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Pilot study on the constant and variable amplitude behavior of transverse stiffener welds
J. Construct. Steel Research 12 (1989) 229-252
Pilot Study on the Constant and Variable Amplitude Behavior of Transverse Stiffener Welds
Karl H. Klippstein Department of Civil Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
& Charles G. Schilling 3535 Mayer Drive, Murrysville, PA 15668, USA
ABSTRACT As part of a pilot study on the long-life variable-amplitude behavior of transverse stiffeners, thirty-nine fatigue specimens were tested as follows: seventeen specimens were tested to establish the constant-amplitude fatigue limit, twelve specimens were used to determine the sloped portion of the constant-amplitude S--N line, and ten tests were performed to study the fatigue behavior under a variable-amplitude random-sequence load-stress spectrum with a truncated Rayleigh distribution. The remaihing variableamplitude random sequence originally planned, which included additional tests with a truncated Rayleigh and the trimodal spectrum based on the combined 1974 truck traffic, were not tested because the project was discontinued for economic reasons. However, because the findings for the completed part of the program might be useful for future investigations, the procedures followed and the results obtained are reported in this paper. Special care was taken during the fabrication of the specimens to reduce geometrical and residual-stress variations. This allows a more meaningful evaluation of the effect of the constant-amplitude fatigue limit on the fatigue life of a specimen exposed to a variable-amplitude random-sequence loadstress spectrum. The constant-amplitude fatigue limit determined by the modified staircase method was 18.2 ksi. This is significantly higher than the lower-bound value of 12 ksi used in the A A S H T O fatigue provisions and as sometimes assumed 229 J. Construct. Steel Research 0143-974X/89/$03.50 © 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain
230
Karl H. Klippstein, CharlesG. Schilling in the literature. The slope of the constant-amplitude tests was close to -4, which is also different from the generally assumed slope o f - 3 . The limited number of variable-amplitude fatigue-life data obtained, which includes tests up to 15 million cycles, are compared to (1) a lowerbound curve obtained by ignoring the effects of the constant-amplitude fatigue limit, and to (2) an upper-bound curve obtained by assuming that the stress cycles below the constant-amplitude fatigue limit cause no fatigue damage. It is anticipated that this information may be useful for future investigations related to the behavior of welded-steel fabrication details exposed to variable-amplitude random-sequence loads, as found predominantly in steel bridge applications.
INTRODUCTION The intention of this paper is to make available test data and findings of a fatigue study initiated in 1979. Due to severe economic conditions at the end of 1983 the study was discontinued. However, it was decided to publish the results that were obtained so that other researchers could utilize the results and possibly include them in future fatigue studies. After the first major study of welded steel small specimens and large beams exposed to variable-amplitude random-sequence stress spectra that resembled those in actual bridges was completed, 1the following conclusions were made. First, a rationale was needed to show that the fatigue life of a given fabrication detail due to a large number of low variable-amplitude stress ranges, and the lesser number of much higher constant-amplitude stress ranges than those specified in the AASHTO specification at that time, ~'3 are compatible and meaningful. Second, the needed rationale appeared to be highly dependent upon the actual constant-amplitude fatigue limit. Third, no research studies could be found which systematically had determined the constant-amplitude fatigue limit for fabrication details typical of welded steel bridges such that the findings could be applied to the results of a variable-amplitude random-sequence fatigue study. It was for these reasons that this research project was developed. The results obtained and conclusions made are reported in this paper. At about the same time as the research plan was developed for this project, and test specimens were fabricated and pilot tests were conducted, studies by Albrecht and Rubeiz 4 resulted in a very meaningful correlation between the high constant-amplitude stress range with small number of cycles specified and the low variable-amplitude stress ranges with large numbers of cycles reported for actual bridges at that time?
Fatigue life of transverse stiffeners
231
R E S E A R C H PLAN The research plan, which was developed and completed in 1980 and 1981, had the following objectives: (1) to make use of a small welded steel specimen that is representative of the most frequent and unavoidable fatigue category in welded bridge girders, made of the most commonly used steel grade, (2) to fabricate test specimens such that normal and abnormal scatter of geometry and residual stress variations is reduced as much as possible, (3) to assure that eccentric gripping of specimens during tests is avoided, or minimized, (4) to p l a n a n d document the precautionary measures chosen in great detail to meet the above objectives and make an evaluation of their effectiveness, and (5) to evaluate test results in accordance with the latest recommendations by other professionals. 6'7 Therefore, the test plan developed for this study is the result of careful and detailed consultation with many colleagues, fabricators, and testing technicians to assure that the project objectives would be met. As a guide to the test plan development, the specimen was assumed to be a small specimen, representative of a transverse (vertical) web stiffener in a web girder, that could be tested in a fatigue-testing machine with a minimum of 50 kips capacity, and be fabricated from a steel with a minimum yield strength of 50 ksi. The specimen envisaged is shown in Fig. 1. The horizontal
2.1/~~~
Transverse stiffener
L Fig. 1. Specimengeometry. (1 in = 25.4 mm.)
Karl H. Klippstein, Charles G. Schilling
232
TABLE 1
Purpose Pilot test Fatigue limit S-N slope Rayleigh
Type of load Static & C A CA CA VA
(£d/S,~ = I)
S,e#/S,t
1.25 2.50 1.25 1.00
0.75 1974 truck trimodal
VA
1.00
0.75
S,~II(k.sO
No. of specimens
18.0 15-21 22.5 45.0 22.5 18.0 13.5 18.0 13-5
2 As needed 6 6 5 5
5 5
5
CA = constant-amplitude stress ranges. V A = variable-amplitude stress ranges, Sren = effective stress range of a given stress spectrum, and S~l = constant amplitude stress-range fatigue limit, all in ksi units
part represents the web of a beam or girder, and the vertical part represents the vertical stiffener. Initially, the tests in Table 1 were planned. The pilot tests were intended to confirm the specimen gripping procedure that would be developed. A well-specified and controlled procedure was expected to ensure that no initial bending moments were introduced before testing commenced. It was planned to use a large number of strain gages for these test specimens to determine how successful the procedures to be developed would be. Apart from the variability expected from the condition of the raw materials to be received and the variability of the geometry of the fabricated specimens to be tested, the gripping procedure was considered to be extremely important and it ensured that the tests were not biased by the testing procedure. It was expected that about fifteen specimens were to be tested in the constant-amplitude stress range of 15-21 ksi to determine the constantamplitude fatigue limit. This was based on the expected fatigue limit of about 18 ksi. However, the plan adopted was to test as many specimens as required. To determine the finite-life fatigue behavior of the selected specimen, or the slope and intercept of the mean of the results, it was proposed to test the selected specimens at two constant-amplitude stress levels: (1) S~n = 1-25 Srl (or 22-5 ksi), and (22 Sren = 2.5 St,, where S~ is the stress range for the constant-amplitude fatigue limit of the selected specimen. As for determining the fatigue damage, or the effects of variableamplitude stress cycles above and below the established constant-amplitude fatigue limit, it was planned to utilize two variable-amplitude stress-range
Fatigue life of transverse sn'ffeners Srm (modal)
233
2Srd
~, i
Conversion factor: lksl : 6.895 kIpg
L
Sr max Stress range, Sr (ksl)
Fig. 2. Truncated Rayleigh probability density distribution. Notes: the effective stress range, Sren, depends on the slope of the log S-N curves. For a slope of - 2 (RMS): Sreu = Srm +0"378" S~d; --3 (RMS): Sren = S~m+0"502" S~d. For other slopes, S~en has to be calculated. 0.03~
>0-02 c 0 ~D
II
0.01
0
I
I
40 60 Gross weight ,W (kq~s)
80
I
100
Fig. 3. Combined truck traffic, 1974. (1 kip = 4.448 kN.) spectra. The first spectrum considered was the unimodal spectrum previously used in the aforementioned N C H R P study, 1 known as the Rayleigh spectrum, and as shown in Fig. 2. The second spectrum considered was the trimodal stress spectrum representing the 1974 combined truck traffic compiled by the authors at that time, which is shown in Fig. 3. For both of these spectra, different Sr~/Sr, levels were considered as shown above.
234
Karl H. Klippstein, Charles G. Schilling
SELECTED SPECIMEN G E O M E T R Y The decision on the final choice of the test specimen geometry was governed by the fatigue categories represented in the AASHTO specifications 2 at that time. Although Category A and B details, represented by as-received or burned surfaces and butt welds ground flush, are always present in welded bridges, they are out-shadowed by the more fatigue critical categories (C, C', D, E, and E') which often cannot be avoided, unless design changes are acceptable before fabrication commences. For instance, if the end of a partial-length cover plate was considered during the preliminary stage of a bridge design (Category E or E'), it is possible to replace the cover-plated region by a thicker and/or wider flange plate, and reduce the earlier design details by less fatigue-critical details such as a butt-welded splice with its reinforcement removed (Category B), or left in place (Category C). Most often the latter is chosen for economical reasons and because other Category C details, such as transverse stiffeners, cannot be avoided anyway. Similar arguments can be made for Category D details, which cover several longitudinal attachments. With great labor-intensive efforts they could possibly be converted to Category B or C details, but only at considerable additional costs. Therefore, a specimen geometry representing Category C fabrication details was chosen for the project, because it is the most representative category of a welded bridge. And the transverse stiffener detail was chosen because it represents the most often encountered detail covered under Category C. The chosen specimen geometry was as originally envisaged, and as shown in Fig. 1. The test specimen consists of a ~-inch-thick by 2½-inch-wide by 16-inch-long web plate to which two transverse stiffener plates, ~-inch-thick by 2-inch-long by 21-inch-wide, are attached transversely on opposite sides of the web plate along its midlength by four -~-inchfillet welds. Thus, the width of the specimens is 2½inches.
SELECTED SPECIMEN M A T E R I A L To determine which material was to be used for the specimen geometry selected, colleagues and engineers from various sources were consulted to determine which grade of steel was mostly used for medium-size bridges over the last five years, and which steel grade was likely to be the most popular for future applications. These sources included representatives of the Federal Highway Administration (FHWA), the American Association
Fatigue life of trann, erse stiffeners
235
of State Highway and Transportation Officials (AASHTO), and the Pennsylvania Department of Transportation (Penn-DOT). As a result of this survey it was decided to use ASTM A572 Grade 50 weathering steel, or specifically USS COR-TEN B with a minimum specified yield point of 50 ksi. This medium-strength steel also allowed for the application of higher maximum (or effective) stress ranges during testing, which would not have been possible by using ASTM A36 steel. Upon receipt of the plate material, the mill certificates were checked and coupon tests were made. These tests indicated that the chemical and mechanical property requirements were met.
