Fatigue Loading and Design Methodology for High-Mast Lighting Towers (2012)

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4C h a p t e r 2 2.1 Field Monitoring Program An extensive field monitoring program was implemented to determine the in-service response of HMLTs. Prior to the research conducted herein, loads provided in the AASHTO Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals (2009), also referred to as AASHTO Signs, were based on results from NCHRP Report 412, which examined a wide range of support structures and a variety of wind loading phenomena. NCHRP Report 412 modeled the response of support structures using spectral analysis to simulate natural wind gusts and modal analysis to simulate vortex shedding (Kaczinski et al., 1998). The current study is fundamentally different in approach by using field-measured experimental data and focusing only on HMLTs. Eleven HMLTs at eight different sites were included in a long-term field monitoring program to establish the in-service response of these structures. Further, data from two other HMLT monitoring programs in the state of Iowa also were used to support the findings from this study. To estimate the response over the lifetime of the structures, the duration of monitoring lasted up to 2 years. Height of the HMLTs varied from 100 feet to 160 feet, which represents the majority of the general population. The taper rate of the supporting pole structures was approximately 0.14 inches per foot. (Previous editions of AASHTO Signs assumed this taper rate to be the minimum associated with disrupting the formation of organized vortices and thus preventing the vortex shedding lock-in effect from occurring.) The cross section of all monitored poles was multi-sided with the exception of one circular cross section. The multi-sided poles were 12-sided or 16-sided, dodecagonal or hexdecagonal, respectively. These are the most common cross sections that fabricators use for these types of structures. In conjunction with long-term monitoring, 14 additional HMLTs were tested to determine their dynamic properties. A procedure called “pluck testing” was used to excite the HMLTs dynamically. These HMLTs had similar dimensional and geometric properties as the ones selected for long-term monitoring. Dynamic data obtained by plucking a series of poles during separate studies conducted by the authors for the Iowa DOT also were reviewed and incorporated. 2.1.1 Setup, Instrumentation, and Testing 2.1.1.1 Setup for Long-Term Monitoring Instrumentation for long-term monitoring consisted of two types of sensors—strain gages to monitor the load effect, and an anemometer to monitor the wind effect acting on the HMLT. Each long-term setup included a data collection system, a wireless cellular modem for remote communication, and an independent power supply. Data for pluck tests were collected using similar data collection equipment. Appendix E (available on the TRB website) contains instrumentation Research Approach

research approach 5 plans for each of the HMLTs monitored in this study. All strain gages used were Measurements Group Model LWK-06-W250B-350 excited at 10 volts. On-site data collection was accomplished using a 16-bit Campbell Scientific CR9000 Data Logger. On-board analog and digital filtering was performed using the CR9000’s 9052 analog input cards. Sample rates varied between 100 Hz and 250 Hz. For long-term monitoring, a CR5000 16-bit data logger was used due to its low cost and low power draw. Sample rates varied during the long-term monitoring depending on the data collected, but were between 20 Hz and 50 Hz. The anemometer was produced by RM Young and was a Model 5103. Strain gages were generally placed at two locations on the pole. The first set of strain gages was located at a minimum of 1.5 times the diameter of the pole above the handhole detail, typically about 6 feet above the baseplate. These strain gages recorded the nominal stress-range in the pole and were placed a sufficient distance above the handhole to avoid local stress concentration effects. These strain gages were equally spaced around the perimeter of the pole to associate the response of the HMLT with a particular wind direction. The second set of strain gages was located immediately above the baseplate to tube wall connection detail or adjacent to the handhole. The intent of these strain gages was to capture local stress effects at the primary fatigue detail(s) of the HMLT and this was for general information only. Hence, the data from these gages were not used to analyze the applied wind load effect because they were influenced by local effects. Since the global response of the pole was of interest, the “nominal” gages were used to determine the applied wind load. Thus, the detail-specific strain gages were omitted from a couple sites installed later in the long-term monitoring program. The typical instrumentation setup showing strain gage placement is illustrated in Figure 2.1. Figure 2.1. Strain gage placement and data collection system.

6 Fatigue Loading and Design Methodology for high-Mast Lighting towers The term “channel” is sometimes used in this report to refer to the data, or signal, recorded from a specific strain gage. This is done to be consistent with labeling practices in the field. An anemometer was installed near each HMLT to capture wind speed and direction. Anemometers were placed approximately 33 feet (10 meters) above the ground, which is the standard for wind measuring instruments and is also the reference height for wind load com- putation used by ASCE and AASHTO. Generally, the anemometers were installed on a separate timber pole provided by the sponsoring agency. If a sponsoring agency could not provide a separate pole, the anemometer was attached to the HMLT using a bracket. However, a separate pole was preferred to avoid any influence of the HMLT on the airflow around the measuring instrument. When a separate pole was used, it was placed at least 10 feet away from the HMLT. The typical instrumentation setup showing the placement of the anemometer is illustrated in Figure 2.2. 2.1.1.2 Pluck Test Setup The setup for pluck testing consisted of a cable and a “come-along” winch. One end was attached to the pole at a point approximately 30 feet from the ground, and the other end was attached to a stationary object, usually a truck hitch. A static load was applied to the structure using the come-along and then quickly released, exciting the structure much like a string is plucked on a musical instrument. A load cell was placed in-line with the cable and the load recorded with the strain data. Instrumentation for pluck testing consisted of two accelerometers placed parallel and orthogonal to the direction of the applied load. Accelerometers were manufactured by PCB Piezotronics, Inc., Model 3711D3FA3G. The action of plucking excites the pole into oscillation and data are recorded until the pole has damped out. The raw data collected from pluck tests are short-term; data collected from each pluck usually lasted less than 3 minutes. 2.1.2 Data Collection Field-test data were collected, sorted, and stored for analysis as five different types: pluck test data, stress-range histogram data, wind data, ambient data, and triggered data. Pluck test data Figure 2.2. Anemometer placement.

