Modelling of reinforced concrete beams strengthened by jacketing

N MacAlevey*, Nanyang Technological University, Singapore H K Cheong, Nanyang Technological University, Singapore

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27 th Conference on OUR WORLD IN CONCRETE & STRUCTURES: 29 - 30 August 2002, Singapore

Modelling of reinforced concrete beams strengthened by jacketing

N MacAlevey*, Nanyang Technological University, Singapore H K Cheong, Nanyang Technological University, Singapore

Abstract

Repair and strengthening of reinforced concrete beams is commonly carried out by "jacketing". Jacketing is the addition of concrete and steel reinforcement (both longitudinal and transverse) to an existing beam. This paper describes the development of a model that can be used for the design of jacketed reinforced concrete beams. This model is based on the use of the Compressive Force Path Concept to describe the behaviour of a monolithic reinforced concrete beam, and a Mohr-Coulomb approach to describe the behaviour of the interface between the new and old concretes. The resulting model is used to explain the experimental failure loads of simply supported and continuous jacketed beam specimens. It is concluded that monolithic behaviour of the jacketed beam is ensured if critical portions of the interface between the two concretes possesses adequate strength. The model is shown to give safe and reliable predictions of published experimental information.

Keywords: Reinforced Concrete Beams, Dynamic loading, Jacketing, Modeling, Preplaced Aggregate Concrete, Repair, Slant Shear Test, Strengthening.

1. Introduction

Strengthening of reinforced concrete beams by "jacketing" is a well established and frequently used technique. It involves the addition of steel reinforcing bars encased in a concrete jacket. In many cases the additional concrete is preplaced aggregate concrete (PA). Fig 1 shows a typical cross­section.

Existing AdditionalBeam

Additional

..---concrete

~~I--- reinforcement

Figure 1 . Jacketed beam

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---

A series of tests on slant shear prisms and simply supported and continuous jacketed beams were carried out. The tests were fully described in an earlier publication (Cheong and MacAlevey 2000). The present paper describes a model developed as a result of these experiments. It is shown that this model can be used to predict the strength of jacketed beams.

2. Interface Failure

The slant shear tests demonstrated that the failure of a concrete-to-concrete interface is sudden. Therefore, it seems logical to consider the interface as being either intact, in which case the jacketed beam behaves monolithically, or failed, in which case the jacket is ineffective. Figure 2 shows the set-up that was used for simply supported and continuous beams. Figure 3 shows the results of the slant shear tests on concrete with a 28-day feu of 35 N/mm2.

IE 1000 1000 1000 ) 1000 1000 1000 1650)1< )1< I IE )IE )IE )I~IE )1

d= 265 Beam Beam

t t t t PC

iI I t I t f t f

Figure 2. Set-up for beam tests

y = 1.19x + 3.24 2R =09414 •.... -..e 12

10 ~~ ~ ~! e fI) 8 fI) ~ a.. 6 ....>PA > VJ-~ ~ a.. 4 tIS ~

.= ~ 2

VJ

PC 0 I

o 2 4 6 8

Normal Stress (N/mm)r 2

Figure 3. Slant shear tests on composite prisms

The values of the cohesion c and the angle of friction ¢J obtained as a result of the slant shear tests on various grades of concrete of "moderate roughness" result in the following Mohr-Coulomb equations:

,,= 2.7 + crtan 48° , for feu = 25 N/mm2 (1 )

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r =3.5 + CTtan 58° , for feu =30 N/mm2 (2) r = 3.2 + CTtan 50° , for feu =35 N/mm2 (3) r =4.5 + CTtan 4]0 , for feu = 40 N/mm2 (4) r =3.8 + CTtan 50° , for feu = 50 N/mm2 (5)

3. Development of Design Model for Jacketed Beams

As a starting point in the development of a model of a jacketed beam, the Compressive Force Path was adopted. This model has been shown to give reliable predictions of the strength of monolithic beams. It assumes that the ultimate strength of a reinforced concrete beam is principally dependant on the strength of the concrete along a path shown for a simply supported beam and a continuous beam in Figure 4. There is considerable experimental evidence in support of this concept and its associated design method (e.g., Kotsovos and Pavlovic 1999).

I~I I~I I~I ~~I ~I PC

265 ./ * ~ 1-;;7 ~ t * "'1 I t * * '--"'" f

Figure 4. Compressive Force Path

3.1 Transfer of Inclined Portion of Compressive Force Path Across Interface:

Any horizontal interface along the length of the beam must be crossed by the inclined portion of the Compressive Force Path. This can happen only if the interface is sufficiently strong to allow it. Hence a check is required on the strength of the interface in the region where this path would be expected to cross it. Figure 5 shows the Compressive Force Path adjacent to a simple support.

2d

I Existing Beam I

~

Interface Jacket

Figure 5. Compressive Force Path at a simply supported end

3.2 Anchorage of Longitudinal Reinforcement

In the beam experiments reported in Cheong and MacAlevey (2000), as the failure load of the beam was approached large stresses were recorded in the additional longitudinal steel near to the supports of simple beams and at the points of contraflexure of continuous beams. Full anchorage was

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recommended. The presence of the horizontal component of the inclined portion of the Compressive Force Path implies the existence of a horizontal anchorage force of approximately 2.0R (where R is the reaction at the support).

