design optimization of mixed concrete-steel beams

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The main objectives of this research are to replace mechanical connection commonly used for mixed steel-concrete girder by bonding joints [Fig. 1]. A preliminary .... Tab. 1 Parameters of the rheological model of the bonded joint. 20°C. 40°C.
Proceedings ISBN 978-80-87158-29-6

fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

DESIGN OPTIMIZATION OF MIXED CONCRETE-STEEL BEAMS CONNECTED BY BONDED JOINTS

Patrice Hamelin

Amir Si Larbi

Emmanuel Ferrier

Abstract In recent years, structural bonding has been much used for the repair of damaged structures considering reinforcement by the addition of composite pultruded plates or by the introduction of additional composite rebars. The performance and durability of epoxy adhesives have been established and the principal characteristics considered in the dimensioning rules are the properties in instantaneous and delayed tensile and shear resistance established from visco-elastic properties measurements. In the case of bonding on concrete, the modes of rupture often depend on the surface treatment of the concrete and of its tensile and shear resistance properties. We are particularly interested, in this research, in optimizing the design of bonded joints to ensure load transfer by shear between the concrete and the steel and also in optimizing the dimensioning of composite concrete-steel beams in order to achieve a non-fragile ultimate behaviour controlled by the plastic deformation of the steel and by the absence of any initiation of cracking in the bonded joints following the HSF methods proposed by P. Hamelin, 2009. Keywords:

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Bonding strength, Bonded joints, Viscoelastic behaviour, Composite concrete-steel beams

Introduction

The main objectives of this research are to replace mechanical connection commonly used for mixed steel-concrete girder by bonding joints [Fig. 1]. A preliminary study [Réf. 1] has confirmed 1

fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

Proceedings ISBN 978-80-87158-29-6

that the best adhesive was epoxy polymer, the best surface treatment for the metal section was corrindon projection and sand blasting for concrete. Considering the geometrical tolerance, the thickness of the joint can vary between 1 to 10 mm and a first evaluation of its shear resistance must be higher than 2MPa.

Concrete slab Pins

Bonding joint

Steel girder

Fig. 1

New concept of connection for steel-concrete structures

The development of technologies of assembly by bonding [Réf. 2] requires an evaluation of the durability and reliability of the joints performance under environmental conditions and for lifespans specific to the structure (50 or 100 years). The standard characterization procedures for behaviour under conditions of creep and fatigue require series of tests in real time and with different load levels. We attempt to develop predictive methods in order to define the weighting coefficients on the nominal characteristics of the adhesives which can be made quickly to facilitate the design of the experimental structures [Ref. 3]: thermostimulated creep test or viscoelasticimetry measurements. For each approach it is possible to identify rheological models and to propose creeping function.

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CONSTRUCTION OF THE MASTER CURVES FOR THE BONDED JOINTS FROM THERMO-STIMULATED CREEP TEST

2.1

Construction of the master curves for the bonded joints from thermo-stimulated creep tests.

The creep tests for temperature are carried out with an average shear stress of 1.5 MPa to 2,5MPa on concrete specimens subjected to tensile-shear stress by steel plates bonded with epoxy on both faces (Fig. 2). The specimen is placed in a thermal chamber at 20°C and is loaded for 3 hours. The specimen is unloaded for 12 hours. This waiting time is the relaxation time considered necessary for the whole overlap to be reached. The temperature is then increased by increments of 10°C, with a lapse of six hours between each level before the force is applied again. Measures are taken up to a temperature of 80°C over the glass temperature Tg.

140 mm

140 mm ∆L ∆L1 ∆L2

40 mm 250 mm 20 mm

Displacement sensor

T 60 ° C Strain gage

Fig. 2

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Concrete specimens assembled by steel plates submitted to tensile load

Proceedings ISBN 978-80-87158-29-6

fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

Exploiting creep deformation allows one to obtain the shear modulus in function of time and temperature (Fig. 3). 3500

MPa modulus Module de cisaillement MPa G Shear

3000 2500 2000 1500 1000 500 0 1

10

60°C

50°C

100 40°C

1000 30°C

Fig. 3

2.2

10000

20°C

100000 1000000

mastermaitresse curve 20°C Courbe 20°C

1E+07

master curve 30°C Courbe maitresse 30°C

1E+08

Time 1E+09 Temps

master curve 40°C 40°C Courbe maitresse

Master curves for creep behaviour

Modelling the creep behaviour of the bonded joint

We chose a Kelvin-Voigt model in series (Fig. 4). The shear deformation in the bonded joint is the product of the shear stress applied and the compliance:

γ (t ) = τ 0 ⋅ D (t ) ⋅ Y (t )

(1)

γ(t): deformation by shear at instant t, D(t): compliance at instant t, τ0: stress Y(t): Heavyside function Y(t)=0 for t=0 and Y(t)=1 for t>0.

