Design strength of axially loaded RC columns strengthened by steel caging

Materials and Design 30 (2009) 4069–4080

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Design strength of axially loaded RC columns strengthened by steel caging Pedro A. Calderón a, Jose M. Adam a,*, Salvador Ivorra b, Francisco J. Pallarés c, Ester Giménez a a b c

ICITECH, Departamento de Ingeniería de la Construcción y Proyectos de Ingeniería Civil, Universidad Politécnica de Valencia, Camino de Vera s/n, 46071 Valencia, Spain Departmento de Ingeniería de la Construcción, Obras Pública e Infraestructura Urbana, Universidad de Alicante, Apartado de Correos 99, 03080 Alicante, Spain Departamento de Física Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46071 Valencia, Spain

a r t i c l e

i n f o

Article history: Received 20 February 2009 Accepted 9 May 2009 Available online 20 May 2009 Keywords: RC columns Strengthening Steel caging Experimental study Numerical study Design strength

a b s t r a c t There are three principal techniques available for strengthening RC columns: concrete jacketing, steel jacketing and composite jacketing (FRP). Steel caging is a variation of the steel jacketing technique and is recognised as being easy to apply and relatively inexpensive. This paper presents a new design proposal that provides a means of calculating the ultimate load of an axially loaded RC column strengthened by steel caging. The formulation of the new proposal is based on the analysis of the failure mechanisms derived from experimental and numerical studies performed on full-scale specimens. The results provided by the application of the new design proposal are compared with those from laboratory tests on full-scale strengthened columns and FE models and are seen to be much more effective than results obtained from other proposals. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Of the different techniques that have been used to strengthen RC columns in recent years, steel caging (see Fig. 1) stands out for its effectiveness [1,2] and low cost [3]. Even though the technique is widely used in many countries [1,4–7], it has to date received very little attention from the scientific community [7], which means that less is known about the behaviour of an RC column strengthened by steel caging than, for example, that of an FRP-strengthened column. The Institute of Concrete Science and Technology (ICITECH) of the Universidad Politécnica de Valencia has for some years been carrying out research on this type of strengthening of RC columns in the form of laboratory tests [8–10] and finite element (FE) modelling [7,11–13], the objective being to continue the work begun by Ramírez [14] and Cirtek [4,15] some years ago. As has been shown by Adam et al. [7], when a column is strengthened with a steel cage there are three ways of dealing with the areas close to the ends of the column: (a) Adding capitals welded to the steel cage so that they are in contact with the beam (see Fig. 2a). (b) Welding tubes to the angles of the strengthening, passing through the beam–column joint (see Fig. 2b). (c) Leaving the area without any additional elements (see Fig. 1). * Corresponding author. Tel.: +34 963877562; fax: +34 963877568. E-mail address: [email protected] (J.M. Adam). 0261-3069/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.05.014

This paper presents the continuation of the work undertaken in Adam et al. [7], which analysed the behaviour of RC columns strengthened by steel cages and arrived at a series of recommendations for the design of the strengthening. The present work presents a new design proposal which will predict the ultimate load of the strengthened column, based on the analysis of the failure modes of a set of specimens obtained from laboratory tests [8] and from the analysis of the results of FE models [7]. The design proposal is verified by comparing its predictions with the ultimate load obtained from the above-mentioned specimens and FE models. The application of this method constitutes an improvement on the results given by other methods used in the design of steel caging to strengthen columns [16,17]. This paper is confined to the case defined in (c) above, as (a) and (b) have already been dealt with by Adam et al. [10,13].

2. Design proposals and review of the literature This paper presents a new design proposal capable of predicting the ultimate load of an axially loaded RC column strengthened by steel caging and without any additional elements in the end sections. This Section describes the different formulations used to date to determine the ultimate load of a RC column strengthened in this way. Eurocode No. 4 [16] does not include any proposal for direct application to an RC column strengthened by steel caging. However, as the strengthened column could be considered to behave similarly to a composite steel–concrete column, according

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Nomenclature Ac AL As Atribut COV b Ec EL est fc fl fyL fys i j K k1 ks kg lang lst Mp N Nc

cross-section area of concrete cross-section area of steel angles cross-section area of longitudinal reinforcement tributary area in accordance with Fig. 10 coefficient of variation side of the column elastic modulus of concrete elastic modulus of steel thickness of strips compressive strength of concrete confinement pressure yield stress of cage steel yield stress of reinforcement steel failure mechanism number of strengthened column iteration number (see Section 5.2) considers the higher compressive strength of the concrete due to confinement pressure confinement effectiveness coefficient shape coefficient coefficient considering distance between strips distance between strips length of strip (see Fig. 10) plastic moment of an angle, related to NL/4 axial load supported by the concrete in the column axial load supported by the concrete in the column at the end of a strip

to Eurocode No. 4 [16] the ultimate load of the strengthened column could be expressed by Eq. (1).

