State of Wisconsin / Department of Transportation RESEARCH PROGRESS REPORT FOR THE QUARTER ENDING: December 31, 2000

Transcription

1 State of Wisconsin / Department of Transportation RESEARCH PROGRESS REPORT FOR THE QUARTER ENDING: December 31, 2000 Program: SPR-0010(36) FFY99 Project Title: Structural Analysis of Sign Bridge Structures and Luminaire Supports Administrative Contact: Nina McLawhorn WisDOT Technical Contact: Stan Woods Approved by COR / Steering Committee: FY 00 $47,372 over 2 years, contract amount $49,969 Project Investigator (agency and contact): C.M. Foley Marquette U. Part II: Research and Development Project ID: Sponsor: Approved Starting Date: 3-May-00 Approved Ending Date: 3-May-02 Description: The project entails analysis of sign and luminaire support structures with specific examination of loading conditions and fatigue behavior. The research will result in inspection criteria and performance prediction for these auxiliary structures. An examination of luminaire support failure(s) and poor in-service performance of overhead sign support structures will be conducted with recommendations of possible causes and solutions. An evaluation of the fatigue characteristics of retrofit and other details for sign support structures including experimental testing will be conducted. Total Study Budget Current FFY Budget Expenditures for Current Quarter Total Expenditures to Date $49,969 $49,969 $1,350 $4,486 Progress This Quarter: The GANTT chart shown below illustrates the present status of the project. A summary description of the activities conducted during this past quarter is contained in the following. From the last quarterly report, two tasks are virtually complete: (a) all wind loading data has been obtained and (b) the wind velocity histograms have been finalized. There is a small amount remaining that consists of input from the project oversight committee and any minor revisions to the manner in which this data is displayed. A summary of this activity has been included with this report as Appendix B (appendb.pdf). The review of past research efforts, review of Wisconsin DoT s experience(s) with sign and luminaire support structures, and review of current inspection procedures continues. Appendix A of this report (appenda.pdf) outlines the present status and results of these ongoing efforts. The present research also includes the effect of truck-induced gusts on the fatigue performance of sign and luminaire support structures. To this end, truck traffic data throughout the state of Wisconsin were obtained from the Wisconsin Department of Transportation - Division of Planning and Budget, Bureau of System Planning (Travel Data Development). The vehicle Foley 4 rd Quarter FY 2000: 1

2 classification data records obtained via traffic counters throughout the State are contained in volumes published each year by WisDOT. Truck traffic data was obtained from these records for various routes where overhead sign and luminaire supports were thought to be present. The truck traffic data for various highways and interstates is given in the plot below AADT Year The plot above indicates the Average Annual Daily Truck Traffic for the years indicated. The numbers in the plots legend indicate traffic counter designations that are keyed to locations throughout the State. Of note is the data for (I-94 in Racine County), (I-94 in Kenosha County), (I-90/ Miles W of STH 82 in Mauston), and (I-94 Dane County). As shown in the plots, there can be upwards of 15,000 to 20,000 trucks a day passing beneath the sign structures. One should note that the data for is presently under review (it is believed that eastbound and westbound traffic are combined in these numbers. A meeting was held with Mr. Kent Bahler and Mr. Craig Wehrle of the Wisconsin Department of Transportation to discuss some the analytical and experimental direction(s) for the research effort. After this meeting, it was decided that several specific overhead sign support structures be evaluated analytically. These configurations were: (a) the present WisDoT standard fourchord configuration; (b) the present WisDOT standard tri-chord configuration; (c) the Minnesota four-chord angle member design; and (d) the welded pipe four chord truss containing a VMS. Specific attention will be made in regard to the details present on these structures and their anticipated fatigue performance. It was decided that the experimental work would focus on retrofit details as originally outlined in the Proposal and RFP. However, smaller scale testing was also discussed. This issues are presently under discussion and no firm decisions have been made at this time. Sign support structures being decommissioned throughout southeast Wisconsin have been sought to obtain experimental specimens for material characteristics and/or fatigue testing. The central segment of an aluminum sign structure recently decommissioned has been obtained from Arbor Green, Inc. Mr. Owen Wade of Arbor Green has been exceedingly helpful in this regard. This aluminum structure is part of S and it has evidence (in the specimens obtained) of cracking near the welds. It is felt that this specimen could be very useful in helping to assess the source of these cracks. A steel support truss is presently being sought and Mr. Charlie Johanic of the Kuehne Company is assisting with this task. Several sign structures in the Milwaukee area are to be taken down this year (2001). November 2000 was the target take down time frame, but the weather delayed these efforts until the spring. It is hoped that several steel specimens can be obtained in the next 3 months. Work Next Quarter: The work that will take place during the next quarter will be focused in two areas: (a) development of the FE models for the various sign support structures; and (b) development of the testing apparatus needed for the physical testing to be undertaken later on in the research effort. Several analytical modeling efforts will need to be completed so that the forces to be applied in the experimental work can be finalized. Work will continue on the synthesis of WisDOT s experiences with these support structures and also the inspection procedures and protocols used by transportation departments throughout the U.S. Foley 4 rd Quarter FY 2000: 2

3 Circumstances Affecting Progress or Budget: There are no circumstances presently felt to affect the Project s budget or progress. Wisconsin DoT personnel have been exceedingly accommodating in allowing the PI access to WisDOT intranet resources and also sign and luminaire support structure design, construction and fabrication drawings. The PI would like to make mention of several individuals that have helped thus far in an extraordinarily congenial and professional manner: Tom Heydel, Arlo Tessemer, and Charles Landey of the District 2 offices in Pewaukee, Wisconsin as well as Kent Bahler, Craig Wehrle, and Joel Aslum of the Madison DoT offices. Foley 4 rd Quarter FY 2000: 3

4 Appendix A Past Research and Synthesis Foley 4 rd Quarter FY 2000

5 Draft: Past Research and Synthesis: 1 Chapter?: Past Research and Synthesis?.1 Introduction One would think that cantilever and overhead sign support structures as well as luminaire support standards would be rather innocuous structures without problems. However, as will be highlighted in the present chapter, these structures have been of great concern to departments of transportation throughout the United States and Canada. A main reason for poorly performing sign and luminaire support structures arises from the difficulties in properly accounting for the applied loads, the presence of fatigue critical details located throughout the structures, and fabrication difficulties. The loading that these structures are subjected to are, by nature, dynamic and the transient component(s) can arise from several sources (Kaczinski et al. 1998): a.) naturally occurring wind gusts; b.) truck-induced wind gusts; c.) vortex shedding induced vibrations; d.) galloping induced vibrations. Quantifying the magnitudes of these transient wind loading components has been the focus of many research efforts undertaken in the last two decades. Furthermore, there is a significant portion of the sign and luminiare structure assembled using welded components. Many of the welded members involve connections with a constant amplitude fatigue life (CAFL) described as E in AASHTO (1996). These details are susceptible to fatigue failures and require accurate computation of stresses to assign appropriate estimates for fatigue performance of these structures. The purpose of this chapter is to provide a review of past research efforts related to sign and luminaire support structures. Research efforts involving truck-induced wind gusts, natural wind gusts, wind tunnel studies of support structures, field experimentation and finite element analysis are reviewed. Upon completion of the review, a synthesis of past research efforts is provided. This synthesis is important as it sheds light on the direction taken in the present research effort.

6 Draft: Past Research and Synthesis: 2 Upon completion of the synthesis of past research efforts, the Wisconsin Department of Transportation experience(s) with unsatisfactorily performing sign and luminaire support structures is reviewed. Past failures, the subsequent failure analyses undertaken, and the information obtained as a result of these studies is also reviewed. Since questionable sign and luminaire support structure performance has been experienced by many state departments of transportation (aside from Wisconsin), a review of inspection procedures used by the Wisconsin DoT and other states is provided. Inspection procedures used by other states give the present research effort insight into problem areas to address in this study. The chapter concludes with an outline of the elements found in the present research effort.?.2 Literature Review This segment of the report contains a literature review pertaining to past research involving sign and luminaire support structures. The review is fairly detailed so that the present research effort can be properly tailored to add to the present literature and properly justify the scope and direction of the present research. Creamer et al. (1979) This research report outlined an experimental and analytical study to quantify the fatigue loading on single and double cantilever sign support structures from gusts produced by passing trucks. The end result of the study was a procedure for designing cantilever highway signs under the influence of this type of gust loading. A field study was conducted to determine the vibrational characteristics of the sign support structures. Three cantilever sign supports were instrumented with strain gauges located on the diagonal (web) members and the chords of the cantilevered truss structure. The natural frequency and inherent damping ratio of the support structure was estimated using the strain gauge readings. Excitation was provided to the truss structure via manually shaking the truss horizontally and vertically. This shaking was done by a person standing on the truss near the upright support. Shaking was done in either the horizontal or vertical direction. The logarithmic decrement method was used to determine the percentage of critical damping inherent

7 Draft: Past Research and Synthesis: 3 in the sign support structure. It should be noted at this point that aeroelastic damping due to the presence of the supported sign (especially in the case of horizontal truss oscillation) was not considered in the damping ratio computations. The experimentally determined horizontal and vertical damping ratios for the three sign support structures studied was found to be very low (eg % of critical). The member forces obtained experimentally were used to help calibrate an analytical model of the sign structure and were used to develop an analytical loading function. The analytical member forces were compared to the experimental member forces for a specific analytical loading function. The loading function was adjusted until the computed member forces were acceptably close to the experimental values. A pressure pulse due to passing trucks was developed using standard equations expressing pressure as a function of velocity. The resulting truck gust pressure loading function is shown in Figure?.1. The accuracy of the analytical model (including the loading function assumed) was quantified via comparison to the experimentally determined member forces. The natural frequencies for vertical and horizontal vibration were very close to the experimentally determined values. However, the member forces show qualitative comparison. Where significant member forces were computed, the comparison was quite favorable. The analytical model neglected base plate and anchor bolt effects. This is where the differences may have been generated. The results of the analytical/experimental comparison indicated that the loading function and FE model adequately simulate the truck-induced gust response. A parametric study was undertaken on actual Texas DoT sign support structures (cantilever) to determine dynamic load amplification factors (DLF s) and natural frequency values for a variety of structures. Two zones were determined to help direct the parameter study. The zones were defined such that upper and lower limits on section sizes and structure flexibility were identified. The parameter study included computation of the three lowest vibration mode frequencies. Three truss spans (lengths) were analyzed (10 ft, 25 ft, 40 ft), three upright heights were included (14 ft, 23 ft, 32 ft), and two zones were evaluated. The zoning was based on both wind speed

8 Draft: Past Research and Synthesis: 4 and ice buildup. The results indicated that the first two modal frequencies of vibration were very close to one another for all sign configurations studied. The third mode of vibration was significantly separated from the first two. The dominant vibrational modes were found to be dependant on the span of the cantilever truss and on the height of the upright(s). The three vibrational modes identified in the study were: (a) a rocking (hatch-type) motion; (b) a torsional (upright twisting-type) motion; and (c) flexural (parallel to traffic upright bending) motion. The following qualitative statements were made regarding vibrational modes. First of all, the shortest truss lengths were found to have the rocking motion as the lowest frequency. The flexural mode was the second (very close to the first mode frequency). The final mode for these short trusses was the torsional mode. The first mode of the 25 foot truss exhibited a transition from rocking to torsion. This transition occurred as the upright height (length) increased. The first mode for the 40 foot span truss was dominated by torsional motion. A dynamic load factor (DLF), defined as the maximum dynamic response to the loading function divided by the maximum response resulting from static application of the loading function at its peak value, was defined. The dynamic load factors for torsional moment and flexural shear at the sign support base were computed analytically. A set of bounding linearized DLF curves were created. The DLF was defined for structure natural frequency ranges studied. These design curves require that the natural frequency of the structure and the pulse loading (truck-induced gust) be known. The pulse duration can be adequately handled by the bounding DLF definition, but the support structure natural frequency is required. The report included a procedure to estimate natural frequencies for the various modes of vibration outlined in the study. However, with today s computational power at current levels, these approximate procedures are not required. Approximate boundary expressions for mode shifts were also contained in the report. Again, with today s software, these approximations are not necessary. A fatigue design procedure for anchor bolts in the sign support structure is also described in the report. A static design loading was used in the design procedure. A pressure of 1.23 psf (refer to Figure?.1) was assumed initially. A frequency of occurrence histogram of experimentally obtained chord forces (at one location), normalized by the analytical chord force

9 Draft: Past Research and Synthesis: 5 determined at that same location, was created. This histogram indicated that the majority of experimental events produced a force less than 50% of the force produced analytically using the assumed loading function. Assuming a Gaussian distribution for the occurrence, it was found that there is a 99% probability that 99% of the loading events produce ratios of experimental to analytical chord forces less than Thus, virtually all analytical chord forces computed would exceed experimentally determined values. The peak static pressure of 1.23 psf was then rounded to 1.25 psf for convenience. The philosophy behind the fatigue design procedure is to determine the number of damaging stress range cycles caused by the truck-induced impulse event. This procedure is very sensitive to the structure damping ratio assumed. It is shown in the report that if 0.70 % damping is present in the structure, and damaging cycles are caused by stress ranges in the envelope defined by DLF*Static and 0.50*DLF*Static, then 16 damaging stress ranges would be expected to occur for each passing truck. If one assumes that the ADTT under a given sign is 1000, this would imply 5.84 million damaging stress ranges per year. One can see the problem that could develop if the damaging stress range is NOT well understood or defined. The previous discussion highlights the importance of establishing adequate allowable stress ranges for fatigue considerations. The CAFL value used in this study for anchor bolt evaluation was the AASHTO Category C detail (10 ksi). It was suggested that the live load (truck-induced and ambient wind gusts) stress range in the anchor bolts (bending stresses) should be below this CAFL value. A design example was provided using the approximate procedure developed in the report. The design example mentions that the axial stress ranges in the bolts can be neglected for most designs. Several conclusions were drawn based on the results of this study. The first conclusion was that vehicle-induced wind gusts can produce significant sign response and due to the very low damping inherent in these structures, a large number of stress fluctuations are created for each vehicle event. It was mentioned that...box-type trailer trucks produced the greatest number forces. The report concluded that the stresses measured in the superstructure members were low and do not present a fatigue problem. Design of the sign structures for vehicle-induced fatigue

10 Draft: Past Research and Synthesis: 6 loading could be accomplished with a pressure of 1.25 psf with appropriate dynamic load amplification factors. The 1.25 psf magnitude is assumed to be the maximum magnitude of a triangular loading pulse. Irwin and Peeters (1980) This research effort dealt with overhead sign support structures. The one major difference is in the sign bridge configuration. A schematic drawing illustrating the sign support structure type evaluated in the study is shown in Figure?.2. A dual tube overhead sign structure was evaluated. A field investigation was commenced to determine the natural frequency and inherent damping in the support structure. A wind tunnel study on model structures was also conducted to determine the aerodynamic stability of the sign bridge. The initial wind tunnel model testing revealed a strong tendency for vortex shedding induced oscillations. Figure?.3 is an depiction of the wind tunnel model used. Investigation thereafter focused on; (a) finding a level of damping that would suppress these oscillations, and (b) development of aerodynamic devices to counter vortex shedding vibrations. The sign structure studied was a dual octagonal tube (129 foot span) with multiple signs mounted to the horizontal (over-roadway) span. The field obtained data indicated the following: Bridge Spans Instrumented: 115 ft. to 145 ft. (non-uniform increments) Natural (inherent) Damping: % to % (w.r.t. critical) Natural Frequency (Hz): to The horizontal aerodynamic damping (sign and support moving horizontally) was measured to be % of critical. The wind tunnel study began with the hypothesis that the octagonal tube structure was an nonessential ingredient to the aerodynamic instability and vibration of the structure. Therefore, the octagonal tubes found in the real structure were replaced with circular tubes in the model. At very low damping ( % critical) a 2 1/2" initial displacement amplitude could induce oscillations. This result might suggest that a sign structure susceptible to vibrations due to ambient wind gustiness may be set-off by a passing truck. At 1.75 % of critical damping, no

