ABSTRACT LANIER, BRYAN KEITH. Study in the Improvement in Strength and Stiffness Capacity of Steel Multi-sided Monopole Towers Utilizing Carbon Fiber Reinforced Polymers as a Retrofitting Mechanism (Under the direction of Dr. Sami Rizkalla) Wireless service is a fast developing market which places inherent demands on providers to maintain constant, reliable networks through which the service is offered. In order to facilitate this growing need, wireless providers must install equipment which creates and strengthens these networks. Telecommunication towers are popular solutions for placing antennas at elevations which develop the line of sight trajectory and signal coverage the networks demand. However, as telecommunication towers have a finite limit to the amount of equipment installation, they must be strengthened to support additional equipment expansion. Research completed at North Carolina State University proposes a strengthening solution utilizing high-modulus carbon fiber polymers as a retrofitting mechanism for monopole telecommunication towers. The experimental program, along with development of an analytical model, investigates the behavior and validates the effectiveness of carbon fiber in increasing the flexural capacity of existing monopole tower structures. The experimental program consists of testing three large scale monopole towers using high-modulus sheets, high-modulus strips and intermediate-modulus strips to determine their respective effectiveness in increasing the flexural strength enhancement. The three tests are designed using approximately the same reinforcement ratios, as well as
166
Embed
ABSTRACT - Nc State University · PDF fileStudy in the Improvement in Strength and Stiffness ... Polymers as a Retrofitting Mechanism ... CHAPTER 1 - INTRODUCTION 1 1
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
ABSTRACT
LANIER, BRYAN KEITH. Study in the Improvement in Strength and Stiffness Capacity of Steel Multi-sided Monopole Towers Utilizing Carbon Fiber Reinforced Polymers as a Retrofitting Mechanism (Under the direction of Dr. Sami Rizkalla)
Wireless service is a fast developing market which places inherent demands on providers
to maintain constant, reliable networks through which the service is offered. In order to
facilitate this growing need, wireless providers must install equipment which creates and
strengthens these networks. Telecommunication towers are popular solutions for placing
antennas at elevations which develop the line of sight trajectory and signal coverage the
networks demand. However, as telecommunication towers have a finite limit to the
amount of equipment installation, they must be strengthened to support additional
equipment expansion.
Research completed at North Carolina State University proposes a strengthening solution
utilizing high-modulus carbon fiber polymers as a retrofitting mechanism for monopole
telecommunication towers. The experimental program, along with development of an
analytical model, investigates the behavior and validates the effectiveness of carbon fiber
in increasing the flexural capacity of existing monopole tower structures.
The experimental program consists of testing three large scale monopole towers using
high-modulus sheets, high-modulus strips and intermediate-modulus strips to determine
their respective effectiveness in increasing the flexural strength enhancement. The three
tests are designed using approximately the same reinforcement ratios, as well as
identically sized monopole towers, to compare the effectiveness of the three
strengthening systems regarding the increase in strength and stiffness. Design nominal
strength and stiffness increases were in the range of 20 to 50% which was found in the
measured values. The three tests were subjected to the same load setup and tested until
failure to capture the elastic and inelastic behavior and the strength increases, as well as
the failure mode of the strengthened tower.
The analytical models were designed to simulate the monopole’s behavior before and
after strengthening using conventional methods of analysis typically applied to tower
design. The analytical model is based on moment-area and transformed section theories
to predict the strain and deflection behavior in the elastic range of the steel and carbon
fiber. Parametric studies are conducted to study the effect of the numerous variables with
respect to strengthening these types of towers.
STUDY IN THE IMPROVEMENT IN STRENGTH AND STIFFNESS CAPACITY
OF STEEL MULTI-SIDED MONOPOLE TOWERS UTIZLING CARBON FIBER
REINFORCED POLYMERS AS A RETROFITTING MECHANISM
By
BRYAN KEITH LANIER
A thesis submitted to the Graduate Faculty of
North Carolina State University
In partial fulfillment of the
Requirements for the degree of
Master of Science
in
CIVIL ENGINEERING
Raleigh, North Carolina
Spring 2005
APPROVED BY:
_____________________________________ Dr. Sami Rizkalla, Chairman of Advisory Committee
_____________________________________ Dr. William Rasdorf, Member, Advisory Committee
_____________________________________ Dr. James Nau, Member, Advisory Committee
ii
BIOGRAPHY
Bryan Keith Lanier was born on December 2, 1977 in Lexington, North Carolina. He
graduated from West Davidson High School in May 1996 and enrolled at North Carolina
State University in the School of Engineering. He completed the Bachelor of Science in
Civil Engineering in May of 2001. After graduation, Mr. Lanier was employed by
SpectraSite Communications. His work there entailed the structural analysis and design
of steel and concrete telecommunication towers. During the spring of 2001, Mr. Lanier
was admitted into the Graduate School at North Carolina State University in pursuit of
the degree of Master of Science in Civil Engineering.
Mr. Lanier is the son of Dennis and Rita Lanier and has one younger brother, Jason Craig
Lanier, who also is a graduate of North Carolina State University from the Department of
Mechanical Engineering. Upon completion of his academic requirements, Mr. Lanier
will continue his career in the field of telecommunication/tower engineering.
iii
ACKNOWLEDGEMENTS
The author wishes to gratefully acknowledge the funds provided by the National Science
Foundation through the Industry/University Collaborative Research Center and the
Mitsubishi Chemical America, Inc for providing the materials needed for the
experimental program. The engineering department staff of SpectraSite
Communications, specifically Douglas Pineo, provided significant assistance in the test
design. J. John Harris, P.E., David Schnerch, and Dr. Amir Fam provided valuable
insight into the test design process. Jerry Atkinson, Lab Technician for the Constructed
Facilities Laboratory, and Bill Dunleavy, Electronics Technician, added valuable
practical knowledge and advice to the actual test setup. The members of the advisory
committee are gratefully thanked for their contributions and reviewing this thesis.
Finally, the author would like to acknowledge Kirk Stanford, Scott Wirgau, Randall
Wilson, Todd Garrison and Joel Howard for their support throughout entire graduate
school process.
iv
TABLE OF CONTENTS
LIST OF TABLES vi LIST OF FIGURES vii CHAPTER 1 - INTRODUCTION 1
3.3 Design of the Specimens 33 3.3.1 Test I Design – High-Modulus Sheets 34 3.3.2 Test II Design – High-Modulus Strips 35 3.3.3 Test III Design – Intermediate-Modulus Strips 37
3.4 Fabrication of the Specimens 38 3.4.1 Monopole Surface Preparation and Cleaning 38 3.4.2 CFRP Preparation 39 3.4.3 Installation 40
4.1 Test I – Monopole Strengthened with High-Modulus Sheets 56 4.1.1 Stiffness and Strength 57 4.1.2 Discussion of Test Results 61
v
4.2 Test II – Monopole Strengthened with High-Modulus Strips 63 4.2.1 Stiffness and Strength Results 63 4.2.2 Discussion of Test Results 68
4.3 Test III - Strengthening with Intermediate-Modulus Strips 70 4.3.1 Stiffness and Strength 71 4.3.2 Discussion of Test Results 76
CHAPTER 5 - ANALYTICAL MODEL 107 5.1 Elastic Flexural Stiffness Model 108 5.2 Test I Model 111
5.2.1 Deflection, Stiffness and Strain 112 5.2.2 Discussion of Tested vs. Modeled Results 113
5.3 Test II Model 115 5.3.1 Deflection, Stiffness and Strain 115 5.3.2 Discussion of Tested vs. Modeled Results 116
5.4 Test III Model 118 5.4.1 Deflection, Stiffness and Strain 118 5.4.2 Discussion of Tested vs. Modeled Results 119
5.5 Parametric Study Using the Proposed Analytical Model 121 5.5.1 Effect of Layers - Test I Model 122 5.5.2 Effect of Modulus - Test II Model 125
CHAPTER 6 - SUMMARY AND CONCLUSIONS 134
6.1 Summary 134 6.2 Conclusions 136 6.3 Recommendations for Further Testing 140
REFERENCES 141 APPENDIX
vi
LIST OF TABLES
Page
CHAPTER 3 3.1 Material Properties of Dialead K63312 and Dialead K63712 48
vii
LIST OF FIGURES
Page
CHAPTER 2 2.1 Lattice/Self-Supporting Tower 24 2.2 Guyed Tower 24 2.3 Tapered Monopole 24 2.4 Stepped Monopole 24 2.5 DualPole Installation 25 2.6 DualPole Cross-section 25 2.7 MUS Steel Band and Epoxy Application 25 2.8 MUS Installation 25 2.9 STSP Completed Installation 25 2.10 STSP Installation 25 2.11 WDMRS Base Installation 26 2.12 WDMRS Installation Looking Up 26 2.13 AMUS Completed Installation 26 2.14 AeroSolutions Adhesive Testing 26 2.15 HTSMTR Completed Installation 26 2.16 HTSMTR Installation 26 CHAPTER 3 3.1 Monopole Shaft Dimensions and Fabrication Method 47 3.2 Baseplate Dimensions and Anchor Bolt Orientations 47 3.3 Monopole Specimen 47 3.4 Stress/Strain Coupon Test Results 47 3.5 CFRP Sheets and Strips 48 3.6 Longitudinal and Transverse Sheet Layout, Test I 49 3.7 Clip Angles at Base, Test I 49 3.8 Longitudinal Strip Layout, Test II & III 50 3.9 Stiffener Placement, Dimension and View, Test II & III 50 3.10 Surface Preparation 51 3.11 Longitudinal and Transverse Sheet Installation 51 3.12 Adhesive Application 52 3.13 Strip Installation 52 3.14 Pi Gauge and Strain Gauge 52 3.15 Pi Gauge Layout 52 3.16 Base Potentiometer Layout 52 3.17 Typical Pi and Strain Gauge Locations 53 3.18 Potentiometer Locations Along Monopole Shaft and Baseplate 53 3.19 Monopole Loading Setup 54 3.20 Monopole Loading Layout 54
viii
CHAPTER 4
Page
4.1 Measured Deflection Locations for Tests I, II and III 79 4.2 Strain Measurement Locations for Tests I, II and III 79 4.3 Net Displacement at 0.25L, 0.5L, 0.75L and L, Test I – First and Second Load Cases 80 4.4 Longitudinal Strain at 150 – 200 mm from Base, Test I – First and Second Load Cases 80 4.5 Longitudinal Strain at 460 mm from Base, Test I – First and Second Load Cases 81 4.6 Longitudinal Strain at 1520 mm from Base, Test I – First and Second Load Cases 81 4.7 Longitudinal Strain at 2900, 3050 and 3250 mm from Base, Test I – First and Second Load Cases 82 4.8 Longitudinal Strain at 4570 mm from Base, Test I – First and Second Load Cases 82 4.9 Longitudinal Strain Profile at 32 kN, Test I – First and Second Load Cases 83 4.10 Net Displacement at 0.25L, 0.5L, 0.75L and L, Test I – Third Load Case with
Nylon Straps 83 4.11 Minor Localized Debonding of Sheets at 75 kN, Test I – Third Load Case with Nylon Straps 84 4.12 Monopole Load Application with Nylon Straps 84 4.13 Monopole Load Application with Steel Chains 84 4.14 Net Displacement at 0.25L, 0.5L, 0.75L and L, Test I – Third Load Case with Steel Chains 85 4.15 Buckling of Monopole Shaft and Rupture of Sheets, Test I – Third Load Case with Steel Chains 85 4.16 Longitudinal Strain at 200, 460 and 1520 mm from Base, Test I – Third Load Case with Nylon Straps 86 4.17 Longitudinal Strain at 2900, 3250 and 4570 mm from Base, Test I – Third Load Case with Nylon Straps 86 4.18 Longitudinal Strain at 200, 460 and 1520 mm from Base, Test I – Third Load Case with Steel Chains 87 4.19 Longitudinal Strain at 2900, 3250 and 4570 mm from Base, Test I – Third Load Case with Steel Chains 87 4.20 Longitudinal Strain Profile at 32 and 95 kN, Test I – First, Second and Third Load Cases 88 4.21 Vertical Strains at 610 and 1220 mm, Test I – Third Load Case with Steel Chains 88 4.22 Net Displacement at 0.25L, 0.5L, 0.75L and L, Test II – First and Second Load Cases 89 4.23 Longitudinal Strain at 80, 150, 200 and 230 mm from Base, Test II – First and Second Load Cases 89
ix
