Computer-Based Sign, Luminaries, and Traffic Signal
Support Design Tools for State and County Engineers
For
The Alabama Department of Transportation
By
James S. Davidson, Fouad H. Fouad, Ramy S. Abdalla
Beth Calvert, Ernie Barton and Robert A Warr
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 at Huntsville
UTCA Report Number 00467
April 30, 2004
Technical Report Documentation Page
1. Report No
FHWA/CA/OR-
2. Government Accession No.
3. Recipient Catalog No.
4. Title and Subtitle
5. Report Date
Computer-Based Sign, Luminaires, and Traffic Signal
Support Design Tools for State and County Engineers
April 30, 2004
7. Authors
8. Performing Organization Report No.
James S. Davidson, Fouad H. Fouad, Ramy S. Abdalla
Beth Calvert, Ernie Barton and Robert A Warr
UTCA Report 00467
9. Performing Organization Name and Address
10. Work Unit No.
Department of Civil & Environmental Engineering
The University of Alabama at Birmingham
1075 13th Street South
Birmingham, AL 35294-4440
12. Sponsoring Agency Name and Address
University Transportation Center for Alabama
The University of Alabama
P.O. Box 870205
Tuscaloosa, AL 35487-0205
6. Performing Organization Code
11. Contract or Grant No.
Alabama Department of Transportation
Research Project 930-4784
13. Type of Report and Period Covered
Final Report: October 1, 2000 – April 30, 2004
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
Computer-based tools for the design of sign, luminaires and traffic signal supports were developed. The
tools incorporate the latest adopted design guides and specifications (AASHTO 2001 Standard
Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals). Design
worksheets were developed using MathCAD. They include overhead truss cantilever sign, overhead
cantilever monotube traffic signal pole, overhead monotube span support, overhead truss span support,
overhead truss VMS support, span wire pole, and roadside sign. Foundation design and connection design
are not included. The project was conducted within the graduate research program at the University of
Alabama at Birmingham and the design worksheets were reviewed by professional engineers. The final
report presents an overview of sign support design methodology, description and verification of the design
worksheets, and conclusions and recommendations for further development. The advantages and
disadvantages of the approach are discussed. Sufficient detail is presented in the final report for it to serve
the technology transfer needs of the industry users as well as serve as an education tool for engineering
students. The technical appendix published as UTCA Report 00467-1 provides an example support
structure analysis using each of the worksheets.
17. Key Words
18. Distribution Statement
Sign support, structural design, specifications
19. Security Classification
(of this report)
Unclassified
20. Security Classification
(of this page)
21. No of Pages
Unclassified
Form DOT F 1700.7 (8-72)
ii
22. Price
Contents
Contents ...........................................................................................................................................iii
Tables...............................................................................................................................................vi
Figures..............................................................................................................................................vi
Executive Summary ........................................................................................................................vii
1.0
INTRODUCTION ............................................................................................................... 1
1.1
General...................................................................................................................... 1
1.2
Objectives ................................................................................................................. 1
1.3
Scope / Project Description....................................................................................... 2
1.4
Report Organization.................................................................................................. 3
2.0
BACKGROUND ................................................................................................................. 4
2.1
Relevant Literature.................................................................................................... 4
2.2
Software Review....................................................................................................... 4
2.3
Common Design Configurations .............................................................................. 4
2.3.1 Single Upright Post Non-Cantilevered Box Truss System ........................... 5
2.3.2 Double Upright Post Non-Cantilevered Box Truss System ......................... 5
2.3.3 Double Pole Upright Tri-Chord System ....................................................... 6
2.3.4 Single Upright Post Cantilevered and
Non-Cantilevered Bi-Chord System ............................................................. 7
2.3.5 Single Upright Post Cantilevered Box Truss System ................................... 8
2.3.6 Single Upright Post Monotube Arm Traffic
Signal Support System.................................................................................. 9
2.3.7 Upright Post Span Wire Traffic Signal and
Sign Support System..................................................................................... 9
2.4
Materials and Design Philosophy ........................................................................... 11
3.0
DESIGN METHODOLOGY AND FLOW........................................................................ 12
3.1
3.2
3.3
3.4
3.5
3.6
Background ............................................................................................................. 12
Structure Geometry................................................................................................. 12
Loads ..................................................................................................................... 13
3.3.1 Dead Load................................................................................................... 13
3.3.2 Live Load .................................................................................................... 13
3.3.3 Ice Load ...................................................................................................... 13
3.3.4 Wind Load .................................................................................................. 14
3.3.5 Load Combinations..................................................................................... 14
Reactions at Upright ............................................................................................... 16
3.4.1 Reactions Due to Design Loads.................................................................. 16
Member Stresses ..................................................................................................... 16
Allowable Stresses .................................................................................................. 17
3.6.1 Allowable Bending Stresses ....................................................................... 17
iii
3.7
4.0
3.6.2 Allowable Tension Stresses ........................................................................ 19
3.6.3 Allowable Compression Stresses................................................................ 19
3.6.4 Allowable Shear Stresses............................................................................ 20
Combined Stress Ratios .......................................................................................... 21
DEVELOPMENT AND VERIFICATION OF DESIGN WORKSHEETS....................... 23
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Design Worksheet Organization ............................................................................. 23
4.1.1 Dimensional and Property Inputs................................................................ 23
4.1.2 Applied Loads............................................................................................. 23
4.1.3 Shear and Moment Forces .......................................................................... 24
4.1.4 Load Combinations..................................................................................... 24
4.1.5 Stresses........................................................................................................ 24
4.1.6 Deflections .................................................................................................. 25
4.1.7 Fatigue......................................................................................................... 25
Illustration of Worksheet Calculations ................................................................... 26
Cantilevered Monotube and Truss Sign Support .................................................... 26
4.3.1 Dimensional and Property Inputs................................................................ 26
4.3.2 Dead Loads ................................................................................................. 26
4.3.3 Shear and Moment Forces .......................................................................... 27
4.3.4 Load Combinations..................................................................................... 27
4.3.5 Member Stresses ......................................................................................... 27
4.3.6 Deflections .................................................................................................. 28
4.3.7 Fatigue......................................................................................................... 28
4.3.8 Wind Gust ................................................................................................... 28
Non-Cantilevered Truss Sign Support .................................................................... 28
4.4.1 Dimensional and Property Inputs................................................................ 28
4.4.2 Dead Loads ................................................................................................. 29
4.4.3 Load Combinations..................................................................................... 29
4.4.4 Reactions at Upright Post............................................................................ 29
4.4.5 Member Stresses ......................................................................................... 30
4.4.6 Combined Stress Ratios .............................................................................. 31
Span Wire Traffic Signal and Sign Support ........................................................... 31
4.5.1 Dimensional and Property Inputs................................................................ 31
4.5.2 Dead Loads ................................................................................................. 31
4.5.3 Forces on Wire............................................................................................ 31
4.5.4 Load Combinations..................................................................................... 32
4.5.5 Member Stresses ......................................................................................... 32
4.5.6 Deflections .................................................................................................. 32
Applicability and Verification ................................................................................ 32
Survey of Local Transportation Engineers ............................................................. 32
Integration of the Design Worksheets with CAD ................................................... 33
External Review...................................................................................................... 34
iv
5.0
CONCLUSIONS................................................................................................................. 35
5.1
Summary ................................................................................................................. 35
5.2
Conclusions............................................................................................................. 35
5.3
Recommendations................................................................................................... 35
6.0
REFERENCES .................................................................................................................. 37
v
List of Tables
Number
Page
3-1
Load combinations.................................................................................................16
List of Figures
Number
Page
2-1
Single upright post non-cantilevered box truss system............................................5
2-2
Double upright post non-cantilevered box truss system ..........................................6
2-3
Double upright post non-cantilevered tri-chord system...........................................7
2-4
Single upright post cantilevered and non-cantilevered bi-chord system .................8
2-5
Single upright post cantilevered box truss system...................................................9
2-6
Single upright post monotube arm traffic signal support system ..........................10
2-7
Double upright post span wire traffic signal and sign support system ..................10
vi
Executive Summary
Highway sign support structures must be designed in accordance with the American Association
of State Highway and Transportation Officials (AASHTO) Standard Specifications for Structural
Supports for Highway Signs, Luminaires, and Traffic Signals. In recent years, the National
Cooperative Highway Research Program (NCHRP) has sponsored projects to update and revise
the AASHTO specifications. The Department of Civil and Environmental Engineering at the
University of Alabama at Birmingham (UAB) conducted NCHRP Project 17-10, “Structural
Supports for Highway Signs, Luminaires, and Traffic Signals” and completed a follow-on
project in 2002, Project 17-10(2), to enhance the specifications developed under Project 17-10.
Because of its involvement in sign support research and specification development over the
years, UAB Civil Engineering is recognized as a leading center of expertise in sign and
luminaires support design and research.
