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New design procedure for FRP composites poles
Article · January 2009
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New Design Procedure for FRP Composites Poles
S. METICHE, R. MASMOUDI AND H. A. EL BAKY
ABSTRACT
Earlier research progress on using fiber-reinforced polymer (FRP) composite
poles for transmission lines revealed that the use of these poles is economically
viable and industrially reliable. While this promising alternative technique is
coming to be widely accepted in practice and evolving to become the future of the
construction in transmission lines, the development of appropriate design guidelines
that deal with detailed analysis of such poles has lagged behind. Design approaches
for conventional steel/wood poles were influential in providing safety and
robustness to these poles. However, little advanced approaches focused on the
design of FRP poles. This is the focus of the present paper. The available design
procedures of FRP poles are based on the allowable stress design theory of
composite material under various states of stress. However, various experimental
results show that cracking and early failure of FRP poles are normally controlled by
the relative location of the hand-holes from the base of the pole. Most of the design
guidelines ignore such effect and accounts only for the effect of these holes by
considering their influence on the abrupt reduction in the cross-sectional area of the
poles. These guidelines do not give a specific attention to the impact of the handholes on the generated stress concentrations in their vicinity. Furthermore, local
buckling at a nearby area of the hand-holes generally dominates the mode of failure
of such poles that requires more attention to the relative locations of the hand-hole.
A new design approach is introduced to advance the design of FRP poles. The
accuracy of both the developed design procedures and that of existing design
approaches are verified by comparison with documented test results of an early
experimental program of the authors.
Key words: Fiber Reinforced Polymers, FRP Structural Shapes, FRP poles,
Flexural behavior, Filament Winding, Design procedure.
__________
Slimane Metiche, NSERC Industrial-Postdoctoral Fellow, FRE Composites (2005) Inc., 75
Wales Street, Saint André d’Argenteuil, Québec, J0V1X0, CANADA, and Department of
Civil Engineering, University of Sherbrooke, Sherbrooke, Québec, J1K2R1, CANADA.
Department
of Masmoudi,
Materials Engineering
AMPEL, University
of of
British
Vancouver,
Radhouane
P.E., PhD., &Professor,
Department
Civil Columbia,
Engineering,
UniversityBC,
Canada
of Sherbrooke, Sherbrooke, Québec, J1K2R1, CANADA
Hussien M. Abd El Baky, Postdoctoral Fellow, Department of Civil Engineering, University
of Sherbrooke, Sherbrooke, Québec, J1K2R1, CANADA.
INTRODUCTION
The mechanical behavior of Fiber-Reinforced Polymer (FRP) materials is a
topic that has attracted several researchers in recent years. These materials have
very high strength-to-weight ratios, and they are steadily being selected over metal
alloys in a variety of structural applications [1].
The resulting material is referred to as a composite material when two or more
distinct materials are combined in a macroscopic scale. The basic constituents of
such a material are usually combined to enhance the mechanical characteristics of
the materials. Fiber Reinforced Polymer (FRP) technology gained its roots during
World War II with the need of light structural products. Composite structural
elements are used today in a variety of components for automotive, aerospace,
marine, architectural structures, and sports equipment.
The majority of the existing electrical poles in Canada as well as in the world are
made from traditional materials such as wood, concrete or steel. The limitation in
length of wooden poles and the vulnerability of steel or concrete poles to climatic
aggressions have motivated the manufacturers and researchers to find alternatives.
While studies have addressed the material failure and buckling of thin-walled
sections such as I-beams, box beams, etc., made from composite materials [2], very
few studies have been conducted on the Behavior of tapered FRP sections [3].
The Behavior of scaled FRP models of transmission poles under cantilever loading
conditions was investigated by Zhi-Min [4]. The four specimens tested were of
prismatic circular hollow cross-section. The outside diameter of the poles was 76
mm and the wall thickness was 6 mm. These were fabricated by filament winding
strips of pultruded sheets arranged in circular pattern. According to the test results,
a linear Behavior of the FRP poles was observed up to failure.
Shakespeare Company [5] provided a report of lateral loading test on 10.65 m
length fiberglass pole. This report shows the minimal effective loss of strength due
to the row of 22.23 mm diameter holes drilled in the side wall to climb the pole.
