Development and Calibration of AASHTO LRFD Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals (2014)

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A-1 Calibration Report CONTENTS Section 1. Introduction ................................................................. A-3 Appendix Context �����������������������������������������������������������������������������������������������A-3 Scope �������������������������������������������������������������������������������������������������������������������A-3 Appendix Organization ��������������������������������������������������������������������������������������A-3 Section 2. Load Model .................................................................. A-5 Dead Load Parameters ����������������������������������������������������������������������������������������A-5 Wind Speed Statistical Parameters ���������������������������������������������������������������������A-5 Information from ASCE/SEI 7-10 and Available Literature �������������������������A-5 Statistical Parameters for Wind Load Variables ��������������������������������������������A-5 Development of Statistical Parameters for Wind Speed �������������������������������A-6 Conclusions���������������������������������������������������������������������������������������������������������A-9 Section 3. Ice Load Parameters ................................................... A-10 Information from ASCE/SEI 7-10 and Available Literature ���������������������������A-10 Development of Statistical Parameters for Uniform Radial Ice Thickness ����A-10 Conclusions�������������������������������������������������������������������������������������������������������A-12 Section 4. Correlation Between Ice Thickness and Concurrent 3-s Gust Wind .......................................... A-19 Information from ASCE/SEI 7-10 and Available Literature ���������������������������A-19 Possible Combination of Uniform Radial Ice Thickness and Concurrent 3-s Gust Speeds ������������������������������������������������������������������������A-19 Conclusions�������������������������������������������������������������������������������������������������������A-19 Secondary Analysis for Wind on Ice ����������������������������������������������������������������A-20 Conclusion ��������������������������������������������������������������������������������������������������������A-20 Section 5. Resistance Model ....................................................... A-26 Statistical Parameters of Resistance �����������������������������������������������������������������A-26 Conclusion ��������������������������������������������������������������������������������������������������������A-26 Section 6. Fatigue Resistance for High-Mast Luminaires ........... A-28 Background �������������������������������������������������������������������������������������������������������A-28 Stress Range Versus Number of Cycles Relationship from Test Results ���������A-28 Stress Range Versus Number of Cycles Relationship for Infinite Life ������������A-28 Statistical Parameters for Resistance ����������������������������������������������������������������A-29 Reliability Analysis for Fatigue Limit State ������������������������������������������������������A-29 Conclusions�������������������������������������������������������������������������������������������������������A-40 A P P E N D I X A

A-2 Section 7. Reliability Analysis ..................................................... A-45 LRFD Reliability Analysis—Flexure ����������������������������������������������������������������A-45 Flexural Resistance ���������������������������������������������������������������������������������������A-45 Load ���������������������������������������������������������������������������������������������������������������A-45 Reliability Indices �����������������������������������������������������������������������������������������A-47 Implementation ��������������������������������������������������������������������������������������������A-47 ASD Reliability Analysis—Flexure �������������������������������������������������������������������A-48 Resistance ������������������������������������������������������������������������������������������������������A-49 Implementation ��������������������������������������������������������������������������������������������A-50 Calibration and Comparison ���������������������������������������������������������������������������A-51 LRFD Reliability Analysis—Torsion ����������������������������������������������������������������A-51 Strength ���������������������������������������������������������������������������������������������������������A-51 Load ���������������������������������������������������������������������������������������������������������������A-53 Implementation ��������������������������������������������������������������������������������������������A-53 ASD Reliability Analysis—Torsion ������������������������������������������������������������������A-53 Strength ���������������������������������������������������������������������������������������������������������A-53 Implementation ��������������������������������������������������������������������������������������������A-54 Calibration and Comparison ���������������������������������������������������������������������������A-54 LRFD Flexure-Shear Interaction ����������������������������������������������������������������������A-55 Monte Carlo Moment/Shear Interaction Simulation ���������������������������������A-56 Section 8. Implementation ......................................................... A-58 Setting Target Reliability Indices ����������������������������������������������������������������������A-58 Implementation into Specifications ������������������������������������������������������������A-58 Computed Reliability Indices�����������������������������������������������������������������������A-58 Sensitivities �������������������������������������������������������������������������������������������������������A-59 Section 9. Summary .................................................................... A-64 Annex A ....................................................................................... A-65 Annex B ....................................................................................... A-69

A-3 Appendix Context The research for NCHRP Project 10-80 required several integrally linked activities: • Assessment of existing literature and specifications, • Organization and rewriting the LRFD-LTS specifications, • Calibration of the load and resistance factors, and • Development of comprehensive examples illustrating the application of LRFD-LTS specifications� The purpose of this appendix is to provide the details regarding the calibration process and results� This appendix is intended for those who are especially interested in the details of the process� The draft LRFD-LTS specifications are being published by AASHTO� In addition, Appendix C provides a series of exam- ple problems that illustrate the application of the LRFD-LTS specifications� Scope The LRFD-LTS specifications consider the loads for design presented in Table 1-1� The combinations considered are based on either judg- ment or experience and are illustrated in Table 1-2� The pro- posed load factors are shown� The Strength I limit state for dead load only (Comb� 1) was calibrated� The Strength I limit state for dead load and live load was considered a minor case and may control only for com- ponents that support personnel servicing the traffic devices (Comb� 2)� The live load factor based on ASCE/SEI 7-10 was used directly and not studied within the present calibration� The Extreme I limit state combines dead loads with wind loads (Comb� 4)� This is an important limit state� This combi- nation was a strength limit in the ASD LTS specification� The combination is termed “extreme” because ASCE/SEI 7-10 uses new wind hazard maps that are associated with a unit load fac- tor� (Note that a unit load factor is also used for seismic events, which are definitely considered extreme events�) Therefore, in the LRFD-LTS specifications, the term “extreme” is used� The Extreme I limit state that combines dead load, wind, and ice (Comb� 5) was studied in detail, and it was deter- mined that it will not be critical in the vast majority of cases, and in the few cases where it will be critical, it is close to the dead load combined with wind (Comb� 4)� The Service I and III limit states were not calibrated, and the same factors that were used in the previous ASD-based specifications were used� The Fatigue I limit is often critical depending on the connection details� Significant work has been conducted on the fatigue performance of LTS connections (Connor et al�, 2012, and Roy et al�, 2011)� The recommendations of the researchers of those projects were used without further calibration� In the case of high-mast towers, recent research for connection resistance (Roy et al�, 2011) and load effects for vortex shedding and along wind vibrations combined (Connor et al�, 2012) was used to determine reliability indices for those structures� These data might be used in the future to change load or resis- tance factors for high-mast towers� In the meantime, this new methodology provides a roadmap for the fatigue limit-state calibration� Also note that improved detailing for new designs is considered economical, and therefore, any savings associ- ated with decreasing loads might be considered minimal in these cases� Appendix Organization This appendix begins by characterizing the dead and wind loads in Section 2� Here, the mean, bias, and variances are established� The ice load parameters are examined in Section 3� Information from the previous sections is used to exam- ine the wind-on-ice combination in Section 4� The resistance S E c t I o N 1 Introduction

A-4 model is provided in Section 5� Sections 2 to 5 provide the necessary prerequisite information for conducting the reli- ability analysis in Section 7 and calibrating the strength limit state� Section 8 illustrates the implementation of the reliabil- ity analysis for the specifications� Section 6 addresses the reliability analysis for the fatigue limit state for high-mast luminaires� This section may be skipped if the reader is only interested in the strength limit state� Finally, the calibration is summarized in Section 9� Annexes are provided for a variety of data used in this study� Table 1-1. LRFD-LTS loads. Load Abbrev. Description Limit State Dead load components DC Gravity Strength Live load LL Gravity (typically service personnel) Strength Wind W Lateral load Extreme Ice IC Gravity Strength Wind on ice WI Lateral Extreme Truck gust TrG Vibration Fatigue Natural wind gust NWG Vibration Fatigue Vortex-induced vibration VIV Vibration Fatigue Combined wind on high- mast towers HMT Vibration Fatigue Galloping-induced vibration GIV Vibration Fatigue Comb. No. Limit State Calibrated? Perm anent Transient Fatigue (loads applied separately) DC LL W IC TrG NWG VIV HMT GIV 1 Strength I Yes 1.25 2 Strength I No 1.25 1.6 3 Strength I Yes 1.1/0.9 4 Extreme I Yes 1.1/0.9 1.0 5 Extreme I Studied in detail X X X 6 Service I No 1.0 1.0 7 Service III No 1.0 1.0 8 Fatigue I No, except for HMT 1.0 1.0 1.0 1.0 1.0 9 Fatigue II No 1.0 1.0 1.0 1.0 1.0 Table 1-2. Limit states considered in the LRFD-LTS specifications.

A-5 Dead Load Parameters Dead load (DC) is the weight of structural and perma- nently attached nonstructural components� Variation in the dead load, which affects statistical parameters of resistance, is caused by variation of the gravity weight of materials (con- crete and steel), variation of dimensions (tolerances in design dimensions), and idealization of analytical models� The bias factor (ratio of mean to nominal) value of dead load is l = 1�05, with a coefficient of variation (Cov) = 0�10 for cast-in- place elements, and l = 1�03 and Cov = 0�08 for factory-made members� The assumed statistical parameters for dead load are based on the data available in the literature (Ellingwood, 1981 and Nowak, 1999)� Wind Speed Statistical Parameters Information from ASCE/SEI 7-10 and Available Literature According to the ASCE/SEI 7-10, the basic wind speed (V) used in the determination of design wind load on build- ings and other structures should be determined from maps included in the ASCE/SEI 7-10 (Fig� 26�5-1), depending on the risk category, with exceptions as provided in Section 26�5�2 (special wind regions) and 26�5�3 (estimation of basic speeds from regional climatic data)� For Risk Category II, it is required to use the map of wind speed V700 (Fig� 26�5-1A), corresponding to an approximately 7% probability of exceedance in 50 years (annual exceedance probability = 0�00143, MRI = 700 years)� For Risk Categories III and IV, it is required to use the map of wind speed V1700 (Fig� 26�5-1B), corresponding to an approxi- mately 3% probability of exceedance in 50 years (annual exceedance probability = 0�000588, MRI = 1,700 years)� For Risk Category I, it is required to use the map of wind speed V300 (Fig� 26�5-1C), corresponding to an approximately 15% probability of exceedance in 50 years (annual exceed- ance probability = 0�00333, MRI = 300 years)� The basic wind speeds in ASCE/SEI 7-10 (Fig� 26�5-1) are based on the 3-s gust wind speed map� The non-hurricane wind speed is based on peak gust data collected at 485 weather stations where at least 5 years of data were available (Peterka, 1992; Peterka and Shahid, 1998)� For non-hurricane regions, measured gust data were assembled from a number of sta- tions in state-sized areas to decrease sampling error, and the assembled data were fit using a Fisher-Tippett Type I extreme value distribution� The hurricane wind speeds on the United States Gulf and Atlantic coasts are based on the results of a Monte Carlo simulation model described in Applied Research Associates (2001), Vickery and Waldhera (2008), and Vickery et al� (2009a, 2009b, and 2010)� The map presents the variation of 3-s wind speeds associ- ated with a height of 33 ft (10 m) for open terrain (Expo- sure C)� Three-second gust wind speeds are used because most National Weather Service stations currently record and archive peak gust wind (see Table 2-1)� Statistical Parameters for Wind Load Variables The wind pressure is computed using the following formula: 0�0256 2P K K G V C psfz z d di i i i i ( )= where: V = basic wind speed, mph, Kz = height and exposure factor, Kd = directionality factor, G = gust effect factor, and Cd = drag coefficient� The parameters V, Kz, Kd, G, and Cd are random variables, and the distribution function of wind pressure and the wind load S E c t I o N 2 Load Model

A-6 statistics are required to determine appropriate probability- based load and load combination factors� The cumulative distribution function of wind speed is particularly significant because V is squared� However, the uncertainties in the other variables also contribute to the uncertainty in Pz� The CDFs for the random variables used to derive the wind load criteria that appear in ASCE/SEI 7-10 are summarized in Table 2-2 (Ellingwood, 1981)� Development of Statistical Parameters for Wind Speed The statistical parameters of load components are neces- sary to develop load factors and conduct reliability analysis� The shape of the CDF is an indication of the type of distri- bution� For non-hurricane regions, measured gust data were fit using a Fisher-Tippett Type I extreme value distribution (Peterka and Shahid, 1998)� The CDF for the extreme Type I random variable is defined by: exp expF x x u( )[ ]( ) ( )= − −α − where u and a are distribution parameters: 1�282 α ≈ σx 0�45u x x≈ µ − σ and mx and sx are mean value and standard deviation, respectively� Based on the type of distribution and statistical parameters for annual wind in specific locations, a Monte Carlo simulation was used to determine the statistical parameters of wind speed (Nowak and Collins, 2000)� The annual statistical parameters are available from the Building Science Series (Changery et al�, 1979)� The data set includes 129 locations; 100 locations are from Central United States, and the remaining 29 locations are from other regions� The data set does not include regions of Alaska; however, based on the other locations, analogs are used� Examples of Monte Carlo simulation are presented on Figures 2-1 to 2-6, with corresponding tables of statistical parameters (see Tables 2-3 to 2-10)� Developed parameters for all locations are listed in Annex A� Table 2-1. Summary of the wind speeds from the maps in ASCE/SEI 7-10 (Fig. 26.5-1). Location V10 (mph) V50 (mph) V300 (mph) V700 (mph) V1700 (mph) Alaska 1 78 90 105 110 115 Alaska 2 78 100 110 120 120 Alaska 3 90 110 120 130 130 Alaska 4 100 120 130 140 150 Alaska 5 100 120 140 150 160 Alaska 6 113 130 150 160 165 Central USA 76 90 105 115 120 West Coast 72 85 100 110 115 Coastal Segment 1 76 90 105 115 120 Coastal Segment 2 76 100 110 120 130 Coastal Segment 3 76 110 120 130 140 Coastal Segment 4 80 120 130 140 150 Coastal Segment 5 80 130 140 150 160 Coastal Segment 6 90 140 150 160 170 Coastal Segment 7 90 140 150 170 180 Coastal Segment 8 90 150 160 170 190 Coastal Segment 9 90 150 170 180 200 Table 2-2. Wind load statistics (Ellingwood, 1981). Parameter Mean/Nominal Cov CDF Exposure factor, Kz 1.0 0.16 Normal Gust factor, G 1.0 0.11 Normal Pressure coefficient, Cp 1.0 0.12 Normal

Figure 2-1. CDFs for annual and MRI 300, 700, and 1,700 years, for Baltimore, Maryland. (Note: Lines top to bottom in key are left to right in figure.) Table 2-3. Statistical parameters of wind speed for Baltimore, Maryland. Baltimore, MD Mean Cov Annual 55.9 0.123 300 Years 87 0.080 700 Years 91 0.075 1,700 Years 96 0.070 Figure 2-2. CDFs for annual and MRI 300, 700, and 1,700 years, for Chicago, Illinois. (Note: Lines top to bottom in key are left to right in figure.) Table 2-4. Statistical parameters of wind speed for Chicago, Illinois. Chicago, IL Mean Cov Annual 47.0 0.102 300 Years 68 0.075 700 Years 72 0.070 1,700 Years 75 0.066 Figure 2-3. CDFs for annual and MRI 300, 700, and 1,700 years, for Omaha, Nebraska. (Note: Lines top to bottom in key are left to right in figure.) Table 2-5. Statistical parameters of wind speed for Omaha, Nebraska. Omaha, NE Mean Cov Annual 55.0 0.195 300 Years 102 0.105 700 Years 109 0.100 1,700 Years 117 0.095 Figure 2-4. CDFs for annual and MRI 300, 700, and 1,700 years, for Rochester, New York. (Note: Lines top to bottom in key are left to right in figure.) Table 2-6. Statistical parameters of wind speed for Rochester, New York. Rochester, NY Mean Cov Annual 53.5 0.097 300 Years 77 0.069 700 Years 80 0.067 1,700 Years 84 0.063

A-8 Figure 2-5. CDFs for annual and MRI 300, 700, and 1,700 years, for St. Louis, Missouri. (Note: Lines top to bottom in key are left to right in figure.) Table 2-7. Statistical parameters of wind speed for St. Louis, Missouri. St. Louis, MO Mean Cov Annual 47.4 0.156 300 Years 80 0.094 700 Years 85 0.088 1,700 Years 90 0.084 Figure 2-6. CDFs for Annual and MRI 300, 700, and 1,700 years, for Tucson, Arizona. (Note: Lines top to bottom in key are left to right in figure.) Table 2-8. Statistical parameters of wind speed for Tucson, Arizona. Tucson, AZ Mean Cov Annual 51.4 0.167 300 years 89 0.096 700 years 95 0.091 1,700 years 101 0.089 Table 2-9. Summaries of statistical parameters of wind speed for Central United States. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov Average 32 52.1 0.144 71.6 85.1 0.088 90.0 0.083 95.2 0.079 Max 48 62.8 0.226 104.0 110.0 0.114 118.0 0.109 127.0 0.104 Min 10 40.9 0.087 53.4 66.0 0.063 69.0 0.060 72.0 0.056 Table 2-10. Summaries of statistical parameters of wind speed for the West Coast. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov Average 30 47.2 0.140 64.8 76.6 0.085 80.9 0.082 85.5 0.077 Max 54 71.5 0.223 104.4 116.0 0.112 123.0 0.108 130.0 0.098 Min 10 34.4 0.080 41.9 50.0 0.060 52.0 0.058 54.0 0.056