PEC4 ¼ 0:85  Ac  fc þ As  fys þ AL  fyL

ð1Þ

NL N0 Ns n PAdam PEC4 PFer Pi PReg Pu Pui qh T s x

ez l rst tc

axial load supported by the cage at the end of a strip axial load supported by the concrete at the beginning of a strip load supported by steel cage (see Fig. 4) possible failure modes of strengthened column ultimate load obtained from Adam et al. [7] (experimental and numerical study) ultimate load according to Eurocode No. 4 [16] ultimate load according to Fernández [20] load applied by the hydraulic testing machine ultimate load according to Regalado [17] ultimate load of strengthened column (new design proposal) ultimate load of strengthened column for failure mechanism i load shown in Figs. 8 and 9 force transmitted to strips (shear stresses mechanism) width of strip distance from the beginning of a strip concrete lateral deformation (ez = ey) friction coefficient stress supported by a strip poisson´s ratio (concrete)

where Ac is the cross-section area of the RC column to be strengthened, fc the compressive strength of the concrete, As the cross-section area of the longitudinal reinforcement of the column, fys the yield stress of the longitudinal reinforcement, AL the cross-section

RC column

strip

mortar

angles

Section A-A´

Fig. 1. RC column strengthened by steel caging (without additional elements at the ends of the cage).

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a

b strip

RC column

RC column

st r i p

A

A

capital

RC beam

tube

RC beam

angle

angle

Section A-A´

Section A-A´ angle

mortar

angle

mortar

capital

tube

Fig. 2. RC column strengthened by steel caging: (a) adding capitals; (b) adding tubes.

area of the angles forming the cage, and fyL the yield stress of the steel used in the angles. Adam et al. [10,13] showed that when capitals or steel tubes are added to the ends of the cage (see Fig. 2), the transmission of the load between column and cage is adequate. In such cases, if the strengthening is correctly designed, the failure occurs in the central section of the strengthened column, with behaviour similar to that of a composite steel–concrete column. Eurocode No. 4 [16] provides an approximate ultimate load suitable for this type of strengthened column. Regalado’s design proposal [17] is among those specifically created for RC columns strengthened by steel caging. This proposal basically consists of reducing the ultimate load obtained from Eurocode No. 4 [16], according to Eq. (2). The idea is to make an allowance for the incompatibility of deformation between the cage and the column.

PReg ¼ 0:6  ð0:85  Ac  fc þ As  fys þ AL  fyL Þ

ð2Þ

Regalado [17] applied his proposal with satisfactory results to the specimens tested by Ramírez [14] with capitals at the ends of the cage. However, it should be pointed out that the specimens tested by Ramirez failed at the heads [18,19], due to the concentration of stresses in these areas. This local effect in the heads caused the failure of the specimens at a load lower than would normally be expected. More recently, Adam et al. [13] demonstrated that Regalado’s proposal [17] is highly conservative for the case of cages with capitals. Adam et al. [13] avoided failure of the heads by means of an appropriate design for this zone. Cirtek’s proposal [4,15] is based on the results of an experimental and numerical study. The main drawback with his proposal lies in the design of the laboratory-tested specimens, in which the angles were welded to a steel plate which supported the load, so that the test conditions did not reflect the actual behaviour of a cagestrengthened column. As Adam et al. [11] and Giménez [8] have shown, there is significant slip between cage and column in the

zones close to the ends. This effect was not taken into consideration in Cirtek’s tests [4,15]. The methodology proposed by Fernández [20], based on designing a cage capable of supporting the total column load and thus completely ignoring the contribution of the concrete in the column, has also been widely used in Spain. That is to say, Fernández [20] proposes obtaining the ultimate load by means of Eq. (3):

