flexural response of polymer concrete filled steel beams-int jo of

Construction and Building Materials 18(2004) 367–376

0950-0618/04/$ - see front matter� 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.conbuildmat.2004.03.009

Flexural response of polymer concrete filled steel beams

Walter O. Oyawa *, Kunitomo Sugiura , Eiichi Watanabea, b b

Department of Civil Engineering, JKUAT, P.O. Box 62000-00200, Nairobi, Kenyaa

Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, 606-8501, Japanb

Received 18 February 2003; received in revised form 11 March 2004; accepted 11 March 2004

Abstract

In view of the mounting cost of rehabilitating deteriorating infrastructure, further compounded by intensified environmentalconcerns, it is now obvious that the evolvement and application of advanced composite structural materials to complementconventional construction materials is a necessity for sustainable construction. This study seeks alternative fill materials(polymer-based) to the much-limited cement concrete used in concrete-filled steel tubular structures. Polymers have been successfully usedin other industries and are known to be much lighter, possess high tensile strength, durable and resistant to aggressive environments.Findings of this study relating to elasto-plastic characteristics of polymer concrete filled steel composite beams subjected touniform bending highlight the enormous increase in stiffness, strength and ductility of the composite beams, over the empty steeltube. Moreover, polymer based materials were noted to present a wide array of properties that could be tailored to meet specificdesign requirements, e.g. ductility based design or strength based design.� 2004 Elsevier Ltd. All rights reserved.

Keywords: Composite beams; Polymer concrete; Flexural strength

1. Introduction

Contemporary structural engineering practice has, fora long time employed traditional materials steel andreinforced concrete as the key construction materials,despite their structural limitations or even their inade-quacy in assuaging rising environmental concerns inrecent times. Concern and worries abound over theenormous cost of rehabilitating dilapidated or old rein-forced concrete structures; some countries like the USAand Japan are already spending colossal amounts ofmoney in the rehabilitation or replacement of old rein-forced concrete structures. It is no wonder that in thisnew century, sustainable construction is becoming anoverriding consideration, where advanced compositeformulations and systems of re-defined performance arebeing vigorously soughtw3x. Indeed the constructionindustry is already in a new era where not only there isinterest in the expansion of mankind’s frontiers enablingnew technologies to be developed, but also the need fora harmonious co-existence with the eco-sphere by min-

*Corresponding author. Tel.:q81-757535079; fax: q81-757535130.

E-mail address: [email protected](W.O. Oyawa).

imizing damage to the natural environment and optimiz-ing material technology and infrastructure to create ahealthy life in harmony with nature. In particular, thecement industry has taken the lead in developing ‘eco-cement’, a product that helps to clean the environmentby utilizing municipal solid wastes in its manufactureand is even said to have the potential of absorbingCO from the environment as it hydratesw2x. The2

concept of eco-materials(ecologically-benign materials)has been introduced to encourage the development ofmaterials that are not only harmless to the globalenvironment but also exert minimal burden on the planetduring their production, by making efficient use of rawmaterials and being highly recyclable.In addition to seeking strong andyor ductile materials

for seismic resistancew8,19,22x, this study was motivat-ed by the cutting edge concept of durable and eco-friendly materials for sustainable development, and wasdirected towards evaluating the suitability of polymerbased materials such as polymer concrete, for use as fillmaterials in filled steel composite members. Polymersor polymer based materials have been successfully usedin other industries and are attracting increased attentionin the construction industry due to the complementary

368 W.O. Oyawa et al. / Construction and Building Materials 18 (2004) 367–376

Fig. 1. Specimen, with fixing end-plates.

Table 1Beam specimen details(nominal)

Specimen Fill Lb D t L yDb Dy2tlabel material (mm) (mm) (mm)

SyE1A-30B Epoxy concrete-HS 288 96 1.6 3 30SyE1A-30B Epoxy concrete-LS 288 96 1.6 3 30SyCN-30B Normal concrete 288 96 1.6 3 30S-30B – 288 96 1.6 3 30SyE1A-50B Epoxy concrete-HS 300 100 1.0 3 50SyE1A-50B Epoxy concrete-LS 300 100 1.0 3 50SyCN-50B Normal concrete 300 100 1.0 3 50S-50B – 300 100 1.0 3 50

