Structural Engineering
KSCE Journal of Civil Engineering Vol. 10, No. 3 / May 2006 pp. 207~217
Fatigue Evaluations of Variable Message Sign Structures Based on AASHTO Specifications By Jong Sup Park* and J. Michael Stallings** ···································································································································································································································
Abstract Variable Message Signs (VMS) have become a new trend in roadway signs. These signs offer an increase in traffic safety by their ability to relay messages to motorists for warnings of hazards ahead such as fog, traffic congestion, accidents, and lane closings. The geometry of these signs sometimes results in significant cyclic loading of the support structure due to wind gusts. This study presents analytical and experimental investigations of bridge-type VMS structures. GTSTRUDL (2003) is used to perform space frame structural analyses of these welded tubular structures. This paper includes measurements from a static filed test and comparisons between the measurements and the structural analyses results. Fatigue evaluations are performed based on the stress ranges from field measurements and structural analyses. According to this comparative study, the fatigue design loadings derived from AASHTO Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals (2001) can be conservatively used to evaluate the fatigue life of the bridge-type VMS structures. Keywords: variable message sign, fatigue evaluation, field test, wind load ···································································································································································································································
1. Introduction Variable Message Signs (VMS) have become a new trend in roadway signs. These signs offer an increase in traffic safety by their ability to relay messages to motorists for warnings of hazards ahead such as fog, traffic congestion, accidents, and lane closings. These signs can also be equipped to monitor traffic speed and flow. The VMS panels are generally installed over traffic lanes on heavily traveled roadways such as interstates and major highways. These sign panels are relatively heavy and larger when compared to a typical flat panel signboard. The increase in size and weight results in greater wind load and inertial effects. Natural winds are a major cause of horizontal vibrations in these structures. Trucks passing beneath these signs create wind gusts, which produce loading on the VMS both in the upward direction and in the direction of traffic flow. As a result, these VMS structures are subjected to large number of loading cycles that can result in fatigue cracking. The AASHTO Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals (1994) offer little guidance in the design for fatigue. Until the recent version of AASHTO Specifications (2001) became available, designers did not have sufficient direction for fatigue related design of signs, signals and luminaire support structures. As a result, some cantilevered sign and signal support structures have exhibited excessive displacement due to wind-induced vibration and have failed because of fatigue cracking. According to AASHTO Specifications (2001), sign, signal, and luminaire support structures are designed to resist fatigue caused by each of the applicable equivalent static wind load
effects. Stress ranges due to these loads on all components, mechanical fasteners, and weld details are designed to satisfy the requirements of their respective detail categories with the constant-amplitude fatigue thresholds given in the specifications. Accurate load spectra and life prediction estimates for defining fatigue loadings are typically not available for designers. Moreover, the assessment of stress histories and the corresponding lifetime wind loading histograms are practically impossible. As a result, the design of support structures for a finite life becomes impractical; therefore, an infinite-life fatigue design approach is recommended.
2. Research Scope and Objectives Significant vibration of a bridge-type VMS structure on a highway shown in Fig. 1(a) was reported by a department of transportation officials. A fatigue evaluation of the Structure-A became a primary goal of this study. The potential failure mode was fatigue cracking at the welded connections of the tubular members of the structure. An analytical and experimental investigation began by performing preliminary structural analyses to determine locations of high stress ranges due to the fatigue design loads. The analytical results were used in planning the field instrumentation. The members were then instrumented with strain gages and monitored for an extended period to evaluate the structural response to natural wind and truckinduced gusts. The nominal stress ranges were measured at these strain gage locations to determine if the stress ranges were large enough to eventually result in fatigue cracking. A second primary goal of the research reported here was to
*Member, Assistant Professor, Department of Civil and Environmental Engrg., SangMyung University, Korea (Corresponding Author, E-mail:G
[email protected]) **Professor and Head, Department of Civil Engineering, Auburn University, Auburn, AL36837, USA (
[email protected]) Vol. 10, No. 3 / May 2006
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Fig. 1. Bridge-Type Sign Structures Investigated
investigate the applicability of the fatigue design provisions in the AASHTO Specifications (2001) to bridge-type structures. The fatigue design provisions of the AASHTO Specifications (2001) were developed for cantilever sign structures, but can be applied to bridge-type structures. The structure-A and another VMS (structure-B) shown in Fig. 1 were used as example structures for application of the AASHTO provisions. Both of these structures were designed before AASHTO Specifications (2001) were published.