PFer ¼ AL  fyL

ð3Þ

Giménez [10] showed that Fernandez’s proposal [20] is highly conservative and leads to non-cost-effective designs. 3. Behaviour of RC columns strengthened by steel caging Even though the behaviour of cage-strengthened RC columns has been analysed in detail in Adam et al. [7], this Section summarises the most important aspects observed in the laboratory tests and FE models in order to introduce the hypotheses that will be used to define the new design proposal. Both the specimens tested at the ICITECH laboratories [8,9] and the FE models [7,11,13] were simulations of full-scale RC columns. The intention was by this means to consider all the mechanisms that intervene in a column that forms an integral part of an actual building. Other authors have studied smaller-scale specimens [4,14,15,21], but this means it is impossible to consider many of the factors involved in the behaviour of RC columns strengthened by steel caging [8,9]. For the type of strengthening analysed there are two fundamental mechanisms that influence the behaviour of RC columns [7]: (a) Confinement imposed by steel caging. The cage produces a confinement effect on the column, since it prevents the expansion of the concrete caused by Poisson’s effect, thus increasing the compressive strength of the concrete. The confinement pressure will be highest in the area of the cage

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a

b steel angle mortar RC column

steel cage

mortar

mortar RC column

Fig. 3. (a) Confinement imposed by steel caging; (b) transmission by shear stresses.

covered by the steel strips, since these are the zones of greatest stiffness as regards transverse deformation. This effect is illustrated in Fig. 3a. (b) Transmission by shear stresses. In this way the load is transmitted between column and cage via the intermediate mortar layer (see Fig. 3b). Considering that confinement is highest in the zones nearest to the strips, transmission by shear stresses will be more effective in these zones. Fig. 4 gives the load distribution between column and cage for different total loads applied (Pi) in the zones nearest to the ends of one of the FE models studied by Adam et al. [7]. It can be seen that load transmission is greatest in the zone closest to the first strips. The failure of the strengthened column occurs when the cage is no longer able to confine the concrete. Adam et al. [7] have shown

that there are two possible failure modes for cage-strengthened RC columns: (a) Yielding of the angles, due to the axial loading absorbed, in combination with the bending produced by the transverse deformation of the concrete in the column (Poisson’s effect). This failure mode is shown in Fig. 5a. The angles fail when a set of three plastic hinges are formed within a section of an angle bounded by two strips (one hinge on each angle-strip joint and one in the centre of the section). This mechanism can also be seen in other laboratory tests [8] and FE models [7]. (b) Yielding of the strips, due to the pressure caused by the transverse deformation of the concrete under Poisson’s effect. Fig. 5b shows an example of this type of failure in a strengthened RC column. It should be noted that no yielding

680

distance (mm)

510

340

Pi = PAdam Pi = 0.75·PAdam Pi = 0.50·PAdam Pi = 0.25 PAdam

170

0 0

0.1

0.2

0.3

0.4

Ns /Pi

Fig. 4. Load distribution between steel cage and column for different Pi values (Pi, load applied by the hydraulic testing machine; PAdam, ultimate load; Ns, load supported by the cage). Specimen FEM-0 analysed by Adam et al. [7].

P.A. Calderón et al. / Materials and Design 30 (2009) 4069–4080

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Fig. 5. Possible failure modes: (a) yielding of the angles; and (b) yielding of the strips.

occurs in the angles (see Fig. 5b), since the distance between the strips is quite small. Adam et al. [7] also noted this failure mode in FE models.

4. Design proposal This Section describes the new design proposal which considers the two possible failure modes of a RC column strengthened by steel caging. In this proposal it is important to take into account the load transmission mechanisms between column and cage. 4.1. Transmission of loads between column and cage In the case of a cage-strengthened RC column the transmission of loads between the column and the cage involves complex mechanisms. This is mainly due to: (a) The confinement pressure imposed by the cage on the column. This is not uniform throughout the length of the column, since the zones nearest to the strips are more rigid and therefore exert greater confinement pressure. The greater the confinement pressure the greater will be the load transmission due to shear stresses between cage and column. (b) Area of load transmission due to shear stresses. These loads are transmitted between the column and the cage, via the layer of mortar between them. However, this area is not uniform throughout the length of the column, since higher loads are transmitted in the zones covered by the strips (with a larger transmission area).

Fig. 6. Transmission of loads between cage and column. Hypothesis adopted (where NL is the axial load supported by the cage).

axial load along dx, and dT is the force transmitted to the strips (by the shear stresses mechanism).The force transmitted to the strips can be expressed by Eq. (5):

dT ¼ l  4  b  fl  dx

ð5Þ

l being the coefficient of friction between the steel and mortar, fl the confinement pressure on the concrete, dx the thickness of the infinitesimal slice, and b the length of the side of the column.From Eqs. (4) and (5) we obtain:

dN ¼ l  4  b  fl  dx

ð6Þ

Dritsos and Pilakoutas [22] observed that the transmission of loads between cage and column occurs largely in the zones where the strips are situated. This aspect has already been pointed out in Section 3, with an illustration in Fig. 4. In order to simplify the load transmission mechanism, the hypothesis is adopted that the transmission occurs (by shear stresses) solely through the layer of mortar under the strips. Fig. 6 shows a scheme of the simplification adopted. The loads are transmitted through the strips and where they are absent no transmission occurs. To evaluate load transmission in the strips, equilibrium of forces is assumed in the infinitesimal slice (thickness = dx) included in Fig. 7a, obtaining:

The stress supported by a strip (rst) can be expressed by (see Fig. 7b):

N  ðN þ dNÞ ¼ dT

rst ¼

ð4Þ

where N represents the axial load absorbed by the concrete in the column (on the left of the infinitesimal slice), 4 is the increase in

The lateral deformation of the concrete can be expressed by Eq. (7):

ez ¼

rz Ec



rx Ec

mc 

ry Ec

mc

ð7Þ

ez being the concrete lateral deformation (ez = ey), rz = ry = fl, tc concrete Poisson´s ratio, and Ec concrete elasticity modulus.Considering that rx ¼  bN2 , from Eq. (7) we obtain:

ez ¼

fl N mc ðmc  1Þ þ 2 Ec b Ec

fl  b  dx fl  b ¼ 2  est  dx 2  est

where est is the strip thickness.

ð8Þ

ð9Þ

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Fig. 7. (a) Equilibrium of forces in an infinitesimal slice (thickness = dx); (b) stress supported by a strip.

rst

ez ¼ EL being the lateral deformation of the strips, solving Eq. (9) will give:

ez ¼

b  fl 2  est  EL

ð10Þ

where EL is the elasticity modulus of the cage steel. Ensuring deformation compatibility between the column and cage (from Eqs. (8) and (10)) we obtain:

fl N mc b  fl  ðmc  1Þ þ 2  ¼ Ec E 2  est  EL c b

ð11Þ

Therefore, from Eq. (11):

fl ¼

mc



N

2 c 1  mc þ 2ebE b st EL

ð13Þ

where

m¼

l  4  tc   c b  1  tc þ 2ebE E st L

Solving Eq. (13) we get the axial load distribution for the concrete column (N), within the zone defined by a strip (as a function of distance x from the beginning of the strip):

NðxÞ ¼ N0  emx

ð14Þ

where N0 is the axial load absorbed by the concrete at the beginning of the strip. Considering the width of the strip to be s (see Fig. 6), the axial load supported by the concrete at the end of the strip (Nc) will be:

Nc ¼ N0  ems

ð15Þ

The axial load transmitted to the cage at the end of the strips will be obtained from NL = N0  Nc.Therefore:

NL ¼ N0  ð1  ems Þ

4.2. Definition of the design proposal The ultimate load of the strengthened column can be expressed by Eq. (17).

Pu ¼ 0:85  Ac  fc þ As  fys þ K  fl  Ac þ NL ð12Þ

If Eq. (12) is included in Eq. (6), we obtain the differential equation:

dN ¼ m  N  dx

In order to simplify the problem defined above, the proposal formulated in this paper is only for application to columns of square cross-section. It is capable of being extrapolated for rectangular cross-section columns with slight modifications to the proposal (considering that two sides of the column will be different).

ð16Þ

Following the simplification adopted at the beginning of this Section, we arrive at Eq. (16), which expresses the axial load supported by the cage after calculating the load transmitted by the strips. Eq. (16) will now be used to define the ultimate load of the strengthened column.

ð17Þ

where K is a parameter that makes allowance for the higher compressive strength of the concrete due to confinement pressure fl, similar to that proposed by Richart et al. [23]. Eq. (17) allows for the increased strength of the concrete due to the confinement imposed by the cage. It also considers the possibility that when the column fails the angles may not be supporting the load AL  fyL (see Eq. (1)). The axial load on the angles will have a value of NL, which will be determined from Eq. (16). Parameter NL is included assuming that column failure is caused by conditions in which the cage is no longer capable of confining the concrete of the column. The following Section deals with the method of obtaining the values of the parameters fl and NL. Cases of failure due to yielding of the angles are treated separately from those due to yielding of the strips. 4.2.1. Failure caused by yielding of the angles One of the possible failure modes of an RC column strengthened by steel caging occurs when the angles are no longer able to confine the concrete of the column and a failure appears similar to the one shown in Fig. 5a, caused by the formation of three plastic hinges in a section of angle located between two strips. Let us suppose that it is required to calculate ultimate load in the case of failure between the two strips shown in Fig. 8 (strips 1 and 2). Assuming that the column is subjected to initial load N0, NL is obtained from Eq. (16), thus arriving at the axial load supported by the angles between the two strips. The maximum confinement pressure that the angles can impose on the strips (fl) is determined from NL. This confinement limit is imposed by the appearance of the three plastic hinges indicated in Fig. 8. The plastic moment of an angle is related to NL/4 (NL is divided by 4 to obtain the axial load on each angle). When Mp has been obtained, fl can be determined by applying Eq. (20) (obtained from Eqs. (18)