11 Draft: Past Research and Synthesis: 7 oscillations could be induced. The wind tunnel study revealed that the sign was able to contribute to the vortex shedding oscillations. As a result, further wind tunnel testing was conducted with airfoils attached to the supported sign. Optimized air foil angles, sizes and locations were determined. Aerodynamic lift coefficients for the air foils were determined in the wind tunnel study. Several observations and conclusions resulted from the study. First of all, reducing the solidity of the sign was found to have a significant effect (beneficial) on the aerodynamic behavior. If % of the sign area is open, no oscillations occurred. Boxing in the back of the sign structure was found to have a non-beneficial effect (aerodynamically). In reality, reducing the solidity of the sign is not possible. Furthermore, VMS/CMS are already in the boxed configuration and therefore, the support structure may be more susceptible to vortex-shedding induced vibrations resulting from the VMS. The probable cause of the sign support structural failure was stated in the report to be vertical oscillations due to vortex shedding. Three foot oscillations (129 ft. span) were reproduced in the wind tunnel model when the wind velocity reached 32 mph. This approximately corresponds to a sign with an 8 ft. dimension orthogonal to the wind direction. Therefore, it can be concluded that the sign can cause significant vortex shedding induced vibrations. An air-foil configuration was suggested to provided aerodynamic damping to the support structure. Also, the wind tunnel testing suggested that 1.8% of the critical damping ratio could eliminate vortex-shedding induced vibrations altogether. Fisher et al. (1983) This paper outlines an experimental and analytical investigation involving the fatigue strength of steel luminaire supports undertaken for the California Department of Transportation (CALTRANS). The testing program involved rather large stress ranges (19 ksi) initially. After a series of tests at this range resulted in limited cycles to failure, the stress ranges for subsequent experiments was reduced (6.5 ksi and 12.5 ksi). An analytical study was undertaken to determine acceptable values for the stress concentration factor (SCF) and also the stress gradient correction factor (F G ) commonly used for fatigue analysis (Anderson 1995; Barsom and Rolfe 1999; Broek 1987,1988; Fuchs and Stephens 1980; Meguid 1989; Peterson 1974).

12 Draft: Past Research and Synthesis: 8 The steel luminaire support structures studied indicated that the fatigue strength of the fillet weld connections at the arm connection plates and the column base plate are consistent with AASHTO category E. All failures that occurred in the experimental investigation were located at the fillet weld toe in the pipe arm or in the vertical column. A reduction in the angle of the fillet weld (eg. a reduction from 45 degrees) provided significant improvement in the fatigue resistance. Unequal leg fillet welds had improved fatigue resistance. The improvement was said to be a result of the reduced fillet weld angle that resulted when unequal legs were formed. Edwards and Bingham (1984) This study was conducted for the North Carolina Department of Transportation by North Carolina State University s Center for Transportation Engineering Studies. The research effort was concerned with wind loading and deflection criteria for cantilevered truss sign support structures. The study included experimental work in a wind tunnel and in the field and analytical efforts geared toward quantifying truss structure response. The wind tunnel experiments involved model two-chord trusses. Two models were studied and their schematic representations are shown in Figures?.4. These models were used to evaluate the vortex shedding characteristics for the truss configuration. The wind tunnel experiments for the configuration shown in Figure?.4(a) revealed that the Strouhal number for the two chord configuration was virtually the same as that for the single cylinder (0.196 vs , respectively). A range of lock-in velocities were found for both the single cylinder and the two chord configuration. A simulated cantilever truss model was also studied in the wind tunnel. The model schematic for this experiment is shown in Figure?.4(b). A Strouhal number equal to was determined for this configuration. A vibrational node was observed in the model at a distance 1/3 from the cantilever supported end (ie. the right end in the figure). An attempt was made to attach a flat plate to the truss model. However, this plate attachment significantly altered the model behavior such that the wind tunnel could not develop the velocity necessary to excite vibration. Finally, the use of mechanisms (strakes) to eliminate (or inhibit the formation of) vortex shedding on the tubular members was evaluated. The study also attempted to measure the wind pressure that resulted from vehicular-induced wind loads. The testing was done using hot film anemometer patches. A sign was

13 Draft: Past Research and Synthesis: 9 instrumented with the patches in the configuration shown in Figure?.5. It should be noted that the vehicular-induced gust loading was measured on the top half of the sign. Furthermore, the patches were located toward the vertical column of the support which was not directly over the main vehicular traveling lanes. In fact, the sensory patches were located over the exit ramp lane. The front and back of the sign was instrumented. The maximum pressure recorded on the sign due to vehicular-induced gusts was 1.41 psf. This is consistent with past research efforts (Creamer et al. 1979). A theoretical investigation of the wind loading applied to sign structures was also undertaken. The study was specifically set up to address the time-varying component of the wind pressure (ie. the gusts). The following loading conditions were considered in analytical studies: (a) vortex shedding from the cylindrical members of the structure where the vertical column was also subjected to vortex-shedding induced loads; (b) wind buffeting against the flat surface of the sign where the time varying component is assumed as an amplitude varying sine function; (c) statistically varied turbulent wind velocities where the wind pressure was assumed to follow a sine function using a wind velocity spectrum (Davenport 1961); and (d) a randomly generated pressure spectrum. Although not completely clear, it appears that the average wind velocities (ie. the non-fluctuating part) used in (c) were taken from standard wind maps. The randomly generated pressure spectrum was developed using a random signal with a power spectral density that corresponded to measured values. The stochastic loading model used in the case of (d) is shown in Figure?.6. The SAP IV program was used to carry out the structural analysis. Three dimensional analyses were carried out for the four chord and two chord configurations. The base conditions for the column in the analytical model were assumed to be rigid. The results of a static analysis (assumed to have used AASHTO (1975) for loading criteria) indicated that all three support structures analyzed exceeded AASHTO (1975) criteria for vertical deflection. It should be noted that the static stresses computed for the three structures analyzed were on the order of 4,000 to 13,660 psi. The first four vibrational frequencies for all of the analytical models were computed. One interesting result of the analysis conducted is that all the cantilever truss models developed first mode vibrational shapes in the horizontal plane (ie. a torsional mode for the vertical

14 Draft: Past Research and Synthesis: 10 column). The second fundamental modes of vibration were the hatchet-type vibrational mode. As a result of this finding, the report goes on to suggest that limiting the vertical deflection of the truss structure may be of little value when the fundamental mode of vibration is in the horizontal direction for the structures studied. This conclusion must be severely tempered with the knowledge that the fluctuating frequency of the wind must match a vibrational mode for uncontrolled (perhaps damaging) vibrations to occur. One could surmise, however, that vortices could form off the vertical edges of the sign structure. This in turn could act to excite the horizontal (fundamental) mode of vibration. At this point, this is purely speculation, however, it may be a worthwhile goal to study this possibility further. The analytical results obtained, assuming vortex-shedding induced loading, indicated that the stresses were very low (ie. negligible). The vortex-shedding in these cases was assumed to form from the cylindrical members of the structure. The method used to load the structure with vortex-shedding induced pressure is not clear from reading the report. One would assume that a lock-in frequency was computed for the diameter of the cylinders considered. One could then easily determine if any of the structure modes of vibration had the same (or similar) frequency. Matching (lock-in) frequencies and their vibrational shapes could then be used to develop vortexshedding induced loading patterns (Johns and Dexter 1998a). However, these very important issues are not clearly outlined in the report. It is therefore, felt that the vortex shedding induced loading analysis is suspect. One item of note is the buffeting wind response analysis. The fluctuating component of the wind in this case was assumed to follow an amplitude-scaled sine function. The frequency of the sine function was assumed to correspond to the frequency of vibration of the horizontal vibrational mode of the structure. This is very much suspect since it assumes that the vibrational characteristics of the wind match those of the horizontal vibrational mode of the structure. In essence, the researchers are computing the resonant stresses in the structure. The report suggests that this method of loading causes large stresses. This is to be expected. Use of a wind power spectrum and a frequency domain analysis would be far more appropriate. The report does include a loading configuration dependent on the frequency content of the wind. A fast Fourier transform (FFT) was used to examine the wind s frequency content.

15 Draft: Past Research and Synthesis: 11 The pressure spectrum used in this analysis is given in Figure?.7. The spectrum corresponds to a mean wind velocity of 82 mph. Although the intention of this analysis is proper, the use of an 82 mph average wind with gustiness is very, very severe. Using a typical probability density function (PDF) for wind, this wind magnitude would be encountered very infrequently (maybe never during the service-life of the sign support). If typical design wind maps were used in this analysis, the recurrence interval for this wind would be approximately 50 years which corresponds to a 2% chance of exceedence in any given year. The stresses computed using this wind velocity were very large when one considers fatigue analysis. It is not clear if a stress range was computed or if the maximum stress was the only value provided. Use of maximum stresses in fatigue analysis is not proper. Therefore, one must be leery of the maximum stress results contained in the report and their extrapolation to quantifying fatigue-related performance. Field studies were carried out on one of the four-chord sign support structures. Strain gauges were mounted at various locations in the structure. The strain was monitored during passage of trucks beneath the sign as well as during ambient wind. An accelerometer was used to measure accelerations at specific points within the structure during different modes of vibration. A shaker mechanism was designed and constructed to determine the vibrational characteristics of the structure in its horizontal (twisting) and vertical (hatchet) modes of vibration Strains measured during the passage of vehicles beneath the sign did not cause stress magnitudes above 900 psi. If it is assumed that a rebound occurs, one might say that the maximum stress range would be 1,800 psi. These stress ranges are well below the CAFL for the typical details in the cantilever structures studied. The report does not mention the passage of semi-tractor-trailer type trucks. It does mention a box van induced the maximum stress measured in the sign support. One could surmise that even if a semi-trailer causes twice the stress range as a box van (assumed to be an H20 type truck) of magnitude 3,600 psi, the stress range would be at or below the CAFL for many, if not all, of the details in the sign structures instrumented. The damping ratio of the cantilever structure was measured using the logarithmic decrement technique. An attempt was made to measure the natural frequencies of vibration and damping percentages for the structure. Vibrational deformations were created by having an individual stand near the vertical pole centroid and shake the cantilever horizontally (pole twisting mode)

16 Draft: Past Research and Synthesis: 12 and also shake the cantilever vertically (hatchet mode). The horizontal mode (pole twisting) frequency was measured to be 1.45 cycles per second, while the hatchet mode vibrational frequency was measured to be 1.48 cycles per second. Damping in the vertical mode (hatchettype) vibration was measured to be 0.58% of critical. The horizontal mode damping was influenced by the aerodynamic damping of the sign, and its magnitude was measured to be 1.17% of critical damping. The shaker was set up to provide vertical (shaker set up beneath cantilever) and horizontal (shaker set up on an adjacent bridge) motions to the cantilever structure. The frequency of the shaker was adjusted to create a resonant condition. The natural frequencies of vibration for the vertical mode and horizontal mode were measured to be 1.49 and 1.46 cycles per second, respectively. The shaker was abruptly shut off and the structure was allowed to naturally dampen the vibrations. The vertical mode of vibration had a natural damping ratio of 1.4% of critical and the horizontal mode had natural damping of 1.85% of critical. It was mentioned in the report that the cable attached to the shaker added damping to the structure and it is believed this added damping skewed the results relative to those obtained previously from manual shaking. Aerodynamic damping provided by the sign for the horizontal mode of vibration is thought to be significant, although its presence was not mentioned nor quantified in the report. An attempt was made to verify the analytical FE model using the results of the field experimentation. The mechanical shaker loading was used as input in the SAP IV program. The shaker input data was passed through a low-band filter to remove noise from the cassette tape used to store the data. The power spectrum density of the load input and structure response were computed for both horizontal and vertical support structure deformations. The report contains several conclusions that resulted from the study. It is mentioned that vortex-induced vibration of the structures studied and vehicle-induced gust loading does not significantly add to the stress in the structure members. One must be a bit careful with this conclusion since it is not mentioned that semi-tractor-trailer trucks passed beneath the sign during the field measurement period. The box van vehicles mentioned in the report do not have tops close to the elevation of the sign and therefore, might not contribute large loading. It

17 Draft: Past Research and Synthesis: 13 also mentions that a d 2 /400 vertical deflection limit (AASHTO 1975) is not an appropriate design criteria. It also mentions that wind buffeting on the sign panels can cause large stress magnitudes. One should be careful in generalizing this conclusion since the frequency of the transient component of the wind load was set at the natural frequencies of vibration for the sign support. This set up an artificial resonant condition and should be carefully scrutinized since the frequency content of the wind was NOT included in the analysis. South (1994) This report is a rather detailed investigation of overhead sign structures. The over-riding goal of the report was to combine pertinent existing wind loading and vibration theory, fatigue damage theory, and experimental data into a usable fatigue analysis method for overhead sign and signal structures. Furthermore, the report sought to develop factor of safety equations in order to estimate fatigue damage susceptibility. The report provides an excellent discussion of wind induced vibration for cylindrical structures. The research included instrumentation of a traffic signal structure for collection of wind speed data. The anemometer was mounted to a pole approximately 4 feet above the traffic signal anchor pole (25 feet above the ground). Data was collected from August 7, 1991 to January 25, The site used for data acquisition was Springfield, Illinois, and it included residential and shopping areas. Nearby structures surrounding the site ranged from one to three stories in height. The nearest building structure was 200 feet from the site and it was approximately two stories high. Wind speed data for calendar year 1992 was collected for a site located in Springfield, Illinois. Typical data recorded for wind speed over a twenty-four hour period is given in Figure?.8. The entire calendar year of data is given in histogram format in Figure?.9. It appears that the wind loading for the year follows an extreme type distribution. Most wind velocity distributions are modeled using Type I, II or III Extreme probability density functions. From these figures, it is obvious that a sign or luminaire support will undergo large variations in wind loading. Typical design procedures (AASHTO 1985,1994; ASCE 1990,1998) use static wind pressures to simulate structural loading. In these procedures, a maximum expected wind velocity (with

18 Draft: Past Research and Synthesis: 14 specified recurrence interval) is used to develop static wind pressure. These procedures can be subject to well-justified scepticism when the variations in wind speeds exhibited in Figures?.8 and?.9 are examined. It should be noted that although a large wind velocity is used (say 75 mph) in the static design procedure, it remains to be seen that this level of design load is capable of providing suitable fatigue related performance for loadings of resulting from more frequent wind speeds of mph applied for millions of cycles. A very useful experimental effort can be made by instrumenting sign and luminaire support structures in the field to acquire strain data. To this end, this presently discussed research effort included instrumentation of a common steel cantilevered signal arm structure (44 ft. mast arm) at the Physical Research Laboratory of the Illinois Department of Transportation. Strain gauges were located on the mast arm at its connection to the vertical support post. These gauges, measured strains near the toe s of the fillet welds. Furthermore, strain gauges were also placed in the anchor bolts. Stress range-frequency data were recorded over a four month period. Strains were measured for dead loads of the mast arm as well as for self-weight of the traffic signals. Strains were also recorded for induced tip deflections at the end of the mast arm. This research effort also made an attempt to measure the vibrational characteristics of the signal structure. The frequency and amplitude of vertical vibration for the signal structure were measured in the field. Vibrational measurements were taken for wind speeds ranging from mph. Structural damping for the mast arm structure was estimated to be > = using the logarithmic decrement procedure. Damping in the signal structure studied was obviously very, very light. Finite element analysis to simulate base plate effects on the vibrational characteristics were eluded to but not discussed in any detail. The effect of the support on the vibrational characteristics was deemed very important in the report. A controlled wind speed test was conducted using the cantilevered mast arm signal structure. A blower was used to apply air-flow to the outermost traffic signal. Strains (and stresses) were acquired over five minute intervals for wind speeds ranging from mph. Using this controlled test, an apparent drag coefficient of the in-place traffic signal, C D, was computed. The apparent drag coefficient computed was 0.39 which was not in agreement with published

19 Draft: Past Research and Synthesis: 15 coefficients (1.20). It was believed that experimental setup was the reason for the disagreement. It was recommended that...additional investigation of the in-situ estimation of drag coefficients for traffic signals and sign panels... be undertaken. The experimental investigations undertaken indicate that both welds and anchor bolts are subjected to a large number of stress cycles at relatively low stress magnitude (with reference to static procedures using 70+ mph wind speeds). The experimental investigation of the mast arm signal structure indicated that the vibration of the structure tends to occur in synchronization with the first and second modes. The report provides a fairly detailed discussion of the means and methods of quantifying fatigue damage. A histogram linear-fatigue procedure is suggested and used in the report. Proper use of stress-concentration factors is emphasized and outlined in the report. The report provides a detailed example computation of the fatigue damage analysis of a cantilevered mast arm traffic signal support structure. Both strain gauge readings and analytical methods are used in the example calculations. The example computations using strain-gauge data indicate that approximately 30% of the fatigue damage is caused by low-level stress cycling (± 4.5 ksi). The report emphasizes that fatigue life estimates should be determined with adequate wind data measurements (over multiple years). The report also outlines a fatigue damage estimating procedure using wind speed histograms. The over-riding goal of the procedure is to develop a stress-range frequency histogram. This histogram can then be used to determine the number of available cycles at a given wind velocity and the fraction of total damage due to that wind speed. The analytical procedure used in the report indicated that all of the significant damage was due to wind speeds in a range from 16 to 27 miles per hour. Comparison with the AASHTO (1994) static procedure indicated that... static methods overestimate the expected fatigue life of a given detail by a significant margin. The final chapter of the report outlines a procedure by which a factor of safety can be developed for fatigue load details.