3. Background and Previous Works Some transportation departments have had problems with cantilever VMS structures such as excessive vibration and fatigue. There was a collapse in 1993 of a VMS in Virginia, USA that was believed to be the result of fatigue cracking due to truckinduced wind gusts. Truck-induced wind gusts were also suspected to be the cause of excessive vibration of VMS structures in New Jersey and Florida, USA (Dexter and Johns, 1998). The VMS have been installed on support structures originally intended to support only flat panel signs that weigh much less than the VMS. This was done without making calculations of the effect of the additional load and area of the VMS. The additional mass was thought to cause problems. However, engineers have assumed that the mass only adds to the dead load and can be mitigated by increasing the stiffness of the supporting structure. Therefore, the additional exposed area of the sign is believed to cause the fatigue problems (Dexter and Ricker, 2002). AASHTO Specifications (2001) define four types of wind loading phenomena that are critical with respect to the design for vibration and fatigue of sign, signal, and luminaire support structures. These are 1) galloping; 2) vortex shedding; 3) natural wind gusts; and 4) truck-induced wind gusts. The bridge-type
VMS support structures are not expected to be susceptible to galloping and vortex shedding due to the torsional rigidity of the sign bridge. However, the bridge-type support structures may be susceptible to natural wind gusts and truck-induced wind gusts. The application of complex dynamic wind loads is simplified in AASHTO Specifications (2001) using equivalent static loads. Although these fatigue loadings were developed for use on cantilevered support structures, the commentary of AASHTO Specifications (2001) specifies that these loads can be applied to bridge-type structures until more appropriate loadings are developed. These equivalent static loads are considered limitstate fatigue loads. Fatigue limit-state stress ranges induced by dynamic wind loads are estimated with static loads that would create similar stress responses. Therefore, a simple static analysis is conducted by designers and the resulting stresses represent stress ranges. These stress ranges are limited to the appropriate constant-amplitude fatigue limit (CAFL) to ensure infinite life of the structure. The infinite life is often interpreted to be a fatigue life greater than the typical service life of the structure, usually 50 years in the case of cantilever signal, sign, and luminaire support structures. Infinite life only occurs if practically all stress ranges due to constant-amplitude or variable amplitude loading are below the CAFL. The number of cycles at each applied stress range is required to calculate an effective stress range. Theoretically, a complete histogram of the loading events for all events during the life of the structure is needed. This is practically impossible to obtain. Hence, field measurements are typically made for a period sufficient to represent the entire service life of the structure.
4. VMS Structure Geometry The structure-A is a four-chord box-pipe truss with fillet welded tubular members as the web of the truss. The truss spans over all six lanes of traffic; three northbound lanes and three southbound lanes with a median between them. The truss consists of four sections connected at each of the four chords by transverse plates bolted together and is geometrically similar about the midspan connection. The horizontal truss is supported at each end by a vertical two post truss support. The two bottom chords of the truss rest on a horizontal member made from a WTsection that spans between two vertical support posts. The bottom chords of the truss are bolted to the WT-section using Ubolts while the two top chords are connected to either vertical post also using U-bolts. The VMS is centered over the three northbound lanes at 5.8 m above the roadway and is attached to W6x9 hangers bolted to the front two chords with U-bolts. The truss of the structure-B consists of three equal sections connected at the four chords by transverse plates bolted together. All connections are similar to the structure-A with the exception of the truss-to-vertical support connection. The vertical support posts do not extend up to the top two chords of the truss so there is no connection between the top two chords and the vertical supports. The two bottom chords rest on the WT-section and are bolted down using U-bolts. The VMS is centered over the four northbound lanes of traffic.
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Fatigue Evaluations of Variable Message Sign Structures Based on AASHTO Specifications
5. Instrumentations and Data Acquisition For convenience and ease of referencing different locations on the VMS structures, the vertical side facing the VMS will be denoted as the front plane. The notations back, top, and bottom will be used to describe the other three planes of the box truss structure relative to the front side. 5.1 Strain Gage Locations The support of the structure-A is geometrically similar on each side of the chord splices at midspan. Strain gages were installed only on the right half. Fig. 2 illustrates the locations of the strain gages. Twenty-six electrical resistance strain gages were installed on 10 members of the structure. These members provide a representative sample of locations where fatigue cracking may occur, and include three of the four main truss chords, diagonals and struts in the truss and supports, and the horizontal WTsection on which the truss is supported. Once these were identified by structural analyses as highly stressed members, a closer review of the analyses results was made to identify where the largest stresses occurred. Gage locations on the structure were chosen to measure nominal stress ranges for use in
predicting fatigue life. The gages were located as close to the ends as possible because the nominal stresses are highest at member ends. However, stress concentrations are prevalent near the welds at the connections; therefore, the gages were installed a short distance away from the member ends as illustrated in Fig. 4. On the diagonal and strut members, the strain gages were placed two outside member diameters (2OD) from the member ends. Two gages were installed on each of the diagonal and strut members on diametrically opposite sides of the circular cross sections (i.e. top and bottom and/or front and back sides of the member). Four gages were installed on each of the main chords at intervals 90 degrees apart around the circumference of the cross section. These strain gages were installed 102mm from the toe of the welds around the member at the chord splices. Two gages were installed on the WT-section. Due to the location of the truss chords bearing on the WT-section, these gages were placed 25.4 mm from the end of the member, too close to avoid the stress concentration effect. The structure-B had a shorter span length compared to the structure-A and all members were accessible for instrumentation. Fourteen strain gages were installed on five members on the
