540 Computer Methods in Composite Materials · PDF file · 2014-05-14concrete-composite specimen Figure 5: Shear-stress distribution In the case of non-linear behavior of a beam in

Composite for building and bridge construction -

Modeling of mechanical behavior of structural

element using mixed steel composite reinforced

concrete or mixed composite prestressed concrete

P. Hamelin

Laboratoire Mecanique Materiaux - IUTA Genie Civil -

Universite Claude Bernard, LyonI-43 Boulevard du 11

Novembre 1918, 69622 Villeurbanne Cedex, France

E-mail: hamelin@iutal2m. univ-lyonl.fr

Abstract

After an examination of the different applications cases of composite materials incivil engineering, we consider the different design methods of reinforced-compositeconcrete and prestressed-composite concrete beams: specific finite elements or non-linear analytical methods.We particularly examine the main problems which concern modeling of interfacebetween concrete and composite sheet. We show that the perfect evaluation of non-linear behavior law of each component (concrete, steel rebars, interface) is veryimportant for a good prediction of beam deflection.Comparison between finite element method and usual design method defined by ACIor CEB code are satisfying. It is obvious that for basic cases, the non-linear methodis enough precise. Numerical method and mixed finite element are particularlyinteresting for modeling specific structures as plate or shell.

Introduction

The composite materials associating fibers of different nature (glass, carbon,aramid, polyester, polyethylene...) with organic matrix (epoxy, polyester,polyurethane...) or with mineral matrix (portland cement, magnesian

Transactions on Engineering Sciences vol 21, © 1998 WIT Press, www.witpress.com, ISSN 1743-3533

540 Computer Methods in Composite Materials

cement...) are certainly the XXIst century construction materials insofar astheir specific properties (ratio between mechanical characteristics anddensity or natural weight), insofar as their moulding arid forming capacities,insofar as their combined properties (multi-properties: mechanical - thermal- acoustic - corrosion...) allow to conceive and make more efficient and moredurable structures than the ones with traditional materials (steel, concrete,reinforced concrete, wood...).The main families of composites and their applications in the field of civilapplications fall into the three following categories: soft composites andtensile architecture and composites tendons for industrial applications assuspension bridge (table 1), stiff composites and high performance structures(table 2), fibers-cement composites for the construction industry.

Soft composites with polymer matrix

Thermoplastics matrix J + Polymer fibers

Geotextiles Geomembranes Soft membranes Cables

Tensilearchitecture

Soft Interface betweenreinforcementsj grounds and structures

Tensile membranes) f Enlarged Ijwind braceused in roofing J structures][ wire

Table 1: "Soft" composites

Independently of the usual characterization problems taking into account theanisotropic and orthotropic characteristics of these materials, their materialnon-linearity under uni-axial and multi-axial solicitation, their thermo-rheological behavior and more particularly their creeping and relaxationfunctions are very important to design these structures. In particular, withrespect to the failure initiation mechanisms in the vicinity of geometricalsingularities and edge effects.


Computer Methods in Composite Materials 541

One can find the same problem in the case of cables for suspension bridgesor for reinforced concrete constructions with post-tensioning. Theperformance of these construction processes is directly dependent on theanchorage system where it is necessary to minimize the effects of stressconcentration and the loss of tension loads due to environmental conditions.In the case of "stiff composites (table 2) associating thermosets and glass,aramid or carbon fibers, the design problem is exactly the same as the onemet for the aeronautical and automotive applications. Industrial applicationsuse manufactured half-products such as pultruded profiles to createstructures with a design similar to metallic ones. In this case, the criticalproblems essentially concern the joint and buckling stability.

S tiff co m posite

T h erm osettin gm atrix

E xpandedtherm osetting

m atrixM ineral fillers Fiber (glass,

carbon,a ram id)

Polymer concrete Laminated structures Sandwich structures

Industrialhousing

Grounds, coatings, roads

Pultrudedsection

D e a inTable 2: "Stiff composite

Composite materials have been considerably developed during the last few years, toensure repair, reinforcement and protection of existing civil engineering structures(reinforced concrete, prestressed concrete, metallic frames). The wrapping of bridgepiles, the beam reinforcement (figure 1) towards traction or shear is particularlyefficient in the case of carbon epoxy composite. The design codes for traditionalmaterials (ACI, Eurocode) might change, in order to take into account these newmaterials. However some difficulties concern some realistic adhesion characteristicsbetween concrete and composite and specific failure modes particularly catastrophicin the case of composites.