A-9 The most important parameters are the mean, bias factor, and the coefficient of variation� The bias factor is the ratio of mean to nominal� Mean values were taken as an extreme peak gust wind speed from the literature (Vickery et al�, 2010)� Bias factors were calculated as follows: 50 50 50 300 300 300 700 700 700 1700 1700 1700V V V V λ = µ λ = µ λ = µ λ = µ where: m50, m300, m700, m1700 = are wind speeds with MRI = 50 years, 300 years, 700 years, and 1,700 years, respectively, taken from maps included in literature (Vickery et al�, 2010); and V50,V300, V700, V1700 = are wind speeds with MRI = 50 years, 300 years,700 years, and 1,700 years, respectively, taken from maps included in ASCE/SEI 7-10� To find standard deviation of distribution, multiple Monte Carlo simulations were conducted� The results are shown in Figures 2-1 to 2-6� The symbol markers in the graphs repre- sent mean values of wind occurring in a considered period of time� The curves are CDFs of basic wind speed for differ- ent MRIs fitted using a Fisher-Tippett Type I extreme value distribution� Conclusions The CDFs of peak gust wind speed were plotted on normal probability paper as the best fit to the statistical parameters available from 129 locations� The distribution for annual wind speed was defined as Fisher-Tippet Type I extreme value distribution (Peterka and Shahid, 1993)� Based on the type of distribution and statistical parameters, a Monte Carlo sim- Table 2-11. Summary of statistical parameters of 300-year return period peak gust wind speeds. Location V300 (mph) 300 = µ300/V300 Cov300 Central United States 105 0.80 0.090 West Coast 100 0.75 0.085 Alaska 105 – 150 0.80* 0.095* Coastal Segments 105 – 170 0.80 0.130 *Statistical parameters determined by analogy. Table 2-12. Summary of statistical parameters of 700-year return period peak gust wind speeds. Location V700 (mph) 700 = µ700/V700 Cov700 Central United States 115 0.80 0.085 West Coast 110 0.75 0.080 Alaska 110 – 160 0.80* 0.090* Coastal Segments 115 – 180 0.80 0.125 *Statistical parameters determined by analogy. Table 2-13. Summary of statistical parameters of 1,700-year return period peak gust wind speeds. Location V1700 (mph) 1700 = µ1700/V1700 Cov1700 Central United States 120 0.80 0.080 West Coast 115 0.75 0.075 Alaska 115 – 165 0.80* 0.085* Coastal Segments 120 – 200 0.80 0.115 *Statistical parameters determined by analogy. ulation was used to determine the statistical parameters of wind speed� For each location, four distributions were plot- ted: annual, 300 years, 700 years, and 1,700 years� Statistical parameter for 300-year, 700-year, and 1,700-year MRI were used for extreme wind combinations� Recommended values are listed in Tables 2-11 to 2-13�

A-10 S E c t I o N 3 Information from ASCE/SEI 7-10 and Available Literature Atmospheric ice loads due to freezing rain, snow, and in- cloud icing have to be considered in the design of ice-sensitive structures� According to ASCE/SEI 7-10, the equivalent uni- form radial thickness t of ice due to freezing rain for a 50-year mean recurrence interval is presented on maps in Figures 10-2 through 10-6 in ASCE/SEI 7-10� The 50-year MRI ice thick- nesses shown in ASCE/SEI 7-10 are based on studies using an ice accretion model and local data� The historical weather data were collected from 540 National Weather Service, military, Federal Aviation Administration, and Environment Canada weather stations� The period of record of the meteorological data is typically 20 to 50 years� At each station, the maximum ice thickness and the maximum wind-on-ice load were deter- mined for each storm� Based on maps in ASCE/SEI 7-10, the ice thickness zones in Table 3-1 can be defined� These ice thicknesses should be used for Risk Category II� For other categories, thickness should be multiplied by the MRI factor� For Risk Category I, it is required to use MRI = 25 years, and for Risk Category III and IV, it is required to use MRI = 100 years� The mean recurrence interval factors are listed in Table 3-2� Using the mean recurrence interval factor for each zone, the ice thicknesses for different MRIs were calculated and are presented in Table 3-3� In addition, ice accreted on structural members, compo- nents, and appurtenances increases the projected area of the structures exposed to wind� Wind load on this increased pro- jected area should be used in design of ice-sensitive struc- tures� Figures 10-2 through 10-6 in ASCE/SEI 7-10 include 3-s gust wind speeds that are concurrent with the ice loads due to freezing rain� Table 3-4 summarizes the 3-s gust for different localizations across the United States� As opposed to ice thickness, 3-s concurrent gust speed does not have a multiplication factor for different risk categories� The values on the map are the same for each risk category� The statistical parameters for 3-s concurrent gust speed can be taken as an average of statistical parameters of wind speed� Development of Statistical Parameters for Uniform Radial Ice Thickness The statistical parameters of load components are neces- sary to develop load factors and conduct reliability analy sis� The shape of the CDF is an indication of the type of distribution� Extreme ice thicknesses were determined from an extreme value analysis using the peak-over-threshold method and generalized Pareto distribution (GPD) (Hosking and Wallis, 1987, and Wang, 1991)� The analysis of the weather data and the calculation of extreme ice thickness are described in more detail in Jones et al� (2002)� Based on the GPD, ice thicknesses for long return periods (Table 3-3), and the probability of being exceeded, a Monte Carlo simulation was used to determine parameters for annual extremes� The family of GPDs has three parameters: k – shape, a-scale, and q – threshold� The typical generalized Pareto probability density function and cumulative distribution function (CDF) are show in Figures 3-1 and 3-2� The results of Monte Carlo simulation for annual extremes are shown in Figure 3-2 and Table 3-5� The threshold, q, for each simulation was zero� This means that in some years, the maximum ice thickness is zero, which would have to be con- sidered part of an extreme population in the epochal method� The shape parameter, k, is constant for each zone because mean recurrence interval factors are the same for each zone� However, these parameters are for annual events� The design minimum load from ASCE/SEI 7-10 is based on 25-year, 50-year, and 100-year events, depending on risk category� To estimate statistical parameters for these recurrence intervals, additional analyses should be performed� Based on the avail- Ice Load Parameters

A-11 able literature, the sample results of annual extremes were found� These data were plotted on normal probability paper to find the most important parameters, such as the mean, bias factor, and coefficient of variation� Bias factor is the ratio of the mean to nominal� The nominal value was taken from Table 3-3, depending on the zone and risk category� The first group of sample results was found in CRREL Report 96-2 (Jones, 1996)� The results include uniform equiv- alent radial ice thicknesses hind-cast for the 316 freezing-rain events in 45 years that occurred at Des Moines, Iowa, between 1948 and 1993 (see Figure 3-3)� The second group of sample results was found in research work of Lott and Jones from 1998� The data were recorded from three weather stations in Indiana, south of the Great Lakes in the central region of the United States (in India- napolis, at Grissom AFB, and in Lafayette)� Ice loads from these three stations, presented as uniform radial ice thick- nesses calculated by simple model (Jones, 1998), are shown in Figure 3-4� Only episodes with a freezing-rain storm at one or more of these three stations are shown, with the graphs divided in decades� The CDFs of the ice thickness were plotted on normal probability paper, as shown in Figures 3-5 through 3-16� The construction and use of normal probability paper can be found in textbooks on probability [e�g�, Nowak and Collins (2000)]� Probability paper allows for an easy evaluation of the most important statistical parameters as well as the type of the distribution function� The horizontal axis represents the considered variable; in this case it is the uniform radial ice thickness� The vertical axis is the inverse normal prob- ability, and it is equal to the distance from the mean value in terms of standard deviations� It can also be considered as the corresponding probability of being exceeded� The test data plotted on the normal probability paper can be analyzed by observing the shape of the resulting curve representing the CDF� The annual extremes for each localization as well as the long return periods predicted from ASCE/SEI 7-10 create a curve that characterizes the generalized Pareto distribution� The dashed line in the graphs is related to the corresponding probability of exceedance for 25-year, 50-year, and 100-year returned periods� The points on the graph marked with stars represent extreme events in 25 years, 50 years, and 100 years� These points were calculated by moving the dashed line to the position of the horizontal axis (standard normal variable = 0)� The x coordinate (ice thickness) was treated as a constant, and the y coordinate (standard normal variable) was recalcu- lated for the new probability of occurrence� Next, the statis- tical parameters were determined by fitting a straight line to the CDF� The mean value can be read directly from the graph, as the horizontal coordinate of intersection of the CDF� The standard deviation can also be determined by the inverse of the slope of the line� Table 3-1. Ice thickness zones. Ice Load Zones Zone 0 Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 MRI = 50 years 0.00” 0.25” 0.5” 0.75” 1.0” 1.25” 1.5” Table 3-2. Mean recurrence interval factors. Mean Recurrence Interval Multiplier on Ice Thickness 25 years 0.80 50 years 1.00 100 years 1.25 200 years 1.50 250 years 1.60 300 years 1.70 400 years 1.80 500 years 2.00 1,000 years 2.30 1,400 years 2.50 Table 3-3. Ice thickness in long return periods. Ice Load Zones Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Mean Recurrence Interval Ice Thicknesses, in. 25 years 0.20 0.40 0.60 0.80 1.00 1.20 50 years 0.25 0.50 0.75 1.00 1.25 1.50 100 years 0.31 0.63 0.94 1.25 1.56 1.88 200 years 0.38 0.75 1.13 1.50 1.88 2.25 250 years 0.40 0.80 1.20 1.60 2.00 2.40 300 years 0.43 0.85 1.28 1.70 2.13 2.55 400 years 0.45 0.90 1.35 1.80 2.25 2.70 500 years 0.50 1.00 1.50 2.00 2.50 3.00 1,000 years 0.58 1.15 1.73 2.30 2.88 3.45 1,400 years 0.63 1.25 1.88 2.50 3.13 3.75

A-12 Table 3-4. 3-s gust speed concurrent with the ice loads. Gust Speed Zones V50 (mph) Cov (mph) Zone 1 30 0.15 4.5 Zone 2 40 0.15 6.0 Zone 3 50 0.15 7.5 Zone 4 60 0.15 9.0 Zone 5 70 0.15 10.5 Zone 6 80 0.15 12 Figure 3-1. Generalized Pareto probability density function, PDF      1 (1 ) 1 1f(x) k z ki and generalized Pareto cumulative distribution function, CDF F(x) k z k1 (1 ) 1   i . (Note: Key for left portion of figure corresponds to top to bottom in the graph; key for right portion of figure is left to right.) Conclusions The CDFs of ice thicknesses recorded in four weather sta- tions were plotted on normal probability paper for a better interpretation of the results� Then, the statistical parameters were calculated for different localizations and for different recurrence intervals� The average of coefficient of variation and bias factor can be used as statistical parameters for uni- form ice thickness (see Table 3-6)� However, the analysis is based on the limited database available in the literature� It is recommended to expand the database and verify the statistical parameters in the future� k = 0.10, α = 0.055, θ = 0.0 k = 0.10, α = 0.110, θ = 0.0 Figure 3-2. Generalized Pareto distribution of uniform ice thickness for different zones with three most important parameters. (continued on next page)

k = 0.10, α = 0.165, θ = 0.0 k = 0.10, α = 0.220, θ = 0.0 k = 0.10, α = 0.275, θ = 0.0 k = 0.10, α = 0.330 θ = 0.0 Figure 3-2. (Continued). Ice Load Zones Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Statistical parameters Generalized Pareto Distribution k – shape 0.10 0.10 0.10 0.10 0.10 0.10 -scale 0.055 0.110 0.165 0.220 0.275 0.330 – threshold 0 0 0 0 0 0 Table 3-5. Summaries of statistical parameters of GPD for annual extremes. Figure 3-3. Uniform radial ice thickness hind-cast by the heat-balanced model for freezing events at the Des Moines airport from 1948 to 1993.

A-14 Figure 3-4. Uniform radial ice thickness calculated using historical weather data-three station in Indiana, from the simple model. Figure 3-5. CDF of uniform radial ice thickness recorded at the Des Moines airport and simulation results for 25-year extremes. 25 = 0.53 in. = 0.19 in. Cov = / = 0.37 Nom25 = 0.60 in. 25 = 25/Nom25 = 0.88 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Des Moines annual extremes 25 year extremes long return periods (ASCE 7) Figure 3-6. CDF of uniform radial ice thickness recorded at the Des Moines airport and simulation results for 50-year extremes. 50 = 0.60 in. = 0.15 in. Cov = / = 0.25 Nom50 = 0.75 in. 50 = 50/Nom50 = 0.80 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Des Moines annual extremes 50 year extremes long return periods (ASCE 7)

A-15 Figure 3-7. CDF of uniform radial ice thickness recorded at the Des Moines airport and simulation results for 100-year extremes. 100 = 0.68 in. = 0.12 in. Cov = / = 0.17 Nom100 = 0.94 in. 100 = 100/Nom100 = 0.72 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Des Moines annual extremes 100 year extremes long return periods (ASCE 7) Figure 3-8. CDF of uniform radial ice thickness recorded at Grissom AFB and simulation results for 25-year extremes. 25 = 0.85 in. = 0.22 in. Cov = / = 0.26 Nom25 = 0.80 in. 25 = 25/Nom25 = 1.06 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Grissom AFB annual extremes 25 year extremes long return periods (ASCE 7) Figure 3-9. CDF of uniform radial ice thickness recorded at Grissom AFB and simulation results for 50-year extremes. 50 = 1.00 in. = 0.22 in. Cov = / = 0.22 Nom50 = 1.00 in. 50 = 50/Nom50 = 1.00 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Grissom AFB annual extremes 50 year extremes long return periods (ASCE 7)

A-16 Figure 3-10. CDF of uniform radial ice thickness recorded at Grissom AFB and simulation results for 100-year extremes. 100 = 1.11 in. = 0.16 in. Cov = / = 0.15 Nom100 = 1.25 in. 100 = 100/Nom100 = 0.88 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Grissom AFB annual extremes 100 year extremes long return periods (ASCE 7) Figure 3-11. CDF of uniform radial ice thickness recorded in Lafayette and simulation results for 25-year extremes. 25 = 0.43 in. = 0.14 in. Cov = / = 0.33 Nom25 = 0.80 in. 25 = 25/Nom25 = 0.54 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Lafayette annual extremes 25 year extremes long period extremes (ASCE 7) Figure 3-12. CDF of uniform radial ice thickness recorded in Lafayette and simulation results for 50-year extremes. 50 = 0.53 in. = 0.14 in. Cov = / = 0.26 Nom50 = 1.00 in. 50 = 50/Nom50 = 0.52 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Lafayette annual extremes 50 year extremes long period extremes (ASCE 7)

A-17 Figure 3-13. CDF of uniform radial ice thickness recorded in Lafayette and simulation results for 100-year extremes. 100 = 0.59 in. = 0.10 in. Cov = / = 0.18 Nom100 = 1.25 in. 100 = 100/Nom100 = 0.47 4 3 2 1 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 St an da rd n or m al v ar ia bl e Ice thickness, in. Lafayette annual extremes 100 year extremes long period extremes (ASCE 7) Figure 3-14. CDF of uniform radial ice thickness recorded in Indianapolis and simulation results for 25-year extremes. 25 = 0.59 in. = 0.20 in. Cov = / = 0.34 Nom25 = 0.80 in. 25 = 25/Nom25 = 0.74 4 3 2 1 0 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 St an da rd n or m al v ar ia bl e Ice thickness, in. Indianapolis annual extremes 25 year extremes long return periods (ASCE 7) Figure 3-15. CDF of uniform radial ice thickness recorded in Indianapolis and simulation results for 50-year extremes. 50 = 0.70 in. = 0.16 in. Cov = / = 0.22 Nom50 = 1.00 in. 50 = 50/Nom50 = 0.70 4 3 2 1 0 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 St an da rd n or m al v ar ia bl e Ice thickness, in. Indianapolis annual extremes 50 year extremes long return periods (ASCE 7)

A-18 100 = 0.78 in. = 0.12 in. Cov = / = 0.15 Nom100 = 1.25 in. 100 = 100/Nom100 = 0.62 4 3 2 1 0 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 St an da rd n or m al v ar ia bl e Ice thickness, in. Indianapolis annual extremes 100 year extremes long return periods (ASCE 7) Figure 3-16. CDF of uniform radial ice thickness recorded in Indianapolis and simulation results for 100-year extremes. MRI = 25 Years MRI = 50 Years MRI = 100 Years Cov 0.32 0.24 0.16 0.80 0.76 0.68 Table 3-6. Average statistical parameters for different mean recurrence interval.

A-19 Information from ASCE/SEI 7-10 and Available Literature Ice accreted on structural members, components, and appurtenances increases the projected area of the structures exposed to wind� The projected area will be increased by adding t to all free edges of the projected area� Wind load on this increased projected area is to be applied in the design of ice-sensitive structures� Figures 10-2 through 10-6 in ASCE/ SEI 7-10 include the equivalent uniform radial thickness t of ice due to freezing rain for a 50-year MRI and 3-s gust wind speeds that are concurrent with the ice loads due to freezing rain� The amount of ice that accretes on a component is affected by the wind speed that accompanies the freezing rain� Wind speeds during freezing rain are typically moderate� However, the accreted ice may last for days or even weeks after the freez- ing rain ends, as long as the weather remains cold� Table 4-1 summarizes the 3-s gust for different locations across the United States� As opposed to ice thickness, 3-s con- current gust speed does not have a multiplication factor for different risk categories� Values on the map are the same for each risk category� The statistical parameters for 3-s concur- rent gust speed can be taken as an average of the statistical parameters of wind speed� It is often important to know the wind load on a struc- ture both during a freezing-rain storm and for as long after the storm as ice remains on the structure� The projected area of the structure is larger because of the ice accretion, so at a given wind speed the wind load is greater than it could be on a bare structure� The wind load results are useful for identify- ing the combination of wind and ice in each event that causes the largest horizontal load� This combination is independent of drag coefficient as long as it can be assumed to be the same for both the pole-ice accretion and the icicle� Possible Combination of Uniform Radial Ice Thickness and Concurrent 3-s Gust Speeds Based on Figures 10-2 through 10-6 from ASCE/SEI 7-10, 24 different combinations of ice thickness and concurrent wind speed were identified� All possible combinations are marked in Table 4-2 as highlighted cells, as shown here: - Possible combination - Not found- The response of traffic sign supports (given example) was calculated using a complex interaction equation for load combination that produces torsion, shear, flexure, and axial force [Equation C-H3-8, AISC Steel Construction Manual (AISC, 2010)]� 1�0 2P P M M V V T T r c r c r c r c +  + +  ≤ where: P = axial force, M = bending moment, V = shear, T = torsion, and the terms with the subscript r represent the required strength (load effect), and those with the subscript c represent the corresponding available strengths (load carrying capac- ity)� The interaction values for the various combinations are illustrated in Figures 4-1 to 4-8� Conclusions The combination that governs in most cases is the extreme wind combination� The combination with ice and wind on ice governs only in a few cases� All possible values of response S E c t I o N 4 Correlation Between Ice Thickness and Concurrent 3-s Gust Wind