SPECIMEN FABRICATION Another m a j o r concern was the fabrication process. On one hand it was desirable to let the specimens be fabricated in accordance with currently accepted practices and requirements of the AASHTO specifications which allow for a large scatter of the weld geometry. On the other hand it was felt desirable to tighten up on the fabrication processes such that the geometrical and residual-stress variations could be reduced as much as possible, with as little bias as possible on the final results. Therefore, two 4-foot-wide by 8-foot-long plates were ordered and checked for flatness upon receipt to determine whether they could be used for further processing. The flatness was found to be within specified ASTM A6 limits. Subsequently, each plate was flame-cut transversely to obtain four 16inch and two 12½-inch strips, with remnants, all 4 feet long, as shown in Fig. 4(a). All cuts were specified to be made simultaneously. This cutting procedure was specified to ensure that each strip was flamecut simultaneously along both edges to maintain flatness and straightness. The large remnant shown at the bottom of Fig. 4(a) was used to determine the material properties of each plate. The 12½-inch-wide strips were then flamecut to obtain five strips approximately 2½ inches wide, as shown in Fig. 4(a). Again, all flamecuts were specified to be made simultaneously to ensure the desired flatness and straightness. The 21-inch-wide strips were then tack-welded to the 16-inch-wide strips at locations as shown in Fig. 4(b). Subsequently, semi-automatic submergedarc fillet welds were placed simultaneously at locations 1 and 3, and at locations 2 and 4, with the 16-inch-wide strip in a horizontal position. This procedure was used to ensure minimum distortion of the 16-inch-wide strip (simulating the web of a bridge girder) and close perpendicularity of the
Karl H. Klippstein, Charles G. Schilling
236
PC1 PC1
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PC2
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J; PC2
qi"
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PC1 PC1 PC1 PC1 PC1
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~///////////////////////~'//~ ~///~/RRemnantfor material p ' yp oerr tests//.~/~/~//'//~
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(a) Fig. 4. Fabrication details. (a) Layout and burning schedule; (b) tacking and welding schedule; (c) band saw schedule. (1 in = 25.4 mm.)
2½-inch-wide strips (simulating the transverse web stiffeners of a bridge girder) could be achieved. Placing two fillet welds simultaneously with an offset of welding heads (one being about 2 or 3 inches ahead of the other) is accepted common practice in bridge-girder fabrication. The welding machine used for this work was a production unit normally used to weld
Fatigue life of transverse stiffeners
. / 1 8
t'
i~lD
d
237
~1 (T~k weld,1VP
--
--
, r-
481:
-
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(b)
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stiffeners. Lincoln L61 wire and 761 flux were used at a machine setting of 400 amp, 31-32 volt, with a 40.5 in/minute travel. Eight welded assemblies were obtained by this fabrication process. Each assembly was then saw-cut as shown in Fig. 4(c). This procedure was specified so that the regions containing tack welds (shaded areas in Fig. 4(c)) could be discarded, and distortion and introduction of residual stresses would be minimized for the specimens. Welding was performed by welders certified according to AWS D 1.1--81. As a result of this fabrication procedure, 128 specimens w i t h ' a geometrical configuration as shown in Fig. 1 were obtained from the two plates ordered.
238
Karl H. Klippstein, Charles G. Schilling
SPECIMEN DESIGNATIONS Each specimen was identified by a number (1 to 128) to permit randomization of the sequence in which the specimens were to be tested later. To define the thickness measurement locations, to measure the out-ofstraightness of the specimens, and to define the fatigue crack initiating sites in the web plate at the toe of the four fillet welds (data which were needed to determine if the fabrication and gripping procedures did or did not bias the test results), the following designations were chosen. Front (F), Rear (R), T o p (T), and Bottom (B) locations were identified as shown in Fig. 5. The technicians were instructed to always install the specimen from the same side of the testing machine, called the 'Front'. Therefore, the plane of the specimen facing the operator was designated to be the front side (F), and the opposite side of the specimen was designated to be the rear side of the specimen (R). However, before any specimen was allowed to be used for testing, thickness and out-of-plane measurements of the web plate element were made. The locations for these measurements, identified as a through h in Fig. 5, were ~ inch away from each edge of the web plate and from the toe of the fillet welds. Thickness measurements were made at locations b, c, f, and g (all adjacent to the welds) because the nominal stress near the weld is most important, which means that the cross-sectional area at these locations must be known accurately. The average thickness of these four measurements was used to adjust the MTS-equipment load such that the desired nominal stresses would be achieved. Flatness (or out-of-straightness) measurements were made at all eight locations (a to h) of each specimen. A three-point support fixture was placed on a flat surface and the web of the specimen was placed on top of it. A dial gage m o u n t e d on a base plate was moved around on the flat surface to measure the distance between the fiat surface and the web plate at all eight locations. The measurements were put on a data file and a small computer program read the raw data, adjusted the measurements such that three corner points were in the same plane, and calculated the largest difference between this plane and the remaining locations of the web. This largest difference was recorded as the out-of-straightness dimension. Specimens with an out-of-flatness of more than & in were to be rejected. The top, bottom, front, and rear designations (T, B, F, and R) were also used to describe the weld toe locations at which fatigue cracks could initiate. Thus, the combined location designations FI', FB, RT, and RB, as shown in Figure 4, define the 'front top', 'front bottom', 'rear top', and 'rear bottom' locations of the fillet toes, respectively. Furthermore, the possible initiation
239
Fatigue life of tratm, erse stiffeners
IP REAR
[
I
I 14
FRONT
]
FT : F r o n t
top
O I~r = Rear too
Possible c r a c k initiation sites
web
Transverse
Possible c r a c k Initiation sites
RB : R e a r b o t t o m
FB = F r o n t
bottom
IP 1~. $. Specimen designations. (1 in = 25.4 mm.)
sites along the width of the specimens were designated as location numbers 0 through 4, starting with 0 at the left edge of the installed specimen, and ending with 4 at the right edge, as seen in Fig. 4 at the top. These location numbers represent the quarter points along the width of the specimen.
TEST SETUP The test setup was basically the same as for NCHRP Project 12-121 except that for constant-amplitude (CA) testing a 50-kip closed-loop hydraulic system (MTS) was used without the EMR load profiler. For variableamplitude (VA) testing the 300-kip closed-loop hydraulic MTS system and the EMR load profiler were used in the load-control mode.
240
Karl H. Klippstein, Charles G. Schilling
Time
Fig. 6. Partial load cellread-outfor Rayleighdistribution. Punched tapes that define 500 individual loads satisfying the Rayleigh and the 1974 Combined Truck Traffic probability-density curves shown in Figs 2 and 3, respectively, were prepared to control the variable-amplitude tests. The loads on each tape were arranged in random sequence. A portion of the load-cell read-out for the tape representing the Rayleigh distribution is shown in Fig. 6. Both ends of the tape were connected to provide a loop, allowing cycling of the 500-load-block tape continuously throughout a test.
TEST PROCEDURES In all CA and VA tests, the nominal dynamic stress at the weld toes was the main test parameter. This stress was directly proportional to the applied load, which was used to control the test, and the relationship between the two was established by a static calibration, which also entailed a gripping procedure. The stress caused by a given cyclic load is theoretically higher than the stress caused by a static load of the same magnitude, but for the given test conditions the difference was less than 1% and was neglected. The following detailed test procedures were developed to ensure repeatability and reduce the variability caused by equipment or operator: (1) (2) (3) (4)
specimen gripping procedure, static calibration procedure, procedures for CA and VA loading, and procedure for CA fatigue limit tests.
These procedures consisted of a very detailed description of each step the operator had to follow when installing the specimens or when conducting
Fatigue life of transverse stiffeners Grip line
241
Strain gages, Typ.
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~ m
N
3(4.) 5 6) ,Tee) [
HH 2 - I12'~n
•
2.1/2in
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Grps, ~ p .
i
~L-
--L-
I
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Conversion f a c t o r 1in s 2 5 . 4 m m
Fig. 7. Pilot test specimenswith strain gages. (1 in = 25.4 ram.) the tests. Two specimens with twelve strain gages as shown in Fig. 7 were used to confirm these procedures through two pilot tests. The procedures and the pilot test results will not be reported here; however, a few brief comments on the procedures and results are made as they show some interesting findings.
Grippingprocedure The purpose of the gripping procedure was to ensure that the hydraulic grips would not cause a bending m o m e n t in the specimen because, if of significant magnitude, it would add considerable and variable bending stresses to the axial stresses imposed during testing. As a result, crack initiation would start much earlier, crack propagation would be faster, and the resulting fatigue life would not be representative of axial stresses only. The final gripping procedure developed included the entire sequence of steps necessary to turn the testing machine on, and---after all intermediate steps are taken---to turn the testing machine off. It showed that the bending stresses introduced by gripping can be significant. Under certain conditions, these stresses were found to be greater than the nominal axial stresses to be applied for the test when using the wrong sequence of locking or unlocking
242
Karl H. Klippstein, Charles G. Schilling
the swiveling heads of the hydraulic testing machine, or when using the locking procedure at the wrong time. The ability to utilize the readings of the twelve strain gages on both sides of the specimens was a significant aid to understanding the sequence of stresses introduced due to gripping, locking heads, and loading. For instance, when the heads were unlocked before gripping of the specimen commenced, the resulting bending stresses would be very small when the hydraulic axial load was zero, but they would sometimes be very high when the axial calibration load was at its maximum. This is because the heads of the hydraulic machine were aligned with the sloped ends of the distorted specimen when the applied axial load was zero, and the gripping process did not cause any bending stresses at that time. However, when the maximum calibration loads were applied, the distorted specimen tried to straighten out while the self-unaligned and locked machine heads could not, thus introducing a high bending stress at a time when the applied axial stresses were also high. Conversely, when a straight machined bar was used to align the machine heads before the specimen was inserted and gripped, the resulting stresses were significantly different. In this case, both the upper and the lower machine heads were unlocked, the specimen was inserted, locked at top and bottom, and an axial load was applied to align the heads. Under this load both heads were locked, the axial load was reduced to zero, and the machined bar was removed. When the slightly out-of-fiat specimen was inserted and gripped, the gripping stresses, without any externally applied load, were very high. However, when the maximum calibration load was applied, the specimen was straightened gradually and the bending stresses were substantially reduced. On the basis of these findings it was decided to align and lock both heads before installing, locking, and testing the specimen.
Static calibration procedure A static calibration procedure was developed because the initial load cycles in a welded specimen cause either residual-stress relief, or additional residual stresses. This results in a non-linear load-strain relationship during the first static load cycle(s) when operating the equipment in the loadcontrol mode. The procedure consisted of instructions that included re-zeroing the gages before or after each load step, what control buttons to use on the MTS console or the EMR (set point and span control), and what strain-gage readings to take during the first, intermediate, and last calibration load cycle.
Fatigue life of transverse su'ffeners
243
Procedures for CA and VA amplitude tests T h e results of the gripping and calibration procedures were used to develop the calibration and testing procedures for the constant- and variableamplitude test procedures. These were necessary because the number of strain gages for the specimens used in these tests was reduced to two gages (at gage locations 5 and 6, Fig. 7). Furthermore, the procedures for the constant-amplitude tests needed to be different from the variable-amplitude tests because the hydraulic systems were different and the E M R load profiler was not used during the constant-amplitude tests. Procedure for CA fatigue limit tests Plans to conduct tests that would determine the mean constant-amplitude fatigue limit were developed by using the modified (ASTM) staircase method. 6-a Using this method, the first specimen is tested at the expected fatiguelimit stress range. If the specimen does not fail after a predetermined n u m b e r of cycles (the investigators used a minimum of 5 million cycles but occasionally extended the number of cycles up to 15 million cycles), the stress range for the next sample is increased by an increment (the investigators initially used 2ksi increments, but after the second increment was completed, 1 ksi was used). If the specimen does fail, the stress range for the next specimen is decreased by an increment. Further details of this methodology, and especially the evaluation procedure required to obtain the mean fatigue limit, will now be described in more detail along with the presentation of the test results.
