Evaluating the Design Safety of Highway Structural Supports by Fouad H. Fouad and Elizabeth A. Calvert Department of Civil and Environmental Engineering The University of Alabama at Birmingham Birmingham, Alabama Prepared by UTCA University Transportation Center for Alabama The University of Alabama, The University of Alabama at Birmingham, and The University of Alabama in Huntsville UTCA Report Number 00218 August 2001
Technical Report Documentation Page 1. Report No FHWA/ 4. Title and Subtitle Evaluating the Design Safety of Highway Structural Supports 7. Authors Fouad H. Fouad and Elizabeth A. Calvert 9. Performing Organization Name and Address Department of Civil and Environmental Engineering The University of Alabama at Birmingham 1075 13 th Street South, Suite 120 Birmingham, Alabama 35294 12. Sponsoring Agency Name and Address University Transportation Center for Alabama University of Alabama Box 870205 Tuscaloosa, AL 35487-0205 15. Supplementary Notes 2. Government Accession No. 3. Recipient Catalog No. 5. Report Date August 2001 6. Performing Organization Code 8. Performing Organization Report No. 10. Work Unit No. 11. Contract or Grant No. DTRS98-G-0028 13. Type of Report and Period Covered Final Report; January 1, 2000 - August 19, 2001 14. Sponsoring Agency Code 16. Abstract The American Association of State Highway and Transportation Officials (AASHTO) Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals was revised in its entirety through a major research project conducted under the auspices of the National Cooperative Highway Research Program (NCHRP Project 17-10). The new document was approved in 1999 by AASHTO for adoption by all state departments of transportation, and was published in 2001. A major change involved new provisions and criteria for wind loads. These provisions differed considerably from those in previous editions of the specifications. This research project studied the impact of the new wind load provisions on the design of structural supports from the standpoint of safety and economy. Wind loads and design examples for various types of structural supports in Alabama were analyzed using both the 2001 and 1994 editions of the AASHTO specifications. The results were compared and the impacts of the 2001 specifications on the design of support structures in Alabama were illustrated by the project. 17. Key Words extreme wind loads, highway signs, roadside signs, street lighting poles, high mast lighting poles, structural supports 19. Security Classif (of this report) 20. Security Classif. (of this page) 18. Distribution Statement 21. No of Pages 65 22. Price Form DOT F 1700.7 (8-72) ii
Contents Contents..... List of Figures List of Tables..... List of Graphs... Executive Summary... iii iv v vi viii 1.0 Introduction... 1 Problem Statement........ 1 Objective and Approach...... 2 Task 1. Identify Changes in Wind Map.. 2 Task 2. Investigate Impact of New Wind Provisions on Design of Structural Supports.. 2 2.0 Historical Perspective.... 3 3.0 Wind Load Comparisons for 1994 vs. 2001 AASHTO Supports Specifications... 4 Wind Maps for Alabama. 4 Selection of Cities 4 Site Groupings. 5 Wind Pressure Comparison. 5 Summary. 6 4.0 Design Comparisons for 1994 vs. 2001 AASHTO Supports Specifications. 7 Design Examples. 7 High Mast Lighting Pole 7 Street Lighting Pole Example No. 1,.. 8 Street Lighting Pole Example No. 2... 8 Roadside Sign. 9 Summary.. 10 5.0 Summary and Recommendations.. 11 Summary 11 Recommended Future Work,. 11 6.0 Acknowledgements.... 12 7.0 References.. 13 Appendix A: Figures..... 14 Appendix B: Tables.. 25 Appendix C: Graphs......... 42 iii
List of Figures Number Page A-1 Wind Map: 50-Year Mean Recurrence Interval (Thom, 1968).. 15 A-2 Wind Map: 25-Year Mean Recurrence Interval (Thom, 1968).. 15 A-3 Wind Map: 10-Year Mean Recurrence Interval (Thom, 1968).. 16 A-4 Basic Wind Speed (ANSI/ASCE 7-95).. 16 A-5 Basic Wind Speed for Alabama (AASHTO, 2001)... 17 A-6 Wind Speed for Alabama, 50-Year Mean Recurrence Interval (AASHTO, 1994)... 18 A-7 Wind Speed for Alabama, 25-Year Mean Recurrence Interval (AASHTO, 1994)... 19 A-8 Wind Speed for Alabama, 10-Year Mean Recurrence Interval (AASHTO, 1994)... 20 A-9 High Mast Lighting Pole Example. 21 A-10 Street Lighting Pole Example No. 1... 22 A-11 Street Lighting Pole Example No. 2.. 23 A-12 Roadside Sign Example. 24 iv
List of Tables Number Page 3-1 Wind Site Classifications for Alabama Cities... 5 B-1 Wind Pressure for 1994 AASHTO Specifications... 26 B-2 Wind Pressure for 2001 AASHTO Specifications (50-Year MRI)... 27 B-3 Wind Pressure for 2001 AASHTO Specifications (25-Year MRI)... 28 B-4 Wind Pressure for 2001 AASHTO Specifications (10-Year MRI)... 29 B-5 Wind Sites Sorted by County 30 B-6 Wind Sites Sorted by Wind Speed 32 B-7 Pole Size and Reactions for High Mast Lighting Pole Example (AASHTO 1994). 35 B-8 Pole Size and Reactions for High Mast Lighting Pole Example (AASHTO 2001). 35 B-9 Difference in Weight and Reactions for High Mast Lighting Pole Example... 36 B-10 Pole Size and Reactions for Street Lighting Pole Example No. 1 (AASHTO 1994). 36 B-11 Pole Size and Reactions for Street Lighting Pole Example No. 1 (AASHTO 2001). 37 B-12 Difference in Weight and Reactions for Street Lighting Pole Example No. 1.. 37 B-13 Pole Size and Reactions for Street Lighting Pole Example No. 2 (AASHTO 1994). 38 B-14 Pole Size and Reactions for Street Lighting Pole Example No. 2 (AASHTO 2001). 38 B-15 Difference in Weight and Reactions for Street Lighting Pole Example No. 2.. 39 B-16 Summary of Support Sized for Roadside Sign Example.. 39 B-17 Member Size and Reactions for Roadside Sign Example (AASHTO 1994) 40 B-18 Member Size and Reactions for Roadside Sign Example (AASHTO 2001)... 41 B-19 Difference in Weight and Reactions for Roadside Sign Example. 41 v