A-20 calculated using the interaction equation [Equation C-H3-8, AISC Steel Construction Manual (AISC, 2010)] are summa- rized in Tables 4-3 and 4-4� The shaded cells are the cases governed by ice and wind on ice� It appears that ice and wind can be reasonably omitted from the required combinations for traffic signal structures� Secondary Analysis for Wind on Ice A second study was conducted to determine whether the wind-on-ice limit state is likely to control for LTS structures� The loads on a horizontal circular tube were considered� The combined loading for maximum wind and dead load was compared to the combined loading for wind on ice, ice weight, and load� The maximum ice thickness and wind speed were selected from ASCE/SEI 7-10� The minimum wind speed was selected from ASCE/SEI 7-10, Figure 3�8-1� By using these extreme values, it was envisioned that the wind-on-ice limit state will control only in extremely rare circumstances� A spreadsheet was used to compute the distributed load on the horizontal member (see Figure 4-9)� The loads acting about different axes (dead load and ice weight acting verti- cally versus wind loads acting horizontally) were combined using vector addition (the square root of the sum of the squares)� Note that the level arms and so forth are the same for both load effects so that nominal loading can be consid- ered directly (e�g�, a cantilever traffic signal pole)� A parametric study was conducted varying the diameter from 12 in� to 16 in�, the thickness from 0�25 in� to 0�50 in�, while hold- ing the steel density at 0�490 kcf and the ice density at 0�058 kcf� With the wind and ice loadings selected to make the wind- on-ice limit state as large as possible, the load for that limit state was varied from 91% to 97�5% of the loading from the extreme wind case� This ratio does not prohibit the wind-on- ice case from controlling (see Table 4-5)� Next, the wind-on-ice speed was increased to determine the speed necessary for the wind-on-ice limit state to control with 1�5 in� of ice� The results of this analysis are presented in Table 4-6� In order to get the load effect from the wind-on-ice limit state equal to the extreme wind limit state, the speed had to be increased to at least 95 mph, which is more than a 50% increase from the maximum value from ASCE/SEI coincident wind speeds� Next, using the maximum (anywhere in the United States) wind-on-ice speed per ASCE/SEI, the ice thickness was increased to determine the thickness required for the wind- on-ice limit state to control� The results of this analysis are presented in Table 4-7� Finally, two examples were computed; first, a design wind of 110 mph was compared to the load effect of that with an ice load of 1�5 in� The coincident wind to equal to the wind-only load effect was 95 mph to 97�5 mph, which is much larger than the fastest coincident wind in the United States (60 mph)� The second example compares a design wind of 110 mph with the load effect of the maximum coincident wind in the United States (60 mph)� To create the same load effect, the ice thickness would be greater than 3 in� (see Table 4-8)� This simple study appears to validate the much more com- plex statistically based analysis� Conclusion Two independent analyses indicate that the wind-on-ice load combination may be eliminated from the typical limit- state analysis because it will not control� This is not to sug- gest that wind on icing will not occur and that the LRFD-LTS specifications should ignore or neglect it� Rather, it consid- ers it and does not require the computation because of the research presented herein� Table 4-2. Possible combination of uniform radial ice thickness and concurrent 3-s gust speeds. Ice Load Zones Gust Speed Zones 0.00” 0.25” 0.5” 0.75” 1.0” 1.25” 1.5” 30 mph - 40 mph - 50 mph - - 60 mph - - 70 mph - - - - - - 80 mph - - - - - - Table 4-1. 3-s gust speed concurrent with ice load. Gust speed zones V50 (mph) Cov (mph) Zone 1 30 0.15 4.5 Zone 2 40 0.15 6.0 Zone 3 50 0.15 7.5 Zone 4 60 0.15 9.0 Zone 5 70 0.15 10.5 Zone 6 80 0.15 12

A-21 Figure 4-1. Values of the interaction equation at the critical section as a function of wind speed on ice—arm. 0.0 0.1 0.2 0.3 0.4 0.5 0 20 40 60 80 100 DL + WL +IL Wind speed, mph Combinations on arm 1.50" 1.25" 1.00" 0.75" 0.50" 0.25" Figure 4-2. Values of the interaction equation at the critical section as a function of wind speed on ice—pole. 0.0 0.1 0.2 0.3 0.4 0.5 0 20 40 60 80 100 DL + WL +IL Wind speed, mph Combinations on pole 1.50" 1.25" 1.00" 0.75" 0.50" 0.25" Figure 4-3. Values of the interaction equation at the critical section as a function of ice thickness—arm. 0.0 0.1 0.2 0.3 0.4 0.5 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 DL + WL +IL Ice thickness, in Combinations on arm 80mph 70mph 60mph 50mph 40mph 30mph Figure 4-4. Values of the interaction equation at the critical section as a function of ice thickness—pole. 0.0 0.1 0.2 0.3 0.4 0.5 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 DL + WL +IL Ice thickness, in Combinations on pole 80mph 70mph 60mph 50mph 40mph 30mph Figure 4-5. Values of the interaction equation at the critical section as a function of wind speed in combination of extreme wind and dead load—arm. 0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 120 140 160 180 DL + WL Wind speed, mph Combinaons on arm Figure 4-6. Values of the interaction equation at the critical section as a function of wind speed in combination of extreme wind and dead load—pole. 0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 120 140 160 180 DL + WL Wind speed, mph Combinaons on pole

A-22 Table 4-3. Values of response at the critical section on an arm calculated using interaction equation. DL + WL DL + WL + IL 100 mph 105 mph 110 mph 115 mph 120 mph 130 mph 140 mph 150 mph 160 mph 0.33 0.36 0.38 0.41 0.44 0.51 0.58 0.66 0.75 Ice Wind 0.25” 30 mph 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 40 mph 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 50 mph 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 60 mph 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 70 mph 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 80 mph 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.50” 30 mph 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 40 mph 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 50 mph 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 60 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.75” 30 mph 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 40 mph 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 50 mph 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 1.00” 30 mph 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 40 mph 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 50 mph 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 60 mph 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 1.25” 30 mph 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 60 mph 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 1.50” 40 mph 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 Figure 4-7. Values of the interaction equation at the critical section due to combination of extreme wind and dead load versus combination of ice load, wind on ice, and dead load—arm. 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.20 0.40 0.60 0.80 1.00 DL +WL DL+IL+WL Combinations on arm Figure 4-8. Values of the interaction equation at the critical section due to combination of extreme wind and dead load versus combination of ice load, wind on ice, and dead load—pole. 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.20 0.40 0.60 0.80 1.00 DL+WL DL+IL+WL Combinations on pole

A-23 Table 4-4. Values of response at the critical section on a pole calculated using interaction equation. DL + WL DL + WL + IL 100 mph 105 mph 110 mph 115 mph 120 mph 130 mph 140 mph 150 mph 160 mph 0.26 0.28 0.31 0.34 0.38 0.44 0.53 0.63 0.75 Ice Wind 0.25” 30 mph 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 40 mph 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 50 mph 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 60 mph 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 70 mph 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 80 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.50” 30 mph 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 40 mph 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 50 mph 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 60 mph 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.75” 30 mph 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 40 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 50 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 1.00” 30 mph 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 40 mph 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 50 mph 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 60 mph 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 1.25” 30 mph 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 60 mph 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 1.50” 40 mph 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 (a) (b) (c) Figure 4-9. Mast arm loads with ice and wind.

steel (lb/ft3) ice (lb/ft3) Center Diameter (inches) Tube Thickness (inches) Outer Diameter (inches) Inner Diameter (inches) Ice Thickness (inches) V (mph) Vice (mph) CD Inner diamter of ice (inches) Outer diameter of ice (inches) Pz (psf) Pz_ice (psf) Area for Wind (in2/ft) Area for Wind on Ice (in2/ft) Area of Pole (self weight) in2/ft Ice area (in2/ft) wpole (plf) wice (plf) wwind (plf) wwind_on_ice (plf) Wtotal (plf) [vectorially added] (1) Wtotal_ice (plf)[vectorially added] (2) % of total (1)/(2) Loads frommaximumwind on ice andmaximum ice thickness. The wind on structure value is the lowest on the map. (summary results are bolded) 490 58 16 0.250 16.3 15.8 1.5 110 60 0.55 16.3 19.3 17.0 5.07 195 231 12.6 20.9 42.8 8.42 23.07 8.13 48.59 44.33 91.2% 490 58 16 0.313 16.3 15.7 1.5 110 60 0.55 16.3 19.3 17.0 5.07 196 232 15.7 21.0 53.5 8.45 23.16 8.16 58.25 54.73 93.9% 490 58 16 0.375 16.4 15.6 1.5 110 60 0.55 16.4 19.4 17.0 5.07 197 233 18.8 21.1 64.1 8.48 23.25 8.18 68.22 65.21 95.6% 490 58 16 0.438 16.4 15.6 1.5 110 60 0.55 16.4 19.4 17.0 5.07 197 233 22.0 21.1 74.8 8.51 23.34 8.21 78.39 75.76 96.7% 490 58 16 0.500 16.5 15.5 1.5 110 60 0.55 16.5 19.5 17.0 5.07 198 234 25.1 21.2 85.5 8.54 23.43 8.24 88.67 86.34 97.4% 490 58 14 0.250 14.3 13.8 1.5 110 60 0.55 14.3 17.3 17.0 5.07 171 207 11.0 18.6 37.4 7.47 20.23 7.29 42.53 38.84 91.3% 490 58 14 0.313 14.3 13.7 1.5 110 60 0.55 14.3 17.3 17.0 5.07 172 208 13.7 18.6 46.8 7.50 20.32 7.31 50.99 47.93 94.0% 490 58 14 0.375 14.4 13.6 1.5 110 60 0.55 14.4 17.4 17.0 5.07 173 209 16.5 18.7 56.1 7.53 20.41 7.34 59.72 57.10 95.6% 490 58 14 0.438 14.4 13.6 1.5 110 60 0.55 14.4 17.4 17.0 5.07 173 209 19.2 18.8 65.5 7.56 20.50 7.37 68.61 66.32 96.7% 490 58 14 0.500 14.5 13.5 1.5 110 60 0.55 14.5 17.5 17.0 5.07 174 210 22.0 18.8 74.8 7.59 20.59 7.39 77.61 75.58 97.4% 490 58 12 0.250 12.3 11.8 1.5 110 60 0.55 12.3 15.3 17.0 5.07 147 183 9.4 16.2 32.1 6.52 17.39 6.44 36.48 33.36 91.4% 490 58 12 0.313 12.3 11.7 1.5 110 60 0.55 12.3 15.3 17.0 5.07 148 184 11.8 16.3 40.1 6.55 17.48 6.47 43.73 41.13 94.1% 490 58 12 0.375 12.4 11.6 1.5 110 60 0.55 12.4 15.4 17.0 5.07 149 185 14.1 16.3 48.1 6.58 17.57 6.49 51.21 48.99 95.7% 490 58 12 0.438 12.4 11.6 1.5 110 60 0.55 12.4 15.4 17.0 5.07 149 185 16.5 16.4 56.1 6.61 17.66 6.52 58.84 56.89 96.7% 490 58 12 0.500 12.5 11.5 1.5 110 60 0.55 12.5 15.5 17.0 5.07 150 186 18.8 16.5 64.1 6.64 17.75 6.55 66.55 64.82 97.4% Input Parameters Computations Table 4-5. Wind on ice with extreme icing (1.5 in.). Table 4-6. Wind on ice controlling the limit state. steel (lb/ft3) ice (lb/ft3) Center Diameter (inches) Tube Thickness (inches) Outer Diameter (inches) Inner Diameter (inches) Ice Thickness (inches) V (mph) Vice (mph) CD Inner diamter of ice (inches) Outer diameter of ice (inches) Pz (psf) Pz_ice (psf) Area for Wind (in2/ft) Area for Wind on Ice (in2/ft) Area of Pole (self weight) in2/ft Ice area (in2/ft) wpole (plf) wice (plf) wwind (plf) wwind_on_ice (plf) Wtotal (plf) [vectorially added] (1) Wtotal_ice (plf)[vectorially added] (2) % of total (1)/(2) Maximum ice thickness, the wind speed needed forwind on ice to control (summary results are bolded) 490 58 16 0.250 16.3 15.8 1.5 110 97.5 0.55 16.3 19.3 17.0 13.38 195 231 12.6 20.9 42.8 8.42 23.07 21.47 48.59 48.58 100.0% 490 58 16 0.313 16.3 15.7 1.5 110 97.5 0.55 16.3 19.3 17.0 13.38 196 232 15.7 21.0 53.5 8.45 23.16 21.54 58.25 58.24 100.0% 490 58 16 0.375 16.4 15.6 1.5 110 97.5 0.55 16.4 19.4 17.0 13.38 197 233 18.8 21.1 64.1 8.48 23.25 21.61 68.22 68.21 100.0% 490 58 16 0.438 16.4 15.6 1.5 110 97.5 0.55 16.4 19.4 17.0 13.38 197 233 22.0 21.1 74.8 8.51 23.34 21.68 78.39 78.37 100.0% 490 58 16 0.500 16.5 15.5 1.5 110 97.5 0.55 16.5 19.5 17.0 13.38 198 234 25.1 21.2 85.5 8.54 23.43 21.75 88.67 88.66 100.0% 490 58 14 0.250 14.3 13.8 1.5 110 96.5 0.55 14.3 17.3 17.0 13.11 171 207 11.0 18.6 37.4 7.47 20.23 18.85 42.53 42.56 100.0% 490 58 14 0.313 14.3 13.7 1.5 110 96.5 0.55 14.3 17.3 17.0 13.11 172 208 13.7 18.6 46.8 7.50 20.32 18.92 50.99 51.00 100.0% 490 58 14 0.375 14.4 13.6 1.5 110 96.5 0.55 14.4 17.4 17.0 13.11 173 209 16.5 18.7 56.1 7.53 20.41 18.98 59.72 59.72 100.0% 490 58 14 0.438 14.4 13.6 1.5 110 96.5 0.55 14.4 17.4 17.0 13.11 173 209 19.2 18.8 65.5 7.56 20.50 19.05 68.61 68.61 100.0% 490 58 14 0.500 14.5 13.5 1.5 110 96.7 0.55 14.5 17.5 17.0 13.17 174 210 22.0 18.8 74.8 7.59 20.59 19.20 77.61 77.63 100.0% 490 58 12 0.250 12.3 11.8 1.5 110 95 0.55 12.3 15.3 17.0 12.71 147 183 9.4 16.2 32.1 6.52 17.39 16.15 36.48 36.49 100.0% 490 58 12 0.313 12.3 11.7 1.5 110 95 0.55 12.3 15.3 17.0 12.71 148 184 11.8 16.3 40.1 6.55 17.48 16.21 43.73 43.74 100.0% 490 58 12 0.375 12.4 11.6 1.5 110 95 0.55 12.4 15.4 17.0 12.71 149 185 14.1 16.3 48.1 6.58 17.57 16.28 51.21 51.21 100.0% 490 58 12 0.438 12.4 11.6 1.5 110 95 0.55 12.4 15.4 17.0 12.71 149 185 16.5 16.4 56.1 6.61 17.66 16.35 58.84 58.83 100.0% 490 58 12 0.500 12.5 11.5 1.5 110 95 0.55 12.5 15.5 17.0 12.71 150 186 18.8 16.5 64.1 6.64 17.75 16.41 66.55 66.54 100.0% Input Parameters Computations

A-25 Table 4-7. Example 1. Design wind load 110 mph CD 0.55 Max ice load on ASCE map 1.5 in Coincident wind for equivalent load effect 95 mph to 97.5 mph Table 4-8. Example 2. Design wind load 110 mph CD 0.55 Max coincident wind 60 mph Ice thickness for equivalent load effect 3.2 in. to 3.4 in.

A-26 S E c t I o N 5 Statistical Parameters of Resistance Load carrying capacity is a function of the nominal value of resistance, Rn, and three factors: material factor, m, repre- senting material properties, fabrication factor, f, representing the dimensions and geometry, and professional factor, p, representing uncertainty in the analytical model: R R m f pn= i i i The statistical parameters for m, f, and p were considered by various researchers, and the results were summarized by Ellingwood et al� (1980) based on material test data available in the 1970s� The actual strength in the structure can differ from structure to structure, but these differences are included in the fabrica- tion and professional bias factors (lf and lp)� Material param- eters for steel were established based on the yield strength data� The considered parameters are listed in Tables 5-1 through 5-4: The resistance (load carrying capacity) is formulated for each of the considered limit states and structural components� Bending resistance, elastic state: =M f Sy i Bending resistance, plastic state: =M f Zy i Shear resistance: 0�57=V A fshear yi i Torsion capacity: 0�5 0�57=T J d fy i i i Axial capacity: =P A fyi The limit state that controls design of luminaries is cal- culated using an interaction equation for load combination that produces torsion, shear, flexure, and axial force [Sec- tion C-H3-8, AISC Steel Construction Manual (AISC, 2010)]� 1�0 2P P M M V V T T r c r c r c r c +  + +  ≤ where: P = axial force, M = bending moment, V = shear, and T = torsion� The terms with the subscript r represent the required strength (load effect), and those with the subscript c represent the cor- responding available strengths (load carrying capacity)� The limit-state function can be written: , 1�0 1 1 2 2 3 3 4 4 2 g Q R Q R Q R Q R Q R i i( ) = − +  − +  The interaction equation is a nonlinear function; there- fore, to calculate combined load carrying capacity, Monte Carlo simulation was used by generating one million values for each of the random variables� This procedure allows for finding function g and calculating reliabil- ity index b� For calibration purposes, using a first-order second-moment approach, the resistance parameters were assumed to have a bias factor of 1�05 and a coefficient of variation of 10%� Conclusion The resistance model and the parametric statistics for resis- tance parameters are presented and available for calibration� Resistance Model

A-27 Parameters Cov Static yield strength, flanges 1.05 0.10 Static yield strength, webs 1.10 0.11 Young’s modulus 1.00 0.06 Static yield strength in shear 1.11 0.10 Tensile strength of steel 1.10 0.11 Dimensions, f 1.00 0.05 Table 5-1. Statistical parameters for material and dimensions (Ellingwood et al., 1980). Limit State Resistance Cov Tension member 1.10 0.11 Braced beams in flexure, flange stiffened 1.17 0.17 Braced beams in flexure, flange unstiffened 1.60 0.28 Laterally unbraced beams 1.15 0.17 Columns, flexural buckling, elastic 0.97 0.09 Columns, flexural buckling, inelastic, compact 1.20 0.13 Columns, flexural buckling, inelastic, stiffened 1.07 0.20 Columns, flexural buckling, inelastic, unstiffened 1.68 0.26 Columns, flexural buckling, inelastic, cold work 1.21 0.14 Columns, torsional-flexural buckling, elastic 1.11 0.13 Columns, torsional-flexural buckling, inelastic 1.32 0.18 Table 5-3. Resistance statistics for cold-formed steel members (Ellingwood et al., 1980). Limit State Resistance Cov Tension member, limit-state yield 1.10 0.08 Tension member, limit-state ultimate 1.10 0.08 Beams, limit-state yield 1.10 0.08 Beams, limit-state lateral buckling 1.03 0.13 Beams, limit-state inelastic local buckling 1.00 0.09 Columns, limit-state yield 1.10 0.08 Columns, limit-state local buckling 1.00 0.09 Table 5-4. Resistance statistics for aluminum structures (Ellingwood et al., 1980). Limit State Professional Material Fabrication Resistance Cov Cov Cov Cov Tension member, yield 1.00 0 1.05 0.10 1.00 0.05 1.05 0.11 Tension member, ultimate 1.00 0 1.10 0.10 1.00 0.05 1.10 0.11 Elastic beam, LTB 1.03 0.09 1.00 0.06 1.00 0.05 1.03 0.12 Inelastic beam, LTB 1.06 0.09 1.05 0.10 1.00 0.05 1.11 0.14 Plate girders in flexure 1.03 0.05 1.05 0.10 1.00 0.05 1.08 0.12 Plate girders in shear 1.03 0.11 1.11 0.10 1.00 0.05 1.14 0.16 Beam columns 1.02 0.10 1.05 0.10 1.00 0.05 1.07 0.15 Table 5-2. Resistance statistics for hot-rolled steel elements (Ellingwood et al., 1980).