Fig. 2. Diagram of Strain Gage Locations for Right Half of Structure-A
Fig. 3. Diagram of Strain Gage Locations on Structure-B Vol. 10, No. 3 / May 2006
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Fig. 4. Detail of Strain Gage Placement on Chords and Diagonals
structure as shown in Fig. 3. Two of the four chords at a splice connection, and three diagonal members were instrumented in the same manner as the structure-A. 5.2 Wind Anemometer and Data Acquisition System A wind anemometer (model 5103V) by RM Young Company was used to continuously record wind speed and direction. This device was monitored with the data acquisition system so that wind data could be stored with the strain data in the datalogger. The anemometer was programmed to output wind speed and direction in miles per hour and degrees using a three-second averaging time. A CR9000 data logger by Campbell Scientific company measured and recorded the stress ranges at all strain gages on the structure. Two external 12-volt batteries powered the data logger. The batteries allowed the system to run unattended for approximately six days; therefore, fully charged batteries were swapped out every six days. Recorded data was downloaded from the logger’s internal memory card each time, and the batteries were swapped out to ensure the program was running properly. The data acquisition system recorded data according to the program instructions input by the operator. The type of data recorded varied depending on the test performed. Time history data was recorded during the calibration and random truck tests and during the pull down test. During continuous monitoring, the system was programmed to perform a rainflow counting algorithm that recorded strain cycles and output a strain cycle histogram every 15 minutes for each gage. The logger stored the individual strain cycle magnitudes in histograms with interval sizes of 8 microstrains. For all strain gage measurements, the data logger was set at a sampling rate of 83.3 Hz.
calibrated in the lab using a load testing machine and a strain indicator. A linear relationship between measured strain and applied load was established during calibration. The load cell was then implemented in the field test to measure the applied loads as shown in Fig. 5(a). The deflections at the midspan connection were measured using a deflectometer attached from the ground to each bottom chord using a small diameter steel wire as shown in Fig. 5(b). The static load test consisted of applying a vertical load near midspan of the structure by using a cable, a pulley, and a hand winch attached to a stationary truck parked in the median. During this test, one person manually loaded and unloaded the structure using the hand winch while a second person recorded the applied load from the strain reading of the load cell as shown in Fig. 5(c). There was also an operator on the shoulder of the highway recording strain data for all of the gages using a laptop computer connected to the data logger as shown in Fig. 5(d). The data logger was programmed to record time history data throughout
6. Static Pull Down Field Test (Structure-A) The objective of the static pull down loading test was to investigate the accuracy of a standard space frame structural analyses of the tubular structure using GTSTRUDL (2003). To achieve this, load increments were applied to the structure, and measurements of the resulting strains and displacements were made. Prior to the static tests, structural analyses were performed to verify that the structure would not be stressed beyond design allowable stresses by a test load of 13.4 kN. Maximum stresses due to the test loading were less than 8% of the yield stress and less than 13% of the allowable stress. 6.1 Testing Preparation and Procedure A load cell was fabricated, instrumented with strain gages, and 210
Fig. 5. Pull Down Field Test KSCE Journal of Civil Engineering
Fatigue Evaluations of Variable Message Sign Structures Based on AASHTO Specifications
the entire duration of the test. For all strain measurements, the data logger sampled the strain gages continuously at 20 Hz and output an average reading at 2 Hz. Five trials of the static pull down test were performed. Once the target maximum load was reached, the loading was decreased and held at a minimal load before the structure was completely unloaded. In GTSTRUDL, three-dimensional beam elements were used to model the cylindrical pipe members of the support structures. There was an offset between the centroid of the chords and the centroid of the WT-section, so the connections of the truss to the vertical supports were modeled using rigid beam elements to connect these members. The anchor bolts, foundation, and soil conditions were not considered in the analyses. Instead, the base of the vertical supports was defined as the bottom of the post and modeled as completely fixed. 6.2 Pull Down Field Test Results Fig. 6 and 7 graphically compare the predicted and measured stresses and deflections for trials 1 and 2 of the static pull down loading test. The stresses and deflections measured during trials 2, 3 and 4 match best with the structural analyses results. Plots
for trial 1 in Fig. 6 and 7 show some nonlinear behavior during the trial. The nonlinear responses are believed to have resulted from seating of the bolted connections and limited local yielding at the welded connections of the tubular members. Conditioning of the structure by applying one cycle of the test loading prior to recording data would have eliminated the confusing data, but this did not appear to be the safest approach to performing the tests. The stresses in the chords were the largest measured responses and matched very well with the stresses calculated from by the structural analyses (Fig. 6(a), (b), (c),and (d)). Table 1 provides comparisons of measured and calculated stresses in the chords. Table 2 shows vertical deflections at midspan for the highest load applied in each trial. The values listed indicate that the calculated values were typically larger than the measured values. Ratios of the measured stress to the calculated stress are shown for each measurement. The plots of Fig. 6(e), (f), (g), and (h) for diagonal and strut members show significant deviations from the predicted stresses in members that experienced low levels of stress. This is apparent in many of the diagonal and strut members where the maximum measured stresses were typically below 1.4 MPa.