The sign, luminaires, and traffic signal supports purchased by government entities are typically
designed outside of the engineering departments of those entities. But state and county engineers
still need an efficient and effective way to check the support structures being constructed in their
districts according to the latest developments in research and design practice. Accordingly, the
objectives of the project were to: (1) develop easy-to-use computer-based design tools for the
design of sign, luminaires and traffic signal supports that incorporates the latest adopted design
guides and specifications, (2) develop a set of design examples using these design tools, and (3)
transfer this technology to state and county engineers. Design worksheets were developed using
MathCAD and include: overhead truss cantilever sign, overhead cantilever monotube traffic
signal pole, overhead monotube span support, overhead truss span support, overhead truss VMS
support, span wire pole, and roadside sign. Foundation design and connection design are not
included. The project was conducted within a traditional graduate student research program at
the University of Alabama at Birmingham and the design worksheets were reviewed by
professional engineers. The final report presents an overview of sign support design
methodology, description and verification of the design worksheets, and conclusions and
recommendations for further development. The advantages and disadvantages of the approach
are discussed. Sufficient background and design methodology detail is presented for the report
to serve the technology transfer needs of industry users, as well as serve as an education tool for
engineering students. MathCAD numerical examples are provided in the Technical Appendix
(published as UTCA Report 00467-1) to illustrate the use of the worksheets in analyzing support
structures.
vii
1.0 INTRODUCTION
1.1 Introduction
Highway sign, luminaires, and traffic signal support structures, hereafter referred to as ‘support
structures’ or simply as ‘structures’, must be designed in accordance with the American
Association of State Highway and Transportation Officials (AASHTO) Standard Specifications
for Structural Supports for Highway Signs, Luminaires, and Traffic Signals. In recent years, the
National Cooperative Highway Research Program (NCHRP) has sponsored projects to enhance
the design specifications and update it to the latest information in the literature.
The Department of Civil and Environmental Engineering at the University of Alabama at
Birmingham (UAB) conducted NCHRP Project 17-10, “Structural Supports for Highway Signs,
Luminaires, and Traffic Signals.” The primary objective of Project 17-10 was to update the 1994
Standard Specifications (Fouad, Calvert, and Nunez, 1999). In 2002, UAB Civil Engineering
completed a follow-on project, Project 17-10(2), to enhance the specification developed under
Project 17-10 and to provide a strategic plan for future development of the specifications in LRFD
format (Fouad et al., 2002). Because of its involvement in sign support research and specification
development over the years, UAB is recognized as a leader in research and design of highway
structural supports.
The support structures purchased by government entities are typically designed outside of the
engineering departments of those entities. Nevertheless, the "owner" must approve submitted
shop drawings, so state and county engineers still need an efficient and effective way to check the
structures being constructed in their districts. They should also integrate the latest developments
in research and design practice. Furthermore, if an easy-to-use tool is available to state and
county engineers, more sign supports will likely be designed “in-house.” Therefore, a project
conducted by the UAB Department of Civil and Environmental Engineering, sponsored by the
Alabama Department of Transportation (ALDOT) in association with the University
Transportation Center for Alabama (UTCA), was initiated to develop computer-based tools for
sign support structures that incorporate the latest adopted design guides and specifications. This
report represents the results from the project.
1.2 Objectives
The objectives of the project were to: (1) develop easy-to-use computer-based design tools for
the analysis or design of sign, luminaires and traffic signal supports that incorporates the latest
adopted design guides and specifications, (2) develop a set of design examples using these design
tools, and (3) transfer this technology to state and county engineers.
1
1.3 Scope / Project Description
The overall scope of the project was to develop worksheets for the analysis and design of sign and
traffic signal support structures. The original proposal outlined 16 support structure types for
potential design worksheet development. A meeting of the research team with the ALDOT
project advisory committee in February of 2001 identified the design of the larger, higher-cost
overhead structures such as the cantilevered and noncantilevered truss structures as the highest
priority. The support structure design worksheets that were developed for this project included:
(1) overhead truss cantilever sign, (2) overhead cantilever monotube traffic signal pole, (3)
overhead monotube span support, (4) overhead truss span support, (5) overhead truss span vms
support, (6) span wire pole, and (7) roadside sign. Another outcome of the February 2001
meeting was that standard plans for foundations were being developed by others and that the
research team should not expend effort on developing design worksheets for foundation design.
The research team selected MathCAD (MathSoft 2000) for the design worksheets due to its easeof-use, extensive capabilities, and widespread availability. The design worksheets for the
structures chosen are self-explanatory, include a printable view of all calculations, and include a
sidebar commentary that describes the source and reasoning for the calculations.
Graduate students under the direction of their faculty advisors conducted the effort within the
Department of Civil and Environmental Engineering at the University of Alabama at
Birmingham. The research team used the UAB Civil Engineering expertise, reference collection,
sign support research results, contacts, and other resources related to the subject to accomplish the
objectives of the project. The research team consisted of Dr. Jim Davidson, Principal Investigator
and Associate Professor; Dr. Fouad H. Fouad, Co-principal Investigator and Professor, Mr. Ramy
Abdalla, a UAB Ph.D. student who had participated in NCHRP Project 17-10(2); and Mr. Ernie
Barton and Mr. Robert Warr, MSCE graduate students who had a strong interest in projects that
involved worksheet programming. Dr. Davidson managed the project. Mr. Abdalla provided
technical support on all aspects of the project. Mr. Barton and Mr. Warr developed the design
worksheets. Dr. Fouad, who was the principal investigator on NCHRP Projects 17-10 and 1710(2), provided technical support. After the worksheets were completed, Beth Calvert, a
professional structural engineer with extensive experience in sign support design and who has
been involved in the previously mentioned NCHRP projects, reviewed the work of the research
team.
The tools developed are in the form of worksheets and are not based on the finite element or
matrix methods of structural analysis. Although the design worksheets were developed as standalone analysis tools with member forces calculated by conservative approximate methods where
feasible, it may be necessary to use external structural analysis programs in conjunction with the
worksheets to accurately calculate member forces. This project can be considered to be a
preliminary step to developing comprehensive design tools that incorporates the structural
analysis needs of all types of sign support design.
2
1.4 Report Organization
This report describes the activities, conclusions, and results of the project, and also presents an
overview of sign support design methodology. Sufficient background and design methodology
detail is presented for it to serve the technology transfer needs of industry users as well as to serve
as an education tool for engineering students. It is organized into the following chapters: Chapter
1, “Introduction,” presents a general introduction, followed by a summary of the main objectives
of the project. The scope of the research and project description is discussed. Chapter 2,
“Background,” provides a summary of background research related to the main objectives of the
project. Included in Chapter 2 is the review of relevant literature, software, and recent problems
encountered with sign support structures. Current design standards and construction practices are
reviewed and considered. Chapter 3, “Design Methodology and Flow,” provides design
methodology and flow for the design worksheets that were developed. Included in Chapter 3 is
an explanation of all the loads and load combinations. An explanation of the calculations of the
reactions at the uprights, member stresses, allowable stresses and stress ratios is also provided.
Chapter 4, “Development and Verification of the Design Worksheets,” discusses the development
and application of the design worksheets and illustrates the utility and applicability of the design
worksheets. The results of a survey of local municipalities are presented to explore potential
interest of the design worksheets. Chapter 5, “Conclusions,” summarizes the main conclusions of
this study and provides recommendations for future development. Finally, examples of each
support structure type are provided in the Technical Appendix (published as UTCA Report
00467-1) to illustrate the use of the worksheets in analyzing support structures.
3
2. BACKGROUND
2.1 Relevant Literature
The design worksheet development process involved several resources. The MathCAD 2000
User’s Guide (MathSoft 2000) was an instrumental tool for understanding how to design the
layout of the design worksheets. MathCAD’s capabilities and limitations were researched and
applied. MathCAD allowed the design worksheets to be developed as a user input program that is
capable of displaying a series of output values that conveyed to the user whether or not the
structural integrity of the structure was adequate and met design criteria.
The 2001 “Standard Specifications for Structural Supports for Highway Signs, Luminaires and
Traffic Signals,” was used as the design specification for the design of the sign support structures
(subsequently referred to as the “Supports Specifications”). The relevant guidelines and design
equations for various types of structural members and materials are provided in the worksheets.
A task of NCHRP Project 17-10(2) was to survey state DOT offices regarding design
methodology and problems that have been encountered. Design plans and member sizes of the
support structures were included in the response to these surveys. The findings of NCHRP
Projects 17-10 and 17-10(2) were reviewed and designs provided by several state departments of
transportation were used to check the applicability of the design worksheets developed during this
project.
2.2 Software Review
The only sign support design software found was that provided by the Florida Department of
Transportation (FDOT). The FDOT web site contains several programs that can be used to
analyze and design highway sign and signal support structures. The FDOT sign support structure
programs include span wire structures, signal pole structures, cantilever sign truss structures,
mast-arm cantilevered signal structures, and span overhead sign truss structures. Each program
prompts the user to enter known or desired values such as dimensions of the overall structure,
feature location, and feature dimensions.