A-28 S E c t I o N 6 Background The previous AASHTO Standard Specifications for Struc- tural Supports for Highway Signs, Luminaires, and Traffic Signals (AASHTO, 2009) requires for certain structures to be designed for fatigue to resist wind-induced stresses� Accurate load spectra for defining fatigue loadings are gen- erally not available or are very limited� Assessment of stress fluctuations and the corresponding number of cycles for all wind-induced events (lifetime loading histogram) are diffi- cult to assess� However, it is predicted that signs, high-level luminaires, and traffic signal supports are exposed to a large number of cycles� Therefore, an infinite-life fatigue design approach is recommended� The infinite-life fatigue design approach should ensure that a structure performs satisfactorily for its design life to an acceptable level of reliability without significant fatigue damage� While some fatigue cracks may initiate at local stress concentrations, there should not be any time-dependent propagation of these cracks� This is typically the case for structural supports where the wind-load cycles in 25 years or more are expected to exceed 100 million cycles, whereas typi- cal weld details exhibit a constant-amplitude fatigue thresh- old (CAFT) at 10 to 20 million cycles� Figure 6-1 presents the design S-N relations for all types of design categories� The design specifications present eight S-N curves for eight categories of weld details, defined as the detail categories A, B, B’, C, C’, D, E, and E’(AASHTO, 2009, Standard Specifications)� Table 6-1 presents the values of factor A, which is a basis for S-N curves for different fatigue categories, and values of constant-amplitude fatigue limit (CAFL) that correspond to the stress range at constant-amplitude loading below which the fatigue life appears to be infinite� Stress Range Versus Number of Cycles Relationship from Test Results Based on data available in the literature (Stam at el�, 2011 and Roy at el�, 2011), about 200 samples tested under a constant stress range were used for analysis (see Table 6-2 and Figures 6-2 to 6-14)� For each sample, a fatigue category has been assigned based on provided information and design specification pro- vided in Table 11�9�3�1–1—Fatigue Details of Cantilevered and Non-cantilevered Support Structures (AASHTO, 2009, Stan- dard Specifications)� Each category group has been plotted separately on a logarithmic scale along with the S-N limit� Stress Range Versus Number of Cycles Relationship for Infinite Life Because the details should be designed for infinite fatigue life, each of the test results has been recalculated for number of cycles at the CAFL using Miner’s rule� Miner’s rule is a linear damage accumulation method developed by Miner in 1945� It assumes that the damage frac- tion due to a particular stress range level is a linear function of the number of cycles that take places at the stress range� An effective, or equivalent, constant-amplitude stress range SRe that would cause an equivalent amount of fatigue damage as the variable stress range at a given number of cycles can be defined as follows: 3 1 1 3 S SRe i Ri i k ∑= γ  = where: gi = fraction of cycles at stress range i to total cycles, and SRi = magnitude of stress range i� Fatigue Resistance for High-Mast Luminaires

A-29 In addition, the statistical parameters are determined by fitting a straight line to the lower tail of the CDF. The most important parameters are the mean value, standard devia- tion, and coefficient of variation. Figures 6-15 through 6-18 present the CDF of fatigue resistance for Category C, D, E, and E’. For the remaining details, the number of tested speci- mens was not sufficient to consider their distribution. The statistical parameters determined by fitting the lower tail with straight lines are summarized in Table 6-3. For comparison, statistical parameters developed for SHRP 2 Project 19B are presented in Table 6-4. Reliability Analysis for Fatigue Limit State The limit-state function for fatigue can be expressed in terms of the damage ratio as: 1 3 3 3 3 D S N S N Q Q i R R i i i i i i i ∑ ∑= = By replacing the nominator by Q and denominator by R, we can obtain the simple limit-state function: , 1 1 0 , 3 3 3 3 3 3 3 3 g Q R S N S N Q R Q R Q R R Q g Q R R Q S N S N Q Q i R R i R R i Q Q i i i i i i i i i ∑ ∑ ∑ ∑ ( ) ( ) = = = ⇒ = ⇒ = ⇒ − = = − = − i i i i Figure 6-1. Stress range versus number of cycles. Table 6-1. Detail category constant (A) with CAFL summary. Category A Times 10 8 (ksi3) CAFL (ksi) A 250.0 24 B 120.0 16 B’ 61.0 12 C 44.0 10 C’ 44.0 10 D 22.0 7 E 11.0 4.5 E’ 3.9 2.6 Et – ≤1.2 Table 6-2. Summary of assigned samples. Category No. of Samples A 2 B 15 B’ – C 24 C’ – D 61 E 43 E’ 40 Et 3 Results for each category were separately plotted on a loga- rithmic scale along with design S-N curves. Statistical Parameters for Resistance Presented S-N data have a scatter associated with number of cycles under this same stress range. For this case, fatigue resistance should be presented in terms of probability. The fatigue resistance design can be expressed in the form of the cube root of the number of cycles times the stress to the third power, (S3N)(1/3). Therefore, the CDFs of the fatigue resistance were plotted on normal probability paper for each category of details, as shown in Figures 6-15 through 6-18. The shape of the CDF is an indication of the type of distribution, and if the resulting CDFs are close to straight lines, they can be considered as normal random variables.

A-30 Figure 6-2. Stress range versus number of cycles for Category A. Figure 6-3. Stress range versus number of cycles for Category B.

A-31 Figure 6-4. Stress range versus number of cycles for Category C. Figure 6-5. Stress range versus number of cycles for Category D.

A-32 Figure 6-7. Stress range versus number of cycles for Category E’. Figure 6-6. Stress range versus number of cycles for Category E.

A-33 Figure 6-8. Stress range versus number of cycles for Category Et. Figure 6-9. Number of cycles at CAFL for Category A.

A-34 Figure 6-10. Number of cycles at CAFL for Category B. Figure 6-11. Number of cycles at CAFL for Category C.

A-35 Figure 6-13. Number of cycles at CAFL for Category E. Figure 6-12. Number of cycles at CAFL for Category D.

Figure 6-14. Number of cycles at CAFL for Category E’. Figure 6-15. CDF for Category C.

A-37 Figure 6-16. CDF for Category D.

A-38 Figure 6-17. CDF for Category E.

A-39 Figure 6-18. CDF for Category E’.

A-40 The statistical parameters of resistance were developed in the previous section and load model is presented in NCHRP Report 718: Fatigue Loading and Design Methodology for High-Mast Lighting Towers. Resistance, R, demonstrates char- acteristics of normal distribution, and the basic statistical parameters, which are required for reliability analysis, were developed based on the straight line fitted to the lower tail� The load data provided in NCHRP Report 718 show very little variation� Moreover, even a coefficient of variation equal to 10% does not change the reliability index significantly� Dis- tribution of fatigue resistance definitely has a dominant effect on the entire limit-state function� For special cases, such as a case of two normal-distributed, uncorrelated random variables, R and Q, the reliability index is given by: 2 2 R Q R Q β = µ − µ σ + σ To calculate the reliability index, the specific fatigue category and total load on the structure are used� The data presented in NCHRP Report 718 are summarized in Table 6-5� (Test site and stream gage abbreviations are as presented in NCHRP Report 718.) The reliability indices were calculated for all tested high masts presented in NCHRP Report 718. The reliability indices Table 6-4. Statistical parameters of fatigue resistance based on data presented for SHRP 2 Project 19B (Report still in progress). Category A B B’ C and C’ D E E’ Nominal, psi 2,924 2,289 1,827 1,639 1,301 1,032 731 Mean, psi 4,250 2,900 2,225 2,175 1,875 1,200 1,125 Bias 1.45 1.27 1.22 1.33 1.44 1.16 1.54 Cov 22% 13% 9% 17.50% 15% 12.50% 19.50% St dev, psi 935 377 200 381 281 150 219 No. of data points 72 623 86 358 114 647 319 were calculated for the period of 10 to 50 years� The results are presented in Figures 6-19 to 6-22 for truncation level > 0�5 ksi and in Figures 6-23 to 6-26 for truncation level > 1�0 ksi� (In the figures, site and gage abbreviations are as presented in NCHRP Report 718.) The results show that all tested high masts are able to carry a load in 50 years with bs above 0� This means that the components and connections have a small probability of damage due to fatigue in these periods of time� Reliability index b = 4 corresponds to 0�001% of probability of failure, Pf, b = 3 corresponds to Pf = 0�1%, b = 2 corresponds to Pf = 2�0%, b = 1 corresponds to Pf = 15�0%, and b = 0 corresponds to Pf = 50�0%� For Category D, the reli- ability indices are close to 0, and this is the effect of low bias and high coefficient of variation of resistance� Verifying the fatigue resistance model is highly recommended� Conclusions The results presented in Figures 6-9 to 6-14 show that many specimens do not fit into a CAFL design line� This indicates that for some details, the finite fatigue life method- ology should be considered instead of using infinite fatigue life, or a more conservative category should be assigned� Hence, further research is needed in this area that will pro- vide more data points� Table 6-3. Statistical parameters of fatigue resistance based on the data presented for luminaries and sign supports. Category A B B’ C and C’ D E E’ Nominal, psi – – – 1,639 1,301 1,032 731 Mean, psi – – – 1,925 1,000 1,175 675 Bias, psi – – – 1.17 0.77 1.14 0.92 Cov – – – 10% 25% 21% 35% St dev, psi – – – 193 250 247 236 No. of data points – – – 24 61 43 40

A-41 Table 6-5. Summary of load based on NCHRP Report 718. ≥0.5 ksi ≥1.0 ksi Test Site Strain Gage Detail Category SReff (ksi) N/Day SReff (ksi) N/Day CA-A CH_3 D 1.28 5,820 1.8 1,793 CA-X CH_5 D 1.12 5,016 1.63 1,234 IAN-A (MT) CH_9 D 1.36 5,927 1.94 1,788 IAN-X (MT) CH_12 D 1.19 7,173 1.7 2,016 IAS-A CH_2 E 0.92 2,805 1.47 356 IAS-X CH_1 E 0.87 3,468 1.41 350 KS-A CH_2 C 1.55 12,730 2.12 4,622 KS-X CH_6 C 1.64 14,359 2.2 5,593 ND-A CH_1 E 0.92 4,547 1.46 579 ND-X CH_5 E 0.97 6,170 1.46 1,100 OKNE-A CH_3 D 1.11 8,294 1.64 1,942 OKNE-X CH_5 E 1.04 8,872 1.55 1,845 OKSW-A CH_8 E 1.08 13,997 1.61 3,165 OKSW-X CH_6 D 1.05 16,832 1.55 3,856 PA-A CH_6 E' 0.81 294 1.35 16 PA-X CH_1 E' 0.83 441 1.36 33 SD-A CH_6 E 0.93 11,515 1.51 1,453 SD-X CH_8 E 0.98 12,750 1.6 1,827 CJE-A (FR) CH_8 E 1.02 18,693 1.57 3,472 CJE-X (FR) CH_6 D 1.08 35,437 1.58 8,254 CJE-A (MT) CH_4 D 1.08 6,037 1.62 1,345 CJE-X (MT) CH_6 D 1.1 7,598 1.62 1,800 CJW-A (FR) CH_8 D 1.06 28,228 1.61 5,721 CJW-X (FR) CH_6 D 1.13 36,382 1.65 9,083 CJW-A (MT) CH_1 E 1.03 6,688 1.59 1,252 CJW-X (MT) CH_2 E 1.02 6,934 1.59 1,258 Figure 6-19. Reliability index versus time for Category C, with truncation level > 0.5 ksi. 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 Re lia bi lit y In de x, β Years KS-A CH_2 KS-X CH_6

A-42 0 1 2 3 4 5 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years CA-A CH_3 CA-X CH_5 IAN-A (MT) CH_9 IAN-X (MT) CH_12 OKNE-A CH_3 OKSW-X CH_6 CJE-X (FR) CH_6 CJE-A (MT) CH_4 CJE-X (MT) CH_6 CJW-A (FR) CH_8 CJW-X (FR) CH_6 Figure 6-20. Reliability index versus time for Category D, with truncation level > 0.5 ksi. 0 1 2 3 4 5 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years IAS-A CH_2 IAS-X CH_1 ND-A CH_1 ND-X CH_5 E OKNE-X CH_5 OKSW-A CH_8 SD-A CH_6 SD-X CH_8 CJE-A (FR) CH_8 CJW-A (MT) CH_1 CJW-X (MT) CH_2 Figure 6-21. Reliability index versus time for Category E, with truncation level > 0.5 ksi.

01 2 3 4 5 6 7 8 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years KS-A CH_2 KS-X CH_6 Figure 6-23. Reliability index versus time for Category C, with truncation level > 1.0 ksi. 0 1 2 3 4 5 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years PA-A CH_6 PA-X CH_1 Figure 6-22. Reliability index versus time for Category E’, with truncation level > 0.5 ksi. -1 0 1 2 3 4 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years CA-A CH_3 CA-X CH_5 IAN-A (MT) CH_9 IAN-X (MT) CH_12 OKNE-A CH_3 OKSW-X CH_6 CJE-X (FR) CH_6 CJE-A (MT) CH_4 CJE-X (MT) CH_6 CJW-A (FR) CH_8 CJW-X (FR) CH_6 Figure 6-24. Reliability index versus time for Category D, with truncation level > 1.0 ksi.

A-44 0 1 2 3 4 5 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years IAS-A CH_2 IAS-X CH_1 ND-A CH_1 ND-X CH_5 E OKNE-X CH_5 OKSW-A CH_8 SD-A CH_6 SD-X CH_8 CJE-A (FR) CH_8 CJW-A (MT) CH_1 CJW-X (MT) CH_2 Figure 6-25. Reliability index versus time for Category E, with truncation level > 1.0 ksi. 0 1 2 3 4 5 0 10 20 30 40 50 60 R el ia bi lit y In de x, β Years PA-A CH_6 PA-X CH_1 Figure 6-26. Reliability index versus time for Category E’, with truncation level > 1.0 ksi.

A-45 LRFD Reliability Analysis—Flexure The calibration between ASD and LRFD is based on the cal- ibration of ASCE/SEI 7-05 50-year V50 wind speed and ASCE/ SEI 7-10 700-year V700 wind speed� The ASCE/SEI 7-10 wind speed maps for a 700-year wind are calibrated to the ASCE/ SEI 7-05 50-year wind speed where the difference between LRFD design wind load factors (ASCE/SEI 7-05 gW = 1�6 vs� ASCE/SEI 7-10 gW = 1�0) is equal to (V700/V50)2 = 1�6� Thus, the LRFD ASCE/SEI 7-05 V50 wind speed is equivalent (for pressures that are proportional to V2) to the ASCE/SEI 7-10 V700-year wind speed� Likewise, the ASCE/SEI 7-10 V300 and V1700 winds speeds are equivalent to ASCE/SEI 7-05 V50 wind speeds adjusted for importance [low Ilow = 0�87 = (V300/V700)2 and high Ihigh = 1�15 = (V1700/V700)2]� The ASCE/SEI 7-05 V50 wind speed is used as the mean wind speed (adjusted for design map values compared to statistical means) for the reli- ability analyses� Flexural Resistance The LRFD design requirement for a structure at the opti- mal design limit is: max 2 1 R M M M n D D D D W W φ = γ γ + γ  where: Rn = nominal resistance, MD = nominal dead load moment, MW = nominal wind load, gD1 = dead load design load factor (used in conjunction with dead + wind case), gD2 = deal load design load factor (dead load only case), gW = wind load design load factor, and f = phi factor� To meet the design limit, the nominal resistance is: max 1 1 2 1 R M M M n D D D D W W[ ] = φ γ φ γ + γ      The mean resistance is: R RR n= λ where: lR = bias factor for strength variable R, and R – = statistical mean of variable R� At the optimal design limit, the mean of R becomes: max 2 1 R M M M R D D R D D W W[ ] = λ φ γ λ φ γ + γ      The coefficient of variation for the strength is CovR� Load The total applied nominal moment at the ASCE/SEI 7-10 700-year wind speed is: 7001M M MT D= + where: MT1 = total nominal moment at ASCE/SEI 7-10 700-year wind speed, MD = dead load moment, and M700 = nominal moment from wind at ASCE/SEI 7-10 700-year wind speed� S E c t I o N 7 Reliability Analysis

A-46 To standardize the comparisons between ASD and LRFD, and for any specified year of wind, all analyses and compari- sons are based on the total nominal moment for the LRFD 700-year total applied moment equal to 1�0: 1�07001M M MT D= + = and, the dead load moment can be represented by: 1 700M MD = − The calibration and comparison varies M700 from 1�0 to 0�0, while MD varies from 0�0 to 1�0 so that the total applied nomi- nal moment at the ASCE/SEI 7-10 700-year load remains 1�0� The total applied nominal moments for ASD and other LRFD year wind speeds are adjusted to be equivalent to the ASCE/ SEI 7-10 700-year wind speed load case� Given that the nominal moment from wind for any year wind can be determined by: 700 2 700M V V MWT T =   where: VT = wind speed for any year T wind speed, and MWT = nominal wind moment at any year T, and the total applied nominal moment becomes: 1 700 700 2 7002M M M M V V MT D WT T( )= + = − +   where MTz = total applied nominal moment at any year T wind speed� To determine the mean wind moment for the reliability analyses, the mean moment at the 50-year wind speed is determined from the ASCE/SEI 7-10 wind speed relation: 0�36 0�10ln 12 50V T VT [ ]( )= + or: 0�36 0�10ln 12 50V V T V T V T( )= + = λ where: lV = bias factor for wind speed at year T, and the nominal wind moment at the 50-year wind speed becomes: 50 2 700M MV= λ The nominal moment at the 50-year wind speed is propor- tional to V2 by: 50 50 2M K K GC Vd z d∝ where: Kd = directionality coefficient, Kz = elevation coefficient, G = gust factor, and Cd = drag coefficient� The mean wind moment for the reliability analyses is: 50 50 2M K K GC Vd z d∝ where the variables are the means� Assuming that Kd does not vary, the other non-wind speed variables’ nominal values are related to the means by the bias factors� Combining them into a single bias factor lP gives: K GC K GC K GCz d K G C z d P z dz d= λ λ λ = λ where: P K G Cz dλ = λ λ λ and: Kd does not vary� Considering that the map design values may differ from the statistical mean of the 50-year wind speed, the mean 50-year wind speed can be represented by: 50 50 700V V VX X V= λ = λ λ where: 50 50 λ = µ V X = bias for the 50-year wind speed, m50 = mean 50-year wind speed, and V50 = map design 50-year wind speed� The mean wind moment for the reliability analyses becomes: 50 2 2 700M MP V X= λ λ λ where: 700 700 2M K K GC Vd z d∝