research approach 7 were collected immediately on-site while the researchers were present. The remaining four types correspond to long-term monitoring and were collected remotely. Their description, collection method, and relevance are discussed below. 2.1.2.1 Pluck Test Data Data from pluck tests were recorded from accelerometers, strain gages, or both, depend- ing on whether the HMLT was set up for long-term monitoring or only for dynamic testing. Accelerometers were mounted both longitudinal and transverse to the plucking direction. Typically, each tower was plucked between two and four times so data could be compared for consistency and repeatability. In total, 25 HMLTs were pluck tested for dynamic properties (11 long-term monitored HMLTs and 14 other HMLTs). The data collected from both the accelerometers and strain gages were used to determine the natural frequencies and damping ratios of a given pole, and both types of data were analyzed using similar methods. Modal frequencies were extracted using either a cycle counting method or Fast Fourier Transform (FFT). Damping ratios were extracted using the log-decrement method. 2.1.2.2 Stress-Range Histogram Data In fatigue analysis, stress-range (SR) and cycle count (N) data provide the foundation for quantifying damage and can be collectively represented in a histogram. Stress-range histograms are derived from time-history data. However, the time-history data are not necessarily stored; the data logger continually buffers and processes the time-history data. From the processed time-history data, the histogram is made using a cycle counting method. Then, at defined intervals, the stress-range histogram data are saved to a file, and the buffer is reset. Storing all the time- history data would rapidly fill the data logger memory and be nearly impossible to transmit back to the data server using a cellular modem. This preprocessing saves significant research time and effort; the histogram data are much more compressed. The interval for this project was set to 10 minutes, which had been shown to be acceptable based on the research team’s experience. Cycle counting is the process through which stress time-history data are broken down into individual stress cycles and sorted into groups of similar magnitude. The cycle counting method used to create the stress-range histograms in this study was the rainflow counting method. Rainflow cycle counting is commonly used in fatigue analysis and is a listed procedure in ASTM Standard E 1049. The algorithm for rainflow counting is relatively simple and easily programmed into the data logger. Throughout this report, the term rainflow data is synonymous with stress-range histogram data. The process through which stress-range histogram data are collected and stored is shown in Figure 2.3. 2.1.2.3 Wind Data Stochastic wind data were continuously recorded over the duration of the study. Three values for wind speed were recorded at 10-minute intervals—average speed, maximum recorded speed, and a sampled speed. Average direction and a sampled direction also were recorded for the same interval. These data are used to calculate the mean wind speed at each HMLT and to account for variability in the proposed fatigue loads. The stochastic data also are compiled in Appendix D (available on the TRB website) as directional rosettes for percent occurrence and mean wind speed. These rosettes were useful in evaluating the HMLT response with regard to wind direction. In addition to the stochastic wind data, wind speed and direction were recorded in a continuous time-history for use with both the ambient and triggered data. 2.1.2.4 Ambient Data Ambient data refers to recording both strain gage data and wind data in a continuous time-history in order to monitor ambient vibration, which is random vibration of an HMLT

8 Fatigue Loading and Design Methodology for high-Mast Lighting towers excited by natural wind. Data of this type were recorded for each of the poles included in the long-term monitoring program. Ambient data were recorded for two different purposes— to determine dynamic properties based on wind excitation and to monitor across-wind excitation due to vortex-induced vibration. Data collected to study dynamic properties were completely random, whereas data collected to study across-wind excitation occurred during periods of low wind speed, typically between 2 and 14 miles per hour. Due to restrictions in computer memory and remote data retrieval, ambient data collection was limited to a few days every month until a sufficient amount of data were obtained. 2.1.2.5 Triggered Data Triggered data refers to strain gage data and wind data recorded in a continuous time-history for periods of high wind speed. When the monitored wind speed reached a pivotal value, data collection was “triggered” to record. These triggers were typically set somewhere between 20 and 60 mph and stored in separate files accordingly. At sites with greater wind activity, the triggers were modified to record at higher wind speeds to keep the amount of data manageable. At sites with lesser wind activity, the triggers were set at lower wind speeds to ensure that a reasonable amount of data was collected. These data were used to monitor the response of the HMLTs during periods of high-velocity buffeting and to verify high stress-range cycles in the stress-range histogram data. Figure 2.3. Stress-range histogram data collection.

research approach 9 2.1.3 Overview of Sites Several parameters were used to select specific locations for the field monitoring program. These parameters include historical data, agency survey data, and wind power generation data. Historical data were consulted to identify states that experienced cracking and collapse of HMLTs and to determine if these states were located in regions with high yearly mean wind velocity. The states also were surveyed to learn about the existing inventory, find any new instances of cracking or collapse, and to identify agencies willing to participate in the field monitoring program. Agency support was imperative for the success of the study. Supporting state agencies provided unique knowledge of site conditions and structure inventory, support during equipment installation, and assistance with maintenance during the monitoring period. Wind power generation data also were useful in pin- pointing locations with consistent, high wind speeds. Areas with consistent wind speeds conducive to power generation also are susceptible to aeroelastic phenomena such as vortex-induced vibration. A map showing the locations of the HMLTs selected for long-term monitoring is presented in Figure 2.4. Additionally, Table 2.1 provides a summary of the locations of all HMLTs in the field monitoring program, along with basic structure geometry. Another critical factor for collecting data used to determine proposed fatigue loads was monitoring duration. A considerable amount of data is required to extrapolate a lifetime loading spectrum, especially for a random system such as wind loading; therefore, an initial goal of 18 to 24 months was set. Based on the research budget, eight HMLTs at six different sites were initially selected and installed during the spring and summer of 2009. These were located in California, North Dakota, Oklahoma, Pennsylvania, South Dakota, and Wyoming. Although the researchers were prepared for maintenance issues with sensors and data acquisition systems, of the eight HMLTs, the two in Oklahoma had to be abandoned after approximately 16 months. Figure 2.4. Map of long-term monitoring HMLTs.

10 Fatigue Loading and Design Methodology for high-Mast Lighting towers Preliminary data from the Pennsylvania HMLT indicated little wind activity, most likely related to local topographical effects. To better utilize the equipment and remaining time available, the site was relocated to Kansas in December 2009. In the spring of 2010, a review of the research budget showed that an additional site could be added to the program at no additional cost; thus, instrumentation was added to an HMLT in Iowa. The last HMLT was added after retrieving equipment from the Oklahoma site, and was installed on a second HMLT at the Iowa site. Table 2.2 lists the collection periods for each of the HMLTs. Data collection was not necessarily continuous over any period due to occasional equipment failure or power outages, as well as when changes to the logger programming were required. 2.2 Aerodynamic Testing Program The aerodynamic testing was separated into two parts. The first was a computational fluid dynamics (CFD) study and the second, which was the bulk of the aerodynamic testing program, was done experimentally. Both of these approaches were implemented to study the pressure and Long-Term Monitored HMLTs ID LOCATION HT (ft) # SIDES DIA. (in) CA Barstow, CA - I-15 & L St. 100 16 19.5 IA-N Clear Lake, IA - I-35 & US-18 (North) 148 12 28.5 IA-S Clear Lake, IA - I-35 & US-18 (South) 148 12 28.5 KS Hays, KS - I-70 & Toulon Ave. 100 12 18 ND Bismarck, ND - I-90, MP 156 WB 160 12 29 OK-NE Henryetta, OK - I-40 & US-75 (Northeast) 130 16 22 OK-SW Henryetta, OK - I-40 & US-75 (Southwest) 120 16 21.5 PA Erie, PA - I-90 & I-79 110 R 21.5 SD Rapid City, SD - US-16 & SD-44 150 16 26 WY-CJE Creston Junction, WY - I-80 & WY789 (East) 120 16 24 WY-CJW Creston Junction, WY - I-80 & WY789 (West) 120 16 24 Additional Plucked HMLTs ID LOCATION HT (ft) # SIDES DIA. (in) ND-83 Bismarck, ND - I-94 & State St. 140 n/a 25 ND-94 Bismarck, ND - I-90, MP 156 WB 140 16 25 ND-EXP Bismarck, ND - I-94 & Expy. 140 n/a 24 ND-MEM Bismarck, ND – I-94 & Memorial n/a 16 18 ND-SUN Bismarck, ND - I-94 & Sunset Dr. 140 12 30 OK-E Henryetta, OK - I-40 & US-75 120 12 22 OK-SE Henryetta, OK - I-40 & US-75 130 16 22 PA-AD Erie, PA - I-90 & I-79 110 R 18 SD-1E Spearfish, SD - I-90, MP1 EB 120 16 21 SD-1W Spearfish, SD - I-90, MP1 WB 120 16 21 SD-42E Sturgis, SD - I-90, MP42 EB 100 16 19 SD-42W Sturgis, SD - I-90, MP42 WB 80 16 17 WY-219E Sinclair, WY - I-80, MP 219 EB 80 18 18 WY-219W Sinclair, WY - I-80, MP 219 WB 120 18 26 WY-228W Rawlins, WY - I-80, MP 228 WB 120 16 26 Notes: R – round (circular) pole n/a – data not available Table 2.1. HMLT summary.