- Brittle conipressive failure

- Concrete - composite interaction

Figure I: Design and durability control (doc. Hexcel)The design of works that includes composite materials must take intoaccount the interaction material - structure described in the table 4. In thistable, it is possible to understand that structure optimization can be made bynew formulations selection (new matrix, new reinforcements, new stackingsequences, new techniques of manufacturing) and not necessarily by thegeometrical structure thickness modification that corresponds to the usualmethods of design in the case of isotropic homogeneous structures.

MATERIAL

Componentsproperties

[jSTiSTRUCTURE

I Formulation [ [ Processing I Geometry II Function II Processing

V

DESIGNOPTIMIZATION

Table 3: Material-structure interactionAs a consequence, it is necessary to know exactly how to define the loadconditions of constructions (load conditions, environmental conditions,expected lifetime...).



General data for infrastructures design

The load conditions of structures are taking into account the own weight ofthe structure, the service loads, the extreme loads. The low density ofcomposite materials is an asset in order to minimize the own weight of theconstruction. Moreover it is known that their use influence the design oftensile structures (tensile architecture, cable stayed bridges...).The service loads are generally standardized, hereby using valuescorresponding to the nature of the building or the bridge. It is important tonotice that the extreme solicitations (impact solicitation, seisms, andexplosions) are taken into account in the traditional design rules by a staticload redefinition. If this approach is not a significant problem, in the case oftraditional materials, it is necessary to take into consideration multiplicationcoefficients that take include the sensitivity, the variation of materialsbehavior laws with respect to the loading conditions.Likewise, in the case of extreme environmental solicitations (temperature,hygrometry, corrosion...), it is imperative to take into account the variationsof resistance, of ultime extensional modulus or damage variables specific forcomposite materials.Consequently, for numerous applications, it is possible to transfer acquiredknowledge on the aging of polymers, composites used in the transportationfield (aeronautic, automotive) to the civil engineering field. Nevertheless, wecan notice that the accelerated aging methods, the prevision methods (time-temperature-dependence) are confronted to estimates of lifetime of 10 years,20 years, 50 years... So, the retrofitting and repair problems are more andmore important when taking into consideration combined solicitations(mechanical - thermal - hygrometric) and are more and more difficult tomodel. In view of effects of composite materials heterogeneity analyzed atdifferent scale levels: (fig.2)

1. - microscopic scale: fiber - matrix - interface,2. - mesoscopic scale: internal structure of stacking or weaving,3. - macroscopic scale: multi-materials, mixed structures...

it is necessary to conceive analysis or design codes that integrate thephysical phenomena which occur at each level.



Fiber-matrix interface degradation

Structural stability ami reliability

MICROSCOPIC SCALE

Damage propagationDelamination interaction

between components

. MESOSCOPIC SCALEMACROSCOPIC SCALE

Figure 2: Multiscale durability analysis

Modeling mechanical behavior of multimaterial

structural element

We essentially develop two different approaches for the design of suchstructures (usual or finite elements or specific formulation for modelinginterface behavior and modified design recommendations followingprescription of CEB or ACI code).Repairing techniques using carbon-epoxy laminates applied on lateral sidesof concrete or prestressed concrete beam allow to modify tensile and shearproperties of concrete. They also influence cracking mechanism and protectconcrete against corrosion and environmental effects.

Sanding of the concrete surface Primary application Cutting of REPLARK sheets

First resin layer application Carbon fabric setting StratificationFigure 3: Different reinforcements



Consequently, the main parameters that influence the structural behavior ofmultimaterial composite beams are the following:

interface properties between composite and concrete,behavior laws and particularly concrete damage level in tensile zonesand transition zones between metallic bars and composite sheets.

Numerical methods: finite element method

Modeling composite-concrete beam or composite-steel beam is particularlydifficult along interface zone. Usually, it is possible to analyze structuralbehavior meshing the beam by classical displacement elements (figure 4).The validity limit of these methods and their precision degree are directlydependent on the meshing quality, on the behavior law that is taken intoconsideration and on the hypotheses of small or large displacement.

15:'ILf.'TYP

AMSY3 9.3FEB 6 199816:34:21NODAL SOtUTIO

RSYS.OOMX ..093337SMH -2.671SMHB—3.73SHX .2.871SHAB-3.73S -2.871-2.233r -i -1.393fc3 -.956981Spi -.318994^ .318993£H -95698W 1.593LgjJ 2.233" 2.871

Figure 4: Tensile-shear test of mixedconcrete-composite specimen

Figure 5: Shear-stressdistribution

In the case of non-linear behavior of a beam in traction induced by concretecracking, rebars slipping, composite peeling off... It is very difficult topredict, to calculate the relation between external bending moment and

curvature.



