BEHAVIOR OF FRP CHIMNEYS UNDER THERMAL AND WIND LOADS by Ahmed Shawky Awad Faculty of Engineering Science Department of Civil and Environment Engineering Submitted in partial fu~1Iment of the reqairements for the degree of Master of Engineering Science Faculty of Graduate Studies The University of Western Ontario London, Ontario December 1998 BAhmed Shwaky Awad 1998
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BEHAVIOR OF FRP CHIMNEYS UNDER THERMAL AND WIND LOADS
by Ahmed Shawky Awad
Faculty of Engineering Science Department of Civil and Environment Engineering
Submitted in partial fu~1Iment of the reqairements for the degree of
Master of Engineering Science
Faculty of Graduate Studies The University of Western Ontario
London, Ontario December 1998
BAhmed Shwaky Awad 1998
uisiins and Acquisitions et Bib iographi Services services bibliographques Y*
The author has granted a non- exciusive licence dowing the National Library of Canada to reproduce, loan, distrïiute or seil copies of this thesis m microform, paper or electronic formats.
The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial extracts fiom it may be printed or otherwise reproduced without the author's pdss ion .
L'auteur a accordé une licence non exclusive permettant à la BWothèque nationale du Canada de reproduire7 prêter, dis6ri'buer ou vendre des copies de cette thèse sous la forme de mic&che/nim, de reproduction sur papier ou sur format électronique.
L'auteur conserve la propriété du droit â'aukur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son
Due to their high corrosion and chemical resistance, nber reinforced plastic (FRP)
materials are increasingly being used in the construction of industrial chimneys.
However, no national code currently exists to guide the design of such type of composite
structures. This thesis attempts to investigate the structural behavior of FRP chimneys
under both thermal and wind Ioads. The study also Uicludes a s w e y to identify the
appropnate type of composite for chimneys applications and an experimental study for
evaluating the damping of such composite.
The thermal study is conducted using an in-house developed h i t e element mode1
which is used to predict values for thermal stresses that can be used in the deign of FRP
chimneys.
A cornputer code that incorporates the classical lamination theory together with a
procedure previously developed by Davenport for estimating wind loads, is developed
and used to study the wind behavior of FRP chimneys. An extensive parametric study for
both the dong and the vortex shedding respomes of FRe chimneys is conducted using the
developed code. Appropriate thicknessa for FRP chimneys that satisfy the strength and
the fatigue limits of the material are presented in a graphical form.
Finaily, dynarrric testing of samples of the materiai, commonly used in the
construction of FRP chirnneys, is conducted and reveals a relatively low damping ratio
Aramid 1.39-1.47 3000-3620 70-1 79 1.9-4.4 -2.0 (long.) ( K e v l a r - 4 9 ) ( r a d i a l ) * Kcivar-49 is the most commonly used aramid fiber in the advanccd composite industry.
It should be mentioned that these types of fiben have different maximum working
temperatures. Depending on the type of glass, the tende strength of glas fibers starts to
decrease between 220 and 260°C, reaching only 50% of its room temperature strength at a
temperature range of 480-560°C. On the other hand, carbon fiben usually start to oxidize
between 300400°C. Aramid fibers have maximum working temperature of 90°C. Carbon
and aramid fibers are characterized by having a negative thermal expansion coefficient in
the longitudinal direction which can be used to produce a composite having zero themal
expansion.
Most of the fibers are mdactured in the fom of Long continuous filaments and
then combined in various fashions to produce strands, tows, rovings, yarns or mats. Short
fibers are obtained by cuning the continuous fiers into lengths ranges fiom 3 to 50 mm.
Fibers have generdly a linearly elastic tende stress-strain response hl1 they fail in a
brittle mamer.
2 3 The Matrix (~olvmers)
The composite matrix is required to hlfill several functions. The matrix binds the
fiben and holds them in the desired direction, acts as a stress transFemng media to the
fibers and protects the f ibm from the mechanical damage, chernical and moisture attack.
The matrix has a minor role in the longitudinal strength and modulus of a unidirectional
continuous fiber composite. However, the matrix properties influences the transverse
strength and modulus as well as shear strength and modulus OF a unidirectional fiber
composite.
The matrix cm either be a thermoset or a thennoplastic polyrner. Thermoset
polymers include epoxies, vinyl esters and polyesters. Phenolics bismaleimides and
polyimides are also thennoset polymers which are used for high temperature applications.
Thermoset polyrners are charactenzed by having low viscosity (i.e. liquid-like polymen)
which are suitable for long continuous fibers. Thennoplastics such as polypropylenes and
nylons have hi& viscosity even at hi& temperature. Therefore, themioplastic polymea
are used more commonly with short fiers because of the difficulty of processing high
viscosity resin with continuous fibers. Thennosets are more thermdy stable and
chemically resistant than thermoplastics. Therefore, thermosets are more suitable for FRP
chimneys applications. A bnef discussion about the properties of the previously
mentioued thermosets will be introduced in the foIlowing ab-sections.
2.3.1 Polvester Resins
Polyester resins are mwively used in numerous FRP applications, e.g. the
construction of pipes and tanks. Polyester resins have a relatively low cost and
meanwhile, have adequate mechanical properties as well as reasonable environmental
durability. Polyester resins can be classified as orthophthalic, isophthalic, Chlorendics
and Bisphenol A fumarates. Orthophthaiic resin is among the least expensive polyesters.
However, this type of resin has relatively poor corrosion resistance. The applications of
that resin is limited to some structural applications where neither corrosion resistance nor
high temperature resistance is required. Isophthalic polyesters cost approximately 10%
higher than the orthophthalics. Meanwhile, this type of resin has improved corrosion
resistance, better water resistance, superior mechanical properties and higher heat
distortion temperature(I3DT); HDT is the sofiening temperature of' the polymer at which
Young's modulus of the material starts to &op. Chlorendics and Bisphenol-A fumarates
are two special polyesters which are fomulated for use in applications requinng supenor
corrosion resistance to that provided by isophthalic polyester. These two types of resins
have a very high rpsistance to concentrated acids. However, their resistance to alkaline
enWonments is poor. Bisphenol-A fumarates polyester resins are used for high durability
and for hi& performance applications where their relatively hi& cost can be justified.
Chlorendic polyesters have high fhe resistance but their strength and toughness properties
are lower than the isophthaiic resins.
2.3.2 Vinvl Esters
Vinyl esters have a higher failure strain as well as better impact darnage resistance
and Fatigue properties than typical polyesters. Vinyl esters have replaceci polyesters and
epoxies as well in many applications. They can be cured at room temperature without
postcuring and still have KDT 90°C (this is a big advantage compared to epoxies). The
vinyl esters cm be classified as Fire retardant, Novolac and high elongation vinyl esters.
Fire retardant version of vinyl esters contains brominated Bisphenol-A epoxy and are
suitable for chemical resistant structures. This type of resin has a high tensile failure
strain (typically 6%). Commercial names of this type of resin which are available in
North Amenca include Derakane 510 series, CoRezyn VE 8400 series, Dion VER
9300NP and Hetron FR9911992. Novolac vinyl ester resin is particularly suited to
applications requiring both high serving temperatures and solvent resistance. The tensile
failure straïn of this resin is relatively low (typically 3%). Commercial names of this type
of resin, which are available in North America include Derakane 5 ION, CoRezyn VE
8730 senes, Dion VER Y480NP, Hetron FR980 and Corin Vibrin E-085 series. High
elongation vinyl esters cm reach up to 10% failure tensile strain. Commercial names of
this resin hclude Derakane 8084 and CoRezyn 85-DA-5000.
Vinyl esters are high performance resins compared to isophthalic polyesters. They
have a superior resisrance to wata and chemical attack, higher stiaess at elevated
temperatures and greater toughness. The fdure shah of these resins is dso higher than
orthophthalic and isophthalic polymer resins (typically twice). Due to their excellent
chernical resistance, low maintenance requirement, design flexibility and ease of
installation, vinyl ester resin based composites have demonstrated low price-to-
performance characteristics compared to steel and its ailoys in many corrosive industrial
applications. As such, vinyl ester resins relliforced with fiber glass have been widely used
in pipes, ducts, Bue stacks and storage tanks.
2.3.3 E ~ o x v resins
Epoxy resins are widely used in aerospace applications. In general, epoxies have
higher values of fracture toughness compaml to polyesters and vinyl esters which usually
result in superior fatigue performance. Epoxies have hi& resistance to water absorption,
high mechanical properties and high working temperature. They are much expensive than
polyesters and vinyl esters and confineci to special applications requiring good
mechanical properties, specially high shear strength and high working temperature.