Page 4.24 Longitudinal Strain at 460 mm from Base, Test II – First and Second Load Cases 90 4.25 Longitudinal Strain at 1520 mm from Base, Test II – First and Second Load Cases 90 4.26 Longitudinal Strain at 2900, 3050 and 3250 mm from Base, Test II – First and Second Load Cases 91 4.27 Longitudinal Strain at 4570 mm from Base, Test II – First and Second Load Cases 91 4.28 Longitudinal Strain Profile at 32 kN, Test II – First and Second Load Cases 92 4.29 Longitudinal Strain at 230 mm from Base, Test II – First and Second Load Cases 92 4.30 Net Displacement at 0.25L, 0.5L, 0.75L and L, Test II – Third Load Case 93 4.31 Failure Modes at Load per Net Displacement Measured at L, Test II – Third Load Case 93 4.32 Compressive Rupture of the Top Strip, Test II – Third Load Case 94 4.33 Delaminating of Bottom Strips, Test II – Third Load Case 94 4.34 Buckling of Monopole, Test II – Third Load Case 94 4.35 Ruptured Strip Remains at Stiffeners, Test II - Third Load Case 94 4.36 Longitudinal Strains at 80, 150 and 230 mm from Base, Test II – Third Load Case 95 4.37 Longitudinal Strains at 460 and 1520 mm from Base, Test II – Third Load Case 95 4.38 Longitudinal Strains at 2900, 3250 and 4570 mm from Base, Test II – Third Load Case 96 4.39 Longitudinal Strain Profile at 32 and 44kN, Test II – First, Second and Third Load Cases 96 4.40 Net Displacement at 0.25L, 0.5L, 0.75L and L, Test III – First and Second Load Cases 97 4.41 Longitudinal Strains at 80, 150 and 230 mm from Base, Test III – First and Second Load Cases 97 4.42 Longitudinal Strains at 460 mm from Base, Test III – First and Second Load Cases 98 4.43 Longitudinal Strains at 1520 mm from Base, Test III – First and Second Load Cases 98 4.44 Longitudinal Strains at 3050 mm from Base, Test III – First and Second Load Cases 99 4.45 Longitudinal Strains at 4570 mm from Base, Test III – First and Second Load Cases 99 4.46 Longitudinal Strain Profile at 32 kN, Test III – First and Second Load Cases 100 4.47 Longitudinal Strains at 230 mm from Base, Test III – First and Second Load Cases 100 4.48 Location of Measured Strain at 230 mm from Base, Test III 101 4.49 Net Displacement at 0.25L, 0.5L, 0.75L and L to Loading of 55 kN, Test III –
Third Load Case 101
x
Page 4.50 Gross Displacement at 0.25L, 0.5L, 0.75L and L, Test III – Third Load Case 102 4.51 Failure Modes at Load per Net Displacement Measured at L, Test III – Third Load Case 102 4.52 Delaminating of Bottom Strips, Test III – Third Load Case 103 4.53 Rupture of Top Strips, Test III – Third Load Case 103 4.54 Buckling of Monopole, Test III – Third Load Case 103 4.55 Air Voids in Epoxy, Test III – Third Load Case 103 4.56 Longitudinal Strains at 80, 150 and 230 mm from Base, Test III – Third Load Case 104 4.57 Longitudinal Strains at 460 and 1520, Test III – Third Load Case 104 4.58 Longitudinal Strains at 3050 and 4570 mm from Base, Test III – Third Load Case 105 4.59 Longitudinal Strains at 230 and 460, Test III – Third Load Case 105 4.60 Longitudinal Strain Profile at 32 and 54 kN, Test III - First, Second and Third Load Cases 106 CHAPTER 5 5.1 Illustration of Existing and Transformed Section 128 5.2 Deflection Diagram 128 5.3 Modeled and Tested Net Deflection Profiles at 32 kN, Test I – First and
Second Load Cases 129 5.4 Modeled and Tested Strain Profiles at 32 kN, Test I – First and Second Load Cases 129 5.5 Modeled and Tested Net Deflection Profiles at 32 kN, Test II – First and Second Load Cases 130 5.6 Modeled and Tested Strain Profiles at 32 kN, Test II – First and Second Load Cases 130 5.7 Modeled and Tested Net Deflection Profiles at 32 kN, Test III – First and Second Load Cases 131 5.8 Modeled and Tested Strain Profiles at 32 kN, Test III – First and Second Load Cases q 131 5.9 Modeled and Tested Net Deflection Profiles at 32 kN, Test I – Parametric Study 129 5.10 Modeled and Tested Strain Profiles at 32 kN, Test I – Parametric Study 129 5.11 Stiffness Increases vs. Reinforcement Ratios for Three Strip Specimens,
Test II 129
1
CHAPTER 1 - INTRODUCTION
The wireless telecommunications industry has enjoyed significant increases in business
within the past ten years. Predictions from several financial analysts suggest the business
will only increase as the use of wireless products becomes more widespread and reliable.
The introduction of wireless fax, internet, and email are some of the more recent
advances in an industry that was previously limited to the availability of phone and fiber
optic lines. The use of cellular phones is the most powerful incentive in the wireless
industry to develop networks capable of supporting the increasing consumer demand.
Their use in the United States and abroad has created numerous revenue streams for
various businesses.
1.1 General
The advantage of wireless technology is its ability to be utilized largely at any location.
No physical lines, wires, or connections on which the electronic or laser frequencies
converge at a motherboard are required. Only strategic locating of antennas, dishes, or
receptacles are needed to transfer the information from the user to the user. These
antennas, which are the basis of the cellular networks, must be mounted at various
locations to ensure coverage capacity to the user. They are mounted on all types of
structures from water tanks to skyscrapers and in some cases even the insides of buildings
and palladiums. One of the most popular mounting devices are large steel and concrete
towers. They can be placed strategically without the requirements of large amounts of
2
land and can elevate the antennas to any height desired. Only cost, local regulations, and
the availability of land hinder their construction.
Several large communication businesses have recognized the opportunity of marketing
telecommunications towers and have built numerous towers on which antennas can be
installed. It is in the best interest of each tower leasing business to have as many
antennas on their towers as possible since this equates to more capital. Towers, like all
structures, are designed and maintained in accordance with national building codes and
standards. They are designed to satisfy serviceability and strength requirements,
including weight, wind and ice loads specific to the tower’s geographic location.
Due to the demand for wireless service, there is a need to increase the number of
antennas a tower can support. Strengthening of cellular towers is required to ensure the
structure can carry the increased loading from the additional antennas. The strengthening
system must be cost effective while not interrupting service of the tower’s current
tenants. There are several alternatives for retrofitting towers but most are expensive and
cumbersome to install. A solution must be developed which significantly enhances the
overall load carry capacity of the tower without altering its overall appearance or
serviceability. It must be rugged and durable, able to withstand the forces and elements
of nature while being easy to prepare and install.
Utilization of high modulus carbon fiber reinforced polymers (CFRP) provides an
excellent potential solution which could greatly enhance the strength capacities of
3
telecommunication towers. The inherent strength qualities of CFRP offer significant load
carrying improvement, introducing itself as a prime candidate for enhancing the strength
of the tower. Installation of the CFRP can be relatively simple and completed in a
relatively short time, offering significant advantages over existing strengthening
techniques. This system eliminates the need for welding, which is a major issue in terms
of cost and function. The light weight of CFRP material also lends itself to be safer and
easy to handle material. CFRP has superior resistance to fatigue, thus enhancing the
serviceability of the tower structure. Finally, CFRP resistance to corrosion enhances its
value to future deterioration of the structure.
1.2 Objectives
The main objective of this study is to determine the effectiveness of using CFRP to
increase in the strength and stiffness of monopole steel towers. The specific aspects
considered in this study are:
1. Evaluation of the stiffness of the tower strengthened with CFRP within the steel
elastic range, with respect to the stiffness of unstrengthened towers.
2. Determination of the overall strength increases of the tower strengthened using
various types of CFRP.
3. Develop an analytical model to predict the flexural stiffness and strength of
unstrengthened steel monopole towers with the steel elastic range.
4
4. Examine the different possible failures modes of the towers strengthened with
CFRP.
5. Study the various factors affecting strengthening these towers with CFRP.
6. Provide design recommendations and installation methods for the proposed
strengthening technique.
1.3 Scope
The scope of this work consists of an experimental investigation using large scale models
of the towers and development of an analytical model. The experimental program
provides detailed information on the behavior and increases of the strength and stiffness,
as well as failure modes, of towers strengthened with CFRP material. The study provides
also insight into the installation process, offering methodology of handling the material
and existing tower structure. The analytical model is proposed to predict the measured
values and validate the increase of the strength and stiffness within the steel elastic range.
The models will also be used to study various parametric factors believed to influence
strength and stiffness values used in the proposed technique.
The experimental program includes testing of three steel towers. The first test utilizes
CFRP in a sheet form. The first load case of Test I include testing of the unstrengthened
tower to 60 percent of its nominal flexural yield strength. The tower is then unloaded and
followed by installing CFRP sheets designed to increase the yield strength and stiffness
between 20 and 40 percent. The strengthened tower was loaded to reach the same
5
midspan deflection measured from the first load case at 60 percent, yield strength of the
unstrengthened tower. The strengthened tower was then loaded up to fail.
The second tower was strengthened with High-Modulus (HM) CFRP and tested in similar
manner to the first tower. The CFRP strips were manufactured using the same carbon
fiber material of the sheets. The design strengthening was also applied to increase yield
strength and stiffness approximately 20 to 40 percent.
The third tower follows the same testing procedure as Test I and II, but uses a
Intermediate-Modulus (IM) CFRP strip. The strips were manufactured using different
fiber material. The strengthening scheme was designed to increase the yield strength
approximately 20 to 40 percent.
The analytical model, used to predict the strength and stiffness of the unstrengthened and
strengthened towers within the steel elastic range, considers the linear behavior of both
the steel and CFRP. This includes modeling of the flexural strains and deflection of the
tower at various locations. The analytical model results are compared to the measured
values obtained from the experimental program results. Parametric studies are focused
on various parameters believed to affect the stiffness and strength.
The following chapters of this thesis include:
6
Chapter 2: Literature review detailing the various types of towers, design loads, and
design codes. Additional review will be related to CFRP research in concrete and steel
bridge girder reinforcement, bond development and fatigue properties. Current tower
strengthening schemes will also be reviewed.
Chapter 3: Description of the experimental program, detailing the three tested steel
towers used in the experimental program. Properties of the epoxy, CFRP and steel
material qualities, tower geometry, CFRP and tower surface preparation, CFRP
installation, test instrumentation and setup will be provided.
Chapter 4: Presentation of the results of the three tests is summarized. Results include
all net strains and deflections, along with detailed account of the structure’s behavior
during each load case. Specific failure modes will be explained for each test.
Chapter 5: Presentation of the analytical models. The analytical model results are
presented with the experimental results to extend discussion into the validity of the
models and the testing procedures. The parametric studies are also listed.
Chapter 6: Summary and conclusion of the study. Recommendations for future studies
are given.
Appendices: Additional data from the experimental investigation.
7
CHAPTER 2 - BACKGROUND & LITERATURE REVIEW
This chapter details the background of the proposed research. Specifically, the types of
towers used in the telecommunications industry, the type and nature of the loads
considered in design and the industry codes governing the design and maintenance of
these towers are discussed. Various alternative solutions for strengthening towers will
also be detailed. Pervious research utilizing CFRP as a strengthening technique is
discussed.