G inf -G 0

Tab. 1 Parameters of the rheological model of the bonded joint

G0

20°C

40°C

G0 (Mpa)

2900

960

Ginfini (Mpa)

3100

1900

η1

5.10

11

5.1010

η2

8.1011

5.1011

η1

G inf -G 0 G0

η2

Fig. 4 Rheological model to describe epoxy adhesive creep

The rheological equation of state is established with the use of operational calculation. With the Laplace-Carson transformation, the creep functions are identified as follows: D(t) =

−t(G0 ⋅(G∞ −G0 )) η1 ⋅G∞

2 G0 −G∞ + ⋅e G0 G0 ⋅ G∞

−t(G0 ⋅(G∞ −G0 )) η2 ⋅G∞

G −G + 0 ∞ ⋅e G0 ⋅ G∞

(2)

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fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

2.3

Proceedings ISBN 978-80-87158-29-6

Notion of critical length and critical shear strength

The use of this data leads us to propose, as a first approach, an efficient length of anchorage for an infinite base of time: l efficient∞ = 3l efficient instantaneous We can also seek to recalculate the length of anchorage necessary for different levels of average shear stress in the adhesive joint considering a quasi-infinite shear modulus value using the expression proposed by Hamelin, 2009 [Réf. 2]. Fig. 5 shows that 250mm is the maximum anchorage value beyond which the effort in the bonded joint cannot vary for the infinite shear modulus value G (1000MPa). Frd (l ) =

τ adh A

b

1 coth Al + M tanh Al

with

A=

GN 4 E1es1

Hamelin, 2009 [Réf. 2]

(3)

F(L)

Force (N) 30000

25000

F[

]

20000

15000

10000

5000

Length (mm)

0 0

50

100

150

200

250

300

L [mm] τ = 6.5MPa & G=1000MPa

Fig. 5

τ = 1.5MPa & G=1000MPa

τ = 4.5 Mpa & G=1000MPa

Variation of load supported as a function of the length of anchorage

In as far as the failure of the adhesive joint occurs in the concrete or the adhesive, the shear stress at the ULS of the interface is equal to 

τ adhu ,d = min α adh * 

τ adh,e f tj ; γ adh γ td

  

(4)

ftj is the characteristic resistance of the concrete support in tension, determined by pelletizing (AFGC [Réf. 5]). ULS



td

= 1; γ

adh

= 1 , 25

SLS : γ

td

= 3 / 2; γ

adh

= 1, 4

:γ = 3 / 2;γ = 1, 4 τSLS ad ,e is the average shear stress at the limit of linearity for the adhesive α adh coefficient for ageing by creep at different temperatures defined by Tab. 2.

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Proceedings ISBN 978-80-87158-29-6

fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

Tab. 2 Coefficients values for

α adh

Creep

α adhf = 0,3 at 20°C if Tg < 50°C α adhf = 0,3 at 40°C if Tg > 80°C α adhf = 0,1 at 40°C if Tg < 50°C

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DIMENSIONING OPTIMISATION FOR COMPOSITE CONCRETESTEEL STRUCTURES ASSEMBLED BY BONDING

3.1

Definition of composite structure and of the properties of concrete and steel

We consider the assembly of a metal section (IPE 100) by bonding (Sikadur 31) with a slab of ultra high performance fibre concrete (BFUP DUCTAL), (Fig. 6). bc tc

Tab. 3 Properties of DUCTAL

Mechanical properties of DUCTAL Compression resistance tc = 50mm bc = 200mm

Fig. 6

Tension resistance

f ck = 150MPa

f tj = 15MPa

Elastic modulus

E b = 45000 MPa

Shear resistance

τ b,d = 4MPa

Geometrical section of the mixed beam (steelconcrete)

We consider a law of elastic-plastic type behaviour for the steel and the laws of behaviour in tension and in compression of the BFUP (Tab. 3) following the recommendations of the AFGC [Ref. 5]. Steel S235

Fig. 7

BFUP traction /compression

Laws of behaviour for materials: steel and BFUP

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fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

Fig. 8

3.2

Proceedings ISBN 978-80-87158-29-6

Principle of equilibrium of the composite section

Principle of dimensioning of the mixed structure

We return to the HSF method developed by P. Hamelin in considering the total interaction between the slab of concrete and the metal beam (perfect adhesion). The optimised position of the neutral axis at the ultimate limit state is situated at the junction between the compression table and the metallic girder [Ref. 2]. Effort supported by the concrete under compression in the slab: N bc 0,85

f ck

beff y

(5)

c

Effort supported by the steel under tension in the beam: N aten N aten.max A s

fy

(6)

a

A Fy c s Position of the neutral axis: y 0,85 b f a eff ck Internal lever arm: z b

d 2

tc

(7)

y 2

(8)

Bending moment of the composite section: M Rd = z b N aten = z b As

fy

γa

(9)

Condition of resistance of the adhesive joint under average shear strain:

Aadh .τ adhu ,d ≥ V d N bc N aten A s

fy

(10)

a

We confirm that it is not necessary to bond the structure with a continuous joint. Consequently, the slab is connected with a discontinuous blob of hard epoxy with a length of 250 mm which correspond to the critical value τ adu = 6 MPa defined from creeping test. To minimize the local concentration at the edge of the joint we insert polyurethane mastic between the epoxy blobs.