2.3 Common Design Configurations
This section discusses the various geometry choices that are available for support structures. The
basic components of any truss type sign support structure are the upright posts, truss chords, and
the struts and diagonals. These elements can be configured in a variety of ways. The basic
components of the monotube arm signal support structure are the upright posts, monotube mast
arm, and the signal or signs attached to the arm. The basic components of the span wire traffic
signal and sign support are the upright posts, the span wire, and the signal or signs attached to the
4
wire. This section provides common configurations that are currently used for sign support
structures. Images of the different configurations of support structures are provided.
2.3.1 Single Upright Post Non-Cantilevered Box Truss System
This structure consists of a single upright post supporting a four-chord box truss, which is braced
vertically and horizontally with diagonals and struts as shown in Figure 2-1.
Figure 2-1. Single upright post non-cantilevered box truss system
The single upright post is predominately a round ASTM A500 Grade B pipe member, but other
structural shapes such as wide flange sections have been used. The truss chords, truss diagonals
and struts are also generally composed of ASTM A500 Grade B round pipe, but like the upright
posts, other structural members such as angles made from ASTM A36 material are commonly
used. The truss chords are composed of four chords positioned to form a square box.
2.3.2 Double Upright Post Non-Cantilevered Box Truss System
This structure consists of a double upright post braced with diagonals and struts supporting a fourchord box truss, which is braced vertically and horizontally with diagonals and struts as shown in
Figure 2-2.
5
Figure 2-2. Double upright post non-cantilevered box truss system
The double upright post (non-cantilevered box-truss system) is the most commonly used noncantilevered sign support structure in Alabama. The double pole upright is predominately a round
ASTM A500 Grade B pipe member, but other structural shapes such as wide flange sections have
been used. The truss chords, truss diagonals, and struts are also typically composed of ASTM
A500 Grade B round pipe, but like the upright posts, other structural members such as ASTM
angles have been used. The truss chords are composed of four chords positioned to form a square
box.
2.3.3 Double Pole Upright Tri-Chord System
The double upright post (tri-chord system) consists of a double upright post braced with diagonals
and struts supporting a tri-chord box truss that is braced vertically and horizontally with diagonals
and struts as shown in Figure 2-3.
6
Figure 2-3. Double upright post non-cantilevered tri-chord system
The double upright post non-cantilevered tri-chord system is the type of non-cantilevered sign
support structure that is currently supported under the FDOT’s design programs. The double pole
upright is predominately a round ASTM A500 Grade B pipe member, but other structural shapes
such as wide flange sections have been used. The truss chords, truss diagonals and struts are also
generally composed of ASTM A500 Grade B round pipe, but like the upright posts, other
structural members such as ASTM angles have been used. The truss chords are composed of
three chords positioned to form an equilateral triangle.
2.3.4 Single Upright Post Cantilevered and Non-Cantilevered Bi-Chord System
This structure consists of a single upright post supporting a vertical single plane truss that is
braced vertically with diagonals and struts as shown in Figure 2-4. The single upright post is
usually a round ASTM A500 Grade B pipe member, but other structural shapes such as wide
flange and square sections have been used. The truss chords, truss diagonals, and struts are also
typically composed of ASTM A500 Grade B round pipe, but like the upright posts, other
structural members such as ASTM angles have been used. The truss chords are composed of two
chords positioned to form a single plane vertical truss.
7
Figure 2-4. Single upright post cantilevered and non-cantilevered bi-chord system
2.3.5 Single Upright Post Cantilevered Box Truss System
This structure consists of a single upright post supporting a four-chord box truss, which is braced
vertically and horizontally with diagonals and struts as shown in Figure 2-5. The single upright
post is predominately a round ASTM A500 Grade B pipe member, but other structural shapes
such as wide flange sections have been used. The truss chords, truss diagonals, and struts are also
typically composed of ASTM A500 Grade B round pipe, but like the upright posts, other
structural members such as angles made from ASTM A36 material have been used. The truss
chords are composed of four chords positioned to form a square box.
8
Figure 2-5. Single upright post cantilevered box truss system
2.3.6 Single Upright Post Monotube Arm Traffic Signal Support System
This structure consists of a single upright post supporting a monotube arm, which is attached
directly to the post with a flange and u-bolt system as shown in Figure 2-6. The single upright
post is predominately a round API-5L-X52. The arm and secondary members are predominately
ASTM A53, Grade B, with the arm having an option of being tapered, which is most common.
This configuration is common on secondary highways and city streets. It can accommodate many
different elements and combinations of luminaires and signs.
2.3.7 Upright Post Span Wire Traffic Signal and Sign Support System
This structure consists of an upright post on each side with a single span wire draped between the
upright posts as shown in Figure 2-7. The upright post span wire traffic signal and sign support
system is the most commonly used sign and signal support structure on non-interstate roads in
Alabama. The upright post is typically a round tapered ASTM A500 Grade B pipe member. The
span wire is typically an elastomer covered steel cable.
9
Figure 2-6. Single upright post monotube arm traffic signal support system
Figure 2-7. Double upright post span wire traffic signal and sign support system
10
2.4 Materials and Design Philosophy
The majority of sign structures are made of steel or aluminum. Structures with overhead trusses
are usually made of steel, but depending on the span and location, the structure may be made of
aluminum. Both steel and aluminum structures are designed using allowable stress design. The
AASHTO 2001 specifications provide allowable stresses for various cross sections. Design
equations and allowable stresses are designated according to the shape of the member. Common
member shapes included I-shaped members, channels, angles, round tubes, hexadecagonal tubes,
dodecagonal tubes, octagonal tubes and square or rectangular tubes. Differences in the allowable
bending stresses for various geometric configurations are discussed in subsequent chapters.
11
3. DESIGN METHODOLOGY AND FLOW
3.1 Background
The methodology and flow process must be defined prior to programming in a design worksheet
format. The first element of the design flow process is to select the overall geometry of the
structure. The choice of geometric configuration and structural material significantly affects the
overall design flow. Determining the geometry of the structure and cross section shape of
members is important and must be investigated before the design process takes place. For
example, the design methodology of a quad-chord truss versus a tri-chord truss would
significantly differ, as would a double pole upright versus a single pole upright. The geometry of
the structure also includes additional elements such as overhead road signs attached to the
structure. This too will affect the design of the structure by the addition of various types of
loading.
Once the overall geometry of the structure is established, the loading conditions must be
determined and applied. There are three basic types of loads applied to sign support structures:
dead load, wind load, and ice load. The dead load includes the weight of the members and is
always included in the design. The wind load is a primary loading condition that is also always
included, but its magnitude depends on the geographic location of the structure. Different wind
zones will have a greater wind velocity causing a larger wind pressure required for the design.
The wind loads affect every part of the structure and must be fully considered in the design. Ice
load is also dependent of the geographic location of the structure. Unlike the wind load, some
geographical locations may not be subject to the ice load requirement. If the structure requires ice
load, it is applied like dead load acting on the members of the structure.
A structural analysis must be performed to determine the moments, forces, and shears determined
by the previously-determined loading condition. Load combinations must be considered. The
member stresses must then be compared to the allowable stresses established in the Supports
Specifications to determine if the member is overstressed. Once comparisons are made, the stress
ratios are determined for the elements in the system. The following sections discuss the overall
methodology used in the design worksheets.
3.2 Structure Geometry
Cantilevered and non-cantilevered truss sign support structures are commonly used to span a
roadway or interstate highway and to support highway signs at varying positions along the span
arm of the structure. Also, a maintenance walkway is generally positioned in front of the signs to
allow required upkeep and changes to the signs. There are many different configurations of both
the cantilevered and non-cantilevered sign support structures. The basic components of these
types of structures are the upright posts, truss chords, struts, and diagonals.
12
The cantilevered monotube traffic signal and sign support structures are regularly used to span a
roadway. They typically support signs and traffic signals positioned at varying locations along
the span arm. There is not a maintenance walkway associated with this type of structure. The
basic components of this structure are the upright post and mast arm.
The span wire traffic signal and sign support structure typically span a roadway to support
direction or instructional signs and traffic signals positioned along the span wire. The basic
components of this structure are the upright post and span wire. It is important to choose a
structure geometry that is capable of supporting the structure under the given loads to which the
structure is subjected. The design methodology is the same for all of the different configurations
except for slight modifications that are necessary to account for the changes of the geometry of
the structure.
3.3 Loads
Requirements are specified for loads and forces, the limits of their application, load factors and
load combinations that are used for the design or structural evaluation of highway signs,
luminaires, and traffic signals. The information in the following sections of this report is based
upon the 2001 “Standard Specifications for Structural Supports for Highway Signs, Luminaires
and Traffic Signals,” (referred to as the “Supports Specifications”).
3.3.1 Dead Load
According to Article 3.5 of the Supports Specifications, the dead load consists of the weight of
the structural support, signs, luminaires, traffic signals, lowering devices, and any other
appurtenances permanently attached to and supported by the structure. The center of gravity of
each item is used as the point of application during the analysis.