ANSVS 5.3APR 16 199816:10*22E-M

WIND=2E-N

Figure 6: Multimaterial beam

Specific finite elements for interface analysis

between composite and concrete

Usual formulations of finite displacement elements assume kinematiccontinuity at interface level but are not very efficient regarding staticvariables along boundaries, along interface.

%g materiau (1) materiau (2).

artificially separatedmoved state interface

X, ~ (a) " (b)

Figure 7: Kinematic continuity of displacement (a); forces equilibrium (b)



Basic equations along the interface: ^n\ = %(2) on Y

Equilibrium of surface load: f(l) + f(2) = 6 on F^

Stress vector along the interface: ay(l)nj(l)+Gjj(2)nj(2)=0 on F,2

Mixed methods combining two kinds of variables (displacement, forces) areable to model mechanical behavior along the interface. Using Reissnerprinciple [1950], different authors like Pian [1964], Washizu [1975] andVerchery [1973, 1987] have developed many others formulations.Variational Reissner principle corresponds to the following relation whereSjju is the material compliance.

Other kinds of static variables

To avoid difficulties induced by the excessive continuity of stress tensorcomponents, we suggest to choose other static variables, for example stress

vector components a^.To solve the problem of the multi-value stress vector at the element nodes,Verchery [1987] proposes to "relocate" the problem and to consider stressvector along the element side. It is also possible to minimize the number ofunknown variable at each node. This method corresponds to the "eliminationtechnique" developed by Aivazzadeh & al. [1986] where specific behaviorlaw and local equilibrium conditions are used. For instance (figure 8), weintroduce Noune, Courtade [1997] a friction Coulomb law along a triangularelement side that can be used to model interface behavior between compositeplate and concrete when displacement is not perfectly satisfying.



U, V, O..

y y yReissnerpure element Interface element Interface element with friction side15 parameters (Mix3) 15 parameters (TRL 7) 14 parameters (TRLIf)

Figure 8: Construction of a finite element with friction side

Numerical modeling combining different elements

The main difficulty for a perfect description of the mechanical behavior ofthe beam depends on the fact that damage mechanisms are numerous:concrete cracking, rebars slipping, reinforcement peeling off, steel yielding.These various phenomena appear at different times and their effects can becombined during the different loading phases. Their development can belocalized or uniformly distributed in the whole volume. In recentcontributions, Limam [1998] shows (figure 9) that it is possible to describethe mechanical behavior of such structures combining different types ofelements (volumic, bars, beam, interface, cracking) and to take into accountdifferent behavior laws and failure criteria for each material.

Concrete (QUA8)

L h. ,J

\ A i i. * .>-*H k#4

T"

"iL&J

Steel/(truss element)

AL'l'Kl' (truss element with or withoutinterface element)

Figure 9: Meshing of a multimaterial beam



Lateralcomposreinforc

\\

j!

t"-LoCOIrei

ites.ement

\Mi^HfMM <

igitudnpositiforcei

|lliii

01— t—

i.nal

nent

oadsiii

"] "" """i"l

r 7 Ti^ * '

1 'T IDisplacement sensors

t m - -

— Couple (for straiimeasure

|H |IW0IUi

)ftine

1

jal

nt

s

300

200

100

00

P1 (exp)P1 (num)

PO (exp)

5 10 15 20pISPLACnMBNTS(mm)

Jl and J2 : strain gaugesFigure 10: Tests Figure 11: Numerical & experimental results

Validity of such methods implies perfect identification of the mainparameters that influence behavior law and imply a reposition of numericalmodeling in confrontation with experimental results.

Non-linear methods using ACI, CEB code

principles

Equilibrium of a steel concrete beam or a prestressed concrete beam can beanalyzed by load and moment equilibrium equation in a given area (figure12). We propose a general formulation in the case of composed flexion andits simplification for elementary flexion.

/'"i

he

V

L J

\\ $

A,

/PI £hAM " -A

(1) (2

1 — 7 •AM

/,Fp2 I*

' )

"™ A p N

(3)

Figure 12: Prestressed concrete design method



In a first approach, the behavior laws taken into consideration are thefollowing:

CONCRETE IN COMPRESSION LONGITUDINAL STEEL

Elastic-plastic with hardening

<7al.06fp0.9 fn

8.