A-47 Referring back to the basis that all comparisons are equated with a total ASCE/SEI 7-10 applied nominal moment of: 1700M MD + = and using that the nominal dead load moment and mean dead load moment are: 1 1 700 700 M M M M D D D ( ) = − = λ − where: lD = bias factor for dead load moment� The mean load effect on the structure becomes: 150 700 2 2 700Q M M M MD D P V X( )= + = λ − + λ λ λ where Q = the mean moment� To find the coefficient of variation for Q, first the coefficient of variation for the mean wind moment is determined from: 2 2 2 2 250Cov Cov Cov Cov CovM V K G Cz d( )= + + + Noting that V in the V2 term is 100% correlated, and the coefficient of V2 (CovV2) is two times the coefficient of varia- tion of V (CovV)� The combination of the statistical properties for the dead and wind moments to determine the coefficient of variation for the total mean moment Q results in: 1 700 2 2 2 700 2 50Cov Q Cov M Cov M Q Q Q D D M P V X[ ] [ ]( ) = σ = λ − + λ λ λ Reliability Indices Assuming Q and R are lognormal and independent: ln ln 1 ln ln 1 ln 1 2 ln 2 ln 2 2 ln 1 2 ln 2 ln 2 2 R Cov Q Cov R R R R Q Q Q Q( ) ( ) µ = − σ σ = + µ = − σ σ = + where s is the standard deviation of the variable indicated� The reliability index b is: ln ln ln ln 2 ln 2 1 2 ln 2 ln 2 ln 2 ln 2 R QR Q R Q R Q R Q ( ) β = µ − µ σ + σ =   − σ + σ σ + σ Implementation The LRFD reliability analysis was coded into a spreadsheet to study four different regions in the United States: • Florida Coastal Region, • Midwest and Western Region, • Western Coastal Region, and • Southern Alaska Region� Inputs for LRFD reliability analyses spreadsheet: V300, V700, V1700 per ASCE/SEI 7-10 design wind speeds m50, Vm50, V50 per ASCE/SEI 7-05 design wind speeds LRFD reliability analyses inputs are in Table 7-1� Global inputs (for all regions): lD, lR, CovD, CovR lKz, lG, lCd, CovKz, CovG, CovCd f, gD1, gD2, gW Table 7-2 shows the global inputs (inputs are highlighted)� The results for the Midwest and Western Region ASCE/SEI 7-10 700-year wind speed are shown in the Table 7-3 (other regions are similar)� For the 300-year wind speed, the results are in Table 7-4� Notice that the total nominal moment, MT2, is less than 1�0 since the wind moment, M300, is less than M700� Likewise, for the 1,700-year wind speed, MT2 is larger than 1�0 since M1700 is greater than M700, as shown in Table 7-5 for the Midwest and Western Region� Using the 300-year wind speed requires less nominal resis- tance; conversely, using the 1,700-year wind speed increases the required nominal resistance� Because the mean load Q and its variation do not change, this difference in required nominal resistance changes the reliability indices b accordingly� V50 µ50 COV 50µ V300 V700 V1700 Florida Coastal 150 130 0.14 170 180 200 Midwest & West 90 75 0.1 105 115 120 West Coast 85 67 0.095 100 110 115 Southern Alaska 130 110 0.105 150 160 165 Table 7-1. LRFD reliability analyses inputs.

A-48 Table 7-2. Global inputs. COV BIAS BIASD 1.03 COVkz 0.16 1.00 COVD 0.08 COVG 0.11 1.00 BIASR 1.05 COVCd 0.12 1.00 COVR 0.10 Total BiasP 1.00 D+W D Only 0.90 D 1.10 1.25 W 1. φ γ γ 00 Table 7-3. Results for the Midwest and Western Region, 700-year wind speed. 700 Year Wind V700 115 T 700 V50 91.00991 Theory BIASX 0.8241 V700/V700 1.00 (V700/V700) 2 COVV 0.100 (V300/V700) 2 1.00 1.00 Equiv BIASV 0.79 M700 MT2 M700/MT2 Rn R lnR Q COVM50 COVQ lnQ LRFD 1.00 1.00 1.00 1.11 1.17 0.10 0.43 0.30 0.30 0.30 3.35 0.90 1.00 0.90 1.12 1.18 0.10 0.49 0.30 0.24 0.24 3.54 0.80 1.00 0.80 1.13 1.19 0.10 0.55 0.30 0.19 0.19 3.69 0.70 1.00 0.70 1.14 1.20 0.10 0.61 0.30 0.15 0.15 3.77 0.60 1.00 0.60 1.16 1.21 0.10 0.67 0.30 0.13 0.13 3.75 0.50 1.00 0.50 1.17 1.23 0.10 0.73 0.30 0.11 0.10 3.60 0.40 1.00 0.40 1.18 1.24 0.10 0.79 0.30 0.09 0.09 3.34 0.30 1.00 0.30 1.19 1.25 0.10 0.85 0.30 0.08 0.08 2.98 0.20 1.00 0.20 1.20 1.26 0.10 0.91 0.30 0.08 0.08 2.57 0.10 1.00 0.10 1.25 1.31 0.10 0.97 0.30 0.08 0.08 2.38 0.00 1.00 0.00 1.39 1.46 0.10 1.03 0.30 0.08 0.08 2.71 Table 7-4. Results for the Midwest and Western Region, 300-year wind speed. 300 Year Wind V300 105 T 300 Theory V300/V700 0.91 (V300/V700) 2 (V300/V700) 2 0.83 0.87 Equiv M300 MT2 M300/MT2 Rn R lnR Q COVM50 COVQ lnQ LRFD 0.83 0.83 1.00 0.93 0.97 0.10 0.43 0.30 0.30 0.30 2.77 0.75 0.85 0.88 0.96 1.00 0.10 0.49 0.30 0.24 0.24 2.92 0.67 0.87 0.77 0.99 1.03 0.10 0.55 0.30 0.19 0.19 3.04 0.58 0.88 0.66 1.02 1.07 0.10 0.61 0.30 0.15 0.15 3.11 0.50 0.90 0.56 1.04 1.10 0.10 0.67 0.30 0.13 0.13 3.12 0.42 0.92 0.45 1.07 1.13 0.10 0.73 0.30 0.11 0.10 3.03 0.33 0.93 0.36 1.10 1.16 0.10 0.79 0.30 0.09 0.09 2.86 0.25 0.95 0.26 1.13 1.19 0.10 0.85 0.30 0.08 0.08 2.61 0.17 0.97 0.17 1.16 1.22 0.10 0.91 0.30 0.08 0.08 2.32 0.08 0.98 0.08 1.25 1.31 0.10 0.97 0.30 0.08 0.08 2.38 0.00 1.00 0.00 1.39 1.46 0.10 1.03 0.30 0.08 0.08 2.71 ASD Reliability Analysis—Flexure Because the LRFD reliability analyses are based on the total nominal moment MD + M700 = 1�0, the ASD analyses must adjust the moments for a consistent comparison� Using the ASCE/SEI 7-05 criteria for the ASD design, the wind moment for a 50-year wind speed is: 50 700 50 700 2 DesignM M DesignV V =  

A-49 Considering that the design V50 may differ from V50 = (lV)2V700, a bias factor, lDesign, is introduced, and: 50 2 50 700 2 700 2 2 700DesignM V V M MDesign Design V= λ   = λ λ 50 50 DesignV V Designλ = The total ASD design moment, MT3, consistent with MD + M700 = 1�0, becomes: 150 700 2 2 7003M M DesignM M MT D Design V( )= + = − + λ λ Resistance The LRFD nominal resistance is assumed to be the plastic moment capacity� To directly compare resistances between LRFD and ASD sections, the nominal resistance for the ASD design is increased by the section shape factor for a compact section: R SF Mn y= where SF is the shape factor� The allowable stress for a compact section using the allowed overstress factor (OSF) of 4/3 for wind loads is: 4 3 0�66 0�66F F OSF Fallow y y( ) ( )( )= = Using moments instead of stresses, the allowable moment is OSF (0�66) My, and the design requirement for an optimal design is: 0�66 50OSF M M DesignM Iy D( )( ) = + where: I = Ilow = 0�87 (low importance) comparable to ASCE/SEI 7-10 300-year wind speed, I = Imed = 1�00 (medium importance) comparable to ASCE/ SEI 7-10 700-year wind speed, and I = Ihigh = 1�15 (high importance) comparable to ASCE/SEI 7-10 1,700-year wind speed� The nominal resistance (to directly compare to the LRFD design) is determined by increasing the design strength by the shape factor: 1 0�66 1 700 2 2 700R SF M SF OSF M M In y Design V[ ]( )= = − + λ λ For the ASD reliability analyses, the statistical properties are: R RR n= λ and: , , and are unchangedlnQ CovQ Qσ The coefficient of variation for the strength (resistance) is CovR� 1700 Year Wind V1700 120 T 1700 Theory V1700/V700 1.04 (V1700/V700) 2 (V1700/V700) 2 1.09 1.15 Equiv M1700 MT2 M1700/MT2 Rn R lnR Q COVM50 COVQ lnQ LRFD 1.09 1.09 1.00 1.21 1.27 0.10 0.43 0.30 0.30 0.30 3.62 0.98 1.08 0.91 1.21 1.27 0.10 0.49 0.30 0.24 0.24 3.84 0.87 1.07 0.81 1.21 1.27 0.10 0.55 0.30 0.19 0.19 4.01 0.76 1.06 0.72 1.21 1.27 0.10 0.61 0.30 0.15 0.15 4.09 0.65 1.05 0.62 1.21 1.28 0.10 0.67 0.30 0.13 0.13 4.06 0.54 1.04 0.52 1.22 1.28 0.10 0.73 0.30 0.11 0.10 3.89 0.44 1.04 0.42 1.22 1.28 0.10 0.79 0.30 0.09 0.09 3.58 0.33 1.03 0.32 1.22 1.28 0.10 0.85 0.30 0.08 0.08 3.17 0.22 1.02 0.21 1.22 1.28 0.10 0.91 0.30 0.08 0.08 2.69 0.11 1.01 0.11 1.25 1.31 0.10 0.97 0.30 0.08 0.08 2.38 0.00 1.00 0.00 1.39 1.46 0.10 1.03 0.30 0.08 0.08 2.71 Table 7-5. Results for the Midwest and Western Region, 1,700-year wind speed.

A-50 The equations for determining the reliability indices are identical to those used for the LRFD cases� Implementation For the four regions, the ASD reliability analyses require additional inputs� Inputs for ASD are: • Importance factors Ilow = 0�87, Imed = 1�00, and Ihigh = 1�15; • Shape factor SF = Zx/Sx = 1�30 for a circular section; and • Wind overstress factor OSF = 4/3 = 1�333� The results for the Midwest and Western Region ASCE/SEI 7-05 medium importance Imed = 1�00 are shown in Table 7-6� The LRFD-required nominal strength is shown for direct comparison� For the Midwest and Western Region for low importance Ilow = 0�87, the results are as shown in Table 7-7� Notice that the total nominal moment, MT3, does not change, but the total design moment MD + M50I changes with the importance factor, resulting in different required nomi- nal strength Rn� Similarly for high importance, the required nominal strength Rn increases as shown in Table 7-8 for the Midwest and Western Region� Table 7-6. Results for the Midwest and Western Region for medium importance. LRFD ASD Strength Total Design Ratio Equiv Moment RnLRFD RnLRFD M50 MT3 M50/MT3 MD+M50I RnASD RnASD ASD 1.11 0.61 0.61 1.00 0.61 0.90 1.23 2.69 1.12 0.55 0.65 0.85 0.65 0.96 1.17 2.94 1.13 0.49 0.69 0.71 0.69 1.02 1.11 3.20 1.14 0.43 0.73 0.59 0.73 1.08 1.06 3.44 1.16 0.37 0.77 0.48 0.77 1.13 1.02 3.63 1.17 0.31 0.81 0.38 0.81 1.19 0.98 3.74 1.18 0.24 0.84 0.29 0.84 1.25 0.94 3.77 1.19 0.18 0.88 0.21 0.88 1.31 0.91 3.71 1.20 0.12 0.92 0.13 0.92 1.36 0.88 3.57 1.25 0.06 0.96 0.06 0.96 1.42 0.88 3.39 1.39 0.00 1.00 0.00 1.00 1.48 0.94 3.19 Table 7-7. Results for the Midwest and Western Region for low importance. BiasDes= 0.988903 LRFD ASD Strength Total Design Ratio Equiv Moment RnLRFD RnLRFD M50 MT3 M50/MT3 MD+M50I RnASD RnASD ASD 0.93 0.61 0.61 1.00 0.53 0.79 1.18 2.25 0.96 0.55 0.65 0.85 0.58 0.86 1.12 2.49 0.99 0.49 0.69 0.71 0.63 0.93 1.07 2.75 1.02 0.43 0.73 0.59 0.67 0.99 1.02 3.00 1.04 0.37 0.77 0.48 0.72 1.06 0.98 3.23 1.07 0.31 0.81 0.38 0.77 1.13 0.95 3.39 1.10 0.24 0.84 0.29 0.81 1.20 0.92 3.48 1.13 0.18 0.88 0.21 0.86 1.27 0.89 3.49 1.16 0.12 0.92 0.13 0.91 1.34 0.87 3.43 1.25 0.06 0.96 0.06 0.95 1.41 0.89 3.33 1.39 0.00 1.00 0.00 1.00 1.48 0.94 3.19

A-51 The importance factors directly change the required nomi- nal resistances� Because the mean load Q and its variation does not change (not shown in these tables and the same as in the LRFD tables), this difference in required nominal resis- tances changes the reliability indices b accordingly� Calibration and Comparison Using the proposed flexure load and resistance factors, and with the statistical properties incorporated into the reli- ability analyses, the plots in Figure 7-1 compare the reliabil- ity indices for the four regions between current ASD design procedures and the proposed LRFD procedures� The Min- imum Beta plots represent the minimum indices over the four regions� Similarly, the Average Beta plots show the aver- ages over the four regions� For the LRFD 300-year, 700-year, and 1,700-year wind speed cases, the equivalent ASD designs use Ilow = 0�87, Imed = 1�00, and Ihigh = 1�15 importance factors, respectively� The proposed LRFD procedures result in comparable but more consistent reliability over the range of designs� For low- importance structures (using 300-year wind speeds), the reliability indices are lower, as intended� Likewise, for higher- importance structures (1,700-year wind speeds), the reliabil- ity indices are higher� This is shown in Figure 7-2 for the LRFD procedures� The ratios are the averages over the four regions� At low wind moments (gD2MD controls the design), there is no difference� However, for higher wind moments, the required strength increases for high-importance structures and decreases for lower-importance structures� As expected, the LRFD-required strength at a higher per- centage of wind load (MWind/MTotal high) is greater than that Table 7-8. Results for the Midwest and Western Region for high importance. LRFD ASD Strength Total Design Ratio Equiv Moment RnLRFD RnLRFD M50 MT3 M50/MT3 MD+M50I RnASD RnASD ASD 1.21 0.61 0.61 1.00 0.70 1.04 1.16 3.14 1.21 0.55 0.65 0.85 0.73 1.08 1.12 3.41 1.21 0.49 0.69 0.71 0.76 1.13 1.07 3.67 1.21 0.43 0.73 0.59 0.79 1.17 1.04 3.90 1.21 0.37 0.77 0.48 0.82 1.22 1.00 4.06 1.22 0.31 0.81 0.38 0.85 1.26 0.97 4.13 1.22 0.24 0.84 0.29 0.88 1.30 0.93 4.09 1.22 0.18 0.88 0.21 0.91 1.35 0.91 3.94 1.22 0.12 0.92 0.13 0.94 1.39 0.88 3.73 1.25 0.06 0.96 0.06 0.97 1.43 0.87 3.47 1.39 0.00 1.00 0.00 1.00 1.48 0.94 3.19 required for ASD� This behavior is demonstrated in Fig- ure 7-3, where the ratios are the average for the four regions� At a total moment where the wind is responsible for approximately 60% or more of the total, the proposed LRFD procedures will require more section capacity than the cur- rent ASD procedures� Below 60%, the LRFD procedures will require less section capacity than ASD� LRFD Reliability Analysis—Torsion The torsion analysis is similar to the flexure analysis, with a few caveats� The loading Q (in a torsional sense) and its associ- ated variability do not change� However, two differences from flexure are recommended in the proposed LRFD procedures� First, the bias factor and the phi factor are changed to 0�95 (from 0�90) and 1�10 (from 1�05)� This is due to the use of the elastic capacity, Tn = C(0�60Fy), instead of the plastic capacity, for the nominal torsion resistance Tn with this adjustment; a shape fac- tor of 1�0 is used with the plastic limit for both LRFD and ASD� Strength The required nominal resistance and the mean resistance become: max 1 1 2 1 T M M M T T n D D D D W W R n [ ] φ = φ γ φ γ + γ      = λ The coefficient of variation for the resistance remains at CovR�

A-52 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Average Beta - 700 Year LRFD ASD0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Minimum Beta - 700 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Minimum Beta - 300 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Average Beta - 300 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Average Beta - 1700 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Minimum Beta - 1700 Year LRFD ASD Figure 7-1. Minimum and average reliability indices. Figure 7-2. Resistance ratios for different return periods. 0.60 0.70 0.80 0.90 1.00 1.10 1.20 00.20.40.60.811.2 R ati o M Wind/M Total Rn300/Rn700 Rn1700/Rn700 LRFD Required Resistance Ratios (RnT/Rn700)