TEST RESULTS All test results are recorded in Tables 2-5, and in Figs 8-10. The results of the pilot tests are not shown. As shown in the tables, a minimum static stress of S~i. = 2 ksi was applied to all specimens before the fatigue stress ranges, Sr, were added. This was done to ensure that the specimens were always under slight tension even when the individual stress ranges returned to zero. The maximum stress for the constant-amplitude tests, S,~, is equal to the m i n i m u m static stress, S~i,, plus the constant-amplitude stress range, St, which is equal to, and shown as, the effective stress range, S~rt. For all variable-amplitude fatigue tests, the minimum stress range of S~in shown in Fig. 2 was equal to zero. Thus, the modal stress range, S.,, shown
244
Karl H. Klippstein, Charles G. Schilling TABLE 2 Constant-Amplitude Fatigue Test Results for Transverse Stiffener Specimens
Stres~ Specimen no.
Stain
S~
S,eff
Out-of-
Number of
flatness
full
Crack initiation
(in)b
cycles
F/Dc
2 067 000 3 638 830 8000000 10 000 000 5 000 000 5 080 000 2 429 080 5 000 000 5 000 000 1853 930 5000000 2 986 710 5000000 1 581 290 2 670 370 2 640 940 5 000 000
F F D D D D F D D F D F D F F F D
Not recorded Front, 0-4 No visible crack No visible crack No visible crack No visible crack Front, 2--4 No visible crack No visible crack Not recorded No visible crack Front, 4 ~in at 4 Rear, 0-4 Rear, 0-2 Rear, 2--4 No visible crack
location d
(A) Tests to establish constant-amplitude fatigue limit 62 68 101 75 109 65 72 66 73 124 115 94 100 89 112 120 79
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
21.0 19.0 17-0 18-0 19.0 20.0 21.0 20.0 21-0 22.0 21.0 22.0 21.0 22.0 21.0 20.0 19.0
19.0 17.0 15.0 16.0 17.0 18-0 19-0 18.0 19.0 20.0 19.0 20,0 19.0 20.0 19.0 18.0 17-0
0.008 5 0.002 9 0.005 8 0.007 5 0.IX)2 9 0.004 1 0.005 1 0-014 3 0-003 0 0.004 5 0.0109 0.005 5 0-0050 0.004 6 0.002 5 0-006 1 0.002 5
(B) Tests to establish sloped constant-amplitude fatigue curve 90 97 82 70 84 122
2.0 2.0 2-0 2.0 2.0 2.0
26-5 26.5 26.5 26.5 26.5 26.5
24-5 24.5 24.5 24.5 24.5 24.5
0.003 1 0.010 0 0-009 5 0.012 9 0.003 0 0-009 0
1 056 520 938 770 826 580 1 030 760 859 460 777 940
F F F F F F
Rear, 0--4 RT, 0--3; FB, 4 Rear, 1 Front, 4 Front Front & Back
114 108 64 106 111 123
2.0 2-0 2.0 2.0 2-0 2.0
49-0 49.0 49.0 49.0 49.0 49.0
47.0 47.0 47.0 47.0 47.0 47.0
0.010 1 0.003 4 0.010 5 0-016 0 0.003 9 0.008 2
55 120 55 140 54 990 79 350 62 560 86 630
F "F F F F F
Front, 0-4 Front, 0-4 Front, 2-3 Front, 0-4 Rear, 0-1 Rear
"(see also Fig. 2. ) minimum static stress, Smi. = 2 ksi for all tests; minimum stress range, Stain -- 0 for all tests, ksi; maximum stress, Smax = Srnin+ Srmax,ksi; maximum stress range, S~m~ = Srcn = Sm~ - Smi,; S,eff = effective stress range, ksi. h Defined as the out-of-plane dimension of any one of eight points measured on the web plate in the Z direction, while at least three of the four comers of the specimen are in a cormnon X - Y plane. "F = Failure (total separation, two parts), or D = Discontinued. 'lFailure locations are defined in the figures. All failures are initiated at the fillet weld toes. Based on shown in shown in deviation
the modified staircase method, the stress-range fatigue limit derived from the data Part A is equal to 18.2 ksi. Based on a linear regression analysis for the results Part B. the log (S-N) slope is -4.062. the intercept is 11.601. and the standard error is 0.0729.
245
Fatigue life o f trann, erse snffeners
TABLE 3 Variable-Amplitude Fatigue Test Results for Transverse Stiffener Specimens
Specimen no.
Stress ~ Srnin
Srnax
Sr~/
Out-offlatness (in) b
Number of full cycles F/D ~
104
2-0
42.6
21.8
0.(~7 5
1 811 550
F
From, 0-4
93 99 96 81 98
2.0 2.0 2.0 2.0 2.0
36.3 36.3 36.3 36.3 36.3
18.4 18-4 18.4 18.4 18.4
0.015 0 0.006 2 0.015 9 0-0048 0.008 0
3 115 150 2 078 200 2 781900 1 870 600 3 182 250
F F F F F
From, 0-4 Front, 0-3 Rear, 0--4 Front/rear Rear, 0-4
77 105 125 117
2.0 2.0 2.0 2.0
27.8 27.8 27.8 27.8
13.8 13.8 13-8 13.8
0.004 0 0.012 8 0.009 6 0.0063
14 979 550 8 060 700 15 523 200 10914450
F F F F
Rear, 0-3 Front, 0--4 Top, 0-1 Bottom, 0-4
Crack initiation location d
(See also Fig. 2 and notes of Table 2) aSmi, = minimum stress, ksi; Sma~= maximum stress, ksi; with Sr~n = 0.538 ( S ~ Smi,) = effective Miner stress range, ksi, based on a log (S-N) constant-amplitude finite-life curve with a slope of -4-062, as obtained from data under Part B of Table 2, assuming the CA fatigue limit has no effect. bDefined as the out-of-plane dimension of any one of eight points measured on the web plate in the Z direction, while at least three of the four comers of the specimen are in a common X - Y plane. CF = Failure (total separation, two parts), or D = Discontinued. alLocations defined in Fig. 5. in Fig. 2, is e q u a l to Srd, which is a m e a s u r e o f the dispersion o f the s t r e s s - r a n g e s p e c t r u m . ~ F u r t h e r m o r e , since the total dispersion (width) o f t h e stress r a n g e s p e c t r u m used is 3Srd (or e q u a l to the m a x i m u m stress r a n g e , Srma~, s h o w n in Fig. 2), the m a x i m u m stress, Sin,, s h o w n in T a b l e 3, is the sum o f Stain a n d S,n~. T h e effective stress r a n g e for the v a r i a b l e - a m p l i t u d e tests s h o w n in T a b l e 3 was calculated b y using the slope o f the finite-life c o n s t a n t a m p l i t u d e tests s h o w n in T a b l e 2.
CA fatigue limit tests P a r t A o f T a b l e 2 shows the results o f the c o n s t a n t - a m p l i t u d e fatigue tests c o n d u c t e d to d e t e r m i n e the m e a n fatigue limit. W h i l e the tests p r o g r e s s e d , t h e d a t a s h o w n in T a b l e 5 and in Figs 8 and 9 w e r e d e v e l o p e d to follow the specified p r o c e d u r e . B e f o r e testing c o m m e n c e d , it was a s s u m e d that the f a t i g u e limit w o u l d b e b e t w e e n 17 and 19 ksi. T h e first test was c o n d u c t e d at a stress range o f 19 ksi a n d the s p e c i m e n
246
Karl H. Kh'ppstein, Charles G. Schilling
TABLE 4 Constant-Amplitude Fatigue Test Results Arranged in Ascending Order of Out-of-Flatness
Specimen no.
Stress" Smm
Sm~x
S,~l~
Out-offlatness (in) b
101
2.0
17.0
15.0
0.005 8
8 000 000
D
No visible crack
75
2.0
18.0
16.0
0.(XY75
10 000 000
D
No visible crack
79 68 109
2.0 2.0 2.0
19.0 19.0 19-0
17.0 17.0 17.0
0.002 5 0.(102 9 0.002 9
5 000 000 3 638 830 5 000 000
D F D
No visible crack Front, 0-4 No visible crack
65 120 66
2.0 2.0 2.0
20-0 20.0 20.0
18.0 18.0 18.0
0.004 1 0.006 1 0.014 3
5 000 000 2 640 940 5 000 000
D F D
No visible crack Rear, 2-4 No visible crack
112 73 100 72 62 115
2-0 2.0 2.0 2.0 2.0 2.0
21-0 21.0 21.0 21.0 21.0 21.0
19.0 19.0 19.0 19.0 19.0 19.0
0.002 5 0-003 0 0.005 0 0.005 1 0-008 5 0.010 9
2 670 370 5 000 000 5 000 000 2 429 080 2 067 000 5 000 000
F D D F F D
Rear, 0-2 No visible crack ~ in at 4 Front, 2-4 Not recorded No visible crack
124 89 94
2.0 2-0 2.0
22.0 22.0 22.0
20.0 20.0 20-0
0.004 5 0-004 6 0.005 5
1 853 930 1 581290 2 986 710
F F F
Not recorded Rear, 0--4 Front, 4
84 90 122 82 97 70
2.0 2.0 2.0 2-0 2.0 2.0
26.5 26.5 26.5 26.5 26.5 26.5
24.5 24.5 24-5 24.5 24.5 24.5
0.003 0 0.003 1 0.009 0 0.009 5 0.010 0 0.012 9
859 460 1 056 520 777 940 826 580 938 770 1030760
F F F F F F
Front Rear, 0-4 Front & Back Rear, 1 T/R 0-3, B/F 4 Front, 4
108 111 123 114 64 106
2.0 2-0 2.0 2.0 2-0 2-0
49.0 49.0 49.0 49.0 49.0 49-0
47-0 47-0 47.0 47.0 47.0 47-0
0.003 4 0.003 9 0.008 2 0-010 1 0-010 5 0.0160
55 140 62 560 86 630 55 120 54 990 79 350
F F F F F F
Front, 0--4 Rear, 0-1 Rear Front, 0--4 Front, 2-3 Front, 0--4
(See notes of Table 2)
Number of ~ll cycles F/ D c
Crack initiation location d
247
Fatigue life of transverse stiffeners TABLE 5 Calculation of Fatigue Limit by Modified Staircase Method
Specimen number
Stress range, Sr, ksi
1 2 3 4 5
62 68 101 75 109
19 17 15 16 17
6 7 8 9 10
65 72 66 73 124
11 12 13 14 15 16 17
Test number
Sum of SrS (ksi) b
Number of tests~ .
.
.
Modified sum of Srs (ksi) c
Average Sr (ksi) a
.