20 Draft: Past Research and Synthesis: 16 McDonald et al. (1995) The purpose of this study was to prepare revisions to the wind load section of the Texas DoT standard for design of signs, luminaires and traffic signal structures and to develop strategies for mitigating certain large amplitude vibrations in single arm traffic signal structures. The report summarizes some of the limitations present in the (then state-of-the-art) design standards (AASHTO 1985). Most notably, the lack of a gust response factor and omission of terrain roughness adjustments were cited as deficiencies. The study concentrated on cantilevered signal mast-arm structures. Several interesting points related to the phenomenon of wind excitation of structures are mentioned. First of all, galloping of a structure (normal to wind vibration) requires initial disturbance caused by vortex shedding and/or wind gusts. If the structure has adequate damping, the galloping due to steady winds can be limited to the amplitude of the structures natural modes of vibration. If adequate damping is not present, the amplitude of vibration during galloping may increase. It was also mentioned (from the literature review) that surface roughness can cause measurable, but not significant, variation from the general cylinder vortex-shedding behavior. From the literature review conducted in this study it was concluded that vortex shedding at sub-critical Reynolds numbers can occur for Strouhal numbers in the range from 0.13 to This reinforces the importance for understanding Strouhal numbers for the shape immersed in the wind flow. The study found that the Strouhal numbers for shapes characteristic of traffic light structures is within this range and therefore, vortex shedding and galloping vibrations can be important considerations in the design of such structures. The literature review concludes that the theory of quasi-steady galloping (Novak 1969,1972) best describes the behavior of traffic signal structures in a wide range of winds. Furthermore, it was concluded that vortex shedding was a factor in traffic signal oscillations at low wind speeds. Vortex shedding is also the mechanism that excites galloping vibrations. Therefore, for the present study purposes, the lock-in velocities for the sign bridge and luminaire support structures should be studied. Furthermore, the quasi-steady galloping theory should be reviewed for applicability.

21 Draft: Past Research and Synthesis: 17 The report summarizes the deficiency with the gust factor approach used in design specifications (AASHTO 1985). The gust factor makes an assumption that peak winds are proportional to peak gusts. In reality, the peak wind load depends on time variation and also spatial variation of wind gusts. Naturally, wind gusts can come in time separated intervals. Furthermore, wind gusts do not occur in the same place at the same time. These are two of the factors the gust response factor (GRF) approach attempts to simulate and the GRF method was considered to be the more accurate means with which to compute wind loading. The development of wind speed maps (ASCE 1990) are discussed in the research report. These maps are based on a 50 year mean recurrence interval. The wind speeds are expressed in terms of fastest mile winds at 33 feet (10 meters) above ground on flat, open terrain. The report examined the contours within the state of Texas in detail. A new design wind speed map was developed for inland locations within Texas as part of the study. Reasons for this development were given as; a.) there were an additional 11 years of wind records since the last map was published, b.) 26 weather recording stations are currently available versus the 9 used in the development of ASCE (1990). The procedure used in the development of the new wind speed maps is interesting and its review is felt to be important to the present study. Inland climates that are well-behaved (Lake Michigan shoreline areas may not be) can be considered to follow a Type I Extreme value probabilistic distribution function. Using the Type I PDF assumption, an estimate for the wind velocity associated with a mean recurrence interval (MRI) of N years was computed. Wind velocities for MRI s of 10, 25, 50 and 100 years were computed for each weather station considered in the study (26 in Texas plus 6 out-of-texas). Wind speeds at the stations used in the study were averaged to obtain an importance factor, I, that relates the 50 year MRI to any other N-year MRI wind velocity. Wind speed records for the study were obtained from the National Climatic Data Center (NCDC) in Asheville, North Carolina. Although 52 stations in Texas were available, the 26 station records used in the study resulted from an examination of all records consistency,

22 Draft: Past Research and Synthesis: 18 quality, and length of record. The data used in the study consisted of the largest annual gust speeds, independent of direction. Furthermore, gust speeds are assumed to be 3-second gusts which are consistent with the National Weather Service (3-cup anemometer). Three second gust speeds are also consistent with ASCE (1998). Upon completion of the screening process, the study recording stations were selected. The annual maximum gust wind velocities for the stations were converted to fastest-mile wind speeds using gust factors (Durst 1960). Sample means and standard deviations were also computed. Equation (1) was then used to compute 10, 25, 50 and 100 year MRI wind velocities. A revised wind speed map for 50 year MRI wind velocities for the state of Texas was proposed. The report also contained a chapter on proposed changes to the national design standard (AASHTO 1985). However, it is felt that many of the proposed changes are contained in Fouad et al. (1998) and comparisons between these two studies will be made later in the literature review. The report provides a design example comparison between AASHTO (1985) and the proposed revisions for the computation of sign panel and horizontal bridge wind loadings. The research report s proposed changes to the wind loading design standard, provide for a significant reduction in the design loading for both sign panels and horizontal bridge trusses. Additional comparisons are made for high-mast luminaire supports and also a double-cantilever roadway illumination assembly. In these cases, the proposed specification provides for considerably more design loading. The report provides details on the finite element analysis conducted to determine vibrational characteristics of cantilevered mast-arm traffic signal support structure. The FEA model was calibrated (compared) with field measured vibrational response. An extensive experimental program was undertaken. The goals of the experimental work were to attain a more complete understanding of the vibrational and flow characteristics of the traffic signal structures and to study vibration mitigation strategies. Experimental work was carried out on a water table, in a tow tank and with a full scale traffic signal support structure in

23 Draft: Past Research and Synthesis: 19 the field. The water table experiments utilized scale model studies of the signal structure arm and the traffic signal. The tow tank allowed full-scale traffic signal and a portion of the support arm to be tested. Finally, the field site testing involved instrumentation of two full-scale traffic signal support structures. A foundation utilized in the field study allowed the angle of wind attack to be varied via rotation. The field study also included measurement of structure vibrational characteristics used for calibration of the previous FE analysis. The water table experiments were used to study the vortex shedding phenomena of the signal arm and traffic signal. Vortex shedding frequencies were determined using video-tape replay. By observing video of the flow one frame at a time, and knowing the speed at which the video image has been acquired (film-speed), the vortex shedding frequencies can be determined within acceptable accuracy. Two signal arm support cross-sections were studied: (a) octagonal and (b) circular. The octagonal section was oriented in two positions: (a) flow across the flats and (b) flow across the corners. Traffic signal models were tested with the signal below the support arm (flow from front and back); signal at same level as support arm (flow from the front and back); signal light alone with backing plate (flow from the front and back); signal light with backing plate below support arm (flow from the front and back). The water table experiments concluded or confirmed the following: a.) The Strouhal numbers determined match values contained in the published literature: for octagonal cross-sections; and for circular cross-sections. b.) The Strouhal numbers depend upon the traffic signal and support arm spatial relationship and also the direction of flow. For the configurations studied, the Strouhal numbers ranged from to which is quite a large range. c.) The traffic signal and signal arm configuration studied gave vortex shedding frequencies in the range of 1.20 < f vs < 2.5 (Hz) for wind speeds of 10 mph. The frequencies increased for wind speeds of 20 mph to 2.40 < f vs < 5.1 (Hz). Based on the FE analysis, vortex shedding could be expected in wind speeds less than 10 mph. It should be noted that pressures resulting from this low level of loading are rarely sufficient to excite a structure. d.) The water table experiments concluded that vortex shedding is not the cause of large amplitude vibrations of cantilever traffic signal support structures.

24 Draft: Past Research and Synthesis: 20 The tow tank experiments were used to evaluate the significance of vortex shedding and galloping in generating the aerodynamic forcing functions observed in the field. Flow visualization experiments were used to determine the onset of vortex shedding and the frequency of the vortex street. The galloping potential was evaluated via steady-state aerodynamic lift and drag experiments and criteria for negative damping (Den Hartog 1956). Eight full-size traffic signal and support arm configurations were tested. Flow from the back and the front were examined. The tow tank allowed three-dimensional flow effects around the ends of the traffic signal to be studied. Texas DoT vibration mitigation devices (damping plates and square cylinders) were also studied in the tow tank tests. The tow tank experiments included flow visualization and also force measurements. The flow visualization was used to determine vortex shedding frequencies and the force measurements were used to study the lift, drag and side forces which would indicate galloping potential. The tow tank experiments also led to the conclusion that vortex shedding from traffic signal heads is an unlikely candidate to produce significant wind-driven oscillations. The shedding found in the tow tank experiments was highly disorganized. Furthermore, the lock-in wind velocities were found to be very low (5 mph) and therefore, the driving forces would be low. The tow tank experiments provided coefficients, C Fy, to be used for analytical galloping studies. This is the coefficient corresponding to the force applied in the direction perpendicular to the free-stream (Den Hartog 1956). Values of C Fy indicate the formation of forces perpendicular to the free stream velocity. The magnitude of this coefficient indicates, qualitatively, the magnitude of vertical (lift) force created in the flow. When the gust subsides, the lifting force is removed and the signal arm is left to vibrate freely to the resting state. The Den Hartog (1956) criteria allows qualitative information to be obtained regarding this coefficient. The field experiments conducted in this study were performed to: (a) determine the vibrational characteristics of actual traffic signal support structures; (b) reproduce the large amplitude vibrations observed in field installations; and (c) evaluate vibration mitigation devices. The anchor bolt configurations used in the field were also used in the field experiments since the stiffness of the bolt and anchor plate are very important to the vibrational response of the

25 Draft: Past Research and Synthesis: 21 structure. Vibrational characteristics (natural frequencies of vibration and damping) were computed for two signal support configurations. Galloping vibrations were successfully reproduced for tow tank configurations that suggested susceptibility to galloping. The experimental results indicated that large damping plates mounted directly above the signal are most effective in mitigating galloping vibrations. The results of the study were coalesced and the following generalizations were made. Galloping of the signal support structure is most likely to occur in relatively few signal-arm spatial configurations. The steady wind speed in which galloping of these structures is to be expected is mph. When a foot arm vibrates in steady wind with amplitude of 4-6 inches, its cause is most probably vortex-shedding. When the amplitude reaches 8 inches, the cause is most likely galloping. Galloping and vortex shedding were found to be highly dependent on wind direction. Therefore, the wind direction that can cause cycles of loading due to galloping is limited. A wind rose can then be used to determine the necessary percentage of time the wind blows from the needed direction and then the number of expected loading cycles can be determined using the natural frequency of the structure. The report also includes several design examples for various signal and sign support structures using the design methodologies developed in the report. Cook et al. (1996) This study was another attempt to quantify the truck-induced gust loading on sign elements. The main difference with this study when compared to Creamer et al. (1979) is that the former study did not include variable message sign (VMS) elements. These signs have a substantial soffit (underside) as well as a large surface perpendicular to traffic. This soffit was thought to receive significant upward pressure from passing trucks and therefore, this study was initiated by the Florida Department of Transportation (FLDoT) to quantify these loading conditions. Truck induced wind gusts were field measured. An existing highway bridge structure was used to support a sturdy apparatus with Pitot-Tube pressure sensors mounted in 15 degree increments to a perpendicular segment of PVC pipe (refer to Figure?.10). The experimental apparatus had the capability of being raised upward and lowered so that a gradient of truck-

26 Draft: Past Research and Synthesis: 22 induced pressures could be measured. Several pressure sensor heights were studied. First of all, random trucks were allowed to pass under the bridge. In this case, the Pitot-tube sensors were set to 17 feet above the roadway. The speed of the oncoming truck was determined using a radar gun. Twenty-three random truck passes were recorded. A power spectrum for the random truckinduced gusts was developed. The dominant frequencies in the power spectrum were approximately 0.6 Hz and 1.8 Hz. Controlled truck passes were also used in the study. Tractortrailer trucks were driven beneath the experimental apparatus at 65 mph. The pressure sensing apparatus was set at four elevations: 17 ft., 18 ft., 19 ft., and 20 ft. The results of the experimental work indicated that passing trucks induced a positive and negative pressure pulse on the VMS elements. Overall, the magnitude of the pressures were low with the average being approximately equal to 1 psf. If the sign is raised upward above the truck, the pressure can be reduced approximately 10 percent for each 1 foot of elevation increase. Lastly, it was found that the dominant frequencies of the truck-induced pressure pulses were at the 1/2 Hz and 2 Hz ranges. As a result, FLDoT currently makes attempts at ensuring that the natural frequency of the supporting structure does not approach these frequencies. It should be noted that a sign support structure (overhead) may be close to the 1/2 Hz range. DeSantis and Haig (1996) This paper outlines an investigation into the cause of the failure of a truss-type cantilever highway sign support structure. The horizontal (mast-arm) was composed of two parallel trusses and the vertical element was a single tapered pole. The sign was located in Virginia. The failure mode described in the paper was one of fatigue and consisted of a circumferential crack around the steel pole at the toe of the base plate weld in the heat affected zone (HAZ). The supported sign was of the variable message type. The soffit of the VMS was 24 inches wide. It was felt that this soffit area was being subjected to vertical pressures due to passing trucks. An analytical investigation into the cause of the VMS collapse as a result of truck-induced gust pressure was undertaken. The investigation of the failure indicated that the only loads that would explain the fatigue failure were vertical oscillations of the arm (DeSantis and Haig 1996). This corresponds to a hatchet-mode vibration. This mode of vibration could be a result of