3.3.2 Live Load
According to Article 3.6 of the Supports Specifications, the live load consists of a single load of
2200 N (500 lb) distributed over 0.6 m (2.0 ft) transversely to the member. This is used for
designing members of walkways and service platforms. This live load represents the weight of a
person and equipment during service of the structure.
3.3.3 Ice Load
According to Article 3.7 of the Supports Specifications, the ice load is 145 Pa (3.0 psf) applied
around the surfaces of the structural supports, traffic signals, horizontal supports, and luminaires,
but shall be considered only on one face of the sign panels. The ice loading is based on a 15 mm
13
(0.60 in.) radial thickness of ice at a unit weight of 960 kg/m3 (60 pcf) applied uniformly over the
exposed surface of the member. Figure 3-1 of the Supports Specifications provides geographic
regions that must consider ice loading.
3.3.4 Wind Load
The wind load is based on the pressure of the wind acting horizontally on the horizontal and
vertical supports, signs, luminaires, and traffic signals computed in accordance to Articles 3.8.1
through 3.8.6 of the Supports Specifications. The design wind pressure is computed using the
following equation, which is based upon ANSI/ASCE 7-95:
pz = 0.00256KzGV 2IrCd (psf)
(Eq. 3-1)
where pz is the wind pressure at a height, z, above ground, Kz is the velocity pressure exposure
coefficient, G is the gust effect factor which is taken as 1.14, V is the basic wind speed expressed
as a 3-second gust wind speed, Ir is the importance factor based upon the desired mean recurrence
interval, r, and Cd is the drag coefficient.
The basic wind speed V used in determining the design wind pressure is shown in Figure 3-2 of
the Supports Specifications, which is a metricated version of the wind speed map published in
ANSI/ASCE 7-95 Standard Minimum Design Loads for Buildings and Other Structures. The
wind map is based on peak gust data collected at 485 weather stations and from predictions of
hurricane speeds on the U. S. Gulf and Atlantic Coasts. The map presents the variation of 3second gust wind speeds associated with a height of 33-ft for open terrain. In addition, the 3second gust wind speeds presented in Figure 3-2 of the Supports Specifications are associated
with a 50-year mean recurrence interval (annual probability of 0.02 that the wind speeds will be
equaled or exceeded), as discussed in Chapter 3 of the Supports Specifications.
The wind importance factor, Ir, is selected from Table 3-2 of the Supports Specification
corresponding to the specified design life of the structure. The importance factors allow the wind
pressures associated with the 50-year mean recurrence interval (3 second gust wind speeds) to be
adjusted to represent wind pressures associated with 10-, 25-, or 100-year mean recurrence
intervals. The height and exposure factor, Kz, are determined from Table 3-6 of the Supports
Specifications.
Kz is a velocity exposure factor that varies with height depending on the local exposure
conditions. The variation is caused by the frictional drag offered by various types of terrain.
Since 1982, widely accepted wind design procedures have involved the use of four different
terrain exposure conditions, which are designated as exposures A, B, C, and D. For a specified
set of conditions, the wind pressures associated with the different exposures increase as the
exposure conditions progress from A to D, with exposure A resulting in the least pressure and
exposure D resulting in the greatest pressure. Exposure C was adopted for use in the 2001
Supports Specifications as it provides a conservative approach for the design of structural
supports. Once the terrain exposure conditions are established, the velocity pressure exposure
14
coefficient, Kz, is calculated using the following relationship, which is presented in ANSI/ASCE
7-95:
Kz = 2.01(z/zg)2/α
(Eq. 3-2)
where z is the height about the ground or 4.57 m (15 ft), whichever is greater, and zg and α are
constants that vary with exposure condition. Based on information presented in ANSI/ASCE 795, α should be taken to be 9.5 and zg should be taken to be 274.3 m (900 ft) for exposure C.
The gust factor, G, corrects the effective velocity pressure for the dynamic interaction of the
structure with the gustiness of the wind. A 3-second gust effect factor, G, is used. The gust effect
factor is derived from the traditional fastest mile gust coefficient of 1.3. The fastest-mile gust
coefficient of 1.3 must be converted to a 3-second gust coefficient. This is accomplished by
multiplying the gust coefficient of 1.3 by the ratio of the fastest-mile wind speed to the 3-second
wind gust speed. This ratio is approximately equal to 0.82 based on the information presented in
ANSI/ASCE 7-95. The equivalent 3-second gust coefficient is thus equal to 1.07 = (1.3)(0.82).
The corresponding gust factor, G, is approximately equal to 1.14 by squaring the 3-second gust
coefficient. It is therefore recommended that a gust effect factor, G, of 1.14 be used for the design
of signs, signals, and luminaires. The wind drag coefficient, Cd, is provided in Table 3-6 of the
Supports Specifications.
The design loads for horizontal supports of sign support structures (cantilevered or noncantilevered) and traffic signal structures are wind loads. Wh is the wind load on an exposed
horizontal support, and Wp is the wind load on a sign panel or traffic signal. These loads are
applied normal to the support at the centers of pressure of the respective areas. The vertical
supports for luminaire structures, traffic signal structures (excluding pole top mounted traffic
signals and post top luminaire structures), and sign support structures are designed for the effects
of wind from any direction. The basic load for the structures with rigid horizontal supports
includes the effects from the wind loads, Wv, Wi, Wp and Wh. Wv is the wind load on exposed
vertical supports, Wi is the wind on the luminaires, and Wp and Wh are defined above. Each of
these loads is applied at the centers of the pressure of the respective areas of the structures and
normal to the faces. The transverse components may be distributed in proportion to the relative
lateral stiffness and conditions of the support restraint.
3.3.5 Load Combinations
The loads described above must be combined into appropriate group load combinations as
stipulated in Table 3-1, which is adopted from Table 3-1 of the Supports Specifications. Each
part of the structure is proportioned for the combination producing the maximum effect, using
allowable stress as indicated for the material and group load.
15
Table 3-1: Load combinations
Group Load
Load Combination
Percent of Allowable Stress
(see Note 1)
I
DL
100
II
DL + W
133
III
DL + Ice +1/2W
133
IV
Fatigue
(see Note 3)
1. No load reduction factors shall be applied in conjunction with these increased
allowable stresses
2. W shall be computed on the basis of the wind pressure formula. A minimum value of
1200 Pa (25.1 psf) shall be used.
3. Fatigue loads and stress range limits discussed in separate section.
3.4 Reactions at Upright
This section describes the acceptable methods for solving for static force reactions at the upright
posts. The reaction forces are used to determine the maximum moments used in the design of the
structures.
3.4.1 Reactions Due to Design Loads
The reactions due to the loading conditions discussed above are determined by summing the
moments around a support considering the loads on the panels, loads on the truss, and loads on
the walkway. The theory of elastic structural analysis is used for determining the maximum load
effects. Analysis and design of the structural supports must conform to generally accepted
engineering practices such as methods of analysis that satisfy the requirements of equilibrium and
compatibility of the structure and use the linear stress-strain relationship for the material. The
centers of gravity are used as points of load application. For statically determinate structures,
taking the moments about a support will give a single reaction, which can be used to obtain the
reaction on the opposing side of the structure.
3.5 Member Stresses
Once all of the loading conditions have been considered, the stresses on each member are
determined by analyzing the forces applied to the structure. For the truss system, the maximum
compression in the truss chords and truss struts and the maximum tension in the diagonals are
determined by analyzing the structural elements from all of the loads used during the analysis.
The maximum forces that must be accounted in the vertical support are the forces in the upright
diagonals, the axial compressive force in the upright columns, the axial tensile force in the upright
columns, the bending forces in the column and the shear forces in the column. The specifications
16
governing the allowable bending stresses, tension stresses, shear stresses and compression stresses
will be discussed.
3.6 Allowable Stresses
This section describes the acceptable methods for solving bending, axial, and shear stresses. The
calculated stresses are compared to allowable stresses defined in the Supports Specifications.
3.6.1 Allowable Bending Stress
Steel sections are classified as compact, non-compact and slender element sections. For a section
to qualify as compact or noncompact, the width-thickness ratios of its compression elements must
not exceed the applicable corresponding limiting values given in the Supports Specifications. If
the width-thickness ratios of any compression element section exceed the noncompact limiting
value, λr, the section is classified as a slender element section. Steel sections are classified as
compact, non-compact, or slender elements sections, based upon three conditions. First, if the
flanges are continuously connected to the web and the width-thickness ratios of all the
compression elements do not exceed the compact limit λp, then the section is compact. Second, if
the width-thickness ratio of at least one of its compression elements exceeds λp, but does not
exceed λr, the section is non-compact. Finally, if the width-thickness ratio of any compression
element exceeds λr, the element is a slender compression element.
A compact section will develop its plastic moment in bending without premature bucking. A
noncompact section will meet or exceed its yield moment in bending. A slender section will
buckle locally prior to reaching the yield moment in bending. The section classifications for
compact, non-compact or slender for tubular and non-tubular sections are provided in Tables 5-1
and 5-2 of the Supports Specifications. The allowable bending stresses for round and multi-sided
tubular members that have compact, noncompact, and slender element sections, are computed
according to Table 5-3 of the Supports Specifications.