Fig. 6. Calculated and Measured Load versus Stress during Pull Down Load Test Vol. 10, No. 3 / May 2006
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Fig. 7. Calculated and Measured Load versus Deflection during Pull Down Load Test Table 1. Peak Load Comparisons at Main Chord Members (Stress, MPa)
Member Gage
Trail 1
Trial 2
Peak Load: 12.0 kN
Peak Load: 13.4 kN
FEM Front Top Chord
Back Top Chord
Back Bottom Chord
Test
Ratio
FEM
Test
Ratio
1
-14.6
-11.6
0.80
-16.3
-10.8
0.66
2
-16.8
-12.1
0.72
-18.8
-16.1
0.86
3
-17.7
-17.7
1.00
-19.8
-19.4
0.98
4
-13.7
-11.6
0.85
-15.3
-16.1
1.05
1
-14.5
-15.3
1.06
-16.2
-14.3
0.88
2
-17.7
-12.2
0.69
-19.9
-15.6
0.78
3
-15.9
-15.8
1.00
-17.8
-17.1
0.96
4
-16.3
-12.5
0.77
-18.3
-16.7
0.91
1
24.9
18.0
0.72
27.9
22.2
0.80
3
12.5
12.1
0.97
14.0
14.6
1.04
4
18.4
18.8
1.02
20.6
19.9
0.97
Table 2. Peak Load Comparisons at Main Chord Members (Deflection, mm)
Member
Trail 1
Trial 2
Peak Load: 12.0 kN
Peak Load: 13.4 kN
FEM
Test
Ratio
FEM
Test
Ratio
Front Chord
18.8
10.2
0.54
20.8
19.3
0.93
Back Chord
18.5
9.1
0.49
20.8
19.8
0.95
7. Field Tests and Fatigue Evaluation The primary goal of the field tests was to measure nominal stress ranges in representative members of the sign support structures due to natural wind gusts and truck-induced gusts to determine if these members were susceptible to fatigue cracking in the future. Time history strain data was recorded in short time increments on several occasions while the structure was stationary to determine the range of electronic noise in the gages.
The noise in the gages was determined to be approximately 5 microstrains, and measured cycles of this magnitude were not counted in the rainflow counting algorithm. 7.1 Response to Truck-Induced Gusts Large trucks passing beneath the Structure-A produce gusts causing vibration of the support structure. Time history data was recorded for three passes of large trucks. For each pass, the truck was traveling in a different lane at an estimated speed of close to the posted speed limit of 72 km/hr. Time history data recording began just before the truck passed beneath the sign and ended a few seconds after the truck had passed. Based on the recorded data and observations throughout this study, the severity of the vibration appears dependent on truck speed, lane in which the truck was traveling, and type of truck. A natural frequency of 1.35 Hz in the first mode of vibration is observed from the data that is consistent with the analyses results. The truck-induced strain data indicated the chord members and diagonal members experienced stress ranges of approximately 6.0 MPa and 4.0 MPa which are 33 percent and 48 percent of the CAFL for the chord and diagonal members, respectively. Table 3 shows comparisons between the maximum measured stress ranges due to a single truck and the stress ranges calculated using the truck-induced design load from AASHTO Specifications (2001). The stress ranges measured at the chord splices are less than the calculated values. The stress ranges measured at some of the diagonals and struts are larger than the calculated stress ranges. According to AASHTO Specifications (2001), the truckinduced loads are applied vertically to the bottom side of all structural members and attachments resulting in a vertical deflection of the structure. Therefore, the stresses obtained from the analyses are representative of these vertical loading and deflection conditions. However, the observed deflections in the field due to truck-induced gusts are primarily in the horizontal direction. This is apparent because the first mode of vibration for the structure is dominated by horizontal motion. Not including a horizontal component of the truck-induced gust loading in the analyses is probably the reason that the measured stress ranges exceed the calculated values. However, this is not a point of concern with AASHTO Specifications (2001) because a
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Fatigue Evaluations of Variable Message Sign Structures Based on AASHTO Specifications Table 3. Comparisons of Calculated and Measured Truck-Induced Stress Ranges (Structure-A) Member Type
Gage
Diagonals & Struts
Front Top Chord
Back Top Chord
Back Bottom Chord WT-Section
Sr (MPa) FEM
Test
S1
0.1
5.6
S2
0.2
2.9
V1
0.9
3.4
V2
2.9
4.3
H1
4.4
H3
Member Type
Gage
Sr (MPa) FEM
Test
V1
7.6
2.3
V2
4.8
1.7
H1
2.6
2.9
H2
1.9
2.3
4.1
H3
2.4
2.6
4.6
3.9
H4
2.1
2.2
H4
5.0
3.9
FT1
4.1
2.1
H5
2.3
1.0
FT2
3.0
1.9
H6
1.8
1.1
FT4
3.7
1.9
V3
9.4
1.4
BB1
3.0
2.1
V4
7.7
1.7
BB2
4.1
2.1
1
5.1
4.3
BB3
3.6
1.6
2
8.5
4.4
BB4
3.6
3.0
3
5.9
5.7
4
7.8
3.9
1
7.0
4.7
2
5.7
3.9
3
5.9
4.4
4
6.9
5.4
1
5.1
4.0
3
4.6
3.8
4
7.4
5.3
T1
8.4
4.3
T2
7.8
3.4
Diagonals
Front Top Chord
Back Bottom Chord
determined from the free vibration response. This is in agreement with the natural frequency of the second mode of vibration obtained from the FEM analyses results. Since the first mode was characterized by side-to-side motion, the strain gages could not accurately measure the response in this direction.