The inner diameters of the specimen at the base and the top ends were 216 mm and
127 mm, respectively. A total of 22 holes were drilled and spaced by 305 mm. The
first one was drilled at 2.13 m far from the base-end of the pole.
Experimental and analytical studies were carried out [3] to validate the predicted
ultimate loads for tapered filament wound FRP scaled poles subjected to cantilever
bending. The specimens were 2500 mm in length; the inner diameters at the base
and the top ends were 100 mm and 74 mm, respectively. The wall thickness varied
depending on the number of layers, the results of this study show that the stiffness
and the strength of FRP poles as well as the mode of failure depend mainly on their
wall thickness. While a local buckling failure is observed for thin walled samples,
compression and tension failures were observed for samples with more significant
thicknesses.
The fiber orientation has a significant effect on the performance of FRP poles. The
same performance of FRP poles having high fiber volume fraction can be achieved
by using less fiber volume fraction but with changing the fiber orientation towards
the longitudinal direction [3] and the incorporation of circumferential layers tends
to increase the critical ovalization load [6]. More tests, however, are required to
determine the optimum values of fiber angle and fiber volume fraction.
A research project is currently carried out at the University of Sherbrooke (Quebec,
Canada). The main objective of this research project is to study the full-scale
flexural Behavior of fiber-reinforced polymer (FRP) tapered poles manufactured by
the filament winding process, in order to optimize the design and to propose
improvement of the manufacturing process [7], [8], [9]. This paper presents a
design method for GFRP poles based on experimental results. The proposed design
method allows to determine for a given ratio (E I) / (L ρ) at the base of an FRP pole,
the ultimate bending moment, the maximum pole top deflection, the ultimate
longitudinal compression and tension strains at the base and the ultimate
longitudinal tension strain at the service hand hole level. In the ratio (E I) / (L ρ), E
is the longitudinal modulus of elasticity, I is the moment of inertia, L is the
cantilever height of the pole and ρ is the linear mass of the fibers.
EXPERIMENTAL PROGRAM
Test prototypes
Mechanical bending tests under lateral loading were performed on 22 full-scale
prototypes of FRP poles with length ranging from 5 to 12 m. The FRP poles having
hollow circular cross section and variable wall thickness were produced with the
filament winding process, using epoxy resin reinforced with E-glass fibers. Each
type of the poles tested in this study is constituted by three zones where the
geometrical and the mechanical properties are different in each zone. The difference
of these properties is due to the number of layers used in each zone and the fiber
orientation of each layer. The mechanical and physical properties of the fibers and
the epoxy resin are presented in Table I.
The characteristics and configuration of the tested poles are presented in Table II.
All test prototypes have been tested in flexural bending up to failure. Two types of
fibers (Type A and Type B) are used to evaluate their effects on the flexural
behavior. Note that the only difference between both types is the linear density, as
shown in Table I.
All the prototypes are identified as follows: From the left to the right: the first
number indicates the total height of the pole in feet, the first letter indicates the type
of fiber, the second number indicates the supported length in feet and the second
letter indicates the hole positioning (in compression or in tension, the number zero
means that the pole was tested without any hole above ground line), the latest
number (in parentheses) indicates the test number under the same parameters.
TABLE I. PROPERTIES OF FIBERS AND RESIN
Properties
Glass fibers type A
Glass fibers type B
Epoxy resin
Tex (*) (g/km)
1100
2000
3
Density (gm/cm )
2.6
2.6
1.2
Modulus of elasticity (GPa)
80
80
3.38
Shear modulus (GPa)
30
30
1.6
Poisson’s ratio
0.25
0.25
0.4
(*) : In the fiber industry, it is common to specify fibers in units of tex, which indicates the weight in
gram of a 1000 m long single fiber (linear density).
TABLE II. CHARACTERISTICS AND CONFIGURATION OF THE TESTED POLES
Principal hole
Pole Id. And
Bottom-Top
(AGL)**
h Total* h Supported*
samples
diameters
(mm)
(mm)
Dimensions
Location
(mm)
Positioning
(mm)
(mm)
17-B-3-C
17-A-3-C
18-B-3-C
18-B-3-T
20-B-4-C
33-B-5-C
35-B-5-C
40-A-5-C
40-B-5-C
40-B-5-T
29-B-5-C
18-B-4-C
18-B-4-T
2
2
2
2
2
2
2
2
1
1
1
1
2
5093
5093
5398
5398
5994
10 058
10 566
12 090
12 090
12 090
8738
5398
5398
914
914
914
914
1219
1524
1524
1524
1524
1524
1524
1219
1219
150-76
150-76
155-76
155-76
164-76
261-114
270-114
291-114
291-114
291-114
247-114
155-76
155-76
64x127
64x127
102x305
102x305
102x305
102x305
102x305
102x305
102x305
102x305
64x127
102x305
102x305
610
610
762
762
1372
1219
1219
1219
1219
1219
457
457
457
Comp.