27 Draft: Past Research and Synthesis: 23 vortex-shedding, galloping or truck-induced gusts on the VMS soffit. The investigators felt that this vibration condition was a result of truck-induced gusts and this decision guided the investigation. Highway workers confirmed this hypothesis. These individuals mentioned that they observed the sign structure oscillating in the hatchet-mode as trucks passed beneath the VMS. The VMS support was designed according to the United State highway design specifications for highway sign and luminaire supports (AASHTO 1985). The fundamental vibrational frequency for the VMS support was determined using the finite element analysis (SAS 1999). Using the computed natural frequency for the fundamental mode of vibration, the critical wind velocity for lock-in was computed to be 1.34 mph. A bluff body dimension normal to the wind assumed was an average diameter of 7.38 inches and the Strouhal number assumed is 0.18 which is consistent with circular bluff bodies. Using the velocity of 1.34 mph it was found that the bending moments that result at the base using conventional pressures (AASHTO 1985) was negligible. This calculation confirmed that vortex shedding induced vibrations were not the cause of the failure. This is questionable since the bluff body dimension perpendicular to the wind is much greater for the VMS and thus the lock-in wind velocity would be much greater. It is interesting to note that vortex shedding on the VMS was not considered in the analysis. The FEA results indicated that a very high mode of vibration (with frequency of 6.5 Hz) corresponded to a vertical cantilever arm vibration. Using the lock-in velocity pressure (AASHTO 1985), stresses at the base of the vertical support (ie. the base plate) exceeded the allowable stress and a limited (very short) fatigue life would be expected. The analytical study indicated that current specification procedures (AASHTO 1985) could accurately predict a limited fatigue life if the proper modes of vibration are considered when establishing vortexshedding induced vibrational pressures. The effect of truck-induced loading was studied anecdotally using engineering rationalization. It was first assumed that a passing truck would have a velocity of 65 mph which is very possible. It was then assumed that the truck would create an upward pulse of air (ie. a gust) with a velocity equal to the passing truck s velocity (65 mph). Using this wind velocity and

28 Draft: Past Research and Synthesis: 24 appropriate drag and gust factors, the force applied to the underside of the VMS is computed using specification procedures (AASHTO 1985). Using this procedure, the pressure exerted to the underside of the sign was computed to be 26.5 psf, which would cause a very short fatigue life. If it is assumed that the upward lifting of the cantilever truss would be followed by a rebound effect, it was shown that approximately 10.8 ksi of stress could exist a the base of the vertical support each time a truck passed. One could also assume that since the VMS support structure has very small damping, these upward pulses could cause further damaging load cycles for each truck. The truck-induced gust theory was further verified by using field crew observations which stated that the sign moved about one foot up and down each time a truck passed beneath. Using this third-hand information, the pressure beneath the sign needed to cause this observed deformation corresponded to a truck speed of approximately 60 mph. Gilani et al. (1997) This report summarizes a research effort conducted for the California Department of Transportation (CALTRANS) after the collapse of a VMS support structure which resulted in motorist injury. The research involved a field investigation of a newly installed VMS (CMS) cantilevered support structure. The field studies were undertaken to quantify the natural frequencies of vibration and modal damping characteristics. Furthermore, a finite element analysis of the support structure was undertaken to evaluate stress distributions around access holes and the base plate. Elastic FEA was utilized and the mast-arm connection plates, as well as the base plate, were modeled. The anchor bolts were not modeled in the analysis. The experimental and analytical investigations revealed that the 4" x 6" conduit hole was a significant source of fatigue concern in the VMS support. Furthermore, it was felt that quality of workmanship was of major concern in the fabrication and erection of the VMS support structures. A mast-arm specimen tested developed micro-cracks as the flange-plate to mast-arm connection bolts were tightened. Further cracking was noticed in these locations during the experimental testing. The following recommendations were made upon completion of the experimental testing phase for the mast-arm. First of all, the conduit hole(s) in the mast-arm should be drilled (not flame cut). Secondly, a pre-qualified weld should be developed for the flange-plate to mast-arm connection. Inspection programs should be improved to ensure quality

29 Draft: Past Research and Synthesis: 25 welding in these very sensitive structures. An out-of-flatness should be specified for flange plates. It was felt that this specification would minimize the formation of micro-cracks as the connection bolts are tightened. The effort concluded that base plate flexibility should be included in the mathematical models. Damping for the cantilever VMS support structure was the order of 0.7% and 0.5% for the first and second modes of vibration, respectively. Lastly, it was mentioned that truck-induced gusts were expected to be severe for the VMS support structure. Chavez et al. (1997) This research report outlines an effort undertaken to retrofit cantilevered VMS support structures with the goal being to eliminate the fatigue problems found in Gilani et al. (1997). The cantilever VMS structure was thought to be subjected to large dynamic stresses resulting from galloping-induced vibrations. The post-to-base plate connection was found to be critical. The retrofit schemes studied in the research effort focused on increasing the support structure stiffness, increasing the support structure damping, and moving the critical section away from the support post-to-base connection. The research program evaluated two retrofit schemes experimentally and analytically. The first scheme involved gusset plates oriented radially around the post at the base plate. The second scheme utilized a concrete jacket at the base extending from the base plate to an elevation six feet above. The experimental testing concluded that the gusset plate scheme did not provide satisfactory performance. It was suggested that if the experimental conditions fully represent the in-field conditions, the concrete jacket retrofit scheme is the preferred approach for the cantilever VMS structure studied. Johns and Dexter (1998b) This research study focused on cantilevered sign, signal and luminaire support structures. Similar to the work of McDonald et al. (1995), it was found that excessive vibration of these types of structures may be caused by three different phenomena: (a) natural wind gust buffeting; (b) buffeting caused by trucks passing beneath the structure; and (c) galloping. These three phenomena require that the structural detailing be examined very closely. The study suggests static load ranges used to simulate the dynamic nature of these phenomena and determine fatigue

30 Draft: Past Research and Synthesis: 26 life. It is further suggested that variable message signs (VMS) are susceptible to truck induced wind gusts on the underside (soffit) flat surface. The primary objective of the research effort was to gather data on the magnitude of truck-induced wind gust loads and, if necessary, refine the equivalent static load range for truck-induced wind gusts. The study involved instrumentation of a cantilevered VMS support structure. Mitigation of the objectionable vibrations was not considered. The report states that overhead sign support structures are not susceptible to galloping, but are potentially susceptible to vortex shedding. As confirmed by the work of McDonald et al. (1995), vortex shedding was not considered in the study. A review of the procedures for modeling structure response to natural wind gusts using spectral finite-element analysis is given. The procedure used is described as follows. The structure is broken up into characteristic loaded areas. Conveniently chosen areas are sign areas or surface areas of the support structure. Each of these areas is subjected to a fluctuating wind force and structure response variables (base plate moment, anchor bolt tension, etc.) during the short gust interval are considered to be random variables. Root mean square (RMS) of the random variable response history is used to assess structural element performance. The constant amplitude response can be estimated from the RMS stress response (Simiu and Scanlon 1996). This effective stress range can then be compared to CAFL predictions. A summary of galloping induced oscillations is provided in the report. A discussion of the galloping sensitive mono-tube cantilevered sign support related research is provided. A review of the research literature related to VMS supports is also provided in the report. The report describes the experimental setup that involved a VMS sign support structure said to have been experiencing large amplitude vibrations. The cantilevered structure studied was reerected at a new test site after it had been removed from its original location due to serviceability problems. A very detailed discussion of the erection of the experimental cantilevered VMS support structure is provided in the report. Dead load stresses in the column and anchor bolts were recorded during erection of the experimental structure.

31 Draft: Past Research and Synthesis: 27 Short term field tests were performed to obtain vibrational characteristics of the erected structure. The stiffness, natural frequency, and damping ratio of the cantilever support structure were determined. Two primary modes of vibration were studied: (a) a hatchet (up-down) mode; and (b) a twisting mode. The twisting mode had the sign pulled and released at a 45 degree angle. The natural damping of the structure was determined using the logarithmic decrement procedure. Fast Fourier Transform (FFT) was performed to determine the characteristic natural frequencies of the structure. The second phase of the short term testing was to measure truck induced wind gusts on the VMS sign. Long term field testing was carried out over a three month period. Strain gages were monitored in the columns, cantilever truss upper chord, and anchor bolts. Wind speed and direction was also monitored over this three month period. No significant events occurred over this monitoring period. Galloping never did occur while the structure was monitored. The structure was found to be constantly vibrating at small amplitudes due to some uncorrelated combination of natural wind gusts and truck-induced wind gusts. It was felt that the stress ranges due to these small vibrations were not sufficient to cause damage. Eight pressure transducers monitored wind gusts. Their locations are shown in Figure?.10. The data taken from the test trucks (driven under the sign at recorded velocities) was found to be unpredictable. The limited data taken from the tests indicated that two trucks running sideby-side under a VMS may have twice the effect on the structure as trucks running behind one another. The truck testing data also suggested a suction introduced to the soffit of the VMS prior to the upward gust of air. This result was consistent with other truck gust studies (Cook et al. 1996). Overall, the pitot-tube system shown in Figure?.10 was thought to be unreliable due to the probable turbulent nature of the wind gusts created by the passing truck. The pitot-tube pressure transducer arrangement was thought to be useful for quantifying pressure gradients along the vertical surface of the VMS. The report therefore, recommends a horizontal pressure gradient on the vertical surface of VMS. One could also argue that this gradient pressure could be present on non-vms signage as well. Column strains were used to assess the response of the cantilever VMS support due to wind gusts.

32 Draft: Past Research and Synthesis: 28 The results suggest that the hatchet mode of vibration results in stresses that are approximately four times as great as the twisting mode. Also, after the initial pulse of the wind gust, the twisting mode has a large amount of natural damping due to the VMS swinging back and forth in the twisting mode. The air resistence on the front and back of the VMS as it swings provides a significant amount of damping. The report seems to contradict itself after recommending that a pressure gradient due to truck induced wind gusts be used. It mentions that due to the natural damping and low column stress ranges in the twisting mode it is not necessary to apply truck-induced wind gusts to the front of the structure. Given the unreliable nature of the pitot tube pressure transducers, one must wonder about the reliability and/or confidence in this statement. Figure?.11 taken from the study illustrates the effect of randomly measured truck induced wind gusts. It can be seen that the measured wind speed was very low: m/s ( mph). However, there was significant stress ranges measured in the column: 10 MPa (1.5 ksi: 0.75 ksi negative and 0.75 ksi positive). One can surmise that the vibration indicated in the figure at this stress range may be of some significance in the fatigue evaluation of details. However, the 1500 psi stress range is rather low and depending on the details, may or may not be a fatigue problem. Using an assumed stress range of 14 MPa, the report back-computed an equivalent uniform pressure on the face of the VMS. This pressure was 525 MPa (11 psf). Therefore, the report suggested that 11 psf was the worse case equivalent pressure found during the long term monitoring of the sign structure. It was rationalized in the report that the presence of air foils over the tractor in a tractor-trailer tandem does not affect the truck-induced gust magnitude. These air dams are placed on the tractor to preserve laminar flow over the trailer. As a result, their presents will actually reduce the upward gust. It was concluded that truck-induced gusts were of potential concern for cantilevered VMS support structures such as the one monitored in this study and a design pressure for truck-induced gust simulation was suggested. The truck-induced pressure can be taken from Table?.1. It should be noted that the range of pressures is a coalescence of recommendations found in several

33 Draft: Past Research and Synthesis: 29 research efforts. For example, the presently described study back-computed a truck induced pressure of 525 MPa as an average pressure over the surface of the sign. DeSantis and Haig (1996) computed a much higher pressure (1760 MPa). The values in Table?.1 are therefore, a rationalization of the current literature. Johns and Dexter (1998a) The state of New Jersey Department of Transportation (NJDoT) presently uses two configurations (eg. cantilevered and straight) luminaire support structures. These configurations are shown in Figures?.12 and?.13. Both luminaire support structures studied in this research effort were constructed from aluminum components. It should be noted that both configurations utilize a shoe base and transformer base. NJDoT suffered failure of 8 straight and 6 cantilevered supports. These failures were the motivating factor for conducting this study. This research effort was conducted to quantify the fatigue resistance of the shoe base socket joint detail used by NHDoT. Twelve luminaire support standards were tested experimentally at ATLSS. Vibrational characteristics of each luminaire support configuration was determined experimentally in the laboratory. Finite element analysis was conducted to determine the vibrational characteristics of the straight and cantilevered support configurations. The FEA assumed fixed support conditions as the base, therefore, it is likely that the vortex shedding conclusions reached in this report are suspect. The FEA and standard procedures for computing lock-in wind velocities for vortex shedding suggested that both the cantilever and straight luminaire supports may be susceptible to vibration in higher modes (not the first mode of vibration). Pull tests were conducted in the laboratory to determine vibrational characteristics and stiffness of the support standards. The experimental stiffness was compared to the stiffness obtained via FEA. The stiffness obtained via FEA underestimated the stiffness by approximately 5%. This seems suspect since the base condition assumed in the FEA was fixed while the breakaway transformer was included in the experimental test. The cantilever luminaire support was found to vibrate in its second mode (hatchet mode) at a frequency very close to the frequency computed using FEA. The natural mechanical damping in the cantilever support

34 Draft: Past Research and Synthesis: 30 configuration was found to be approximate 0.4%. The stiffness of the straight support standard was found to be very similar to that of the cantilever support. This is to be expected. Mechanical damping in the straight support was found to be approximate 1.0% of critical. A lap splice in the straight support standard was thought to have contributed to the increase in mechanical damping. Fatigue testing on the luminaire supports were also conducted. Constant amplitude fatigue tests were carried out on the twelve support standards (6-cantilever, 6-straight). Strain control during the CAF testing allowed very small loads to be applied. This resulted in a load controlled (via strain) fatigue test. Load control was used to ensure a constant stress range in the testing. If displacement control is used, the stress range will change as cracks form in the components. Two goals for the stress ranges used in the experimental effort were to simulate the stress ranges found in the failed supports and also to quantify the constant amplitude fatigue limit (CAFL). The fatigue testing of the cantilever support standard included five specimens without the transformer base and one specimen that included the transformer base. The fatigue testing yielded the following results. Three of seven experiments that included transformer bases (2-cantilever, 1-straight) suffered cracking in the transformer base. In general, the transformer base fatigue cracks were a result of fabrication (casting imperfections), and workmanship (careless grinding). Fatigue cracking also occurred in the pole. These cracks were induced by bending deformations. Two types of cracks formed at the shoe base-to-pole connection. The first type of crack formed at the weld toe and propagated through the pole. The second type of crack formed behind the weld toe. The first crack type was thought to be a result of predominantly bending deformations, while the second type was thought result from shear on the effective weld area. The weld fatigue cracking was a result of quality control problems (ie. the design weld was 7/16" and the effective weld size in some locations was a small as 1/4"). The report provided the following conclusions and recommendations. The fatigue strength of the aluminum (or steel) shoe base detail was AASHTO Category E. The casting process and inadvertent notch creation during grinding of the transformer bases can easily cause fatigue problems in the transformer bases. These should be subjected to very strict quality control procedures. The largest experimental stress range was 12.2 ksi. This stress range was thought to