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qh Section A-A´ A

qh

NL/4 A

lang

Mp

Mp

angle

Mp angle strip 1

strip 2

RC column

angle

s

lang

s

Fig. 8. Formation of three plastic hinges in a section of angle located between strips 1 and 2.

and (19)). Figs. 8 and 9 show the schemes on which Eqs. (18) and (19) are based.

qh ¼

16 2 lang

 Mp

fl ¼

ð19Þ

strip

pffiffiffi 2

ð20Þ

2

lang  b

where qh is the load shown in Figs. 8 and 9, lang the distance between two strips, and Mp the plastic moment of one of the angles, related to NL/4. The ultimate load for the case of failure by yielding of the angles will be obtained from Eq. (17) after adding the NL and fl parameters, which were obtained by the procedure described above.

ð18Þ

pffiffiffi qh  2 fl ¼ b

16  M p 

fl·b/2

fl·b/2 b

RC column

fl

fl·b/2 qh

qh =

angle

fl·b/2 Fig. 9. Equilibrium of forces in a strengthened column section.

f l ·b 2

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lst

strip yielding

b

lt

Atribut = b·lt

Fig. 10. Tributary area affecting the strip in which yielding is evaluated.

4.2.2. Failure caused by yielding of the strips A strip will yield when it is subjected to an axial load of est  lst  fyL perpendicular to the longitudinal axis of the column; est being the strip thickness, lst the length (see Fig. 10) and fyL the yield stress of the cage steel. The confinement pressure applied by the cage on the column when a strip yields is expressed by Eq. (21):

2  est  lst  fyL fl ¼ Atribut

ð21Þ

where Atribut represents the tributary area affecting the strip in which yielding is evaluated (see Fig. 10). Atribut is obtained by multiplying b by the sum of the two semi-lengths of the pieces of steel angle on both sides of the strip under study (parameter lt included in Fig. 10). When fl and NL have been obtained (from Eqs. (21) and (16), respectively), the value of the ultimate load of the strengthened column can be obtained from Eq. (17). Following the process de-

scribed above, the failure of the column is simulated for the case of yielding of one of the strips.

5. Application of the design proposal 5.1. General It is a relatively simple matter to put the design proposal described in Section 4 into practice. The initial data are as follows:  Geometry of the column and cage.  Mechanical parameters of the concrete of which the column is composed (fc, Ec and tc).  Mechanical parameters of the longitudinal reinforcement of the column (As and fys).  Mechanical parameters of the cage steel (EL and fyL).  l and K parameters.

Fig. 11. Geometry of the FE model (specimen FEM-0) analysed by Adam et al. [7].

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(a) l coincides with the parameter adopted for the FE models in Adam et al. [7]. (b) K includes the product of three coefficients: confinement effectiveness coefficient (k1, as indicated e.g. by Teng et al. [25]), shape coefficient (ks, based on the area actually confined within a cross-section of the column), and another coefficient that considers the separation between the strips (kg, which makes an allowance for the loss of confinement effect with distance from strips). Considering the range of variation of each of the coefficients (k1, ks and kg), Adam [24] carried out a statistical study, varying the value of K, and concluded that the best approach for the value of the ultimate load was obtained with the values l = 0.20 and K = 2.5.

5.2. Summary of the calculation procedure To determine the ultimate load of the strengthened column (Eq. (17)) all possible failure mechanisms must be considered:  Possible yielding of the angles, evaluating all the angle sections located between two strips. This will done following the procedure described in Section 4.2.1.  Possible yielding of the strips, evaluating each of the strips involved, following the procedure described in Section 4.2.2. Bearing in mind that column failure could be due to n failure mechanisms (yielding of angles or strips), the ultimate load will be obtained for each of these mechanisms (Pui, i varying between 1 and n). The value of the ultimate load of the strengthened column (Pu) will be the lowest of all the possible Pui values. Each Pui value (i varying between 1 and n) will be obtained by an iterative process. The initial iterative process value will be N0, which in this case will correspond to the axial load absorbed at the end of the column. The next process will depend on the failure mechanism studied:  Yielding of the angles: From the initial N0 value adopted, load transmission will be evaluated through the strips (applying Eq. (16)) to determine the axial load absorbed by the angles above the strip under study (NLi,j). When NLi,j has been determined, the confinement pressure applied by the angles on the column (fli,j) will be evaluated, by means of the method described in Section 4.2.1. When NLi,j and fli,j have been determined, Pui,j will be evaluated by Eq. (17). From this point on, an iterative process will take place using Pui,j as the new initial value (in the same way as N0 was used in the first iteration). This process will be repeated until Pui,j1 = Pui,j (j being the number of the iteration). At this point the value of Pui will have been defined.  Yielding of the strips: As in the preceding case, an iterative process will be initiated with the value of N0, obtaining also NLi,j (from Eq. (16). The value of (fli,j) will be obtained as explained in Section 4.2.2. When NLi,j and fli,j are known, Pui will be obtained as before.