3.3

Validation of the dimensioning principle

The beams with a length of 3m are instrumented with strain gauges (Fig. 9) and displacement sensors; they are subjected to 4-points flexural test (Fig. 10). We can now draw load-deflection curves until failure and test the distribution of deformation in the concrete and the steel during loading cycle (Fig.12).

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Proceedings ISBN 978-80-87158-29-6

Fig. 9

fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

Strain gage position

Fig. 10 Flexural test (L = 3 m)

The comparison between the experimental results and the ultimate load calculated from the expression above confirms (Tab. 4) that the prediction is good. Tab. 4 Comparison of ultimate load P1

P2

Experimental ultimate load (MN)

0.075

0.0816

Theorical ultimate load (MN)

0.071

0.08

Experimental /theorical discrepancy

5.

3

Beam

Fig. 11 Residual deflection on BFUP beams after flexural tests

When we examine the curve which gives us the variation of the deflection in function of the load (Fig. 12), we note that the failure mode is not brittle and the large deflection is controlled by the steel ductility of the girder (Fig. 11).

Load (daN)

Distance to the bottom fiber (mm)

Strain distribution for the maximum load

Mid-span deflection Deflection under loading point

Deflection (mm)

Fig. 12 Load-deflection curve of beam P2

Strain

Fig. 13 Strain diagram for the maximum load

The Fig. 13 which represents the variation of the strain in the middle section confirms that the neutral axis position for the maximum load is located at the interface between the concrete slab and the steel girder.

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fib Symposium PRAGUE 2011 Session 5-4: Composites and Hybrids

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Proceedings ISBN 978-80-87158-29-6

Conclusions

We have established how it is possible to determine the resistance of an adhesive joint according to the calculation of its efficient length. We have proposed weighting coefficients on the levels of stress of the adhesive joints in type SLS and ULS dimensioning conditions. From a technological point of view we recommend gluing by blobs incorporating zones of hard adhesive (epoxy) and zones of flexible adhesive (polyurethane mastic). Following this principle of discontinuous assembly, the proposed dimensioning method aims to verify the equality between the maximum shear flux induced either by the resistance of the concrete in compression or the steel in tension and some of the shear forces supported by each blob. As long as the position of the neutral axis is maintained in the zone of compressed concrete, we have validated these dimensioning principles and have demonstrated that the failure mode of the structure assembled by bonding was not fragile but ductile by the plastification of the metal beam under tension. We have confirmed the validity of this dimensioning method for a quasi-infinite lifetime considering an effective length of bounding join which is 3 times longer than the length defined for instantaneous behaviour.

References [1] [2] [3] [4] [5]

A. SI-LARBI, E. FERRIER, P. HAMELIN, Concrete to steel lap joint failure criteria under combined shear and peeling stress, Journal of Constructional Steel Research, volume 65, issue 2, February 2009, pages 386-394 HAMELIN P., La connexion par collage, p227-254, pont mixtes acier – beton, un guide pour des ouvrages innovants, projet national MIKTI – Presse Des Ponts ISBN 978-2-85978449-2. FERRIER E., HAMELIN P., Material and structures long-term concrete-composite interface characterization for reliability prediction of RC beams strengthened with FRP, Material And Structures Rilem, vol 35, n°253, Novembre 2002. WILLIAN LANDEL, FERRY, Viscoelastic properties of polymers, New York – London – Sydney – Toronto, John Wiley and Sons, 1970, 671p AFGC: Recommandations Méthode de dimensionnement des ouvrages en béton fibre ultra haute performance. SETRA, Bagneux, 1998.

Prof. Patrice Hamelin, C.Eng.

Amir Si Larbi, C.Eng.





University Lyon 1 Laboratoire LGCIE site Bohr 82 bd Niels Bohr 69622 Villeurbanne cedex  +33 4.72.69.21.30  +33 4.78.94.69.06 ☺ [email protected] URL http://l2m.univ-lyon1.fr/

Prof. Emmanuel Ferrier, C.Eng. 

University Lyon 1 Laboratoire LGCIE site Bohr 82 bd Niels Bohr 69622 Villeurbanne cedex  +33 4.72.69.21.30  +33 4.78.94.69.06 ☺ [email protected] URL http://l2m.univ-lyon1.fr/ 8

University Lyon 1 Laboratoire LGCIE site Bohr 82 bd Niels Bohr 69622 Villeurbanne cedex  +33 4.72.69.21.30  +33 4.78.94.69.06 ☺ [email protected] URL http://l2m.univ-lyon1.fr/