23.4 Phenolic resins
Phenolic resins have low thermal expansion coefficient as weil as excellent
electrical M a t i o n properties, creep &stance, hardness and flammability
characteristics. Pheno lic resins are convenient for performance under heat with retention
of p r o p d w under fk conditions. There are two basic types of phenolic resins: resole
and novolacs. Resole phenolics have mechanical properties comparable with those of
orthophthalic polyesters with extra thermal stability and fïre resistance. ïhe Iow failure
strain of phenolic resins, which leads to composite having poor mechanical properties,
has limited the application of this type of resin.
2.3.5 Polyimides resins
Polyimide resins have hi& thermal stability which results in service temperatures
of about 300°C (among the highest of currently available resins). A study done by Buyny
(1990) has shown that composite laminates having polyimide as a resin suffer &tom
microcrackings upon thermal cycling. These lead ta a significant reduction in the
mechanical properties and the t h m a l stability of the laminates.
Table 2-2 shows a typical range for the mechanicd properties of thermoset resins,
(Neil, 1994). As stated by Neil (1994), this information is just indicative and the actual
properties of the polymer depend on the exact system used and the curing schedule.
Fiber aiignment in ma& can be unidirectional, two directional, three directional
or random (discontinuous fibers). Contmuous fibers are used in filament-winding,
pulmided or larninated structures in which the fibers can be oriented precisely. Two
directional fiber alignent is used with larninated composite and three directional is
usually used when delamination is anticipated to be a problem. The unidirectional
arrangement provides the most effective use of the fiben when the load is acting in the
fiber direction. For such anangement, the strength and the modulus in the transverse
direction of that lamina are very low compared to those in the longitudinal direction (such
composite is highly anisotropic). Randomly oriented fibers give equal properties in al1
directions on plane of the lamina (ahost isotropie). in a two dimensional alignment,
Fibers are woven in both 0" and 90' directions which brings the lamina properties in the
two directions to be identical if the f i e r content is the same in the two directions.
A fiber reinforced plastic structure is usually a multiple layered structure. Each
Iayer is called a lamina and the whole composite is called the laminate. nie typical
thickness of a lamina varies between 0.8 to l.Omm. The order in which various laminae
(having different fibers orientation) are stacked in the laminate is engineered to obtain the
desired global properties. A laminate denoted by (0/+30/-30/-30/+30/0) is a symrnenic
laminate consisting of six lamina whose angle of f i e r orientation are 0°,+300,-30°,-
30°,+300 and 0°, respectively. A laminate which is symmetric about its mid plan is
prefemd because it does not exhibit extension-bending coupling (as will be discussed in
details in chapter 4).
The possibility of combining different fiber orientations in different Iayers gives a
tremendous design flexibiiity for the laminated composites that is not available with any
other structural matenal. As such, the mechanical properties and the thermal
charactenstics of a laminate can be tailored and suited to the desired application.
2.5 Environmental Effect on Glas Fiber Reinforced Plastics
The mechanicd properties of polymeric composites depend on their constituents
and their interaction with the environmental conditions such as moisture and temperature.
Two major environmental problems are usually associated with polyrners; moisture
absorption and thermal instability.
2.5.1 Maisture Absomtion
in environmental conditions, polymeric composites absorb water. This leads to
change in the mechanical properties of these composites. The absorption rate depends on
the matrix type, exposure time, operating temperature, geometry of the composite and
relative humidity. The moisture absorption generally reduces the HDT of polyrnen. As
reponed by Delasi (1987), a 10% increase of the moisture content of five different types
of epoxy r e s h has led to 50% reduction in the HDT of these resins. Both the strength
and modulus of a composite are dkcted by its moisture content but the modulus is less
sensitive. in general, the moisture absorption of glass-epoxy composite is less than glas-
polyester composite. The effect of moisture absorption has to be taken into account in the
design of poiymeric composites especiaily if the composite is highly stresseci (compared
to its ultimate strength) or if the operating temperature is close to the HDT of the min. A
usehl survey is presented by Bulder (1991) on the effects of moisture on mechanical
properties of glass and carbon reinforced plastics and is shown in Table 2-3. As seen fiom
Table 2.3, the glass/epoxy absorbs less moisture thau glasdpolyester composite. So that
the change in the properties is greater with polyester as a matrix than with epoxy.
Carbonkpoxy composite absorbs the lest arnount of moisture and consequently it is the
less affected by water than glasskpoxy composite.
Matrix (weight %) ( YO ) (_%) 103cycle(%) 10'cycle(%) Glasdpo lyest er 4 -10 -15 -35 - 1 O Glasdepoxy 2 - 10 - 10 -20 O ,
Carbon/polyester - - -5 - - Carbon/epoxy 1.5 +1 -2 O O Glass-carbon/epoxy 1 < 2 1 O / -3 1 -
2.5.2 Thermal Instabilitv
As mentioned before, most of the polymeric matrices possess a certain HDT after
which a significant loss of the composite strength and modulus usually occur. The
reinforcing fibers have a much higher thermal stability cornpared to the matrix. As such,
the presence of the fibers in the matrix causes signincant improvement in the HDT of the
composite. By studying three ciiffirent types of matrix resin reinforced by E-glas and K
g l w fibers, Ghosh (1995) has reported that glas fiber reinforcement has trernendously
improved the HDT of the m a h . R d t s of this study are presented in Table 2-4. As c m
be noted fiom Table 2.4, the HDT of the polyester resin changed h m 79OC to 1 70°C due
to adding 33% (by weight) of N-glas fibea to the resin. A significant improvement of
the HDT of the epoxy and the phenolic resins is also noted nom the table. The British
Standard Specification For GRP Pipes (BS 5480, 1991) recommends an upper limit for
the working temperature of polymeric composite to be 20°C less than the HDT of the
composite to ensure that the composite possesses its ambient mechanical properties.
A typical environment can have hot andlor wet conditions. The stiffhess and
strength of a composite in such environment may be considerably reduced in cornparison
to its mbient properties due to the combined effect of temperature and moisture
(hygrothermai). The composite matrix is more sensitive than Abers to the hygrothermal
effect. For that, the composite properties that are dominated by the matrix are much more
affected. The hygrothermal conditions generate the most severe degradation of the plastic
composite properties; mainly the transverse normal and in-plane shear strength and
stiffhess properties. On the other hand, longitudinal properties of the plastic composites
are very slightly alfected as they are dominated by the fiber properties.
Table 2-4 Cornparison of HDT of some unreùiforced m a h resins and fiber reinforced composites (Ghosh, 1995)
4 3 . 4 ~ 10-6 mlmPC, where a, and a, are the coefficient of thermal expansion in the Bbers
direction and perpendicular to the fibers, respectively.
The curing temperature (reference temperature of the composite) is assurned to be
equal to 100°C and the chimneys are analyzed at interior (operating) temperature and
extenor (arnbient) temperature equal to 70°C and -3 O°C, respectively . This leads to
temperature change (relative the curing temperature) at the interior (AT,J and the exterior
(AT.3 surfaces of the chimneys equd to -30°C and -130°C. respectively. The above
mechanicd properties and temperature variation are used to perforrn a parametric study
hvestigating the effect of various parameters (thickness of the shell, number of laminate
layen, orientation angle of' the fibers, diameter and height of the chimney) on the themal
messes induced in FRP chimneys during their operating stage. in al1 analyses, the
boundary conditions are assumed to be full £kation at the bottom of the chimney and fkee
displacements and rotations at the top.
3.4.1 The Effect of the Laminate Thickness
A FRP chimney having a diameter D = 3 . h and a height L = 40.0 m is
considered for thermal stress analysis. The larninate of the chimney consists of 5 angle-
ply layers (5S0/-55" 155"/-55"/55"). Notice that these angles are measured relative to the
axis x', x' is an axis tangent to the surface and located in a horizontal plane. The andysis
is carried out by varying the laminate thickness in the range of 1 Omm to l3Ornm. The
temperature distribution is assumed to be linear with values of -30°C and -130°C at the
interior and exterior surfaces, respectively (as described in the previous section). The
thermal stresses that resulted h m the analysis are plotted in Figs.3.5 and 3.6 for a
location away nom the boundary and for a point located at the base of the chimney,
respectively. Fig.3.5 indicates that the thickness has no effect on the thermal stresses at
sections located away nom the boundary. This is due to the fact that by increasing the
thickness of the shell, both the initial thermal strains (extemal load) and the stifiess of
the shell increase and thus the same values of final thermal stresses are obtained. Fig.3.6
shows that up to a thickness of 3 0 m , an increase in the thickness leads to a
corresponding increase in the themial stresses at the base of the chimney. The same figure
shows that beyond a thickness value of 30mm, stresses become almost constant. This
behavior was also reported for laminated plates by Thangaratnam et al. (1987).