List of Graphs Number Page C-1 Wind Pressures for 50-Year MRI. 43 C-2 Wind Pressures for 25-Year MRI. 44 C-3 Wind Pressures for 10-Year MRI. 45 C-4 Site No. 1: Effective Wind Pressure..... 46 C-5 Site No. 1: Ratio of Wind Pressures (2001 to 1994 Specifications) 46 C-6 Site No. 2: Effective Wind Pressure..... 47 C-7 Site No. 2: Ratio of Wind Pressures (2001 to 1994 Specifications) 47 C-8 Site No. 3: Effective Wind Pressure..... 48 C-9 Site No. 3: Ratio of Wind Pressures (2001 to 1994 Specifications) 48 C-10 Site No. 4: Effective Wind Pressure..... 49 C-11 Site No. 4: Ratio of Wind Pressures (2001 to 1994 Specifications) 49 C-12 Site No. 5: Effective Wind Pressure..... 50 C-13 Site No. 5: Ratio of Wind Pressures (2001 to 1994 Specifications) 50 C-14 Site No. 6: Effective Wind Pressure..... 51 C-15 Site No. 6: Ratio of Wind Pressures (2001 to 1994 Specifications) 51 C-16 Site No. 7: Effective Wind Pressure..... 52 C-17 Site No. 7: Ratio of Wind Pressures (2001 to 1994 Specifications) 52 C-18 Site No. 8: Effective Wind Pressure..... 53 C-19 Site No. 8: Ratio of Wind Pressures (2001 to 1994 Specifications) 53 C-20 Site No. 9: Effective Wind Pressure..... 54 C-21 Site No. 9: Ratio of Wind Pressures (2001 to 1994 Specifications) 54 C-22 Site No. 10: Effective Wind Pressure... 55 C-23 Site No. 10: Ratio of Wind Pressures (2001 to 1994 Specifications). 55 C-24 50-Year MRI: Range of Ratios of Wind Pressures (2001 to 1994 Specifications).. 56 C-25 25-Year MRI: Range of Ratios of Wind Pressures (2001 to 1994 Specifications).. 56 C-26 10-Year MRI: Range of Ratios of Wind Pressures (2001 to 1994 Specifications).. 57 C-27 Comparison of Support Weight for High Mast Lighting Pole Example.. 57 C-28 Comparison of Ground Line Moments for High Mast Lighting Pole Example 58 C-29 Comparison of Shear Forces for High Mast Lighting Pole Example... 58 C-30 Percent Change in Weight, Moment, and Shear for High Mast Lighting Pole Example 59 C-31 Comparison of Support Weight for Street Lighting Pole Example No. 1. 59 C-32 Comparison of Ground Line Moments for Street Lighting Pole Example 1 60 C-33 Comparison of Shear Forces for Street Lighting Pole Example No. 1. 60 C-34 Percent Change in Weight, Moment, and Shear for Street Lighting Pole Example No. 1.. 61 vi
List of Graphs (continued) C-35 Comparison of Support Weight for Street Lighting Pole Example No. 2. 61 C-36 Comparison of Ground Line Moments for Street Lighting Pole Example No. 2.. 62 C-37 Comparison of Shear Forces for Street Lighting Pole Example No. 2. 62 C-38 Percent Change in Weight, Moment, and Shear for Street Lighting Pole Example No. 2... 63 C-39 Comparison of Support Weight for Roadside Sign Example... 63 C-40 Comparison of Ground Line Moments for Roadside Sign Example 64 C-41 Comparison of Shear Forces for Roadside Sign Example.... 64 C-42 Percent Change in Weight, Moment, and Shear for Roadside Sign Example... 65 vii
Executive Summary The American Association of State Highway and Transportation Officials (AASHTO) Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals was revised in its entirety through a major research project conducted under the auspices of the National Cooperative Highway Research Program (NCHRP Project 17-10). The new document was approved in 1999 by AASHTO for adoption by all state departments of transportation, and was published in 2001. A major change involved new provisions and criteria for wind loads. These provisions differed considerably from those in previous editions of the specifications. This research project studied the impact of the new wind load provisions on the design of structural supports from the standpoint of safety and economy. Wind load calculations in the 2001 Supports Specifications were revised to use a three-second gust wind speed, rather than a fastest-mile wind speed. A series of maps, representing 10, 25, and 50-year mean recurrence intervals, was reduced to one 50-year mean recurrence interval map with importance factors used to adjust the intervals. Height factors were adjusted for the threesecond gust wind speed, and drag coefficients were slightly modified. The increase or decrease in calculated wind pressures, which result from the use of the 2001 Supports Specifications, is primarily due to the differences in the 1994 and 2001 wind speed maps. The Alabama wind map in the 2001 Supports Specifications can be divided into two wind speed regions: 1) 90 mph for the upper 80% of the state, and 2) 100 mph to 140 mph in the hurricane region. These correspond to fastest-mile wind speeds ranging from 60 to 100 mph depending on the site location and the mean recurrence interval as depicted by the AASHTO 1994 Supports Specifications wind maps. Differences in wind loads computed according to the two specifications are therefore site-specific. Comparisons to illustrate the effect of the new wind map should take into consideration specific site locations across the State of Alabama. The tasks conduced during this research project included identifying changes in the wind map by comparing Alabama wind pressures for the 1994 and new 2001 specifications for the 10, 25, and 50-year mean recurrence intervals. Design wind loads from the different wind speed maps and calculation methods were compared for a large number of cities across Alabama to determine the effect of the new wind provisions on the design of structural supports. Wind load calculations and design examples for various types of structural supports in Alabama were performed using both the newly published 2001 AASHTO specifications and the 1994 edition of the specifications. The results are compared and impact of the 2001 specifications on design of support structures in Alabama is illustrated. For 80% of the land area in Alabama (the northern and central portions of the state), only a slight increase in wind pressure occurred from the 1994 to the 2001 specifications. The design weight for the four examples changed by 10% or less. viii
For the lower 20% of Alabama, the wind pressures increased significantly, especially near the coastline. Support structures designed for the 25-year and 10-year mean recurrence intervals were affected the most. In comparing the 1994 and 2001 wind specifications, it is apparent that changes in wind pressure, either decreasing or increasing, are highly site-specific. Changes are also dependent on wind elevation and structure type (i.e., mean recurrence interval). It should also be pointed out that several other changes in the 2001 specifications, not directly related to the wind map, may significantly influence the design. These changes are related to the allowable stress equations for steel, the increase in allowable stress for Group II loading, and the calculation of second-order effects. ix