2.1 Introduction
Telecommunication antennas and dishes are installed at various heights, azimuths and
orientations on large steel and pre-stressed concrete towers. These towers are typically
located in high density population regions and along major travel routes. They are
maintained according to local and national building codes from the government and
telecommunications industry. With the growing demand for wireless services, there is a
need to strengthen towers to accommodate additional equipment. The optimum solutions
are highly dependent on the cost, space and local building restrictions.
Carbon Fiber Reinforced Polymer (CFRP) is a relatively new construction material which
is gaining widespread popularity in rehabilitating existing structures. Due to it’s light
unit weight and high strength characteristics, this material has been used for many years
with great success in the aerospace industry, where weight to strength ratio is of great
8
importance. In the construction industry, CFRP is used to increase the strength capacity
and ductility of structures resisting wind, live, seismic loads. Most research in the
construction industry utilizing CFRP has been centered on strengthening bridges.
Specifically, the research has been aimed at establishing bond properties and
characteristics. Ductility and the strength of CFRP composite systems can provide has
also been investigated. Additional research within the construction industry has been
focused on fatigue resistance of CFRP.
2.2 Telecommunication Towers
Towers are fabricated with various geometries and are used for a variety of
telecommunication applications. They are largely designed to resist wind, ice, and
seismic loading in accordance with recognized structural design building codes. The
towers are made primarily categorized in three types: lattice/self-supporting, guyed and
monopoles. Each tower has a specific geometry and unique design characteristics.
2.2.1 Lattice/Self-Supporting Towers
Lattice/self-supporting towers are steel trusses constructed to form a cantilever beam
perpendicular to the ground surface. Figure 2.1 illustrates the typical size and geometry
of a self-supporting tower. They are constructed of moderate (A36) to high grade (A572)
steel with the truss members welded or bolted in place using A325 high strength bolts.
These towers typically range from 15 m to 150 m in height and 1 m to 20 m in width,
although towers with heights upward of 300 m have been erected [FWT, 2]. They are
9
usually tapered with decreasing width as elevation increases and have triangular or square
cross-sections.
Lattice/self supporting towers earn the name due to their geometry and design
characteristics. The tower is a lattice-trussed structure. The truss members can be steel
pipes, solid rods, angles, flat or bent plates, channels, or cables. Each member is
designed to resist a specific load or provide support to adjoining members. The members
connect to each other to form a frame with rigid axial and lateral stiffness. Because of
this stiff frame, the term self-supporting evolved. This frame keeps the tower erect
during its lifetime as no other supports are in place.
This inherent stiffness is one of the design strengths of self-supporting towers. A
standard self-supporting tower will typically deflect laterally less than 5 percent of its
height at it’s maximum designed wind load. Operational requirements of some antennas
and dishes are very dependent on their direction and orientation, so a rigid structure is
necessary to ensure the antenna service reliability. Self-supporting towers are the most
reliable for maintaining this twist and sway serviceability. Another advantage is they can
be built on small plots of land. This is particularly advantageous in urban areas or along
roadways where space is at a premium. A key disadvantage, however, is their cost. In
order to maintain the high stiffness and strength capacity, lattice/self-supporting towers
tend to require more steel to fabricate and labor to install. Of the three tower types, they
tend to be the heaviest. Also, potentially they can be viewed as eyesores as typically they
are not designed to be aesthetically pleasing.
10
2.2.2 Guyed Towers
Guyed towers are similar to self-supporting towers in that they are also lattice structures
but have a much lower lateral stiffness. Illustration of a typical guyed tower is shown in
Figure 2.2. These tower’s heights can be in excess of 450 m with shaft widths ranging
from 0.5 m to 3 m [PiRod, 4]. Their shafts are typically prismatic throughout their
elevation and composed of the same variety of structural members and connections as a
self-supporting tower.
The main difference is the attachment of guy lines at various elevations to the tower’s
shaft. These guy lines maintain the stability of the tower. Design is similar to that of a
multi-span bridge. Essentially, the guys act in tension to counteract the lateral loads
applied by the wind, like a bridge column. The trussed shaft resists lateral moments and
shears as well axial loads from its own weight, ice and the guy line tension forces, like a
bridge girder. The bases of the towers are typically designed as pinned connections to
eliminate bending, which lowers lateral stiffness in the entire truss section, allowing the
guy lines to resist the lateral wind loads. Guy lines are made of steel braided wire of
various diameters and strengths with specific stiffness and weights. The guy lines are
attached at the ground using any type of anchor foundation.
The advantage of guyed towers is the ability to build them to great heights at a lower cost
than a self-supporting tower. The members of a guyed tower do not have to be sized to
be as large because the guy lines transfer most of the lateral loads to the ground. The
11
heights obtainable for a guy tower at a reasonable cost are impossible to achieve using a
self-supporting design.
The disadvantage of guyed towers is the amount of land necessary for installation.
Where self-supporting tower uses a ground area of 230 m2 or less, a guyed tower with
identical height may need in excess of 23,000 m2. The guy wire anchors typically are
installed at a radius of 75 percent of the tower height away from the tower base. Towers
over 300 m in height can require as much as 45,000 m2 (10 acres) of land. Also, because
the stiffness of a guyed tower is less, deflection and rotation of the tower can also be
much greater. Antennas requiring specific twist and sway tolerances must be placed
carefully on the tower to remain within their service limits
2.2.3 Monopole Towers
Monopoles are single circular or polygonal cross-sectioned shafts extending to heights of
up to 75 m (250 ft). The shafts can be one piece or slip fit/bolted on top of one another.
Each shaft section usually is between 6 m to 15 m long. Typically, the shafts are non-
prismatic, with decreasing diameter as elevation increases. This taper can be constant
with height or stepped inward at various elevations. Illustration of two types of
monopoles is shown in Figures 2.3 and 2.4. The shafts are made from moderate (A53) to
high grade steel (A572) or pre-stressed concrete. Their shaft thickness is typically small,
15 mm or less for steel and 120 mm for pre-stressed concrete. Average diameters range
from 200 mm to 2400 mm [FWT, 2].
12
The main advantages to monopoles are their ease of installation and mounting equipment
and their general reliability to resisting natural elements. Very little land is required to
install them, as most foundations require less than 4 m2 of ground space. As they are
made up of only a few elements, monopoles can be installed very quickly, outside of the
construction the foundation. Equipment is easily mounted to a monopole as well. Also,
unlike self-support and guyed towers, there are no bolts or gussets that can be eroded or
removed, potentially causing premature failure and leading to reduced reliability.
Finally, monopoles tend to be less noticeable and can be designed to be camouflaged
with their surroundings, so the potential for resistance by zoning ordnances to allow
installation is minimized.
Some disadvantages of monopoles are the height limitations and in upgrading the
structure’s strength capacity. Monopole heights are usually limited to 60 m as heights
greater than this are usually economically unfeasible and inherently unstable structures.
Next, monopoles can be difficult to strengthen. The difficultly in strengthening a
monopole is in attaching the reinforcement. Unlike guyed or self-supporting towers,
where reinforcement is as simple as replacing a smaller, over-stressed member with a
larger, stronger one, a monopole has only one member, thus replacement means installing
a new pole. Developing a design to attach additional steel to the monopole surface is
fairly simple, but establishing a sound bond between the two surfaces typically requires
extensive construction work. Finally, monopoles have lower lateral stiffness as
compared to self-supporting or guyed towers. Monopoles typically deflect between 10 to
15 percent of their overall height laterally. Although the monopole may be structurally
13
stable, it’s lack of stiffness may exceed the twist and sway tolerances of some antenna or
dish equipment.
2.2.4 Tower Design Loads
Towers are built to withstand various loading scenarios. These differ depending on
location, functionality, and importance. Dead, live, wind, earthquake, and ice loads must
be taken into account when designing or analyzing the tower for strength and
serviceability.
Dead loads tend to stress the tower slightly as weight of the tower, antennas, mounts and
transmission lines are very small compared to the buckling capacity of the tower
elements. Typically, a tower member or cross-section as a whole will buckle at ten to
fifteen times the element or tower weight, respectively. Also, because towers are
relatively light, base shears from earthquakes tend to be mild as the acceleration exists
but large mass needed to develop significant base shears does not. Hence, seismic
concerns typically are moderate. Ice loads also tend to be slight, although their impact
must be carefully reviewed for guyed towers. Large amounts of ice can severely impact
the loads from the guy lines.
Resistance to the forces generated by wind is the primary objective when designing and
analyzing towers. Evaluating the wind effects on towers is a complex problem in
aerodynamics. Wind is considered to be a fluid impacting an immovable object at a
plane normal to the wind direction. The resulting forces are derived from wind pressure,
14
cross-sectional area of the object, shape of the object and gust effects of the wind on the
object. Wind is to be considered to be nonviscous and incompressible [4, Gaylord].
Bernoulli’s equation for streamline flow is used to calculate wind pressure. This pressure
is known as the velocity, dynamic, or stagnation pressure. As air weighs 9.82 x 10-4
kg/m3 at 15° C at sea level, the equation reduces to:
q = 0.613 x V2 (a)
• q = Wind Pressure (Pa)
• V = Wind Velocity (m/s)
From this, height above ground, wind gust and shape of the impacted object must be
considered. Most published wind speeds are measured approximately 0 - 50 feet above
the surface of the ground. As friction with the ground greatly decreases the wind’s
velocity, increase in wind pressure as height above the ground increases is accounted for
by the exposure coefficient KZ. This function, also know as the escalation factor, is
added to equation (a) when calculating pressure at specific elevations and varies
depending on the topography and roughness of the terrain. Areas with more hills, trees,
and buildings will result in more lower KZ values whereas areas that are flat, continuous,
or near or over water will have higher KZ values.
Gusting must be considered to account for the dynamic effects of the wind on the
structure. Depending on the manner in which the design wind speed is measured, gusting
effects may or may not be significant. Wind speed is measured in terms of fastest mile,
or sustained wind, or in terms of a three second, or gusting wind. A fastest mile wind
15
speed is based on the amount of time it takes one mile of wind to pass a stationary point.
A three second wind is the amount of wind that passes a stationary point in three seconds.
Thus, gusting is already accounted for when three second wind speeds are used but must
be accounted for when considering a fastest mile wind speed in a structure’s strength
design. Gusting is given lower significance for a taller structure as the likelihood of a tall
structure being entirely enveloped in a large wind gust is minimal. However, when tall
structures have low lateral stiffness, dynamic wind effects can be significant and wind
pressure is increased to account for this. The pressure is increased by a factor known as
GH, or gust effect factor, with the dynamic effects being accounted as a static load. Other
factors, including directionality and site specific increases, are typically included in code
design as they account for statistical studies revealing the likely hood a specific wind
event in specific terrains [26, ASCE].
Shape factor, CF, is the most complex issue when considering force applied to a structure
by wind. The shape factor must take into account the drag on the element as well as the
lift. These factors are not constant as wind velocity changes them continuously. Shape
factors are functions of air density (ρ), velocity (v), diameter/width and shape of the
structure (d) and viscosity of the air (µ) [5, Sachs]. The only reliable way to determine a
shape factor for a specific structure is to place the structure in a wind tunnel with
controlled wind speed and derive CF from the force applied to the structure. However,
enough testing has been completed such that all design codes offer generic shape factors
based on shape, the objects dimensions and the pressure being super or sub-critical to
gain a conservative estimate of the wind loads on a structure. Equation (b) below relates
16
the calculation of a wind force on to a specific structure due to size, drag, elevation and
wind speed.
F = q x GH x KZ x CF x A (b)
• F = Wind Force
• A = Cross-sectional Area
2.2.5 Industry Design Codes
Telecommunication towers are designed in accordance with local and national building
codes. These codes include the International Building Code, the BOCA National
Building Code and the Uniform Building Code. These national codes note towers must
resist design loads in accordance with the latest revision of ASCE7. These codes also
recognize TIA/EIA-222 (Telecommunications Industry Association/Electronic Industries
Association) as the industry standard by which telecommunication tower are designed,
built, and maintained. The standard’s official title is “Structural Standards for Steel
Antenna Towers and Antenna Supporting Structures.” This code dictates every aspect of
design of any of the three types of telecommunication towers. Design windspeed,
exposure coefficients, gust and drag factors, ice considerations, strength design and
twist/sway limits are just a few of the articles defined explicitly within this standard.