Comp.
Comp.
Tension
Comp.
Comp.
Comp.
Comp.
Comp.
Tension
Comp.
Comp.
Tension
(*) h Total: Total length of the pole, h Supported : Supported length
(**) AGL: Located Above Ground line.
Each type of pole tested in this study is constituted by three zones, where the
geometrical and the mechanical properties are different in each zone. The difference
of these properties is due to the different number of layers used in each zone and the
fiber orientation of each layer (Figure 1). The stacking sequence as well as the
average thickness and length for the three zones of poles are presented in Table III
and Table IV, respectively. The fiber content of each prototype, expressed in
volume ratio Vf was determined experimentally by pyrolysis tests [10] and is
presented in Table IV.
It should be mentioned that all the prototypes presented in this study are single
segment and were fabricated with extra reinforcing provided around the principal
holes except for the prototypes 17-B-3-C and 17-A-3-C. On the other hand, there
was no extra reinforcing provided around the hole located under the ground line.
All the holes were cut at the manufacturer site, after the poles were fabricated.
Total length
Principal Hole
Embedded hole
FRP pole
Zone I
Zone II
Zone III
Figure 1. Zones and Thickness of FRP poles.
TABLE III. STACKING SEQUENCE FOR THE THREE ZONES OF THE POLES
Zone I (Degrees)
Zone II (Degrees)
Zone III (Degrees)
Pole ID
17-B-3-C [-70/70/-60/60/(-15/15)2/-60/70] [(-60/60)2/(-15/15)2/-60/70] [±15/15/-30/-60/70]
[-60/±60/(±15)2/-60/70]
[±15/-70/70]
17-A-3-C [-60/±70/60/±30/-60/70]
[90/(-15/15)2/-60/90]
[25/-25/-75/75]
18-B-3-C [-60/60/-30/±30/-60/70]
[90/(-15/15)2/-60/90]
[25/-25/-75/75]
18-B-3-T [-60/60/-30/±30/-60/70]
[90/-60/60/15/-15/-60/60]
[±15/-60/70]
20-B-4-C [-60/60/-25/25/-70/70]
[90/±15/70/-80]
[±15/90]
33-B-5-C [70/-80/±20/70/-80]
[90/±70/±15/70/-80]
[±70/-10/-10/+10/70/-80]
35-B-5-C [70/-75/±20/70/-80]
[90/-20/20/±70]
[±70/-10/10/±70]
40-A-5-C [±70/±30/±70]
[90/-75/-15/+15/70/-80]
[80/-70/±10/70/-80]
40-B-5-T [±75/±20/30/70/-80]
[90/-75/-15/+15/70/-80]
[80/-70/±10/70/-80]
40-B-5-C [±75/±20/30/70/-80]
[90/(-15/15)2/-60/90]
[25/-25/-75/75]
18-B-4-C [-60/60/-30/±30/-60/70]
[-60/60/-30/±30/-60/70]
[90/(-15/15)2/-60/90]
[25/-25/-75/75]
18-B-4-T
TABLE IV. AVERAGE THICKNESS AND LENGTH FOR THE THREE ZONES OF THE
POLES
Zone I
Zone II
Zone III
Vf
Average
Average
Average
Prototypes
Length
Length
(%) Length
thickness
thickness
thickness
(mm)
(mm)
(mm)
(mm)
(mm)
(mm)
49
2133
4.78
2219
4.30
740
5.18
17-B-3-C
49
2133
4.78
2219
4.30
740
5.18
17-A-3-C
51
1220
3.27
980
7.20
3198
3.04
18-B-3-C
51
1220
3.27
980
7.20
3198
3.04
18-B-3-T
50
2000
2.81
1200
6.73
2794
2.84
20-B-4-C
59
2200
4.56
1000
8.35
6858
5.97
33-B-5-C
57
2200
3.87
1000
9.69
7366
5.37
35-B-5-C
51
2200
4.72
1000
9.80
8890
6.70
40-A-5-C
55
2200
5.54
1000
10.44
8890
7.73
40-B-5-T
55
2200
5.54
1000
10.44
8890
7.73
40-B-5-C
51
1220
3.27
980
7.20
3198
3.04
18-B-4-C
51
1220
3.27
980
7.20
3198
3.04
18-B-4-T
Test setup
A new test-setup (Figure 2) was designed and built according to the
recommendations of the Standards ASTM D 4923-01 [11] and ANSI C 136.201990 [12] as well as the Proposed California Test 683-1995 [13]. This test-setup
consists mainly of three parts: a "ground-line support", a "butt support" and a
"lifting jaws". This fixture provides a practical way to test all types of utility poles.