Section 1.0 Introduction An examination of the 1994 American Association of State Highway and Transportation Officials (AASHTO) Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals (AASHTO, 1994), hereafter referred to as the Supports Specifications, reveals that the wind loading criteria are based primarily on information and procedures that were first advanced in the early 1960 s and 1970 s. Through the work of National Cooperative Highway Research Program (NCHRP) Project 17-10 (Fouad et al, 1998), significant changes were introduced in the 2001 Supports Specifications (AASHTO, 2001), which affect the presentation, terminology, and calculated wind loads. The major changes in the 2001 Supports Specifications are primarily due to an updated wind map. These changes may result in either an increase or a decrease in the magnitude of calculated wind pressure depending on the site location. The 2001 Supports Specifications was approved in 1999 by AASHTO for adoption by all state departments of transportation, and was published in 2001. Wind load calculations in the 2001 Supports Specifications were revised to use a three-second gust wind speed, rather than a fastest-mile wind speed. A series of maps, representing 10, 25, and 50-year mean recurrence intervals, was reduced to one 50-year mean recurrence interval map with importance factors used to adjust the intervals. Height factors were adjusted for the threesecond gust wind speed and drag coefficients were slightly modified. The increase or decrease in calculated wind pressures, which result from the use of the 2001 Supports Specifications, is primarily due to the differences in the 1994 and 2001 wind speed maps. The 2001 Supports Specifications has been updated to reflect currently accepted design procedures to calculate wind loads. The wind loads portion of the 2001 specifications is based on the 1995 version of ASCE 7 (ASCE, 1995), and modified specifically for structural supports for highway signs, luminaries, and traffic signals. ASCE 7 Minimum Design Loads for Buildings and Other Structures is considered the most authoritative standard on wind loading in the United States, and most design codes and specifications have generally adopted or referenced ASCE 7. Problem Statement A major concern about the newly published 2001 Supports Specifications was the use of a new wind map and wind provisions that may result in significant changes in the applied loads on structural supports. As a result, structures can be under-designed or over-designed based on their geographic location. Until this project, no studies had been performed to investigate the impact of the new 2001 Supports Specifications on the design of structural supports in Alabama. The wind map for Alabama in the 2001 Supports Specifications can be divided into two wind speed regions: 1) 90 mph for the upper 80% of the state, and 2) 100 mph to 140 mph in the hurricane region; corresponding fastest-mile wind speeds range from 60 to 100 mph depending on the site location and the mean recurrence interval depicted by the AASHTO 1994 Supports Specifications wind maps. Differences in wind loads computed according to the two 1
specifications are therefore site-specific. Comparisons to illustrate the effect of the new wind map should take into consideration specific site locations across the State of Alabama. Objective and Approach The main objective of this study was to evaluate the safety and economy of structural supports for highway signs, luminaires, and traffic signals in the State of Alabama that are designed in accordance with the new wind load provisions adopted by AASHTO. The following tasks were performed as part of the project. Task 1. Identify Changes in Wind Map Generalized comparisons of wind pressures for the State of Alabama were performed to compare the 1994 and newly published 2001 specifications for the 10, 25, and 50-year mean recurrence intervals. These comparisons illustrated the differences between both specifications as related to the wind speeds, height coefficients, gust factors, and mean recurrence intervals (or importance factors). Task 2. Investigate Impact of the New Wind Provisions on Design of Structural Supports Analysis and design were performed on three types of support structures located in sites across Alabama. Comparisons of structure weights, ground line moments, and shear forces were made between the 1994 and 2001 specifications. Main member sizes and weights were provided to illustrate the magnitude of changes in safety margins and economy of structural supports designed in accordance with the new wind load provisions. 2
Section 2.0 Historical Perspective The first wind load standard containing wind speed maps was published by the American National Standards Institute (ANSI, formerly ASA), Standard A58.1, in 1972 (ANSI, 1972). The design basis wind speed was given as the fastest-mile wind speed. Figures A-1, A-2 and A- 3 (in Appendix A) provide the 50, 25, and 10-year mean recurrence interval wind maps (Thom, 1968) that were published by ANSI and later adopted by the AASHTO 1985 Supports Specifications (AASHTO, 1985). Up until 1994, the AASHTO Supports Specifications (AASHTO, 1994) continued to use these maps that were produced by Thom in the late 1960s. A revision to the wind load standard was published by ANSI in 1982 (ANSI, 1982). This standard separated loads for the main wind-force resisting system and the components and cladding of buildings. In addition, it used one wind speed map for 50-year mean recurrence interval (MRI) and introduced the importance factor to obtain wind speeds for other MRIs. In the mid-1980s, the American Society of Civil Engineers (ASCE) assumed responsibility for the committee that establishes design loads for buildings and other structures. ASCE Committee 7 made minor changes to the ANSI A58.1-1982 provisions and published the revised version as ASCE 7-88 (ASCE, 1990). A revised version of ASCE 7-88 was published as ASCE 7-93 (ASCE, 1993) with no changes in wind load provisions. In 1995, ASCE published ASCE 7-95 (ASCE, 1995), which included major changes to wind load provisions and featured a new wind map based on