This code considers steel design per the 1989 American Institute of Steel Construction
(AISC), “Specifications for Structural Steel Buildings – Allowable Stress Design and
Plastic Design” and the American Concrete Institute (ACI) 3.18-89, “Building Code
Requirements for Reinforced Concrete” as the standard for reinforced concrete design.
17
ASCE has also published design guidelines specific to transmission structures, which is
applicable for telecommunication towers. This guideline, ANSI/ASCE 10-90, Design of
Latticed Steel Transmission Structures, reviews the procedures for determining member
strengths and stability, as well as stiffness. This standard has been adopted by TIA/EIA-
222 and most of its design parameters can be found in within the TIA/EIA-222 text.
2.3 Current Conventional Strengthening Methods for Monopoles
There are several solutions available on the market for strengthening monopoles. The
design principle is to enhance the flexural strength capacity of monopoles by adding
longitudinal steel plates, bars, tubes or fiber composites onto the outside of the existing
monopole surface. All strengthening solutions can be designed to increase strength or
stiffness to the desired capacity demands. The main difference between the various
solutions is in it’s attachment to the existing monopole and the material used for
strengthening the monopole.
Morisson Hershfield markets a solution known as the DualPole system. The concept
behind this solution is to build a new tower around the existing tower. Figures 2.5 and
2.6 illustrate the installation and cross-section of the DualPole system. Two sections of
high grade sheet steel are fabricated exactly to fit over the outside surface and encase the
existing monopole. The sections are welded onto the existing structure using low heat
welding and repair of galvanization is completed using zinc rich paint. The DualPole
18
solution utilizes low heat welding to eliminate the possible of heat or fire damage to the
monopole or other equipment on the tower [12].
Fort Worth Tower, a leading fabricator of towers within the industry, markets a solution
known as the FWT Monopole Upgrade Solution (MUS). The design concept behind this
system is to add longitudinal plates to the outside of the monopole surface. The plates
are bolted at the ends to steel bands. The steel bands and plates are then bonded to the
shaft surface using an epoxy adhesive, which is shown in Figures 2.7 and 2.8. Per FWT
documentation, actual testing has been conducted to validate the upgrade. The testing
followed ASCE Manuel 72, section 4 [FWT, 2].
The ScienTel Tower Strengthening Program (STSP), referred to as “The Boot,” is similar
to the MH DualPole System except it doesn’t conform exactly to the existing tower’s
shaft. Figures 2.9 and 2.10 illustrate the installation and completed installation of the
Boot. Two strengthened sections are bolted at each ends and longitudinally along the
shaft to create a new tower section outside the existing monopole. The strengthening
sections are installed slightly off the existing monopole surface, separated by strips of
rubber attached inside of the new shaft. New sections are bolted together at their ends
and along longitudinal seams at the shaft edge, compressing the rubber strips into the
existing tower shaft and creating a friction seal. The seal theoretically transfers load to
the strengthening system along the existing monopole shaft, creating a composite section.
High grade steel, similar to the existing tower’s shaft, is used to create the strengthening
sections [ScienTel, 13].
19
Westower Communications offers a solution uses high strength, threaded bars installed
parallel with the monopole shaft as the backbone of it’s strengthening mechanism. This
system, shown in Figures 2.11 and 2.12, is built from steel bars are manufactured by
Dywidag-Systems International. These bars range in diameter from 30 mm to 45 mm
and are fabricated from A722 steel. Normal application for the bars marketed by
Dywidag is for post-tensioning of concrete [Dywidag, 14]. Clip angles are bolted into the
existing monopole at approximately 750 mm increments and the Dywidag bars are
attached via two u-bolts through the clip angles. Bars are linked together using couplers
at each end of the bar and the bars are grouted into the existing foundation [Westower,
15].
AreoSolutions offers the AeroForce Monopole and Tower Upgrade System (AMUS).
This package is different from the above noted strengthening solutions as it uses CFRP
installed laterally along the monopole shaft. Bonded to the exterior surface of the
existing structure using epoxy adhesive, as shown in Figure 2.13, the CFRP adds
additional flexural strength. The upgrade can also be completed using high strength steel
plates, as opposed to CFRP [Aero, 16]. AeroSolutions also has completed extensive
adhesive testing, as shown in Figure 2.14, to account for the reliability of the epoxy bond.
The final monopole strengthening solution is marked by Hutter Trankina Engineering and
is listed as the HT Simplified Monopole Tower Reinforcing System (HTSMTRS).
Figures 2.15 and 2.16 illustrate the completed installation of the HTSMTRS. The design
concept for this solution is to weld continuous, high strength, flat, steel plates parallel
20
with the existing monopole shaft. The flat plates are spot-welded approximately 250 to
500 mm to create a composite structure. Each end of the flat plates is extensively welded
to assure the development of each installed plate. Stiffeners are welded at the base of the
monopole to distribute the forces throughout the baseplate.
2.4 Carbon Fiber Reinforced Polymers
The majority of research investigating composite CFRP/steel relationships deals with
establishing bond strength and durability. Specifically, surface preparation of the
adherends, role of galvanization, environmental effects, and strength of the adhesive bond
are several topics which have been researched. Additional large scale testing of bridge
girders strengthened with CFRP has also been investigated.
2.4.1 Previous Testing and Applications
Research completed by Moulds and Price suggests the width and thickness of the
adhesive, as well as the width, thickness and modulus of the adherends play the most
significant roles in establishing bond strength. Using single lap shear tests, their work
observed that wider splices and thicker adhesive bonds reduced bond stress. Increased
shear lag, however, was a by product of these changes. Their work also found when two
adherends have varying modulus, the bond stress is increased on the bonding surface with
the adherend having the lower modulus. This behavior is noted again when thickness of
the two adherends is different. Assuming the adherends have identical modulus, bond
21
stress was increased at the bonding surface with the thinner adherend. Observations also
noted maximum stresses occurring along the edges of the adhesion bond [18].
Single lap shear tests completed by Bourban studied the improvement in bond strength
when silane coupling agents are applied to metal surfaces. After prepping the steel
adherend surface by bead blasted and cleaning, a silane adhesive promoter was added to
the splice prior to epoxy application. Their work noted significant strength and durability
increases, especially when exposed to moisture [21].
Additional single lap shear tests completed by Nakazawa examining into the effects of
galvanization on adhesive bonds also indicated moisture had a negative effect on bond
strength in steel. Identical single lap shear tests were completed with the differences
being the steel surface was either untreated, galvanized or galvannealed. Unlike the tests
by Bourban, the steel surfaces were not blasted, only cleaned with degreaser. All tests
were exposed to moisture, with the results indicated adhesive failure with the untreated
and galvannealed, whereas the galvanized failed due to a combination of cohesion and
adhesive breakdown. All experienced lower durability magnitudes. Also, aside from the
moisture content, the zinc coating used for the galvanization promoted poor adhesion
between the steel surface and the epoxy [Nakazawa, 19].
Fusion bonding, which is heating of the steel prior to application of the epoxy resin, was
examined by Bourban. Results show lower bonding time and equivalent strength to
22
standard adhesives. However, only specific adhesives can be utilized as some adhesive
strengths are reduced through this curing process [20].
Changing environmental conditions have also been found to have adverse effects on bond
strengths. Wedge tests completed by Karbhari examined the effect of different moisture
types and temperatures on bond strengths during application and loading and revealed
elevated temperatures (65° C) lower bond strengths. Salt water also resulted in
significant reduction in strength, although its effects were not nearly as severe as the hot
water. Testing completed in freezing (-18° C) conditions showed greatest bond durability
and retainage of strength [22].
Bridge girders offer a unique design problem from which use of CFRP has been studied
as a potential strengthening solution. Due to corrosion and fatigue, steel bridge girders
lose much of their original design strength. According to the National Bridge Inventory
(NBI) update in 1998, over 172,000 bridges have been found to need repair
[Tavakkolizadeh, 18].
Testing by Mertz and Gillespie in 1996 and Tavakkolizadeh and Saadatmanesh in 2003
have shown steel/concrete composite beams can be strengthened significantly. The tests
utilized the CFRP as a tensile reinforcement with CFRP material adhesively bonded to
the bottom flange of the steel girder. The existing concrete superstructure is considered
to resist compressive bending loads. Tests by Mertz and Gillespie indicated average
strength increases over existing structures of 60 to 100 percent while Tavakkolizadeh and
23
Saadatmanesh tests showed improvement between 41 to 76 percent. Also, analytical
models published by Tavakkolizadeh and Saadatmanesh proved conservative,
underestimating the composite sections strength. Failure modes included CFRP
debonding and compressive crushing of concrete, with the later being dominating for the
majority of the tests [23].
Additional work by Tavakkolizadeh and Saadatmanesh also has shown fatigue strength
of a steel/concrete composite beam reinforced with CFRP can be significantly improved.
Strengthened specimens experienced useable lifespan of 2.6 to 3.4 times longer than an
unstrengthened specimen, and the total number of cycles to failure after cracking was 3.5
times longer for the strengthened specimen to the unstrengthened specimen [24].
Figure 4.47 Longitudinal Strains at 230 mm from Base
Test III – First and Second Load Cases
101
Figure 4.48 Location of Measured Strain at 230 mm from Base
Test III
0
10
20
30
40
50
60
0 30 60 90 120
Displacement (mm)
Lo
ad
(k
N)
0.25L 0.5L 0.75L L
Figure 4.49 Net Displacement at 0.25L, 0.5L, 0.75L and L, to Loading of 55 kN Test III – Third Load Case
102
0
20
40
60
80
100
0 100 200 300 400
Displacement (mm)
Lo
ad
(k
N)
0.25L 0.5L 0.75L L
Figure 4.50 Gross Displacement at 0.25L, 0.5L, 0.75L and L Test III – Third Load Case
0
20
40
60
80
100
0 100 200 300 400
Displacement (mm)
Lo
ad
(k
N)
Initial Delaminating of Bottom Strips
Delaminating and Rupture of the Strips
Buckling of the Monopole
Final delaminating and rupture of the remaining strips.
Figure 4.51 Failure Modes at Load per Net Displacement Measured at L Test III – Third Load Case
103
Figure 4.52 Delaminating of Bottom Strips
Test III – Third Load Case Figure 4.53 Crushing of Top Strips
Test III – Third Load Case
Figure 4.54 Buckling of Monopole
Test III – Third Load Case
Figure 4.55 Air Voids in Epoxy Note: Black Pockets are Air Voids in Bond
Test III – Third Load Case
104
0
25
50
75
100
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Strain (%)
Lo
ad
(k
N)
80 mm
150 mm
230 mm
Figure 4.56 Longitudinal Strains at 80, 150 and 230 mm from Base
Test III – Third Load Case
0
20
40
60
80
100
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Strain (%)
Lo
ad
(k
N)
460 mm
1520 mm
Figure 4.57 Longitudinal Strains at 460 and 1520 mm from Base Test III – Third Load Case
105
0
20
40
60
80
100
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Strain (%)
Lo
ad
(k
N)
3050 mm
4570 mm
Figure 4.58 Longitudinal Strains at 3050 and 4570 mm from Base
Test III – Third Load Case
0
20
40
60
80
100
-0.4 -0.2 0.0 0.2 0.4
Strain (%)
Lo
ad
(k
N)
Steel CFRP
230 mm 460 mm
Figure 4.59 Longitudinal Strains at 230 and 460 mm from Base
Test III – Third Load Case
106
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 1500 3000 4500 6000
Distance from Base (mm)
Str
ain
(%
)
Unstrengthened at 32 kN
Strengthened at 32 kN
Strengthened at 54 kN
Figure 4.60 Longitudinal Strain Profile at 32 and 54 kN (Base = 0 mm) Test III – First, Second and Third Load Cases
107
CHAPTER 5 - ANALYTICAL MODEL
This chapter discusses three analytical models designed to predict the strain and
deflection behavior measured from Tests I, II and III of the monopoles strengthened with
the sheets and strips. An elastic stiffness model is designed to account for lateral flexural
stiffness of the monopoles both with and without the sheets and strips. Specific modeling
parameters used for building this model include the monopole and CFRP geometry and
mechanical properties, design load and application, and the finite amount of elements
which make up the monopole. The model is designed to predict the behavior under the
effect of the first two load cases of Test I, II and III. Inelastic steel deformation, non-
linear strain and deflection behavior, rupture and delaminating of the CFRP and buckling
of the monopole included in the model design. The results from the first two load cases
of Test I, II and III are compared to the model’s results to validate the proposed model.