In summary, it can be concluded that beyond a certain thickness value, an increase
of the thickness of FRP chimney bas no effect on the induced thermal stresses.
3.4.2 EfKect of the Diameter of the Chimnev
A chimney having a height equal to L = 40m, a thickness H = 65mm and
consisting of 5 layers symmetric angle-ply laminate (8 = t5s0 ) is considered for thermal
stress analysis in order to asses the efTect of the diameter of the chimney. The temperature
variation follows the linear dishibution previously described when studying the effect of
the thickness. The parametric study is perfomed by varying the diameter of the chimney
in the range between 1.5m and 6m. The variation of the themal stresses induced ai the
base of the chimney versus the diameter is presented in Fig.3.7. It could be concluded
from the figure that the change in the diameter has no significant effect on the thermal
stresses. in Fig.3.8 both the hoop thermal stresses (q) and the axial (meridional) thermal
stresses (a,) are ploaed along the height of one of the analyzed chimneys. As might be
expecied, both the hoop and the axial thermal stresses have rapid fluctuations near the
boundaries (for both the fixed and the fiee botindaries). In general. the thermal stress
distributions show hi& stress values occmhg very close to the boundaries and are
localized in a narrow region.
3.4.3 The Effect of the Heieht of the Chimnev
The effect of the height of the chimney on the induced thermal stresses is studied
by fixing both the diameter and the thickness of the FRP chimney and varying its height.
Analyses indicated that the maximum values of thermal stress (occurring near the fixed
bottom of the chimney) are independent of the height of the chimney. The stress
distniutions along the height are Clpcaily as shown in Fig.3.8; the change of the height
only aects the length of the region having constant stress distriiution.
3.4.4 The Effect of the Number of Lavers and Fiber Orientation
In this section, the effects of varying both the number of layers (keeping the total
thickness constant) and the orientation of the fibers on the thermal stresses induced in
FRP chimneys are studied. The parametric study is conducted by considering a FRP
chimney having a height L = 4ûm, a diameter D = 3m and a total thickness H = 65mm.
This thickness was chosen by considering 2 , 4 5, 6 and 10 layers larninate, respectively.
The laminates 2, 4, 6 and 10 consist of anti-syrnrnetric angle-ply layers (28) and the 5
layer laminate is a symmetric angle-ply laminate. For each larninate configuration, the
angle of orientation 8 has been varied between 0' and 90'. In Fig.3.9, the variations of the
maximum longitudinal stresses a, and transverse stresses q (occurring near the base) for
the outside face of the c b e y are plotted versus the angie of orientation 8 for different
laminate configurations. Fig.3.10 shows similar graphs plotted for the inside face. Both
figures indicate that the number of layers has no significant effect on both the
longitudinal and the transverse stresses. At the inside face of the shell, the increase of the
fiber orientation 8, increases the longitudinal stresses reaching maximum values at 0 =
90" and decreases the transverse stresses which reach minimum values at O = 90"- For the
outside face, the increase of the angle ply 8 leads to a slight decrease in the stresses which
is then followed by a significant increase of the stresses with the angle 8 (at 0 = 37.5" for
the case of 0,).
3.4.5 Summary of the Results of the Parametric Studv
From the above conducted parametric study, it can be concluded that the height,
the diameter, the thickness and the number of layen used to achieve the thickness have
almost no effect on the maximum thermal stresses induced in FRP chimneys. Such
stresses are usually very localized in a nanow region near the base of the chimney. The
main parameten affecting the values of the stresses are the temperature profile, the angle
of the orientation of the fibers, the coefficient of thermal expansion and the modulus of
elasticity along the fibea direction. For practical FRP chimneys consisting of glass fibers
and vinyl ester resin, the last two parameten depend rnainly on the percentage of the
fibers content.
The practical range for the angle of inclination 0 is between 3S0 and 55". Examining
the stress values shown in Figs.3.6 and 3.7 (these figures represent results for chimney
having 0 = 5 5 O ) , it cm be concluded that the maximum value for the stresses a, (along
the fiben direction) and q (perpendicdar to the fibers direction) are approxirnately 100
MPa and 80 MPa, respectively. Typical d t h a t e strength dong the fiben a,, and
perpendicular to the fibers ou have approximately the following values o,, =il00 MPa
and sZu = 33.5 MPa (for 70% E-glas content based on weight). Cornparison between the
induced stresses and the ultimate strength indicates that although large factor of safety is
achieved along the libers direction, the cross &ers direction is unsafe. As such, one
would expect that cracks localized at the bottom part of the chimneys paralle1 to the fiber
direction would occur (independent of the value of the thkkness) due to thermal stresses.
3.5 Practical Considerations for Attern~tinp Desipu Procedure of FRP Chimnevs
From the above discussions, it is clear that the temperature distribution assumed
in the analysis results in across thermal stresses which are approxirnately 2.5 times the
allowable stresses in that direction. As such, it is aixnost impossible to avoid cracking in
the across fiber direction. Moreover, if the design is govemed by preventing such cracks,
the fiber reinforcement would be redundant. Knowing that cracks will occur, it has been
decided to anaiyze the FRP chimneys under thermal loads by assuming that the stiffhess
in the direction perpendicular to the fibers alrnost vanishes (Le. & is very mall). R i s
assumption is made for al1 layers along the height of the chimney. The author believes
that this assumption is conservative because, in practice, cracks will not occur in al1
layen and not necessary along the whole height of the chimney. The safety of an FRP
chimney analyzed under such an assumption can be checked by assuring that the stresses
dong the fiben do not exceed the ultimate strength divided by a suitable factor of safety
and also that the interlarninar shear stresses are also well below the ultimate shear
snength. By assuring that the interlaminar shear stresses are safe and using an angle-ply
configuration, it is expected that the cracks in one layer will be very much controlled by
the stifiess of the two adjacent layers along the fibers direction. Figure 3.1 I shows the
variation of the longitudinal stresses o, with the angle ply 0 for a typicd FRP chimney
using the temperature distriiution descrihi above (after degrading the across fibers
stiflhess). It should be noted that the anaiysis has been perfomed for a practical range of
8 varying between 3S0 and 60". From Fig.3.11, it c m be concluded that the maximum
stresses o, do not exceed value of 180 MPa This value leads to a factor of safety of
approximately six when compared to the ultimate strength. in order to check safety
against shear failure, the in-plane shear stress r,, as well as the transverse shear stresses
r,, and r,, resulted from the same analyses are plotted in Fig.3.12 versus the angle of
orientation 8. The typical values For the ultimate shear strength in-plane and transverse
are given by r,, = 70.6 MPa , r,, = 70.6 MPa and 7, = 18.85 MPa Cornparison between
the induced shear stresses and the ultimate ones reveals that factor of safety of
approximately 3.5, 15 and 5.6 are achieved for the in-plane and the transverse shear
stresses, respectively.
3.6 Thermal Stress Vaiues to be Used in Practical Desien of FRP Chirnnevs
As mentioned before, the thermal stresses induced fiom temperature variation in
FRP chimney depend on the followuig factors:
1. Fibers content
2. Angle of inclination of the fibm
3. Temperature pro file
4. Type of fibers and resin
Restrainîng the design to FRP chimneys constnicted nom vinyl ester resin
reinforced by 70% (based on weight) E-glas fibers, for a certain angle of inclination 8 of
the fibers, the themal stresses depend only on the temperature profile. This profile is
govemed by two parameters which are:
1. The variation of mid-dace tempcratrne with respect to the curing temperature Tm.
2. The Merence between the temperahire at the inside and the outside faces (AT); AT =
Using the approach described in sub-section 3.5. analyses have been conducted to
determine the maximum stresses o, as function of Tm and AT for huo angle
configurations, 8 = f 35' and k 55'. respectively. Figures 3.13 and 3.14 show the
variation of the maximum dong fiber stresses CF, vems the temperature variation AT for
different values of' Tm for 0 = f 35" and i 5S0, respectively. These graphs can be used to
estimate the stresses induced in a FRP chimney, having the above-described properties
under various temperanite variations. Cornparison between the two graphs indicates that
in general higher themal stresses are introduced when the fiben become more vertically
inclined (i.e. 0 = f 55' leads to higher thermal stresses than 0 = + 35'. The shear stresses
associated with various temperature profiles are shown in Tables 3.4 and 3.5 for 0 = + 35O and f 5S0, respectively. It should be noted that the shear stresses Vary linearly with the
parameter Tm and independently of AT. The designer of FRP chimney has to assure that a
sufficient factor of salety is achieved against shear failure.