The allowable bending stress for flanged I-shaped members and channels with compact and
noncompact sections as defined in Table 5-2 of the Supports Specifications, and loaded through
the shear center and braced laterally in the region of compression stress at intervals not exceeding:
0.4463 b f
E
Fy
(Eq. 3-3)
the allowable stress is given by the equation:
Fb = 0.60Fy
(Eq. 3-4)
17
For I-shaped members and channels with compact or noncompact sections as defined in Table 5-2
of the Supports Specifications, and with the unbraced length Lb greater than Lc as defined above,
the allowable bending stress in tension is:
Fb = 0.60Fy
(Eq. 3-5)
For I-Shaped members, symmetrical about and loaded in the plane of their minor axis, the
allowable bending stress in compression Fb shall be determined as the larger value from:
2
⎞
⎛
⎛ L⎞
⎟
⎜
⎜⎜ ⎟⎟
⎟
⎜2
r
⎝ t⎠
Fb = ⎜ −
⎟ Fy
⎜ 3 52.759 C E ⎟
b
⎜
Fy ⎟
⎠
⎝
(Eq. 3-6)
for
3.517 C b
Fb =
E
L
≤ ≤
F y rt
5.862 Cb
⎛L⎞
⎜ ⎟
⎝ rt ⎠
2
17.586 C b
E
Fy
(Eq. 3-7)
(Eq. 3-8)
E
for
L
E
≥ 17.586 C b
rt
Fy
(Eq. 3-9)
or
Fb =
0.4138 C b
E
d
L
Af
(Eq. 3-10)
For doubly symmetrical I-shaped members with compact flanges, continuously connected to the
web and bent about their weak axes (except members with yield points greater than 65 ksi (450
MPa), the allowable bending stress is given by:
Fb = 0.75Fy
(Eq. 3-11)
18
For noncompact sections bent around their minor axis, and for compact or noncompact channels
bent about their minor axis, the allowable stress is given by:
Fb = 0.60Fy
(Eq. 3-12)
For solid round and square bars, and solid rectangular sections bent about their weak axis, the
allowable bending stress is given by:
Fb = 0.75Fy
(Eq. 3-13)
3.6.2 Allowable Tension Stress
The allowable tensile stress cannot exceed 0.6Fy on the gross area Ag, or 0.5Fu on the effective net
area Ae. The effective net area Ae must be taken to equal the net area An, where the load is
transmitted directly to each of the cross sectional elements by bolts. The net area, An, must be
calculated as the sum of the individual net areas along a potential critical section. When
calculating An, the width of the bolt hole must be taken as 1/16 in. (1.5 mm) greater than the
nominal dimension of the hole. When the load is transmitted through some but not all of the
cross-sectional elements, shear lag must be accounted for. The effective net area is computed as:
Ae = UA
(Eq. 3-14)
where,
A = area
U = reduction coefficient (U = (1 – x/L) ≤ 0.9
x = connection eccentricity
L = length of connection in the direction of loading
3.6.3 Allowable Compression Stress
The allowable axial compression stress, Fa, is calculated as follows:
a) When kL/r < Cc
19
Fa =
⎛ ⎛ kL ⎞
⎜ ⎜ ⎟
⎜ ⎝ r ⎠
⎜1 −
2
2C c
⎜
⎜
⎝
2
⎞
⎟
⎟
⎟Fy
⎟
⎟
⎠
⎛ kL ⎞ ⎛ kL ⎞
3⎜ ⎟ ⎜ ⎟
5
r
r
+ ⎝ ⎠ − ⎝ ⎠3
3
8C c
8C
(Eq. 3-15)
3
c
b) When kL/r ≥ Cc
Fa =
12π 2 E
⎛ kL ⎞
23⎜ ⎟
⎝ r ⎠
(Eq. 3-16)
2
where kL / r is the largest slenderness ratio of any unbraced segment Cc = √(2π 2E / Fy). Both
equations have been presented to be consistent with the AISC Manual of Steel Construction –
Allowable Stress Design (1989). Equation 3-19 is the Euler equation for long columns subject to
elastic buckling.
3.6.4 Allowable Shear Stress
For sections not subject to local buckling, the maximum allowable shear stress of 0.33Fy is used
in the absence of wind load. For wind loadings, this stress is increased by 33%. The allowable
shear stress due to shear and torsion for round tubular shapes is:
Fv = 0.33F y
Fv =
0.41 E
⎛ D⎞
⎜ ⎟
⎝t ⎠
2/3
for
for
D
E 2/3
≤ 1.16 ( )
t
Fy
D
E 2/3
> 1.16 ( )
t
Fy
(Eq. 3-17)
(Eq. 3-18)
Little information is available in the literature regarding shear stresses in round tubes. The
allowable shear stress equations for round tubular sections are based on elastic torsional buckling
of long cylindrical tubes developed in Theory of Elastic Stability by Timosheko and Gere (1961).
20
The allowable shear stress is compared to the maximum shear stress of the section. The allowable
shear stress equation for multi-sided tubular shapes is:
Fv = 0.33F y
b
≤ 2.23
t
for
E
Fy
(Eq. 3-19)
The allowable shear stress is compared to the maximum shear stress of the section.
Fv =
1.64 E
⎛b⎞
⎜ ⎟
⎝t⎠
2
b
> 2.23
t
for
E
Fy
(Eq. 3-20)
The allowable shear stress equation for I-shaped sections and channels is as follows:
Fv = 0.33F y
for
h
≤ 2.23
tw
E
Fy
(Eq. 3-21)
The allowable shear stress is applied over an effective area consisting of the full member depth
times the web thickness.
3.7 Combined Stress Ratios
Members subjected to combined bending, axial compression or tension, shear and torsion are
proportioned to meet the limitations discussed below. The equations for combined stress are
derived from the maximum principal stress theory found in many mechanics of materials
textbooks. In terms of allowable stress, the general equation that considers axial, bending, and
shear stresses, can be developed as:
⎛ f
+
+⎜ v
Fa Fb ⎜⎝ Fv
fa
fb
2
⎞
⎟ ≤ 1.0
⎟
⎠
(Eq. 3-22)
The combined stress equations can be found in other specifications and literature, such as the
AASHTO Standard Specifications for Highway Bridges (1994) and the AISC Manual of Steel
Construction – Allowable Stress Design (1989). All members that are subjected to axial
compression, bending moment, shear, and torsion, except vertical cantilever pole type supports,
must meet the following criteria:
⎛ f
+
+⎜ v
0.60 F y Fb ⎜⎝ Fv
fa
fb
2
⎞
⎟ ≤ 1.0
⎟
⎠
(Eq. 3-23)
21
⎛ f
+⎜ v
+
⎜F
f ⎞
Fa ⎛
⎜1 − a ⎟ F b ⎝ v
⎜ F' ⎟
e ⎠
⎝
fa
fb
2
⎞
⎟ ≤ 1.0
⎟
⎠
(Eq. 3-24)
The term,
f ⎞
⎛
⎜1 − a ⎟
⎜ F' ⎟
e ⎠
⎝
in Equation 3-27 is a factor that accounts for secondary bending caused by the axial load when
members deflect laterally. This factor may be ignored when fa / Fa ≤ 0.15.
F 'e =
12π 2 E
⎛ kL ⎞
23⎜ ⎟
⎝ r ⎠
(Eq. 3-25)
2
is the Euler stress divided by a factor of safety, which is calculated in the plane of bending. Both
Equation 3-26 and Equation 3-27 of the combined stress equations are provided to check
combined bending and compression stresses. Equation 3-27 considers the second order moments
that appear as a result of P-delta effects. The equation is intended for intermediate unbraced
locations where the member is susceptible to lateral displacements. Equation 3-26 is intended for
locations at the end of the member where lateral displacement is restrained. The following
equation is permitted, in lieu of Equation 3-26 and Equation 3-27, when fa / Fa ≤ 0.15:
⎛ f
+
+⎜ v
Fa Fb ⎜⎝ Fv
fa
fb
2
⎞
⎟ ≤ 1.0
⎟
⎠
(Eq. 3-26)
Members that are subjected to axial tension, bending moment, shear and torsion, must meet the
following criteria:
⎛ f
+
+⎜ v
Fa Fb ⎜⎝ Fv
fa
fb
2
⎞
⎟ ≤ 1. 0
⎟
⎠
(Eq. 3-27)
22
4. DEVELOPMENT AND VERIFICATION OF DESIGN WORKSHEETS
4.1 Design Worksheet Organization
The development of the design worksheets incorporates all of the areas discussed previously
dealing with design methodology and flow. The following sections describe how design
methodology and flow were implemented in the development of the worksheets. MathCAD was
chosen due to its user interactive capabilities and simplistic programming qualities. It is also a
common and affordable engineering tool with which most engineers are familiar. Using
MathCAD facilitates the objective of constructing an “easy-to-use” computer based tool capable
of interactively designing and evaluating sign support structures. The reader should refer to the
worksheet examples provided in the Technical Appendix (UTCA Report 00467-1).