35 Draft: Past Research and Synthesis: 31 be much smaller than the stress range(s) thought to be present in the field. Therefore, the experimental results did not allow conclusions regarding the in-field stress or fatigue conditions. Several design recommendations were made. These design recommendations are essentially the same as those contained in Kaczinski et al. (1998). A design procedure for a tapered cantilever luminaire support is included in an appendix of the report. Improvements to the base-to-pole connection were suggested. It was recommended to bevel the top inside edge of the shoe base to allow a larger weld leg along the pole and to reduce the shear stress acting on the weld. It was suggested that an unequal leg-length fillet weld (long leg against pole) would accomplish a similar reduced weld stress. The nominal bending stress in the pole should be decreased. It was suggested that this be done by increasing the size or wall thickness of the pole. Finally, it was suggested that steel, rather than aluminum, be used. It was emphasized that the manufacturer recommendations be followed to the letter during installation and that all manufacturersupplied washers be used in the installation of the transformer base. Johns and Dexter (1998c) This journal paper is another condensed version of the Lehigh ATLSS research (Johns and Dexter 1998b; Johns and Dexter 1999; Kaczinski et al. 1998). However, there are several pieces of information found in this paper not easily found in the other research reports. Furthermore, its condensed state allows very direct interpretation of results and therefore, it will be reviewed in the present document. One very nice piece of information available in the paper is a table containing a condensed susceptibility matrix for various sign and luminaire support structures. This matrix is reproduced in Table?.2. Several conclusions (which may overlap with previous ATLSS research reports) were drawn in relation to sign support structure design. First of all, it was suggested that cantilevered sign and signal support structures should be designed for galloping induced loads using a static (shear) pressure of 21 psf. This shear pressure should be made to act on the vertical face of the supported sign and it should be a vertical loading. Truck-induced gust loadings can be considered in design using an equivalent static pressure of 37 psf multiplied by the appropriate drag coefficient. This pressure is to be applied to the horizontal surfaces of the

36 Draft: Past Research and Synthesis: 32 support structure and/or the soffit of a VMS/CMS. The length of this pressure along the VMS or support structure should be 12 feet (the width of a passing truck). Kaczinski et al. (1998) The report reveals the results of a survey sent to state DOT s regarding performance of their cantilever sign and signal support structures. Approximately 18 of the 36 respondents to the survey reported problems with their cantilevered structures. The report suggest that truck and natural wind-induced vibrations are responsible for the accumulation of fatigue damage in structures that have been in service for years. It is suggested that a displacement limit of 8 inches in these structures is required for motorists to clearly read/see the signs/signals. The survey also reported a total of 80 occurrences of fatigue damage in cantilevered support structures. The majority of damage reported occurred in the mast-arm-to-column connection, column-to-base-plate connection, and/or anchor bolts. This report also concurs with the idea that design specifications (AASHTO 1985; 1994) are rather vague in relation to vibration and fatigue design. Four wind loading types are identified in the report: (a) vortex shedding; (b) galloping; (c) natural wind gusts; and (d) truck-induced wind gusts. The report reviews each of these phenomena in great detail. Sign support structures are normally comprised of circular crosssection elements. As a result, they are not susceptible to galloping on their own. Circular crosssections always exhibit positive aerodynamic damping. However, once a sign (VMS or otherwise) is attached to the support structure, the composite bluff body may make the structure susceptible to galloping. This is especially true in signal and cantilever sign supports. One would have to wonder if a composite bluff body (overhead truss and sign) could not cause galloping type vibrations. This would suggest that the torsional stiffness of the sign bridge may allow sufficient angle of attack change in the wind pressure to allow galloping. Vortex shedding is correctly stated to be the main concern in luminaire supports. It is stated that structures may be susceptible to vortex shedding induced vibrations for wind velocities in the range 10 to 35 mph. Wind speeds below 10 mph are usually not sufficient to excite most structures and wind speed greater than 35 mph do not easily allow the formation of periodic (organized) vortices.

37 Draft: Past Research and Synthesis: 33 Natural wind gusts are characterized by a spectrum of fluctuating velocity components. These fluctuations in flow velocity induce fluctuating flow pressures on the various structural components which in turn, create vibrations in the structure. The magnitudes of the variable stress ranges induced in the connection details of a structure may, in some cases, cause fatigue cracking due to the long-term cumulative effect of the natural wind gusts. Vibration of sign support structures is highly dependent on inherent damping in the structure. Overhead sign and cantilever luminaire supports have very low inherent damping and therefore, these structures could be susceptible to fatigue damage due to natural wind gusts. Truck-induced wind gusts were also mentioned as a source of vibrations in cantilevered sign structures. The report states that... for the purposes of fatigue design, truck-induced wind loads normal to the sign are not critical. The report goes on to mention that the vertical component of the truck-induced wind gust is important in the evaluation of fatigue performance. The magnitude of the vertical truckinduced gust can be reduced significantly by simply raising the lower surface of the sign structure with respect to the road surface. A nice definition of constant amplitude fatigue limit (CAFL) is provided. The CAFL is a stress range below which fatigue life appears to be infinite. It implies a fatigue life greater than the typical service life of the structure (25 years for sign and luminaire support structures). The report mentions that in order to perform a cumulative damage calculation to predict a finite fatigue life, the numbers of cycles of stress ranges in certain intervals of magnitude are required (ie. the complete histogram of the loading for all future events). The report highlights an infinitelife fatigue design approach (Fisher et al. 1993). The nature of the stress ranges resulting from wind loading consists of large variation in amplitude. Therefore, there may be instances where the stress range exceeds the CAFL. As long as the percentage of time that the CAFL is acceptably low, there is essentially infinite life in any detail. Experimental results indicate that fatigue failure can occur if 0.05 percent or more of the stress ranges applied to a detail exceed the CAFL and infinite life resulted when fewer than 0.01 percent of the stress ranges exceeded the CAFL (Fisher et al. 1993). A nice synopsis of the infinite-life variable-amplitude fatigue design approach (Fisher et al. 1993) is provided in the report. Using this approach, structure response and stress ranges

38 Draft: Past Research and Synthesis: 34 (including any dynamic amplification) which have a probability of exceedence of 0.01 percent must be estimated. The 0.01 percent probability of exceedence stress ranges are termed the fatigue limit-state ranges. These stress ranges must be less than the CAFL of any detail considered. The infinite life approach is considerably simpler than trying to account for cumulative damage caused by a future distribution of wind loads as done by South (1994). The complete loading spectrum is immaterial using this approach. All one needs to do is compute the strength limit state as provided in the design specifications (AASHTO 1985, 1994) and the fatigue limit-state governed by the 0.01 probability of exceedence. The research effort outlined in the report covered five areas related to fatigue performance of sign and signal support structures. The first task performed as part of the effort was aerodynamic and aeroelastic studies performed at MIT in the Wright Brothers Memorial Wind Tunnel. Due to size limitations, scale models of the sign and signal support structures were constructed and used for the testing. Scaling effects were studied in the wind tunnel and were found to be negligible in evaluating the real structures. The aerodynamic research program was conducted to measure forces generated on the model cantilever structures and evaluate their susceptibility to galloping-induced oscillations. Several conclusions were reached upon completion of aerodynamic portion of the research effort. First of all, signal attachments are more susceptible to galloping when the wind flow is from the rear. Backplates contained on signal attachments increase the susceptibility of galloping. These results were similar to conclusions drawn by other researchers (McDonald et al. 1995). Lastly, it was concluded that the galloping susceptibility of sign attachments is independent of sign aspect ratio (height-to-width-ratio) and direction of wind flow. The aeroelastic test program was used to further evaluate the conclusions reached in the aerodynamic wind tunnel study. This secondary study was needed to determine the forces (at the support structure base) generated if galloping induced oscillations occurred in the structure. A dynamic finite element analysis was then undertaken to estimate applied loading on the signal and sign attachments via matching uniform attachment loading with forces generated at the base during wind tunnel testing. Both vortex shedding vibrations (of the structure without attachments) and galloping-induced vibrations (of the structure with attachments) were studied.

39 Draft: Past Research and Synthesis: 35 The aeroelastic study allowed the following conclusions to be drawn. Galloping was found to be possible for most types of sign and signal structures. However, it was also concluded that the galloping phenomena is very sensitive to a variety of conditions. Many very specific conditions related to the dynamic properties of the structure, the aerodynamic properties of the attachments, and the wind flow characteristics, must all be aligned properly for galloping to take place. While the aerodynamic properties of the structure and attachments would lead one to assume that galloping may occur, galloping-induced oscillations were not observed in the wind tunnel for these situations (in one case, galloping was observed, but could not be reproduced). One interesting conclusion made was that, once galloping instability is initiated, the resulting acrosswind vibration persists even after the wind velocity is reduced. This causes concern with respect to fatigue damage, as the vibrations causing damage may be occurring even after the critical velocity that created them ceases. The final conclusion related to galloping was that truss cantilever sign support structures were not susceptible to galloping-induced vibration. However, the sign attachments did exhibit the tendency to gallop in the wind tunnel. Therefore, one can conclude that when signs are attached to the cantilever support structure galloping could occur (provided all the conditions are right). It was also concluded that vortices shed from attachments on cantilevered sign structures could not drive excessive vibrations. Furthermore, it was suggested that vortex shedding need not be considered in the design of cantilevered sign support structures when lock-in velocities are lower than 5 mph. It was felt that this wind velocity was insufficient to cause significant force to excite a structure. It also was suggested that signal and sign attachments disrupt the formation of organized vortex streets due to threedimensional effects. Therefore, vortex shedding could be a problem prior to attachment installations. This leads to some concern since most of the overhead sign support structure is void of attachments in many cases (ie. very sparse signage is present). Therefore, vortex shedding may be a problem with these structures. Lastly, it was concluded that tapered structural members within the support structure inhibit vortex-shedding induced vibrations. This conclusion can only be made in relation to signal support structures. Static and dynamic finite-element analyses were used to estimate wind pressures applied to cantilevered support structures during galloping, vortex shedding, natural and truck-induced vibrations. The FEA neglected foundation flexibility and soil-structure interaction. The base

40 Draft: Past Research and Synthesis: 36 plate condition was assumed to be fixed. This was thought to develop worse-case estimates for stress ranges at the support structure base. It is believed that this omission will significantly effect the results. The effect of base plate fixity on fundamental modes of vibration should be studied as it may significantly affect which modes are excited by wind. The FEA in this study consisted of the following: a.) Eigenvalue analysis to determine the natural frequencies and mode shapes corresponding to the first six modes of vibration. The number of modes chosen was arbitrary. b.) Load models for galloping and vortex-shedding were developed based on the results of the aeroelastic and aerodynamic wind tunnel studies. The load model for galloping of the sign-support structures was represented as a uniformly distributed load applied in the vertical plane over the length of the sign panel. The load model for vortex shedding on the sign support structure was represented by a uniformly distributed load applied to the structure in the vertical plane over the length of the horizontal mast arm. The dynamic analyses performed consisted of linear modal analysis to determine the steadystate dynamic response of the sign support structure subjected to vortex-shedding and/or galloping. The applied loading was assumed to be a sinusoidal wave of the form. Static FEA was also performed. An equivalent static pressure range (SPR eq ) was computed determined. Several recommendations were made regarding equivalent static lift pressures to simulate galloping-induced vibrations. An equivalent static lift-pressure range equal to 21 psf was recommended for the design of cantilevered sign support structures. This equivalent static wind pressure is to be applied vertically as a shear stress on the surface area of all sign and signal attachments mounted to the horizontal mast-arm as seen in the normal elevation. Furthermore, it is suggested that only those cantilevered support structures NOT having attachments be evaluated for vortex-shedding induced vibrations. The magnitude of the critical (lock-in) wind velocity should be greater than 10 mph for vortex-shedding to be considered. In most cases, provisions contained in design specifications (AASHTO 1985, 1994) were thought to be adequate in this regard.

41 Draft: Past Research and Synthesis: 37 The FE analyses also consisted of spectral analyses to simulate the effects of wind gustiness on the cantilevered support structures. Anchor bolt fatigue testing was also part of this study. The goal(s) of the testing was to develop CAFL for snug-tight and fully-tightened anchor bolts. The anchor bolt testing was motivated by the uncertainties involved in using welded component fatigue results for anchor bolt fatigue. The report briefly summarized previous research by Frank (1980) that concluded that nominal diameter, galvanizing, thread forming process (eg. cut vs. rolled), thread series, and type of steel have negligible effect on fatigue life. Dusal (1984) performed similar testing and reached similar conclusions. These research efforts suggest that snug-tight anchor bolts adhere to AASHTO category E details while fully-tightened anchors adhere to category D details. Unfortunately, these past efforts did not arrive at a CAFL for snug- and fully-tightened anchor bolts. This was the motivation for the presently discussed effort. The report provides a fairly detailed comparison of the fatigue provisions found in the European, U.S., and British design specifications. The review of these specifications revealed that significant uncertainty exists with respect to anchor bolt design for infinite fatigue life. That is, there is a lack of well-defined CAFL for anchor bolts with varying degrees of tightness. The experiments conducted in the study involved AASHTO Grade 55 and 105 anchor rods with 6 UNC threads and 1/2-1/2 rolled/cut threads. All nuts, rods, etc..., were galvanized. Concentric and misaligned bolts were tested. This is important for WI DoT high-mast light supports since masts considered deficient involved misaligned anchor rods. The misalignment tested in the present study was 1:40. All specimens were double nut configuration. Sinusoidal loading frequencies of 10 and 25 Hz were used in the testing. Maximum applied tensile stress (on tension areas) were: Grade 55: 0.60 F y Grade 105: 0.32 F y or 0.38 F y The results of the anchor bolt study indicated that the crack initiation life is a much greater portion of the total fatigue life for anchor bolts. Also, the effect of mean stress and yield strength

42 Draft: Past Research and Synthesis: 38 is much more pronounced in anchor bolts since the initiation life is so large. It was suggested that the CAFL for snug-tight, concentrically loaded rods corresponds to category D (7 ksi stress range). A statistical analysis further indicated that lower bound CAFL can be taken as category E. In general, as the maximum stress is reduced, the fatigue life increases irrespective of the material yield stress. Thread forming process was found to NOT significantly affect the fatigue strength of Grade 55 specimens. It did, however, affect the Grade 105 bolts. It was believed that the (beneficial) compressive residual stresses at the root of the threads in the rolled thread specimens was the reason for improved performance over the cut threads. It was hypothesized that the thread forming process benefits were not seen in Frank (1980) due to the very high maximum tensile stress applied and that the entire stress range may have been tensile. Lower grade anchor bolts (ie. Gr. 55) exhibited slightly better fatigue performance than the higher grade bolts (ie. Gr 105). Therefore, the results of this research indicates a penalty for high-strength bolts with respect to fatigue performance. Beveled washers were found to provide negligible improvement in the fatigue performance of misaligned anchor bolts. The following CAFL values were suggested as a result of the misaligned anchor bolt testing: Cat. D (7 ksi): no misalignment consideration required or use of beveled washers; < Cat. D: if no beveled washers are used and anchors are misaligned. The anchor bolt experimental investigation allowed the following conclusions to be made. First of all, axially loaded, snug-tight anchor rods should be designed for fatigue using Category E in regions of finite fatigue life. Fully-tightened bolts can be designed using Category E in the finite fatigue life region. The CAFL for all anchor bolts was suggested as Category D provided beveled washers were utilized for a misaligned (1:40 max.) condition. Bending stresses resulting from misalignments less than 1:40 need not be explicitly considered if firm contact between the nut(s) and ply(s) exists (eg. beveled washers). Furthermore it was suggested that prying should be minimized. If F max < 0.6F y, the CAFL increases significantly. Also, if F max < 0.3F y rolled threads perform better than cut threads. The effect is more pronounced as F y increases. Higher strength anchor bolts must be designed with consideration of fatigue. In addition to the anchor bolt testing carried out, base plate bolt group experiments were conducted. These experiments studied the following parameters: misalignment; exposed bolt