1 2 3 4
17 32 48 65
-33 49 66
-16.50 16-33 16-50
18 19 18 19 20
5 6 7 8 9
83 102 120 139 159
84 101 121 140 158
16.80 16.83 17-29 17.50 17.56
115 94 100 89 112
19 20 19 20 19
10 11 12 13 14
178 198 217 237 256
179 197 218 236 255
17.90 17.91 18-17 18-15 18.21
120 79
18 17
15 16
274 291
273 292
18-20 18.25
Mean fatigue limit (rounded off):
18.2
a Last test prior to first reversal is chosen as # 1. bAccumulation of stress ranges used. CWhen the next stress level would be increased, 1 ksi is added to the sum of stresses; when the next stress level would be decreased, 1 ksi is deducted. dAverage stress = (modified sum of stress ranges)/(number of tests conducted).
failed at about 2 million cycles. The required entries were made in Table 5, and an X was entered on Fig. 8. Table 5 summarizes the test number, specimen number, etc., and other information as explained in the table. Figure 8 is a plot of the test n u m b e r versus stress range. Because the first specimen failed, the stress range for the second specimen was lowered to 17 ksi, and the specimen failed at about 3.6 million cycles. Table 5 and Fig. 8 were updated, and the third test was conducted at a stress range o f 15 ksi. Test 3 did not fail at 5 million cycles and was eventually discontinued at 8 million cycles. Therefore, a circle was entered in Fig. 8, and the stress range for the fourth specimen was increased to 16 ksi. All further stress-range changes from then on were m a d e by using 1 ksi increments.
248
Karl H. Klippstein, Charles G. Schilling
21
x
x
x
u
\
m
= 17 o m 16
14
I
I
I
I
I
I
I
1
2
3
4
S
6
7
I
I
I
8 9 10 Test n u m b e r
I
I
I
I
I
I
I
I
tl
12
t3
t4
15
16
17
18
Fig. 8. Graphic bookkeeping of staircase tests. (1 ksi = 6.895 MPa.)
19
O
O
E e
rl
b.
16 0
I
I
I
I
I
I
I
1
2
3
4
5
6
7
I
I
8 9 Test number
I
I
I
I
I
I
I
I
I
10
11
12
13
14
15
16
17
18
Fig. 9. Variation of fatigue limit. (1 ksi = 6-895 MPa.)
Since Test 3 constituted a reversal in the trend from decreasing to increasing stress ranges, the average stress range in the last column of Table 5 was used to start Fig. 9, which is a plot of the test number versus the average stress range. Further steps taken to conduct additional tests, the stress-range levels used, and the number of cycles applied, are as shown in Table 5 and in Figs 8 and 9. All tests follow the above logic.
Fatigue life o f transverse st/ffeners
9 8 7 G
249
Mean f a t i g u e
Mean finite-life curve
I
\
a~ 4
____
\ _
4.
3
2
2
x e-
AASHTO c a t e g o r y C'
~ ~ tp
9 e 7
0 .~
5 4
~
3
W
2
10 0 lO 4
log iN) : 1 1 - 6 0 1 - 4 - 0 6 2 log ( S r e f f ) S t a n d a r d e r r o r = 0<)729 ( f o r 12 d a t a p o i n t s ) F o r AASHTO c a t e g o r y C', log (N) = 9 . 5 6 6 - 3 . 0 log (St') log (St.) = log ( S r e f f ) f o r C.A. ,
2
,
,
.
, ,,,I
~
I
. . . . . .
~ , 56~8~1oe
Cycles to failure
O0
12
Convet . sl on f a c t o r l k s l = 6 . 8 9 5 MPa
. . . . . .
3 .$67.~
~
~
I
~ , 56~--1o7
~
(N)
Fig. 10. Results f o r C A tests. (1 ksi = 6-895 MPa.)
sl" ~.
M e a n log S - N c u r v e f r o m Fig. 10
I ~ r e T T l ~ , : I'~'U ~ . | SrL,,ff/Srl : 1.01 ' m 'I S t ' e f f l S r l = ( > 7 6
\
21-8 ksi ~
~
18"4ksl
~
~---,
18.2 ksi \ ~
am 13"8 ksi
a110'1__ t.
.
9
g
&[-
Extension of
~
finite-life cut.ve--
10ol 105
/
,
,
2
3
, , , ,,,I 4
56789106
,
,
, .....
2
3
4
,,I
5 6789107
Cycles to failut.e
- ~ ~__ ~
"-
- -
/
,
,
, , ,,,,I
2
3
4
5 6789108
(N)
Fig. 11. Variable- and constant-amplitude test comparison. Constant-amplitude parameters: log (N) = 11.601- 4.062 log (S,~e); standard error = 0.0729; Sd = constant-amplitude fatigue limit, 18.2 ksi.
250
Karl H. Klippstein, Charles G. Schilling
As seen from Table 5 and Fig. 8, seventeen specimens were tested and resulted in a mean constant-amplitude fatigue limit, S~, of 18.2 ksi. This value was essentially reached after Test 13, and is significantly higher than the fatigue stress range of 12 ksi allowed by the A A S H T O specifications for transverse stiffeners. Finite life CA tests
Since the constant-amplitude fatigue limit had been established previously at a stress-range level of S~ = 18.2 ksi, it was decided to conduct tests at Sre stress ranges of 24.5 and 47.0 ksi, which correspond to Sro/S~ levels of 1.35 and 2.58, respectively. Six tests each were conducted at both stress levels. The results of these tests were used to determine the slope and intercept of the finite-life portion of the S-N curve. As shown in Fig. 10, the slope is -4.062, the intercept is 11-601, and the standard error is 0.0729. The slope of -4.062 is substantially different from the results of other welded fabrication details, which generally have a slope of about -3-0. This difference may be attributed primarily to the fact that the fabrication of the specimens was carefully controlled, which tends to influence the slope of the S-N curve and reduce the standard error. Variable amplitude tests
Ten tests were conducted with a truncated Rayleigh probability density distribution, which was subdivided into 500 randomly arranged load levels. The results are shown in Table 3 and in Fig. 11. Only one test was conducted at an effective stress range, S~n, of 21.8 ksi. This test corresponded to an S~n/S, ratio of 1.20. The life of 2 067 000 cycles is higher than 1 459 000 cycles predicted by the constant-amplitude S-N curve, but within the 95% confidence limit. Five tests were performed at an effective stress range of 18.4 ksi, which corresponds to an Sroer/S,ratio of 1.01. The log-mean life for these tests was 2 547 000 cycles, as compared with a mean life of 2 906 000 cycles predicted from the constant-amplitude S-N curve. Four tests were made at an effective stress range of 13-8 ksi, which corresponds to an S~e~/S, ratio of 0.76. The log-mean life for these tests is 11 960 000 cycles, which is higher than 9 350 000 cycles predicted by the extension of the constant-amplitude finite-life S - N curve. Because the log-mean value of four tests is compared with the extension of the constantamplitude finite-life S-N curve, the difference appears to be significant. This means that the fatigue life predicted by the finite-life portion of the constant-amplitude fatigue curve is over-conservative (resulting in lower
Fatigue life of transverse stiffeners
251
fatigue lives than those actually attained), and is not realistic if a substantial part of the variable-amplitude stress-range spectrum is located below the constant-amplitude fatigue limit. Consequently, a more realistic approach to predict the variable-amplitude fatigue life for such conditions is needed. One approach, which neglects all damage of stress ranges with peaks below the constant-amplitude fatigue limit, ~'4 offers a possible and more accurate fatigue-life prediction method. Hopefully, this method will be substantiated by ongoing variable-amplitude tests at the University of Pittsburgh and at the University of Maryland. Out-of-flatness and gripping effect checks To check if the out-of-flatness of the specimens, or the gripping procedure adopted, had any effects on the fatigue life, the constant-amplitude fatigue test results were arranged in ascending order of out-of-flatness and grouped by the applied stress ranges, as summarized in Table 4. Based on the data shown, there appears to be no evidence that the out-of-flatness, as experienced in the specimens tested, consistently significantly affected the fatigue life. Higher out-of-flatness measurements were expected to introduce higher out-of-plane bending stresses and cause earlier crack initiation and fatigue failure; however, the minimization of the actual out-of-flatness achieved assured that the test results were not biased by this parameter. Table 4 also gives an indication of the gripping effects when the last column is investigated more closely. Since there appears to be no dominance of crack initiation locations at the front, rear, top, or bottom weld toes, it is concluded that gripping effects, which could have introduced additional bending stresses during the tests, were essentially eliminated.
CONCLUSIONS The results of a carefully conducted study of the fatigue life of transverse stiffeners welded to the web of steel bridge girders are presented. This study includes meticulous procedures to fabricate the test specimens so that test result variations due to out-of-flatness, which may cause additional bending stresses, and residual-stress effects would be reduced as much as possible. Also, gripping procedures were carefully developed and observed because they may result in additional bending stresses which could distort the test results. These effects were essentially eliminated and did not appear to affect the results of the study.
252
Karl H. Klippstein, Charles G. Schilling
Based on twenty-nine constant-amplitude tests conducted, the slope of the finite-life portion of the S - N fatigue curve is -4-062, which is different from the slope of - 3 usually encountered in welded steel specimens.. The difference is attributed to the more careful fabrication procedure used. The fatigue limit determined by the modified staircase method was found to be 18.2 ksi. Ten variable-amplitude fatigue tests were conducted at effective stress range to constant-amplitude fatigue limit ratios of 1.20, 1.01, and 0.76. The results appear to indicate that stress cycles below the constant-amplitude fatigue limit do not significantly contribute to the fatigue life. Ongoing variable-amplitude fatigue tests presently being conducted at the University of Pittsburgh and at the University of Maryland will hopefully provide an improved method to predict the fatigue life for any load spectrum encountered in welded steel bridges.
REFERENCES 1. Schilling, C. G., Klippstein, K. H., Barsom, J. M. & Blake, G. T., Fatigue of welded steel bridge members under variable-amplitude loadings. National Cooperative Highway Research Program, Report 188, Transportation Research Board, Washington, DC, USA, 1978. 2. American Association of State Highway and Transportation Officials, 1lth edn, 1973, with Interim Specifications, 1974--80. 3. Klippstein, K. H. & Romito, P. A., Variable amplitude load fatigue, Task A---Literature review, Volume II, Constant-amplitude fatigue behavior. US Department of Transportation, Federal Highway Administration, Washington, DC 20590, USA, December 1987. 4. Albrecht, P. & Rubeiz, C. G., Variable amplitude load fatigue, Task A--Literature review, Volume III, Variable-amplitude fatigue behavior. US Department of Transportation, Federal Highway Administration, Washington, DC 20590, USA, December 1987. 5. Schilling, C. G., Variable amplitude load fatigue, Task A--Literature review, Volume I, Traffic loading and bridge response. US Department of Transportation, Federal Highway Administration, Washington, DC 20590, USA, December 1987. 6. American Society for Testing and Materials, A Guide for Fatigue Testing and the Statistical Evaluation of Fatigue Data. ASTM Special Technical Publication No. 91-A, 2nd edn, ASTM, Philadelphia, PA, USA, 1963. 7. Reemsnyder, H. S., Procurement and analysis of structural fatigue data. J. Struct. Div., ASCE, ST7 (July 1969). 8. Committee on Fatigue and Fracture Reliability of the Committee on Structural Safety and Reliability of the Structural Division, Fatigue reliability: variable amplitude loading. American Society of Civil Engineers, J. Struct. Div., ASCE, ST7 (January 1969).