Nomenclature: Specimen identification, e.g. SyE1A-50B implies composite beam specimen of steel(S) filled with epoxy polymer concrete ofhigh stiffness, ofDy2t ratio equal to 50 and tested in bending(B); Abbreviations: HS-High stiffness; LS-Low stiffness.

properties to concrete that they posses viz higher tensilecapacity and ductility, lower weight, high damping orresilience and resistance to physical and chemical attackthat ensures their longevity or durabilityw4,7,12x. Theywere first introduced to hydraulic-cement system in 1923because of an increased need at that time for durableconstruction materialsw20x. Although the cost of poly-mers may be comparatively high at present, a situationattributed to their use in other highly lucrative industriessuch as the defence and aeronautical industries, it isenvisaged that continued research directed towards seek-ing optimal conditions and cheap derivatives, e.g.municipal wastesw16,17,21x for use specifically in theconstruction industry will eventually lead to satisfactorycost reduction. Moreover, the trend towards the evalua-tion of full life-cycle cost of structuresw5x, to includesuch parameters as maintenance, repair, demolition andenvironmental degradation, rewardingly place the dura-bility of polymer based materials at the forefront of costanalysis.Previous tests have already been conducted concen-

trating on the behavior of different types of filled steelcomposite stub columns subjected to compressive loadand also composite beams filled with fiber latex cementmortar and pure epoxiesw13–15x. Results obtainedindicate the great potential of fiber latex-cement mortarand epoxies as alternative fill materials to cement

concrete or which could be combined with cementconcrete to form advanced composites for enhancedstrength, ductility and durability. This present work is asequel to the above mentioned study, and focuses on theflexural behavior, namely moment–curvature relationsas well as cross-sectional strain and stress distributions,of different types of filled steel composite beams.

2. Experimentation

2.1. Outline of experimental program

Circular filled steel composite beams filled withvarious types of fill materials were gradually subjectedto two-point bending load until limiting load or defor-mation was attained, while recording load, strain anddisplacement measurements for curvature determination,at suitable increments. The variable parameters were theouter radius to thickness ratio of the steel tube expressedas Dy2t, where ‘D’ is the outer diameter of the steeltube and ‘t’ is the thickness, and there were threedifferent types of fill materials. The ratio of effectivelength to diameter of steel tube(that is theL yD ratio)b

was maintained constant at 3. The three fill materialsinvestigated were epoxy polymer concrete of high stiff-ness(E1A), epoxy polymer concrete of low stiffness(E2A) and normal concrete(CN). The epoxy concreteswere special products from a manufacturer. In addition,empty circular steel beams were also tested.Fig. 1 shows a typical specimen, while a summary of

the testing program and details is presented in Table 1.To facilitate identification, the test specimens for bend-ing test were designated according to material type andthe value of radius to thickness ratio of the steel tubeas is illustrated in the nomenclature below Table 1.Preparation of each of the filled steel composite speci-mens involved mixing of the constituents of the relevantfill material, followed by filling the steel tube with themixture. The specimens were then left to cure up to therequired day of testing. Specimens were tested afterapproximately 1 month(epoxies are rapid curing andnormally gain 90% of their full strength within 7 days).

369W.O. Oyawa et al. / Construction and Building Materials 18 (2004) 367–376

Table 2Properties of the fill materials

Fill material Fill Unit Young’s Poisson’s Ultimate Strain at Bulkdescription material weight modulus ratio strength ultimate modulus

designation (Kgym )3 (KNymm )2 (Nymm )2 strength(%) (KNymm )2

Epoxy concrete-HS E1A 2054 12.9 0.316 52.0 0.7208 11.7Epoxy concrete-LS E2A 2114 3.0 0.480 19.0 4.845 25.0Normal concrete CN 2326 29.6 0.171 26.0 0.4035 15.0

Abbreviations: HS-High stiffness; LS-Low stiffness.