4.1.1 Dimensional and Property Inputs
The dimensional and property input step contains two major elements. A pictorial representation
of the structure is provided in each worksheet to orient required dimensions of the support
structure and elements of interest attached to the structure. The definition of needed dimensional
input is clearly marked by colored boxed sections that have the variables defined. The user can
modify the dimensions as needed. Material property input and dimensions are defined by
instruction close to or following the pictorial model. Elements such as yield strength of steel, arm
and post diameters, pole wall thickness, estimated pressure areas of signals, and unit weights are
defined by the instructions.
4.1.2 Applied Loads
Dead loads and ice loads per Article 3.5 and 3.6 of the Supports Specifications are calculated
from the dimensional and property inputs. Ice loads from Article 3.7 of the Supports
Specifications are calculated based on the assumed unit weight of ice as given in the Supports
Specifications. Areas for ice loads are calculated from the given dimensional and property inputs.
These areas are then multiplied by the unit weight of ice. Wind loads from Article 3.8 of the
Supports Specifications require additional input. Basic wind speed must be identified for the area
in which the sign support structure is to be located. This is found from Figure 3.2 of the Supports
Specifications. Next the wind importance factor and height and exposure factor are determined.
They are found from Table 3-2 and 3-5 of the Supports Specifications, respectively. Once the
wind speed and both factors are determined, they are input using the same colored boxed input
prompts as is found in the dimensional and property input section. For traffic signals and signs,
an additional wind drag coefficient is defined. All of the speeds and factors are then input into the
wind pressure formula, which is based upon theories presented in ANSI/ASCE 7-95. This unit
pressure value is then multiplied by the area of the sign or signal to derive the wind load force that
23
is applied to each feature of the sign support structure. Elements of the structure are then
determined using the same method as the sign support structure features. Finally, some of the
structures require the application of transverse wind loading. Load cases, as defined in Article
3.9.3 of the Supports Specifications, are used to determine the proper load to apply. All elements
and features that have substantial transverse areas should be taken into account in each load case.
4.1.3 Shear and Moment Forces
Shear and moment forces are calculated from the dead, ice, and wind loads. Shear from each
dead, ice, and wind load is summed from the elements and features involved in each load.
Moments are also calculated based on dead, ice, and wind loads summed from the end at which
the moment is to be applied. Forces are transferred from each of the features to the element in
which it is connected, and then through each element, ending with the base or foundation of the
sign support structure. Load cases for the wind loading force, as defined in Article 3.9.3 of the
Supports Specifications, are also used to determine the proper applied force.
4.1.4 Load Combinations
Load combination, as defined in Table 3-1 of the Supports Specifications, is then calculated from
the forces for each defined load combination. Various loads must be applied simultaneously. The
resulting worst combination must be used in the remainder of the analysis. Each worksheet was
programmed with a subroutine to report the results of the load combinations. This result is
identified with a bright color and boxed. Load combinations for each sign support structure
element are reported.
4.1.5 Stresses
Axial, bending, and shear stresses for the post and bending and shear stresses for the arm and
other members are then determined based on the worst load combination case. A stress ratio
check is performed for each element to determine if the element has been over stressed from
applied load stresses. Allowable combined stress ratios are given in Article 5.12 of the Supports
Specifications and can be increased according to Table 3-1 of the Specifications. Each worksheet
has been programmed with a subroutine to report the results of the stress calculation. This result
is identified with a bright color and boxed. Stresses for each sign support structure element are
reported as being within or exceeding the allowable limits. This feature is easily identified by the
user and serves as a checkpoint in the analysis to uncover potential failures of the support
structure.
24
4.1.6 Deflections
Vertical deflection is checked for all elements of the sign support structure. Deflection is limited
to a percentage of the height of the structure according to Article 10.4.2.1 of the Supports
Specifications.
4.1.7 Fatigue
Fatigue design, as defined in Section 11 of the Supports Specifications, is checked for all
elements and features of the structure. Currently, fatigue is only applicable to cantilevered
support structures. Four fatigue loads are considered in the support specification. These loads are
galloping, vortex shedding, natural wind gusts, and truck induced gusts. Table 11-1 of the support
specifications gives the importance factors that can be used with each load for different types of
structures. Three types of fatigue loadings were applicable, and design worksheets were
developed for them by this project. These three types are explained below in more detail. In each
case, a load is applied to the features of the sign support structure. A moment is calculated from
the loads, and stresses are calculated at the connections due to these moments. These stresses are
checked against the constant-amplitude fatigue threshold given in Table 11-3 of the Supports
Specifications.
Galloping
Galloping loads are applied as a static vertical shear pressure to the surface area of signs and
traffic signals. The values for this pressure are calculated according to Equation 11-1 of the
Supports Specification.
Natural Wind Gust
Natural-wind gust loads are applied as static pressure to the members and attachments of the
supports structures. The static load value is estimated according to Equation 11-5 of the Supports
Specifications and is based on a yearly mean wind velocity of 11.2 mph. It can be adjusted using
Equation C11-5 of the Supports Specification.
Truck-Induced Gust
Truck-induced gust load must be applied on the projected surfaces of all signs, walkways, and
luminaires in the positive vertical direction. The pressure to be applied to the sign and arm must
have an importance factor as defined in Article 11-6 of the Supports Specifications and must be
adjusted to reflect the maximum speed limit as defined for the location the structure will reside.
The coefficient of drag is the maximum as given in Table 3-6 of the Supports Specifications.
25
4.2 Illustration of Worksheet Calculations
Several examples were developed to illustrate the use of the design worksheets. Example designs
for a cantilevered truss sign support, non-cantilevered truss sign support, cantilevered monotube
sign and signal support, span-wire sign and signal support are provided in the Technical Appendix
(UTCA Report 00467-1). Specific attributes of the various design worksheets are described in
Section 4.3 through 4.5 below.
4.3 Cantilevered Monotube and Truss Sign Support
The cantilevered monotube and cantilevered truss sign support structures are similar in design
approach and layout. The major difference is the mast arm versus the truss system arm. These
two structures have been combined below for simplicity and expedience in showing the major
differences of each structure in this section.
4.3.1 Dimensional and Property Inputs
The worksheet is arranged similar to the layout and format described above. A set of instructions
and design statement is provided. The dimensional and property input area is then arranged as
outlined previously. First, a pictorial representation of an actual sign support structure is shown
to provide orientation of required dimensions of the support structure and elements of interest
attached to the structure. Each boxed input is color coded to let the user know that information is
needed or can be modified. Each input is assigned a letter or abbreviation for the value of the
dimension or property input. Material property elements and dimensions not shown in the
pictorial model are called to the attention of the user by instructions which prompt for the needed
information close to or following the pictorial model. Elements such as yield strength of steel,
arm and post diameters, pole wall thickness, estimated pressure areas of signals, and unit weights
are some of the information that is called out.
After the dimension and property inputs, the page layout of the cantilevered truss sign support
changes in appearance. The left side of the page is the mathematical section that displays all of
the calculations for the section. The right side offers commentary to indicate how the calculation
is being performed and to refer to the appropriate reference of the Supports Specifications. This
provides the user with an understanding of the calculation and its source.
4.3.2 Dead Loads
Dead loads for the cantilevered monotube and cantilevered truss sign support are automatically
derived from the dimensional and property inputs given. All volumes are calculated based on
dimensions and material density. The cantilevered monotube and cantilevered truss sign support
ice loads are calculated based on the assumed unit weight of ice as given in the Supports
26
Specifications. Areas of the ice-affected zone are calculated from the dimension and property
inputs given. These areas are then multiplied by the unit weight of ice.
Wind loads for the cantilevered truss sign support, from Article 3.8 of the Supports
Specifications, require additional input. Basic wind speed is needed for the geographic area in
which the sign support structure is to be located. Once the wind speed, wind importance factors,
and height and exposure factors are determined, they are input using the colored boxed input
prompts. For traffic signals and signs, an additional wind drag coefficient is defined. All of the
speeds and factors are then input into the wind pressure formula. This unit weight value is then
multiplied by the areas of the sign or signal to derive the wind load force that is applied to each
feature of the sign support structure. Elements of the structure itself are then determined using the
same method as the sign support structure features. Finally, some sign support structures require
the application of transverse wind loading. All elements and features that have substantial
transverse areas must be taken into account in each load case.
4.3.3 Shear and Moment Forces
The cantilevered monotube and cantilevered truss sign support shear and moment forces are
derived from the dead, ice, and wind loads. Moments are also calculated based on dead, ice, and
wind loads summed from the end to which the moment is to be applied. Forces are transferred
from each of the features to the element to which it is connected, and then through each element,
ending with the base or foundation of the sign support structure.