Table 3.4. The in-plane and transverse shear stresses associated with the longitudinal
Table 3.5. The in-plane and transverse shear stresses associated with the longitudinal stresses in Fig.3.14 for an angle.
Middle surface 1 Maximum in-plane s-
Maximum transverse shear stresses
In this chapter, the formulation of the consistent laminated shell element is
extended to include thermal stress analysis. A number of plate and shell structures are
rnodeled for themial stress anaiysis and the redts are compared with those available in
the literature. in al1 examples, the elernent gives adequate predictions for thermal stresses.
The developed h i t e element formulation is then used to study the effect of various
parameters which might influence the thermal stresses induced in angle-ply laminated
fiber reinforced plastic chimneys. Redts of the parametric midy indicate that the
thickness, the diameter, the height and the number of laminae have no significant effect
on the induced thermal stresses. Analyses indicate that the thermal stresses depend
rnainly on the through thiclmess temperature distnàution (relative to the curing
temperature), the angle of orientation of the fiers, the coefficient of tfiennal expansion
and the moduîus of elastici@ dong the fîôers direction. The last two parameters depend
on the mer content in the matrix. The thermal stress analyms of typical FRP chimneys
shows high stress concentration near the boundaries with in-plane across fiber stresses
exceeding the typical ultimate strength in this direction. As such, cracks are expected to
occur in FRP chimneys as a result of through thickness temperature variations. However,
it is believed that these cracks will be controlled if the interlarninar shear stresses are less
than the ultimate shear strength divided by an appropriate factor of safety.
The analysis then proceeds by assuming a negligible value for the modulus of
elasticity in the direction perpendicular to the fibers. Results of this 1 s t set of analysis
indicate that for the practical range of the early mentioned influential parameters, the
dong fiber direction stresses as well as the shear stresses of cracked chimneys are within
acceptable values. Finally charts predicting the dong fiber thermal stresses induced in
typical cracked FRP chimneys (but lirnited to 70% nber content and angles of inclination
9 = f 35 O and f 55') as a function of the through thickness temperature distribution are
presented These stress values cm be considered when the design of a FRP chimney is
atternpted.
0 u , % W , c C P i
A sR 0 4 v, W'
Fig.3.1 Coordinate systems and nodal de- of M o m of CLS element.
i Elasticity
A
0 present B
1 I 6
O 1 2 3 Y (ml
Fig.3 -2 Variation of outer and mid-dace longitudinal and cucumferentid stresses at fÎee end of cylinder due to ünearly varying temperature change.
Fig.3.3 Cross-ply cylindrical panel
Fig3.4 Cross section of FRP chimney and vertical projection of the laminate.
Fig.3.5 Thermal stresses of 5 layers angle-ply (+/O 55' ) FRP chimney versus the laminate thickness at a section away fiom the boundaries of the chimney.
0.02 0-04 0-06 0.08 O. 1 O 0.12 0.14
thickness (m)
a" O -
bF -25 -
-50 -
-75 -
Fig3.6 Thermal stresses of 5 layers angle-ply (+/- 5 9 ) FRP chimney versus the laminate thickness at the base section of the chimney.
-, 02
inside Face
-100 -
Fig.3.7 The eKect of the diameter on the thexmai stresses induced at the base of a FRP chimney .
Fig.3.11 The maximum longitudinal stresses at the inner and outer Face of the laminate vs the angle of orientation after degrading the across fibers stitfness of the layers.
Fig.3.12 In-plan shear stress s,, , transverse shear stresses r,, , r, of 10 layer lamiBate at the bottom of the chimney after degxading the across fibers dffhess of the layers.
1 . . . - . - - inside face 1
Fig.3.13 The longitudinal thermal stresses of 3 5' angle-ply FRP chimney for Merent temperature fields (degraded across fibers modulus E, = E,!1000)
AT,, T r\ inside face 10 layers antisymrnetric angle-ply laminate +l-55"
Fig.3.14 The longitudinal themai stresses of 55' angle-ply RIP chimney for different temperature fields (degraded across fibers modulus E, = E ,11000)
CEAPTER 4 COMPUTER A[DED-DESIGN CODE TO EVALUATE WIND RESPONSES OF
FlBER REINFORCED PLASTIC CEfIMNEYS
4.1 Introduction
The design of industrial chimneys is usuaily govemed by the stresses and
displacements induced by the wind loads. Meanwhile, a proper design should also
account for various phenomenae associated with wind loads acting on slender structures
such as vortex shedding and ovalling.
One of the engineering problerns that interest the researchea and the designers of
industrial chimneys is understanding the complete behavior of the vortices in the
downstream of cylinden created by the oncoming flow. Strouhal stated the relationship
between the fkequency of the vortices, the wind speed and the diameter of the cylinder
more than a cenhny ago. Many efforts have been made in the past to estimate the
magnitude of the fluctuating forces acting on cyünders and associated with the turbulent
wind in the wake of the structure (Van Koten (1969), Scurton (1963), Vickery (1997),
Davenport (1993)). The vortex shedding phenornenon is stilI an open area of research. As
stated by Vickery (1997). the difficulty in predicting the across-wind behavior of
chimneys is that the current available wind hmneis are not capable of achievkg high
Reynolds number associated with prototype chimneys.
The purpose of this chapter is to investigate anaiytically the response of FRP
chimneys under wind loads. A simple and efficient computer code, to be used in
achieving this task, is developed and desdeci in this chapter. The developed computer
code can be used to perforrn static and dynamic analysis of tapered cantilever like
laminated structures (e.g. FRP fiee standing chimneys) subjected to wind loads. The
developed computer code is based on the following:
1) Classical lamination theory to obtain apparent elastic properties of the laminate based
on the mechanical properties of each lamina in its local axes.
2) The Stodola method to evaluate the natural fiequemies and the correspondhg mode
shapes of a FRP tapered chimney.
3) The wind loads acting on the chimney (dong, across and vortex shedding) treated as
an equivalent static loads according to the CICIND code for steel chimneys (1988), or
as a combination of static and dynamic loads based on a procedure developed by
Davenport ( 1993).
4) Tsai and Wu (1971) failure criterion used to constnict a failure envelope representing
the limit bearing capacity of each lamina.
5) Fatigue stresses due to vortex shedding evduated and encountered in the design by
applying the fatigue damage indicator defined by the EUROCOMP Design Code of
FRP (1997).
in this chapter, a bnef description for the above theones and procedures and how
they are incorporated in the development of a computer design-aided code for EXP
chimneys subjected to wind loads, is presented. A flow chart showing the interaction
between different parts of the cornputer code is givm. A verification for the developed
code using results of detailed finite element is presented and a parametnc study on the
parameters affecthg the vortex shedding respome is performed. Finally, design
thicknesses for different aspect ratios and factors of safety are provided for FRP chirnneys
Fig.4.7 Nomdized across-wind tip deflection versus the mass density for 1, II and m.
0.0 10
Damping ratio (Q
Fig.4.8 N o d i z e d tip deflections versus damping ratio for chimneys 1, II and 111.
Damping ratio (Q
Fig.4.9 The estimated across-wind response versus the structural damping for chimney with height H= 40m, bottom diameter @=3.Om for 0.0,03 and 0.6 tapering ratios.
120 -
Factor of safety = 2.0 30m 5 = 0.7 % - - 40m alang-w ind
*..-.. Som -c- 30m -- 40m along-wind --A-. and vortex
---- O-, k 1 I 1 1
HfD Fig.4.10 Estimated thicknesses of FRP chimney s vernis the aspect ratio
for factor of safety = 2.0,5 = 0.70%.
A--. Factor of safety = 3.0 5 = 0.7 %
- 30m - - 40m along-w ind
4 30m -r- 40m along-w ind - - & - - Som and vortex
Fig.4. i 1 Estimated thicknesses of FRP chimneys vernis the aspect ratio for factor of dety = 3.0, & = 0.70%.