research approach 11 velocity fields around the model. There are marked differences between both approaches. The CFD yields more points and helps visualize the flow; locations with low pressure or high velocity can be easily identified. For the experimental work, the velocity or pressure is only probed at points of interest. Using these results, the CFD models can be calibrated. Pressure and velocity fields are examined at the surface and near wake of three types of tapered models (8-, 12-, and 16-sided models). By studying these two fields, the associated forces that act on the HMLT pole can be inferred and applied to the design of future HMLTs. 2.2.1 Wind Tunnel Testing The wind tunnel testing section includes a view of the experiment setup and rationale for the different instruments and hardware used. 2.2.1.1 Oscillation Forcing Rig The oscillation forcing rig was constructed to replicate the oscillatory movement of the HMLTs. The natural wind-forced movement in the wind tunnel is high frequency (16 Hz) but very low amplitude (<1 mm). It is hard to detect by eye but shows up on the hot-wire signals. The setup is constructed out of steel and aluminum. The base is made out of steel I-beams and square aluminum extrusions and has two steel ½-inch diameter rods that hold springs and linear bearings. The linear bearings are attached to a bar that holds an aluminum airfoil extrusion that holds the model mount. The model mount is made out of copper and has tapped bolt holes with 31 degrees between each hole (i.e., 0, 31, 62, 93, etc.). The model has holes every 30 degrees, so when the model is rotated 1 degree, one of the model holes lines up with the 31-degree mount hole. There are a total of three copper mounts that can be interchanged and each mount covers a different range. The first range covers degrees 0–10, the next covers 11–20 (starts at 11, then 42, 73, etc.), and the last covers 21–30 (starts at 21, then 52, 83, etc.). In this way, 30 degrees of travel is achieved in 1-degree increments. The models themselves are made of fiberglass foam-core, wood, and aluminum tubes to hold the model itself. A picture of the entire hardware setup can be seen in Figure 2.5. 2.2.1.2 Hot-Wire Anemometry Hot-wire anemometry is the use of a very thin gold or tungsten wire (some being 30 times thinner than a human hair) to measure the wind speed at a certain probe point. A single hot wire can be used effectively to assess the wind velocity at a certain location. A hot wire works by keeping a constant temperature through a wire. As air flows past it, the wire cools and needs to draw more power to keep the wire at the same temperature. The hot wire is used as one of the resistances on Table 2.2. Long-term data collection periods. ID START END OK - NE April 10, 2009 Sept. 4, 2010 OK - SW April 10, 2009 Sept. 14, 2010 PA May 30, 2009 Nov. 10, 2009 ND June 9, 2009 June 8, 2011 SD June 18, 2009 May 24, 2011 WY - CJE July 4, 2009 June 6, 2011 WY - CJW July 4, 2009 June 6, 2011 CA July 21, 2009 June 15, 2011 KS Dec. 3, 2009 June 6, 2011 IA - N July 14, 2010 June 9, 2011 IA - S Dec. 22, 2010 June 9, 2011

12 Fatigue Loading and Design Methodology for high-Mast Lighting towers a Wheatstone Bridge such that as the hot wire requires more voltage, the change in voltage can be accurately measured using an oscilloscope or data acquisition card. One hot-wire drawback is that it cannot tell which way the wind direction is moving, so flow in recirculation zones can be difficult to instrument. If two hot wires are placed in the same probe in perpendicular configuration, the device is then called an X-wire and it has a much more complicated setup and calibration procedure. However, an X-wire can be used for flow angularity, x-y flow direction (not downstream-upstream direction, however), and turbulence checks. In this report, single hot wires were used for all of the testing. The hot wires were set at two different locations. The first was mounted on a moving motorized traverse that could be controlled through an RS-232 port and a LabView program. The second hot wire was set on a static stand and was used as a reference to check for shedding correlation between two different span-wise positions. Two different instrumentation setups were used, one early and one later. The early setup, as shown in Figure 2.6, used a Tektronix TDS50348 oscilloscope and a custom-made Bruhn electronics box. The second setup, as shown in Figure 2.7, used a LeCroy oscilloscope and an Intelligent Flow Analyzer (IFA) 100 for two hot wires used at the same time. No connection to the computer is necessary for data acquisition; the waveforms are captured and post-processed later to get the shedding frequency. The setup was changed for two reasons—the need to use two hot wires at the same time and the need for a more accurate pressure sensor. Figure 2.5. Wind tunnel instrumentation and hardware setup. Model Hot-wires and Motorized Traverse Oscillation rig, springs, and forcing rig Instrumentation

research approach 13 Figure 2.6. Early wind tunnel instrumentation setup. Te kt ro ni x TD S5 0348 M u l t im et e r Bruhn CTA v.6 Ch.9 Traverse y-axis lock PSI pressure scanner 9010 Figure 2.7. Later wind tunnel instrumentation setup. LeCroy WaveA300 Intelligent Flow Analyzer 100

14 Fatigue Loading and Design Methodology for high-Mast Lighting towers 2.2.1.3 Pressure Scanner The other set of experimental data acquired used a pressure scanner. The early pressure scanner used was a Pressure Systems Inc. (PSI) 9010 that featured 20 inches of water (approximately 2⁄3 of a psi) and sampled at about 5 samples/channel/second with a total of 16 channels, of which 12 were used during testing. The pressure scanner was later changed to a PSI-ESP 16HD, as shown in Figure 2.8. This scanner has a sampling rate of 20,000 samples per second and a pressure range of 4 inches of water, providing much better resolution for testing. The pressure scanner data aid in recreating the pressure fluctuations on the surface of the poles. From these pressure fluctuations, an empirical equation for the forces acting on the structure can be derived. Although the models are not a complete scaled model due to not being able to create an aeroelastically accurate wind tunnel replica, the current model can represent a section of the HMLT. The effects of the wind shedding vortex cells on tapered structures can be accurately studied this way. 2.2.1.4 Smoke Wand The smoke wand was used as a check for the quantitative pressure and hot-wire data. It is composed of a pump, a kerosene tank filled with deodorized kerosene, a power supply, and a heating rod. The wand was placed upstream of the model, and the location of separation was identified. The smoke wand also was used to check where the separated shear layer would be located and the hot-wire probe was set at this location. Results from the smoke wand do not provide quantitative data, but they do provide qualitative information about the flow that can be correlated to the readings from the hot wire and pressure scanner. 2.2.2 Computational Fluid Dynamics The computational fluid dynamics studies for this project focused on the pressures applied to the structure and were set to be a check against the experimental results. There were two pieces of software used—Cfdesign by Blue Ridge Numerics/Autodesk, and FLUENT from ANSYS. 2.2.2.1 FLUENT The FLUENT CFD study was done during the design stage to look for potential trouble areas (separation, pressure fluctuations) to better assess pressure tap placement. As the testing started, Figure 2.8. PSI-ESP 16HD pressure scanner (sensor).