structure must also be designed for significant horizontal loading due to natural wind gusts. Large trucks passing beneath the sign at high rates of speeds did not cause visible vibrations of the structure-B, but some truck-induced gust data was recorded. Time history data was recorded for three conditions of trucks passing underneath the VMS: a single truck; 2-trucks traveling side-by-side and 3-trucks in a row traveling in the same lane. For all conditions, the trucks were estimated to be traveling between 112 km/hr and 120 km/ hr. Strain recorded for all three conditions revealed the stress ranges were very low due to the truck-induced gusts. A particular gage had the highest predicted stress range from the structural analyses (7.6 MPa); however, the largest measured stress range due to the passing of a single truck for this member was approximately 2.3 MPa. Table 4 shows comparisons between the maximum measured stress ranges due to a single truck and the stress ranges calculated using the truck-induced gust design load from AASHTO Specifications (2001). The measured stress ranges at gages on some of the diagonal members are above the calculated values by a small amount. The stress ranges measured in the chords are below the calculated values. A natural frequency of 3.0 Hz was Vol. 10, No. 3 / May 2006
Table 4. Comparisons of Calculated and Measured Truck-Induced Stress Ranges (Structure-B)
7.2 Long-Term Monitoring Accurate calculation of the effective stress range in each member required large samples of stress ranges from normal daily loading conditions. During the long-term monitoring, the CR9000 datalogger continuously recorded strain ranges occurring from normal daily truck traffic and natural winds using a rainflow cycle counting algorithm. This provided a record of the number and magnitude of all significant strain cycles that occurred during the monitored period. The stress ranges measured during long-term monitoring represented a combination of truck-induced and natural winds. The results of the random truck test indicate that stress ranges experienced in all instrumented members were well below the CAFL. The majority of the stress cycles counted during the long-term monitoring is a result of natural winds. For the structure-A, strain gages and anemometer data were collected for a total of 31 days. During this period, stress ranges above the CAFL were recorded in several members. Table 5 lists for each strain gage the total number of cycles above the threshold of 20% of the CAFL and the percentage of those cycles above the CAFL. Stress ranges above the CAFL were recorded only at times when the natural wind speed was above 24 km/hr. The only exception was for strain gage S1 on the diagonal member of the vertical support. The S1 gage could be primarily affected by truck-induced wind gust. The recorded wind data indicates that the prevailing wind direction is out of the north-northwest direction. This prevailing wind direction is approximately perpendicular to the VMS panel and creates a worst case wind loading condition. Both strain gage locations on the WT section in the vertical support were located 25.4 mm
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from the weld at the end of the member, and the measurements from these gages include a stress concentration effect. For the structure-B, data were collected for a period of approximately 82 days. Very few cycles above the CAFL were recorded during this period even though wind gusts exceeding 32 km/hr were recorded on several occasions. A summary of the
measurements is provided in Table 6. The wind anemometer data revealed that the wind direction was variable on any given day that is expected for locations near the coast. 7.3 Stress Range Occurring at 1 in 10,000 Cycles The normal loading conditions on the sign structure due to
Table 5. Field Measured Stress Cycle Summary (Structure-A) Member Type
Diagonal & Struts
Front Top Chord
Back Top Chord
Back Bottom Chord WT Section
Sr (MPa) Occurring at 1/10,000
Gage
CAFL (MPa)
Total number of cycles above 20% of CAFL
% of cycles above CAFL
S1
8.3
2350992
0.056
10.4
29.5
2.83
S2
8.3
1086293
0.002
7.2
23.3
3.25
V1
8.3
1370275
0.006
7.2
15.7
2.18
Test
FEM
Ratio
V2
8.3
1740686
0.011
8.8
17.9
2.02
H1
8.3
1798189
0.012
8.8
16.4