Factor of safety = 4.0
m Fig.4.12 Estimated thicknesses of FRP chimneys vernis the aspect ratio
r, - 30m 4- 40rn along-wind .. \ -*&.- Som and vortex
m Fi& 1 8 Estunated thicknesses of FRP chimneys versus the aspect ratio
for factor of safety = 2.0, < = 1 .O%
Factor of safety = 3.0 A- . - <= i.0 % - 30rn
-. 40m along-w ind -*...* - . 50m 4 30m
k 4- 40m along-w ind -\ .\ --).- 50m and vonex
\ =A - \
FigA. 19 Estimated thicknesses of FRP chimneys v e n u the aspect ratio for factor of s a f i = 3.0,< = 1 .OYO
A-** Factor of safety = 4.0
- 9 . - 0 - c;= 1.0% - 30 m
Y. - - 40 m dong-wind .... 0 . 50 m
Lm Fig.4.20 Estimated thicknesses of FRP chimneys versus the aspect ratio
for factor of safety = 4.0.6 = 1 .O%.
Factor of safety = 5.0 - 30m along-w ind
aiong-wind and vonex
8 10 12 14 16 18 20 22 L/D
Fig.421 Estimated thicknesses of FRP chimneys vernis the aspect ratio for factor of safety = 5.0, < = 1 .O%
Factor of safty = 2.0 <=û.70 %
Lm Fig.4.22 Tip deflection normaüzed to diameter of FRP chimneys versus the aspect ratio
for factor of safety = 2.0 and 5 = 0.7%.
180 -, Factor of safety = 5.0
A- < = 0.7 % _.-- a r . -
* : - * . . . - -
along-w ind
4- 40m along-w ind --A-. Som and vortex
8 10 12 14 16 18 20 22
m Fig.4.23 Estimateci thicknesses of FRP chllnneys versus the aspect ratio for factor
of sâfety = 5.0, & = 0.7%, 0 = +/- 35'.
CHAPTER 5
DAMPING OF FRP MATERIALS
5.1 Introduction
For structural applications which are requked to withstand a harsh dynarnic
environment, damping is a very important parameter. The damping capacity of the
structure plays a vital role by limiting the resonant response and forcing the transient
response to die out quickly. One of such applications are fiber reinforced plastic
chimneys which are constantly subjected to dynamic forces in the form of wind loads.
Material damping is the ability of the material to dissipate energy by converting
the mechanical energy to heat. Composite plastic materials have multiple sources of
energy dissipation, such as the viscoelastic Cesponse of the ma&, thennoelastic
conversion of mechanical energy into heat, fiction at fiber-matrix interface and energy
dissipated berneen layers due to delamination.
The damping of FRP materials depends on many parameters such as: the rnatrix
property, fibers content, fibm onentaiion, fkquency, strain amplitude and method of
manufacturing. Although a number of studies exists in the iiterature for evaluating the
damphg of FRP mater&, no &ta exkt for typical materiai used in the construction of
FRP chimneys. The purpose of this chapter is to evaluate experimentally the material
damping of glass reinforced Vinyl ester materials which are typicaiiy used in the design
of FRP stacks.
This chapter starts by presenh'ng a bnef review of the research existing in the
literature and pertaùiing to the damping of FRP matends in general. This is followed by a
description of two techniques which are used to evaiuate the material damping
experimentally. Finally, the experiments conducted in this study are described and the
obtained results are presented.
5.2 Review of Dam~inp Evaluation of Fiber Reinforced Plastic Materials
For more than three decades, f ibs reinforced plastic materials have been
investigated for dynamic properties and damping capacity. In general, results of the
studies indicate that for FRP materiais tested at low strain levels, the material damping is
independent of the snain amplitude but does depend on the fiber content, fiber
orientation, temperature, moisture, fkequency of load and matrix properties.
In the late sixties, Schultz (1968) published remarkable resuits of damping ratios
of unidirectionai (UD) glass-epoxy cantilever beam using the decrement and the
bandwidth techniques. In this study, it was observed that the damping capacity mainly
depends on the fkequency of Ioading and the angle of orientation of the fiers. In generd,
it was found that the damping capacity increases with the increase in kquency.
Meanwhile, by varyhg the angle of orientation, it was found that the maximum damping
is achieved at an angle of 45". Damping values for unidirectional and cross-ply E-glass
fiber reinforced epoxy beams under flexurai vibration were reported by Gibson (1976) for
a wide range of frequency (20-500 Hz). It was found that the damping values
considerably increase with the increase of the load frequency and are independent of
strain amplitude (up to 0.002 strain for cross-ply laminate). Mymon, Biley and Rehfield
(1 978) conducted an experimental investigation studying the effoct of temperature,
moisture content and angle of orientation on the damping capacity of a variety of graphite
epoxy laminates. It was found that the angle-ply [+4S0] laminate exhibits higher damping
than [O0], and [0°J+450J900,/-450,] laminates for both dry (2S°C) and hot-wet (93°C)
conditions. The same shidy showed that the hot-wet environment increases the damping
for the [O0] laminate by about 29 %. Meanwhile, a remarkable decrease for the damping
(about 28%) was observed for the other two laminates due to the effect of the hot-wet
environment.
The effect of the frequency of the loading on the damping values of FRP materials
was studied by Robert (1982) showhg in grnerai an inmase of 10%-20% in the darnping
ratio for tenfold increase in the fkquencies. It should be mentioned that d l of these
studies dealt with linear viscoelastic damping, at low strain, well bonded and undamaged
composite. A complete Litazture review about theoretical and experimental studies
conducted for evaiuating the damping capacity of FRP materiais is done by Gibson ( 1979
and 1977) and Vantomme (1995).
5.3 Measnres And Techniaues For Determioinp Material Dam~ing
Material damping is of€en characterized by the specific darnping capacity
(SDC), loss factor q, darnping ratio 5 and logarithrnic decrement d. Specific Damping
capacity y is defined as the ratio of the energy dissipated during one cycle of loading to
the maximum strain energy stored in the specirnen during this cycle. Loss factor q is
equal to the tangent of the phase angle 6 which represents the phase shift between the
response and the hannonic excitation. The damping ratio t; is defined using the following
C relation: -, where c is the damping coefficient and c, is the criticai damping coefficient
c m
defined as c, = 2.rn.o; m is the m a s and o is the naturd frequency. The logarithmic
decrement d characterizes the decay of the fke vibration response of a single degree of
teedom system and is defined by the n a d logarithm of the ratio of two successive
maximum amplitudes. The relations between the above defined damping parameters are
given as:
qj =2nq=41r(;=Zntan6=2d (5- 1)
Numerous testîng techniques can be used to determine the above damping
properties. niese include: the forced oscillation technique which is based on resonance
testing (half power band width, resonant dwell), the modally tmed impulse technique, the
logarithmic decranent (sometimes called the fke decay technique) and the off-resonance
impedance technique. A brief description of the logarithmic decrement technique and the
half power band-width methoci, which are used in this study, are presented in the next
sub-sections.
5.3.1 Lo~arithmic Decrement Techniaue
n i e logarithmic decrement technique represents the classical way for estimating
the damping ratio of a material. The technique is based on free vibration testing of the
specimen. The test is conducted by exciting one ofthe natural modes of the specimen and
then measuring the decay amplitudes after mnoval of the driving force. The decay of the
measured time history cuve can be used to atimate the modal damping coefficient for
that particular mode using the following expression:
where 4, and &, are the response amplitudes at the nh and n + m' cycles. It should be
mentioned that the expression given by Eq.5.2 is based on the assumption that the
damping ratio is very maIl i.e.5 cc 1 .O%. As such, the fiee decay method is most suited
to the determination of damping values for lightly damped systems (typically less than
0.0 1 ).
53.2 Half Power Band-Width Method
This technique is the most wideiy used method in damping testing. For structures
with well separated modes, single de- of fieedom modeliug of each nanual mode
when excited resonantiy gives very accurate results. In this methoâ, the steady state
amplitudes correspondhg to discrete fkquency values of forced harmonic excitations,
covering a wide range around the natural frequency of interest, are measured. For a given
fiequency response curve, the damping ratio can be calculated fkom
where and f, are the fbquencies at which the amplitudes of response are 1 I f i tirnes
the maximum amplitude. For tightly damped structures, fitting the modal peaks of
continuous structure to the steady state response of single degree of keedorn system is
more convenient than applying Eq.5.3 to estimate the modal damping. in the current
study, the measured response of the specimens ovet the fkequency range in the
neighborhood of the modal fkequency of interest has been fitted to the following equation
(which represents the steady state response of single degree of fieedom system excited by
a harmonic load).
where y( E T ) is the measured amplitude of the response, p,, is the amplitude of the applicd
hamonic force, k is the stiffiiess of the specimen, m is the dnving fiequency, o is the
naturai fiequency of the specirnen, 5 is damping ratio of the specimen and = -. In the k
tests, the response of the specimen due to varying hquency of harmonic load is
measured. in view of Eq.5.4 and using the above measured response, a curve fitting
technique can be used to estimate o , & and y .