research approach 15 the smoke wand was used to check for the separation point, and the location was checked with the results obtained from the CFD velocity field. 2.2.2.2 Cfdesign The Cfdesign study was done later in the experimentation process. This study was done as a check to see if it could reproduce the 3-D flow on a tapered structure. It was a new software program to experiment with, and was discontinued after some initial work so that it wouldn’t detract from the experimental work already under way. The Cfdesign software had some problems with the taper—the software was smoothing it out—and did not seem to predict separation where the experiments showed. 2.3 Factors Affecting Fatigue Loading of HMLTs 2.3.1 Wind Characteristics—Buffeting and Vortex Shedding Two types of wind-induced structural vibration have been identified as contributing to fatigue damage of HMLTs: buffeting due to wind gusts, and vortex shedding (Phares et al., 2007). Buffeting is the result of turbulence in the airstream upwind of the structure, which causes rapid changes in wind velocity. Whereas buffeting is characterized by behavior upwind of the structure and is associated with varying wind velocity, vortex shedding is characterized by behavior downwind of the structure and is associated with more consistent wind velocity. Vortex shedding, and associated vortex-induced vibration, occurs when alternating series of vortices are shed from the flow wake at a specific frequency, forming what is called the von Karman vortex street (Anderson, 2007; Liu, 1991). An example of the von Karman vortex street is shown in Figure 2.9. 2.3.1.1 Vortex Shedding For a circular cylinder, the von Karman vortex street forms at a Reynolds number of about 40 (Edwards and Bingham, 1984). At this point, the vortex street is laminar and stable. As the Reynolds number increases to 300, the vortex street becomes turbulent; however, the shedding frequency remains regular. Here, the vortex shedding is turbulent yet coherent along a length of the cylinder. This type of vortex shedding originates from the flow becoming unstable; instead of having two attached vortices in the wake, the vortices are shed periodically. When each vortex is shed, it accelerates the flow on the opposite side of the pole while slowing the flow on the side that creates the vortex (Ruscheweyh, 1996). The accelerations, in turn, create alternating areas of low pressure that drive the wake structure back and forth creating periodic loads on the poles. These periodic loads are of great interest in the fatigue-tolerant design of HMLTs. The turbulent flow continues Figure 2.9. Picture of von Karman vortex street (Anderson, 2007).

16 Fatigue Loading and Design Methodology for high-Mast Lighting towers up to Reynolds numbers of 3 × 105, where the wake becomes disorganized and vortex shedding becomes random. In terms of wind speed, vortex shedding of HMLTs can be expected to occur at wind velocities less than 30 mph as shown in Equation 2.1. Since vortex shedding is contingent upon steady flow upstream of the body, and natural wind is rarely steady at velocities of that magnitude, vortex shedding of HMLTs typically occurs at wind speeds even lower than 30 mph. Given R vD ft mph For D ft v ft mp e, .≅ = = × • •9400 1 3 105 , h ft mph ( ) ( ) ≈9400 1 30 Equation 2.1: Reynolds number solved for velocity One may wonder why there is such an interest in describing the wake when the loads on the poles are conceptualized by air pressure at the surface of the pole. It is important to note that there is some viscous, or “skin friction” drag, but on a blunt body such as a pole, the pressure drag dominates over the skin friction. The wake, or more specifically, the structure of the flow in the wake, is a result of the flow separation process, including any unsteadiness in the separation process. As such, the structure of the wake is an easily viewed symptom of the important aerodynamic events occurring at the surface of the pole. A highly periodic wake implies a highly periodic pressure loading on the pole. Therefore, the wake structure is critical for understanding the effects of vortex shedding. Vortex shedding frequency can be estimated using the non-dimensionalized Strouhal relation. The Strouhal relation solved for the frequency at which vortex shedding will occur is shown in Equation 2.2. f SV D s = Equation 2.2: Strouhal relation (Kaczinski et al., 1998) where S is the Strouhal number, V is the wind velocity, and D is the diameter of the pole. The Strouhal number of a circular cylinder has been compiled extensively and equals 0.20 (Every et al., 1982). As the “roundness” of the section decreases so does the Strouhal number. For multi-sided sections typically used for HMLTs, the Strouhal number decreases to 0.18 to 0.15, and for square or rectangular sections the Strouhal number may be as low as 0.11. Occasionally, the structure may resonate at the same frequency as the frequency of vortex shedding, creating an aeroelastic effect. This is where the structure deflects and alters the flow field with its back-and-forth rocking. Motion of this type can lock the vortex shedding into a resonant frequency of the structure. Resonate vibration is called “lock-in” and has been observed by a number of researchers (Burt and LeBlanc, 1974; Edwards and Bingham, 1984; Every et al., 1982; Krauthammer et al., 1987; Phares et al., 2007; Vickery et al., 1983). Vortex shedding at a lock-in condition is “fixed” at a certain frequency for a range of velocities as shown in Figure 2.10. Locking-in to a range of velocities means that small fluctuations in wind speed or pole diameter do not alter the frequency of the vortex shedding and therefore results in continued resonance. If the lock-in or aeroelastic effect causes the amplitude of vibration to increase, then aeroelastic instability, or negative damping, occurs. Negative damping may have a considerable effect on the fatigue life of an HMLT by increasing the stress-range associated with each vortex shedding cycle. Figure 2.10 assumes a constant cross section, meaning the Reynolds number only changes with velocity. However, with a tapered pole such as an HMLT, the Reynolds number varies with both diameter (i.e., position along the pole) and velocity. Therefore, diameter changes in a uniform wind also may be subject to vortex shedding lock-in, thereby creating a larger periodic loading

research approach 17 than without lock-in. The length of the pole over which lock-in occurs is also a matter of study since it is required to accurately predict the movement of the structure. The behavior of HMLTs subject to vortex shedding is characterized by an across-wind response. The nature of alternating pressures in the wake causes the motion to be orthogonal to the direction of the wind. Based on the results of this study and the results of Connor and Hodgson (2006), this response is generally limited to the second mode of vibration and, to a lesser extent, the third mode. 2.3.1.2 Buffeting Buffeting is the result of changes in wind velocity and direction. Buffeting does not have constant velocity and may result from free-stream turbulence due to meteorological phenomena or have instabilities from upstream obstacles such as vortex shedding with other bluff bodies or ground surface roughness. Buffeting inherently has a wide range of velocities that apply pressure to a structure and induce vibration. In other words, buffeting is not limited to high wind speeds, and can occur whenever turbulence exists in the wind stream. Vibrations due to buffeting have variable amplitudes contrary to the behavior of vortex shedding, which is more steady state. Buffeting vibration is the vibration produced by turbulence or other disturbances of the flow not generated by the vibrating object itself (Liu, 1991). Unlike vortex shedding, buffeting is mostly aerodynamic in nature, that is, there is no aeroelastic response. Therefore, changing the stiffness or damping of a structure will not necessarily change the fatigue loading due to buffet- ing. Previous studies have shown such vibrations occur primarily in the first mode for HMLTs and are responsible for the upper-limit stress-range cycles; however, the upper-limit stress-range cycles may not significantly contribute to fatigue damage (Phares et al., 2007). In addition to a response in the first modal frequency, the behavior of HMLTs subject to buffeting is characterized by an along-wind response. In other words, the motion of the HMLT excited by buffeting causes the structure to move parallel with the wind. This may be visualized in the traditional sense of wind pressure acting on the frontal area of the structure. 2.3.1.3 Combined Wind Effect The current AASHTO Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals (2009) considers vortex shedding and buffeting as independent fatigue loads. However, these two load effects rarely act independently of each other. Both along- wind behavior, indicative of buffeting, and across-wind behavior, indicative of vortex shedding, can be observed acting together. It is difficult to separate the two effects using field-measured data. Where vortex shedding is effectively mitigated, a direct comparison of the two load effects is made; however, this approach is somewhat limited by the amount of data collected. A clearer picture Figure 2.10. Lock-in phenomenon.