Two parametric studies reviewing the effect of the additional layers of sheets and strips to
the strengthening solutions used in Test I and II complete this chapter.
To evaluate the accuracy of the proposed analytical model with respect to the measured
results from the experimental program, the term difference error is used. This term will
give a numerical percentage of the differences between the prediction and the measured
values as shown in equation 1:
1001Values Measured
Prediction AnalyticalError Difference ×−=
(1)
108
5.1 Elastic Flexural Stiffness Model
The flexural stiffness model predicting the behavior is based on the Moment-Area
Method and the Transformed-Section Method [Gere, 25]. The Moment-Area Method is
based on two theorems. The first moment-area theorem is related to curvature (θ) of a
beam and states the angle (θB/A) between two tangential points is equal in magnitude to
the area (A) of the moment (M) divided by flexural modulus (EI) between points A and
B, as shown in equation 2:
dxEIMB
AAB ∫=/θ (2)
The second moment-area is related to deflection (δ) and states the deflection (δB/A)
between two tangential points is equal in magnitude to the moment of the area of the
M/EI diagram between points A and B, as shown in equation 3:
dxEIMx
B
AAB ∫=/δ (3)
Deflection is analytically measured by summing the results from a boundary condition to
the location of the defection.
The transformed-section method is a procedure for converting the cross-section of a
composite beam into beam having the mechanical properties of only one the composite
materials. Specific limits to this theory are the composite materials must be linearly
109
elastic and the neutral axis and moment-resisting capacity of the transformed beam must
be identical to the composite beam. The modular ratio (N) is given in equation 4:
2
1
EEN = (4)
E1 and E2 are the flexural modulus of material 1 and 2 comprising the composite section.
The composite cross-section is transformed by multiplying either the height or the width
of the one of the composite materials by N to generate an equivalent EA product which
does not alter the location of the neutral axis, as shown in equation 5:
21112211 AENAEAEAE +=+ (5)
The transformed-section method applies to the strengthened monopole as shown in
Figure 5.1. The mechanical properties of the monopole steel are used as the control
material and the CFRP mechanical properties are adapted to the steel. The sheets and
strips are isolated on three top and bottom flats and the thickness of each sheet and strip
is multiplied by N to achieve a new, equivalent EA cross-section. The centroid of each
sheet and strip is considered to remain at its original location. Using this model, the
inertia (I) is calculated at each cross-section.
The moment-area method was applied to the monopole as shown in Figure 5.2. The
stiffness model used for the monopoles was made up of 240 elements 25.4 mm in length
(l). Each individual element has specific cross-section geometry and mechanical
properties, based on the results from the transformed-section method. Material properties
110
of the monopole steel were based on tested data from the steel coupon tests and CFRP
material properties were based on material properties from the manufacturer. Material
property values are listed in sections 3.2.1 and 3.2.2. Moment was calculated based on
shear on the element and distance of the element from the applied load. Strain was
calculated based on transformed section mechanical properties and moments derived
from both methods as shown in equation 6:
EIMy
=ε (6)
Several assumptions were included in the model to predict the load deflection and strain
behavior of the unstrengthened and strengthened monopoles. These assumptions are:
1. Strains varying linearly across the depth of the cross-section.
2. Perfect composite action was considered. No bond slippage or failure between
the monopole shaft and CFRP surfaces was assumed to occur.
3. Linear elastic behavior for the steel. Elastic modulus taken from the coupon tests
was used in all models.
4. Linear elastic behavior for the CFRP.
5. Shear deformation calculations were not included in the model.
6. Perfect boundary conditions, i.e. no rotation or slippage at the base and complete
moment resisting, fixed connection to the mounting wall.
7. Loading in the model was limited to the rupture strain of the fiber.
8. Development length was not considered in the model. The sheets and strips were
assumed to be fully developed at all points along there length.
111
9. Only the cross-section of the CFRP was used in calculating strength and stiffness.
The adhesive thickness was ignored.
10. Sign convention for the calculated strain is negative for compressive strain and
positive for tensile strain.
5.2 Test I Model
The high-modulus sheet modulus in compression was not supplied by the manufacturer.
However, both tensile and compressive modulus was supplied by the manufacturer for
the high-modulus strips, thus the compressive modulus of the sheet was calculated as
given in Equation 7:
TSheetTStrip
CStripCSheet E
EE
E = (7)
The resulting magnitude of the modified sheet compressive modulus is 569 GPa. The
adhesive was assumed to provide infinite resistance to buckling of the sheets, so a pure
compressive resistance would be achieved.
The clip angles used at the base to anchor the sheets were considered to have no
contribution towards the lateral strength and stiffness of the strengthened monopole. The
transverse sheets installed along the circumference of the monopole were also considered
to have no impact to the lateral strength and stiffness of the structure. This assumption is
due to the strength of the sheet wrappings being in the transverse, not longitudinal
direction. Their assumed impact was only to support the bond between the sheets and
112
steel surface, immobilizing the sheets to develop full stiffness in compression and
tension.
5.2.1 Deflection, Stiffness and Strain
Applied loads of 32 and 40 kN were used to examine the prediction capability of the
unstrengthened and strengthened monopole models, respectively. These loads are
identical to the loads applied from the first and second load cases of Test I of the
experimental program. Figure 5.3 illustrates the load deflection profile measured during
the first and second load cases of Test I and the calculated from the models simulating the
first and second load cases of Test I at 32 kN. Based on the predicted load deflection
slope, the stiffness values of the monopole before strengthening with high-modulus
sheets at 0.25L, 0.5L, 0.75L and L were 4.93, 1.28, 0.60 and 0.37 kN/mm, respectively.
The stiffness values predicted for the model after the monopole was strengthened
increased to 7.04, 1.76, 0.78 and 0.46 kN/mm at 0.25L, 0.5L, 0.75L and L, respectively.
Comparison of the stiffness values at the respective locations shows the strengthened
monopole stiffness increased 43, 38, 31 and 26 percent at 0.25L, 0.5L, 0.75L and L,
respectively in comparison to the unstrengthened monopole stiffness.
Figure 5.4 shows the strain profiles measured from the experimental program and
predicted values from the analytical model at 32 kN per Test. Neutral axis shift away
from the centroid of the monopole were towards the tensile strains, however varied less
than 10 mm from the base to the end for the strengthened monopole and no neutral axis
shift away from the centroid of the monopole was noted for the unstrengthened
113
monopole. Comparison of the predicted longitudinal strain of the monopole before and
after strengthening shows that the strains were reduced by an average of 31 percent from
the base to 3050 mm due to the strengthening system. Strain predicted at 3050 mm to the
tip had equivalent magnitude for both the strengthened and unstrengthened monopole.
5.2.2 Discussion of Tested vs. Modeled Results
Based on review of Figure 5.3, the analytical model predicts deflection for the
unstrengthened monopole very accurately. Comparison of the modeled vs. measured
deflection at 0.25L, 0.5L, 0.75L and L found difference error of 14, 8, 1 and 2 percent,
respectively. Predicted values for the strengthened monopole were not as accurate as the
unstrengthened monopole model. Difference error in the modeled vs. measured
deflection was 32, 17, 9 and 5 percent at 0.25L, 0.5L, 0.75L and L, respectively. Due to
the lack of conformance of the modeled strengthened results to the measured
strengthened deflection results, the modeled stiffness increases was significantly higher
than measured in the experimental program. Predicted strain, shown in Figure 5.4,
conformed fairly closely on average to the measured strain from the experimental
program, although predicted strain reductions from the base to 3050 mm were
significantly different. The neutral axis characteristics found by the experimental
program were predicted very accurately by the analytical model.
The results of the analytical model suggest that this approach was valid for modeling the
strains of both the unstrengthened and strengthened monopole and for calculating
deflection from 0.5L to the tip. However, conservative prediction of the strain and
114
deflection was found inside the midspan. The discrepancy may be attributed to the
inability of simulating the boundary conditions used in the model and the assumption of
full development of all the high-modulus sheets in compression. Development of an
infinitely stiff, moment resisting joint is impossible to achieve in testing, but good
conformance can be achieved if a rigid joint is supporting a tested member whose
stiffness is significantly less in comparison. The monopole shaft near the base was very
stiff, therefore poor conformance was noted near the base. The deflection measurements
taken at 0.25L likely reflected shear deflection as well as flexural deflection, which were
not captured in the model. Also, predicted results tend to improve as modeled results are
examined at greater distances away from the boundary condition, due to its lowered
influence. This was found with the monopole model as deflections calculated at 0.75L
and L showed great conformance to the measured deflections.
Lack of full development of the 1220 and 2440 mm strips in compression and tension is
the other likely cause for the inconsistent comparison of the measured vs. modeled
results. Examination of the strain profile revealed the strains measured from the base to
1500 mm decreased as they were measured away from the base. However, strains
measured from 1500 to 3000 mm remained almost constant. Examination of the
predicted strains reveals the strains to be largely constant from the base to 3000 mm.
This observation indicates the 1220 and 2440 mm strips are not providing strength
capacity to the monopole as expected in the calculated results. This observation is
investigated further in a parametric study in section 5.5.1.
115
Bond failure and sheet rupture did not occur during the first or second loading case of
Test I, so assuming no impact from these issues is acceptable. During the first two
loadings, no strains measured along the axis of the monopole exceeded the steel yield
strain and, after unloading, the monopole showed no effects of permanent deformation,
so the assumption of all materials remaining linearly elastic is also validated.
5.3 Test II Model
Specific characteristics of this model included modeling of the stiffeners part of the
monopole cross-section. The stiffeners were included in the inertia calculations, forming
a complete composite section. Although the stiffeners were made from steel with a lower
yield stress, the section with stiffeners never approached its yield stress during the first or
second loading, thus no permanent deformation of the was occurred. The tested elastic
modulus from the coupons was used for the stiffener elastic modulus.
5.3.1 Deflection, Stiffness and Strain
An applied load of 32 kN and 42 kN was used to examine the predicting capabilities of
the analytical model for the unstrengthened and strengthened monopoles. The load
deflection profile at 32 kN measured from the first and second load cases of Test I and
the predicted from the models simulating the first and second load cases of Test I are
shown in Figure 5.5. The stiffness values, based on the load deflection slope, of the
monopole before strengthening with high-modulus strips was 5.90, 1.40, 0.64 and 0.39
kN/mm at 0.25L, 0.5L, 0.75L and L, respectively. The stiffness values predicted from
116
the model after the monopole was strengthened at 0.25L, 0.5L, 0.75L and L were to 8.73,
2.08, 0.91 and 0.53 kN/mm, respectively. Comparison of the predicted stiffness values
shows the stiffness of the monopole strengthened with high-modulus strips indicate an
increase of 48, 48, 42 and 37 percent at 0.25L, 0.5L, 0.75L and L, respectively in
comparison to the unstrengthened monopole stiffness.
The strain profiles measured from the experimental program and predicted values are
shown in Figure 5.6. The illustrated strains are the results or calculations of the
monopole loaded to 32 kN. Shift of the neutral axis from the centroid of the monopole
was less than 5 mm from the base to 3660 mm and no shift was found at 3660 mm to the
tip. The shifts were towards the tensile strains from the base to 3660 mm. Average strain
reduction due to the strengthening system was 39 percent from the base to 3660 mm.
Strain calculated from 3660 mm to the tip had equivalent magnitude for the
unstrengthened and strengthened monopole.