A-53 Figure 7-3. Required resistance ratios. Load Torsion acts similar to flexural moment� Thus: 150 700 2 2 700Q M M M MD D P V X( )= + = λ − + λ λ λ 1 700 2 2 2 700 2 50Cov Q Cov M Cov M Q Q Q D D M P V X[ ] [ ]( ) = σ = λ − + λ λ λ where M is now a torsional moment� The reliability indices equations remain the same as presented for flexure� Implementation The reliability analyses were coded into a spreadsheet for the four regions where the inputs are the same except for the aforementioned changes, as shown in Table 7-9 (inputs are highlighted)� In Table 7-10, only the results for the Midwest and West- ern Region ASCE/SEI 7-10 700-year wind speed are shown Table 7-9. Statistical parameters. COV BIAS BIASD 1.03 COVkz 0.16 1.00 COVD 0.08 COVG 0.11 1.00 BIASR 1.10 COVCd 0.12 1.00 COVR 0.10 Total BiasP 1.00 D+W D Only 0.95 D 1.10 1.25 W 1.00 because the reliability indices are nearly identical to the flex- ural cases shown previously� All of the other regions and wind speed cases show similar results in comparison to the flexural analyses� ASD Reliability Analysis—Torsion For the calibration and comparison to ASD, again, the load does not change� However, the strength equations are differ- ent enough between flexure and torsion that the comparison is necessary� Strength The ASD allowable torsion stress for a compact section, and using the OSF of 4/3 for wind loads is: 4 3 0�33 0�33F F OSF Fallow y y( ) ( )( )= = Given the LRFD elastic strength stress limit of 0�60Fy and the ASD allowable torsion stress of 0�33Fy, the equivalent ASD factor of safety for torsion becomes 1�818 (0�60/0�33) instead of the flexural case of 1�515 (1/0�66)� Thus, the nomi- nal resistance for the ASD torsion case becomes: 1 0�55 1 700 2 2 700T SF M SF OSF M M In y Design V[ ]( )= = − + λ λ For the ASD reliability analyses, the statistical properties are: = λT TR n and: Q, CovQ, and slnQ are unchanged�

A-54 700 Year Wind V700 115 T 700 V50 91.00991 Theory BIASX 0.8241 V700/V700 1.00 (V700/V700) 2 COVV 0.100 (V300/V700) 2 1.00 1.00 Equiv BIASV 0.79 M700 MT2 M700/MT2 Rn R lnR Q COVM50 COVQ lnQ LRFD 1.00 1.00 1.00 1.05 1.16 0.10 0.43 0.30 0.30 0.30 3.32 0.90 1.00 0.90 1.06 1.17 0.10 0.49 0.30 0.24 0.24 3.51 0.80 1.00 0.80 1.07 1.18 0.10 0.55 0.30 0.19 0.19 3.66 0.70 1.00 0.70 1.08 1.19 0.10 0.61 0.30 0.15 0.15 3.73 0.60 1.00 0.60 1.09 1.20 0.10 0.67 0.30 0.13 0.13 3.70 0.50 1.00 0.50 1.11 1.22 0.10 0.73 0.30 0.11 0.10 3.55 0.40 1.00 0.40 1.12 1.23 0.10 0.79 0.30 0.09 0.09 3.28 0.30 1.00 0.30 1.13 1.24 0.10 0.85 0.30 0.08 0.08 2.92 0.20 1.00 0.20 1.14 1.25 0.10 0.91 0.30 0.08 0.08 2.51 0.10 1.00 0.10 1.18 1.30 0.10 0.97 0.30 0.08 0.08 2.32 0.00 1.00 0.00 1.32 1.45 0.10 1.03 0.30 0.08 0.08 2.65 Table 7-10. Computed values (V700). Table 7-11. Results for the Midwest and Western Region for medium importance. LRFD ASD Strength Total Design Ratio Equiv Moment RnLRFD RnLRFD M50 MT3 M50/MT3 MD+M50I RnASD RnASD ASD 1.05 0.61 0.61 1.00 0.61 0.84 1.26 2.58 1.06 0.55 0.65 0.85 0.65 0.89 1.20 2.81 1.07 0.49 0.69 0.71 0.69 0.94 1.14 3.04 1.08 0.43 0.73 0.59 0.73 0.99 1.09 3.25 1.09 0.37 0.77 0.48 0.77 1.05 1.05 3.42 1.11 0.31 0.81 0.38 0.81 1.10 1.01 3.51 1.12 0.24 0.84 0.29 0.84 1.15 0.97 3.52 1.13 0.18 0.88 0.21 0.88 1.21 0.93 3.45 1.14 0.12 0.92 0.13 0.92 1.26 0.90 3.31 1.18 0.06 0.96 0.06 0.96 1.31 0.90 3.13 1.32 0.00 1.00 0.00 1.00 1.36 0.96 2.93 The coefficient of variation for the strength (resistance) is CovR� The equations for determining the reliability indices are identical to those used for the LRFD cases� Implementation For the four regions, the ASD reliability analyses require the same additional inputs as for the flexure analyses, except the shape factor is equal to 1�0� The results for the Midwest and Western Region ASCE/SEI 7-05 medium importance Imed = 1�00 is shown in Table 7-11� The torsional indices are nearly identical to the flexural reliability indices for the different load cases for the four regions� Calibration and Comparison Using the proposed torsion load and resistance factors, and with the statistical properties incorporated into the reliability analyses, the plots in Figure 7-4 compare the reliability indices for the four regions between current ASD design procedures and the proposed LRFD procedures� The Minimum Beta plots represent the minimum indices over the four regions� The

A-55 Average Beta plots show the averages over the four regions� For the LRFD 300-year, 700-year, and 1,700-year wind speed cases, the equivalent ASD designs use Ilow = 0�87, Imed = 1�00, and Ihigh = 1�15 importance factors, respectively� The proposed LRFD procedures result in comparable but more consistent reliability over the range of designs for tor- sion compared to the flexural analyses� The discussion on flexure in terms of comparisons with ASD and required strengths also applies to torsion� LRFD Flexure-Shear Interaction Monte Carlo simulation (using a spreadsheet) was used to verify target reliability when there is a presence of moment and torsion� It was assumed that the flexural moment com- prised dead and wind load moment, and that the torsion was from wind load only� This would be consistent with a traffic signal mast arm and pole structure� The interaction design equation limit is in the form: 1�0 1 2 M M R T T D D W W n W W T n γ + γ φ     + γ φ     ≤ At the optimum design, the interaction is equal to 1�0� Thus, there is a combination of a certain amount of flexure and a certain amount of torsion that results in an optimum design� Using the flexure and torsion analyses shown pre- viously, where the design capacity fMn = [gD1MD + gWMW] and fTTn = [gD1MD + gWMW] are based on the factored loads (resulting in a performance ratio of 1�0 for the individual Figure 7-4. Reliability indices for torsion. 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Average Beta - 700 Year LRFD ASD0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Minimum Beta - 700 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Minimum Beta - 300 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Average Beta - 300 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Average Beta - 1700 Year LRFD ASD 0.00 1.00 2.00 3.00 4.00 00.511.5 Be ta M Wind/M Total Minimum Beta - 1700 Year LRFD ASD

A-56 designs), this can be represented by the percentages a and b shown as: 1�0 1 2 2 ( ) ( )γ + γ φ     + γ φ     = + = a M M R b T T a b D D W W n W W T n The terms a and b represent the percentage of flexure and torsion, respectively� For instance, if the factored applied flex- ural moment is 70% of the design capacity (a = 0.70), then the factored applied torsion moment would be at 54�8% (a + b2 = 1�0) of the torsion design capacity for an optimal design� For the reliability analyses, the limit-state equation for the design limit is: 1 2a M M M b T T D W W( )( ) ( )+ + ≤ Each term is a random variable with its associated log- normal statistical properties� The properties are determined from the previous flexure and torsion analyses� Failure is represented by the limit-state equation exceeding 1�0� The contribution from flexure is the total applied moment compared to the strength and is represented by the term a from the design limit� The contribution from torsion is the total applied torsion compared to the strength and is represented by the term b from the design limit� The terms for the flexure moment and strength and the torsion moment and strength can be determined from the previous analyses� The torsion values are for the 100% wind load case� For the flexure values, a choice must be made on percentage of wind and dead load moment� Monte Carlo Moment/Shear Interaction Simulation The reliability analysis for the moment-shear interaction is demonstrated (see Table 7-12)� The LRFD ASCE/SEI 7-10 700-year wind speed is used for the Midwest and Western Region with the wind load representing 60% of the total MD + M700 = 1�0 (M700 = 0�60 and MD = 0�40)� The flexure contribu- tion to the interaction is 70% (a = 0�70, b = 0�548)� The statistical properties for the flexural dead and wind load effects, the torsional wind, and the strengths are as shown in Table 7-13� Monte Carlo simulation was used for each of the random variables and combines the terms, along with the a and b per- centage terms, into the interaction equation� To verify the inputs and the analysis, for 10,000 samples, the statistical results shown in Table 7-14 are determined for each of the variables� Because the analysis computes values for flexure, torsion, and the interaction, the flexure-only case and the torsion- only case can also be verified, along with determining the reli- ability index for the interaction equation� For instance, the probability distribution for the flexure-only case is shown in Figure 7-5� Collecting the data and checking for samples that exceed the limit of 1�0 results in typical percentage of failures of 0�0001, which represents a reliability index of b = 3�72� The reliability index determined from the associated flexure analy- Midwest & Western Region M700/MT1 MD/MT1 % Wind of 0.60 0.40 Total Flexure Moment % Flexure in Interaction Eqn a b 0.7 0.548 Table 7-12. Inputs for wind-to-total-load effect ratio. Table 7-13. Intermediate computations. Parameter MD MW MT1 Mn T Tn Assigned Mean 0.41 0.26 0.67 1.21 0.43 1.16 COV 0.08 0.30 0.10 0.30 0.10 Std Dev 0.03 0.08 0.12 0.13 0.12 lnX -0.89 -1.41 0.19 0.14 lnX 0.08 0.29 0.10 0.10 Table 7-14. Intermediate computations. Computed MD MW MT1 Mn T Tn Mean 0.41 0.25 0.67 1.21 0.42 1.16 COV 0.08 0.30 0.13 0.10 0.30 0.10 Std Dev 0.03 0.08 0.08 0.12 0.13 0.12

A-57 Figure 7-5. Monte Carlo–generated probability density for flexure only. Figure 7-6. Monte Carlo–generated probability density for torsion only. Figure 7-7. Monte Carlo–generated probability density for moment- torsion interaction only sis is b = 3�75� For the torsion case of wind load only, typical percentage of failures is 0�0004, which represents a reliability index of b = 3�35� The reliability index determined from the associated torsion analysis is b = 3�32, with the probability distribution shown in Figure 7-6� This confirms the equation- based analysis in an independent manner� The interaction probability density results are similar� Application of the interaction equation with the individual variable sample values results in the probability distribution shown in Figure 7-7� Collecting the data and checking for samples that exceed the limit of 1�0 results in typical percentage of failures of 0�0003, which represents a reliability index of b = 3�43� The results demonstrate that the reliability indices for moment- torsion interaction are consistent with the moment-only and torsion-only cases�

A-58 S E c t I o N 8 Setting Target Reliability Indices The statistical characterization of the limit-state equa- tion and the associated inputs are presented in the preced- ing sections� The reliability indices are computed based on the current ASD practice and the LRFD-LTS specifications� The comparisons made and presented previously are based on the recommended load and resistance factors� These factors are illustrated for the 700-year wind speeds (MRI = 700 years)� This MRI is for the typical structure; however, some consideration is warranted for structures that are located on travelways with low ADT and/or that are located away from the travelway, whereby failure is unlikely to be a traveler safety issue� Similarly, consideration is also warranted for structures that are located on heavily traveled roads where a failure has a significant chance of harming travelers and/ or suddenly stopping traffic, creating an event that causes a traffic collision with the structure and likely chain-reaction impacts of vehicles� Ultimately, judgment is used to set the target reliability indi- ces for the different applications� This is often based on typical average performance under the previous design specifications (i�e�, ASD)� However, even in the ASD methods, an impor- tance factor was considered: 0�87 and 1�15 for less important and more important applications, respectively� Some varia- tions are also considered for hurricane versus non-hurricane regions� There were similar concerns for the LRFD-LTS specifi- cations’ assignment of the MRI considered for design� Less important structures are assigned an MRI of 300, while an important structure uses an MRI of 1,700-years� Typical structures are assigned an MRI of 700 years� The description of this implementation is provided next with the resulting reliability indices for each region� Implementation into Specifications The possible structure locations were divided into two pri- mary categories: 1� Failures where a structure is likely to cross the travelway and, within those structures, those that are located on a typical travelway versus a lifeline travelway, which are those that are critical for emergency use/egress; and 2� Failures where a structure cannot cross the travelway and that, consequently, are of lesser importance� Within these categories, the ADT is used to further distin- guish the consequence of failure� The traffic speed was initially considered in the research but was not used in the final work based on simplicity and judgment� Table 8-1 summarizes this approach� From this design approach, Table 8-1 establishes the MRI and the associated wind maps� The maps provide the design wind speed based on the structure’s location� Computed Reliability Indices Based on the load and resistance statistical characteristics, the reliability indices b are computed for the four regions for a wind-to-total-load ratio of 0�5 and 1�0� The 0�5 ratio is typi- cal of traffic signal poles, and the 1�0 ratio is typical of high- mast poles� Other ratios were computed; however, these two are provided for brevity� Figure 8-1 illustrates the relationship between Table 8-1 and the computed values� For example, assume that a struc- ture is located on a travelway with ADT of between 1,000 and 10,000, and a failure could cross the roadway� The MRI is 700� The statistical properties for the 700-year wind in the region Implementation

A-59 The resulting indices are reasonable for the various appli- cations, and the load and resistance factor were accordingly set� The load factors are summarized in Table 8-6� The resistance factors f for the primary limit states are illustrated in Table 8-7� For brevity, not all are illustrated� The resistance factors are provided in the individual mate- rial resistance sections� The resistance factor for service and fatigue limit states is 1�0� Sensitivities The previous discussion outlines the results of assign- ment of load and resistance factors and the resulting reliabil- ity indices� It is useful to illustrate the sensitivities of these assignments to the resulting reliability indices� The minimum and average values for all regions are used to demonstrate by varying the dead load, wind load, and resistance factors for steel flexure strength and extreme limit states� Note that an increase in resistance factor f decreases the reliability index b� An increase in load factor g increases b� The typical traffic signal structures have load ratios in the region of one-half, while high-mast poles have very little dead load effect and ratios that are nearer to unity� In Table 8-8, the area contained within the dotted lines indicates the region that is of typical interest� Table 8-1. MRI related to structure location and consequence of failure. Traffic Volume Typical High Low ADT<100 300 1700 300 100<ADT≤1000 700 1700 300 1000<ADT≤ 10000 700 1700 300 ADT>10000 1700 1700 300 Mean Recurrence Interval Importance Typical: Failure could cross travelway High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway Roadway sign supports: use 10 years of interest are then used to compute b� The computed value of b = 3�89 is shown Figure 8-1� Other indices were computed for load ratios in each region� The results are illustrated in Tables 8-2 to 8-5� Note that for the same region and location, the load ratio of 0�5 has a higher b than that for the ratio of 1�0� This is because a wind-dominated structure will experience a higher load variability (all wind) than one that is 50% dead load� Compare the same application (cell) across regions, and the region with the lower wind variability will have a higher b� Figure 8-1. Relationship between MRI and computed reliability indices. Traffic Volume Typical High Low ADT<100 300 1700 300 100<ADT≤1000 700 1700 300 1000<ADT≤ 10000 700 1700 300 ADT>10000 1700 1700 300 Mean Recurrence Interval Importance Typical: Failure could cross travelway High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway Roadway sign supports: use 10 years Traffic Volume Typical High Low ADT<100 3.03 3.89 3.03 100<ADT≤1000 3.60 3.89 3.03 1000<ADT≤ 10000 3.60 3.89 3.03 ADT>10000 3.89 3.89 3.03 Roadway sign supports: use 10 years Importance Typical: Failure could cross travelway High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway (Midwest and West) Load Ratio [WL/(DL+WL) = 0.5] Table 8-2. Reliability indices for the Midwest and Western United States. Traffi c Volume Typical High Low ADT<100 3.03 3.89 3.03 100<ADT≤1000 3.60 3.89 3.03 1000<ADT≤ 10000 3.60 3.89 3.03 ADT>10000 3.89 3.89 3.03 Roadway sign supports: use 10 years Importance Typical: Failure could cross travelway High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway (Midwest and West)Load Ratio [WL/(DL+WL) = 0.5] Traffi c Volume Typical High Low ADT<100 2.77 3.62 2.77 100<ADT≤1000 3.35 3.62 2.77 1000<ADT≤ 10000 3.35 3.62 2.77 ADT>10000 3.62 3.62 2.77 (Midwest and West)Load Ratio [WL/(DL+WL) = 1.0] Importance Typical: Failure could cross travelway High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway Roadway sign supports: use 10 years

A-60 Table 8-3. Reliability indices for the West Coast. Traffi c Volume Typical High Low ADT<100 3.38 4.31 3.38 100<ADT≤1000 4.00 4.31 3.38 1000<ADT≤ 10000 4.00 4.31 3.38 ADT>10000 4.31 4.31 3.38 (West Coast)Load Ratio [WL/(DL+WL) = 0.5] Importance Typical: Failure could cross travelway Low: Support failure could not cross travelway Roadway sign supports: use 10 years High: Support failure could stop a life-line travelway Traffi c Volume Typical High Low ADT<100 3.23 4.14 3.23 100<ADT≤1000 3.85 4.14 3.23 1000<ADT≤ 10000 3.85 4.14 3.23 ADT>10000 4.14 4.14 3.23 (West Coast)Load Ratio [WL/(DL+WL) = 1.0] Importance ypical: Failure could cross travelway ow: Support failure could not cross travelway Roadway sign supports: use 10 years T L High: Support failure could stop a life-line travelway Table 8-4. Reliability indices for the Florida coast. Traffi c Volume Typical High Low ADT<100 2.46 3.42 2.46 100<ADT≤1000 2.78 3.42 2.46 1000<ADT≤ 10000 2.78 3.42 2.46 ADT>10000 3.42 3.42 2.46 (Coastal)Load Ratio [WL/(DL+WL) = 0.5] Importance Typical: Failure could cross travelway High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway Roadway sign supports: use 10 years Traffi c Volume Typical High Low ADT<100 2.05 2.94 2.05 100<ADT≤1000 2.37 2.94 2.05 1000<ADT≤ 10000 2.37 2.94 2.05 ADT>10000 2.94 2.94 2.05 (Coastal)Load Ratio [WL/(DL+WL) = 1.0] Importance ypical: Failure could cross travelway igh: Support failure could stop a life-line travelway T H Low: Support failure could not cross travelway Roadway sign supports: use 10 years Table 8-5. Reliability indices for Southern Alaska coast. Traffi c Volume Typical High Low ADT<100 2.88 3.47 2.88 100<ADT≤1000 3.27 3.47 2.88 1000<ADT≤ 10000 3.27 3.47 2.88 ADT>10000 3.47 3.47 2.88 (Southern Ak)Load Ratio [WL/(DL+WL) = 0.5] Typical: Failure could cross travelway Importance High: Support failure could stop a life-line travelway Low: Support failure could not cross travelway Roadway sign supports: use 10 years Traffi c Volume Typical High Low ADT<100 2.56 3.15 2.56 100<ADT≤1000 2.96 3.15 2.56 1000<ADT≤ 10000 2.96 3.15 2.56 ADT>10000 3.15 3.15 2.56 (Southern Ak)Load Ratio [WL/(DL+WL) = 1.0] Importance ypical: Failure could cross travelway igh: Support failure could stop a life-line travelway T H Low: Support failure could not cross travelway Roadway sign supports: use 10 years