1.86
H3
8.3
1692191
0.009
7.2
15.5
2.16
H4
8.3
1703093
0.008
7.2
17.9
2.50
H5
8.3
583
0.172
-
5.6
-
H6
8.3
69957
0.021
8.8
4.6
0.52
V3
8.3
379952
0.004
7.2
9.4
1.31
V4
8.3
429514
0.001
8.8
7.7
0.87
1
17.9
15725
0.000
15.2
16.3
1.08
2
17.9
21802
0.000
16.8
20.5
1.22
3
17.9
142776
0.006
15.2
21.9
1.44
4
17.9
9802
0.000
-
15.0
-
1
17.9
52155
0.008
15.2
20.4
1.35
2
17.9
4517
0.000
-
16.4
-
3
17.9
27099
0.004
16.8
14.8
0.88
4
17.9
129374
0.007
16.8
22.1
1.32
1
17.9
15854
0.006
16.8
18.5
1.10
3
17.9
8876
0.000
-
15.0
-
4
17.9
101420
0.007
16.8
22.1
1.31
T1
8.3
1777433
0.010
8.8
23.4
2.66
T2
8.3
1339216
0.008
7.2
23.2
3.24
Table 6. Field Measured Stress Cycle Summary (Structure-B) Member
Diagonal
Front Top Chord
Back Bottom Chord
Gage
CAFL (MPa)
Total number of cycles above 20% of CAFL
% of cycles above CAFL
V1
8.3
724831
V2
8.3
257176
H1
8.3
H2 H3
Sr (MPa) Occurring at 1/ 10,000
Ratio
Test
FEM
0.001
1.93
4.0
1.93
0.000
1.19
4.0
1.19
6112755
0.002
1.62
7.2
1.62
8.3
2656829
0.000
2.22
4.0
2.22
8.3
6853216
0.001
1.59
7.2
1.59
H4
8.3
2957895
0.000
1.72
5.6
1.72
FT1
17.9
139
0.000
-
-
-
FT2
17.9
29
0.000
-
-
-
FT4
17.9
21
0.000
-
-
-
BB1
17.9
113
0.000
-
-
-
BB2
17.9
42
0.000
-
-
-
BB3
17.9
202
0.000
-
-
-
BB4
17.9
1158
0.000
-
-
-
214
KSCE Journal of Civil Engineering
Fatigue Evaluations of Variable Message Sign Structures Based on AASHTO Specifications
truck traffic and natural winds produce a variable amplitude history of stress ranges. As long as the highest stress ranges in the history occur at a frequency of less than 1 in 10,000, the sign structure should not experience fatigue cracking, but should have infinite life (Fisher et al., 1993). Therefore, it is necessary to estimate the stress range that was measured at a frequency of 1 in 10,000 for use in performing a finite life check. This stress range is also referred to as the limit-state stress range. Tables 5 and 6 show the results for each structure including the measured stress range occurring at 1 in 10,000 cycles. Table 5 provides comparisons of the calculated and measured limit-state stress ranges (Sr) for the structure-A. The stress range values represent total stress (i.e. axial and bending stress). The results show that the majority of the measured limit-state stress ranges were below the calculated values, but not all. Four of the gages did not measure more than 10,000 loading cycles during the monitoring period, therefore the stress range occurring at a 1 in 10,000 frequency could not be accurately determined from the recorded data. Table 6 presents the comparisons of the calculated and measured limit-state stress ranges (Sr) for the structure-B. During the monitoring period, less than 10,000 loading cycles were recorded in all gages on the two main chords. Thus, the stress range occurring at a frequency of 1 in 10,000 loading cycles could not be accurately determined from the recorded data. As shown in this table, all measured limit-state stress ranges in the diagonal members were less than the calculated values. 7.4 Effective Stress Range A stress range histogram was required for the calculation of the effective stress range of each strain gage. The numbers of stress cycles measured at each gage during the long-term monitoring were extrapolated to estimate the number of cycles expected per year. Only stress cycles at or above 25 to 30 percent of the CAFL contribute to fatigue crack initiation and growth. Therefore measured stress cycles of small amplitude were omitted from the effective stress range calculations. The cutoff point used in the calculations was 22.3 percent and 20 percent of the CAFL for the truss chord splices (fatigue category E’) and diagonals (fatigue category ET), respectively. Tables 7 and 8 list the effective stress ranges (Sre) from the field measurements at each strain gage. These effective stress ranges converged to a reasonably constant value after only a few days of measurements at each location. To illustrate the variability of the measurements, effective stress ranges calculated for individual days during the monitoring period are plotted in Fig. 8. The plot shows that even the effective stress ranges for each day were reasonably constant. This provides confidence that the effective stress ranges calculated for the entire monitoring period are representative of the stress ranges experienced by the sign structures. Table 7 lists measured effective stress ranges (Sre), limit-state stress ranges (Sr) and the maximum stress ranges (Sr,max) for each strain gage on the structure-A. This table also includes ratios of Sr/Sre and Sr,max/Sr. The ratio of the measured limit-state stress range to measured effective stress range (Sr/Sre) was reasonably consistent for all gage locations and had an average of 3. The ratio of maximum stress range to limit-state stress range (Sr,max/ Vol. 10, No. 3 / May 2006