Table 3Properties of steel

Thickness Young’s Poisson’s Yield Yield Ultimate Elongation Bulk(mm) modulus ratio stress strain strength at break modulus

(KNymm )2 (Nymm )2 (%) (Nymm )2 (%) (KNymm )2

1.6 216 0.347 225 0.1042 325 46.9 2351.0 211 0.337 230 0.1092 340 42.8 216

2.2. Material properties

Fundamental properties of the fill materials used inthis study were determined from compressive testsconducted on 100 mm diameter by 200-mm lengthcylindrical specimens. During the tests, compressiveaxial load provided by a 1000 kN capacity UniversalTesting Machine, was applied gradually on the topsurface of each specimen, which had been suitablycapped into a near flat surface by means of fitting steelplates. Data monitored, included longitudinal and hori-zontal strains through appropriate strain gages for eachmaterial, pasted around the middle circumference ofeach specimen, axial shortening as measured by fourlinear variable displacement transducers(LVDTs)between the loading heads and fixed equidistant aroundthe specimen, and the applied load as monitored fromthe load meter. The data were monitored by a computervia a connection to a data logger. Accordingly, ultimatestrength was obtained as the ultimate load per cross-sectional area, Young’s modulus(E) as the initialtangent gradient of the load–axial strain curve, andPoisson’s ratio(v) as the ratio of the lateral strain tothe longitudinal strain. Bulk modulus(K), regarded asa measure of incompressibility of the fill material, hasalso been determined from the expressionKsEy3(1y2v). Table 2 gives the properties and characteristics ofthe fill materials.As for the enclosing steel shell, SS400 grade steel

was used. Material properties for the two differentthickness sizes of steel used were determined fromtensile tests on strips cut from steel sheets used to formthe tubes. Test strips with a test region of approximately15 mm width and 75 mm height and grip length of 25mm width and 70 mm height at both ends, were eachtested by clamping between the heads of the UniversalTesting Machine and applying constant load rate while

monitoring the axial and lateral strains as well as theapplied load through a data logger connected to acomputer. Results obtained are shown in Table 3.

2.3. Test set-up and loading

Bending tests were carried out on six filled steelcomposite beams and two empty steel beams. The beamtests were in two series formed from tubular steel pipesof radiusythickness ratio,Dy2ts30 and 50, and foreach of the series several fill materials were involved.A specimen for test was first pasted with seven equallyspaced strain gages circumferentially on one side at themid-span. The circular specimen having rectangularrigid end plates was then firmly bolted to rigid rectan-gular steel attachments at either end. The whole masswas in turn rested on simple supports fixed to a firmrigid beam base as shown in Fig. 2. The setup wasrested and aligned on the bottom platen of 1000 kNcapacity Universal Testing Machine. Two linear variabledisplacement transducers(LVDTs) with magnetic baseswere fixed, one at the top and one at the bottom of thebeam in such a way as to measure the relative horizontalmovement between two known points of gage lengthsL , in order to determine the average curvature. Theb

vertical distance between the LVDTs(S) was recordedfor every test.Load application on the specimen was a two-point

load meant to induce a state of pure bending in the testregion, and supplied by the Universal Testing Machinethrough a rigid loading beam as shown in Fig. 2. Theloading beam and its attachments had to be securelyclamped to prevent possible disastrous consequences.Commencement of the loading process was by slowapplication so as to avoid abrupt jolting loads. Loadingthen proceeded gradually and at suitable constant incre-ment, data namely the applied load, displacements of


Fig. 2. Test set-up before loading.

Fig. 3. Schematic representation of structural and loading conditions.

Fig. 4. Normalized moment–curvature relationships.(a) Dy2ts30; (b) Dy2ts50.

the LVDT heads and strains, as monitored by a computervia a data logger were recorded. The constant incremen-tal load rate was followed until the anticipated yieldpoint of steel, following which the measurement timeinterval was reduced. Loading was continued beyondthe peak load up to a stage where it was judged that nofurther useful information could be obtained from the

test results. Failure load was taken as the peak load afterthe specimen shed off any additional load increment.

3. Results and discussions

3.1. Moment–curvature relationships

The moment–curvature relationship of a short beamor column is of prime importance in the analysis of anylong beam-column, providing required parameters suchas the stiffness of the beam-column. For the case ofcomposite beams, other uncertain phenomena such assectional interaction, interface slip and cracking of thefill material come into play, and may manifest in themoment–curvature response. The obtained normalizedmoment–curvature relationships(from idealized repre-sentation in Fig. 3) are presented in Fig. 4, the summaryof which is given in Table 4. The moment(M) for anyapplied load(P) can be obtained from the expression;

MsPL y2 (1)a


Table 4Summary of bending test results

Specimen Elastic Hardening M yMult y f yfult y Hoopyaxial strain ratio on beam surfacelabel stiffness stiffness