Pilot Study on the Constant and Variable Amplitude Behavior of Transverse Stiffener Welds
Karl H. Klippstein Department of Civil Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
& Charles G. Schilling 3535 Mayer Drive, Murrysville, PA 15668, USA
ABSTRACT As part of a pilot study on the long-life variable-amplitude behavior of transverse stiffeners, thirty-nine fatigue specimens were tested as follows: seventeen specimens were tested to establish the constant-amplitude fatigue limit, twelve specimens were used to determine the sloped portion of the constant-amplitude S--N line, and ten tests were performed to study the fatigue behavior under a variable-amplitude random-sequence load-stress spectrum with a truncated Rayleigh distribution. The remaihing variableamplitude random sequence originally planned, which included additional tests with a truncated Rayleigh and the trimodal spectrum based on the combined 1974 truck traffic, were not tested because the project was discontinued for economic reasons. However, because the findings for the completed part of the program might be useful for future investigations, the procedures followed and the results obtained are reported in this paper. Special care was taken during the fabrication of the specimens to reduce geometrical and residual-stress variations. This allows a more meaningful evaluation of the effect of the constant-amplitude fatigue limit on the fatigue life of a specimen exposed to a variable-amplitude random-sequence loadstress spectrum. The constant-amplitude fatigue limit determined by the modified staircase method was 18.2 ksi. This is significantly higher than the lower-bound value of 12 ksi used in the A A S H T O fatigue provisions and as sometimes assumed 229 J. Construct. Steel Research 0143-974X/89/$03.50 © 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain
230
Karl H. Klippstein, CharlesG. Schilling in the literature. The slope of the constant-amplitude tests was close to -4, which is also different from the generally assumed slope o f - 3 . The limited number of variable-amplitude fatigue-life data obtained, which includes tests up to 15 million cycles, are compared to (1) a lowerbound curve obtained by ignoring the effects of the constant-amplitude fatigue limit, and to (2) an upper-bound curve obtained by assuming that the stress cycles below the constant-amplitude fatigue limit cause no fatigue damage. It is anticipated that this information may be useful for future investigations related to the behavior of welded-steel fabrication details exposed to variable-amplitude random-sequence loads, as found predominantly in steel bridge applications.
INTRODUCTION The intention of this paper is to make available test data and findings of a fatigue study initiated in 1979. Due to severe economic conditions at the end of 1983 the study was discontinued. However, it was decided to publish the results that were obtained so that other researchers could utilize the results and possibly include them in future fatigue studies. After the first major study of welded steel small specimens and large beams exposed to variable-amplitude random-sequence stress spectra that resembled those in actual bridges was completed, 1the following conclusions were made. First, a rationale was needed to show that the fatigue life of a given fabrication detail due to a large number of low variable-amplitude stress ranges, and the lesser number of much higher constant-amplitude stress ranges than those specified in the AASHTO specification at that time, ~'3 are compatible and meaningful. Second, the needed rationale appeared to be highly dependent upon the actual constant-amplitude fatigue limit. Third, no research studies could be found which systematically had determined the constant-amplitude fatigue limit for fabrication details typical of welded steel bridges such that the findings could be applied to the results of a variable-amplitude random-sequence fatigue study. It was for these reasons that this research project was developed. The results obtained and conclusions made are reported in this paper. At about the same time as the research plan was developed for this project, and test specimens were fabricated and pilot tests were conducted, studies by Albrecht and Rubeiz 4 resulted in a very meaningful correlation between the high constant-amplitude stress range with small number of cycles specified and the low variable-amplitude stress ranges with large numbers of cycles reported for actual bridges at that time?
Fatigue life of transverse stiffeners
231
R E S E A R C H PLAN The research plan, which was developed and completed in 1980 and 1981, had the following objectives: (1) to make use of a small welded steel specimen that is representative of the most frequent and unavoidable fatigue category in welded bridge girders, made of the most commonly used steel grade, (2) to fabricate test specimens such that normal and abnormal scatter of geometry and residual stress variations is reduced as much as possible, (3) to assure that eccentric gripping of specimens during tests is avoided, or minimized, (4) to p l a n a n d document the precautionary measures chosen in great detail to meet the above objectives and make an evaluation of their effectiveness, and (5) to evaluate test results in accordance with the latest recommendations by other professionals. 6'7 Therefore, the test plan developed for this study is the result of careful and detailed consultation with many colleagues, fabricators, and testing technicians to assure that the project objectives would be met. As a guide to the test plan development, the specimen was assumed to be a small specimen, representative of a transverse (vertical) web stiffener in a web girder, that could be tested in a fatigue-testing machine with a minimum of 50 kips capacity, and be fabricated from a steel with a minimum yield strength of 50 ksi. The specimen envisaged is shown in Fig. 1. The horizontal
2.1/~~~
Transverse stiffener
L Fig. 1. Specimengeometry. (1 in = 25.4 mm.)
Karl H. Klippstein, Charles G. Schilling
232
TABLE 1
Purpose Pilot test Fatigue limit S-N slope Rayleigh
Type of load Static & C A CA CA VA
(£d/S,~ = I)
S,e#/S,t
1.25 2.50 1.25 1.00
0.75 1974 truck trimodal
VA
1.00
0.75
S,~II(k.sO
No. of specimens
18.0 15-21 22.5 45.0 22.5 18.0 13.5 18.0 13-5
2 As needed 6 6 5 5
5 5
5
CA = constant-amplitude stress ranges. V A = variable-amplitude stress ranges, Sren = effective stress range of a given stress spectrum, and S~l = constant amplitude stress-range fatigue limit, all in ksi units
part represents the web of a beam or girder, and the vertical part represents the vertical stiffener. Initially, the tests in Table 1 were planned. The pilot tests were intended to confirm the specimen gripping procedure that would be developed. A well-specified and controlled procedure was expected to ensure that no initial bending moments were introduced before testing commenced. It was planned to use a large number of strain gages for these test specimens to determine how successful the procedures to be developed would be. Apart from the variability expected from the condition of the raw materials to be received and the variability of the geometry of the fabricated specimens to be tested, the gripping procedure was considered to be extremely important and it ensured that the tests were not biased by the testing procedure. It was expected that about fifteen specimens were to be tested in the constant-amplitude stress range of 15-21 ksi to determine the constantamplitude fatigue limit. This was based on the expected fatigue limit of about 18 ksi. However, the plan adopted was to test as many specimens as required. To determine the finite-life fatigue behavior of the selected specimen, or the slope and intercept of the mean of the results, it was proposed to test the selected specimens at two constant-amplitude stress levels: (1) S~n = 1-25 Srl (or 22-5 ksi), and (22 Sren = 2.5 St,, where S~ is the stress range for the constant-amplitude fatigue limit of the selected specimen. As for determining the fatigue damage, or the effects of variableamplitude stress cycles above and below the established constant-amplitude fatigue limit, it was planned to utilize two variable-amplitude stress-range
Fatigue life of transverse sn'ffeners Srm (modal)
233
2Srd
~, i
Conversion factor: lksl : 6.895 kIpg
L
Sr max Stress range, Sr (ksl)
Fig. 2. Truncated Rayleigh probability density distribution. Notes: the effective stress range, Sren, depends on the slope of the log S-N curves. For a slope of - 2 (RMS): Sreu = Srm +0"378" S~d; --3 (RMS): Sren = S~m+0"502" S~d. For other slopes, S~en has to be calculated. 0.03~
>0-02 c 0 ~D
II
0.01
0
I
I
40 60 Gross weight ,W (kq~s)
80
I
100
Fig. 3. Combined truck traffic, 1974. (1 kip = 4.448 kN.) spectra. The first spectrum considered was the unimodal spectrum previously used in the aforementioned N C H R P study, 1 known as the Rayleigh spectrum, and as shown in Fig. 2. The second spectrum considered was the trimodal stress spectrum representing the 1974 combined truck traffic compiled by the authors at that time, which is shown in Fig. 3. For both of these spectra, different Sr~/Sr, levels were considered as shown above.
234
Karl H. Klippstein, Charles G. Schilling
SELECTED SPECIMEN G E O M E T R Y The decision on the final choice of the test specimen geometry was governed by the fatigue categories represented in the AASHTO specifications 2 at that time. Although Category A and B details, represented by as-received or burned surfaces and butt welds ground flush, are always present in welded bridges, they are out-shadowed by the more fatigue critical categories (C, C', D, E, and E') which often cannot be avoided, unless design changes are acceptable before fabrication commences. For instance, if the end of a partial-length cover plate was considered during the preliminary stage of a bridge design (Category E or E'), it is possible to replace the cover-plated region by a thicker and/or wider flange plate, and reduce the earlier design details by less fatigue-critical details such as a butt-welded splice with its reinforcement removed (Category B), or left in place (Category C). Most often the latter is chosen for economical reasons and because other Category C details, such as transverse stiffeners, cannot be avoided anyway. Similar arguments can be made for Category D details, which cover several longitudinal attachments. With great labor-intensive efforts they could possibly be converted to Category B or C details, but only at considerable additional costs. Therefore, a specimen geometry representing Category C fabrication details was chosen for the project, because it is the most representative category of a welded bridge. And the transverse stiffener detail was chosen because it represents the most often encountered detail covered under Category C. The chosen specimen geometry was as originally envisaged, and as shown in Fig. 1. The test specimen consists of a ~-inch-thick by 2½-inch-wide by 16-inch-long web plate to which two transverse stiffener plates, ~-inch-thick by 2-inch-long by 21-inch-wide, are attached transversely on opposite sides of the web plate along its midlength by four -~-inchfillet welds. Thus, the width of the specimens is 2½inches.
SELECTED SPECIMEN M A T E R I A L To determine which material was to be used for the specimen geometry selected, colleagues and engineers from various sources were consulted to determine which grade of steel was mostly used for medium-size bridges over the last five years, and which steel grade was likely to be the most popular for future applications. These sources included representatives of the Federal Highway Administration (FHWA), the American Association
Fatigue life of trann, erse stiffeners
235
of State Highway and Transportation Officials (AASHTO), and the Pennsylvania Department of Transportation (Penn-DOT). As a result of this survey it was decided to use ASTM A572 Grade 50 weathering steel, or specifically USS COR-TEN B with a minimum specified yield point of 50 ksi. This medium-strength steel also allowed for the application of higher maximum (or effective) stress ranges during testing, which would not have been possible by using ASTM A36 steel. Upon receipt of the plate material, the mill certificates were checked and coupon tests were made. These tests indicated that the chemical and mechanical property requirements were met.