5.3.2 Discussion of Tested vs. Modeled Results
Examination of the deflection and strain profiles reveal the modeled results accurately
predict the deflection, stiffness and strain values at load. The deflection difference error
was less than 10 percent at 0.5L, 0.75L and L for the strengthened monopole and the
deflection difference error of the unstrengthened monopole was less than 5 percent at
these locations. The modeled stiffness increases conformed closely to the measured
stiffness increases all quarter points, accurately predicting the measured stiffness found in
the experimental program. The calculated strains showed greatest conformance to the
117
measured results of the experimental program. Aside from the calculated strain variance
from the measured strains near the base from the unstrengthened monopole, difference
error between the calculated vs. measured strains was negligible.
Data on the specific material characteristics of the strips in compression and the
monopole shaft steel is the likely the main justification of the good conformity of the
predicted results from this model to the measured results from Test II. The modulus of
the strips in compression was supplied by the manufacturer, so exact stiffness, as opposed
to a modified assumption which was used in section 5.2.1, could be used to complete the
model. An additional influence which would positively impact the model was the strip
layering. The strips were installed in two layers, therefore load transfer between the
strips could be easily developed. Shear lag or lack of development of the outside strip
was minimized. Additional strip layers added to the strengthening solution would likely
have compromised the design assumption of strains varying linearly across the cross-
section. Finally, the stiffeners at the base aided in creating the theoretical infinitely stiff
fixed boundary condition. An infinitely stiff, moment resisting base cannot be
completely attained in the manufacturing process, but a rigid base supporting a flexible
structure can closely simulate this boundary condition. By adding stiffeners, the base
was made significantly more rigid, positively influencing the flexural behavior of the
monopole. The analytical model is purely on flexural behavior, so the stiffeners would
cause the model to adhere closely with the measured deflection results near the base.
118
5.4 Test III Model
Specific characteristics of this model include the stiffeners as a design parameter for
calculating the flexural strength and stiffness and the location of the applied load to 5740
mm from the base, as opposed to the 5790 mm used for the Test I and II. Section 3.5.2
explains the purpose of relocating of the applied load used in testing this monopole. The
stiffeners were manufactured from a lower grade steel than the monopole shaft and
baseplate, but as the yield stress of the section was never reached during the first two
loading cases of Test III, the section remained elastic. The elastic modulus of the
stiffeners was assumed to be identical to the elastic modulus based on the results of the
coupon tests of the monopole shaft steel.
5.4.1 Deflection, Stiffness and Strain
An applied load of 33 and 42 kN was used in the analysis for the unstrengthened and
strengthened monopoles for the first and second load cases. The predicted load
deflection profiles from the models, based on an applied load of 32 kN, is shown in
Figure 5.7, along with the measured load deflection profiles form the first and second
load cases from the experimental program. The predicted stiffness values based on the
modeled load deflection relationship of the unstrengthened monopole is 3.78, 1.29, 0.62
and 0.39 kN/mm at 0.25L, 0.5L, 0.75L and L, respectively. Predicted stiffness values
from the modeled monopole strengthened with the intermediate-modulus strips at 0.25L,
0.5L, 0.75L and L were 7.88, 2.21, 0.98 and 0.59 kN/mm, respectively. The resulting
119
monopole stiffness increase due to the installation of the intermediate-modulus strips is
68, 68, 60 and 52 percent at 0.25L, 0.5L, 0.75L and L, respectively.
Figure 5.8 illustrates the strain profiles measured at 32 kN from the first and second load
cases from the experimental program and the predicted strain profiles based on models of
the monopole before and after strengthening. Shift of the neutral axis from the centroid
of the monopole was less than 10 mm from the base to 3660 mm and no shift was
calculated from 3660 mm to the tip. The shifts calculated from the base to 3660 mm
were towards the tensile strains. Comparison of the monopole strain before and after
strengthening revealed a 55 percent decrease in strain from the base to 3660 mm due to
the intermediate-modulus strip installation. Strains calculated at 3660 mm to the tip from
the model before and after the monopole was strengthened were equivalent in magnitude.
5.4.2 Discussion of Tested vs. Modeled Results
Model prediction of the deflection behavior and the reduction of the measured strain from
the experimental program of Test III were very accurate. Deflection and stiffness
difference error of both the unstrengthened and strengthened monopole were less than 10
percent at 0.5L, 0.75L and L. Difference error between the calculated and measured
deflection and stiffness values at 0.25L varied between 26 and 58 percent. Average strain
reduction due to the intermediate-modulus strip installation was also very similar, as the
calculated average strain reduction from the base to 3660 mm from the base was within 3
percent of the measured average strain reductions. The model was not accurate in
predicting the tensile strains of the strengthened monopole from Test III from the base to
120
3000 mm from the base. The model also did not accurately predict the unstrengthened
monopole strains measured at the base to 1000 mm from the base.
Specific detailed data regarding the material properties of the intermediate strips and the
monopole shaft steel is the likely the reason for the high conformance of the calculated
values from the analytical model to the measured values from the experimental program.
Specific knowledge of the intermediate-modulus strips in compression was especially
important as this eliminated an unknown variable, as opposed to assuming a modified
value as discussed in section 5.2.2. Installing the strips in only two layers also aided in
conforming the calculated values to the measured values. Installation of the strips in
layers greater than two would have likely compromised the assumption of strain varying
linearly throughout the cross-section. Additional layers of strips would possible have
experienced some shear lag and would not allow full development of the strength of the
material. The use of the stiffeners also likely aided in developing the design assumption
of a fixed base. Through installing the stiffeners at the base, the connection became
much stiffer, especially in comparison to the monopole shaft. Flexural stiffness models
using fixed boundary conditions are most accurate when the tested boundary condition
stiffness is significantly greater than the beam stiffness, thus installing the stiffeners
would have contributed to the boundary condition stiffness.
The lack of conformance of the predicted tension strains in comparison to the measured
tension strains may also be attributed to the irregular bonding surfaces found during the
post failure examination of the intermediate-modulus strips. The irregular bonding
121
surface, as discussed in section 4.3.2, is likely the cause of stress concentrations within
the strips which were not uniform. The stress concentrations would have resulted in
greater stiffness from the strips, which were accurately predicted by the model, but not
lower strains, which were predicted by the model. The flexural model assumed full
development of the strips at all locations, thus the presence of stress concentrations
compromises the design assumption. With a more uniform bond applied to the adherend
surfaces, the measured strain likely would have been much closer in magnitude to the
predicted strains.
The lack of conformance of the predicted strains in comparison to the measured strains
near the base of the unstrengthened monopole could also be due to the stress
concentrations induced by welding of the stiffeners to the base. Heat stress from the
welds, which is also discussed in section 4.3.2, likely imparted additional stress into the
monopole of which was not accounted in the model. Use of smaller stiffeners and welds,
along with better quality welding, would have likely resulted in measured strains which
would have conformed to the predicted values.
5.5 Parametric Study Using the Proposed Analytical Model
Two parametric studies are considered to study the influence of specific parameters on
behavior of the strengthened monopoles. The first parametric study will review the
influence of the quantity of high-modulus sheet layers used in Test I. The design
parameters of this study are identical to the analytical model designed to predict the
122
measured results of Test I with the exception of various sheet layers being removed from
the model to alter the reinforcement ratio. Comparison of the resulting predicted stiffness
increases will be made with the original model results. The purpose of this study is to
reveal the potential impacts to the tower’s composite behavior assuming limited amounts
of layers are installed for strengthening. The second parametric study will review the
influence of the strip compressive and tensile elastic modulus based on modeled results.
The analytical model designed to predict the behavior measured from the second load
case of Test II will be used to show the effect modulus has on monopole stiffness. The
unique design parameters of this study are three strip specimens having specific
compressive and tensile modulus. Each specific strip will be considered with varying
reinforcement ratios, or cross-sectional strip area divided by cross-sectional steel area at
the base of the monopole. The purpose of this study is to illustrate the stiffness increases
with respect to modulus and the reinforcement ratio.
5.5.1 Effect of Reinforcement Ratio - Test I Model
Specific detail into the analytical model used for the first parametric study is described in
sections 5.1 and 5.2.1. The only significant difference between the model used to predict
the results from Test I and the model used for the first parametric study is the quantity of
high-modulus sheets considered. The reinforcement ratio was changed by varying the
number of layers of high-modulus sheets on the monopole. The first model considered
the 3050 mm sheets only installed on the top and bottom of the monopole. The second
considered the 2440 and 3050 mm sheets and the third model considered the 1230, 2440
and 3050 mm sheets installed on the top and bottom of the monopole. The purpose of
123
this parametric study is to study the impact the additional sheets towards the stiffness of
the monopole at the quarter points.
Figure 5.9 shows the stiffness increases at the quarter points along the monopole shaft for
the one, two and three sheet layer calculations along with the stiffness increases found in
the four sheet layers detailed in section 5.2.1. At 0.25L (1525 mm), each additional sheet
doubles the percent increase in stiffness, which results in each sheet adding the same
amount of stiffness as the sheet preceding it. However, at L (6100 mm), the impact is
diminished as each additional sheet applies only 2/3rd the stiffness as the sheet preceding
it. Results calculated from 0.5L and 0.75L fall in between the 2/3rd and double stiffness
increase of each additional sheet.
These results illustrate that the shorter, additional layers of sheets provide greatest
stiffness enhancement near the base. Their effect, although significant, is becomes
diminished as the stiffness is measured near the tip. Exact stiffness increase becomes
more difficult to predict near the tip as the additional increases become very similar as
the reinforcement ratios are increased. However, the results also prove that with
significant stiffness increases due to higher reinforcement, greater strength can also be
expected near the base. Therefore, as the largest stresses are typically found near or at
the base of a monopole, a reinforcing design can adequately satisfy the strength
requirements without using excess sheets, assuming stiffness is not a design
consideration.
124
The first parametric study results also offers insight into the lack of complete conformity
of the analytical model to the tested results. The tested result percent stiffness increases
fell in between the stiffness increases predicted by the two and three high-modulus sheet
layer models. Based on the parametric study results, only marginal development of the
third and fourth sheet layers would have significantly limited stiffness. Therefore, the
parametric study lends evidence of the third and fourth sheets layers never fully
developing, only partially reaching their full strengths. This possibility cannot be
concluded without further testing, but does offer insight behind the Test I stiffness
increases not reaching the predicted values.
5.5.2 Effect of Strip Modulus - Test II Model
The model designed to predict the strength and stiffness results from the first and second
load cases of Test II was used to complete the second parametric study. Sections 5.1 and
5.3.1 detail the design parameters and assumptions used to build the model. Specific
design parameters of the strip strengthening system, including orientation, number of and
length of each strip on the monopole shaft was identical to the strip orientation and
installation for Test II. The design parameters altered for this study were the tensile and
compressive modulus and the cross-section area of the strip. Three types of strips were
used. The first was the high-modulus strips used in Test II. The second strip used was
the intermediate-modulus strip utilized for Test III. Figure 3.1 details the tensile and
compressive modulus of the high and intermediate-modulus strips used for the second
parametric study. The third strip used is a generic CFRP strip with modulus in
compression and tension of 100 and 140 GPa, respectively. Cross-sectional area of the
125
strips was evaluated in terms of a reinforcement ratio. The reinforcement ratio (RR) was
calculated as given in equation 8:
Monopole
Strips
AA
RR = (8)
To achieve the varied reinforcement ratios, the thickness of the strips was changed
uniformly throughout their lengths. Reinforcement ratios would then be linearly
proportionate along the length of the monopole. For listing of the results, the
reinforcement ratio was calculated from the base of the monopole. The reinforcement
ratio was evaluated based on a range varying from 0 (no strips installed) to 0.5 (strip
cross-sectional area = half of steel cross-sectional area). Stiffness increase was based on
the calculated stiffness at the tip (L) of the monopole strengthened with a specific total of
strips divided by the calculated stiffness at the tip (L) of the monopole prior to
strengthening with strips. The purpose of the parametric study is to illustrate the potential
stiffness increases by using the strips with higher tensile and compressive modulus over
the standard low modulus strips.