three-second gust wind speeds. Adopting the use of three-second gust design wind speed instead of fastest-mile wind speed required modification of exposure (height and terrain) coefficients, gust effect factors, importance factors, and some pressure coefficients. The ANSI/ASCE 7-95 is the basis for the wind load provisions of the newly published 2001 AASHTO Supports Specifications. This map has been adopted for use in the 2001 Supports Specifications and is shown in Figure A-4. ASCE published a new edition of the loading standard in 2000. ASCE 7-98 (ASCE, 2000) included some additional revisions to the wind load provisions such as refinement of wind speed contours in hurricane regions and the addition of a directionality factor. However, these changes were not as drastic as those presented in ASCE 7-95. The ASCE 7-98 wind map is now being considered by the AASHTO committee for possible inclusion in the next revision of the 2001 AASHTO Supports Specifications. 3
Section 3.0 Wind Load Comparisons for 1994 Vs. 2001 AASHTO Supports Specifications The changes in the wind loading criteria provided by the 2001 AASHTO specifications represent a major and fundamental update to the wind loading criteria of 1994 Supports Specifications. These changes, representing over 20 years of progress in the wind technology, update the Supports Specifications to the most current wind methodology. The effects of changing the wind loading criteria and wind map are reviewed in this section of this report. Differences in design wind loads as a result of using different wind speed maps and calculation methods were compared for a large number of cities across the State of Alabama in an effort to ascertain the effect of the new wind provisions on the design of structural supports. A comprehensive list of 69 cities in Alabama was selected for evaluation in this study. The list was representative of urban and rural areas in Alabama. Comparisons were made between the 2001 and 1994 specifications for counties that had the same wind speed design criteria. For each site, comparisons were made between the 2001 and 1994 specifications by calculating wind pressures for the 10, 25, and 50-year mean recurrence intervals (MRI). For the 1994 specifications, wind pressures were calculated per Section 1.2.5(A) with a drag coefficient of 1.0. For the 2001 specifications, wind pressures were calculated per Section 3.8.1 with a drag coefficient of 1.0. Wind Maps for Alabama The three wind maps of the 1994 specifications and the basic wind speed map of the 2001 specifications have been trimmed and enlarged to focus on Alabama. For the 2001 specifications, Figure A-5 provides the basic wind speed for Alabama. Importance factors are used to vary the mean recurrence interval. Three wind maps for Alabama, based on the 1994 specifications, are shown in Figures A-6 through A-8. They represent the 50, 25, and 10-year mean recurrence interval. The 50-year mean recurrence interval (Figure A-6) is generally used for high mast lighting poles and overhead sign structures. For structure types such as street lighting poles and traffic signal poles, the 25-year mean recurrence interval map (Figure A-7) is normally used. The 10-year mean recurrence interval map (Figure A-8) is typically used for roadside signs. Wind pressures have been calculated for the 1994 specifications in Table B-1 and for the 2001 specifications in Tables B-2, B-3, and B-4 for the 50, 25, and 10-year MRI, respectively. Graphs C-1, C-2, and C-3 provide a general comparison of wind pressures of the 1994 and 2001 specifications for the 50, 25, and 10-year MRI. For the 50-year MRI, design wind speeds of 70, 80, 90, and 100 mph in the 1994 specifications are comparable to 90, 100, 115, and 125 mph in the 2001 specifications. For the 25-year MRI, design wind speeds of 70 and 80 mph are comparable to 95 and 115 mph in the 2001 specifications. For the 10-year MRI, the 60 mph design wind speed in the 1994 specifications is comparable to 90 mph in the 2001 specifications. Selection of Cities A list of 69 cities selected for study is shown in Table B-5, sorted by county. This list provides wind sites that include population centers, as well as the rural parts of Alabama. The county seats for the 67 counties of Alabama, plus two coastline cities, are provided in the list. 4
Site Groupings The basic wind speed and importance factors for the 50, 25, and 10-year mean recurrence intervals for the 2001 AASHTO specifications, as well as the 50, 25, and 10-year wind speeds from the 1994 AASHTO specifications, were determined for each of the 69 cities, as shown in Table B-5. The 69 cities were sorted by three-second gust wind speed for the 2001 specifications, and by the 50, 25, and 10-year wind speeds for the 1994 AASHTO specifications (Table B-6). As shown in Table B-6, the 69 cities can be grouped into 10 site-specific locations, which have the same three-second gust wind speed, as well as the same 50, 25, and 10-year wind speeds from the 1994 AASHTO specifications. The 10 wind sites that are the basis of this study are summarized below in Table 3-1. It is interesting to note that approximately 80% of the cities are located in Wind Site Number 1. Table 3-1: Wind Site Classifications for Alabama Cities. Wind Site No. No. of Cities Representing 1 53 Approximately upper 80% of Alabama 2 1 3 2 4 4 5 3 6 1 7 1 8 1 9 1 Transitional hurricane winds for approximately lower 20% of Alabama 10 2 Coastline of Alabama Total 69 Wind Pressure Comparison For each of the 10 site-specific locations, the wind pressure was calculated for heights from ground line to 200 feet above ground line for the 2001 and 1994 specifications. Graphs C-4 through C-23 show the effective wind pressure for 50, 25, and 10-year mean recurrence intervals, as well as the ratio of wind pressures for the 2001 to 1994 specifications. The numbers in parentheses are the number of cities out of 69 that are represented by the data. As shown in the graphs, the wind pressure distribution according to the 1994 specifications exhibits a step function, whereas the 2001 specifications has a gradual change of wind pressure with height. The ratio of wind pressures varies with height, but can be divided into two sets of data, those with heights above 15 feet and those with heights less than 15 feet. All graphs show a higher wind pressure ratio for heights less than 15 feet than for heights greater than 15 feet. The graphs for heights less than 15 feet would be applicable for small and medium roadside signs, which typically employ a 10-year mean recurrence interval. The graphs also indicate that the wind pressure ratios for the 2001 to 1994 specifications vary with the mean recurrence interval, which implies that changes in wind pressures, when upgrading from the 1994 to 2001 specifications, will vary for different structure types at a specific site. Graphs C-24 through C-26 show the average and range of ratios of wind pressures for the 2001 to 1994 specifications for the 50, 25, and 10-year mean recurrence intervals for the ten sites in 5
