

29

30

31

33

34

35

36

37

38

39

Figure

17

18

Comparison of Second~Anal·yticalModel toTest Results - K = 2.52

Comparison of Second Analytical Model toTest Results - K = 3.08

vi

40

41

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.

-1-

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

-2-

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

-3-

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.

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

-5-

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.

-6-

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

-7-

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

-8-

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

-9-

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.

-10-

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.

-12-

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.

-13-

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.

-14-

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

-15-

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.

-17-

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,

-18-

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

-19-

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.

-20-

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.

-21-

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

-71-

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.

-72-

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.

-73-

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

-74-

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

-75-

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

-76-

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.

-78-