A-61 Table 8-6. Load factors (same as Table 3.4.1 in the proposed LRFD-LTS specifications). Live Load (LL) Wind (W) Truck Gust (TrG) Natural Wind Gust Vibration (NWG) Vortex- Induced Vibration (VVW) Combined Wind on High- level Towers Galloping- Induced Vibration (GVW) Max/Min Mean Strength I Gravity 3.5, 3.6, and 3.7 1.25 1.6 Extreme I Wind 3.5, 3.8, 3.9 1.1/0.9 1.0a Service I Translation 10.4 1.0 1.0b Service III Crack control for Prestressed Concrete 1.0 1.00 Fatigue I Infinite-life 11.7 1.0 1.0 1.0 1.0 1.0 1.0 Fatigue II Evaluation 17.5 1.0 1.0 1.0 1.0 1.0 1.0 b. Use wind map 3.8-4 (service) a. Use Figures 3.8-1, 3.8-2, or 3.8-3 (for appropriate return period) Apply separately Permanent Dead Components (DC) Load Combination Limit State Description Reference Articles Transient Fatigue Note: Table numbers within table are for tables in the LRFD-LTS specifications. Table 8-7. Resistance factors for strength and extreme limit states. Material Action Resistance Factor Steel Flexure 0.90 Torsion and Shear 0.95 Axial Compression 0.90 Axial Tension (yield) 0.90 Axial Tension (rupture) 0.75 Aluminum Flexure (yield) 0.90 Flexure (rupture) 0.75 Torsion and Shear 0.90 Axial Compression 0.9 Axial Tension (yield) 0.90 Axial Tension (rupture) 0.75 Wood Flexure 0.85 Torsion and Shear 0.75 Axial compression 0.90 Tension 0.80 Concrete Flexure 1.00 Torsion and Shear 0.90 Axial compression 0.90 FRP Flexure 0.67

Table 8-8. Sensitivity of the reliability index to load and resistance factors. Parameters Minimum Average Resistance Ratio Baseline = 0.9 dead-only = 1.25 dead = 1.1 wind = 1.0 = 0.9 dead-only = 1.35 dead = 1.1 wind = 1.0 = 0.9 dead-only = 1.25 dead = 1.2 wind = 1.0

= 0.95 dead-only = 1.25 dead = 1.1 wind = 1.0 = 1.0 dead-only = 1.25 dead = 1.1 wind = 1.0 = 0.85 dead-only = 1.25 dead = 1.1 wind = 1.0 Table 8-8. (Continued).

A-64 S E c t I o N 9 Judgment must be employed in the calibration regard- ing the performance of existing structures under the current specifications and setting the target reliability index b for the LRFD-LTS specifications� The LRFD-LTS specifications were calibrated using the stan- dard ASD-based specifications as a baseline� The variabilities of the loads and resistances were considered in a rigor- ous manner� The wind loads have higher variabilities than the dead loads� Therefore, a structure with high wind-to- total-load ratio will require higher resistance and associated resistances compared to ASD� This was shown to be on the order of a 10% increase for high-mast structures� For struc- tures with approximately one-half wind load (e�g�, cantilever structures), on average the required resistance will not change significantly� It is important to note that resistance is propor- tional to section thickness and proportional to the square of the diameter [i�e�, a 10% resistance increase may be associated with a 10% increase in thickness (area) or a 5% increase in diameter or area]� The reliability index for the LRFD-LTS specifications is more uniform over the range of load ratios of practical inter- est than the current ASD-based specifications� Summary

A-65 Annex A Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Birmingham, Alabama 34 46.6 0.139 62.3 76.0 0.085 80.0 0.082 84.0 0.080 2 Prescott, Arizona 17 52.2 0.169 66.0 92.0 0.096 98.0 0.091 104.0 0.089 3 Tucson, Arizona 30 51.4 0.167 77.7 89.0 0.096 95.0 0.091 101.0 0.089 4 Yuma, Arizona 29 48.9 0.157 65.1 83.0 0.093 88.0 0.089 93.0 0.084 5 Fort Smith, Arkansas 26 46.6 0.150 60.7 78.0 0.091 83.0 0.085 87.0 0.082 6 Little Rock, Arkansas 35 46.7 0.206 72.2 90.0 0.111 96.0 0.106 103.0 0.102 7 Denver, Colorado 27 49.2 0.096 62.3 70.0 0.073 73.0 0.069 76.0 0.066 8 Grand Junction, Colorado 31 52.7 0.102 69.9 76.0 0.073 80.0 0.069 84.0 0.065 9 Pueblo, Colorado 37 62.8 0.118 79.2 95.0 0.079 100.0 0.075 105.0 0.071 10 Hartford, Connecticut 38 45.1 0.151 66.8 75.0 0.090 80.0 0.085 84.0 0.080 11 Washington, D.C. 33 48.3 0.135 66.3 78.0 0.085 82.0 0.082 86.0 0.078 12 Atlanta, Georgia 42 47.4 0.195 75.5 88.0 0.102 94.0 0.097 100.0 0.092 13 Macon, Georgia 28 45.0 0.169 59.7 79.0 0.100 84.0 0.095 89.0 0.088 14 Boise, Idaho 38 47.8 0.111 61.9 71.0 0.078 74.0 0.073 78.0 0.070 15 Pocatello, Idaho 39 53.3 0.128 71.6 84.0 0.079 88.0 0.075 92.0 0.071 16 Chicago, Illinois 35 47.0 0.102 58.6 68.0 0.075 72.0 0.070 75.0 0.066 17 Moline, Illinois 34 54.8 0.141 72.1 89.0 0.086 94.0 0.080 99.0 0.076 18 Peoria, Illinois 35 52.0 0.134 70.2 83.0 0.086 88.0 0.080 92.0 0.076 19 Springfield, Illinois 30 54.2 0.111 70.6 81.0 0.079 85.0 0.075 89.0 0.070 20 Evansville, Indiana 37 46.7 0.130 61.3 74.0 0.079 77.0 0.075 82.0 0.070 21 Fort Wayne, Indiana 36 53.0 0.125 69.0 82.0 0.082 87.0 0.077 91.0 0.074 22 Indianapolis, Indiana 34 55.4 0.200 93.0 103.0 0.105 110.0 0.098 119.0 0.092 23 Burlington, Iowa 23 56.0 0.164 71.9 97.0 0.094 103.0 0.090 110.0 0.085 24 Des Moines, Iowa 27 57.7 0.147 79.9 95.0 0.091 101.0 0.086 107.0 0.081 25 Sioux City, Iowa 36 57.9 0.157 88.1 98.0 0.096 104.0 0.091 111.0 0.085 26 Concordia, Kansas 16 57.6 0.160 73.7 98.0 0.095 104.0 0.092 111.0 0.085 27 Dodge City, Kansas 35 60.6 0.099 71.5 87.0 0.068 91.0 0.064 95.0 0.061 28 Topeka, Kansas 28 54.5 0.150 78.8 91.0 0.095 96.0 0.087 102.0 0.084 29 Wichita, Kansas 37 58.1 0.146 89.5 96.0 0.090 101.0 0.085 107.0 0.080 30 Louisville, Kentucky 32 49.3 0.136 65.7 79.0 0.088 84.0 0.082 88.0 0.078 31 Shreveport, Louisiana 11 44.6 0.121 53.4 69.0 0.078 72.0 0.076 76.0 0.073 32 Baltimore, Maryland 29 55.9 0.123 71.2 87.0 0.080 91.0 0.075 96.0 0.070 33 Detroit, Michigan 44 48.9 0.140 67.6 79.0 0.086 84.0 0.083 89.0 0.078 34 Grand Rapids, Michigan 27 48.3 0.209 66.8 93.0 0.108 99.0 0.102 107.0 0.093 35 Lansing, Michigan 29 53.0 0.125 67.0 83.0 0.082 87.0 0.079 92.0 0.076 Table A1. Statistical parameters of wind for Central United States. (continued on next page)

A-66 Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 51 Ely, Nevada 39 52.9 0.117 70.1 80.0 0.078 85.0 0.074 89.0 0.070 52 Las Vegas, Nevada 13 54.7 0.128 70.1 85.0 0.083 90.0 0.079 95.0 0.074 53 Reno, Nevada 36 56.5 0.141 76.6 92.0 0.088 97.0 0.082 103.0 0.077 54 Winnemucca, Nevada 28 50.2 0.142 62.6 82.0 0.088 87.0 0.083 92.0 0.078 55 Concord, New Hampshire 37 42.9 0.195 68.5 80.0 0.105 85.0 0.100 92.0 0.094 56 Albuquerque, New Mexico 45 57.2 0.136 84.8 92.0 0.090 97.0 0.085 102.0 0.080 57 Roswell, New Mexico 31 58.2 0.153 81.6 98.0 0.096 104.0 0.088 110.0 0.085 58 Albany, New Mexico 40 47.9 0.140 68.5 77.0 0.085 82.0 0.078 87.0 0.075 59 Binghamton, New York 27 49.2 0.130 63.8 77.0 0.085 82.0 0.078 86.0 0.075 60 Buffalo, New York 34 53.9 0.132 78.6 85.0 0.086 92.0 0.079 96.0 0.076 61 Rochester, New York 37 53.5 0.097 65.4 77.0 0.069 80.0 0.067 84.0 0.063 62 Syracuse, New York 37 50.3 0.121 67.2 77.0 0.082 82.0 0.075 86.0 0.071 63 Charlotte, N. Carolina 27 44.7 0.168 64.6 78.0 0.092 83.0 0.087 88.0 0.082 64 Greensboro, N. Carolina 48 42.3 0.180 66.8 76.0 0.098 81.0 0.092 87.0 0.086 65 Bismarck, North Dakota 38 58.3 0.096 68.9 83.0 0.068 87.0 0.064 91.0 0.062 66 Fargo, North Dakota 36 59.4 0.185 100.5 108.0 0.100 115.0 0.095 123.0 0.090 67 Williston, North Dakota 16 56.5 0.117 69.3 86.0 0.078 90.0 0.074 95.0 0.070 68 Cleveland, Ohio 35 52.7 0.125 68.5 82.0 0.082 86.0 0.078 91.0 0.074 69 Columbus, Ohio 26 49.4 0.133 61.3 78.0 0.085 83.0 0.080 88.0 0.078 70 Dayton, Ohio 35 53.6 0.142 72.0 87.0 0.087 93.0 0.082 98.0 0.078 71 Toledo, Ohio 35 50.8 0.177 82.2 91.0 0.098 97.0 0.092 103.0 0.088 72 Oklahoma City, Oklahoma 26 54.0 0.110 69.3 81.0 0.073 84.0 0.070 88.0 0.067 73 Tulsa, Oklahoma 35 47.9 0.145 68.3 79.0 0.088 84.0 0.082 88.0 0.077 74 Harrisburg, Pennsylvania 39 45.7 0.164 64.4 79.0 0.096 84.0 0.090 89.0 0.085 75 Philadelphia, Pennsylvania 23 49.5 0.115 62.4 75.0 0.078 79.0 0.073 83.0 0.068 76 Pittsburgh, Pennsylvania 18 48.4 0.120 59.6 74.0 0.078 78.0 0.073 82.0 0.068 77 Scranton, Pennsylvania 23 44.6 0.107 54.2 66.0 0.074 69.0 0.070 72.0 0.065 78 Greenville, South Carolina 36 48.5 0.226 71.9 97.0 0.112 105.0 0.108 112.0 0.104 79 Huron, South Dakota 39 61.4 0.132 78.8 98.0 0.085 102.0 0.081 108.0 0.078 80 Rapid City, South Dakota 36 61.0 0.087 70.5 85.0 0.063 88.0 0.061 92.0 0.058 81 Chattanooga, Tennessee 35 47.8 0.218 75.9 94.0 0.114 101.0 0.109 109.0 0.104 82 Knoxville, Tennessee 33 48.8 0.141 65.9 79.0 0.090 84.0 0.085 89.0 0.080 83 Memphis, Tennessee 21 45.4 0.137 60.7 73.0 0.088 77.0 0.082 81.0 0.079 84 Nashville, Tennessee 34 46.8 0.171 70.2 82.0 0.096 87.0 0.091 93.0 0.086 85 Abilene, Texas 34 54.7 0.192 99.9 102.0 0.102 107.0 0.098 116.0 0.092 36 Sault Ste. Marie, Michigan 37 48.4 0.159 67.0 83.0 0.090 87.0 0.086 92.0 0.082 37 Duluth, Minnesota 28 50.9 0.151 69.6 85.0 0.090 90.0 0.087 96.0 0.081 38 Minneapolis, Minnesota 40 49.2 0.185 81.6 90.0 0.099 96.0 0.094 102.0 0.088 39 Columbia, Missouri 28 50.2 0.129 62.4 79.0 0.084 84.0 0.079 88.0 0.075 40 Kansas City, Missouri 44 50.5 0.155 75.2 85.0 0.094 91.0 0.089 96.0 0.085 41 St. Louis, Missouri 19 47.4 0.156 65.7 80.0 0.094 85.0 0.088 90.0 0.084 42 Springfield, Missouri 37 50.1 0.148 71.2 83.0 0.090 88.0 0.085 93.0 0.080 43 Billings, Montana 39 59.4 0.135 84.2 95.0 0.085 100.0 0.083 106.0 0.079 44 Great Falls, Montana 34 59.0 0.110 74.2 88.0 0.075 92.0 0.073 97.0 0.069 45 Havre, Montana 17 58.0 0.159 77.7 99.0 0.095 105.0 0.093 115.0 0.087 46 Helena, Montana 38 55.2 0.118 71.2 84.0 0.078 89.0 0.075 93.0 0.070 47 Missoula, Montana 33 48.3 0.122 70.9 74.0 0.078 79.0 0.075 83.0 0.070 48 North Platte, Nebraska 29 62.0 0.108 74.4 92.0 0.076 96.0 0.073 101.0 0.069 49 Omaha, Nebraska 42 55.0 0.195 104.0 102.0 0.105 109.0 0.100 117.0 0.095 50 Valentine, Nebraska 22 60.6 0.142 74.1 99.0 0.088 105.0 0.083 111.0 0.078 Table A1. (Continued).

A-67 Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Montgomery, Alabama 28 45.3 0.185 76.7 82.0 0.104 88.0 0.095 94.0 0.090 2 Jackson, Mississippi 29 45.9 0.155 64.4 78.0 0.092 82.0 0.087 87.0 0.082 3 Austin, Texas 35 45.1 0.122 58.0 70.0 0.074 73.0 0.071 77.0 0.067 4 Portland, Maine 37 48.5 0.179 72.8 87.0 0.100 92.0 0.096 99.0 0.089 Table A2. Statistical parameters of wind for Costal Segment 1. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Boston, Massachusetts 42 56.3 0.172 81.4 100.0 0.098 106.0 0.093 113.0 0.088 2 New York, New York 31 50.3 0.143 61.4 82.0 0.086 87.0 0.079 92.0 0.076 3 Norfolk, Virginia 20 48.9 0.182 68.9 88.0 0.102 94.0 0.097 100.0 0.093 Table A3. Statistical parameters of wind for Costal Segment 2. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Jacksonville, Florida 28 48.6 0.206 74.4 93.0 0.112 100.0 0.106 107.0 0.099 2 Tampa, Florida 10 49.6 0.163 65.1 85.0 0.095 90.0 0.090 96.0 0.084 3 Savannah, Georgia 32 47.6 0.202 79.3 90.0 0.108 96.0 0.099 104.0 0.094 4 Block Island, Rhode Island 31 61.4 0.142 86.2 100.0 0.085 106.0 0.081 112.0 0.076 Table A4. Statistical parameters of wind for Costal Segment 3. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 86 Amarillo, Texas 34 61.0 0.117 80.7 93.0 0.079 98.0 0.075 103.0 0.071 87 Dallas, Texas 32 49.1 0.132 66.8 78.0 0.088 82.0 0.084 86.0 0.078 88 El Paso, Texas 32 55.4 0.087 66.7 77.0 0.065 80.0 0.060 83.0 0.056 89 San Antonio, Texas 36 47.0 0.183 79.5 86.0 0.099 91.0 0.094 97.0 0.087 90 Salt Lake City, Utah 36 50.6 0.142 69.0 83.0 0.090 87.0 0.087 92.0 0.082 91 Burlington, Vermont 34 45.7 0.160 66.5 78.0 0.093 83.0 0.090 88.0 0.087 92 Lynchburg, Virginia 34 40.9 0.149 53.4 68.0 0.086 72.0 0.082 76.0 0.078 93 Richmond, Virginia 27 42.2 0.152 61.3 70.0 0.092 75.0 0.085 80.0 0.080 94 Green Bay, Wisconsin 29 56.6 0.212 103.0 110.0 0.112 118.0 0.108 127.0 0.100 95 Madison, Wisconsin 31 55.7 0.190 80.2 102.0 0.105 110.0 0.098 117.0 0.091 96 Milwaukee, Wisconsin 37 53.7 0.121 67.9 82.0 0.082 87.0 0.075 91.0 0.070 97 Cheyenne, Wyoming 42 60.5 0.093 72.6 86.0 0.070 89.0 0.065 93.0 0.060 98 Lander, Wyoming 32 61.2 0.160 80.4 104.0 0.092 111.0 0.086 118.0 0.080 99 Sheridan, Wyoming 37 61.5 0.116 82.0 94.0 0.076 98.0 0.073 103.0 0.071 100 Elkins, West Virginia 10 51.1 0.160 68.5 88.0 0.092 93.0 0.088 98.0 0.084 Table A1. (Continued).