The calculated results of the second parametric study are shown in Figure 5.11. The
results indicate linear increases in stiffness at the tip for the three strips based on
increasing reinforcement ratios. The results also show significant increases in stiffness
based on the magnitude of the modulus of the strips. Specifically, installation of identical
volumes of low, intermediate and high-modulus strips onto the monopole shows
intermediate and high-modulus strips provide 2 and 3 times the stiffness of the low-
modulus strip installation, respectively. The high-modulus strips also provide
126
approximately 50 percent greater stiffness than the intermediate-modulus strips at
identical reinforcement ratios.
Conclusions to the second parametric study show the potential increases in stiffness due
to installation of the three strips are linearly related to the reinforcement ratio.
Specifically, significant savings in strip volumes can be found by using the intermediate
or high-modulus strips. Through reduction in volume of strips needed for strength and
stiffness requirements, installation time and cost of material is reduced. The uncertainty
due to layering of the strips is also reduced few layers will be needed to attain equivalent
strength and stiffness to the lower modulus strips. Significantly greater strength and
stiffness can be attained by using the higher modulus strips. The result is higher factors
of safety for the strength and serviceability design can be utilized with approximately the
same material.
127
Figure 5.1 Illustration of Existing and Transformed Section
Figure 5.2 Deflection Diagram
128
0
25
50
75
100
0 1525 3050 4575 6100
Length from Base (mm)
Dis
pla
ce
me
nt
(mm
)
Unstrengthened - Modeled
Unstrengthened - Tested
Strengthened - Modeled
Strengthened - Tested
Figure 5.3 Modeled and Tested Net Deflection Profiles at 32 kN Test I – First and Second Load Cases
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0 1500 3000 4500 6000
Length from Base (mm)
Str
ain
(%
)
Unstrengthened-Tested
Strengthened-Tested
Unstrengthened-Modeled
Strengthened-Modeled
Figure 5.4 Modeled and Tested Strain Profiles at 32 kN
Test I – First and Second Load Cases
129
0
25
50
75
100
0 1525 3050 4575 6100
Length from Base (mm)
Dis
pla
ce
me
nt
(mm
)
Unstrengthened - Modeled
Unstrengthened - Tested
Strengthened - Modeled
Strengthened - Tested
Figure 5.5 Modeled and Tested Net Deflection Profiles at 32 kN
Test II – First and Second Load Cases
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 1500 3000 4500 6000
Distance from Base (mm)
Str
ain
(%
)
Unstrengthened - Tested
Strengthened - Tested
Unstrengthened - Modeled
Strengthened - Modeled
Figure 5.6 Modeled and Tested Strain Profiles at 32 kN
Test II – First and Second Load Cases
130
0
25
50
75
100
0 1525 3050 4575 6100
Length from Base (mm)
Dis
pla
ce
me
nt
(mm
)
Unstrengthened - Modeled
Unstrengthened - Tested
Strengthened - Modeled
Strengthened - Tested
Figure 5.7 Modeled and Tested Net Deflection Profiles at 32 kN
Test III – First and Second Load Cases
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 1500 3000 4500 6000
Distance from Base (mm)
Str
ain
(%
)
Unstrengthened - Tested
Strengthened - Tested
Strengthened - Modeled
Unstrengthened - Modeled
Figure 5.8 Modeled and Tested Strain Profiles at 32 kN Test III – First and Second Load Cases
131
0
10
20
30
40
50
0 1525 3050 4575 6100
Length from Base (mm)
Sti
ffn
ess
In
cre
ase
(%
)
1 Sheet Layer
2 Sheet Layers
3 Sheet Layers
4 Sheet Layers
Tested Results
Figure 5.9 Stiffness Increases per Reinforcement Ratio at Quarter Points
Test I – First Parametric Study
0
25
50
75
100
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Area of CFRP / Area of Steel
Sti
ffn
es
s I
nc
rea
se
(%
)>
High-Modulus Strips
Intermediate -Modulus Strips
Low-Modulus Strips
Figure 5.10 Stiffness Increases vs. Reinforcement Ratios for Three Strip Specimens
Test II – Second Parametric Study
132
CHAPTER 6 - SUMMARY AND CONCLUSIONS
This chapter summarizes the measured results of the experimental program and the
analytical models. Specifically, the ultimate strength capacity and failure modes of each
strengthening solution are listed. The measured strength and stiffness increases taken
from Test I, II and III, along with the calculated strength and stiffness increases from the
analytical model is included. Conclusions and evaluations to the effectiveness of each
system are provided. Recommendations towards further research complete this chapter.
6.1 Summary
Listed are the significant results from the experimental program and the analytical
models:
1. The ultimate strength capacity of the monopoles used in Test I (High-Modulus
Sheets), Test II (High-Modulus Strips) and Test III (Intermediate-Modulus
Strips) was 95, 79, and 85 kN, respectively.
2. The failure mode observed from Test I was simultaneous rupture of the high-
modulus sheets in tension and buckling of the monopole 200 mm from the base.
Aside from minor localized debonding near the base, no deformation of the high-
modulus sheets or monopole occurred before the coinciding rupture/buckling.
3. The failure mode observed from Test II ultimately was buckling of the monopole
near the base. Prior to buckling, the high-modulus strips installed on top of the
133
monopole crushed in compression at 0.15 percent strain. Following this rupture,
the bottom high-modulus strips simultaneously delaminated and ruptured in
tension at 200 mm from the base of the monopole. The rupture strain in tension
was measured at approximately 0.18 percent. All high-modulus strips had
ruptured or delaminated prior to the buckling of the monopole.
4. The failure mode observed from Test III ultimately was buckling of the
monopole. Prior to buckling, the intermediate-modulus strips installed on the
bottom of the monopole delaminated and ruptured 200 mm from the base.
Following the delaminating, the intermediate-modulus strips crushed in
compression at 200 mm from the base. The measured rupture strain was between
0.2 and 0.25 percent. All intermediate-modulus strips had ruptured or
delaminated prior to buckling of the monopole. However, buckling of the
monopole followed shortly after the rupture of the intermediate-modulus strips in
compression.
5. The stiffness of the monopoles before and after strengthening with CFRP was
measured at the quarter (0.25L), mid (0.5L), three quarter (0.75L) and full span
(L) or tip for each test. The stiffness increases due to the CFRP installation
within the steel elastic zone for Test I was 13, 25, 20 and 17 percent at 0.25L,
0.5L, 0.75L and L, respectively. The stiffness increases measured from Test II at
the same quarter points was 50, 43, 40, and 41 percent, respectively. The
stiffness increases measured from Test III at these quarter points was 86, 64, 48
and 44 percent, respectively.
134
6. The stiffness increases per the analytical model due to the CFRP while the steel
remained elastic was calculated for each test. Calculated results from Test I were
43, 38, 31 and 26 percent at 0.25L, 0.5L, 0.75L and L, respectively. Calculated
results from Test II predicted stiffness increases of 48, 48, 42 and 37 percent at
0.25L, 0.5L, .75L and L, respectively. Stiffness increases calculated from Test
III were 68, 68, 60, and 52 at 0.25L, 0.5L, 0.75L and L, respectively.
7. The measured strain reductions due to the CFRP installation from Test I, II and
III were 20, 31 and 52 percent, respectively, from the base to the midspan (0.5L)
of the monopole. Strains measured from 0.5L to the tip (L) showed no reduction
due to the strengthening system for all three tests.
8. The calculated strain reduction due to the CFRP from the analytical models of
Test I, II and III was 31, 39 and 52 percent, respectively from the base to 0.5L of
the monopole. Strains calculated from 0.5L to L were not reduced due to the
strengthening system for all three tests.
6.2 Conclusions
Listed are the conclusions of this investigation based on the results measured, observed
and calculated from the experimental program and the analytical models.
1. High and intermediate-modulus CFRP can significantly enhance the strength and
stiffness of a monopole tower, especially while the design loads are within the
monopole steel’s elastic range.
135
2. The high-modulus sheets provide the greatest reliability for sustaining strength
during increasing load and provide the largest strength increases, but are the least
efficient of the three tested CFRP for increasing stiffness. The greater strength
and reliability is due to the excellent adhesion between the sheets and monopole
steel surface. Lack of stiffness as compared to the results from the high and
intermediate-modulus strips is likely due to the inability to properly develop the
additional layers needed to promote greater stiffness.
3. The high-modulus strips provide the greatest stiffness of the three tested CFRP
but provide the lowest strength. The high-modulus eliminates the need to add
many layers of strips to the monopole and reduces the thickness of the strips.
Thus, greater conformance to the anticipated results was found and can be
expected. Due to its low crushing strain in compression, the high-modulus strips
have the lowest ductility of the three CFRP. Therefore, it is considered to be the
least efficient for increasing strength of the monopole.
4. The intermediate-modulus strips provide a good compromise between the
advantages and disadvantages of the high-modulus sheets and strips. The
intermediate-modulus strips can be manufactured to a larger thickness to achieve
similar axial stiffness to the high-modulus strips but still retain the higher
crushing strain in compression, leading to greater strength capacity. The stiffness
increases can also be calculated with more accuracy than found with the high-
modulus sheets as the layers needed to generate the necessary stiffness can be
reduced.
136
5. The clip angles clamping the sheets to the base plate and monopole shaft and the
stiffeners welded to the base plate and monopole shaft provide excellent
immobilization of the shaft section. This immobilization allows the CFRP to
develop its entire strength and stiffness at their ends at the base of the monopole.
The highest stresses are developed at the base of the tower, thus full development
of the CFRP strengthening system is essential at this location.
6. The neutral axis does not shift significantly while the monopole loading is
within the steel elastic range for the sheets and strips. Therefore, a compressive
modulus equivalent to the tension modulus is developed for all three CFRP
tested. Continued development of the compressive modulus after yielding of the
monopole steel cannot be confirmed for the high-modulus sheets but is believed
to have continued to contribute stiffness to the monopole. The high-modulus
strips ruptured prior to yielding of the monopole shaft, thus no contribution to
strength or stiffness was measured from them. Significant loss of strength and
stiffness after the intermediate-modulus strips ruptured in compression was
measured, thus continued development of the compressive modulus was
confirmed.
7. Significant surface pressure must be applied to the strips during installation to
ensure a uniform adhesive bond. Installation must be completed quickly as well.
Failure to apply pressure and complete rapid installation of the strips leads to
significant air voids within the adhesive bond which creates stress concentrations
in the strips, leading to premature failure.
137
8. The high-modulus strips can be accurately designed for strength and stiffness
assuming one or two layers is used. Additional layers likely do not provide same
strength and stiffness increases that the first two layers of high-modulus sheets
provide. This is based on the results from the first parametric study. However,
use of adhesives with higher strengths and modulus likely can develop the full
strength of sheets installed in layers greater than two.
9. Due to its low compressive crushing strain, the high-modulus strips should not be
used for increasing the strength of monopoles. They can be used effectively for
providing stiffness assuming an appropriate factor of safety is applied to the
rupture stress of the strip.
10. The intermediate-modulus strips can be used effectively for increasing the
strength and stiffness of a monopole. However, the design strength must be
limited to the yield strain of steel and a uniform bond between the strips and steel
must be applied.
11. The moment area method and transformed section method produces very accurate
deflection and stiffness calculations of the monopole before and after
strengthening as compared to the tested results. These methods are most accurate
when compared to the tested results from the strips, which is due to the greater
control of the material properties of the strips. The transformed section method
also accurately predicts the strain behavior of the monopole before and after
strengthening, especially with the strips. The inability of the additional high-
modulus sheets to develop their tensile and compressive strength and stiffness
limits the conformance of the model to the tested results. The calculated
138
deflections and strains showed very good conformance to the tested
measurements and conformance to the tested results is greater as comparisons are
made along the monopole shaft away from the base.
6.3 Recommendations for Further Research
Listed are suggestions for further research on this topic.
1. The effectiveness of layering the sheets for increasing strength and stiffness
should be evaluated to determine the development of the additional sheets.
2. Coupon tests aimed at determining the compressive modulus of the sheets should
be examined to evaluate the behavior of the sheets at high strain.