43 Draft: Past Research and Synthesis: 39 length (stand-off) above the foundation; nut tightness; base plate thickness; and moment:torsion:shear ratio. It was found that thin base plates could allow prying to occur (this is an intuitive conclusion as well). The thin plate prying increased the mean normalized stress in the bolts and also increased the scatter in the experimental results. It was suggested that the axial load in the anchor bolts can be determined using the flexure formula provided prying is prevented. The bending stress in the anchor bolts resulting from direct shear can be neglected when the stand-off distance of the anchor bolt is less than the diameter of the bolt. It is felt that this is a limited conclusion since clearance issues encountered during plumbing procedures may require this stand-off distance to be much greater. If the stand-off distance is greater than the diameter of the anchor rod, then a fixed-fixed beam model is appropriate (intuitive?). The report also re-iterates the conclusions of Keating and Fisher (1986) who found that material yield strength, mean stress levels and operating temperatures have little influence on the fatigue resistance of full-scale welded details. The critical factors for fatigue performance found in this study were nominal stress range and notch severity. A very useful section of this report categorizes cantilever support structure details according to the AASHTO A-E fatigue curves. A nice table containing category classifications is provided. Welded tubular member connections are classified as ET. These connections are prevalent throughout the overhead sign structures studied in the present research effort. The current design specifications (AASHTO 1994) were reviewed and changes to the present U.S. specifications for design were suggested. The provisions contained in the Canadian specifications (ONT 1992) were reviewed and compared to the U.S. specifications. Conclusions made as a result of the study involved many aspects of sign and luminaire support structure design. It was concluded that the flexure formula can be used to determine the anchor bolt axial stresses using I for the anchor bolt group as long as prying is not present. Anchor bolt bending stresses can be ignored when the stand-off distance is less than or equal to the diameter of the anchor bolt. AASHTO category D (7 ksi) can be used as a lower-bound estimate for axially loaded, snug-tight and fully-tightened anchor bolts as long as full contact is

44 Draft: Past Research and Synthesis: 40 maintained. The fatigue resistance of most sign and luminaire support details can be categorized with CAFL values of E (4.5 ksi) or E (2.6 ksi). The research effort identified 4 wind loading phenomena as being important in sign and luminaire support structures: (a) galloping; (b) vortex shedding; (c) natural wind gusts; and (d) truck-induced wind gusts. The report contains the final recommendation that overhead sign and signal bridges should be studied. Specifically, it recommends that the literature and other design codes should be reviewed. Furthermore, dynamic and static analyses should be conducted to determine and estimate equivalent static load ranges for vortex shedding, natural wind gusts, and truck-induced wind gusts. Johns and Dexter (1999) This paper outlines the ATLSS research undertaken to evaluate the effect of passing trucks on cantilevered sign support structures (Johns and Dexter 1998b). There are no additional pieces of information contained in this paper that are not contained in the other reports discussed in this section of the report. Kashar et al. (1999) This paper outlines an investigation into the cause of a failed VMS structure for CALTRANS. It is believed that this investigation was conducted in parallel with that of (Chavez et al. 1997; Gilani and Whittaker 2000a,b; Gilani et al. 1997) for the same VMS support structure. The metallurgical investigation results provided in the paper suggest that the material and weld used in the VMS structure were satisfactory and were not likely the cause of the shortened fatigue life of the VMS support. The investigation estimated that approximately 1,000,000 trucks passed beneath the sign support prior to failure. A similar CMS/VMS structure was instrumented with strain gauges and dead load stresses measured were compared with analytically obtained quantities. The results of this comparison indicated that the grout used beneath the base plate provided for significant restraint such that the fixed base condition assumed in the analytical studies described was adequate.

45 Draft: Past Research and Synthesis: 41 It was assumed that the Strouhal number for the 25.4 ft. high by 32.8 ft. wide VMS was This led to a lock-in velocity for vortex shedding of 30 mph. It was mentioned in the paper that the wind averaged 31 mph during the 24 hours prior to failure and had gusts to 60 mph. This would suggest that vortex shedding-induced vibrations were a cause for the fatigue failure (or at least contributed to it). The instrumentation and field observation described in the paper resulted in the following. The measured results indicated that mild to strong winds and typical truck passings generated significant stresses within the support structure (6 ksi at height 3 feet from the base; ksi just above the weld). The measured natural frequency of vibration was 1.05 Hz which was very close to the analytically obtained value using FEA. The paper reports that galloping was observed, with vertical excursions (amplitudes) of approximately 12 inches. Gilani and Whittaker (2000a) and Gilani and Whittaker (2000b) These research papers basically summarizes the research conducted at the University of California - Berkeley related to cantilever VMS support structures (Chavez et al. 1997; Gilani et al. 1997). There are several conclusions related to the Berkeley research that are more pointedly stated in these research papers. First of all, it is mentioned that evaluation of the field recorded response data and the work of Kaczinski et al. (1998) suggest that galloping instability is a potential cause of the VMS/CMS support failure. Furthermore, the paper mentions that the design procedure suggested in Kaczinski et al. (1998) should be re-evaluated in light of the stress-ranges measured during the field experimentation. The second paper provided a concise summary of the laboratory experimentation conducted. Fouad et al. (1998) This?.3 Wisconsin Department of Transportation Experience?.4 Synthesis of Past Research the WI DoT Experience?.5 Current Inspection Procedures and Manuals

46 Draft: Past Research and Synthesis: 42?.6 Outline of Present Research Approach

47 Table?.1: Truck-Induced Gust Pressures Johns and Dexter (1998b). Draft: Past Research and Synthesis: 43 Elevation above Road Surface (m) P (Pa) and above 0 Table?.2: Susceptibility Matrix for Sign, Signal and Luminaire Supports Johns and Dexter (1998c). Galloping Vortex Shedding Natural Wind Gusts Truck-Induced Gusts Sign X (1) X X Signal X X X Luminaire X X X - Indicates support structure susceptible to wind loading phenomenon. (1) - Vortex shedding was reported in an overhead sign support structure (Irwin and Peeters 1980).

48 Draft: Past Research and Synthesis: 44 Figure?.1: Pressure Distribution and Impulse Function Due to Truck Induced Gusts (Creamer et al. 1979).

49 Draft: Past Research and Synthesis: 45 Figure?.2: Overhead Sign Support Structure Studied (Irwin and Peeters 1980). Figure?.3: Overhead Sign Support Structure Wind Tunnel Model (Irwin and Peeters 1980).

50 Draft: Past Research and Synthesis: 46 (a) Free Segment Wind Tunnel Model Schematic (b) Cantilever Wind Tunnel Model Schematic Figure?.4: Wind Tunnel Model Schematics used to Study Vibrational Response (Edwards and Bingham 1984). Figure?.5: Pressure Transducer Layout and Experimental Setup (Edwards and Bingham 1984).

51 Draft: Past Research and Synthesis: 47 Figure?.6: Randomly Generated Power Spectrum Density Function for Wind Pressure (Edwards and Bingham 1984). Figure?.7: Random Forcing Function used for Dynamic Analysis (Edwards and Bingham 1984).

52 Draft: Past Research and Synthesis: 48 Figure?.8: Wind Speed Data Collected in Springfield Illinois (South 1994). Figure?.9: Wind Speed Histogram for Springfield, Illinois (South 1994).

53 Draft: Past Research and Synthesis: 49 Figure?.10: Overpass Mounted Wind Velocity Measurement Device (Cook et al. 1996). Figure?.11: Pressure Transducer Set-Up Used to Measure Truck-Induced Wind Gusts (Johns and Dexter 1998b).

54 Draft: Past Research and Synthesis: 50 Figure?.12: Maximum Recorded Stress Ranges in Column Due to Truck-Induced Gusts (Johns and Dexter 1998b). Figure?.13: Cantilever Luminaire Support Standard (Johns and Dexter 1998a).

55 Figure?.14: Straight Luminaire Support Standard (Johns and Dexter 1998a). Draft: Past Research and Synthesis: 51

56 Draft: Past Research and Synthesis: 52 References 1.) AASHTO. (1975). Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals, American Association of State Highway Transportation Officials, Washington, D.C. 2.) AASHTO. (1985). Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals, American Association of State Highway Transportation Officials, Washington, D.C. 3.) AASHTO. (1994). Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals, American Association of State Highway and Transportation Officials, Washington, D.C. 4.) AASHTO. (1996). Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, Washington, D.C. 5.) Anderson, T.L. (1995). Fracture Mechanics - Fundamentals and Applications, 2nd Edition, CRC Press, Inc., Boca Raton, FL. 6.) ASCE. (1990). Minimum Design Loads for Buildings and Other Structures (ASCE 7-88), American Society of Civil Engineers, Reston, VA. 7.) ASCE. (1998). Minimum Design Loads for Buildings and Other Structures (ASCE 7-98), American Society of Civil Engineers, Reston, VA. 8.) Barsom, J.M., and Rolfe, S.T. (1999). Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics, 3rd Edition, ASTM, West Conshohocken, PA. 9.) Broek, D. (1987). Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers, Dordrecht, Netherlands. 10.) Broek, D. (1988). The Practical Use of Fracture Mechanics, Kluwer Academic Publishers, Norwell, MA. 11.) Chavez, J.W., Gilani, A.S., and Whittaker, A.S. (1997). Fatigue-Life Evaluation of Changeable Message Sign Structures, Volume 2 - Retrofitted Structures. Report No. UCB/EERC-97/10, Earthquake Engineering Research Center, University of California, Berkeley, CA. 12.) Cook, R.A., Bloomquist, D., Agosta, A.M., and Taylor, K.F. (1996). Wind Load Data for Variable Message Signs. FL/DOT/RMC/ , Florida Department of Transportation.

57 Draft: Past Research and Synthesis: ) Creamer, B.M., Frank, K.H., and Klingner, R.E. (1979). Fatigue Loading of Cantilever Sign Structures from Truck Wind Gusts. FHWA/TX-79/ F, Center for Highway Research, University of Texas - Austin, Austin, TX. 14.) Davenport, A.G. (1961). Applications of Statistical Concepts to the Wind Loading of Structures. Proceedings of the Institute of Civil Engineers, 19, ) Den Hartog, J.P. (1956). Mechanical Vibrations, 4th Edition, McGraw-Hill, Inc., New York, NY. 16.) DeSantis, P.V., and Haig, P.E. (1996) Unanticipated Loading Causes Highway Sign Failure. ANSYS Convention, ) Durst, C.S. (1960). Wind Speeds Over Short Periods of Time. The Meteorological Magazine(608), ) Dusal, J.J. (1984). Fatigue of Anchor Bolts.. 19.) Edwards, J.A., and Bingham, W.L. (1984). Deflection Criteria for Wind Induced Vibrations in Cantilever Highway Sign Structures. North Carolina Department of Transporation FHWA/NC/84-001, Center for Transportation Engineering Studies, North Carolina State University, Rayleigh, NC. 20.) Fisher, J.W., Miki, C., Slutter, R.G., Mertz, D.R., and Frank, W. (1983). Fatigue Strength of Steel Pipe-Base Plate Connections. Engineering Structures, 5(April), ) Fisher, J.W., Nussbaumer, A., Keating, P.B., and Yen, B.T. (1993). Resistance of Welded Details Under Variable Amplitude Long-Life Fatigue Loading. NCHRP Report 354, National Cooperative Highway Research Program, Transportation Research Board, National Research Council, Washington, D.C. 22.) Fouad, F.H., Calvert, E.A., and Nunez, E. (1998). Structural Supports for Highway Signs, Luminaires, and Traffic Signals. National Cooperative Highway Research Program, Report 411, Transportation Research Board, National Research Council, Washington, D.C. 23.) Frank, K.H. (1980) Fatigue Testing of Anchor Bolts.. 24.) Fuchs, H.O., and Stephens, R.I. (1980). Metal Fatigue in Engineering, John Wiley & Sons, Inc., New York, NY. 25.) Gilani, A., and Whittaker, A. (2000a). Fatigue-Life Evaluation of Steel Post Structures. I: Background and Analysis. Journal of Structural Engineering, 126(3),

58 Draft: Past Research and Synthesis: ) Gilani, A., and Whittaker, A. (2000b). Fatigue-Life Evaluation of Steel Post Structures. II: Experimentation. Journal of Structural Engineering, 126(3), ) Gilani, A.S., Chavez, J.W., and Whittaker, A.S. (1997). Fatigue-Life Evaluation of Changeable Message Sign Structures, Volume 1 - As Built Structures. Report No. UCB/EERC-97/10, Earthquake Engineering Research Center, University of California, Berkeley, CA. 28.) Irwin, H.P., and Peeters, M. (1980). An Investigation of the Aerodynamic Stability of Slender Sign Bridges, Calgary. LTR-LA-246, National Research Council Canada - Aeronautical Establishment. 29.) Johns, K., and Dexter, R. (1998a). Fatigue Testing and Failure Analysis of Aluminum Luminaire Support Structures , Center for Advanced Technology for Large Structural Systems, Lehigh University, Bethlehem, PA. 30.) Johns, K., and Dexter, R.J. (1998b). Fatigue Related Wind Loads on Highway Support Structures , Center for Advanced Technology for Large Structural Systems, Lehigh University, Bethlehem, PA. 31.) Johns, K.W., and Dexter, R.J. (1998c). The Development of Fatigue Design Load Ranges for Cantilevered Sign and Signal Support Structures. Journal of Wind Engineering and Industrial Aerodynamics, 77 & 78(Sep-Dec), ) Johns, K.W., and Dexter, R.J. (1999) Truck Induced Wind Loads on Highway Sign Support Structures. Structural Engineering in the 21st Century, Proceedings of the 1999 Structures Congress, New Orleans, LA, ) Kaczinski, M.R., Dexter, R.J., and Van Dien, J.P. (1998). Fatigue Resistance Design of Cantilevered Signal, Sign and Light Supports. (NCHRP Report Project 10-38), ATLSS Engineering Research Center, Bethlehem, PA. 34.) Kashar, L., Nester, M.R., Johns, J.W., Hariri, M., and Freizner, S. (1999) Analysis of the Catastrophic Failure of the Support Structure of a Changeable Message Sign. Structural Engineering in the 21st Century, Proceedings of the 1999 Structures Congress, New Orleans, LA, ) Keating, P.B., and Fisher, J.W. (1986). Fatigue Resistance Design of Cantilevered Signal, Sign and Light Supports. (NCHRP Report Project xx-xx), ATLSS Engineering Research Center, Bethlehem, PA.

59 Draft: Past Research and Synthesis: ) McDonald, J.R., Mehta, K.C., Oler, W., and Pulipaka, N. (1995). Wind Load Effects on Signs, Luminaires and Traffic Signal Structures. Texas Department of Transportation Report No F, Wind Engineering Research Center - Texas Tech University, Lubbock, TX. 37.) Meguid, S.A. (1989). Engineering Fracture Mechanics, Elsevier Science Publishers Ltd. 38.) Novak, M. (1969). Aeroelastic Galloping of Prismatic Bodies. Journal of the Engineering Mechanics Division, 95(EM1), ) Novak, M. (1972). Galloping Oscillations of Prismatic Structures. Journal of the Engineering Mechanics Division, 98(EM1), ) ONT. (1992). Ontario Bridge Design Code,, Ottawa. 41.) Peterson, R.E. (1974). Stress Concentration Factors, John Wiley & Sons, Inc., New York, NY. 42.) ANSYS, rev. 5.4 (1999) SAS IP, Inc., ver. 43.) Simiu, E., and Scanlon, R.H. (1996). Wind Effects on Structures: Fundamentals and Applications to Design - 3rd Edition, John Wiley & Sons, Inc., New York, NY. 44.) South, J. (1994). Fatigue Analysis of Overhead Sign and Signal Structures. FHWA/IL/PR-115, Illinois Department of Transportation, Springfield, IL.