A-68 Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Fresno, California 37 34.4 0.140 46.5 55.0 0.090 58.0 0.086 62.0 0.080 2 Red Bluff, California 33 52.1 0.141 67.3 85.0 0.089 90.0 0.086 95.0 0.082 3 Sacramento, California 29 46.0 0.223 67.8 92.0 0.112 98.0 0.108 105.0 0.098 4 San Diego, California 38 34.5 0.130 46.6 54.0 0.085 57.0 0.082 60.0 0.080 5 Portland, Oregon 28 52.6 0.196 87.9 99.0 0.104 105.0 0.100 112.0 0.092 6 Roseburg, Oregon 12 35.6 0.169 51.1 62.0 0.095 66.0 0.090 70.0 0.085 7 North Head, Washington 41 71.5 0.141 104.4 116.0 0.088 123.0 0.083 130.0 0.078 8 Quillayute, Washington 11 36.5 0.085 41.9 50.0 0.060 52.0 0.058 54.0 0.056 9 Seattle, Washington 10 41.9 0.080 49.3 57.0 0.060 59.0 0.058 61.0 0.056 10 Spokane, Washington 37 47.8 0.133 64.6 76.0 0.084 80.0 0.077 84.0 0.074 11 Tatoosh Island, Washington 54 66.0 0.106 85.6 97.0 0.073 102.0 0.072 107.0 0.069 Table A8. Statistical parameters of wind for the West Coast. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Key West, Florida 19 51.0 0.337 89.5 127.0 0.138 140.0 0.125 152.0 0.115 Table A7. Statistical parameters of wind for Costal Segment 8. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Brownsville, Texas 35 43.7 0.185 66.1 80.0 0.098 85.0 0.092 91.0 0.088 2 Corpus Christi, Texas 34 54.5 0.288 127.8 124.0 0.125 134.0 0.118 146.0 0.112 3 Port Arthur, Texas 25 53.1 0.181 81.0 96.0 0.097 102.0 0.092 108.0 0.087 4 Cape Hatteras, N. Carolina 45 58.0 0.214 103.0 113.0 0.110 121.0 0.105 130.0 0.100 5 Wilmington, N. Carolina 26 49.9 0.218 84.3 98.0 0.112 105.0 0.102 113.0 0.096 Table A6. Statistical parameters of wind for Costal Segment 5. Annual 300 Year 700 Year 1,700 Year n Mean Cov Max Mean Cov Mean Cov Mean Cov 1 Nantucket, Massachusetts 23 56.7 0.141 71.3 92.0 0.086 98.0 0.083 103.0 0.078 Table A5. Statistical parameters of wind for Costal Segment 4.

A-69 Annex B Table B1. Test results (from Stam et al., 2011). Connection Detail Sr [ksi] No. of Cycles to Failure A [ksi3] Category as in ASSHTO- CAFL No. of Cycles Using Miner’s Rule for CAFL Socket 11.9 249,446 4.2E+08 Ep 2.39E+07 Socket 12 453,948 7.84E+08 Ep 4.46E+07 Socket 6.3 2,072,592 5.18E+08 Ep 2.95E+07 Socket 6.1 2,199,343 4.99E+08 Ep 2.84E+07 Socket 6.1 2,816,706 6.39E+08 Ep 3.64E+07 Socket 11.9 389,428 6.56E+08 Ep 3.73E+07 Socket 11.9 265,540 4.47E+08 Ep 2.55E+07 Socket 11.9 5,144,528 8.67E+09 C 8.67E+06 Socket 11.9 1,683,127 2.84E+09 D 8.27E+06 External Collar 11.9 4,245,460 7.15E+09 C 7.15E+06 External Collar 11.9 2,363,152 3.98E+09 D 1.16E+07 Full Penetration 17.7 422,400 2.34E+09 D 6.83E+06 External Collar 12 2,345,896 4.05E+09 D 1.18E+07 External Collar 12 2,889,260 4.99E+09 C 4.99E+06 External Collar 12 5,755,111 9.94E+09 C 9.94E+06 External Collar 12 3,304,490 5.71E+09 C 5.71E+06 External Collar 12 2,382,309 4.12E+09 D 1.20E+07 Socket 12 235,854 4.08E+08 Ep 2.32E+07 Socket 12 260,700 4.5E+08 Ep 2.56E+07 Socket 12 622,928 1.08E+09 Ep 6.12E+07 External Collar 12 3,939,099 6.81E+09 C 6.81E+06 External Collar 12 6,927,606 1.2E+10 C 1.20E+07 External Collar 12 5,384,143 9.3E+09 C 9.30E+06 External Collar 12 2,863,521 4.95E+09 C 4.95E+06 Full Penetration 12 4,997,925 8.64E+09 C 8.64E+06 Full Penetration 12 7,527,441 1.3E+10 B 3.18E+06 Socket 12 253,657 4.38E+08 Ep 2.49E+07 Socket 12 310,352 5.36E+08 Ep 3.05E+07 Socket 12 792,576 1.37E+09 E 1.50E+07 Socket 12 376,291 6.5E+08 Ep 3.70E+07 Full Penetration 12 6,734,487 1.16E+10 C 1.16E+07 Full Penetration 12 5,219,304 9.02E+09 C 9.02E+06 (continued on next page)

A-70 Table B1. (Continued). Full Penetration 21.14 3,516,775 3.32E+10 A 2.40E+06 Full Penetration 24 222,649 3.08E+09 D 8.97E+06 Full Penetration 24 212,891 2.94E+09 D 8.58E+06 Full Penetration 24 1,873,499 2.59E+10 A 1.87E+06 Full Penetration 24 677,763 9.37E+09 C 9.37E+06 Full Penetration 24 633,458 8.76E+09 C 8.76E+06 Full Penetration 28 286,526 6.29E+09 C 6.29E+06 Full Penetration 28 123,072 2.7E+09 D 7.88E+06 Full Penetration 28 129,090 2.83E+09 D 8.26E+06 Full Penetration 12 3,051,996 5.27E+09 C 5.27E+06 External Collar 12 10,652,284 1.84E+10 B 4.49E+06 External Collar 12 10,652,284 1.84E+10 B 4.49E+06 Full Penetration 24 1,272,665 1.76E+10 B 4.30E+06 Full Penetration 24 1,210,499 1.67E+10 B 4.09E+06 External Collar 24 137,220 1.9E+09 E 2.08E+07 External Collar 24 244,763 3.38E+09 D 9.86E+06 Full Penetration 24 292,468 4.04E+09 D 1.18E+07 Full Penetration 24 328,833 4.55E+09 C 4.55E+06 External Collar 24 169,059 2.34E+09 D 6.81E+06 External Collar 24 119,289 1.65E+09 E 1.81E+07 Connection Detail Sr [ksi] No. of Cycles to Failure A [ksi3] Category as in ASSHTO- CAFL No. of Cycles Using Miner’s Rule for CAFL Full Penetration 24 856,122 1.18E+10 C 1.18E+07 Full Penetration 24 747,510 1.03E+10 C 1.03E+07 External Collar 18 512,860 2.99E+09 D 8.72E+06 External Collar 18 653,208 3.81E+09 D 1.11E+07 Full Penetration 18 1,053,554 6.14E+09 C 6.14E+06 Full Penetration 18 880,807 5.14E+09 C 5.14E+06 External Collar 18 468,601 2.73E+09 D 7.97E+06 External Collar 18 337,390 1.97E+09 E 2.16E+07 Full Penetration 24 439,511 6.08E+09 C 6.08E+06 Full Penetration 24 343,175 4.74E+09 C 4.74E+06 Full Penetration 19.07 2,232,742 1.55E+10 B 3.78E+06 Full Penetration 24 490,061 6.77E+09 C 6.77E+06 Table B2. Test results (from Roy et al., 2011). Connection Detail Sr [ksi] No. of Cycles to Failure A [ksi3] Category as in ASSHTO- CAFL No. of Cycles Using Miner's Rule for Given CAFL Arm Base 12 1.80E+05 3.11E+08 E 3.41E+06 Hand hole 7 1.78E+06 6.11E+08 B 1.49E+05 Arm Base 12 3.70E+05 6.39E+08 E 7.02E+06 Hand hole 7 1.55E+06 5.32E+08 B 1.30E+05 Hand hole 7 2.10E+06 7.2E+08 B 1.76E+05 Arm Base 12 1.26E+06 2.18E+09 E 2.39E+07 Hand hole 7 2.47E+06 8.47E+08 B 2.07E+05 Arm Base 7 2.30E+06 7.89E+08 E 8.66E+06 Arm Base 7 3.11E+06 1.07E+09 E 1.17E+07

A-71 Arm Sleeve to Pole Connection 16 6.80E+05 2.79E+09 E 3.06E+07 Arm Sleeve to Pole Connection 12 4.30E+05 7.43E+08 E 8.15E+06 Connection Detail Sr [ksi] No. of Cycles to Failure A [ksi3] Category as in ASSHTO- CAFL No. of Cycles Using Miner's Rule for Given CAFL Arm Sleeve to Pole Connection 7.7 1.54E+06 7.03E+08 E 7.72E+06 Arm Sleeve to Pole Connection 16 6.80E+05 2.79E+09 E 3.06E+07 Arm Sleeve to Pole Connection 16 9.40E+05 3.85E+09 E 4.23E+07 Arm Base 11.9 1.61E+06 2.71E+09 D 7.91E+06 Hand hole 7 1.72E+06 5.9E+08 B 1.44E+05 Pole Base 6.9 1.98E+06 6.5E+08 D 1.90E+06 Arm Base 9.9 1.32E+06 1.28E+09 D 3.73E+06 Arm Base 11.9 1.88E+06 3.17E+09 D 9.24E+06 Hand hole 7 2.03E+06 6.96E+08 B 1.70E+05 Arm Base 9.9 1.41E+06 1.37E+09 D 3.99E+06 Hand hole 7 2.21E+06 7.58E+08 B 1.85E+05 Arm Base 9.9 1.17E+06 1.14E+09 D 3.31E+06 Arm Base 11.9 1.81E+06 3.05E+09 D 8.89E+06 Arm Base 9.9 1.29E+06 1.25E+09 D 3.65E+06 Arm Base 9.9 1.49E+06 1.45E+09 D 4.22E+06 Arm Base 11.9 1.55E+06 2.61E+09 D 7.62E+06 Arm Base 12 9.80E+05 1.69E+09 E 1.86E+07 Arm Base 12 1.86E+06 3.21E+09 E 3.53E+07 Arm Base 12 1.25E+06 2.16E+09 E 2.37E+07 Arm Base 10 6.96E+06 6.96E+09 E 7.64E+07 Arm Base 10 9.23E+06 9.23E+09 E 1.01E+08 Arm Base 16 5.84E+06 2.39E+10 E 2.63E+08 Arm Base 16 2.70E+05 1.11E+09 E 1.21E+07 Arm Base 16 4.79E+06 1.96E+10 E 2.15E+08 Arm Base 12 2.80E+05 4.84E+08 ET 2.80E+08 Arm Base 12 2.90E+05 5.01E+08 ET 2.90E+08 Arm Base 7 4.99E+06 1.71E+09 ET 9.90E+08 Pole Base 12 2.70E+05 4.67E+08 E 5.12E+06 Pole Base 12 1.10E+06 1.9E+09 E 2.09E+07 Pole Base 12 1.46E+06 2.52E+09 E 2.77E+07 Arm Sleeve to Pole Connection 7.7 4.51E+06 2.06E+09 E 2.26E+07 Arm Sleeve to Pole Connection 7.7 4.77E+06 2.18E+09 E 2.39E+07 Arm Sleeve to Pole Connection 7.7 5.82E+06 2.66E+09 E 2.92E+07 Arm Sleeve to Pole Connection 7.7 3.61E+06 1.65E+09 E 1.81E+07 Arm Sleeve to Pole Connection 7.7 3.61E+06 1.65E+09 E 1.81E+07 Arm Sleeve to Pole Connection 7.7 4.90E+06 2.24E+09 E 2.45E+07 Arm Sleeve to Pole Connection 7.7 1.11E+07 5.07E+09 E 5.56E+07 Arm Sleeve to Pole Connection 7.7 1.49E+07 6.8E+09 E 7.46E+07 Arm Sleeve to Pole Connection 7.7 1.54E+06 7.03E+08 E 7.72E+06 Arm Sleeve to Pole Connection 7.7 1.54E+06 7.03E+08 E 7.72E+06 Table B2. (Continued). (continued on next page)

A-72 Pole Base 11.6 5.90E+05 9.21E+08 D 2.68E+06 Pole Base 14 1.00E+05 2.74E+08 D 8.00E+05 Pole Base 14 1.00E+05 2.74E+08 D 8.00E+05 Pole Base 13.5 3.90E+05 9.6E+08 D 2.80E+06 Pole Base 13.5 4.70E+05 1.16E+09 D 3.37E+06 Pole Base 13.5 4.70E+05 1.16E+09 D 3.37E+06 Connection Detail Sr [ksi] No. of Cycles to Failure A [ksi3] Category as in ASSHTO- CAFL No. of Cycles Using Miner's Rule for Given CAFL Arm Sleeve to Pole Connection 12 6.30E+05 1.09E+09 E 1.19E+07 Arm Sleeve to Pole Connection 12 5.50E+05 9.5E+08 E 1.04E+07 Arm Sleeve to Pole Connection 12 7.50E+05 1.3E+09 E 1.42E+07 Arm Sleeve to Pole Connection 16 1.40E+05 5.73E+08 E 6.29E+06 Arm Sleeve to Pole Connection 16 3.40E+05 1.39E+09 E 1.53E+07 Pole Base 13.1 1.00E+06 2.25E+09 E 2.47E+07 Arm Base 12 4.00E+04 69120000 Ep 3.93E+06 Pole Base 6.6 9.00E+04 25874640 Ep 1.47E+06 Arm Base 12 4.00E+04 69120000 Ep 3.93E+06 Pole Base 6.6 9.00E+04 25874640 Ep 1.47E+06 Arm Base 12 1.00E+04 17280000 Ep 9.83E+05 Pole Base 6.6 1.00E+05 28749600 Ep 1.64E+06 Arm Base 4.5 1.03E+06 93858750 Ep 5.34E+06 Hand hole 26 3.27E+06 5.75E+10 B 1.40E+07 Arm Base 4.5 3.90E+05 35538750 Ep 2.02E+06 Hand hole 2.6 1.25E+07 2.2E+08 B 5.36E+04 Arm Base 2.5 7.00E+04 1093750 Ep 6.22E+04 Stiffener 12 5.90E+05 1.02E+09 Ep 5.80E+07 Stiffener 12 5.90E+05 1.02E+09 Ep 5.80E+07 Stiffener 12 2.70E+05 4.67E+08 Ep 2.65E+07 Stiffener 12 2.70E+05 4.67E+08 Ep 2.65E+07 Stiffener 12 5.10E+05 8.81E+08 Ep 5.01E+07 Stiffener 12 1.07E+06 1.85E+09 Ep 1.05E+08 Stiffener 10 4.50E+05 4.5E+08 Ep 2.56E+07 Stiffener 10 5.20E+05 5.2E+08 Ep 2.96E+07 Stiffener 7 3.08E+06 1.06E+09 Ep 6.01E+07 Stiffener 7 2.57E+06 8.82E+08 Ep 5.02E+07 Stiffener 4.5 2.64E+06 2.41E+08 Ep 1.37E+07 Stiffener 4.5 4.00E+06 3.65E+08 Ep 2.07E+07 Stiffener 16 1.20E+05 4.92E+08 Ep 2.80E+07 Stiffener 16 7.00E+04 2.87E+08 Ep 1.63E+07 Stiffener 16 1.30E+05 5.32E+08 Ep 3.03E+07 Stiffener 16 2.80E+05 1.15E+09 Ep 6.53E+07 Stiffener 16 1.20E+05 4.92E+08 Ep 2.80E+07 Stiffener 16 1.20E+05 4.92E+08 Ep 2.80E+07 Pole Base 8 1.75E+06 8.96E+08 E 9.83E+06 Pole Base 8 6.80E+05 3.48E+08 E 3.82E+06 Pole Base 12 7.50E+05 1.3E+09 D 3.78E+06 Pole Base 11.6 1.13E+06 1.76E+09 D 5.14E+06 Pole Base 12 1.56E+06 2.7E+09 D 7.86E+06 Pole Base 11.6 3.13E+06 4.89E+09 D 1.42E+07 Pole Base 12 3.30E+05 5.7E+08 D 1.66E+06 Pole Base 12 3.30E+05 5.7E+08 D 1.66E+06 Table B2. (Continued).

A-73 Table B2. (Continued). Stiffener 12 2.30E+05 3.97E+08 D 1.16E+06 Stiffener 12 5.30E+05 9.16E+08 D 2.67E+06 Pole Base 8.5 3.80E+05 2.33E+08 D 6.80E+05 Stiffener 12 4.00E+05 6.91E+08 D 2.02E+06 Stiffener 12 4.00E+05 6.91E+08 D 2.02E+06 Stiffener 12 5.80E+05 1E+09 D 2.92E+06 Stiffener 7 4.06E+06 1.39E+09 D 4.06E+06 Stiffener 16 1.50E+05 6.14E+08 D 1.79E+06 Stiffener 16 5.00E+04 2.05E+08 D 5.97E+05 Pole Base 11.3 5.00E+04 72144850 D 2.10E+05 Pole Base 11.3 3.00E+05 4.33E+08 D 1.26E+06 Pole Base 11.3 9.00E+04 1.3E+08 D 3.79E+05 Pole Base 11.3 3.00E+05 4.33E+08 D 1.26E+06 Stiffener 16 2.00E+05 8.19E+08 D 2.39E+06 Stiffener 16 3.80E+05 1.56E+09 D 4.54E+06 Stiffener 16 5.00E+04 2.05E+08 D 5.97E+05 Stiffener 16 1.10E+05 4.51E+08 D 1.31E+06 Pole Base 11.3 2.70E+05 3.9E+08 D 1.14E+06 Pole Base 16 1.40E+05 5.73E+08 D 1.67E+06 Pole Base 16 1.40E+05 5.73E+08 D 1.67E+06 Pole Base 15.4 6.00E+05 2.19E+09 D 6.39E+06 Pole Base 16 6.00E+04 2.46E+08 D 7.17E+05 Pole Base 16 1.50E+05 6.14E+08 D 1.79E+06 Pole Base 15.4 3.40E+05 1.24E+09 D 3.62E+06 Connection Detail Sr [ksi] No. of Cycles to Failure A [ksi3] Category as in ASSHTO- CAFL No. of Cycles Using Miner's Rule for Given CAFL

Abbreviations and acronyms used without definitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S.DOT United States Department of Transportation