SPECIMEN FABRICATION Another m a j o r concern was the fabrication process. On one hand it was desirable to let the specimens be fabricated in accordance with currently accepted practices and requirements of the AASHTO specifications which allow for a large scatter of the weld geometry. On the other hand it was felt desirable to tighten up on the fabrication processes such that the geometrical and residual-stress variations could be reduced as much as possible, with as little bias as possible on the final results. Therefore, two 4-foot-wide by 8-foot-long plates were ordered and checked for flatness upon receipt to determine whether they could be used for further processing. The flatness was found to be within specified ASTM A6 limits. Subsequently, each plate was flame-cut transversely to obtain four 16inch and two 12½-inch strips, with remnants, all 4 feet long, as shown in Fig. 4(a). All cuts were specified to be made simultaneously. This cutting procedure was specified to ensure that each strip was flamecut simultaneously along both edges to maintain flatness and straightness. The large remnant shown at the bottom of Fig. 4(a) was used to determine the material properties of each plate. The 12½-inch-wide strips were then flamecut to obtain five strips approximately 2½ inches wide, as shown in Fig. 4(a). Again, all flamecuts were specified to be made simultaneously to ensure the desired flatness and straightness. The 21-inch-wide strips were then tack-welded to the 16-inch-wide strips at locations as shown in Fig. 4(b). Subsequently, semi-automatic submergedarc fillet welds were placed simultaneously at locations 1 and 3, and at locations 2 and 4, with the 16-inch-wide strip in a horizontal position. This procedure was used to ensure minimum distortion of the 16-inch-wide strip (simulating the web of a bridge girder) and close perpendicularity of the
Karl H. Klippstein, Charles G. Schilling
236
PC1 PC1
PCl eCl
PC2
PC2 .c: m
J; PC2
qi"
PCl
PC1 PC1 PC1 PC1 PC1
.c
Ifl
~///////////////////////~'//~ ~///~/RRemnantfor material p ' yp oerr tests//.~/~/~//'//~
I///////
/////////////////////
I-
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(a) Fig. 4. Fabrication details. (a) Layout and burning schedule; (b) tacking and welding schedule; (c) band saw schedule. (1 in = 25.4 mm.)
2½-inch-wide strips (simulating the transverse web stiffeners of a bridge girder) could be achieved. Placing two fillet welds simultaneously with an offset of welding heads (one being about 2 or 3 inches ahead of the other) is accepted common practice in bridge-girder fabrication. The welding machine used for this work was a production unit normally used to weld
Fatigue life of transverse stiffeners
. / 1 8
t'
i~lD
d
237
~1 (T~k weld,1VP
--
--
, r-
481:
-
-
(b)
Remnants
WiiiHi,l H
!!i!.,i!
(c) Fig. 4.--contd.
stiffeners. Lincoln L61 wire and 761 flux were used at a machine setting of 400 amp, 31-32 volt, with a 40.5 in/minute travel. Eight welded assemblies were obtained by this fabrication process. Each assembly was then saw-cut as shown in Fig. 4(c). This procedure was specified so that the regions containing tack welds (shaded areas in Fig. 4(c)) could be discarded, and distortion and introduction of residual stresses would be minimized for the specimens. Welding was performed by welders certified according to AWS D 1.1--81. As a result of this fabrication procedure, 128 specimens w i t h ' a geometrical configuration as shown in Fig. 1 were obtained from the two plates ordered.
238
Karl H. Klippstein, Charles G. Schilling
SPECIMEN DESIGNATIONS Each specimen was identified by a number (1 to 128) to permit randomization of the sequence in which the specimens were to be tested later. To define the thickness measurement locations, to measure the out-ofstraightness of the specimens, and to define the fatigue crack initiating sites in the web plate at the toe of the four fillet welds (data which were needed to determine if the fabrication and gripping procedures did or did not bias the test results), the following designations were chosen. Front (F), Rear (R), T o p (T), and Bottom (B) locations were identified as shown in Fig. 5. The technicians were instructed to always install the specimen from the same side of the testing machine, called the 'Front'. Therefore, the plane of the specimen facing the operator was designated to be the front side (F), and the opposite side of the specimen was designated to be the rear side of the specimen (R). However, before any specimen was allowed to be used for testing, thickness and out-of-plane measurements of the web plate element were made. The locations for these measurements, identified as a through h in Fig. 5, were ~ inch away from each edge of the web plate and from the toe of the fillet welds. Thickness measurements were made at locations b, c, f, and g (all adjacent to the welds) because the nominal stress near the weld is most important, which means that the cross-sectional area at these locations must be known accurately. The average thickness of these four measurements was used to adjust the MTS-equipment load such that the desired nominal stresses would be achieved. Flatness (or out-of-straightness) measurements were made at all eight locations (a to h) of each specimen. A three-point support fixture was placed on a flat surface and the web of the specimen was placed on top of it. A dial gage m o u n t e d on a base plate was moved around on the flat surface to measure the distance between the fiat surface and the web plate at all eight locations. The measurements were put on a data file and a small computer program read the raw data, adjusted the measurements such that three corner points were in the same plane, and calculated the largest difference between this plane and the remaining locations of the web. This largest difference was recorded as the out-of-straightness dimension. Specimens with an out-of-flatness of more than & in were to be rejected. The top, bottom, front, and rear designations (T, B, F, and R) were also used to describe the weld toe locations at which fatigue cracks could initiate. Thus, the combined location designations FI', FB, RT, and RB, as shown in Figure 4, define the 'front top', 'front bottom', 'rear top', and 'rear bottom' locations of the fillet toes, respectively. Furthermore, the possible initiation
239
Fatigue life of tratm, erse stiffeners
IP REAR
[
I
I 14
FRONT
]
FT : F r o n t
top
O I~r = Rear too
Possible c r a c k initiation sites
web
Transverse
Possible c r a c k Initiation sites
RB : R e a r b o t t o m
FB = F r o n t
bottom
IP 1~. $. Specimen designations. (1 in = 25.4 mm.)
sites along the width of the specimens were designated as location numbers 0 through 4, starting with 0 at the left edge of the installed specimen, and ending with 4 at the right edge, as seen in Fig. 4 at the top. These location numbers represent the quarter points along the width of the specimen.
TEST SETUP The test setup was basically the same as for NCHRP Project 12-121 except that for constant-amplitude (CA) testing a 50-kip closed-loop hydraulic system (MTS) was used without the EMR load profiler. For variableamplitude (VA) testing the 300-kip closed-loop hydraulic MTS system and the EMR load profiler were used in the load-control mode.
240
Karl H. Klippstein, Charles G. Schilling
Time
Fig. 6. Partial load cellread-outfor Rayleighdistribution. Punched tapes that define 500 individual loads satisfying the Rayleigh and the 1974 Combined Truck Traffic probability-density curves shown in Figs 2 and 3, respectively, were prepared to control the variable-amplitude tests. The loads on each tape were arranged in random sequence. A portion of the load-cell read-out for the tape representing the Rayleigh distribution is shown in Fig. 6. Both ends of the tape were connected to provide a loop, allowing cycling of the 500-load-block tape continuously throughout a test.
TEST PROCEDURES In all CA and VA tests, the nominal dynamic stress at the weld toes was the main test parameter. This stress was directly proportional to the applied load, which was used to control the test, and the relationship between the two was established by a static calibration, which also entailed a gripping procedure. The stress caused by a given cyclic load is theoretically higher than the stress caused by a static load of the same magnitude, but for the given test conditions the difference was less than 1% and was neglected. The following detailed test procedures were developed to ensure repeatability and reduce the variability caused by equipment or operator: (1) (2) (3) (4)
specimen gripping procedure, static calibration procedure, procedures for CA and VA loading, and procedure for CA fatigue limit tests.
These procedures consisted of a very detailed description of each step the operator had to follow when installing the specimens or when conducting
Fatigue life of transverse stiffeners Grip line
241
Strain gages, Typ.
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~ m
N
3(4.) 5 6) ,Tee) [
HH 2 - I12'~n
•
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i
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Conversion f a c t o r 1in s 2 5 . 4 m m
Fig. 7. Pilot test specimenswith strain gages. (1 in = 25.4 ram.) the tests. Two specimens with twelve strain gages as shown in Fig. 7 were used to confirm these procedures through two pilot tests. The procedures and the pilot test results will not be reported here; however, a few brief comments on the procedures and results are made as they show some interesting findings.
Grippingprocedure The purpose of the gripping procedure was to ensure that the hydraulic grips would not cause a bending m o m e n t in the specimen because, if of significant magnitude, it would add considerable and variable bending stresses to the axial stresses imposed during testing. As a result, crack initiation would start much earlier, crack propagation would be faster, and the resulting fatigue life would not be representative of axial stresses only. The final gripping procedure developed included the entire sequence of steps necessary to turn the testing machine on, and---after all intermediate steps are taken---to turn the testing machine off. It showed that the bending stresses introduced by gripping can be significant. Under certain conditions, these stresses were found to be greater than the nominal axial stresses to be applied for the test when using the wrong sequence of locking or unlocking
242
Karl H. Klippstein, Charles G. Schilling
the swiveling heads of the hydraulic testing machine, or when using the locking procedure at the wrong time. The ability to utilize the readings of the twelve strain gages on both sides of the specimens was a significant aid to understanding the sequence of stresses introduced due to gripping, locking heads, and loading. For instance, when the heads were unlocked before gripping of the specimen commenced, the resulting bending stresses would be very small when the hydraulic axial load was zero, but they would sometimes be very high when the axial calibration load was at its maximum. This is because the heads of the hydraulic machine were aligned with the sloped ends of the distorted specimen when the applied axial load was zero, and the gripping process did not cause any bending stresses at that time. However, when the maximum calibration loads were applied, the distorted specimen tried to straighten out while the self-unaligned and locked machine heads could not, thus introducing a high bending stress at a time when the applied axial stresses were also high. Conversely, when a straight machined bar was used to align the machine heads before the specimen was inserted and gripped, the resulting stresses were significantly different. In this case, both the upper and the lower machine heads were unlocked, the specimen was inserted, locked at top and bottom, and an axial load was applied to align the heads. Under this load both heads were locked, the axial load was reduced to zero, and the machined bar was removed. When the slightly out-of-fiat specimen was inserted and gripped, the gripping stresses, without any externally applied load, were very high. However, when the maximum calibration load was applied, the specimen was straightened gradually and the bending stresses were substantially reduced. On the basis of these findings it was decided to align and lock both heads before installing, locking, and testing the specimen.
Static calibration procedure A static calibration procedure was developed because the initial load cycles in a welded specimen cause either residual-stress relief, or additional residual stresses. This results in a non-linear load-strain relationship during the first static load cycle(s) when operating the equipment in the loadcontrol mode. The procedure consisted of instructions that included re-zeroing the gages before or after each load step, what control buttons to use on the MTS console or the EMR (set point and span control), and what strain-gage readings to take during the first, intermediate, and last calibration load cycle.