4.3.4 Load Combinations
Load combinations combine various loads that are simultaneously applied. The resulting worst
combination, or highest value, governs the remainder of the analysis. The cantilevered monotube
and cantilevered truss sign support worksheet have been programmed to report the results of the
load combinations. This result is identified with a bright color and boxed. Load combinations for
the cantilevered truss sign support element are reported. This feature is easily identified by the
user and serves as a checkpoint in the analysis to uncover potential failures of the cantilevered
monotube and cantilevered truss sign support. Two load cases are considered for the design of the
post. This is according to Section 3.9.3 of the Supports Specifications to cover the effects of wind
from any direction.
4.3.5 Member Stresses
Axial, bending, and shear stresses for the post element and bending and shear stresses for the arm
and truss elements for the cantilevered truss sign support are then determined based on the worst
load combination case. A stress ratio check is performed for each element to determine if the
element has been over stressed from all applied load stresses. Stresses for cantilevered monotube
and cantilevered truss sign support structure elements are reported as being within or exceeding
27
the allowable limits. This feature is easily identified by the user and serves as a checkpoint in the
analysis to uncover potential failures of the cantilevered monotube and cantilevered truss sign
support structure.
4.3.6 Deflections
Vertical deflection is checked for all elements of the cantilevered monotube and cantilevered truss
sign support structure due to moments from dead and ice loads and self-weight. Each of these
structures uses dead and ice loads to check the deflections of the post, the truss system, and top of
support.
4.3.7 Fatigue
Fatigue design is checked for all elements and features of the structure. Fatigue Category III is
applicable to both cantilevered structures. Importance factors for this category are given in Table
11-1 of the Supports Specifications. For galloping, the pressures are applied to the horizontal
areas of the sign and signal. Natural wind gust pressures are applied to the sign, signals, and
structure in the horizontal direction. A galloping unit load is applied to the features of the sign
support structure. A moment is derived from the galloping loads. Natural wind gusts are then
calculated for each element and feature of the sign support structure.
4.3.8 Wind Gust
Truck-induced wind gust is the final analysis required to complete the design of cantilevered
structures. The pressure applied to the sign and arm has an importance factor defined in Article
11-6 of the Supports Specifications and has been adjusted to reflect the maximum wind speed
limit.
4.4 Non-Cantilevered Truss Sign Support
The non-cantilevered truss sign support varies from the cantilevered structures in almost all of the
design categories. This is primarily due to the shape and supporting members of the structure. A
complete design example is shown in the Technical Appendix (UTCA Report 00467-1).
4.4.1 Dimensional and Property Inputs
The user is asked to provide several values concerning the geometry and makeup of the structure,
and to input various heights, spans, and depths of the non-cantilevered truss system. The user can
also specify the position of the road signs and maintenance walkway. Letters corresponding to
specific regions of the structure are shown on the schematic to indicate required user input. The
28
sizes of all members are provided by the user. The shaded regions in the design sheet symbolize
values that require user-input data in order to perform the design calculations.
4.4.2 Dead Loads
For the non-cantilevered sign support structure, the major loads considered in the development of
the design sheet are discussed below. The permanent dead loads include signs, maintenance
walkway, and self-weight of the truss and double pole uprights. The user is asked to enter the
load per square foot of the sign panels along with the weight of the walkway per linear foot. The
self-weight of the truss and double pole upright are calculated based on the structure geometry
user input. To determine the dead load contribution of the signs, the area is multiplied by the
weight per square foot to determine the dead load. The point of application is taken at the center
of gravity of the signs. The points of application for the walkway and truss are taken at each
center of gravity. The dead load of the double pole uprights, including struts and diagonals, is
calculated based on the self–weights of all of the members making up the uprights. The point of
application is also taken at the center of gravity.
The design sheet allows for ice load. From the calculated wind pressure, the basic wind loads on
the signs, walkway, and truss are calculated by multiplying the wind pressure by the area of
contact of each individual element. The user is only required to enter the wind velocity, the wind
importance factor, and the height and exposure factor. All of these values can be found in the
Supports Specifications. The wind drag coefficients are automatically calculated based on the
guidelines discussed in Chapter 3. The wind load on the upright normal to the structure is
calculated by multiplying the wind pressure times the area of contact of the upright structure. The
transverse wind loads on the truss, signs, maintenance walkway and uprights are calculated
accordingly to the guidelines of design loads for vertical supports found in Chapter 3 of the
Supports Specifications. Similar to the dead load, the design sheet automatically generates all of
the wind loads based on the methodology discussed above. A schematic can be found below and
within the design sheet showing the location of the wind loads.
4.4.3 Load Combinations
Load combination II (DL+WL) produces the maximum design stresses for this design scenario,
using allowable stresses increased as indicated for the material and group load.
4.4.4 Reactions at Upright Post
The reactions due to the dead loads are determined by summing the moments around a support
considering the dead loads of the panels, walkway, and truss. The reactions due to wind loads are
determined by taking the sum of moments around a support considering the wind load on the
panels, wind load on the walkway, and wind load on the truss similar to the dead loads. The
points of application of the wind loads and dead loads on the individual items are their respective
29
centers of gravity. Taking the moments about a support will give a single reaction, which can be
used to obtain the reaction on the opposing side of the structure. The non-cantilevered truss
structure design sheet determines the reactions due to dead and wind load based on the procedure
discussed above. A comprehensive plot can be found within the design sheet showing the
magnitude and the direction of the reactions for both cases.
4.4.5 Member Stresses
To determine the member stresses for each of the overhead truss structure elements, the sectional
properties of each of the elements must be calculated. Basic engineering mechanics principles are
used to determine the section modulus, moment of inertia, and radius of gyration of all the
necessary elements. The design worksheet calculates these properties based on the member size
values provided by the user. From these calculations and the loads calculated from the Group II
Load Combinations, the stresses in the truss chords, truss diagonals and struts, post, and upright
diagonals and struts can be determined. Below is a brief description of the methodology used to
determine the member forces and stresses present in non-cantilevered sign support structures
members.
The axial load at truss chords is calculated from a coupling force composed of both dead load and
wind load forces. The maximum moment at the truss chords is a localized effect based on the
maintenance walkway/sign hanger supports. The maximum axial load at the vertical diagonals is
calculated from the maximum dead load reaction being transferred into the vertical truss
diagonals. The maximum axial load at the horizontal diagonals is calculated from the maximum
horizontal wind load being transferred into the horizontal truss diagonals. The maximum axial
load at the vertical struts is calculated from the maximum reaction produced from the dead load.
The maximum axial load at the horizontal struts is calculated from the maximum reaction
produced from the horizontal wind load. The maximum axial load at the upright is calculated
from the maximum reaction produced from the dead load plus the self-weight of the upright
configuration. The maximum shear load at the upright is calculated from the maximum reaction
produced from the horizontal wind load plus the wind load acting normal to the structure. The
maximum normal moment at the upright is calculated based on the shear load and wind load
acting normal to the structure. The maximum transverse moments at the upright are calculated
based on transverse loads present on the signs, truss, walkway, and upright post.
The Group II loads described above are automatically calculated by the design worksheet based
on the user input. Specific values can be found in Section D (Group II Load Combination DL +
WL) of the design worksheet.
The allowable stresses are calculated based on the criteria discussed in Chapter 3. The design
worksheet automatically determines the applicable allowable stress category based on user input.
This is done through a series of “if” statements that use Boolean relationships to evaluate the
necessary mathematical equations. The example in the Technical Appendix (UTCA Report
00467-1) shows how the allowable bending stresses for truss chords are determined. For this
example, the “if” statements allow the program to determine whether the member is compact,
30
non-compact, or slender by using simple Boolean functions. This type of logic is typical for all of
the allowable stresses for the structural members of the non-cantilevered sign support structures.
4.4.6 Combined Stress Ratios
Members subjected to combined bending, axial compression or tension, shear and torsion are
proportioned to meet the limitations of Supports Specifications Article 5.12.1 or 5.12.2. Each of
the overhead truss structure elements is checked for the combined stress ratios pertaining to the
specific element in question. The design worksheet determines which stress ratio is applicable and
uses this ratio as the means for determining the combined stress present on the member. Each
member’s allowable stress can be found in the stress section on the design sheet.
4.5 Span Wire Traffic Signal and Sign Support
The span wire support structure is similar in overall layout to the previous examples. The major
areas of difference are described below. The worksheet is shown in entirety in the Technical
Appendix (UTCA Report 00467-1).
4.5.1 Dimensional and Property Inputs
After instructions and design statement sections, the dimensional and property input area is
arranged. A pictorial model representation is shown to help explain and orient required
dimensions of the support structure and elements of interest attached to the structure.
4.5.2 Dead Loads
Dead loads for the span wire support structure are automatically derived from the dimensional
and property inputs given. Dead loads are calculated using the same principals discussed in other
examples.
4.5.3 Forces on Wire
The span wire support structure shear and moment forces are derived from the dead, ice, and wind
loads. Moments are also calculated based on dead, ice, and wind loads summed from the end in
which the moment is to be applied. Forces for the span wire are calculated in this section. These
forces are determined using the equations presented in the Technical Appendix (UTCA Report
00467-1). This section also determines the total length of the wire.