Table 7. Comparisons of Measured Limit-State Stress Range to Measured Maximum and Effective Stress Ranges (Structure-A) Member
Diagonals & Struts
Front Top Chord
Back Top Chord
Back Bottom Chord WT Section
Gage
Sre (MPa)
Sr (MPa) Occurring at 1/10,000
Sr,max
S1
3.2
10.4
24.8
3.2
2.4
S2
2.5
7.2
12.0
2.9
1.7
V1
2.6
7.2
20.0
2.7
2.8
V2
2.8
8.8
20.0
3.1
2.3
H1
2.8
8.8
20.0
3.2
2.3
H3
2.7
7.2
20.0
2.7
2.8
H4
2.7
7.2
18.4
2.7
2.6
H5
3.4
-
23.2
-
-
H6
2.5
8.8
21.6
3.6
2.4
V3
2.4
7.2
10.4
3.0
1.5
V4
2.5
8.8
26.4
3.6
3.0
1
5.8
15.2
15.2
2.6
1.0
2
5.8
16.8
16.8
2.9
1.0
3
5.9
15.2
21.6
2.6
1.4
4
5.8
-
15.2
-
-
1
5.8
15.2
18.4
2.6
1.2
2
5.8
-
13.6
-
-
3
5.8
16.8
18.4
2.9
1.1
4
5.9
16.8
23.2
2.9
1.4
1
5.8
16.8
18.4
2.9
1.1
3
5.8
-
15.2
-
-
4
5.9
16.8
21.6
2.9
1.3
T1
2.8
8.8
18.4
3.1
2.1
T2
2.6
7.2
15.2
2.7
2.1
Sr/Sre S /S (MPa) r,max r
Table 8. Comparisons of Measured Limit-State Stress Range to Measured Maximum and Effective Stress Ranges (Structure-B) Member
Diagonals
Front Top Chord
215
Back Bottom Chord
Gage
Sr (MPa) Sre Occurring (MPa) at 1/10,000
Sr,max
Sr/Sre (MPa)
Sr,max/Sr
V1
2.4
4.0
7.2
1.7
1.8
V2
2.4
4.0
5.6
1.7
1.4
H1
2.6
7.2
12.0
2.8
1.7
H2
2.4
4.0
7.2
1.7
1.8
H3
2.6
7.2
13.6
2.8
1.9
H4
2.4
5.6
7.2
2.3
1.3
FT1
5.8
-
8.8
-
-
FT2
6.1
-
8.8
-
-
FT4
5.7
-
7.2
-
-
BB1
6.3
-
12.0
-
-
BB2
5.9
-
7.2
-
-
BB3
6.2
-
10.4
-
-
BB4
5.7
-
8.8
-
-
Jong Sup Park and J. Michael Stallings Table 9. Fatigue Life Estimates for All Gage Locations (StructureA) Member Type
Diagonals & Struts Fig. 9. Effective Stress Ranges for One-Day Periods for Front Top Chord on Structure-A
Sr) varied from 1.0 to 2.8. Table 8 lists measured effective stress ranges, limit-state stress ranges and the maximum stress ranges for each strain gage on the structure-B. The ratio of measured limit-state stress range to measured effective had an average of 2.2. The ratio of maximum stress range to limit-state stress range varied from 1.0 to 2.0. 7.5 Finite Life Evaluation A finite life check was performed by comparing the measured stress ranges occurring at a frequency of 1 in 10,000 loading cycles to the respective CAFL for each member. The required data are shown in Tables 5 and 6. Table 5 shows that six of the diagonal and strut members on the structure-A did experience limit-state stress ranges above the CAFL. Therefore, the structure has finite life and is susceptible to fatigue cracking. Table 6 for the structure-B shows that no limit-state stress ranges above the CAFL were measured during the monitored period. Hence, the structure-B is predicted to have infinite life. Fatigue lives were calculated using the effective stress ranges measured at each strain gage location in each structure. These fatigue lives were calculated using the detail constants and procedures outlined in the AASHTO Specifications (2001). The number of stress cycles measured at each gage during the longterm monitoring were extrapolated to estimate the number of cycles expected per year. This allowed the fatigue lives to be reported as a number of years instead of a number of cycles. The results for the structure-A and structure-B are listed in Table 9 and 10, respectively. As stated in the previous fatigue life check, finite fatigue life is expected at only six of the strain gages locations, all of which are in the structure-A. Since both structures are relatively new, the total fatigue lives are essentially equal to the remaining life. As indicated in Tables 9 and 10, the support diagonal (gage S1) in the structure-A is the only member in which cracking is predicted prior to the 50 year design life of the structure. There are two other locations in the structure-A and two in the structure-B where the calculated fatigue lives are between 50 and 60 years.