Alabama. In general, the range of wind pressure ratios will vary from approximately 12% to +16% from the average ratio, with a slightly larger range near the coastline. Changes in wind pressures for Site 1, which represents approximate 80% of the land area in Alabama, indicate, on average, a change in wind pressure of 5% increase, 9% decrease, and 1% increase for 50, 25, and 10-year mean recurrence intervals, respectively. The change in wind pressure for all sites could vary as much as 18% to +110% and is dependent on wind speed, elevation, and mean recurrence interval. The largest increase occurs for the 10-year mean recurrence interval on the coastline. For the 50-year mean recurrence interval structures (Graph C-24), Site 2 shows an average of 10% decrease in wind pressure. Sites 5 and 7 show the greatest average increase in wind pressure of 35% and 31%, respectively. Sites 1, 3, 4, and 6 show an average increase of 5%, 17%, 13%, and 20%, respectively. For Sites 8, 9, and 10 near the coastline, wind pressures show an increase of 26%, 22% and 24%. For the 25-year MRI structures (Graph C-25), Sites 1 and 2 show an average of 10% decrease in wind pressure. Sites 3, 4, 5, 6, and 7 show an average increase of 1%, 12%, 25%, 25%, and 37%, respectively. Sites 8, 9, and 10 near the coastline show an average of 50%, 68%, and 55% increase in wind pressure. For the 10-year MRI structures (Graph C-26), Sites 1 and 2 show an average of 1% increase in wind pressure. Site 3 shows an average of 15% increase in wind pressure. Sites 4, 5, 6, and 7 show an average increase of 25%. Sites 8, 9, and 10 near the coastline show an average of 37%, 48%, and 86% increase in wind pressure. Summary Only a slight change in wind pressure will occur for 80% of Alabama, which is represented by Site 1. The greatest increase in wind pressure will occur near the coastline, as represented by Sites 8, 9, and 10, for 25-year MRI structures (i.e., street lighting poles and traffic signal structures) and for 10-year MRI structures (i.e., roadside signs). For 50-year MRI structures (overhead signs and high mast lighting structures), the greatest increase in wind pressure occurs in Sites 5 and 7. In comparing the 1994 versus the 2001 wind specifications, it is apparent that changes in wind pressure, either decreasing or increasing, are highly site-specific. Changes are also dependent on wind elevation and structure type (i.e., mean recurrence interval). 6
Section 4.0 Design Comparisons for 1994 Vs. 2001 AASHTO Supports Specifications Design Examples Three structure types were selected so that structure weights, ground line moments, and shear forces could be compared between the 1994 and 2001 specifications for all ten wind sites. The structure types were a high mast lighting pole, two street lighting poles, and a roadside sign structure, which are recommended to be designed for 50, 25, and 10-year mean recurrence intervals as provided in Section 3.8.3 and Table 3-3 of the 2001 specifications and in Section 1.2.4 of the 1994 specifications. High Mast Lighting Pole A 160-foot high mast lighting pole was designed for a 50-year mean recurrence interval. The configuration is shown in Figure A-9. The structure was designed based on an effective project area of 50 square feet at the top of the pole and a light fixture dead weight of 1000 pounds. The pole is a hollow tapered steel pole with a hexdecagonal cross section. The yield stress for the steel is 65 ksi. For the 1994 specifications, group load combination II (dead load plus wind) was applied per Section 2 with an increase in allowable stresses of 1.4. Design considerations for the 1994 specifications include meeting the allowable stresses of Section 4 for a hexdecagonal steel shape. Second-order moments were calculated using the alternative method of Section 1.3.3.A(2). Deflections were limited to 15%, as recommended in the commentary of Section 1.9.1(B). For the 2001 specifications, group load combination II (dead load plus wind) was applied per Section 3 with an increase in allowable stress of 1.33. Design consideration for the 2001 specifications included meeting the allowable stresses of Section 5 for a hexdecagonal steel shape. Second-order moments were calculated using the detailed method of Section 4.8.2. Deflections were limited to 15%, as required by Section 10.4.2.1. In general, limits on allowable stresses and deflection controlled the design for the 1994 and 2001 specifications. Pole sizes and reactions are provided in Table B-7 for the 1994 specifications and in Table B-8 for the 2001 specifications. Comparisons between the two specifications for weights, ground line moments, and ground line shear forces can be found in Graphs 27, 28, and 29. Percent difference in weight, ground line moments, and shear forces are provided in Table B-9 and Graph C-30. Site 1 shows an 8% increase in pole weight even though there was little increase in wind load. This design indicates that changes in the specifications that are unrelated to wind loads could also influence the design. For the high mast lighting pole, these changes include the following: 1. changes in allowable stress equations for hexdecagonal steel sections. 2. changes in the method of calculating the second-order moments (i.e., factor in the detailed method was changed from 1.38 to 1.45). 3. changes in the increase in allowable stresses under dead load plus wind from 1.4 to 1.33. Site 2 shows a 3% decrease in weight. Site 4 shows a 4% increase in weight. Sites 3, 5, 6, 7, 8, 9, and 10 show 12 to 20% increase in weight. 7