CONCRETE IN TENSIONLinear elastic with post

strength

ft"

COMPOSITE SHEET

Linear elastic until failure

dp

8u

Figure 13: Materials mechanical behavior

The following chart of non-linear method has been established byVarastehpour, Nasseri, Hamelin [1997]. First of all, compositecharacteristics are introduced from evaluation of global equivalent elasticconstant (engineer constants). After solving the different equations, the F<.force applied to the composite plate is distributed in the thickness of thematerial following classical laminated theory. The software developed byL2M Laboratoire Mecanique Materiaux can take into account propertiesvariations and essentially slipping effect along the interface concrete-composite established from experimental test as direct shear testmeasurement (figure 14).General equations for beam equilibrium:ZF, = 0 ZM = 0Fb+F.+Fe+N = 0 M = MI,+M,+F,, = JabdA,, My = |oy YdA,,


Computer Methods in Composite Materials 55]

tot* cdch domainNeutral axis position

Z=Zp-5Z

IpWcj \Material behaviour lawsPrestress forceInitial loading

r imBW n_^. concrete strain

8 — 6*. 4- 5s

^ ^ ^ ^ ^ ^ 1 ^bottom fibre concrete strain

Stress diagramInternal forces

„•<*, - ?-,Equilibrium condition?

ZF<5

Aberrant polnL

££• <V*t*f,«tr, ty-~* *»\* •*"»j" >• t «" .' * *Moment Af/ Curvature fy

Figure 14: Non-linear program chart (Nasseri, Hamelin, 1998)

The major interest of this design method is a double one: on one hand, weuse the classical design principles of steel reinforced concrete andprestressed concrete structures corresponding to construction codes, on theother hand the iterative non-linear design method is adapted to model thefatigue and creep behavior of structures and to take into account the interfacebehavior law.

Conclusion

Whatever the used design method, it is necessary to have at disposalbehavior laws valid for each material. The precision level of each designmethod is directly dependent on the knowledge of concrete damage level andon polymer thermorheological properties. The fact that the composites arecharacterized by their macroscopic properties is not so bad insofar as thefailure mechanisms of the more efficient reinforcement systems are locatedin the concrete in tension, not in the composite and not in the composite-concrete interface.



Bibliography

Meier, U. & Betti, R. [1997J. Recent advances in Bridge engineering.Proceeding of US-Canada-Europe Workshop on Bridge Engineering,Dubendorf & Zurich / Switzerland 11-16 July 1997, EMPA,Ueberlandstrasse 129, CH-8600 Dubendorf, Switzerland.

Hamelin, P. & Verchery, G. [1990]. Proceedings of Textile Composites inBuilding Construction Symposium, Lyon France 16-18 July 1990, Ed.Pluralis, 24 rue Descartes 75005 Paris, ISBN 2-862-16-022-9.

Hamelin, P. & Verchery, G. [1992]. Proceedings of Textile Composites inBuilding Construction Symposium, Part 1 & Part 2, Lyon France 23-25 June1992 Ed. Pluralis, 24 rue Descartes 75005 Paris, ISBN 2-862-16-031-8.

Advanced composite materials in bridge and structures. [1996[. Proceedingsof The International Conference Montreal Canada, Ed. M. El Badry,ACMBS Network of Canada, ISBN 0-921-303-645.

Hamelin P. & Courtade R.M. [1992]. Mechanical modeling of interfaces incementitious fiber composites. RILEM International Conference oninterfaces in cementitious composites, Toulouse, 21-23 October 1992.

Noune A. [1997] Methodes d'approximation a deux champs pour ['analysede la fissure, du contact de leur evolution. These de doctorat, UniversiteLyon I, 13 may 1997.

Verchery G. [1987]. Methodes numeriques de calcul des champs decontraintes dans les materiaux heterogenes. Calcul des structures etintelligence artificielle. Vol. 1 Editeurs J.M. Faret et P. Ladeveze, Pluralis,PR 7-21.

Varastehpour H. & Hamelin P. [1997] Characterization of concrete-composite plate adhesion. Euromech 358, Nevers, France, Editions Pluralis,1997.


Documents

540 Computer Methods in Composite Materials · PDF file · 2014-05-14concrete-composite specimen Figure 5: Shear-stress distribution In the case of non-linear behavior of a beam in