3.2
27671176
28
S2
2.5
12785669
137
V1
2.6
16128137
93
V2
2.8
20487874
59
H1
2.8
21164685
58
H3
2.7
19917088
68
H4
2.7
20045405
67
H5
3.4
6862
102184
H6
2.5
823394
2085
V3
2.4
4472035
417
V4
2.5
5055380
350
1
5.8
185083
3578
2
5.8
256610
2603
3
5.9
1680474
372
4
5.8
115370
5724
1
5.8
613864
1074
2
5.8
53165
12185
3
5.8
318955
2088
4
5.9
1522732
410
1
5.8
186602
3467
3
5.8
104471
6305
4
5.9
1193713
533
T1
2.8
20920386
56
T2
2.6
15762572
94
Back Top Chord
Back Bottom hord WT-Section
Cycles/Year Fatigue Life Sre,meas (MPa) (above 20% of CAFL) (years)
S1
Front Top Chord
Table 10. Fatigue Life Estimates for All Gage Locations (Structure-B) Member Type
Diagonals
Front Top Chord
Gage
Sre,meas (MPa)
V1
2.4
3242197
593
V2
2.4
1150358
1669
H1
2.6
27342593
57
H2
2.4
11884100
158
H3
2.6
30654704
52
H4
2.4
13230780
140
FT1
5.8
622
1040522
FT2
6.1
130
4341883
Cycles/Year Fatigue Life (above 20% of CAFL) (years)
FT4
5.7
94
7360433
BB1
6.3
505
1033170
Back Bottom BB2 Chord BB3
5.9
188
3419339
6.2
904
590706
BB4
5.7
5180
134725
6. Summary and Concluding Remarks Stress ranges were measured at critical locations on both the VMS structures. These critical locations were chosen based on structural analyses results to provide a representative sample of
Gage
locations fatigue cracking might occur. Stress ranges were measured for an extended period of time to capture the effects of natural and truck-induced wind gusts. Limited data indicate that
216
KSCE Journal of Civil Engineering
Fatigue Evaluations of Variable Message Sign Structures Based on AASHTO Specifications
the most significant stress cycles at each structure result from natural wind gusts. Some of the important findings of the study are listed here. 1. Vibrations of the sign structure-A are noticeable, and stress ranges measured indicated that the structure does not have infinite life. At one strain gage location, the fatigue life was calculated using the measured stress ranges to be 28 years. Because this fatigue life is less than the 50-year design life, and because there are additional locations where fatigue cracking is possible, the structure-A should be considered to develop a strategy for inspection, retrofit, or replacement of the structure. 2. Based on the comparisons of the structural analyses and static test results, the results from a standard structural analyses of the structure-A should be sufficiently accurate for fatigue design of the structure. The stresses measured in some of these members matched very well with the calculated stresses. The difference between the measured and calculated values for the struts and diagonals is primarily the result of the low magnitude of stress in these members. 3. The ratios of the measured limit-state stress ranges to measured effective stress ranges (Sr/Sre) for the structure-A and structure-B were reasonably consistent for all gage locations to be 3.0 and 2.2, respectively. These results can be useful to define the characteristics of the VMS structures investigated and other similar VMS structures. 4. Stress ranges calculated at the truss chord splices and in several diagonal and strut members of the structure-A were larger than the CAFL and did not satisfy AASHTO Specifications (2001). For structure-B, the calculated stress ranges did not exceed the CAFL. The structure-B is predicted to have infinite life. 5. The amount of field measurements of stress ranges due to
natural wind gusts and truck-induced wind gusts do not provide strong conclusions regarding the accuracy or appropriateness of the AASHTO (2001) fatigue design loadings. However, the results presented here suggest that the design loadings are reasonable for use at this time. Comparisons of measured and calculated limit-state stress ranges (Tables 5 and 6) show that the calculated values are generally larger than the measured values. The largest measured limit-state stress ranges in either structure studied here were at the truss chord splices of the structure-A. At those locations, the calculated limit-state stress ranges were no more than 44% higher than the measured values. This difference does not appear overly conservative.
References American Association of State Highway and Transportation Officials (1994). Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals. Washington, D.C. American Association of State Highway and Transportation Officials (2001). Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals. Washington, D.C. Dexter, R.J. and Johns, K.W. (1998). Fatigue Related Wind Loads on Highway Support Structures, Report to New Jersey Department of Transportation, ATLSS Report No. 98-03, Lehigh University. Dexter, R.J. and Ricker, M.J. (2002). Fatigue-Resistant Design of Cantilevered Signal, Sign, and Light Supports, NCHRP Report 469, National Cooperative Highway Research Program. Fisher, J.W., Nussbaumer, A., Keating, P.B., and Yen, B.T. (1993). Resistance of Welded Details under Variable Amplitude Loading, NCHRP Report 354, National Cooperative Highway Research Program, USA. GTSTRUDL (2003). User Guide, Georgia Institute of Technology, Atlanta, Georgia, USA. (Received November 2, 2005/Accepted April 2, 2006)
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