3.3 Design

A summary of the recommended design approach is as follows:

1. Proportion the reinforcement as for a monolithic beam (this can be done using the Compressive Force Path Concept).

2. Detail the beam according to the detailing rules derived in Cheong and MacAlevey (2000), i.e. additional longitudinal reinforcement should be fully anchored at simple supports and at the points of contraflexure of continuous beams.

3. Check the capacity of the interface in the region where the Compressive Force Path crosses it (using Eqn. 1, 2, 3, 4, or 5, as appropriate).

4. Predictions of the model

Table 3 shows predictions of upgraded beam strengths. Column (a) shows the total reaction that can be sustained by the beam should failure of the beam be due to failure of the interface between the original and additional concrete. The reaction shown is the result of checking the strength of the interface in the region where it is crossed by the inclined compression. The results of applying the design model of the Compressive Force Path Concept to the strengthened beams are shown in column (b), i.e., the reaction that could be sustained should the beam behave monolithically. Thus, the prediction of the load carrying capacity of the strengthened beam (shown in bold type) is the lower of values shown in columns (a) and (b). As also shown in Table 3, the model can be used to explain the behaviour of a number of experiments done by others on strengthened beams. For beams with a plain concrete (PC) underlay or overlay, values of c and t/J derived by Regan (1979) were used in the calculation.

5. Implications of the model

1. The full composite beam reaction has to be transferred across the interface, regardless of the quantity of additional reinforcement provided. Of course, a larger amount of additional longitudinal reinforcement is more likely to cause failure of the interface, as flAt, and thus R, increases, implying both the normal stress u and shear stress r on the interface increase, putting them closer to the failure envelope.

2. The conventional approach to composite concrete beam design is to assume that the bottom and/or top surface along the entire length of the beam contributes to the strength. The model implies that it is only the parts of the interface crossed by the inclined force path that contribute to the strength of the composite beam. Therefore efforts to improve bond should concentrate on these areas.

3. The bearing length at simple supports of composite beams, e.g., precast beams with cast-in­place topping, affects the width of the compressive force path, and hence the stresses along the path and at the interface. Predictably, larger bearing lengths lead to lower stresses.

4. Failure of the interface where the compressive force path crosses it means a complete breakdown in composite behaviour. Therefore, failure of the interface leads to brittle failure of a com posite beam.

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Table 3: Comparison of Test Results and Predictions

Predicted Max. Reaction {kN} Actual Failure

Beam Mark Strengthening Proposed Model CFPCM Mode Reaction

(a) (b) (kN)~

2-2 PA Jacket 292 195 Flexure 199

2-3 PA Jacket 292 195 Flexure 219

2-4 PA Jacket 175 176 Flexure 218

2-8 PA Jacket 135 198 Interface 178

2-9 PA Jacket 315 198 Flexure 212

4-1 PA Underlay 58 73 Interface 70

6-211 PA Jacket 180 151 Flexure 190

B5 in [9] PC Overlay 64 30 Flexure 30

C-2 in [8] PC Overlay 95 94 Interface 94

T-1 in [8] PC Underlay 99 116 Interface 109

B3/B4 in [4] PC Underlay 129 82 Flexure 90

B8 in [4] PC Underlay 135 82 Flexure 85

B7 in [4] PC Underlay 182 110 Flexure 119

Notes: Lower of two predictions in bold type; M = Monolithic Beam; # = Continuous Beam

6. Conclusions

Using the Compressive Force Path concept and the results of slant shear tests and beam tests, it is possible to derive a model to explain the behaviour of jacketed reinforced concrete beams.

References

[1] ACI Committee 318 (1989), Building Code Requirements for Reinforced Concrete (ACI 318­89), American Concrete Institute, Detroit.

[2] British Standards Institution (1997). BS8110 Structural Use of Concrete: Part 1: Code of Practice for Design and Construction, London, British Standards Institution, 101 pp.

[3] Cheong, H. K. and MacAlevey, N. F. (2000) "Experimental Behaviour of Jacketed Reinforced Concrete Beams, Journal of Structural Engineering, ASCE, Vol. 126, No.6, June 2000, pp 692-699.

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[4] Climaco, J. C. T. S. (1990). "Repair of Structural Concrete Involving The Addition of New Concrete", Ph.D. Thesis, The Council for National Academic Awards, Polytechnic of Central London, 254 pp.

[5] Kotsovos, M.D. and Pavlovic, M.N. (1999) "Ultimate limit-state design of concrete structures: a new approach", Thomas Telford, London, 164pp.

[6] MacGregor, J. G. (1992), "Reinforced Concrete Mechanics and Design", 2nd ed., Prentice­Hall, Inc., Englewood Cliffs, N.J., 936 pp.

[7] Regan, P. E. (1979). "Shear Resistance of Construction Joints--Comparison of 'Hy-rib' and scabbled joints", Structures Research Group, Polytechnic of Central London, 24 pp.

[8] Saiidi, M., Vrontinos, S., and Douglas, B. (1990), "Model for the Response of Reinforced Concrete Beams Strengthened by Concrete Overlays", ACI Structural Journal, Vol. 87, No.6, November-December, pp. 687-695.

[9] Ziara, M. M. and Haldane, D. (1995), "New Approach to Strengthening Structural Concrete Bridge Girders", Proceedings, IABSE Conference on Extending the Lifespan of Structures, San Francisco, December, pp. 119-124.

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