The ground-line support or front support is used with wooden saddle to support the
pole at ground line and is designed to allow a vertical and/or horizontal translation
to anchor the various possible diameters of the poles. The pole butt support or rear
support is used with wooden saddle to support the lower end of the pole and is
designed to allow longitudinal translation to test various burial lengths of the poles.
The lifting jaws constitute the load application point on the pole and consist of two
quarters of a metallic tube assembled so as to form two jaws (Figure 2). After the
pole were mounted and leveled on the test fixture, a bridge crane was positioned
with its hook centered above the lifting jaws, 305 mm far from the top of the pole.
Instrumentation
A 225 KN load-capacity cell was used while the displacement rate of the bridge
crane was 12 mm/sec (Figure 2). The deflection of the FRP poles was measured
with a draw wire transducer (DWT) at hc/4; hc/2 as well as under the load
application point (Figure 2), where hc is the cantilever length or free length of the
pole. Electrical strain gages were mounted on the two faces (compression and
tension) near the ground line support, at hc/4; hc/2; 3/4hc as well as around the hole.
The strain gages were used to monitor the deformations in the longitudinal,
circumferential directions and at 45 degrees from the longitudinal axis of the pole.
Two LVDTs used to measure displacement at the pole base were positioned against
either the test fixture or the lower wall of the pole. LVDT # 1 was centered on the
underside of the pole at the ground line. LVDT # 2 was centered on the topside of
the FRP pole above the wooden support on the rear pole butt support. Two other
LVDTs were positioned laterally in order to measure the possible ovalisation of the
pole near the ground line support. An automatic data acquisition system was used to
collect the load, LVDTs, DWTs and strain gages data.
Load direction
Steel cable
Chain
Ground line support
FRP prototype
Lifting jaws
DWT
DWT
DWT
Ground line
Load cell
h Cantilever
Web strap
Rubber lined
wooden
support saddle
bl
Pole butt
support
h Supported
Figure 1. Schematic drawing of the full- scale test setup.
Winch binder
Lifting jaws
Ground line support
FRP pole
Pole butt support
Figure 2. Full- scale test setup.
PROPOSED DESIGN PROCEDURES
A new design approach is introduced to advance in the design of FRP poles.
The proposed design method allows to determine for a given ratio (E I) / (L ρ) at the
base of an FRP pole, the ultimate bending moment, the maximum pole top
deflection, the ultimate longitudinal compression and tension strains at the base of
the FRP pole. In the ratio (E I) / (L ρ), E is the longitudinal modulus of elasticity, I
is the moment of inertia, L is the cantilever height of the pole and ρ is the linear
mass of the fibers. The following relationships (Equation 1 to Equation 3) [14] were
used to determine the modulus of elasticity E in the longitudinal direction at the
base of the pole.
n
E = ∑ { (Pi ) E xi }
i =1
(1)
Where
E xi =
And
1
⎛ 1
cos 4 θ i sin 4 θ i
ν ⎞
+
+ cos 2 θ i sin 2 θ i ⎜⎜
− 2 tl ⎟⎟
El
Et
Et ⎠
⎝ Glt
ν tl
Et
=
ν lt
(2)
(3)
El
Where Exi is the Young’s modulus in the longitudinal direction of the ith layer, (n) is
the total number of layers at the base of the pole,νtl and νlt are the Poisson’s ratios,
θi is the fiber angle of the ith layer evaluated experimentally by a pyrolysis test, Pi is
the rate representing the ith layer of the laminate constituting the base zone of the
pole. The percentage representing each layer was evaluated by determining the
thickness of each layer using scanning electron microscope.