5.4 Exaerimental Evaluation of the Damaine Prmerties of Glass Reinforced
Vinvl Ester Com~osite
Damping is a very important parameter controlling the dynarnic response of
chimneys in general. As discussed in ctiapter 2, glass reinforced vinyl ester represents the
favorable composite to be used in the construction of FRP chirnneys. Due to the Iack of
damping values of this specific composite, it was decided in this study to conduct some
dynarnic tests in order to evaluate the damping capacity of this type of polymeric
composite.
Four cyiindrical specimens having diameten equal to 2", 3", 4" and 6" and
thicknesses equai to O. 19", O. 19", 0.2" and 0.24", respectively, are used in the dynamic
testing. Al1 specimens conskt of filament winding angle-ply g las reinforced vinyl ester
laminates. The specimens have an equivalent axial modulus of elasticity E = 1.3.10' psi
(8.97 GPa) and an axial tensile strength o = 9000 psi (62 MPa). The specimens are
stacked as follows: 0.0 1 " chemical barrier reinforced with Nexus Veil having 10% fiber
content, 0.1" Anti-wicking barrîer of two chopped sîrand mats 1 10 oz with 25% fiber
content, structurai layers of a continuous nlament winding with fis0 (angle-ply)
orientation angle measured h m the longitudinai axis of the specimen with 70% fiber
content, and W y 0.01" exterior protection resh coating. In order to cover a wide range
of ~ u e n c i e s , various lengths of each s p e c h (Le. hawig different naturai
fkequencies) are used in the testing. The specimens are donated by Reinforced PIarrc
Systern hc..
5.4.1 Ex~eriment Set-u~ and Procedure
The damping testes are perforrned using a uni-directional shake table recently
constnicted at ïïze University of Watern Ontario. The shake table system consists of an
electro-magnetic shaker connected to a 4'x4' slide table, an amplifia and a PC based data
acquisition system. The output sipds which excite the shaker are generated and
controlled by enomous speed data acquisition board.
Figure 5.1 represents a photo showhg various components of the shaker system.
The schematic illustration of the shake table system is shown in Fig.5.2. For more details
about the shake table and the data acquisition system, the reader is referred to ECDamaty
( 1998).
The dynamic tests are conducted by mounting the specimens to the slide table.
The specimens' clamping is designed such that there is no extraneous loss mechanisrn
neither from any created damage in the matend nor through fiction losses at the clamped
end. As such, the specimens have been carefully glued to steel plates using epoxy glue
and then mounted on the table using four corner steel bolts comected to the steel plates as
s h o w in the photo provided in Fig.5.3.
The response of the specimen is monitored by mounting high sensitive charge
signal accelerometers at various locations dong the specimen height. The signals are
conditioned (nltered and amplifïed) using high accuracy charge signal amplifier. The
signals are then stored to the hard disk of the PC through the data acquisition system.
Figure 5.4 shows a photo of a typicd specimen mounted to the slide table.
The haif power band-width technique is adopted to evaluate the damping of the
specimens. The following steps are applied to identify the darnping ratio of each
specimen:
1) The specimen is driven by a harmonic excitation having a specific fiequency.
2) The steady state response (acceleration) of the specimen (usually at the top of the
specimen) is measured and stored.
3) Step (1) and (2) are repeated for a fkequency range in the vicinity of a naturai
fkequency of the specimen.
4) The fiequency response cuve, the relation between the steady state acceleration and
the kequency, is plotted for each naiural mode of excitation.
5) The fkequency response c w e is fitted to the response of a single degree of fkedorn
system, Le. to Eq.5.4, to give the estimated damping value.
Steps (1) to (5) are repeated for the fkst and second modes of vibration of each specimen.
Low amplitudes of excitation are chosen to minimize the effect of aerodynamic darnping
and also to Limit the specimens' strain to the level at which damping of the composite is
independent of the amplitude. Fig.5.5 shows a typical fkquency response curve as
measured h m a test, togetha with the response of an quivalent single degree of
needom system. It shodd be mentioned that in order to represent accurately the
fkequency response curve (specially around the natural fkquency), a very small step of
kquency variation has been usd
Logarithmic decrement tests have bem conducted as well for the fiat mode of
each specimen by sirnply pulling the top of the specimen and measuring the decay
response after removing the applied force. Since exciting only the Fbndarnental mode of
the specimen manually is possible, the acquired sigals for the decay test have been
filtered to eliminate the contributions of the higher modes to the response. Exciting the
second mode of vibration manually for the decay test was not possible because the
specimens are relatively stiff. For that, the fint mode of vibration has been only tested
using the decay test. These decay tests are conducted for cornparison with the resonant
tests results and also to check the dependency of the damping ratios on the strain
ampli tude.
5.4.2 D a m ~ i n ~ Results and Discussion
Resonant tests have been conducted for the first two modes of vibration of the
specimens dacribed in section 5.4. Table 5.1 shows the measured natural Eequencies and
dampuig values for various tested specimens. in Fig.5.6, The damping values
corresponding to the first mode are plotteci vernis the fundamental Eequency. The
damping ratios are fitted with a second order polynomial bction. However, the results
of the c w e fitting shows an almost Linear behavior. It is clear fiom the figure that the
variation of the damping ratio with the fkquency is almost negligible for the considered
rage of kequencies. Figure 5.7 shows the variation of the damping ratios of both the first
and the second mode with the modal fkequencies. It is clear firom the figure that the
results of the second mode show more scattered damping values about the fitting curve
compared to those corraponding to the fint mode.
The damping ratios corresponding to the fiindamental mode of the specirnens and
based on decrement decay tests are presented in Table 5.1 as well as Fig.5.8. in general,
most of the tests results show a good agreement between the decrement and the resonant
tests. It has been noted that typically the damping values obtained from the decay test are
slightly larger than those obtained nom the resonant test. Meanwhile, the dependency of
the damping ratios on the fkquency is much stronger for the decay test results compared
to those obtained using the resonant tests (specially for kquencies higher than 40 Hz).
The average damping ratios obtained h m all the conducted tests are equai to 0.6551 %
for the resonant tests and 0.75 14 % for the decay tests.
During the tests, the strains at the base of the specimens have not been measured.
However, these cm be easily caiculated using the values of the measured acceleration at
the top of the specimen. As mentioned earîier the decay tests are conducted by pulling the
specimen at its top point and measuring the free decay acceleration. Ignoring the
contribution of the higher modes is a reasonable approximation since the initial imposed
deflection shape is very close to the k t mode shape and consequently the expected
behavior is mostly according to the first mode. Assuming that the specimen is vibrating
with only its fundamental mode, the base moment M(t) can be evaluated by considenng
the moment of the inertia forces about the base, i.e.
where Y(t) is the measured tip acceleration of the specimen, m(x) is the m a s per unit
length, m, is the mass of the acc~ierumeter at level i, $(x) is the fhdarnentai mode shape
of cantilever beam normalized to be equal to unity at the top of the specimen, x, is the
distance between the base and the iLh acceleforneter and x is the vertical coordinate
measured from the base of the specirnen. Having evaluated the base moment M(t) using
Eq.5.5, the longitudinal saains ~ ( t ) at the base of the specimen are given by:
where R is the outer radius of the specimen, E is the &ai longitudllial modulus and 1 is
the moment of inertia of the section.
Figure 5.9 shows the variation of the damping ratios vernis the maximum
amplitude of the bending strain obtabed nom a decay test (for a specimen having a
diameter D = 2 in and length L = 1.45 m). Figure 5.9 indicates that the increase of the
damping ratio with the strain level is fairly srnall. The small increase in the damping ratio
can be related to an added aerodynamic darnping and not to permanent damage in the
composite. The later usually results in a significant and rapid increase in darnping.
The maximum O ff-axes longitudinal strain amplitude show in Fig.5.9 is 0.0009 1 .