60 Appendix B Modeling Wind Velocity and Turbulence Foley 4 rd Quarter FY 2000

61 Draft: Modeling Wind Velocity and Turbulence: 1 Chapter? Modeling Wind Velocity and Turbulence?.1 Introduction Naturally occurring winds are by nature highly variable in that wind speeds vary with time of day, time of year, height above ground, etc. This variability comes from many sources. In general, natural wind speed variability has been quantified using several characteristic measures: (a) wind speed profile; (b) topography or surface roughness; (c) turbulence (via averaging time); and (d) directionality. The goal of this chapter of the report is to define these characteristic measures within the context of wind engineering terminology and their effect in determining wind loading for sign and luminaire support structures. Furthermore, a discussion of wind speed data obtained for five ASOS (Automated Surface Observing System) stations of the National Weather Service (NWS) and the Federal Aviation Administration (FAA) within Wisconsin will be provided. Statistical models of the extreme wind speed and directionality for these stations will be discussed. The final section of this chapter provides discussion related to simulating turbulent wind speeds for use in time history analysis of sign and luminaire support structures.?.2 Variation of Wind Speed with Height and Surface Roughness Much like water flowing in an open channel, the wind flows over the surface of the earth. There are many obstructions on the earth s surface (eg. buildings, trees, etc...) and therefore, the surface of the earth retards the free flow of the wind stream. As a result, turbulent eddies in the wind flow form at the surface of the earth. This turbulence causes fluctuations in wind speed and therefore, the wind pressure acting on man-made structures. The variation of wind speed with height and surface roughness begins with a quantity called the gradient wind speed, V g. The gradient wind speed occurs at a height called the gradient height, Z g. The gradient wind speed is constant above the gradient height. Thus, the interference of the ground s surface terminates at heights above the gradient height.

62 Draft: Modeling Wind Velocity and Turbulence: 2 There are two empirical relationships commonly used to describe the variation of wind speed with height above the earth s surface: the log law and the power law. The log law is deemed slightly more accurate for large heights (Liu 1991; Simiu and Scanlon 1996) it is more difficult to use. In the present research the power law is used. The wind speed at any height above the ground can be determined using the power law as follows, U U z z = 1 z 1 1 α 0 z z g (?.1) where; z is the height above the ground; " is the power law exponent which ranges from 5.0 to 11.5 dependent upon the surface roughness; U 1 is a reference wind velocity (usually that measured); and z 1 is a reference height (usually 10 m or 33 feet for standard wind recording stations). In general, smooth terrain (eg. open water) has a larger value of " than rough terrain (eg. urban landscape).?.2 Averaging Time and Wind Gust The most important characteristic used to describe wind gusts is something called the averaging time. Wind recording stations do not report instantaneous wind speeds, but report wind speeds averaged over differing time intervals. The ASOS sites used in this study report both 5 second gust speeds and 2 minute gust speeds with their associated directions. These maximum gust speeds are reported once daily. As will be shown, the averaging time can affect the magnitude of the gust speed. The value of the wind speed reported varies with the averaging time used while recording the wind speed. The averaging time can be defined with the aid of Figure?.1. As a general rule, as the averaging time is increased, the mean wind velocity over that time period is reduced. Over the last several decades, wind speed has been acquired by the NCDC using many averaging times. The anemometer used to acquire the data can affect the quality of the measurements. A very common averaging method is that obtained through consideration of the fastest mile wind. The fastest mile wind is the peak wind speed averaged over 1 mile of wind passing through and anemometer (Liu 1991). There are methods available to determine the averaging time given the

63 T Draft: Modeling Wind Velocity and Turbulence: 3 peak wind speed averaged over one hour (Durst 1960). The averaging time of the fastest mile wind can be obtained rather simply using (Liu 1991), = 3600 (?.2) V F where; T is the averaging time for the fastest mile wind; and V F is the value for the fastest mile wind in miles per hour. The mean hourly wind is often used to help convert peak wind speeds between varying averaging times. Wind loading standards (ASCE 1998) utilize the curve proposed by Durst (1960) for smooth terrains as illustrated in Figure?.2. Fastest mile winds ranging from 75 to 100 mph have averaging times ranging from 48 seconds to 36 seconds, respectively. Design standards use a gust factor to account for wind gusts or high velocity, very short duration winds. The gust factor is commonly determined using an averaging time that is appropriate for quantifying gust (eg. 2 seconds). Thus, if the fastest mile wind is 90 mph, the averaging time can be determined as, 3600 T = = 40 V V V V = 129. = sec Using this averaging time, the ratio of peak wind to peak hourly wind is taken from the curve given in Figure?.2. With T = 40 seconds, If a 2 second wind gust is used, the averaging time is 2 seconds. Thus, the velocity ratio for this averaging time is, The 2 second wind gust is therefore, related to the 40 second fastest mile wind via, V V2 = 155. V3600 = 155. V V = =.. where the gust effect factor is In the present study, the dynamic nature of the wind gusts will be determined analytical using simulated turbulent winds with several averaging times. Design of structures according using standards usually includes gust effect factors.

64 Draft: Modeling Wind Velocity and Turbulence: 4?.3 Wind Speed Data for Wisconsin Wind speed records for the United States can be obtained from the NCDC for a variety of recording stations. Although there are many stations within the state of Wisconsin, there are relatively few that contain detailed short averaging time wind speed records. These stations are given in Table?.1. The recording stations provide a reasonably diverse area throughout the southern one-half of the state. The locations of these stations within the State are shown on the map contained in Figure?.3. All stations given in the table are ASOS stations and they record peak 5 second and 2 minute daily wind speeds. These two averaging times will allow generation of turbulent wind gusts from which transient (time history) analysis of sign structures can occur. The 5 second and 2 minute peak wind speeds have been recorded for the sites in Wisconsin since July Data collection for this project stopped with data taken in November Therefore, over four continuous years of daily wind data has been collected. Histograms for the maximum 5 second and 2 minute wind speed magnitudes for the five recording stations are given in Figures?.3 through?.23. These peak gust histograms illustrate that as the averaging time increases, the peak gust magnitude decreases. This was discussed previously. However, given the correct frequency content of natural wind gusts, two minutes of sustained turbulent wind may have the capacity to cause damaging fatigue cycles in sign and luminaire support structures. Polar histograms of maximum wind gust directionality for these stations are also given in the Figures. It should be noted that North is 0 and/or 360 degrees. The traditional histograms can be used to determine expected probabilities for wind gust magnitudes on an annual basis, while the directionality histograms give qualitative indication of the direction of prevailing winds within the State. While the directionality histograms shown in Figures?.3 through?.23 give indication for the direction of general winds, they do not give any indication as to the direction from which the high speed wind gusts come from. This information was obtained via queries on the maximum wind speed data to window intervals of gust speeds. Several intervals where chosen for convenience: (a) 20 mph to 30 mph; (b) 30 mph to 40 mph; (c) 40 mph to 50 mph; and (d) over 50 mph. These windows were then used to develop relative frequency histograms of direction for the windowed wind gust speeds. The windowed wind speed directionality histograms are

65 Draft: Modeling Wind Velocity and Turbulence: 5 given in Figures?.24 through?.34. Upon examination of Figures?.26 and?.32 for Mitchell Field in Milwaukee, Wisconsin, it can be seen that the peak wind speeds between 20 and 30 mph are fairly well distributed throughout all directions. There is slight preference towards the North, Northeast, South, Southwest and Northwest directions. As the wind speed window is increased, the preferred directions tend to decrease. In the case of 5 second gusts, two prevalent directions are present: Southwest and Northwest. For 2 minute gusts, the Southwest and Northwest directions are preferred. There were no instances of 2 minute peak wind speeds over 50 mph at WBAN for the four and one-half year data records.?.3 Probabilistic Modeling of Wind Loading Wind loading variation has been approximated with a Type I Fisher-Tippett Extreme Value probability density function (PDF) and corresponding cumulative distribution function (CDF). In general, design procedures have been developed where the Type I extreme value distribution has been used for yearly maximum wind speed records. Since the structures to be analyzed in the present study have not failed due to maximum wind conditions, the Fisher-Tippet Extreme Value distribution will be used to estimate the probabilities of occurrence for daily maximum wind speeds. Random variables (such as wind speeds) are probabilistically characterized using probability density functions (PDF) and cumulative distribution functions (CDF). A Type I random variable, X, can be characterized by the following CDF; F ( x) = e for x X ( x u) α e (?.3) and a PDF given by, f ( x) = α e e X α ( x u) e α ( x u) (?.4) Two parameters are needed to develop the theoretical Type I Extreme value distribution using equations (?.3) and (?.4). The first parameter, ", controls the rate of decay from the peak of the distribution and is defined here as the reciprocal of the scale parameter Simiu and Scanlon (1996). The second parameter, u, controls the level of skew in the distribution is sometimes referred to as the location parameter Simiu and Scanlon (1996).

66 Draft: Modeling Wind Velocity and Turbulence: 6 The CDF defines the probability that a value of the random variable will be less than x. Thus, the probability that the wind speed will be greater than x is given by 1 - F(x). Thus, the daily probability that the maximum wind speed will exceed x can be defined as, F( x) = 1 P d where; P d is the probability that the daily maximum wind speed will be greater than x. The distribution parameters for the Type I distribution can be determined if the statistical parameters of the measured random variable data are known. For example, if the mean and standard deviation of the measure wind speed (eg. 5 second gust or 2 minute gust) are known, the parameters u and " can be computed using (Benjamin and Cornell 1970); and α σ X (?.5) u µ X 0 45σ X. (?.6) The measured data acquired at the five recording stations have the statistical parameters given in Table?.2 and using these parameters, the Type I Extreme distribution variables can be determined using equations (?.3) and (?.4). Table?.2 also includes the Type I distribution parameters. Wind speeds to be expected on a daily basis can be estimated using the Type I distribution. The parameters determined from the daily data from Wisconsin found in Table?.2 were used to construct Type I distributions. These distributions for 5 second and 2 minute daily wind speed maximums are plotted with the data histograms of relative frequency in Figures?.35 -?.44 for the five Wisconsin recording stations. Overall, the Type I distribution models the daily wind speed probabilities quite nicely. Expected daily maximum wind speeds and error bands in the expected values can also be determined using the measured data and the Type I distribution(s) model. The expected maximum daily wind speed associated with a probability, P d can be expressed as (Simiu and Scanlon 1996),

67 V = x + σ (ln d ) [ [ P d ]] 6 π The value for lnd can be approximated as (Simiu and Scanlon 1996), Draft: Modeling Wind Velocity and Turbulence: 7 lnd = ln ln 1 (?.8) As an example, we can compute the maximum expected daily 5 second gust wind speed for Mitchell Field in Milwaukee, Wisconsin (WBAN 14839) in which the probability that this wind will be exceeded is 0.01 (ie. 1 percent chance of exceeding). From Table?.2, the mean and standard deviation wind speeds are, x = 24. 6mph and σ = 7. 8 mph With P d equal to 0.01, the expected maximum daily 5 second gust is 49 mph. From Figure?.39, this corresponds to the area underneath the probability density function from 49 mph to 4. Therefore, daily probabilities of wind loading can now be attached to 5 second and 2 minute maximum wind speeds. (?.7) There were approximately 4 ½ years of data used to create the wind speed probability density functions. Therefore, there is error associated with these maximum wind speed predictions. Obviously, more data will reduce the error in the expected values given by equation (?.7). The error band or sampling error in the estimate can be computed using (Simiu and Scanlon 1996), SE( V ) = ( ln d ) ( ln d ) 2 σ n (?.9) where; n is the sample size. The sample size for the 5 second maximum speed data for Mitchell Field is n = The error in predicting expected maximum daily 5 second wind gusts is therefore (using equation?.9 with P d = 0.01): SE(V) = 0.8 mph. Thus, the expected daily maximum 5 second wind gust will be in the range, -2*SE(V) < V < +2*SE(V) for 95% percent confidence. As a result, a 5 second gust of magnitude ranging from 47 mph to 51 mph will have a 1% chance of being exceeded with 95% confidence.

68 Draft: Modeling Wind Velocity and Turbulence: 8 The former discussion allows one to generate 5 second and 2 minute maximum daily wind gust magnitudes for various daily probabilities of exceedence. Furthermore, these wind speeds can be determined with a theoretical confidence limit. Since structures such as sign and luminaire supports are gust sensitive structures, the remaining task needed to be done to assess fatigue performance is to generate simulated turbulent wind speed histories.?.4 Analytical Modeling of Turbulent Wind Natural wind has been characterized as having two components: (a) a mean wind velocity that is constant; and (b) a fluctuating component that accounts for the turbulence created when the wind flow interacts with the surface of the earth. Mathematically, these two components can be stated as (Buchholdt 1997), (, ) = ( ) + (, ) U z t U z u z t (?.10) The turbulent component of the wind requires that special analytical procedures take place and that this wind velocity component be appropriately modeled using spectra. The spectra employed should adequately represent the frequency content of the turbulent wind. The mean wind component, U(z), can be taken as the quantity measured at reference height (usually 10 m). In general, a height can be established for both components and therefore, the spatial variability implied in equation (?.10) can be removed. This results in the following, U ( t) = U + u( t) (?.11) The turbulent component of wind can be considered a random function of time. The classification of wind as a random function can be easily seen upon examination of measured hourly wind speeds for Mitchell Field as that shown in Figure?.45. The statistical variation of turbulent wind is needed to quantify the dynamic response of structures to the naturally occurring wind gusts and turbulence. Variable winds are classified as random variables. Much of the nice statistical analysis that can be used in wind engineering depends on the wind being a stationary, ergodic random variable. Without these assumptions, simulating wind and modeling the turbulent component becomes cumbersome, and for engineering purposes, intractable. Thus, it is prudent to review the definition of the stationary ergodic random variable in order to justify the relationships used to model turbulent wind.