Figure 3 presents the curve of the ultimate bending moment (Mu,b) at the base of an
FRP pole for a given ratio (E I) / (L ρ) at the base of the pole. The ultimate bending
moment (Mu,b) was induced by the ultimate load (Fu). Figure 3 presents the
prototypes that failed at the base. Equation 4 was obtained from the curve presented
in the Figure 3 with a coefficient of regression (R2) of 0.99. The coefficient of
regression (R2) indicates the rate of correspondence between the trend curve and the
experimental results. Figure 4 presents the curve of the ultimate bending moment
(Mu,o) at the principal hand hole of an FRP pole for a given ratio (E I) / (L ρ) at the
base of the pole. The ultimate bending moment (Mu,o) was induced by the ultimate
load (Fu). Figure 4 presents the prototypes that failed at the principal hand hole.
Equation 5 was obtained from the curve presented in the Figure 4 with a coefficient
of regression (R2) of 1.00.
Failure at the base :
M u ,b = 1496
EI
Lρ
(4)
Failure at the principal
hand hole
3
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
M u ,o = 13.9⎜⎜
⎟⎟ − 390.59⎜⎜
⎟⎟ + 2957.5⎜⎜
⎟⎟
⎝ Lρ ⎠
⎝ Lρ ⎠
⎝ Lρ ⎠
(5)
Figure 5 presents the prototypes that failed at the base and the prototypes that failed
at the principal hand hole as well as the respective trend curves. Figure 5 shows that
for a ratio (E I) / (L ρ) greater than 23.5 kN.m2/g, the failure occurs at the base of
the pole.
By the same manner, the design curves of the maximum deflection (Δmax) at the
loading position of an FRE pole were determined for a given ratio (E I) / (L ρ) at the
base of the FRP pole. Figure 6 presents the prototypes that failed at the base and the
prototypes that failed at the principal hand hole as well as the respective trend
curves and coefficients of regression (R2). Equation 6 and Equation 7 were obtained
from the curves presented in the Figure 6 respectively for a failure at the base and a
failure at the principal hand hole with a coefficient of regression (R2) of 0.89 and
0.96 respectively.
⎛ EI ⎞
⎟⎟ + 187.79
Δ max = 715.07 Ln⎜⎜
⎝ Lρ ⎠
Failure at the base :
Failure at the principal
hand hole
(6)
2
Δ max
⎛ EI ⎞
⎛ EI ⎞
= 16.093⎜⎜
⎟⎟ − 396.2⎜⎜
⎟⎟ + 2640.7
⎝ Lρ ⎠
⎝ Lρ ⎠
(7)
Figure 7 presents the ultimate longitudinal compression strain (εCx,b) at the base of
an FRP pole for a given ratio (E I) / (L ρ) at the base of the pole. The ultimate
bending moment (Mu,b) will be determined from the curve of Figure 5 or by using
the Equation 4. Figure 7 presents the prototypes that failed at the base. Equation 8
was obtained from the curve presented in the Figure 7.
Failure at the
base :
ε xC,b
M u ,b
3
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
= 0.054⎜⎜
⎟⎟ − 4.6647⎜⎜
⎟⎟ + 129.13⎜⎜
⎟⎟ − 1342.7 (8)
⎝ Lρ ⎠
⎝ Lρ ⎠
⎝ Lρ ⎠
Figure 8 presents the ultimate longitudinal tension strain (εTx,b) at the base of an
FRP pole for a given ratio (E I) / (L ρ) at the base of the FRP pole. The ultimate
bending moment (Mu,b) will be determined from the curve of Figure 5 or by using
the Equation 4. Figure 8 presents the prototypes that failed at the base. Equation 9
was obtained from the curve presented in the Figure 8.