Fatigue life of transverse su'ffeners
243
Procedures for CA and VA amplitude tests T h e results of the gripping and calibration procedures were used to develop the calibration and testing procedures for the constant- and variableamplitude test procedures. These were necessary because the number of strain gages for the specimens used in these tests was reduced to two gages (at gage locations 5 and 6, Fig. 7). Furthermore, the procedures for the constant-amplitude tests needed to be different from the variable-amplitude tests because the hydraulic systems were different and the E M R load profiler was not used during the constant-amplitude tests. Procedure for CA fatigue limit tests Plans to conduct tests that would determine the mean constant-amplitude fatigue limit were developed by using the modified (ASTM) staircase method. 6-a Using this method, the first specimen is tested at the expected fatiguelimit stress range. If the specimen does not fail after a predetermined n u m b e r of cycles (the investigators used a minimum of 5 million cycles but occasionally extended the number of cycles up to 15 million cycles), the stress range for the next sample is increased by an increment (the investigators initially used 2ksi increments, but after the second increment was completed, 1 ksi was used). If the specimen does fail, the stress range for the next specimen is decreased by an increment. Further details of this methodology, and especially the evaluation procedure required to obtain the mean fatigue limit, will now be described in more detail along with the presentation of the test results.
TEST RESULTS All test results are recorded in Tables 2-5, and in Figs 8-10. The results of the pilot tests are not shown. As shown in the tables, a minimum static stress of S~i. = 2 ksi was applied to all specimens before the fatigue stress ranges, Sr, were added. This was done to ensure that the specimens were always under slight tension even when the individual stress ranges returned to zero. The maximum stress for the constant-amplitude tests, S,~, is equal to the m i n i m u m static stress, S~i,, plus the constant-amplitude stress range, St, which is equal to, and shown as, the effective stress range, S~rt. For all variable-amplitude fatigue tests, the minimum stress range of S~in shown in Fig. 2 was equal to zero. Thus, the modal stress range, S.,, shown
244
Karl H. Klippstein, Charles G. Schilling TABLE 2 Constant-Amplitude Fatigue Test Results for Transverse Stiffener Specimens
Stres~ Specimen no.
Stain
S~
S,eff
Out-of-
Number of
flatness
full
Crack initiation
(in)b
cycles
F/Dc
2 067 000 3 638 830 8000000 10 000 000 5 000 000 5 080 000 2 429 080 5 000 000 5 000 000 1853 930 5000000 2 986 710 5000000 1 581 290 2 670 370 2 640 940 5 000 000
F F D D D D F D D F D F D F F F D
Not recorded Front, 0-4 No visible crack No visible crack No visible crack No visible crack Front, 2--4 No visible crack No visible crack Not recorded No visible crack Front, 4 ~in at 4 Rear, 0-4 Rear, 0-2 Rear, 2--4 No visible crack
location d
(A) Tests to establish constant-amplitude fatigue limit 62 68 101 75 109 65 72 66 73 124 115 94 100 89 112 120 79
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
21.0 19.0 17-0 18-0 19.0 20.0 21.0 20.0 21-0 22.0 21.0 22.0 21.0 22.0 21.0 20.0 19.0
19.0 17.0 15.0 16.0 17.0 18-0 19-0 18.0 19.0 20.0 19.0 20,0 19.0 20.0 19.0 18.0 17-0
0.008 5 0.002 9 0.005 8 0.007 5 0.IX)2 9 0.004 1 0.005 1 0-014 3 0-003 0 0.004 5 0.0109 0.005 5 0-0050 0.004 6 0.002 5 0-006 1 0.002 5
(B) Tests to establish sloped constant-amplitude fatigue curve 90 97 82 70 84 122
2.0 2.0 2-0 2.0 2.0 2.0
26-5 26.5 26.5 26.5 26.5 26.5
24-5 24.5 24.5 24.5 24.5 24.5
0.003 1 0.010 0 0-009 5 0.012 9 0.003 0 0-009 0
1 056 520 938 770 826 580 1 030 760 859 460 777 940
F F F F F F
Rear, 0--4 RT, 0--3; FB, 4 Rear, 1 Front, 4 Front Front & Back
114 108 64 106 111 123
2.0 2-0 2.0 2.0 2-0 2.0
49-0 49.0 49.0 49.0 49.0 49.0
47.0 47.0 47.0 47.0 47.0 47.0
0.010 1 0.003 4 0.010 5 0-016 0 0.003 9 0.008 2
55 120 55 140 54 990 79 350 62 560 86 630
F "F F F F F
Front, 0-4 Front, 0-4 Front, 2-3 Front, 0-4 Rear, 0-1 Rear
"(see also Fig. 2. ) minimum static stress, Smi. = 2 ksi for all tests; minimum stress range, Stain -- 0 for all tests, ksi; maximum stress, Smax = Srnin+ Srmax,ksi; maximum stress range, S~m~ = Srcn = Sm~ - Smi,; S,eff = effective stress range, ksi. h Defined as the out-of-plane dimension of any one of eight points measured on the web plate in the Z direction, while at least three of the four comers of the specimen are in a cormnon X - Y plane. "F = Failure (total separation, two parts), or D = Discontinued. 'lFailure locations are defined in the figures. All failures are initiated at the fillet weld toes. Based on shown in shown in deviation
the modified staircase method, the stress-range fatigue limit derived from the data Part A is equal to 18.2 ksi. Based on a linear regression analysis for the results Part B. the log (S-N) slope is -4.062. the intercept is 11.601. and the standard error is 0.0729.
245
Fatigue life o f trann, erse snffeners
TABLE 3 Variable-Amplitude Fatigue Test Results for Transverse Stiffener Specimens
Specimen no.
Stress ~ Srnin
Srnax
Sr~/
Out-offlatness (in) b
Number of full cycles F/D ~
104
2-0
42.6
21.8
0.(~7 5
1 811 550
F
From, 0-4
93 99 96 81 98
2.0 2.0 2.0 2.0 2.0
36.3 36.3 36.3 36.3 36.3
18.4 18-4 18.4 18.4 18.4
0.015 0 0.006 2 0.015 9 0-0048 0.008 0
3 115 150 2 078 200 2 781900 1 870 600 3 182 250
F F F F F
From, 0-4 Front, 0-3 Rear, 0--4 Front/rear Rear, 0-4
77 105 125 117
2.0 2.0 2.0 2.0
27.8 27.8 27.8 27.8
13.8 13.8 13-8 13.8
0.004 0 0.012 8 0.009 6 0.0063
14 979 550 8 060 700 15 523 200 10914450
F F F F
Rear, 0-3 Front, 0--4 Top, 0-1 Bottom, 0-4
Crack initiation location d
(See also Fig. 2 and notes of Table 2) aSmi, = minimum stress, ksi; Sma~= maximum stress, ksi; with Sr~n = 0.538 ( S ~ Smi,) = effective Miner stress range, ksi, based on a log (S-N) constant-amplitude finite-life curve with a slope of -4-062, as obtained from data under Part B of Table 2, assuming the CA fatigue limit has no effect. bDefined as the out-of-plane dimension of any one of eight points measured on the web plate in the Z direction, while at least three of the four comers of the specimen are in a common X - Y plane. CF = Failure (total separation, two parts), or D = Discontinued. alLocations defined in Fig. 5. in Fig. 2, is e q u a l to Srd, which is a m e a s u r e o f the dispersion o f the s t r e s s - r a n g e s p e c t r u m . ~ F u r t h e r m o r e , since the total dispersion (width) o f t h e stress r a n g e s p e c t r u m used is 3Srd (or e q u a l to the m a x i m u m stress r a n g e , Srma~, s h o w n in Fig. 2), the m a x i m u m stress, Sin,, s h o w n in T a b l e 3, is the sum o f Stain a n d S,n~. T h e effective stress r a n g e for the v a r i a b l e - a m p l i t u d e tests s h o w n in T a b l e 3 was calculated b y using the slope o f the finite-life c o n s t a n t a m p l i t u d e tests s h o w n in T a b l e 2.
CA fatigue limit tests P a r t A o f T a b l e 2 shows the results o f the c o n s t a n t - a m p l i t u d e fatigue tests c o n d u c t e d to d e t e r m i n e the m e a n fatigue limit. W h i l e the tests p r o g r e s s e d , t h e d a t a s h o w n in T a b l e 5 and in Figs 8 and 9 w e r e d e v e l o p e d to follow the specified p r o c e d u r e . B e f o r e testing c o m m e n c e d , it was a s s u m e d that the f a t i g u e limit w o u l d b e b e t w e e n 17 and 19 ksi. T h e first test was c o n d u c t e d at a stress range o f 19 ksi a n d the s p e c i m e n
246
Karl H. Kh'ppstein, Charles G. Schilling
TABLE 4 Constant-Amplitude Fatigue Test Results Arranged in Ascending Order of Out-of-Flatness
Specimen no.
Stress" Smm
Sm~x
S,~l~
Out-offlatness (in) b
101
2.0
17.0
15.0
0.005 8
8 000 000
D
No visible crack
75
2.0
18.0
16.0
0.(XY75
10 000 000
D
No visible crack
79 68 109
2.0 2.0 2.0
19.0 19.0 19-0
17.0 17.0 17.0
0.002 5 0.(102 9 0.002 9
5 000 000 3 638 830 5 000 000
D F D
No visible crack Front, 0-4 No visible crack
65 120 66
2.0 2.0 2.0
20-0 20.0 20.0
18.0 18.0 18.0
0.004 1 0.006 1 0.014 3
5 000 000 2 640 940 5 000 000
D F D
No visible crack Rear, 2-4 No visible crack
112 73 100 72 62 115
2-0 2.0 2.0 2.0 2.0 2.0
21-0 21.0 21.0 21.0 21.0 21.0
19.0 19.0 19.0 19.0 19.0 19.0
0.002 5 0-003 0 0.005 0 0.005 1 0-008 5 0.010 9
2 670 370 5 000 000 5 000 000 2 429 080 2 067 000 5 000 000
F D D F F D
Rear, 0-2 No visible crack ~ in at 4 Front, 2-4 Not recorded No visible crack
124 89 94
2.0 2-0 2.0
22.0 22.0 22.0
20.0 20.0 20-0
0.004 5 0-004 6 0.005 5
1 853 930 1 581290 2 986 710
F F F
Not recorded Rear, 0--4 Front, 4
84 90 122 82 97 70
2.0 2.0 2.0 2-0 2.0 2.0
26.5 26.5 26.5 26.5 26.5 26.5
24.5 24.5 24-5 24.5 24.5 24.5
0.003 0 0.003 1 0.009 0 0.009 5 0.010 0 0.012 9
859 460 1 056 520 777 940 826 580 938 770 1030760
F F F F F F
Front Rear, 0-4 Front & Back Rear, 1 T/R 0-3, B/F 4 Front, 4
108 111 123 114 64 106
2.0 2-0 2.0 2.0 2-0 2-0
49.0 49.0 49.0 49.0 49.0 49-0
47-0 47-0 47.0 47.0 47.0 47-0
0.003 4 0.003 9 0.008 2 0-010 1 0-010 5 0.0160
55 140 62 560 86 630 55 120 54 990 79 350
F F F F F F
Front, 0--4 Rear, 0-1 Rear Front, 0--4 Front, 2-3 Front, 0--4
(See notes of Table 2)
Number of ~ll cycles F/ D c
Crack initiation location d
247
Fatigue life of transverse stiffeners TABLE 5 Calculation of Fatigue Limit by Modified Staircase Method
Specimen number
Stress range, Sr, ksi
1 2 3 4 5
62 68 101 75 109
19 17 15 16 17
6 7 8 9 10
65 72 66 73 124
11 12 13 14 15 16 17
Test number
Sum of SrS (ksi) b
Number of tests~ .