18 Fatigue Loading and Design Methodology for high-Mast Lighting towers forms when the entire wind loading spectrum is examined. For this reason, the proposed fatigue load effect (developed herein) is arrived at using a combined wind effect, which includes both buffeting and vortex shedding. 2.3.2 Dynamic Properties 2.3.2.1 Modal Frequencies The following two methods were implemented to extract modal frequencies from field- measured data: 1. Cycle counting in the time domain and 2. Peak picking in the frequency domain. Peak picking was performed first using pluck data and served as a quick way to extract the frequency values. These values were then verified using a cycle counting method. Modal frequency values were later computed to a greater degree of accuracy using ambient data, if available. In addition to examining field data, computational methods were examined for estimating modal frequencies. The computational methods include closed-form solutions such as those currently found in AASHTO Signs, a multiple degree-of-freedom eigenvalue solution using discretized beam elements, and finite element analysis. To extract the natural frequencies from the acceleration and strain gage data obtained during pluck tests, a fast Fourier transform (FFT) was performed. An FFT is a mathematical algorithm that converts raw data recorded in the time domain to the frequency domain. Once the FFT has been executed, the natural frequencies can be determined by “peak picking.” Simply, the peaks from the resulting FFT plot are recorded as the natural frequencies. Figure 2.11 shows sample accelerometer data from a pluck test. Note, for this research, only the first four modes of vibration were of interest. Typically, it was found that the accelerometers captured the higher frequencies better than the lower frequencies, whereas the strain gages better captured the lower frequencies. Data from the long-term poles include both accelerometer and strain gage data, while data from the other plucked poles consist solely of accelerometer data. Both accelerometer data and strain gage data, if available, were used to calculate natural frequencies and damping ratios. Figure 2.11. Sample pluck data— time domain and frequency domain.

research approach 19 After extracting the modal frequencies using the peak picking method, they were verified using cycle counting. The original time-domain signal was filtered using a relatively wide passband about the frequencies determined from peak picking. (This filtering process was essential for calculating damping ratios using the log-decrement method discussed in the following section.) Then, the number of cycles in the signal were counted and divided by the amount of time elapsed. This proved to be a simple and effective means of checking the initial values. 2.3.2.2 Damping Ratios The following two methods were implemented to extract damping ratios from field-measured data: 1. Log-decrement in the time domain and 2. Half-power bandwidth in the frequency domain. The half-power bandwidth method could only be used on the long-term monitored poles where ambient data could be collected. The log-decrement method was used on all poles using pluck test data. Pluck test time-history data, or time-domain signals, are composed of sinusoidal components of each mode of vibration excited by the pluck test. To use the log-decrement method, the individual modes must be isolated from the others as well as any surrounding noise. This is done by subjecting the raw signal to a filter that removes frequencies outside of the modal frequency passbands, leaving a decay profile for the mode of interest. Knowing the modal frequencies obtained from the FFT and peak picking methods, passbands can be established for each mode. Examples of original and filtered pluck test signals are shown in Figure 2.12. After the signals are filtered for each mode of interest, a mathematical algorithm isolates the positive and negative peaks and then scans the series of peaks for a period of steady decay. From Figure 2.12. Signal filtering.

20 Fatigue Loading and Design Methodology for high-Mast Lighting towers this decay period, a graph of the natural log of the ratio of successive peaks versus number of cycles is plotted. The graph follows a liner relationship according to Equation 2.3. ln v v n n 1  = δ Equation 2.3: Log-decrement where v1 is the initial peak value, vn is the value of any successive peak, and n is the cycle number. The log decrement, d, is equal to the slope of this line. To determine the slope, a best-fit line is applied to the plot using a linear least-squares regression, and Equation 2.3 may be rewritten in terms of relative peaks as shown in Equation 2.4. δ =  +ln v v n n 1 Equation 2.4: Log-decrement in terms of relative peaks An example of a best-fit line using typical data collected during this research is shown in Figure 2.13. The damping ratio, x, can then be calculated using Equation 2.5. ξ δ pi δ = +4 2 2 Equation 2.5: Damping ratio Using ambient data, frequency response curves were created for each of the HMLTs. Damping ratios could then be calculated from the frequency response curves by the half-power bandwidth method. Frequency response curves are typically created by subjecting a given system to a forced vibration and measuring the response amplitude for a range of known forcing frequencies. The response amplitude can then be plotted against the forcing frequency to create a curve in the frequency domain. Damping ratios also can be obtained from ambient time-history data. For ambient data, the forced vibration is the result of random natural wind and the response is recorded as strain in the time domain. To create the frequency response curve, the ambient data must be converted to the frequency domain using an FFT. This was done by subdividing the ambient data into suites, passing each suite through an FFT, and averaging the suites together Figure 2.13. Best-fit line for log-decrement calculation (Mode 2).

research approach 21 to create a high-resolution frequency response curve. An example of a curve generated from ambient data is shown in Figure 2.14. Damping ratios were then calculated using the half-power bandwidth method. From the frequency response curve, a modal frequency is isolated and its peak value is established. Then half-power points are determined on either side of the peak where the curve equals the peak value divided by the root of 2. An illustration of the half-power points is given in Figure 2.15. Frequencies f1 and f2 at the half-power points then can be used to calculate the damping ratio using Equation 2.6. ξ = − + f f f f 2 1 1 2 Equation 2.6: Damping ratio using half-power bandwidth method Modal frequencies also can be calculated using Equation 2.7. f f f = +1 2 2 Equation 2.7: Modal frequency using half-power bandwidth method Figure 2.14. Example of frequency response curve from ambient data. Figure 2.15. Definition of points for half-power bandwidth method.