5.3. Example The value of Pu will be calculated for the particular case of one of the FE models analysed by Adam et al. [7] and will serve as a general guide to the process.

The dimensions of the strengthened column are those given in Fig. 11. The column concrete has a compressive strength of 12 MPa. Reinforcement of the column consists of four 12 mm diameter longitudinal rods with 6 mm diameter cross ties every 0.20 m. The yield stress of the reinforcement steel is 400 MPa. Strengthening consists of L80.8 angles (leg size 80  80 m and thickness 8 mm) and rectangular strips measuring 270  160  8 mm. Yield stress of the cage steel is 275 MPa. Bearing in mind the characteristics of the strengthened column, ultimate load will be evaluated for the four possible failure mechanisms:    

Yielding Yielding Yielding Yielding

of of of of

the the the the

angles in the first section (Pu1). angles in the second section (Pu2). first strip (Pu3). second strip (Pu4).

The iterative calculation process described in Section 5.2 can be easily implemented on a spreadsheet to obtain the Pui values associated with each failure mechanism. The ultimate load of the strengthened column (Pu) will be the minimum value of Pu1, Pu2, Pu3 and Pu4. To be able to evaluate fl in the case of a failure mechanism due to yielding of the angles, the value of Mp associated with NL/4 (see Section 4.2.1) must be known. Mp will be easy to obtain from an axial load-moment interaction diagram (see Fig. 12 for the case of an L80.8 angle). The Pui values included in Table 1 are obtained by following the iterative process described in Section 5.2 for each iteration. As can be seen in Table 1, four iterations are sufficient to obtain Pui. The ultimate load in the case dealt with here will be 2152.5 kN. Fig. 13 summarizes the calculation procedure for the case analysed in this Section. The N0 value used to initiate the iterative process was 2614.0 kN, which coincides with the value that would be obtained by Eurocode No. 4 [16].

400

300 N (kN)

Certain observations should be made concerning parameters l and K:

200

100

0 0

2

4

6

8

10

M (kN·m) Fig. 12. Axial load-moment interaction diagram (L80.8 angle and fyL = 275 MPa).

Table 1 Pu1, Pu2, Pu3 and Pu4 for each of the iterations. Failure mode (kN)

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Pu1 Pu2 Pu3 Pu4

2166.2 2241.2 3191 4306.6

2152.9 2219.5 3177.7 4284.8

2152.5 2218.2 3177.3 4283.6

2152.5 2218.2 3177.3 4283.6

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Fig. 13. Calculation procedure (example in Section 5.3).

6. Comparison with results obtained by Adam et al. [7] Table 2 compares the ultimate load value obtained by the new design proposal (Pu) with that obtained by laboratory tests and FE models (PAdam). The chosen specimens and FE models were those analysed by Adam et al. [7], who studied the effect of different parameters on the behaviour of the strengthened

column (size of angles, yield stress of the cage steel, compressive strength of the concrete in the column, size of the strips, addition of an extra strip at the top and bottom of cage). The results from the FE models used to analyse the effect of the friction coefficient between cage and column are not considered here, since these models do not reproduce the real behaviour of strengthened columns [7].