Failure at the
base :
ε xT,b
M u ,b
3
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
= −0.0483⎜⎜
⎟⎟ + 4.5078⎜⎜
⎟⎟ − 136.04⎜⎜
⎟⎟ + 1477.1 (9)
⎝ Lρ ⎠
⎝ Lρ ⎠
⎝ Lρ ⎠
The design curves presented in figure 7 and Figure 8 show that the ration (εCx,b) /
(Mu,b) (respectively the ratio (εTx,b) / (Mu,b)) decreases when increasing the ratio (E
I) / (L ρ) for values of (E I) / (L ρ) less than 17 kN.m2/g. For the values of (E I) / (L
ρ) greater than 17 kN.m2/g, the ratio (εCx,b) / (Mu,b) (respectively the ratio (εTx,b) /
(Mu,b)) is almost constant.
FAILURE AT THE BASE
70
Fu
Mu,b (AT THE BASE) (kN.m)
EI
Lρ
M u ,b = 1496
60
50
2
R = 0.9869
L
40
30
Mu,b
E,I, ρ
Poles that failed at the base
20
10
0
0
5
10
15
20
25
30
35
40
45
E I / (L ρ) AT THE BASE (kN.m2/g)
Figure 3. Design curve - Ultimate bending moment (Mu,b) at the base – Failure at the base.
FAILURE AT THE HAND HOLE
35
3
M u ,o
Mu,o (AT THE HAND HOLE) (kN.m)
30
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
⎟⎟
⎟⎟ + 2957.5⎜⎜
⎟⎟ − 390.59⎜⎜
= 13.9⎜⎜
⎝ Lρ ⎠
⎝ Lρ ⎠
⎝ Lρ ⎠
Fu
2
R = 0.9962
25
20
L
15
Mu,o
Poles that failed at the
principal hand hole
10
E,I, ρ
5
0
0
5
10
15
20
25
2
E I / (L ρ) AT THE BASE (kN.m /g)
Figure 4. Design curve - Ultimate bending moment (Mu,o) at the hand hole – Failure at the hand hole.
3
Fu
Fu
M u ,b = 1496
100
L
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
⎟⎟ − 390.59⎜⎜
⎟⎟ + 2957.5⎜⎜
⎟⎟
M u ,o = 13.9⎜⎜
⎝ Lρ ⎠
⎝ Lρ ⎠
⎝ Lρ ⎠
120
EI
Lρ
Failure at the hand hole
L
2
R = 0.9962
Mu (kN.m)
80
Mu,o
Mu,b
60
40
Failure at the base
2
R = 0.9869
20
Poles that failed at the base
Poles that failed at the principal hand hole
0
0
5
10
15
20
25
30
35
40
45
50
E I / (L ρ) AT THE BASE (kN.m2/g)
Figure 5. Design curve - Ultimate bending moment.
2
⎛ EI ⎞
⎛ EI ⎞
Δ m ax = 16.093⎜⎜
⎟⎟ − 396.2⎜⎜ Lρ ⎟⎟ + 2640.7
L
ρ
⎝
⎠
⎝
⎠
12000
2
R = 0.9625
Poles that failed at the base
Poles that failed at the principal hand hole
10000
Fu
Failure at the hand hole
8000
Δmax (mm)
Δmax
6000
⎛ EI ⎞
Δ m ax = 715.07 Ln⎜⎜
⎟ + 187.79
Lρ ⎟⎠
⎝
2
R = 0.8857
4000
E,I, ρ
2000
Failure at the base
0
0
10
20
30
40
E I / (L ρ) AT THE BASE (kN.m2/g)
Figure 6. Design curve – Pole top deflection.
50
60
FAILURE AT THE BASE
0
5
10
15
20
25
30
35
40
45
(με / kN.m)
0
-200
ε xC,b
x
εx,b Compression / Mu,b
-400
M u ,b
Fu
3
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
⎟⎟ − 1342.7
⎟⎟ + 129.13⎜⎜
⎟⎟ − 4.6647⎜⎜
= 0.054⎜⎜
⎝ Lρ ⎠
⎝ Lρ ⎠
⎝ Lρ ⎠
2
R = 0.9484
-600
Poles that failed at the base
L
-800
ε
x,b Compression : Ultimate longitudinal
compression strain at the base of an FRP pole.
Mu,b : Ultimate bending moment at the base of an
FRP pole
-1000
Mu,b
E,I, ρ
-1200
E I / (L ρ) AT THE BASE (kN.m2/g)
Figure 7. Design curve – Ultimate longitudinal compression strain (εCx,b) at the base.