3. Addition work can be completed to determine optimum bonding conditions for
the strips and monopole surface and for the strip to strip surface. Specifically, the
amount of applied pressure to the strip surface to form a uniform, void free
adhesive bond can be investigated further.
4. Application of CFRP onto the individual elements which make up self-supporting
and guyed tower can be investigated to determine potential strength and stiffness.
5. The effect of pre-stressing the high and intermediate modulus strips can be
investigated to determine potential strength and stiffness increases for the
monopole.
139
REFERENCES [1] Rohn Industries, Inc. http://www.rohnnet.com/. (November 17, 2002). [2] Fort Worth Tower, Inc. http://www.fwtinc.com/default.asp. (April 9, 2004). [3] PiRod, Inc. Monopole Information Website http://www.pirod.com/monopole.html. (November 17. 2002). [4] PiRod, Inc. Guyed Tower Information Website http://www.pirod.com/gt.html. (November 17. 2002). [5] Gaylord, Jr., Edwin, Charles N. Gaylord, and James E. Stallmeyer. Design of Steel
Structures. 3rd Edition. B.J. Clark and David A. Damstra, McGraw-Hill, Inc. Boston. 1992. pgs. 15-21.
[6] Sachs, Peter. Wind Forces in Engineering. 2nd Edition. Pergamon Press, Inc.
Maxwell House, Fairview Park, Elmsford, NY. 1978. [7] Mosallam, A.S., P.R. Chakrabarti & E. Spencer. “Experimental Investigation on
the Use of Advanced Composites & High-Strength Adhesives in Repair of Steel Structures.” 43rd International SAMPE Symposium. May 31-June 4, 1998. pgs. 1826-1837.
[8] McKnight, Steven H., Pierre E. Bourban, John W. Gillespie, Jr., and Vistasp M.
Karbhari. “Surface Preparation of Steel for Adhesive Bonding in Rehabilitation Applications.” Infrastructure Repair Methods: Steel for Adhesive Binding. Center for Composite Materials and the Materials Science Program, University of Delaware. Newark, DE. pgs. 1148-1155.
[9] Price, A. and R.J. Moulds. “Repair and Strengthening of Structures Using Plate
Bonding.” Construction and Building Materials. Volume 5, Number 4. Butterworth-Heinemann, Ltd. December 1991. pgs. 189-192.
[10] Moriarty, Jim. “The Use of Carbon Fiber Composites in the London Underground
[11] Cannon, Jr., D.D. and R.A. LeMaster. “Local Buckling Strength of Polygonal
Tubular Poles.” American Society of Civil Engineers: Manuel 72, Reference 210. [12] Morrison Hershfield Group, DualPole Monopole Reinforcing Solution http://www.dualpole.com/index.htm. April 9, 2004.
140
[13] ScienTel Tower Strengthening Program http://www.scientech.com/scientel/solutions/tower.html. April 9, 2004. [14] Dywidag-Systems International Threaded Post-tensioning Bars. http://www.dywidag-systems.com/docs/dsi_index.php#. April 9, 2004. [15] Westower Dywidag Monopole Reinforcing System. http://www.dywidag-systems.com/docs/dsi_index.php#. April 9, 2004. [16] AeroSolutions, LLC. AeroForce Systems, Monopole and Tower Upgrades. http://www.aerosolutionsllc.com/index.html. June 19, 2003. pgs 1-8. [17] Hutter Trankina Simplified Monopole Tower Reinforcing. http://www.htedesign.com/tower_reinforcing.htm. April 9, 2004. [18] Moulds, R.J. and A. Price. “Repair and Strengthening of Structures Using Plate
Bonding.” Construction and Building Materials. Volume 5, Number 4. Butterworth-Heinemann, Ltd. December 1991. pgs. 189-192.
[19] Nakazawa, M. “Mechanism of Adhesion of Epoxy Resin to Steel Surface.”
Nippon Steel Technical Report. Number 63, October 1994.
[20] Bourban, P. E., S. H. McKnight, S. B. Shulley, V. M. Karbhari, and J. W. Gillespie, Jr. “Infrastructure: New Materials and Methods of Repair. Durability of Steel/Composites Bonds for Rehabilitation of Structural Components.” Third Materials Engineering Conference. Materials Engineering Division of the American Society of Civil Engineers. San Diego, Ca. November 13-16, 1994. pgs. 295-302.
[21] Bourban, P.E., S.H. McKnight, J. W. Gillespie, Jr., and V. M. Karbhari. “Surface Preparation of Steel for Adhesive Bonding in Rehabilitation Applications.” Infrastructure Repair Methods: Steel for Adhesive Binding. Center for Composite Materials and the Materials Science Program, University of Delaware. Newark, DE. pgs. 1148-1155.
[22] Karbhari, V.M. and S.B. Shulley. “Use of Composites for Rehabilitation of Steel Structures – Determination of Bond Durability.” Journal of Materials in Civil Engineering. Volume 7, Number 4. November 1995. pgs. 239-245.
[23] Tavakkolizadeh, M and H. Saadatmanesh. “Strengthening of Steel-Concrete Composite Girders Using Carbon Fiber Reinforced Polymer Sheets” Journal of Structural Engineering. January 2003. pgs. 30-40.
141
[24] Tavakkolizadeh, M and H. Saadatmanesh. “Fatigue Strength of Steel Girders Strengthened with Carbon Fiber Reinforced Polymer Patch” Journal of Structural Engineering. February 2003. pgs. 186-196.
[25] Gere, James M. and Stephen P. Timoshenko. Mechanics of Materials. 4th Edition. PWS Publishing Company. Boston, MA. 1997. pgs. 400-403.
142
APPENDIX
Included are the gross deflection and base rotation measurements from all load cases of
Test I, II and III. Also included are the transverse strain measurements from the first and
second load cases of Test I. All locations noted in the following graphs are with respect
to the base, thus the base of the monopole is 0.0 or 0L. Graphed results include
measurements taken throughout the entirety of each loading case. All other pertain
information is listed with the respective graphed measurements.
143
0
10
20
30
40
50
0 30 60 90 120
Displacement (mm)
Lo
ad
(k
N)
Unstrengthened Strengthened
0.25L 0.5L 0.75L L
Figure A1 - Gross Displacement at 0.25L, 0.5L, 0.75L and L Test I – First and Second Load Cases
0
10
20
30
40
50
0.00 0.05 0.10 0.15 0.20
Rotation (°)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A2 - Base Rotation Test I – First and Second Load Cases
144
0
10
20
30
40
50
0.0 0.5 1.0 1.5 2.0
Displacement (mm)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A3 - Base Slip Test I – First and Second Load Cases
0
10
20
30
40
50
0.00 0.02 0.04 0.06
Strain (%)
Lo
ad
(k
N)
90 Degrees 60 Degrees 30 Degrees
(a)
0
10
20
30
40
50
0.00 0.02 0.04 0.06
Strain (%)
Lo
ad
(k
N)
90 Degrees 60 Degrees 30 Degrees
(b) Figure A4 Transverse Strains at 610 (a) and 1220 (b) mm
Test I – First and Second Load Cases
145
0
25
50
75
100
0 100 200 300 400
Displacement (mm)
Lo
ad
(k
N)
0.25L 0.5L 0.75L L
Figure A5 - Gross Displacement at 0.25L, 0.5L, 0.75L and L
Test I – Third Load Case with Nylon Straps
0
20
40
60
80
100
0.0 0.1 0.2 0.3 0.4
Rotation (°)
Lo
ad
(k
N)
Figure A6 - Base Rotation
Test I – Third Load Case with Nylon Straps
146
0
20
40
60
80
100
0.0 1.0 2.0 3.0 4.0 5.0
Displacement (mm)
Lo
ad
(k
N)
Figure A7 - Base Slip
Test I – Third Load Case with Nylon Straps
0
20
40
60
80
100
-0.20 -0.10 0.00 0.10 0.20
Strain (%)
Lo
ad
(k
N)
90 Degrees 60 Degrees 30 Degrees
(a)
0
20
40
60
80
100
-0.20 -0.10 0.00 0.10 0.20
Strain (%)
Lo
ad
(k
N)
90 Degrees 60 Degrees 30 Degrees
(b) Figure A8 Transverse Strains at 610 (a) and 1220 (b) mm
Test I – Third Load Case with Nylon Straps
147
0
25
50
75
100
0 100 200 300 400
Displacement (mm)
Lo
ad
(k
N)
0.25L 0.5L 0.75L L
Figure A9 - Gross Displacement at 0.25L, 0.5L, 0.75L and L
Test I – Third Load Case with Chains
0
20
40
60
80
100
0.0 0.1 0.2 0.3 0.4
Rotation (°)
Lo
ad
(k
N)
Figure A10 - Base Rotation
Test I – Third Load Case with Chains
148
0
20
40
60
80
100
0.0 1.0 2.0 3.0 4.0 5.0
Displacement (mm)
Lo
ad
(k
N)
Figure A11 - Base Slip Test I – Third Load Case with Chains
0
20
40
60
80
100
-0.20 -0.10 0.00 0.10 0.20
Strain (%)
Lo
ad
(k
N)
90 Degrees 60 Degrees 30 Degrees (a)
0
20
40
60
80
100
-0.20 -0.10 0.00 0.10 0.20
Strain (%)
Lo
ad
(k
N)
90 Degrees 60 Degrees 30 Degrees (b)
Figure A12 Transverse Strains at 610 (a) and 1220 (b) mm Test I – Third Load Case with Chains
149
0
10
20
30
40
50
0 30 60 90 120
Displacement (mm)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A13 - Gross Displacement at 0.25L, 0.5L, 0.75L and L Test II – First and Second Load Cases
0
10
20
30
40
50
0.00 0.05 0.10 0.15 0.20
Rotation (°)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A14 - Base Rotation Test II – First and Second Load Cases
150
0
10
20
30
40
50
0.0 0.5 1.0 1.5 2.0
Displacement (mm)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A15 - Base Slip Test II – First and Second Load Cases
0
20
40
60
80
100
0 100 200 300 400
Displacement (mm)
Lo
ad
(k
N)
0.25L 0.5L 0.75L L
Figure A16 - Gross Displacement at 0.25L, 0.5L, 0.75L and L
Test II – Third Load Case
151
0
20
40
60
80
100
0.0 0.1 0.2 0.3 0.4
Rotation (°)
Lo
ad
(k
N)
Figure A17 - Base Rotation Test II – Third Load Case
0
20
40
60
80
100
0.0 1.0 2.0 3.0 4.0 5.0
Displacement (mm)
Lo
ad
(k
N)
Figure A18 - Base Slip Test II – Third Load Case
152
0
10
20
30
40
50
0 30 60 90 120
Displacement (mm)
Lo
ad
(k
N)
Unstrengthened Strengthened
0.25L 0.5L 0.75L L
Figure A19 - Gross Displacement at 0.25L, 0.5L, 0.75L and L
Test III – First and Second Load Cases
0
10
20
30
40
50
0.00 0.05 0.10 0.15 0.20
Rotation (°)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A20 - Base Rotation Test III – First and Second Load Cases
153
0
10
20
30
40
50
0.0 0.5 1.0 1.5 2.0
Displacement (mm)
Lo
ad
(k
N)
Unstrengthened Strengthened
Figure A21 - Base Slip Test III – First and Second Load Cases
0
20
40
60
80
100
0 100 200 300 400
Displacement (mm)
Lo
ad
(k
N)
0.25L 0.5L 0.75L L
Figure A22 - Gross Displacement at 0.25L, 0.5L, 0.75L and L
Test III – Third Load Case
154
0
20
40
60
80
100
0.0 0.1 0.2 0.3 0.4
Rotation (°)
Lo
ad
(k
N)
Figure A23 - Base Rotation to Loss of Instrumentation Test III – Third Load Case
0
20
40
60
80
100
0.0 1.0 2.0 3.0 4.0 5.0
Displacement (mm)
Lo
ad
(k
N)
Figure A24 - Base Slip to Loss of Instrumentation Test III – Third Load Case