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P.A. Calderón et al. / Materials and Design 30 (2009) 4069–4080 Table 2 Comparison of ultimate load obtained by Adam et al. [7] with PEC4, PReg and Pu. Specimen

PAdam(kN)

Design proposal

Comparison

Adam et al. [7]

PEC4 (kN)

PReg (kN)

Pu (kN)

PAdam/PEC4

PAdam/PReg

PAdam/Pu

FEM-0

2185.7

2614.0

1568.4

2152.5

0.84

1.39

1.02

FEM-L40 FEM-L60 FEM-L100 FEM-L120

1611.2 1842.7 2582.5 3065.8

1599.8 2021.1 3373.0 4286.0

959.9 1212.6 2023.8 2571.6

1546.7 1781.2 2549.4 3108.5

1.01 0.91 0.77 0.72

1.68 1.52 1.28 1.19

1.04 1.03 1.01 0.99

FEM-fy235 FEM-fy355

2109.8 2349.4

2417.2 3007.6

1450.3 1804.5

2048.4 2339.8

0.87 0.78

1.45 1.30

1.03 1.00

FEM-fc4 FEM-fc20 FEM-fc30

1572.8 2944.6 3992.3

1894.0 3334.0 4234.0

1136.4 2000.4 2540.4

1442.6 2873.9 3788.2

0.83 0.88 0.94

1.38 1.47 1.57

1.09 1.02 1.05

FEM-St80 FEM-St120 FEM-St200

1898.1 1961.9 2396.1

2614.0 2614.0 2614.0

1568.4 1568.4 1568.4

1845.1 1947.6 2364.4

0.73 0.75 0.92

1.21 1.25 1.53

1.03 1.01 1.01

FEM-aSt

2678.3

2614.0

1568.4

2473.9

1.02

1.71

1.08

Exp-A Exp-B Exp-C Exp-D

1954.8 2324.1 2599.4 2451.9

2281.0 2650.0 2929.0 2281.0

1368.6 1590.0 1757.4 1368.6

1996.4 2370.7 2569.8 2280.9

0.86 0.88 0.89 1.07

1.43 1.46 1.48 1.79

0.98 0.98 1.01 1.07

0.87 0.101

1.45 0.169

1.03 0.033

Mean COV

– –

– –

– –

4500

PAdam (kN)

3000

1500

FEM Exp 0 0

1500

3000

4500

Pu (kN) Fig. 14. PAdam versus Pu.

As can be seen in Table 2, the new design proposal achieves excellent results in estimating the ultimate load of RC columns strengthened by steel cages. The mean value of PAdam/Pu is 1.03, and the corresponding coefficient of variation (COV) is 0.033. The validity of the proposal is also verified by Fig. 14. Table 2 also analyses the validity of the design proposals contained in Eurocode No. 4 [16] and those of Regalado [17], by means of the PEC4 and PReg values, respectively. The proposals of Cirtek [4,15] and Fernández [20] were not considered, due to the limitations pointed out in Section 2. Determining ultimate load by Eurocode No. 4 [16] is non-conservative (see Table 2). This is made clear in Fig. 15a, which shows the relation between PAdam and PEC4. It can be stated that Eurocode No. 4 [16] is not suitable for application in determining ultimate load of RC columns strengthened by steel caging. Furthermore, Regalado’s proposal [17] is very conservative (see Table 2 and Fig. 15b), which means that a cage designed from this proposal would involve excessive costs. It should be emphasised that in order to determine Pu, PEC4 and PReg, the 0.85 factor (reduction of concrete strength) was not taken into account, since the axial load was applied for a short period of

b

4500

3000

PAdam (kN)

PAdam (kN)

a

– –

1500

4500

3000

1500

FEM Exp

0

FEM Exp

0 0

1500

3000

4500

0

1500

PEC-4 (kN) Fig. 15. (a) PAdam versus PEC4; and (b) PAdam versus PReg.

3000

PRe g (kN)

4500

4080

P.A. Calderón et al. / Materials and Design 30 (2009) 4069–4080

time only (short-term loading) in the laboratory specimens and FE models. 7. Conclusions This paper presents a new design proposal for axially loaded RC columns strengthened by steel caging without additional elements at both ends of the cage. The data from this paper, in addition to those from Adam et al. [7], can be used as the basis for designing the strengthening required for axially loaded RC columns. The proposal presented considers the two possible mechanisms involved in the failure of strengthened columns (yielding of the angles or strips). Following Dritsos and Pilakoutas [22] and for the reasons indicated in Section 4, load transmission (by shear stresses) between column and cage was considered to take place solely through the strips. The results provided by the application of the new design proposal were compared with those from laboratory tests on full-scale strengthened columns and FE models and were seen to be much more effective than results obtained from Eurocode No. 4 [16] and Regalado [17]. Acknowledgements The authors wish to express their gratitude for the financial support received from the Spanish Ministry of Science and Technology under the research Project MAT 2003-08075, co-financed with FEDER funds. References [1] Wu YF, Liu T, Oehlers DJ. Fundamental principles that govern retrofitting of reinforced concrete columns by steel and FRP jacketing. Adv Struct Eng 2006;9(4):507–33. [2] CEB-FIB. Seismic assessment and retrofit of reinforced concrete buildings. Bulletin no. 24, Task Group 7.1; 2003. [3] Oey HS, Aldrete CJ. Simple method for upgrading an existing reinforcedconcrete structure. Pract Period Struct Des Constr 1996;1(1):47–50. [4] Cirtek L. RC columns strengthened with bandage – experimental programme and design recommendations. Constr Build Mater 2001;15(8):341–9. [5] Fukuyama H, Sugano S. Japanese seismic rehabilitation of concrete buildings after the Hyogoken-Nanbu Earthquake. Cem Concr Compos 2000;22(1):59–79. [6] Tamai S, Sato T, Okamoto M. Hysteresis model of steel jacketed RC columns for railway viaducts. In: Proceedings of the 16th congress of IABSE, Lucerne; 2000.