22 Fatigue Loading and Design Methodology for high-Mast Lighting towers Calculating modal frequencies using the response curve shown above results in a higher level of accuracy than if obtained using peak picking and pluck data. This is because the ambient data stream is much larger and a higher number of FFT points may be used, resulting in a higher resolution frequency spectrum. This method was used as an additional check of modal frequencies mentioned above. It is well established that there are numerous methods to calculate the damping ratio of a given structure, and the two methods used above often yielded different results for the same structure, sometimes with considerable scatter. For instance, it is common for structures to respond differ- ently to different types of dynamic excitation. Plucking excites the HMLT by displacement at a certain location along its height, while ambient excitation is due to natural effects such as wind gusts or vortex shedding. In addition to differences due to excitation, different sources of damping may affect the results. For example, aerodynamic or negative damping most likely was not present during pluck tests; the action of the test itself likely mitigated any response due to vortex shedding. Damping values calculated using the log-decrement method and pluck data refer to structural damping. In contrast, it is likely that aerodynamic damping was included in the ambient data collected. In summary, the damping values listed in this study most likely include contributions from both structural and aerodynamic damping, and scatter does exist. The half-power method used in conjunction with ambient wind data is more consistent with the objectives of this study. Ambient excitation by wind is the true source of cyclic stress leading to fatigue damage. Plucking is a valuable tool for retrieving dynamic data since it can be done quickly and does not require any long-term equipment; however, it is not a natural source of excitation or fatigue stress to the HMLTs. The half-power bandwidth method is also the preferred method of computing damping ratios according to ASTM E756 (1998)— Standard Test Method for Measuring Vibration-Dampening Properties of Materials. The standard states that other computational methods may be used provided results are consistent with half-power bandwidth. 2.3.3 HMLT Geometry—Luminaire Area and Pole Cross Section According to AASHTO Signs, the wind load effect applied to a support structure is a func- tion of two basic parameters—projected area and static wind pressure. The projected area is the area of the structure projected on a vertical plane in any given direction and is directly proportional to wind load. Two separate elements exist for HMLTs where the frontal area must be considered—the pole and the luminaire. The area of the pole is relatively straightforward, but the area of the luminaire is somewhat subjective and is typically given in terms of an effective projected area (EPA). The static wind pressure is a modified form of the Bernoulli equation and is a function of wind velocity, drag coefficient, and other factors. Drag coefficient is of particular importance since it varies for different shapes and Reynolds numbers. The EPA of the luminaire is assumed to include the drag coefficient, so this is no concern to the designer when calculating loads on the luminaire; however, the drag coefficient must be considered for the pole. The luminaires for the HMLTs monitored in this study vary dramatically. (For the remainder of this discussion, “luminaire” will refer to the group of lighting elements and their supporting upper-works, and the individual lighting elements will be referred to as “lights.”) The number of lights varies from three at the Kansas site to nine at the South Dakota site. At all sites, the lights are distributed evenly around the pole, with South Dakota being unique in that the lights are arranged in three banks of three. Correspondence with HMLT manufacturers indicated that an EPA of 20 square feet was a reasonable average value for design. However, for the purposes

research approach 23 of establishing a wind load, it was decided to account for the variability. A mathematical model estimating the EPA of a luminaire based on the number of lights was created according to the following assumptions: 1. The upper bound EPA was 22 square feet corresponding to about 10 or 12 lights. 2. The lower bound EPA was 4 square feet accounting for the upper works without any lights attached. 3. The change in the EPA of the luminaire decreases with increasing number of lights due to the overlap in the projected area of individual elements. A parabolic curve was chosen to model this effect since no other data for modeling this effect could be found. This method is conservative in relation to using a blanket value of 20 square feet since smaller EPAs result in larger static wind pressures. This is because the measured load effect must be maintained and a reduction in projected area needs to be balanced by increasing the applied static pressure. A plot of estimated EPA versus number of lights is shown in Figure 2.16, and the estimated EPA values used for analysis are listed in Table 2.3. Table 3-6 in AASHTO Signs (2009) provides drag coefficients for members of varying shapes. With regard to circular, 16-sided, and 12-sided shapes—cylindrical, hexdecagonal, and Figure 2.16. Estimated EPA of luminaires. ID # LIGHTS EST. EPA (ft2) KS 3 11.9 CA 4 14.0 ND 4 14.0 OK - NE 5 15.9 OK - SW 5 15.9 WY - CJE 6 17.5 WY - CJW 6 17.5 IA - N 8 20.0 IA - S 8 20.0 PA 8 20.0 SD 9 20.9 Table 2.3. Estimated EPA of luminaires for monitored sites.

24 Fatigue Loading and Design Methodology for high-Mast Lighting towers dodecagonal respectively—the drag coefficient is known to vary with Reynolds number. This is reflected in the table; for a given dimension, the coefficients will reduce with greater wind velocity. To accurately determine the proposed fatigue load, this variation had to be considered. The three plots in Figure 2.17 illustrate the variation. These plots were arrived at using a velocity conversion factor of 1 for a 50-year recurrence interval and the most conservative values for corner radius. The diameter range considered bounds the typical sizes for a tapered HMLT pole. Cylinder 16 Sides 12 Sides Figure 2.17. Variation of drag coefficient with regard to velocity, size, and shape.

research approach 25 For most of the wind velocities encountered in the wind-loading spectrum, the maximum value for drag coefficient could safely be assumed to be constant. Values of 1.1 were used to calculate wind loads for circular and 16-sided poles and a value of 1.2 was used for 12-sided poles. Furthermore, the current edition of AASHTO Signs (2009) states the location-specific yearly mean wind velocity shall be used to determine the drag coefficient, which is typically 11.2 mph, well below the break points shown in Figure 2.17. 2.3.4 Vortex Shedding Mitigation Vortex shedding mitigation strategies have long been identified as a potential way to increase the fatigue life of existing structures as well as to improve the fatigue resistance for new structures. Many different strategies and devices exist that can alleviate the effects of vortex-induced vibration (Ahearn and Puckett, 2010). However, the focus of mitigation in this study was not on different strategies but on the response of an HMLT after a mitigation device was installed. Helical strakes were selected as the means of mitigation. In theory, the addition of strakes sufficiently disrupts the flow of steady wind around the pole, thereby preventing the formation of organized vortices that drive the structure to vibrate perpendicular to the flow of wind. Using rope, strakes were easily installed on the existing HMLTs by wrapping them around the exterior in a helical pattern. To do this, a maintenance worker would lower the luminaire, attach the ropes, lift the luminaire back onto position, and wrap the ropes “maypole” fashion. For luminaire maintenance, the strakes could simply be unwrapped prior to lowering the luminaire and rewrapped when completed. 2.3.4.1 Test Setup—WY-CJE and WY-CJW The Creston Junction, Wyoming, site was specifically selected for the mitigation study since both HMLTs are identical and any experiment on one HMLT could easily be reproduced on the other. The initial setup was placed on the west HMLT and used a half-inch rope wrapped in a single helix with a frequency of about one wrap every 10 feet. The half-inch rope was arbitrarily chosen at the time of installation due to materials available at the local hardware store. About 90 days of data were collected for this configuration, and preliminary results showed a diminished number of accumulated stress cycles due to vortex shedding, but varied for different wind direc- tions (further discussion of this result is provided in the next chapter). To achieve more uniform mitigation, a double rope strake was subsequently installed. The double-helix pattern created by the double stake provided greater coverage of the pole surface area by the strake, the frequency of the wrap being increased to one wrap every 5 feet. In addition to adopting the double-strake pattern, the size of the rope was increased to 1 inch, approximately one-tenth the average diameter of the pole. Previous research suggests one-tenth is a better ratio of strake-to-structure diameter for vortex shedding mitigation (Warpinski, 2006). The double strake was first installed on the west HMLT and then moved to the east HMLT in order to reproduce the results. An illustration of the two strake patterns is shown in Figure 2.18, and a summary of data collection periods with regard to stake pattern is listed in Table 2.4. 2.3.4.2 Test Setup—IA-N The strake test setup at the Iowa site examined the placement of the strake along the length of the HMLT. Dynamic analysis indicated the majority of the oscillations due to vortex shedding occurred in the top one-third of the pole, near the upper antinodes of the second and third mode shapes. Observed behavior of HMLTs during vortex shedding events agreed with this hypothesis; oscillations appeared most pronounced in the upper portion of the pole. To experimentally verify if a strake is only required on the top third of an HMLT, the Iowa strake was installed in two separate segments. The two segments met at the first slip joint down from the luminaire. The top segment covered approximately the top third of the pole, while the bottom segment covered the remaining portion. After sufficient data were collected to confirm the full-length strake was