Top of the beam Bottom of the beamke kp

ye yp ye yp

S-30B 0.645 0.0228 1.57 14.0 0.335 0.563 0.389 0.828SyE1A-30B 1.207 0.0308 3.26 25.7 0.349 0.709 0.387 0.202SyE2A-30B 1.00 0.0334 2.51 26.2 0.378 0.679 1.319 0.563SyCN-30B 1.65 0.0282 2.91 23.5 0.348 0.789 0.098 0.071

S-50B 0.807 early buckle 1.43 5.88 0.345 0.690 0.342 0.638SyE1A-50B 1.57 0.0500 3.40 17.0 0.346 0.730 0.365 0.0402SyE2A-50B 0.966 0.0464 2.69 23.9 0.468 0.753 0.458 0.482SyCN-50B 2.04 0.0394 3.17 19.7 0.390 0.853 0.130 0.020

Note: k andk are as defined in the side Fig., whiley andy represent the elastic and plastic values of the hoopyaxial strain ratio, respectively.e p e p

and curvature(f), rotation per unit length, is derivedfrom the expression:

Øfs(yU qU )y(S L ) (2)top bottom b

whereL is the distance from the beam support to thea

point of load application on the beam assuming sym-metry of loading,U and U are displacementstop bottom

measured by the top and bottom linear variable displace-ment transducers, respectively,L is test section length,b

while S is the vertical distance between the two LVDTs.Schematic representation of the structural and loading

conditions as drawn in Fig. 3 implies that the test sectionshould be subjected to a state of pure bending. Accord-ingly, the assumptions and theories of pure bending maybe expected to apply to the elastic structural behaviorof the beam specimens, e.g. plane sections before bend-ing should remain plane even after bending.The yield moment(M ) and yield curvature(f ) cany y

be determined from the expressions below.

s Isy sM s (3)y ye

ssyf s (4)y E ys e

where,s : yield strength of steel;I : moment of inertiasy s

of the empty steel tube;y : distance from the elastice

neutral axis of the circular cross-section of empty steeltube to the extreme point;E : modulus of elasticity ofs

steelSeveral distinct features may be observed from the

results presented in the figures. First and foremost, thesuperior strength and ductility of composite beams vis-a-vis the empty steel tube is evident. This clearly depicts`the beneficial interaction between the steel tube and thefill material. The confined fill material considerablydelays local buckling of the steel tube on the compres-

sion side, only permitting minor outward local defor-mations in the post-yield response, thereby inducing theextensive exploitation of the bottom tensile yieldstrength of the steel tube. In other words, although thesecomposite specimens were observed to have undergoneconsiderable plastic deformations in bending, they con-tinued to resist load because local buckling in the steeltube was strictly limited by the presence of the fillmaterial, consequently resulting in increased strengthand ductility. Increase in strength and ductility due tothe presence of fill material has been recorded forconcrete-filled steel beams by other researchers. Partic-ularly, it was recognized that the restriction of longitu-dinal movement of the fill material by providing endplates or intermediate diaphragms significantly affectsductility w11x. The general shape of the composite beamcurves depict an initial elastic linear portion, followedby a bend as the steel yields and transfers some of itsload to the fill material in the compression zone. Whenthis transfer stabilizes, the hardening gradient takes anear linear gradient again as the confined fill materialin the compression zone takes up most of the load,while the stretched steel in the tension zone resists mostof the tensile load.The highest overall performance in terms of stiffness,

strength and ductility is that shown by epoxy concretefilled beam(SyE1A), illustrating the great potential ofpolymer concrete as an alternative or supplementarymaterial to ordinary cement concrete. The performanceof SyE1A is even better than that of composite beamof pure epoxy SyE1 observed in previous workw14x,and it has the added advantage in that epoxy concreteit is comparatively cheaper than pure epoxy formulationdue to reduced resin content. A similar observation ismade in the case of SyE2A and its corresponding epoxyfilled steel beam SyE2 w14x where epoxy concrete-filledbeam (SyE2A) has higher strength and ductility thanepoxy-filled (SyE2). However, the polymer concretesare much heavier than the pure polymers, having weights