This corresponds to strains equal to 0.000299 and 0.00061 in the fibers and the across
fibers directions, respectively. This level of strain is much lower than the maximum strain
level(0.002) at which the damping ratio is independent ofthe strain amplitude as reported
by Gibson (1976).
It should be mentioned that the maximum level of strain expected for FRP
chirnneys subjected to wind loads, varies between 0.0003-0.0005 (see chapter 4). These
values are Iess than the threshold value desmibed earlier by Gibson (1976). As such, the
values of damping obtained nom the experirnentai work conducted in this study can be
used in the design of FRP chùnneys if giass resorced vinyl ester angle ply laminates (0
= f i 5 O with the longitudinal axis) are used in the construction or the chirnneys. It is
obvious that the evaluated damping ratios are luniteci to a construction involving an
angle-ply 0 = S S O (measured with the longitudinal axis of the specimen). However, by
contacting many FRP manufacturers in Canada, it has been infonned that due to the ease
of Fabrication, this value of angle-ply is the most commody used in practice.
5.5 Correction for Aerodvnamic Damnine
If a structure vibrates in a Buid environment, the motion is retarded by the fluid
drag. Due to the interaction between the structure and the surroundhg Buid, some energy
transfers to the Buid through the work done by the drag forces. This source of energy
dissipation is known as the aerodynamic damping. The drag forces FD acting on structure
vibrating in still air is given as
where, CD is the drag coefficient, D is the diameter of the structure, p, is the air density
and y is velocity of the structure. For a continuous structure vibrating in a single mode,
the displacernent is w&en as Y(x,t) = y(t) +(x), where y(t) is the modal amplitude and
$(x) is the mode shape. The equivalent viscous damping factor for a single mode of
vibration in still air (mode shape is always positive dong the height such as the
iündamental mode of fiee standing structure) can be written as
where T is the penod of oscillation, m is the m a s per unit length and L is the length of
the structure. The drag coefficient is not constant as the stmcture vibrates in the Buid, it is
in fact a function of Reynolds number which in hmis is a fimction of the relative velocity
(Le. the structure velocity assuming that the air is still). The drag coefficient of a cùcular
cyhder in steady flow can be approximated as a function of Reynolds nimiber (Blevins,
1986) as
CD = b, + bJRe
w here
b, = 1.3 and 4 = 10 for the following range of Reynolds nurnber: 1 < Re c 1 04, and v is
the kinematic viscosity of the air.
The aerodynamic darnping associateci with the tested specimens has been
calculated using Eqs.S.8 to 5.10. These values have been subtracted fiom the measured
darnping values to obtain the tnie material damping and are plotted in Figs.5.6 and 5.7.
Figures 5.6 and 5.7 show that the aerodynamic damping did not change the general trend
of the results and in general can be neglected for both the first and second modes of
vibration. The maximum value of the aemdynarnic damping is only 2.7% of the total
measured darnping. It should be noted that no correction for aerodynamic damping are
needed for the values obtained nom the decay tests presented in Fig.5.8. This is due to the
fact that the ploned values are obtained by extending the ntting curve of the rneasured
data to intersect with the vertical axes (which basicaüy corresponds to zero amplitudes).
On the other hand, the damping ratios which are plotted versus the strain amplitudes in
Fig.5.9 need to be corrected for aerodynamic damping. Figure 5.9 shows the values of the
cdcuiated aerodynsunic damping ratio as well as those evaiuated by subtracting the
aerodynamic damping nom the measirrwi one. It can be easily concluded fiom the graph
that values of aerodynamic damping corresponding to the shains adopted in the tests are
negligi'ble.
5.6 Conclusions
Experimental testing has been conducted to evaluate the darnping values of FRP
laminates commonly used in the construction of FRP chimneys. Such laminates consist of
angle-ply (0 = f 5 5 O with the longitudinal axis of the specimens) glass reinforced vinyl
ester composite. Both resonant and logarithmic decrement tests have been conducted on a
number of cylindrical specirnens. The damping results h m the decay test exhibited
slightly higher darnping ratios. For the range of frequency tested the damping value has
shown slight increase with the increase of the frequency. For the range of the applied
snain , results indicate that the damping values are strain-independent. The added
damping fkom the surrounding air has b m i calculated and found to be negligible. The
average darnping values fiom al1 conducted tests are equal to 0.66 % for the resonant tests
and 0.75 % for the decay tests.
Fig.5.1 A photo showing various components of the shaker system.
Conditioned Signais
f
AT-MIO- lm- 10
Charge Signal Conditioning
Amplifier Shaker Table
# The Dampmg Ratio
aculations
* 2692-A-OS4
1 1 Pentiumpc 1
Accckromctcrs Output Sqpah
Fig.S.2 Schematic diagram of the Shake Table and the Data Acquisition System.
Fig.5.3 A photo showing the epoxy glue and steel plate used in mounting the specimen.
Fig.5.4 A photo of a typical specimen mounted to the slide table.
f (Hz) Fig.5.5 Typical experimental fiequency-response curve and the fitted response of single degree of freedom system.
Measured (mode 1 ) - 2 order fitting - t
<-d - L,
8 8 a Y Y
- 8 O O
8
a
Fig.5.6 The damping of the nrst mode versus the fkquency h m the resomnt test.
First and second mode Mode 1 a - 2 nd order
0 Mode2
L - 5 U t
Fig.5.7 The damping of both first and second mode versus the fkquency fiom the resonant test.
Fig.5.8 The damping ratio of the fïrst mode versus the hdamental hquency fiom the decay test.
Strain amplitude .1 o5 Fig.5.9 The damping ratio versus the maximum bending strain amplitude in the longitudinal direction for specimen (2 in diameter).
CaAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1 Introduction
This thesis includes an extensive investigation about the application of FRP
materials in the construction of industrial chunneys. An attempt to answer the following
questions has been provided in the thesis:
1) What type of FRP materials suit the chimneys application and what are the mechanical
and envuonmental properties of this materials?
2) What level of thermal stresses is expected during the operation of a FRP chimney?
3) How to assess the wind response of FRP stacks?
4) What is a typical value for damping ratio that c m be used in designing FRP chimneys?
The nrst three questions are addressed using an analyticai approach, while an
experimental study is conducted to a t l ~ ~ ~ e r the fourth question.
Conclusions that can be drawn nom the whole study are summarized in the
following sub-sections.
6.2 Suitable FRP Material For Chimnevs' Construction
Knowing that the serviceability conditions of industrial chunneys include hi&
thermal eff- an aggressive chernical environment and a loading haWig a cyclic nature,
the constituents of FRP should be carefidly chosen in order to provide a durable structure.
Following the discussion in Chapter 2, Wiyl ester polymer reinforced by E-glas fibers
are suitable to be used in the construction of industrial chimneys as long as the service
temperature of the chimney is less than the continuous service temperature of the vinyl
ester polymer. For the case of chimneys having hi& service temperature, epoxy polymea
reinforced by E-glas f ibm can be the alternative though a higher cost is expected.
6.3 Thermal Stresses Induced in II'RP Chimnevs
in this study, the formulation of a consistent laminated shell element has been
extended to include themal stress analysis. The thermal formulation has been checked by
modeling and analyzing a number of benchmark problems and comparing the results of
the analyses with those availabie in the titerature. An excellent agreement has been shown
in all the analyzed examples. The effect of various parameten which might influence the
thermal stresses induced in angle-ply laminated mer reinforced plastic chimneys have
been studied using the developed model. Results of the pararneûic study indicate that the
thickness, the diameter, and the height of the chimney as well as the nurnber of laminae
bave no signincant effect on the induced thmal stresses. Analyses indicate that the
thermal stresses mainly depend on the through thickness temperature distribution (relative
to the curing temperature), the angle of orientation of the nbers, the coefficient of thermal
expansion and the modulus of elasticity dong the fibers direction. The last two
parameters depend mainly on the fiber contait in the mat*. The thermal stress analysis
of typical FRP chimneys shows high stress concentration near the boundaries with in-
plane across fiber stresses usually exceedmg the ultimate strength of the matrix. As such,
cracks are expected to occur in FRP chimneys as a result of a through thickness
temperature variation. Xowever, it is beiieved that these cracks can be controlled if the
interlaminar shear stresses are less than the ultimate interlaminar shear strength divided
by an appropriate factor of safety. The andysis then pmceeds by wuming a negligible
value for the modulus of elasticity in the direction perpmdicular to the fiben to simulate
a cracked chimney. Results of this last set of analysis indicate that for typical FRP
chimney, the along fibers stresses as well as the shear stresses of cracked chimneys are
within acceptable values. Finally, charts predicting the dong fibers thermal stresses
induced in typicd cracked FFtP chimneys as a fhction of the through thickness
temperature distribution are presented. These stress values can be considered when the
design of a FRP chimney is attempted.