.
.
Modified sum of Srs (ksi) c
Average Sr (ksi) a
.
1 2 3 4
17 32 48 65
-33 49 66
-16.50 16-33 16-50
18 19 18 19 20
5 6 7 8 9
83 102 120 139 159
84 101 121 140 158
16.80 16.83 17-29 17.50 17.56
115 94 100 89 112
19 20 19 20 19
10 11 12 13 14
178 198 217 237 256
179 197 218 236 255
17.90 17.91 18-17 18-15 18.21
120 79
18 17
15 16
274 291
273 292
18-20 18.25
Mean fatigue limit (rounded off):
18.2
a Last test prior to first reversal is chosen as # 1. bAccumulation of stress ranges used. CWhen the next stress level would be increased, 1 ksi is added to the sum of stresses; when the next stress level would be decreased, 1 ksi is deducted. dAverage stress = (modified sum of stress ranges)/(number of tests conducted).
failed at about 2 million cycles. The required entries were made in Table 5, and an X was entered on Fig. 8. Table 5 summarizes the test number, specimen number, etc., and other information as explained in the table. Figure 8 is a plot of the test n u m b e r versus stress range. Because the first specimen failed, the stress range for the second specimen was lowered to 17 ksi, and the specimen failed at about 3.6 million cycles. Table 5 and Fig. 8 were updated, and the third test was conducted at a stress range o f 15 ksi. Test 3 did not fail at 5 million cycles and was eventually discontinued at 8 million cycles. Therefore, a circle was entered in Fig. 8, and the stress range for the fourth specimen was increased to 16 ksi. All further stress-range changes from then on were m a d e by using 1 ksi increments.
248
Karl H. Klippstein, Charles G. Schilling
21
x
x
x
u
\
m
= 17 o m 16
14
I
I
I
I
I
I
I
1
2
3
4
S
6
7
I
I
I
8 9 10 Test n u m b e r
I
I
I
I
I
I
I
I
tl
12
t3
t4
15
16
17
18
Fig. 8. Graphic bookkeeping of staircase tests. (1 ksi = 6.895 MPa.)
19
O
O
E e
rl
b.
16 0
I
I
I
I
I
I
I
1
2
3
4
5
6
7
I
I
8 9 Test number
I
I
I
I
I
I
I
I
I
10
11
12
13
14
15
16
17
18
Fig. 9. Variation of fatigue limit. (1 ksi = 6-895 MPa.)
Since Test 3 constituted a reversal in the trend from decreasing to increasing stress ranges, the average stress range in the last column of Table 5 was used to start Fig. 9, which is a plot of the test number versus the average stress range. Further steps taken to conduct additional tests, the stress-range levels used, and the number of cycles applied, are as shown in Table 5 and in Figs 8 and 9. All tests follow the above logic.
Fatigue life o f transverse st/ffeners
9 8 7 G
249
Mean f a t i g u e
Mean finite-life curve
I
\
a~ 4
____
\ _
4.
3
2
2
x e-
AASHTO c a t e g o r y C'
~ ~ tp
9 e 7
0 .~
5 4
~
3
W
2
10 0 lO 4
log iN) : 1 1 - 6 0 1 - 4 - 0 6 2 log ( S r e f f ) S t a n d a r d e r r o r = 0<)729 ( f o r 12 d a t a p o i n t s ) F o r AASHTO c a t e g o r y C', log (N) = 9 . 5 6 6 - 3 . 0 log (St') log (St.) = log ( S r e f f ) f o r C.A. ,
2
,
,
.
, ,,,I
~
I
. . . . . .
~ , 56~8~1oe
Cycles to failure
O0
12
Convet . sl on f a c t o r l k s l = 6 . 8 9 5 MPa
. . . . . .
3 .$67.~
~
~
I
~ , 56~--1o7
~
(N)
Fig. 10. Results f o r C A tests. (1 ksi = 6-895 MPa.)
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M e a n log S - N c u r v e f r o m Fig. 10
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250
Karl H. Klippstein, Charles G. Schilling
As seen from Table 5 and Fig. 8, seventeen specimens were tested and resulted in a mean constant-amplitude fatigue limit, S~, of 18.2 ksi. This value was essentially reached after Test 13, and is significantly higher than the fatigue stress range of 12 ksi allowed by the A A S H T O specifications for transverse stiffeners. Finite life CA tests
Since the constant-amplitude fatigue limit had been established previously at a stress-range level of S~ = 18.2 ksi, it was decided to conduct tests at Sre stress ranges of 24.5 and 47.0 ksi, which correspond to Sro/S~ levels of 1.35 and 2.58, respectively. Six tests each were conducted at both stress levels. The results of these tests were used to determine the slope and intercept of the finite-life portion of the S-N curve. As shown in Fig. 10, the slope is -4.062, the intercept is 11-601, and the standard error is 0.0729. The slope of -4.062 is substantially different from the results of other welded fabrication details, which generally have a slope of about -3-0. This difference may be attributed primarily to the fact that the fabrication of the specimens was carefully controlled, which tends to influence the slope of the S-N curve and reduce the standard error. Variable amplitude tests
Ten tests were conducted with a truncated Rayleigh probability density distribution, which was subdivided into 500 randomly arranged load levels. The results are shown in Table 3 and in Fig. 11. Only one test was conducted at an effective stress range, S~n, of 21.8 ksi. This test corresponded to an S~n/S, ratio of 1.20. The life of 2 067 000 cycles is higher than 1 459 000 cycles predicted by the constant-amplitude S-N curve, but within the 95% confidence limit. Five tests were performed at an effective stress range of 18.4 ksi, which corresponds to an Sroer/S,ratio of 1.01. The log-mean life for these tests was 2 547 000 cycles, as compared with a mean life of 2 906 000 cycles predicted from the constant-amplitude S-N curve. Four tests were made at an effective stress range of 13-8 ksi, which corresponds to an S~e~/S, ratio of 0.76. The log-mean life for these tests is 11 960 000 cycles, which is higher than 9 350 000 cycles predicted by the extension of the constant-amplitude finite-life S - N curve. Because the log-mean value of four tests is compared with the extension of the constantamplitude finite-life S-N curve, the difference appears to be significant. This means that the fatigue life predicted by the finite-life portion of the constant-amplitude fatigue curve is over-conservative (resulting in lower
Fatigue life of transverse stiffeners
251
fatigue lives than those actually attained), and is not realistic if a substantial part of the variable-amplitude stress-range spectrum is located below the constant-amplitude fatigue limit. Consequently, a more realistic approach to predict the variable-amplitude fatigue life for such conditions is needed. One approach, which neglects all damage of stress ranges with peaks below the constant-amplitude fatigue limit, ~'4 offers a possible and more accurate fatigue-life prediction method. Hopefully, this method will be substantiated by ongoing variable-amplitude tests at the University of Pittsburgh and at the University of Maryland. Out-of-flatness and gripping effect checks To check if the out-of-flatness of the specimens, or the gripping procedure adopted, had any effects on the fatigue life, the constant-amplitude fatigue test results were arranged in ascending order of out-of-flatness and grouped by the applied stress ranges, as summarized in Table 4. Based on the data shown, there appears to be no evidence that the out-of-flatness, as experienced in the specimens tested, consistently significantly affected the fatigue life. Higher out-of-flatness measurements were expected to introduce higher out-of-plane bending stresses and cause earlier crack initiation and fatigue failure; however, the minimization of the actual out-of-flatness achieved assured that the test results were not biased by this parameter. Table 4 also gives an indication of the gripping effects when the last column is investigated more closely. Since there appears to be no dominance of crack initiation locations at the front, rear, top, or bottom weld toes, it is concluded that gripping effects, which could have introduced additional bending stresses during the tests, were essentially eliminated.
CONCLUSIONS The results of a carefully conducted study of the fatigue life of transverse stiffeners welded to the web of steel bridge girders are presented. This study includes meticulous procedures to fabricate the test specimens so that test result variations due to out-of-flatness, which may cause additional bending stresses, and residual-stress effects would be reduced as much as possible. Also, gripping procedures were carefully developed and observed because they may result in additional bending stresses which could distort the test results. These effects were essentially eliminated and did not appear to affect the results of the study.
252
Karl H. Klippstein, Charles G. Schilling
Based on twenty-nine constant-amplitude tests conducted, the slope of the finite-life portion of the S - N fatigue curve is -4-062, which is different from the slope of - 3 usually encountered in welded steel specimens.. The difference is attributed to the more careful fabrication procedure used. The fatigue limit determined by the modified staircase method was found to be 18.2 ksi. Ten variable-amplitude fatigue tests were conducted at effective stress range to constant-amplitude fatigue limit ratios of 1.20, 1.01, and 0.76. The results appear to indicate that stress cycles below the constant-amplitude fatigue limit do not significantly contribute to the fatigue life. Ongoing variable-amplitude fatigue tests presently being conducted at the University of Pittsburgh and at the University of Maryland will hopefully provide an improved method to predict the fatigue life for any load spectrum encountered in welded steel bridges.
REFERENCES 1. Schilling, C. G., Klippstein, K. H., Barsom, J. M. & Blake, G. T., Fatigue of welded steel bridge members under variable-amplitude loadings. National Cooperative Highway Research Program, Report 188, Transportation Research Board, Washington, DC, USA, 1978. 2. American Association of State Highway and Transportation Officials, 1lth edn, 1973, with Interim Specifications, 1974--80. 3. Klippstein, K. H. & Romito, P. A., Variable amplitude load fatigue, Task A---Literature review, Volume II, Constant-amplitude fatigue behavior. US Department of Transportation, Federal Highway Administration, Washington, DC 20590, USA, December 1987. 4. Albrecht, P. & Rubeiz, C. G., Variable amplitude load fatigue, Task A--Literature review, Volume III, Variable-amplitude fatigue behavior. US Department of Transportation, Federal Highway Administration, Washington, DC 20590, USA, December 1987. 5. Schilling, C. G., Variable amplitude load fatigue, Task A--Literature review, Volume I, Traffic loading and bridge response. US Department of Transportation, Federal Highway Administration, Washington, DC 20590, USA, December 1987. 6. American Society for Testing and Materials, A Guide for Fatigue Testing and the Statistical Evaluation of Fatigue Data. ASTM Special Technical Publication No. 91-A, 2nd edn, ASTM, Philadelphia, PA, USA, 1963. 7. Reemsnyder, H. S., Procurement and analysis of structural fatigue data. J. Struct. Div., ASCE, ST7 (July 1969). 8. Committee on Fatigue and Fracture Reliability of the Committee on Structural Safety and Reliability of the Structural Division, Fatigue reliability: variable amplitude loading. American Society of Civil Engineers, J. Struct. Div., ASCE, ST7 (January 1969).