Street Lighting Pole Example No. 1 Two street lighting poles were designed for the 25-year mean recurrence interval. The configuration for street lighting pole example number 1 is shown in Figure A-10. The structure was designed for a single 10-foot mast arm weighting 75 pounds and a luminaire weighing 50 pounds. The effective projected area is 4.4 square feet for the mast arm and 1.4 square feet for the luminaire. The 40-foot pole is a hollow tapered steel pole with a round cross section. The yield stress for the steel is 65 ksi. For the 1994 specifications, group load combination II (dead load plus wind) was applied per Section 2 with an increase in allowable stresses of 1.4. Design considerations for the 1994 specifications include meeting the allowable stresses of Section 4 for a round steel shape. Second-order moments were calculated using the alternative method of Section 1.3.3.A(2). Slope at the tip under dead load is recommended to be limited to 0.35 inch per foot at the tip per Section 9. For the 2001 specifications, group load combination II (dead load plus wind) was applied per Section 3 with an increase in allowable stress of 1.33. Design consideration for the 2001 specifications included meeting the allowable stresses of Section 5 for a round steel shape. Second-order moments were calculated using the detailed method of Section 4.8.2. The slope at tip was limited to 0.35 inch per foot as required by Section 10.4.2.1. The serviceability criteria of limiting the slope at the tip under dead load to 0.35 inch per foot controlled the design for the 1994 and 2001 specifications. Pole sizes and reactions are provided in Table B-10 for the 1994 specifications and in Table B-11 for the 2001 specifications. Comparisons between the two specifications for weights, ground line moments, and ground line shear forces can be found in Graphs C-31, C-32 and C-33. Percent difference in weight, ground line moments, and shear forces are provided in Table B-12 and Graph C-34. The pole size for this structure configuration is the same from both specifications and for all wind speeds. The serviceability requirement of limiting the slope at the tip controlled the pole design. Since this requirement is the same in both specifications, no differences in pole weight occurred. The significant increases in moments and shear forces (up to 48% for Site 9) did not influence the pole design (size) for this particular configuration. Street Lighting Pole Example No. 2 The configuration for street lighting pole example number 2 is shown in Figure A-11. The structure was designed for a double 10-foot mast arm and luminaire. The weight is 75 pounds per mast arm and 50 pounds per luminaire. The effective projected area is 4.4 square feet for each mast arm and 1.4 square feet for each luminaire. The 40-foot pole is a hollow tapered steel pole with a round cross section. The yield stress for the steel is 65 ksi. For the 1994 specifications, group load combination II (dead load plus wind) was applied per Section 2 with an increase in allowable stresses of 1.4. Design considerations for the 1994 specifications include meeting the allowable stresses of Section 4 for a round steel shape. Second-order moments were calculated using the alternative method of Section 1.3.3.A(2). Deflections were limited to 15%, as recommended in the commentary of Section 1.9.1(B). Slope 8
limit under dead load as provided in Section 9 is not applicable, since the balanced twin mast arm configuration eliminates the dead load moment at the tip of the pole. For the 2001 specifications, group load combination II (dead load plus wind) was applied per Section 3 with an increase in allowable stress of 1.33. Design consideration for the 2001 specifications included meeting the allowable stresses of Section 5 for a round steel shape. Second-order moments were calculated using the detailed method of Section 4.8.2. Deflections were limited to 15%, as required by Section 10.4.2.1. In general, limits on allowable bending stresses and deflection controlled the design for the 1994 and 2001 specifications. Pole sizes and reactions are provided in Table B-13 for the 1994 specifications and in Table B-14 for the 2001 specifications. Comparisons between the two specifications for structure weights, ground line moments, and ground line shear forces can be found in Graphs C-35, C-36 and C-37. Percent difference in weight, ground line moments, and shear forces are provided in Table B-15 and Graph C-38. Sites 1 and 2 show very little change in pole weight even though there is an 8% decrease in wind loads per the 2001 specifications. This design indicates that other changes in the specifications that are unrelated to wind loads are influencing the design. For the street lighting pole example number 2, these changes include the following 1. changes in allowable stress equations for round steel sections. 2. changes in the method of calculating the second-order moments (i.e., factor in the detailed method was changed from 1.38 to 1.45). 3. changes in the increase in allowable stresses for the dead load plus wind load case from 1.4 to 1.33. Site 8, 9, and 10 show the greatest increase in ground line shear forces and moments. Shear forces increased for each of these sites by 44%, 54%, and 44%, and pole weights increased by 18%, 24%, and 31%, respectively, which was primarily due to the increase in bending moments. Roadside Sign The roadside sign structure shown in Figure A-12 was designed for the 10-year mean recurrence interval. The sign had dimensions of 8 feet tall by 16 feet wide and was supported by two steel wide flange posts with yield stress of 36 ksi. For the 1994 specifications, group load combination II (dead load plus wind) was applied per Section 2 with an increase in allowable stresses of 1.4. Design considerations for the 1994 specifications include meeting the allowable stresses of Section 4 for a wide-flange steel shape. For the 2001 specifications, group load combination II (dead load plus wind) was applied per Section 3 with an increase in allowable stress of 1.33. Design consideration for the 2001 specifications included meeting the allowable stresses of Section 5 for a wide flange steel shape. The limits on allowable bending stresses controlled the design for the 1994 and 2001 specifications. Post sizes are summarized in Table B-16. Post sizes and reactions are provided in Table B-17 for the 1994 specifications and in Table B-18 for the 2001 specifications. Comparisons between the two specifications for weights, ground line moments, and ground line 9