[7] Adam JM, Ivorra S, Pallarés FJ, Giménez E, Calderón PA. Axially loaded RC columns strengthened by steel caging finite element modelling. Constr Build Mater 2009;20(6):2265–76. [8] Giménez E. Experimental and numerical study of reinforced concrete columns strengthened with steel angles and strips subjected to axial loads. PhD thesis, Technical University of Valencia; 2007 [in Spanish]. [9] Giménez E, Adam JM, Ivorra S, Moragues JJ, Calderón PA. Full-scale testing of axially loaded RC columns strengthened by steel angles and strips. Adv Struct Eng 2009;12(2):169–81. [10] Adam JM, Giménez E, Calderón PA, Pallarés FJ, Ivorra S. Experimental study of beam–columns joints in axially loaded RC columns strengthened by steel angles and strips. Steel Compos Struct 2008;8(4):329–42. [11] Adam JM, Ivorra S, Giménez E, Moragues JJ, Miguel P, Miragall C, Calderón PA. Behaviour of axially loaded RC columns strengthened by steel angles and strips. Steel Compos Struct 2007;7(5):405–19. [12] Adam JM, Ivorra S, Pallarés FJ, Giménez E, Calderón PA. Column-joint assembly in RC columns strengthened by steel caging. Proc. ICE – Struct Build 2008;161(6):337–48. [13] Adam JM, Ivorra S, Pallarés FJ, Giménez E, Calderón PA. Axially loaded RC columns strengthened by steel caging. Proc. ICE - Struct Build 2009;162(3): 199–208. [14] Ramírez JL. Ten concrete column repair methods. Constr Build Mater 1996;10(3):195–202. [15] Cirtek L. Mathematical model of RC banded column behaviour. Constr Build Mater 2001;15(8):351–9. [16] ENV 1994-1-1 (Eurocode No. 4). Design of composite steel and concrete structures. Part 1: General rules and rules for buildings; 1992. [17] Regalado F. Los pilares. Criterios para su proyecto cálculo y reparación. Alicante: CYPE Ingenieros;1999 [in Spanish]. [18] Ramírez JL, Bárcena JM. Eficacia resistente de pilares de hormigón armado de baja calidad reforzados por dos procedimientos diferentes. Informes de la Construcción 1975;272:89–98. in Spanish. [19] Ramírez JL, Bárcena JM, Feijóo JM. Comparación resistente de cuatro métodos de refuerzo de pilares de hormigón armado. Informes de la construcción 1977;290:57–68 [in Spanish]. [20] Fernández M. Patología y terapéutica del hormigón armado. Colegio de Ingenieros de Caminos, Canales y Puertos, Madrid; 1994 [in Spanish]. [21] Dolce M, Masi A, Cappa T, Nigro D, Ferrini M. Experimental evaluation of effectiveness of local strengthening on columns of R/C existing structures. In: Proceedings of fib-symposium concrete structures in earthquake regions, Athens, Greece; 2003. [22] Dritsos S, Pilakoutas K. Composite technique for repair/strengthening of RC members. In: Second international symposium on composite materials and structures. China: Peking University Press; 1992. [23] Richart FE, Brantzaeg A, Brown RL. The failure of plain and spirally reinforced concrete in compression. Bulletin no. 190. Engineering Experiment Station, University of Illinois, Urbana; 1929. [24] Adam JM. Contribution to the study of RC columns strengthened with steel angles and strips. Analysis of the column and the beam column joint subjected to axial loads. PhD Thesis, Technical University of Valencia; 2007 [in Spanish]. [25] Teng JG, Chen JF, Smith ST, Lam L. FRP-strengthened RC structures. West Sussex: John Wiley & Sons; 2002.