that are close to that of ordinary cement concrete.Accordingly, in constructions where low weight of thefill material is desirable such as the construction ofcomposite railway beamsw6x or retrofitting of hollowsteel structures, pure polymers are preferable over poly-mer concrete. However, where weight is of less concern,then polymer concretes are definitely preferable overpure polymers due to their cheaper cost. It is evidentthat depending on the needs of construction, polymersor polymer composites may be suitably adjusted to meetthe specific requirements, highlighting the versatility ofpolymers and polymer based materials. Previous studieson epoxy filled steel stub columnsw13,15x gave inter-esting results in that a particular type of epoxy andepoxy concrete produced composite columns thatshowed considerable increase in ductility but only nom-inal increase in strength. This is very desirable in thecurrent seismic design methods, because foundationstructures of lesser size and cheaper cost can be usedw9,10x. The advantage is most magnified in the retrofit-ting of structures where modifications in foundationsare most unwelcome from economic point of view. Inother words, the ductility of bridge piers needs to beincreased without increasing their yield strength for thesake of economic designw10x.Elsewhere in the world, many design codes now

recommend two levels of design seismic force in thatstructures should be able to resist moderate earthquakeswithout structural damage, and be able to resist severeearthquakes without collapse but perhaps with somestructural and non-structural damage. To satisfy theseperformance criteria, all structures should be designedto have adequate strength and stiffness to meet theserviceability limit states when responding to moderateearthquakes, and to have adequate strength, stiffness andductility to satisfy the ultimate limit states whenresponding to severe earthquakes. Under severe seismicattack, the emphasis is on high ductility structures,designed employing equal energy(constancy) assump-tion. Polymer-based materials are best suited to take onthis challenge, even when used as a replacement forcement concrete in ordinary reinforced concrete works.Studies by Abdel-Fattah et al.w1x on the flexuralbehavior of polymer concrete also concluded that poly-mer concrete beams are very ductile.Table 4 provides a quantified summary of the flexural

response of the tested beams, with the unique valuesshown in bold numbers. The table confirms the obser-vations noted in Fig. 4 such as the higher elastic stiffnessof SyCN specimen, while the epoxy specimens SyE1Aand SyE2A give higher hardening stiffness and ductility.Table 4 further shows a dramatic reduction in hoopyaxial strain ratio of concrete-filled steel beams(SyCN)in the bottom tensile zone. This is thought to be due tothe low tensile strength of the stiff concrete, thusinitiating early cracking with consequent haphazard

expansion of the concrete and redistribution of stresspossibly leading to biaxial tension in the bottom tensilezone of the steel tube. The effect of low tensile strengthof concrete is vividly demonstrated, as it results in non-uniform interaction with the steel tube. It is also notedthat the composite effect of filled beams is most realizedfor the thinner steel tube ofDy2ts50, where both theelastic and hardening stiffness are higher than that forDy2ts30. Steel tube ofDy2ts50 being the thinnersteel tube is more susceptible to rapid buckling in theabsence of fill material, hence the delay of local bucklingby the fill material is more effective.

3.2. Buckling deformations

Fig. 9 displays the buckling and plastic bendingdeformations of some of the tested specimens. Localbuckling on the compression side is clearly visible inthe case of empty steel beam(S-50), where the bucklingoccurs in the form of ripples at the ends. However, forthe composite beams, permanent bent or curved shapeof the whole specimen results illustrating the moderatingeffect of fill material as it interacts with the steel tube.This interaction between the fill material and the enclos-ing steel tube limits buckling deformations in the steeltube, and in addition prevents ovalization of the tube asload is applied on the top. In general, two modes ofdeformation are known to manifest themselves in thebuckling of empty uniform cylindrical shells acted uponby moments at their extreme ends. The first is theBrazier effect, which involves increasing ovalization ofthe cylindrical cross-section with increasing moment,with the result that the moment–curvature relationshipis non-linear; and the moment eventually reaches amaximum or limit-point value. The second type ofdeformation is termed the bifurcation buckling wherebyaxial waves form along the length of the cylinder, havingmaximum amplitude at the extreme compression side ofthe shell and gradually around the circumferencew18x.In a real situation, it must be expected that both theseeffects will be present simultaneously with one or theother dominating, depending on the proportions of thetube and the distribution of initial imperfections.