31
4.5.4 Load Combinations
Load combinations group various loads that are most probable to occur at a given time. The
major difference in the span wire support structure is the tension calculation of the wire under
these load combinations. This calculation must converge with the dead load and wind load by a
trial and error solution for Ax, the horizontal longitudinal reaction, until it converges with L0
variables from Group I and II.
4.5.5 Member Stresses
Axial, bending, and shear stresses for the post element and bending and shear stresses for the arm
and truss elements for the span wire support structure are then determined based on the worst load
combination case. A stress ratio is performed for each element to determine if the element has
been over stressed. Stresses for span wire support structure elements are reported as being within
or exceeding the allowable limits.
4.5.6 Deflections
Vertical deflection is checked for all elements of the span wire support structure due to tension
from dead and ice loads and self-weight. Each of these structures uses dead and ice loads to
check the deflections at the top of the post.
4.6 Applicability and Verification
Sign support designs from several departments of transportation, including Wyoming, Arkansas,
and Illinois, along with the typical dimensions of support structures found in Alabama, were used
to evaluate the appropriateness and completeness of the design worksheets, as well as to
determine whether the worksheets produced results consistent with actual designs. Once the
values from the actual designs were entered into the design worksheets, the results were examined
for indication of problems or errors. Upon reviewing the results of each type of worksheet, it was
concluded that the design sheets produced results that were consistent with the example designs
considered. The output statements incorporated in the design worksheet indicated that each
structural element was under the stress limit designated in the program.
4.7 Survey of Local Transportation Engineers
One of the activities of the project was to investigate whether county and municipal engineers
have a need for the design worksheets. ALDOT has expressed a need to have the capability of
designing and evaluating structural supports for highway signs, luminaires and traffic signals.
Municipal, county and district levels were contacted to determine if local government engineers
32
would be interested in the same technology of being able to design and evaluate support
structures.
Engineering departments from the City of Hoover, ALDOT Fifth District (Shelby County), and
ALDOT Third Division (Birmingham) were contacted. The project was described to engineers
within engineering departments. The contacts were asked if there is a need at their level for this
technology. All three levels of engineering contacted stated that they did not perform structural
calculations on structural supports, and did not need such a tool. All three departments stated that
the contractor erecting the structure is responsible for the integrity of the structure. The contractor
purchases a sign support structure from a manufacturer that has conducted the design and
engineering.
Questions were also asked to determine what types of structural supports were most commonly
outsourced. All three engineering departments stated that the majority of the structures being
constructed at their levels were mast arm support structures, and span wire traffic signal supports.
Larger sign support structures such as the cantilevered and non-cantilevered truss sign support
structures were rarely owned by local governments.
4.8 Integration of the Design Worksheets with CAD
The Team investigated the possibility of linking the MathCAD design sheets to CAD drawings.
MathCAD contains specialized OLE (Object Link Exchange) objects which allow a user to
exchange data with other applications or sources and to build user interface controls. Application
components allow a user to access functions and data from other computational applications that
are compatible with MathCAD. One OLE application that is included in MathCAD that
possesses the capability of producing CAD drawings is the SmartSketch component.
SmartSketch is a 2D drawing and design tool developed by Intergraph that has similar capabilities
to AutoCad and MicroStation. The SmartSketch component allows a user to create drawings in a
MathCAD sheet whose dimensions are computationally linked to MathCAD calculations, which
makes MathCAD the ideal platform for creating technical details that can be used to produce
drawings. The dimensions that are linked to MathCAD calculations can be drawn to a user
specified scale, which makes the drawings accurate enough for construction drawings. A design
worksheet approach may be used to send values from MathCAD to SmartSketch, using
SmartSketch to manipulate the data dynamically without leaving the MathCAD environment, and
sending values from SmartSketch back to MathCAD.
While this function exists within MathCAD, it was only investigated on a preliminary basis to see
if it was applicable to this type of worksheet. The capability looks promising. Further
investigation, analysis, and programming can be considered to incorporate the SmartSketch
function into these worksheets.
33
4.9 External Review
A thorough review of the worksheets was conducted by professional engineers who have
extensive experience in the design of support structures. This was done to ensure the applicability
and accuracy of the worksheets. All changes suggested by the reviews were implemented. The
review resulted in confirmation that the design examples were within the limits of the Support
Specifications and yielded satisfactory output.
34
5. CONCLUSIONS
5.1 Summary
Computer based design worksheets for designing and evaluating non-cantilevered, cantilevered,
span wire, and cantilevered monotube signal and sign support structures were developed. The
latest adopted design specifications and guidelines were applied in accordance with the AASHTO
“Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic
Signal” 2001 Edition.
The worksheets require a minimum amount of user input. Output statements found within the
body of the program identify components of the structure that are overstressed. If an element of
the structure is overstressed, simple changes can be made in the user input section until the
structure is under the stress limits. Designs from state DOT’s including Arkansas, Wyoming,
and Illinois were used to verify the adequacy of the results produced by the worksheets. A
sidebar commentary is provided that describes the source and reasoning for the calculations. The
worksheets were reviewed by professional engineers with sign support design experience.
5.2 Conclusions
Developing a complete and versatile sign support design and analysis aid in the form of
MathCAD worksheets is a complicated and arduous task. The Team underestimated the work
required. However, design worksheets for the most difficult sign support structure geometries
were completed. This project demonstrates the ability to generalize and program a complicated
structural analysis and design problem into a MathCAD-type of software. The approach offers
the following advantages: (1) all calculations are visible and easily related to design
specifications; (2) the worksheets are easily altered to accommodate specific needs of the user; (3)
the approach facilitates commentary concurrent with design calculations; and (4) the final
engineering product, including all calculations, can be printed for engineering records.
Disadvantages of this approach include: (1) the user must purchase the worksheet software; (2)
each worksheet is specific to support structure and signage geometry; and (3) depending on the
type of support structure, an external structural analysis may be required to accurately calculate
member forces.
5.3 Recommendations
Further development of the design sheets is needed to strengthen the capabilities and generality of
the program. The design sheets developed during this effort are specific to certain common sign
support geometries and sign placement configurations. Developing interactive sign support
35
software capable of evaluating any geometric configuration as well as different types of material
with a user-defined number of signs would prove more useful. The design sheet would be able to
cover a wider range of design alternatives making it more valuable to the user. Additional
programming to prompt the user through a Windows based graphical interface would provide a
better understanding of the required inputs. This interface could prompt the user for input and
give examples or explanations as to why the input is required.
Integration of CAD input and output would also be more effective. By utilizing SmartSketch, or
other OLE applications, the output can be updated to provide working design drawings of the
exact design. The SmartSketch component allows a user to create drawings in a MathCAD sheet
whose dimensions are computationally linked to MathCAD calculations, which makes MathCAD
the ideal platform for creating technical details that can be used to produce drawings.
Finally, the investigators must follow through from development to implementation by working
with the users to ensure that the design worksheets are useable in the form developed. Although
great interest in the product has been noted, utility and value have not yet been proven.
Recommendations for improvements and the next generation of sign support design software will
certainly evolve from interaction between users and the research team.
36
6. LIST OF REFERENCES
American Association of State Highway and Transportation Officials, “AASHTO LRFD bridge
design specifications,” First Edition. Washington, D.C. 1994.
AISC, “Manual of Steel Construction”, American Institute of Steel Construction, New York, NY,
1989.
ASCE, “Standard Minimum Design Loads for Buildings an Other Structures,” ANSI/ACSE 7-95,
American Society of Engineers, New York, NY, 1996.
Fouad, F.H., Calvert, E.A., and Nunez, E. (1997). “Structural Supports for Highway Signs,
Luminaires and Traffic Signals.” National Cooperative Highway Research Program,
Preliminary Draft Final Specification – NCHRP Project 17-10, Transportation Research
Board, Washington, D.C.
Fouad, F. H., Calvert, E. A., and Nunez, E., (1997). “Structural Supports for Highways Signs,
Luminaires, and Traffic Signals.” Draft Final Design Examples - NCHRP Project 17-10,
Transportation Research Board, Washington, D.C.
Fouad, F.H., Calvert, E.A., and Nunez, E. (1999). “Proposed revisions to AASHTO standard
specifications for Highway Signs, Luminaires and Traffic Signals.” National Cooperative
Highway Research Program Rep. No. 411, Transportation Research Board, Washington, D.C.
Fouad F.H., Davidson J.S., Delatte N.J., Calvert E.A., Chen S.E., Nunez E., Abdalla R.S., (2002)
“NCHRP Report 494: Structural Supports for Highway Signs, Luminaires, and Traffic
Signals,” National Cooperative Highway Research Program, Transportation Research Board,
Washington, D.C.
MathSoft, Inc. (2000), “MathCAD 2000 User’s Guide,” Cambridge, MA.
Timoshenko, S.P., and Gere, J.M., “Theory of Elastic Stability,” McGraw-Hill Book Co., New
York, 1961.
37