shear forces can be found in Graphs C-39, C-40 and C-41. Percent difference in weight, ground line moments, and shear forces are provided in Table B-19 and Graph C-42. For the roadside sign, all sites show an increase in weight that is comparable to the increase in wind loads. Designs were influenced by the fact that the greatest increase for all sites occurred for wind elevations that are less than 15 feet. Almost all roadside signs are in this category. The design modification where the increase in allowable stresses under dead load plus wind changed from 1.4 to 1.33 also influenced the design. Sites 1, 2, and 3 show an increase in post weight by approximately 10%. Sites 4 through 9 show an increase in weight of 40%. Site 10 shows the greatest impact on roadside sign design, where the post weight increased by 100%, while shear forces at ground line increased by approximately 118%. Summary Site 1, which covers 80% of Alabama, had moderate changes in structure weights. The high mast lighting pole had an 8% increase in pole weight. Street lighting poles numbers 1 and 2 had no change in pole weight. The roadside sign had a 10% increase in post weight. The sites that are close to the coastline in the lower 20% of Alabama had significant increases in wind loads and greater increases in structure weights. The weights for high mast lighting pole for Sites 5 through 10 increased between 10 and 20%. The pole weights for street lighting pole number 2 increased by 12%, 18%, 24%, and 31% for Sites 7, 8, 9, and 10, respectively. The post weights for Sites 4 through 9 increased by 44%, while post weight at Site 10 increased by 100%. 10
Section 5.0 Summary and Recommendations Summary For 80% of the land area in Alabama (the northern and central portions of the state), only a slight increase in wind pressure occurred from the 1994 to the 2001 specifications. The design weight for the four examples changed by 10% or less. For the lower 20% of Alabama, the wind pressures increased significantly, especially near the coastline. Support structures designed for the 25-year and 10-year mean recurrence intervals were affected the most. In comparing the 1994 and 2001 wind specifications, it is apparent that changes in wind pressure, either decreasing or increasing, are highly site-specific. Changes are also dependent on wind elevation and structure type (i.e., mean recurrence interval). It should also be pointed out that several other changes in the 2001 specifications, not directly related to the wind map, may significantly influence the design. These changes are related to the allowable stress equations for steel, the increase in allowable stress for Group II loading, and the calculation of second-order effects. Recommended Future Work Recommendations for future work include the following: 1. Present the impact of the 2001 specifications on the design of support structures in a workshop for the Alabama DOT. 2. Determine the impact of the new Section 11: Fatigue in the 2001 specifications on the design of structures. 3. Determine the impact of the 2001 specifications on other types of support structures, specifically overhead sign structures and traffic signal structures. 4. Study the new wind load provisions of ASCE 7-98, including the revised wind map, to determine if such changes should be incorporated in the future revisions of the AASHTO Supports Specifications. 11
Section 6.0 Acknowledgments This project was sponsored by The University Transportation Center for Alabama, which is supported by the U.S. Department of Transportation. Matching funds for the project were provided by the Department of Civil and Environmental Engineering at The University of Alabama at Birmingham. 12
Section 7.0 References AASHTO, Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals. American Association of State Highway and Transportation Officials, Washington, D.C. (1985) 69 pp. AASHTO, Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals. Third Edition, American Association of State Highway and Transportation Officials, Washington, D.C. (1994) 78 pp. AASHTO, Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals. Fourth Edition, American Association of State Highway and Transportation Officials, Washington, D.C. (2001) 270 pp. ANSI, Building Code Requirements for Minimum Design Loads in Buildings and Other Structures. ANSI A58.1-1972, American National Standards Institute, New York, NY (1972) 60 pp. ANSI, Minimum Design Loads for Buildings and Other Structures. ANSI A58.1-1982, American National Standards Institute, New York, NY (1982) 100 pp. ASCE, Minimum Design Loads for Buildings and Other Structures. ASCE 7-88, American Society of Civil Engineers, New York, NY (1990) 92 pp. ASCE, Minimum Design Loads for Buildings and Other Structures. ASCE 7-93, American Society of Civil Engineers, New York, NY (1993) 134 pp. ASCE, Minimum Design Loads for Buildings and Other Structures. ASCE 7-95, American Society of Civil Engineers, Reston, VA (1995) 214 pp. ASCE, Minimum Design loads for Buildings and Other Structures. ASCE 7-98, American Society of Civil Engineers, Reston, VA (2000) 330 pp. Fouad, Fouad H.; Calvert, Elizabeth A.; and Nunez, Edgar, Structural Supports for Highway Signs, Luminaires, and Traffic Signals. NCHRP Report 411, Transportation Research Board, Washington, D.C. (1998) 114 pp. Fouad, Fouad H.; Mehta, Kishor C.; and Calvert, Elizabeth A., Wind Loads Report: Final Draft. NCHRP Project 17-10(2), Prepared for National Cooperative Highway Research Program, Transportation Research Board, National Research Council, The University of Alabama at Birmingham, Birmingham, AL (Sept. 1999) 168 pp. Thom, H.C.S., New Distributions of Extreme Winds in the United States, Journal of the Structural Division. Proceedings, ASCE, Vol. 94, No. ST7 (1968) pp. 1787-1801. 13