6.4 Effect of Wind Loads on FRP Chimnevs
The response of FRP chimneys to wind loads depends on the wind characteristics,
the laminate properties and the geometry of the chimney. From the paramenic study
conducted to assess the effect of various pisrazeters on the wind responses of FRP
chimneys, one can conclude the foiiowing:
The fibers orientation defines most of the lammate properties such as stiffiiess and
strength. To achieve a considefable improvement in the longitudinal stifniess of the
chimney and consequently reduce the wind response, fibers have to be onented by an
angle 0 S 5 " (O is measured with a horizontal direction).
The across-wind load response of FRP chimneys is vey sensitive to the combined
effect of the composite mass density and the damping ratio. Since FRP are very light
materials and do not have a weil dehed damping ratio, a consmative approach must
be used in estimahg the across-wind response of such chimneys.
Tapering ratio is very efficient way of reducing the vortex shedding.
The CICIND code for steel chimneys (1988), when applied to FRP chimneys leads to
overly conservative results in some cases and slightly unconsetvative in other cases.
When vortex shedding is considad, the design of FRP chimneys is show to be
governed by the fatigue strength for the range of aspect ratio and height considered in
this shidy.
The optimum aspect ratio (height to diameter ratio) which produces minimum
thickness of FRP chimneys subjected to both wind and thermal loads varies between
15 and 20.
6.5 Ex~erimeutai Evaluation of D a r n ~ i n ~ Ratio of Vinvl Ester Glass Reinforced
Com~osite
Dynamic testing has been performed to evaluate the damping ratio of E-
glassNinyl ester fiber reinforceci plastic materiai. Both the resonant and the logarithmic
decrement techniques are used in this study. Based on the d t s of the damping tests, the
following conclusions cm be drawn:
The damping ratios obtained f hn the decay tests are shown to be slightiy higher than
those obtained fkom the resonant tests,
For the range of fkquencies applied in the tests, the decay tests show damping values
which are more f?equency-dependent compared to those obtained from the resonant
tests. However, the variation of the damping ratio with the fixquency is usually small.
For the range of strains applied in the tests (maximum expected strains in reai
chimneys are within this range), the damping ratios are show to be strain-
independent.
The average damping value obtained fkom the whole experimental study are equal to
0.66% and 0.75% for the resonant and the decay tests, respectively.
6.5 Recommendations For Further Research
As mentioned previously in the thesis, this investigation represents the fint
extensive study conducted on FRP chimneys. Future research is needed, as extension to
this study, to obtain a full understanding about the behavior of FRP chimneys. The
following points are suggested as a fùture direction for research to be conducted on FRP
chimneys.
1) The uneven distniution of wind loads around the top part of cylindrical chimneys
might lead to ovalling of the chimneys in these Locations. This phenomenon, which
was s h o w to happen for steel chimneys, was not considered in this study. An
investigation for such effect is needed.
2) The fatigue strength for E-giassNinyl esta angle-ply composite which was shown in
this study to be corivenient for chimneys applications, is not well defined in the
fiterature speciaily for variable angles of orientation of the fibers. As such,
expenmental testing for evaluating the fatigue strength of E-glassNiny1 ester
composite is highly recommended.
3) The pararnetric studies conducted in this thesis to wess the behavior of FRP
chimneys under thermal and wind loads assume constant thickness through the height
of the chimney. Practical design of FRP chimneys includes often variation of the
thickness through the height of the chimney. As such, it is recommended to
investigate the effect of varying the thickness of the chimneys on the induced thermal
stresses and also on the wind responses.
4) The local buckling of thin shells is very much important when assessing the stability
of such type of structures. FRP chimneys are very susceptible to local buckling
specially due to the highly localized thermal stresses at the base of the shell.
Therefore, buckliag of FRP chimney has to be investigated.
APPENDIX A (Davenport, 1993)
Mean drag force
F(Y) = (q,D,HC,) +,'(Y) +,(Y)
where
- L is the height of the chimney.
- CD is the drag coefficient.
- DL is the diameter at the top of the chimney.
- UL is the mean wind speed at the top of the structure.
- q, is the reference velocity pressure at the top q, = I / PU ,' , p is the air density
1,
- ( , (y) is function defines the wïnd speed pmfùe ( U(y) = (, (y).U, ), 4, (y) = (t) and
1, is intensity of the turbulence at the top of the chimney.
- #, (y) is function d e W the variation of the diameter of the chimney dong the height
( WY) = O,(Y)-D, ).
The mean drag remonse
The rms of backeroand remonse
where Lu is the scale of turbulence, Lu=30-60m.
The expression between parenthesis in Eq.3 is a reduction factor to accommodate the
correlation of the forces with the height of the structure.
The rms of resonant remonse
The mean square resonant response of the j' mode is;
where 4 is the naturai frequency of the jm mode,+, (y) is the variation of the mass dong
the height, 5, and 5, are the structural and the aerodynamic damping and p(y) is the
mode shape.
- Along-wind generaiized force spectnim is;
where C is the decay constant =6-10
- Along-wind aemdynamic damping
where rn, is the mass at the top of the chimney.
Vortex shedding
The generalized force spectrum of vortex shedding is;
fiSGf, (fi ) =
where CL is the mis of the left coefficient. h is a coefficient defines the correlation of
the wake forces at fiequencies near F, and approximately is equal 1 as suggested by
Vickery (1997). f ' = FD, 1 U, is the reduced frequency. The mis of the lift coefficient
is believed to be strongly dependent on the scde and intensity of turbulence, based on
full-scale measurernents Vic kery (1 983). The suggested value for m i s Ii R
where i' = 1 @/L) and L =100(y/10)'" the scale of turbulence. There is a reduction to
the ms Ieît coefficient with the aspect ratio and to accommodate the rapid decrease of
the left coefficient nea. the tip of the chimney. Strouhal number S, is surface roughness.
Reynolds number, turbulent and aspect ratio dependent. The suggested value for
S trouhal number S, is
S(1)=0.14 + 0.05 h(h/4) for 4< h > 25 (A- 10)
and constant above A=25, where h is the aspect ratio (Lm).
In the across-wind vibration at a fkquncy near the vortex shedding fkquency, the
aemdynamic damping is expresseci by;
where K ( u ' ~ ) is the aerodynamic damping coefficient. With the associated uncertainty
of the aerodynamic coefficient and with the dramatic change nom positive to negative
in the vicinity of the aitical wind speed, it was suggested by Vickery that the maximum
negative aerodynamic is
D' and rn' are the average diarneter
1 (A. 12)
and average m a s over the upper third of the
chimney. It should be noted that the non-linear ternis were neglected from the general
expression of the aerodynamic damping given by Vickery. This assumption is valid if the
vibrations have relatively small amplitudes.
Set a laminate configuration
Obtain the lamina properties E,, E, G,,, v , , h and 8 Determine lamina reduced stifhess QG h m Eq.4.2
Calculate the lamina transformed reduced stiffhess from Eq.4.7 I
r Calculate the extensional, couplhg and bending stifkess matrices (A, B, D) for the larninate from Eq.4.15
Calculate the equivalent elastic properties of the larninate trom the inverse of the matrices A, D kom Eq.4.23,4.24 - - --
Calculate the dynamic properties of the chimney, naturai fkequencies and the mode shapes by usmg the equivalent bending rnodulus E,
Calculate the maximum wind response fiom the three cases of toading For each section dong the height
I Calculate the maximum strains for each tamina h m Eq.4.37 in x-y axes
Transforrn the maximum strains to 1-2 axes fiom Eq.4.3 8
1 Calcdate the maximum stresses in 1-2 in each Iamina fiom Eq.4.39 1
r
Apply the failure criteria for each lamina fkom Eq.4.40 I
l Check the fatigue stresses EqA-42 1 1
Compare the deflection with the maximum pamisïble deflection
Ftow chart descri-bes the design sequence of FRP chimney.
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Related codes
Amencan Concrete Institute: AC1 1 307 (1 995)
Australia Standard AS1 1702 SAA Loading Code, Part 2: Wind Loads
ASME RTP- 1 b ( 1 997)
BS 5480 (1991): Specification For GRP Pipes, Joints And Finings For Use For Water Supply and Sewerage, BSI. Milton Keynes.