FAILURE AT THE BASE
ε xT,b
1400
εx,b Traction / Mu,b
(με / kN.m)
M u ,b
1200
3
2
⎛ EI ⎞
⎛ EI ⎞
⎛ EI ⎞
= −0.0483⎜⎜
⎟⎟ + 4.5078⎜⎜
⎟⎟ − 136.04⎜⎜
⎟⎟ + 1477.1
L
ρ
L
ρ
⎝
⎠
⎝
⎠
⎝ Lρ ⎠
2
x
R = 0.9354
Fu
1000
Poles that failed at the base
800
εx,b Traction : Ultimate longitudinal
L
tension strain at the base of an FRP pole.
Mu,b : Ultimate bending moment at the base
of an FRP pole.
600
400
E,I, ρ
Mu,b
200
0
0
5
10
15
20
25
30
35
40
E I / (L ρ) AT THE BASE (kN.m2/g)
Figure 8. Design curve – Ultimate longitudinal tension strain (εTx,b) at the base.
45
CONCLUSION
Design approaches for conventional steel/wood poles were influential in
providing safety and robustness to these poles. However, little advanced approaches
focused on the design of FRP poles. This is the focus of the present paper. The
available design procedures of FRP poles are based on the allowable stress design
theory of composite material under various states of stress. However, various
experimental results show that cracking and early failure of FRP poles are normally
controlled by the relative location of the hand-holes from the base of the pole. Most
of the design guidelines ignore such effect and accounts only for the effect of these
holes by considering their influence on the abrupt reduction in the cross-sectional
area of the poles. These guidelines do not give a specific attention to the impact of
the hand-holes on the generated stress concentrations in their vicinity. Furthermore,
local buckling at a nearby area of the hand-holes generally dominates the mode of
failure of such poles that requires more attention to the relative locations of the
hand-hole. A new design approach is introduced to advance in the design of FRP
poles. The accuracy of both the developed design procedures and that of existing
design approaches are verified by comparison with documented test results of an
early experimental program. Different types of FRP poles, having different
geometrical properties and made of two different types of glass fibers were
subjected to full scale flexural static testing. Each type of the poles tested in this
study is constituted by three zones where the geometrical and the mechanical
properties are different in each zone. The difference of these properties is due to the
different number of layers used in each zone and the fiber orientation of each layer.
The following conclusions can be drawn:
•
For a ratio (E I) / (L ρ) greater than 23.5 kN.m2/g the failure occurs at the base
of the pole.
•
The ratio (εCx,b) / (Mu,b) (respectively the ratio (εTx,b) / (Mu,b)) decreases when
increasing the ratio (E I) / (L ρ) for values of (E I) / (L ρ) less than 17 kN.m2/g.
For the values of (E I) / (L ρ) greater than 17 kN.m2/g, the ratio (εCx,b) / (Mu,b)
(respectively the ratio (εTx,b) / (Mu,b)) is almost constant.
The contribution of this research work lies mainly in the characterization of new
fiber-reinforced polymer (FRP) composite poles and describes a new design
approach to advance in the design of FRP poles.
LIST OF SYMBOLS
E
Young’s modulus in the longitudinal direction of the lamina which constitutes the pole’s
base zone (N/m2).
El
Modulus of elasticity in the fiber direction (unidirectional layer) (N/m2).
Et
Modulus of elasticity in the transverse direction (unidirectional layer) (N/m2).
Exi
Young’s modulus in the longitudinal direction of the ith layer (N/m2).
Fu
Ultimate applied load (N).
Glt
Shear modulus (unidirectional layer) (N/m2).
I
Moment of inertia at the base of the pole (m4).
L
Cantilever height of the pole (m).
Mu,b
Ultimate bending moment at the base of an FRP pole (kN.m).
Mu,o
Ultimate bending moment at the principal hand hole of an FRP pole (kN.m).
n
Total number of layers in the pole’s base zone.
Pi
The rate representing the ith layer of the laminate constituting the base zone of the pole.
Vf
Fiber volume content (%).
ρ
Linear mass of the fibers (g/km). See Table I.
εCx,b
Ultimate longitudinal compression strain at the base of an FRP pole (με / kN.m).
εTx,b
Ultimate longitudinal tension strain at the base of an FRP pole (με / kN.m).
Δmax Maximum deflection at the loading position of an FRE pole (mm).
Fiber angle of the ith layer.
θi
νlt ;
Poisson’s ratios.
REFERENCES
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