26 Fatigue Loading and Design Methodology for high-Mast Lighting towers successful in reducing the daily cycle count, the lower segment of rope was removed. The strake segments evaluated are illustrated in Figure 2.19. Like the double strake installed at the Wyoming site, the Iowa strake consisted of a double wrap with one-inch rope. The frequency of wrapping for a single rope was about one revolution per eight feet making the wrap for the double strake about once every four feet. The upper segment used a high quality one-inch nylon rope, which was securely installed with hose clamps top and bottom to ensure it did not unwrap or come down in the wind. The lower segment used a one-inch polypropylene rope secured at the top with duct tape and at the bottom with a ratchet strap. The duct tape allowed easy removal of the lower segment once the data collection period ceased. A summary of data collection periods with regard to strake segment coverage is listed in Table 2.5. 2.3.4.3 Methods of Evaluating Mitigation To evaluate the effectiveness of the strake test setups described above, two independent methods were used. First, stress-range histogram data were evaluated using traditional fatigue analysis. The effective constant-amplitude stress range, fatigue-limit-state stress range, and cycle frequencies were calculated for periods with and without strakes and compared. This provided a quantitative means of evaluating the fatigue effect. Second, the occurrences of across-wind excitation were noted for periods with and without strakes and compared. This provided a more qualitative means of evaluating the vortex shedding phenomena. The method used to determine across-wind excitation is included in Appendix F (available on the TRB website). PERIOD WY-CJE WY-CJW July 4 – Oct. 6, 2009 N S Oct. 6, 2009 – Jan. 20, 2010 N N Jan. 20 – Apr. 15, 2010 N D Apr. 15, 2010 – Mar. 15, 2011 D N Mar. 15 – June 6, 2011 N N N—No strake S—Single strake, ½” diameter D—Double strake, 1” diameter Table 2.4. Strake periods for Creston Junction, Wyoming, HMLTs. Figure 2.18. Single- and double-strake configurations.

research approach 27 PERIOD COVERAGE July 16 – Nov. 30, 2010 Full Nov. 30, 2010 – June 9, 2011 Top Third Table 2.5. Strake periods for IA-N HMLT. Figure 2.19. IA-N strake sections.

28 Fatigue Loading and Design Methodology for high-Mast Lighting towers 2.4 Fatigue Wind Load Methodology To establish rational loads for fatigue design of HMLTs, the following methodology was developed to analyze collected data. This methodology proposes the creation of a “fatigue wind” similar to the fatigue truck used in the design of highway bridges. The following analogy explains the similarity: as trucks are used to define highway bridge live load, wind is used to define HMLT live load. Both truck loading and natural wind produce stress ranges that are variable in amplitude and difficult to characterize in both magnitude and frequency. Whereas the AASHTO LRFD Bridge Design Specifications allow for either finite or infi- nite fatigue design life, this study focuses on the infinite life approach. The current AASHTO signs guidance (2009) state that estimating the lifetime loading histogram for such structures is “practically impossible” and an infinite life fatigue design approach is recommended. During this study, considerable data were collected to extrapolate a lifetime loading histogram for an HMLT, but the total number of cycles over the lifetime is large enough to render finite life design impractical. For example, if the lifetime cycles for a given HMLT exceed the number of cycles at the constant-amplitude fatigue limit (CAFL) for a Category E′ detail, infinite life design must be used. This is consistent with AASHTO LRFD Bridge Design Specifications, Section 6.6.1.2.3, where provisions for finite/infinite life design are given (AASHTO LRFD, 2010). A flowchart illustrating the methodology used is shown in Figure 2.20. The flowchart may be divided into three basic steps: 1. Stress-range histogram data: Collect, edit, and verify stress-range cycle data in the form of stress-range histograms. 2. Fatigue life: Calculate effective constant-amplitude stress-range, cycle frequency, and fatigue- limit-state stress-range, and then determine appropriate fatigue life design—finite versus infinite. 3. Fatigue load: Calculate corresponding fatigue load effect in terms of moment range, static pressure range, and wind velocity range. Each of these will be discussed in the following sections. The purpose of the methodology is to show how the fatigue-limit-state load is determined and to show that infinite life design is most practical. Using the proposed fatigue-limit-state load, some existing HMLTs may be limited to finite life. Considering these circumstances, the extrap- olated lifetime loading histogram can be used for finite fatigue life evaluation. Guidance is given later in the report for evaluation of HMLTs subject to finite life. 2.4.1 Stress-Range Histogram Data The stress-range histogram data collected on-site were considered “raw” because the data required further reduction. Before analyzing the data to determine fatigue damage, they were verified and edited if necessary. For example, the buffered stress time-history recorded on-site may have included noise that was interpreted as stress cycles by the rainflow algorithm. Typical noise spikes manifested themselves as high stress-range cycles in the histogram; they might have been identified as outliers or counted with true values. Since higher stress ranges account for greater fatigue damage, these errors affected calculating both the effective constant-amplitude stress range (SReff) and the fatigue-limit-state stress range (SRfls), inflating the cumulative results. Due to the extremely large number of cycles experienced by the HMLTs over the long duration of monitoring, the impact of false cycles on the SReff calculation was likely negligible; however, the impact on the 1:10,000 SRfls calculation used for infinite life design could have yielded overly- conservative results. For this reason, a quality control plan was implemented verifying high stress- range cycles by searching through the trigger data for high cycle events and visually inspecting for

research approach 29 noise. Another common error found in the histogram data resulted from the zero routine used by the data logger. The strain gage readings drifted over time and were digitally reset to compensate. If the drift was larger than the natural stress cycle at the time of the reset, it was counted as an exceedingly large cycle. Even though the trigger files were designed to minimize the amount of time-history data collected, they still resulted in large, cumbersome files containing data stored piecemeal over many months of the project. To aid in sorting through the trigger files to find the critical stress-range cycles, a computer routine was written. The routine broke the data into time intervals matching the rainflow routine, identified maximum stress-range cycles, and sorted them from highest to lowest. The top stress-range events were then printed on-screen so the user could verify them. Figure 2.20. Methodology flowchart for development of fatigue wind load.