69 Draft: Modeling Wind Velocity and Turbulence: 9 One could imagine that hourly wind speeds could be recorded not just at Mitchell Field in Milwaukee, but at sites throughout the metropolitan area. Each record collected would be considered a sample of the random variable. All samples taken together are termed an ensemble composing the random process - turbulent wind. If we took the ensemble and computed the average wind speed at time t 1 for all samples included in the ensemble, a stationary random process would require that the ensemble average at a different time, t 2 be the same. Furthermore, we could take an instantaneous wind velocity magnitude from each sample at t 1 and t 1 + J, where J is a time offset and multiply them together. This time would be selected for all samples and the average of the ensemble would be taken. A second time t 2 and offset J could then be chosen and a second ensemble average taken. The stationary random variable would require that both these multiplied averages be the same. An ergodic random process has the additional requirement that the average wind speed of any sample in the ensemble be equal to the average wind speed across the ensemble of records at any arbitrarily chosen time. The present study assumes that the wind speed can be defined as a stationary ergodic random process, and therefore, one record can be used to describe the random process of wind speed variation with time. As eluded to previously, time averaging is used to describe maximum wind speeds as a result of the turbulent nature of the wind. There are several important statistical quantities that need to be defined in order that the turbulent nature of the wind can be quantified and used in the simulation of turbulent wind. With reference to the random wind speed record shown in Figure?.1 and mathematically modeled using equation (?.11), we can define the average of the turbulent wind as, 1 u( t) = lim T u ( t ) dt T T 0 (?.12) Equation (?.12) also defines the expected wind speed. The mean square value of the turbulent wind component is defined as, T u( t) = lim ( ) T T 0 [ u t ] dt (?.13)

70 Draft: Modeling Wind Velocity and Turbulence: 10 Since our assumed random process (wind speed) is ergodic, we can switch all our efforts to only the turbulent component. As a result, we can write the turbulent component in the form of a Fourier series (Thomson and Dahleh 1998), 1 u( t) = Cne + Cn e 2 n= 1 inωit * inω1t ( ) (?.14) where; C n is a complex number and C n * is its complex conjugate. Substituting equation (?.14) into (?.13) results in a clean expression for the mean square value of the random turbulent component of the wind (Thomson and Dahleh 1998), u( t) 2 = 2 n= 1 C n (?.15) Equation (?.15) states that the mean square value of the harmonic component is the sum of the mean square values of each harmonic present in the function. There is a second form of equation (?.15) that contains the real and complex conjugate Fourier coefficients. This form is given below (Thomson and Dahleh 1998), u( t) 2 1 = 2 n= 1 C C n * n (?.16) The term inside the summation can be defined as the power spectrum represented as, ( ) S f n ( ) G f * n n n = 1 C C 2 The discrete summation leading to the root mean square value of the turbulent wind velocity given in equation (?.16) allows the power spectral density to be defined. The power spectral density is obtained from the power spectrum by dividing the power spectrum into frequency intervals of small size. The power spectral density is then (Thomson and Dahleh 1998), ( ) G f = = f * n CnCn 2 f (?.17)

71 Draft: Modeling Wind Velocity and Turbulence: 11 The mean squared value of the turbulent wind response can then be defined with the aid of the discrete power spectral density of the turbulent wind given by equation (?.17). Equations (?.17) and (?.16) lead to, ( ) u( t) 2 = S f n f = 1 n (?.18) As the frequency intervals approach infinitely small size in the limit, the root mean square value of the turbulent wind component can be written in terms of the continuous power spectral density function for positive frequencies as, ( ) u( t) 2 = S f df 0 (?.19) Equation (?.19) forms the basis for computing the power spectral density function for a random signal using Fourier Transforms. Parseval s theorem can be used to converge integration in the time domain to integration in the frequency domain. The integration necessary to determine the mean square component of the wind in the time domain can be written using Parseval s theorem as, * ( ) ( ) u( t) u( t) dt = U f U f df T 2 where; U(f ) and U * (f ) are the real and complex Fourier transforms of the turbulent wind component. If the averaging time of the turbulent wind component, T, is allowed to approach infinity in the limit, the root mean square value of the turbulent wind component (equation?.13) can be written in the frequency domain as Thomson and Dahleh (1998), * ( ) ( ) (?.20) 2 1 u t T u t u t dt 1 ( ) = lim ( ) ( ) = lim T U f U f df T T T 2 Equation (?.19) can be restated for the moment assuming that both positive and negative frequencies are present. This is not true in the case of wind loading, but it keeps the derivation for the power spectral density function mathematically consistent. Thus, the root mean square value can be considered two-sided if the integration limits are changed to allow the presence of

72 Draft: Modeling Wind Velocity and Turbulence: 12 negative frequencies. The root mean square value can then be re-written in terms of a two-sided power spectral density function as, u( t) 2 = ( ) S f df which upon comparison to equation (?.20) leads to an expression for the two sided power spectral density function, ± * ( ) = lim ( ) ( ) S f T 1 T U f U f (?.21) where; U(f ) and U * (f ) are now more directly defined as two-sided Fourier transforms. Therefore, as long as the Fourier transforms (complex conjugate pair) can be determined for the random process (signal), the power spectral density function of the signal may be determined. In wind engineering, negative frequencies are not possible and therefore the power spectral density function is defined to be one-sided. A discrete form of the one-sided power spectral density function can be determined by defining one-sided Fourier transforms and equation (?.17), ( ) S f = lim f 0 * ( ) ( f ) G f G f (?.22) Computation of one-sided transforms of random processes is always accomplished using computer software. Furthermore, the Fast Fourier Transform (FFT) algorithm is used to speed the computational process. The user determining the power spectral density function of a random signal must choose the incremental frequency to be used in the determination. As this incremental frequency approaches zero, a continuous spectral density function is approached. In the present study, FFT values and the power spectral density functions are computed using software (Irvine 1999a;b).?.5 Engineering Representation for Spectral Density There are several techniques that have been proposed to model the spectral density function for turbulent wind speed for practical engineering purposes. The present study will consider and

73 ( u ) f ( 1 + f ) Su ( n ) 4 * = n f n = 1200 U Draft: Modeling Wind Velocity and Turbulence: 13 use one commonly found or referred to in the literature. The first model is that proposed by (Davenport 1961a;b), where; U 10 is the mean wind velocity at 10 m above the surface of the ground, and u * is the shear velocity. The shear velocity accounts for the turbulence in the wind speed resulting from interference with the ground surface. (?.23) The spectral density given by equation (34) was originally thought to be inaccurate due to the lack of dependence upon the height above the ground. It can be seen that the spectrum is fixed to the mean velocity at 10 meters above the ground surface. Several modifications to equation (34) have been suggested, but that proposed by Kaimal (1972) will be considered in the present study. This approximation is given by, Su( z, n) = n 200u 2 * f ( z, n) [ f ( z, n) ] 5 3 (?.24) with; f ( z, n) = z n U z where; z is the height above the ground, and U z is the mean wind speed at that height. The spectral density given by equation (?.24) is thought to be more accurate in the higher frequency range for which most engineered structures respond (Buchholdt 1997; Simiu and Scanlon 1996). The power spectral density function given by equation (?.24) can be used to simulate turbulent wind speed records. Time varying wind speed histories (over averaging times) can be generated to follow the spectral density function. This is the goal of the next section in the report.

74 Draft: Modeling Wind Velocity and Turbulence: 14?.x Simulating Turbulent Wind Velocity The improvement of computational power in the last ten years has made simulation of turbulent wind histories viable analytical tools in vibration analysis of structures. The techniques frequently used to simulate turbulent wind usually involve generation of the zero mean random wind speed using a predetermined spectrum as a target. The target spectrum ensures that the simulated wind speeds have frequency contents compatible with measured winds. A structure can then be subjected to turbulent wind pressures using varying total wind velocities based upon simulated turbulent speeds. Thus, the turbulent wind record will be simulated using average recorded peak winds with known averaging times. As a result, the recorded peak wind speed averaged over time, T, and the power spectral density function given by equation (?.24) can be used to create a simulated turbulent wind record. These in turn can allow very accurate assessment of structure response to natural wind gust. Random time histories of turbulent wind can be developed (simulated) using a variety of techniques. One common approach is to simulate the turbulent wind using summations of sine functions (Irvine 1999a) or cosine functions (Shinozuka and Jan 1972). Much of the research effort related to simulated wind histories has been focused in on reducing the computational effort. However, at present random wind speed simulation can be easily accomplished (for records of moderate length) using summation of cosine functions of varying frequencies and random phase angles. This is the approach taken in the present effort. Consider the power spectral density function of naturally occurring wind given by equation (?.25). This spectra can be used to develop simulated wind histories using superimposed cosine functions. The turbulent wind speed at any time t in an averaging time, T, can be simulated using (Iannuzzi and Spinelli 1987; Levy 1996; Shinozuka and Jan 1972), N u( t) = 2 S( f k ) f cos( 2πf k t + φ k ) (?.25) k = 1 where: N is the number of frequencies for which S(f k ) has been digitized for the simulation; k is the central frequency number; )f is the frequency increment contained, f is the frequency; t is the time value in the simulation; and N k is a randomly generated phase angle chosen at each

75 Draft: Modeling Wind Velocity and Turbulence: 15 central frequency, k. Equation (?.25) has been evaluated by Iannuzzi and Spinelli (1987) and has been found to generate accurate wind histories when compared to recorded wind records. A computer program written in MATLAB (2000) found in Levy (1996) was used to generate random wind histories for defined averaging times. It should be noted that simulating wind histories requires that the spectrum be defined at frequencies beyond those to be found in the structures analyzed. Thus, 100 Hz was used as the upper-limit frequency of the spectrum and 0.01 Hz was the lower-limit. This will ensure that the simulation will follow the spectral density function over the frequency ranges expected in the sign and luminaire support structure to be studied. As an example, a turbulent wind simulation was undertaken for an averaging time of 2 minutes. Equation (?.25) was used to simulate the turbulent component of the wind as a function of time. The height used for the simulation was 30 feet (360 inches). The friction velocity was defined as, u 2 * = 2 v σ 6 where the variance of the turbulent wind component is taken as, 2 σ v = 6 K U 2 1 The surface drag coefficient, K, was assigned as corresponding to open terrain. The mean velocity, U 1, at the reference height, z ref = 33 feet, was assumed to be 50 mph (880 in/s). The mean velocity at the assumed height was determined using the power law (equation?.1) with "=7). The resulting simulated turbulent wind record is given in Figure?.46. In order to verify the simulation, several statistical parameters can be computed for the simulation as well as a comparison of the power spectral density for simulated record to the original target spectra. Unfortunately, simulation of turbulent wind requires that we consider multiple wind histories. In the present example, ten simulated wind records were generated. These ten records had the power spectral density function computed for each. At each frequency,

76 Draft: Modeling Wind Velocity and Turbulence: 16 the spectra value was averaged. This averaged power spectral density was then compared with the original spectra defined by equation (?.24). The comparison of the two power spectral densities is given in Figure?.47. As one can see, the comparison is very favorable within the expected range of frequencies of vibration for the sign and luminaire support structures. There is some drift at very high frequencies (eg. > 10 cycles/sec), but this is not expected to affect the present analysis. The magnitude of the random process (in this case, turbulent wind velocity) should adhere to several statistical measures to be considered valid. The magnitude of the wind velocity in the turbulent component can be assumed to vary from zero mean in the form of a Gaussian distribution (Irvine 1999a; Thomson and Dahleh 1998). This can be checked in the present simulation using frequency count histograms for the turbulent wind velocity magnitudes. Such a histogram is present in Figure?.48 for one of the wind record simulations. As shown in the figure, the simulation does deviate from the Guassian slightly. Overall, the comparison is quite good. A second measure of the statistical variation in the random signal is called the kurtosis. A pure Gaussian random signal has a kurtosis of 3.0. The kurtosis is a measure of peakedness in the random signal. The kurtosis is a second measure that one can use to determine how close a random signal is to the pure Gaussian signal. Table?.3 contains the kurtosis values for the ten records simulated. The average kurtosis for all records is 2.78 which is very close to the Gaussian signal. The deviation is acceptable. The final assessment of the generated records is comparing the root mean square of the signal with the integration under the power spectral density function assumed in the generation. Table?.3 contains the rms values for each simulated wind record. The average for all signals is Integration of the power spectral density function yield an rms value for the velocity of There is a slight difference in the values, but the comparison is quite favorable. Overall, the random signals generated adhere quite well to the power spectral density function assumed for the wind engineering. Furthermore, the signals generated adhere closely to a

77 Draft: Modeling Wind Velocity and Turbulence: 17 Gaussian distribution about the zero mean velocity. As a result, the random wind turbulence can be approximated using the statistics of the Gaussian probability density function within engineering tolerances.?.6 Conclusion This chapter in the report has been written to help the reader understand the process by which turbulent wind simulations will be undertaken to simulate fatigue behavior of sign and luminaire support structures. Daily maximum wind speeds (gusts) for five minute and two minute averaging times were collected from five recording stations throughout the State. Histograms of this data allowed the modeling of the probabilistic variation to be conducted using Type I Extreme (Fisher-Tippett) probability density functions. As a result, one can determine the probability of averaged gust speeds occurring on any given day of the year. These averaged speeds can be used as the basis for simulated turbulent wind histories. Turbulent wind simulations can be conducted using superposition of cosine functions at various frequencies corresponding to those found in power spectral density function models for wind. The present study will utilize the PSD function given in equation (?.24) to simulate turbulent wind history using equation (?.25). Simulations using this procedure have been shown to follow a Gaussian distribution about the mean to within acceptable engineering tolerance. Thus, a probabilistic gust speed (with defined averaging time) can be transformed to a time varying wind speed using the procedures outlined in this chapter. As a result, probabilistic turbulent wind histories can be generated for the life of a sign or luminaire support structure.

78 Draft: Modeling Wind Velocity and Turbulence: 18 References 1.) ASCE. (1998). Minimum Design Loads for Buildings and Other Structures (ASCE 7-98), American Society of Civil Engineers, Reston, VA. 2.) Buchholdt, H. (1997). Structural Dynamics for Engineers, Thomas Telford Publications, London, U.K. 3.) Davenport, A.G. (1961a). Applications of Statistical Concepts to the Wind Loading of Structures. Proceedings of the Institute of Civil Engineers, 19, ) Davenport, A.G. (1961b). The Spectrum of Horizontal Gustiness Near the Ground in High Winds. Journal of the Royal Meteorological Society, 87, ) Durst, C.S. (1960). Wind Speeds Over Short Periods of Time. The Meteorological Magazine(608), ) Iannuzzi, A., and Spinelli, P. (1987). Artificial Wind Generation and Structural Response. Journal of Structural Engineering, 113(12), ) Irvine, T. (1999a), "Schock and Vibration Response Spectra Course: Unit 12 - Synthesizing a Time History to Satisfy a Power Spectral Density Using Sinusoids", Vibration Data Publications, 2000, (December), 8.) Irvine, T. (1999b), "Schock and Vibration Response Spectra Course: Unit 6A - The Fourier Transform", Vibration Data Publications, 2000, (December), 9.) Irvine, T. (1999c), "Schock and Vibration Response Spectra Course: Unit 7A - Power Spectral Density Function", Vibration Data Publications, 2000, (December), 10.) Kaimal, J.C. (1972). Spectral Characteristics of Surface-Layer Turbulence. Journal of the Royal Meteorological Society, 98, ) Levy, R. (1996). Structural Engineering of Microwave Antennas, Institute of Electrical and Electronic Engineers, Inc., New York, NY. 12.) Liu, H. (1991). Wind Engineering: A Handbook for Structural Engineers, Prentice Hall, Inc., Englewood Cliffs, NJ. 13.) MATLAB (2000) The MathWorks, Inc., ver. 6.0, 14.) Shinozuka, M., and Jan, C. (1972). Digital Simulation of Random Processes and Its Applications. Journal of Sound and Vibration, 25(1),

79 Draft: Modeling Wind Velocity and Turbulence: ) Simiu, E., and Scanlon, R.H. (1996). Wind Effects on Structures: Fundamentals and Applications to Design - 3rd Edition, John Wiley & Sons, Inc., New York, NY. 16.) Thomson, W.T., and Dahleh, M.D. (1998). Theory of Vibration with Applications, 5th Edition, Prentice Hall, Inc., Upper Saddle River, NJ.

80 Draft: Modeling Wind Velocity and Turbulence: 20 Table?.1: National Climatic Data Center (NCDC) WBAN Numbers for Various Data Collection Stations in the State of Wisconsin WBAN Number Description Green Bay Austin Straubel International Airport Green Bay, WI Brown County Madison Dane County Regional Airport Madison, WI Dane County Milwaukee Mitchell International Airport Milwaukee, WI Milwaukee County Oshkosh Wittman Regional Airport Oshkosh, WI Winnebago County Wisconsin Rapids Alexander Field Wisconsin Rapids, WI Wood County

81 Draft: Modeling Wind Velocity and Turbulence: 21 Table?.2: Statistical Parameters Needed to Generate Type I Extreme Value Probability Models. WBAN Number Maximum 5 Second Gust Speed (mph) µ 5sec σ 5sec " u WBAN Number Maximum 2 Minute Gust Speed (mph) µ 2 min σ 2 min " u

82 Draft: Modeling Wind Velocity and Turbulence: 22 Table?.3: Statistical Data for Ten Turbulent Wind History Simulations for Averaging Time of Two Minutes. Simulated History Kurtosis Value RMS Value Averages

83 Draft: Modeling Wind Velocity and Turbulence: 23 Figure?.1: Variation of Wind Speed with Time (Adapted from Liu 1991).

84 Draft: Modeling Wind Velocity and Turbulence: 24 Figure?.2: Peak Wind Speed Variation with Averaging Time Adapted from Liu (1991).