3.3. Strain distributions over the cross-section

Figs. 5–8 give the normalized axial(´ ) and hoopsa

strain (´ ) distributions over the beam cross-section,sh

normalized by the steel yield stress(´ ), where com-sy

pressive strain is taken as positive. A first look of thegraphs promptly shows the non-linearity of the straindistribution, even for the empty steel tube. This high-lights the unique behavior of thin-walled circular steelmembers, inconsistent with the fundamental assumptionin the theory of pure bending, i.e. plane sections shouldremain plane before and after bending. It is further


Fig. 5. Variation of sectional strains as monitored on the surface(S-50B). (a) Axial strains;(b) hoop strains.

Fig. 6. Variation of sectional strains as monitored on the surface SyE1A-50B). (a) Axial strains;(b) hoop strains.

observed that the plastic hoop strains are quite high, insome instances almost equaling the axial strains. For thecase of the empty steel tube, these observations areprobably due to bifurcation andyor ovalization of thesteel tube as discussed in the previous section, causingcross-sectional instability and complex distribution ofstrains or stresses.A noteworthy difference in behavior of the different

types of filled steel specimens is the degree of upwardmovement of the neutral axis as loading progresses. Itis observed that upward movement of the neutral axisis more pronounced for the cases of stiff epoxy concrete(SyE1A) and normal concrete(SyCN) filled steel spec-imens than for SyE2A. The explanation of this occur-rence lies in the lower tensile strength or brittleness ofconcrete. However, the flexible epoxy concrete type hashigher tensile and adhesive strengths, and is thus able

to interact effectively with the steel tube both in thecompressive and tensile zones. This is a factor ofenormous value if one considers that the design ofreinforced concrete structures completely neglects thetensile zone of concrete due to excessive cracking.Worse still, it is the tensile cracks in concrete that allowfor the ingress of deleterious substances or chemicalsthat severely compromise the durability of concretestructures.Generally, the level of confinement for the fill material

in beam bending as indicated by the hoop strain distri-bution is less than that in stub column under compres-sion w13,15x because of the existence of bothcompressive and tensile zones in the case of bending.The hoop strain distribution also depicts similarity inthe behavior of stiff epoxy concrete(SyE1A) andnormal concrete(SyCN) filled steel beams, with low


Fig. 7. Variation of sectional strains as monitored on the surface(SyE2A-50B). (a) Axial strains;(b) hoop strains.

Fig. 8. Variation of sectional strains as monitored on the surface(SyCN-50B). (a) Axial strains;(b) hoop strains.

hoop strains in the tensile zone. However, for epoxyconcrete (SyE2A) filled steel beams, approximatelyequally balanced high axial and hoop strain distributionis detected. Epoxy E2 is an interesting material, owingto its very high bulk modulus and Poisson’s ratio, inthat it seems to behave somewhere in-between liquidsand solids depending on the extent to which it isstressed. Thus, under initial loading, epoxy E2 exertsnear equal pressure on the steel tube in all directionsjust like a liquid, resulting in high level of confinementof E2. This behavior was identified during compressivetests on filled steel stub columnsw13x.

4. Conclusions

In close conformity with results from previous com-pressive tests on stub columns, bending tests havefurther reaffirmed the immense potential of the moredurable polymer-based fill materials as complementaryfill materials to cement concrete for enhanced stiffness,strength and ductility. It is presented that:

a Epoxy polymer concretes produce composite steelbeams of much increased strength andyor ductility.

b Epoxy polymer concretes have an extensive inter-action with the steel component in both tension and


Fig. 9. Buckling and plastic bending deformations of some of the beam specimens(Dy2ts50).

compression, even in the inelastic range as is indi-cated by the lesser upward translation of the section-al neutral-axis, attributable to their high tensileyadhesive strength.

c Epoxy polymer concretes, due to their varied mate-rial properties, produce composite beams of diversecharacteristics hence presenting the constructionindustry with a broadened horizon of application.For example epoxy concrete E1A would supplementordinary concrete for high strength composite struc-tures, while epoxy concrete E2A would complementordinary concrete for structures whose design isductility-based.

Future work should seek to provide means of reducingthe high cost of polymers, through inclusion of munici-pal wastes in eco-friendly polymer blends. In addition,appropriate life-cycle costing techniques ought to bedeveloped to take advantage of the range of propertiesoffered by polymers, especially with regard to durabilityand resistance against aggressive environments.

Acknowledgments

This research was initiated through the financialsupport of the Ministry of Education, Science, Sportsand Culture, Japan. The work is continuing in earnestthrough the assistance of Japan Society for the Promo-tion of Science(JSPS), to whom the authors are mostgrateful.

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