Appendix A Figures 14
Figure A-1. Wind Map: 50-Year Mean Recurrence Interval (Thom, 1968) Figure A-2. Wind Map: 25-Year Mean Recurrence Interval (Thom, 1968) 15
Figure A-3. Wind Map: 10-Year Mean Recurrence Interval (Thom, 1968) Figure A-4. Basic Wind Speed (ANSI/ASCE 7-95) 16
90 mph 100 mph 110 mph 120 mph 140 mph 130 mph Figure A-5. Basic Wind Speed for Alabama (AASHTO, 2001) 17
70 mph 70 mph 80 mph 100 mph 90 mph Figure A-6. Wind Speed for Alabama, 50-Year Mean Recurrence Interval (AASHTO, 1994) 18
70 mph 80 mph 70 mph Figure A-7. Wind Speed for Alabama, 25-Year Mean Recurrence Interval (AASHTO, 1994) 19
60 mph 60 mph Figure A-8. Wind Speed for Alabama, 10-Year Mean Recurrence Interval (AASHTO, 1994) 20
Luminaire EPA: 50 ft^2 Weight: 1000 lbs 160'-0" High Mast Lighting Pole Example Figure A-9. High Mast Lighting Pole Example 21
10'-0" Luminaire EPA: 1.4 ft^2 Weight: 50 lbs Mast Arm EPA: 4.4 ft^2 Weight: 75 lbs 40'-0" Street Lighting Pole Example No. 1 Figure A-10. Street Lighting Pole Example No. 1 22
10'-0" Luminaire EPA: 1.4 ft^2 Weight: 50 lbs Mast Arm EPA: 4.4 ft^2 Weight: 75 lbs 40'-0" Street Lighting Pole Example No. 2 Figure A-11. Street Lighting Pole Example No. 2 23
16'-0" 8'-0" 17'-9" 9'-9" Roadside Sign Example Figure A-12. Roadside Sign Example 24
Appendix B Tables 25
Table 1. Wind Pressure for 1994 AASHTO Specifications AASHTO (1994) Wind Speed, (mph) 60 70 80 90 100 Height Wind Wind Wind Wind Wind Above Grade Pressure Pressure Pressure Pressure Pressure (ft) (psf) (psf) (psf) (psf) (psf) 0 12.5 17.0 22.2 28.0 34.6 5 12.5 17.0 22.2 28.0 34.6 10 12.5 17.0 22.2 28.0 34.6 15 15.6 21.2 27.7 35.0 43.3 20 15.6 21.2 27.7 35.0 43.3 25 15.6 21.2 27.7 35.0 43.3 30 17.1 23.3 30.5 38.5 47.6 35 17.1 23.3 30.5 38.5 47.6 40 17.1 23.3 30.5 38.5 47.6 45 17.1 23.3 30.5 38.5 47.6 50 19.5 26.5 34.6 43.8 54.1 60 19.5 26.5 34.6 43.8 54.1 70 19.5 26.5 34.6 43.8 54.1 80 19.5 26.5 34.6 43.8 54.1 90 19.5 26.5 34.6 43.8 54.1 100 21.8 29.7 38.8 49.1 60.6 110 21.8 29.7 38.8 49.1 60.6 120 21.8 29.7 38.8 49.1 60.6 130 21.8 29.7 38.8 49.1 60.6 140 21.8 29.7 38.8 49.1 60.6 150 23.4 31.8 41.5 52.6 64.9 160 23.4 31.8 41.5 52.6 64.9 170 23.4 31.8 41.5 52.6 64.9 180 23.4 31.8 41.5 52.6 64.9 190 23.4 31.8 41.5 52.6 64.9 200 24.9 33.9 44.3 56.1 69.2 AASHTO (1994): Pz = 0.00256 * (1.3 * V) 2 * (C d = 1) * C h 26
Table B-2. Wind Pressure for 2001 AASHTO Specifications (50-Year MRI) Wind Pressure (50-Year Mean Recurrence Interval) Wind Speed, (mph) Importance Factor AASHTO (2001) 90 100 110 120 130 140 1.00 1.00 1.00 1.00 1.00 1.00 Height Wind Wind Wind Wind Wind Wind Above Grade Pressure Pressure Pressure Pressure Pressure Pressure (ft) (psf) (psf) (psf) (psf) (psf) (psf) 0 20.1 24.8 30.0 35.7 41.9 48.6 5 20.1 24.8 30.0 35.7 41.9 48.6 10 20.1 24.8 30.0 35.7 41.9 48.6 15 20.1 24.8 30.0 35.7 41.9 48.6 20 21.3 26.3 31.8 37.9 44.5 51.6 25 22.3 27.6 33.4 39.7 46.6 54.1 30 23.2 28.7 34.7 41.3 48.4 56.2 35 24.0 29.6 35.8 42.6 50.0 58.0 40 24.7 30.5 36.9 43.9 51.5 59.7 45 25.3 31.2 37.8 45.0 52.8 61.2 50 25.9 31.9 38.6 46.0 53.9 62.6 60 26.9 33.2 40.1 47.8 56.1 65.0 70 27.8 34.3 41.5 49.3 57.9 67.2 80 28.5 35.2 42.6 50.7 59.6 69.1 90 29.3 36.1 43.7 52.0 61.1 70.8 100 29.9 36.9 44.7 53.2 62.4 72.4 110 30.5 37.7 45.6 54.3 63.7 73.9 120 31.1 38.4 46.4 55.3 64.9 75.2 130 31.6 39.0 47.2 56.2 66.0 76.5 140 32.1 39.6 48.0 57.1 67.0 77.7 150 32.6 40.2 48.7 57.9 68.0 78.8 160 33.0 40.8 49.3 58.7 68.9 79.9 170 33.5 41.3 50.0 59.5 69.8 81.0 180 33.9 41.8 50.6 60.2 70.6 81.9 190 34.2 42.3 51.2 60.9 71.5 82.9 200 34.6 42.7 51.7 61.5 72.2 83.8 AASHTO (2001) : P z = 0.00256 * K z * G * V 2 * I r * (C d = 1) 27
Table B-3. Wind Pressure for 2001 AASHTO Specifications (25-Year MRI) Wind Pressure (25-Year Mean Recurrence Interval) Wind Speed, (mph) Importance Factor AASHTO (2001) 90 100 110 120 130 140 0.87 0.87 0.80 0.80 0.80 0.80 Height Wind Wind Wind Wind Wind Wind Above Grade Pressure Pressure Pressure Pressure Pressure Pressure (ft) (psf) (psf) (psf) (psf) (psf) (psf) 0 17.5 21.6 24.0 28.5 33.5 38.8 5 17.5 21.6 24.0 28.5 33.5 38.8 10 17.5 21.6 24.0 28.5 33.5 38.8 15 17.5 21.6 24.0 28.5 33.5 38.8 20 18.5 22.9 25.5 30.3 35.6 41.3 25 19.4 24.0 26.7 31.8 37.3 43.3 30 20.2 24.9 27.7 33.0 38.8 44.9 35 20.9 25.8 28.7 34.1 40.0 46.4 40 21.5 26.5 29.5 35.1 41.2 47.8 45 22.0 27.2 30.2 36.0 42.2 49.0 50 22.5 27.8 30.9 36.8 43.2 50.1 60 23.4 28.9 32.1 38.2 44.8 52.0 70 24.1 29.8 33.2 39.5 46.3 53.7 80 24.8 30.7 34.1 40.6 47.6 55.3 90 25.5 31.4 35.0 41.6 48.8 56.6 100 26.0 32.1 35.8 42.6 49.9 57.9 110 26.6 32.8 36.5 43.4 50.9 59.1 120 27.0 33.4 37.2 44.2 51.9 60.2 130 27.5 34.0 37.8 45.0 52.8 61.2 140 27.9 34.5 38.4 45.7 53.6 62.2 150 28.3 35.0 38.9 46.3 54.4 63.1 160 28.7 35.5 39.5 47.0 55.1 63.9 170 29.1 35.9 40.0 47.6 55.8 64.8 180 29.5 36.4 40.5 48.2 56.5 65.5 190 29.8 36.8 40.9 48.7 57.2 66.3 200 30.1 37.2 41.4 49.2 57.8 67.0 AASHTO (2001): p z = 0.00256 * K z * G * V 2 * I r * (C d = 1) 28
Table B-4. Wind Pressure for 2001 AASHTO Specifications (10-Year MRI) Wind Pressure (10-Year Mean Recurrence Interval) Wind Speed, (mph) Importance Factor AASHTO (2001) 90 100 110 120 130 140 0.71 0.71 0.59 0.54 0.54 0.54 Height Wind Wind Wind Wind Wind Wind Above Grade Pressure Pressure Pressure Pressure Pressure Pressure (ft) (psf) (psf) (psf) (psf) (psf) (psf) 0 14.2 17.6 17.7 19.3 22.6 26.2 5 14.2 17.6 17.7 19.3 22.6 26.2 10 14.2 17.6 17.7 19.3 22.6 26.2 15 14.2 17.6 17.7 19.3 22.6 26.2 20 15.1 18.7 18.8 20.5 24.0 27.9 25 15.9 19.6 19.7 21.5 25.2 29.2 30 16.5 20.4 20.5 22.3 26.2 30.3 35 17.0 21.0 21.1 23.0 27.0 31.3 40 17.5 21.6 21.7 23.7 27.8 32.2 45 18.0 22.2 22.3 24.3 28.5 33.0 50 18.4 22.7 22.8 24.8 29.1 33.8 60 19.1 23.6 23.7 25.8 30.3 35.1 70 19.7 24.3 24.5 26.6 31.3 36.3 80 20.3 25.0 25.2 27.4 32.2 37.3 90 20.8 25.6 25.8 28.1 33.0 38.2 100 21.2 26.2 26.4 28.7 33.7 39.1 110 21.7 26.8 26.9 29.3 34.4 39.9 120 22.1 27.3 27.4 29.8 35.0 40.6 130 22.4 27.7 27.9 30.4 35.6 41.3 140 22.8 28.1 28.3 30.8 36.2 42.0 150 23.1 28.6 28.7 31.3 36.7 42.6 160 23.5 29.0 29.1 31.7 37.2 43.2 170 23.8 29.3 29.5 32.1 37.7 43.7 180 24.0 29.7 29.8 32.5 38.1 44.2 190 24.3 30.0 30.2 32.9 38.6 44.7 200 24.6 30.3 30.5 33.2 39.0 45.2 AASHTO (2001): p z = 0.00256 * K z * G * V 2 * I r * (C d = 1) 29