30 Fatigue Loading and Design Methodology for high-Mast Lighting towers If the user found an anomaly, it was eliminated from the stress-range histogram. This verification process is illustrated in Figure 2.21. The data presented, and subsequent results, are based on selection of two strain gage data sets per HMLT. After a thorough review of the response of the HMLTs and characterization of the general behavior, two strain gages, one along-wind and one across-wind, were determined sufficient to represent the cumulative loading effects on a given HMLT. The prevailing wind direction was determined from the wind direction rosettes for percent occurrence. The nearest strain gages to the prevailing direction were termed along-wind and the nearest gages orthogonal to the prevailing direction were termed across-wind. In most instances, there were two strain gages to choose from for each direction—most gages being opposite of one another. In choosing between these two, the strain gage with a greater time length of data collection was chosen (some gages having failed over the duration of this study). If the time of collection was the same for both, the strain gage exhibiting the higher effective constant-amplitude stress was chosen. In other words, the other gages were found to provide redundant data and hence, Figure 2.21. Verification of stress-range cycles.

research approach 31 were not essential in the development of the loading. Throughout this report, data from the along-wind strain gages are noted with an “A” and data from across-wind strain gages are noted with an “X.” 2.4.2 Fatigue Life The current edition of AASHTO Signs recommends an infinite life approach since the number of wind load cycles expected over the life of a sign, signal, or luminaire support structure is unknown. This uncertainty makes infinite life the most practical approach because the number of cycles is not required for infinite life design. However, due to the HMLT failures prompting this study, the anticipated load effect and number of loading cycles during the life of the structure came into question. To prove infinite life design is sound, both load effect and number of cycles had to be examined. The load effect is quantified by the effective constant-amplitude stress-range (SReff) and the 1:10,000 fatigue-limit-state stress range (SRfls). The life of the structure is quantified by cycle counts (N). All three parameters are determined from the stress-range histogram. For design purposes, the detail (and thus the limiting cycle count, Nlim) is determined by the design engineer and must provide adequate resistance against the fatigue-limit-state load effect. The task of this study is the opposite—experimentally determine a reliable fatigue-limit-state load effect and the corresponding total cycles for design life (Ntot) and then compare with the appropriate stress-life (S-N) curve. 2.4.2.1 Limiting Cycle Count SRfls is the minimum stress-range that can be used for infinite life design and is found by statistical analysis. This concept is illustrated in Figure 2.22. In summary, a statistical distribution was fit to each data set, and the 1:10,000 stress range was extracted from the probability density function. The 1:10,000 return period is an established value commonly used in fatigue analysis and is the basis for the current AASHTO LRFD Bridge Design Specifications provision for infinite life. In other words, the Fatigue I load combination is the truck loading associated with this probability of occurrence (AASHTO LRFD, 2010). In order for infinite life to be valid, the fatigue resistance of a given detail must exceed SRfls. The fatigue resistance associated with the endurance limit of a detail is known as the constant-amplitude fatigue limit, or CAFL. CAFL values are determined from the stress-life (S-N) curves for different detail categories. The cycle count associated with the endurance limit is herein referred to as the limiting cycle count (Nlim). The CAFL and limiting cycle count for a Category D detail is illustrated in Figure 2.23. Figure 2.22. Fatigue-limit-state stress range.

32 Fatigue Loading and Design Methodology for high-Mast Lighting towers 2.4.2.2 Total Cycles for Design Life SReff is an effective stress-range representing the effect of all the stress cycles in the variable- amplitude spectrum, and is calculated using Miner’s Rule (Miner, 1945), which is shown in Equation 2.8. S NS N ff R Re =     ∑ ∑ 3 1 3 Equation 2.8: Miner’s Rule SReff along with the accumulated number of cycles (SN) are used to determine fatigue damage and remaining fatigue life in an existing structure. With regard to infinite fatigue life design, SReff and SN are used to estimate the total cycles for design life, Ntot. These values vary based on the level of truncation selected for the histogram. Truncation is an important step in determining a useful value of SReff, one that is neither too high nor too low for the type of detail considered. If Ntot is greater than Nlim for a given detail, then infinite fatigue life design should be used. If Ntot is less than Nlim, then finite fatigue life should be used. 2.4.3 Fatigue Load After establishing stress range values—SReff and SRfls—for each of the HMLTs in the study, they needed to be converted to a normalized parameter applicable to any given HMLT structure. Unique to any structure, stress range depends on loading, geometry, and section properties. The normalized parameter, typically expressed as a load, can be applied to any structure to determine an appropriate fatigue stress range. For example, the fatigue truck used in the AASHTO Bridge Specifications can be applied to any bridge, regardless of type, span length, connections, etc. To do the same for HMLTs, the parameter needs to be expressed as a wind load, or more precisely, a pressure range or velocity range. Converting stress range to wind velocity requires a series of calculations. The first step in this procedure is to convert the stress-range values to moment range using specific HMLT geometry and basic mechanics of materials. The next step is to convert the moment range to a normalized parameter using fluid equations for static pressure and velocity. Figure 2.24 shows the equations for converting moment range to static pressure and wind velocity. The design wind pressure is based on Figure 2.23. Stress-life curve illustrating Nlim (AASHTO LRFD, 2010).

research approach 33 the fundamental wind pressure equation given in AASHTO Signs (2009). The height and exposure factor, Kz, is excluded due to variation in individual pole heights, and the gust effect factor, G, is excluded for use with lower wind speeds. The importance factor for HMLTs, as suggested by AASHTO Signs C11.6 (2009), is taken as unity. The experimental wind pressure is related to bending moment by basic statics. Note that the drag coefficient is included in the equation for experimental wind pressure instead of design wind pressure. As given in Table 3.6 of AASHTO Signs (2009), separate drag coefficients should be used for the pole and luminaire. Furthermore, the drag coefficient for the luminaire attachment is typically included in the EPA of the luminaire. The wind load for the proposed specification is presented in terms of static pressure-range. The concept of velocity range is included to provide an intuitive feel for the proposed load since the velocity range may be compared to other design wind speeds. Pressure range was chosen for the specification due to its simplicity; velocity range would need to be converted to a static pressure-range in the design process anyway. The applied pressure range will yield the desired stress range, which is necessary for fatigue design. The same concept is utilized in the existing AASHTO Bridge Specifications (2010), except that the Fatigue I load combination is used instead of a static pressure range. The fatigue-limit-state static pressure-range, Pfls, is the basis for the proposed methodology for infinite life design of HMLTs. It is determined from SRfls using the process shown above. The load in the proposed specification is termed the combined wind effect as described in an earlier section. It is a function of Pfls, drag coefficient, and importance category. The development of this load and associated findings are presented in the next chapter. Design wind pressure: Experimental wind pressure: ( )e d p p L L MP psf C A y EPA y = + Setting the two equations equal, wind speed can be calculated from the applied moment using the equation, ( ) ( )0.00256 d p p L L MV mph C A y EPA y = + where: EPAL = Projected area of luminaire, equal to projected area times drag coefficient (ft2) Ap = Projected area of pole (ft2) Cd = AASHTO drag coefficient applied to pole M = Applied moment (lb-ft) V = Effective wind speed (mph) ygages = Height of strain gages (ft) yp = Distance to C.G. of pole (ft) yL = Distance to luminaire (ft) Figure 2.24. Fatigue static pressure and wind velocity computation.