Scholarly article on topic 'Strengthening of RC columns by steel angles and strips'

Strengthening of RC columns by steel angles and strips Academic research paper on "Civil engineering"

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Abstract of research paper on Civil engineering, author of scientific article — A.M. Tarabia, H.F. Albakry

Abstract The purpose of this paper is to study the behavior and efficiency of reinforced concrete square columns strengthened by steel angles and strips (steel cage). An experimental program was conducted on ten axially loaded column’s specimens till failure. Size of the steel angles, strip spacing, grout material between column sides and angles, and the connection between the steel cage to the specimen head, were the main studied parameters in this paper. Also, an analytical model was developed using a simple stress mechanics and strain compatibility to obtain the ultimate loads of the strengthened columns including the effect of the confining stress due to the steel cage and axial forces in the vertical angles considering both directly and indirectly connected cases. It was concluded that using this strengthening method is very efficient and a gain in the axial load capacity of the strengthened columns was obtained. This gain was due to the confinement effect of the external steel cage, and the ability of the steel angle to resist an extensive part of the applied axial load. The failure in most of the strengthened specimens was due to the buckling of the steel angle followed by crushing of the original columns.

Academic research paper on topic "Strengthening of RC columns by steel angles and strips"

Alexandria Engineering Journal (2014) xxx, xxx-xxx

Alexandria University Alexandria Engineering Journal

www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Strengthening of RC columns by steel angles and strips

A.M. Tarabia *, H.F. Albakry

Department of Structural Engineering, Alexandria University, Alexandria, Egypt Received 4 March 2014; revised 2 April 2014; accepted 15 April 2014

KEYWORDS

Reinforced concrete column;

Strengthening;

Steel angles;

Steel strips;

Abstract The purpose of this paper is to study the behavior and efficiency of reinforced concrete square columns strengthened by steel angles and strips (steel cage). An experimental program was conducted on ten axially loaded column's specimens till failure. Size of the steel angles, strip spacing, grout material between column sides and angles, and the connection between the steel cage to the specimen head, were the main studied parameters in this paper. Also, an analytical model was developed using a simple stress mechanics and strain compatibility to obtain the ultimate loads of the strengthened columns including the effect of the confining stress due to the steel cage and axial forces in the vertical angles considering both directly and indirectly connected cases. It was concluded that using this strengthening method is very efficient and a gain in the axial load capacity of the strengthened columns was obtained. This gain was due to the confinement effect of the external steel cage, and the ability of the steel angle to resist an extensive part of the applied axial load. The failure in most of the strengthened specimens was due to the buckling of the steel angle followed by crushing of the original columns.

© 2014 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria

University.

1. Introduction

There are many ways to increase the axial load capacity and available ductility of concrete columns. Adding new concrete jacket with additional reinforcement, using external steel angles and horizontal strips, and wrapping the original column

* Corresponding author. Tel.: +20 1203743743; fax: +20 34245091.

E-mail address: amtarabia@gmail.com (A.M. Tarabia).

Peer review under responsibility of Faculty of Engineering, Alexandria

University.

section with Fiber-reinforced polymers, FRP, are the most popular methods of strengthening and retrofitting concrete columns. Strengthening of reinforced concrete columns using steel angles connected by horizontal strips is one of the cheapest and fairly easiest available techniques. In this technique, four steel angles are fixed at the corners of the concrete columns and steel strips; spaced at a rational spacing; are welded to the angles to form a steel cage. A small gap left between the steel cage and the surface of the concrete column is then grouted using cement or epoxy grout to ensure full contact between the two of them. This strengthening method requires a limited space around the column section when compared with concrete jackets. It also requires less fire protection than wrapping with FRP which needs a special protection from fire hazards.

1110-0168 © 2014 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. http://dx.doi.org/10.1016/j.aej.2014.04.005

Many researchers conducted experiments on square columns strengthened by steel cage to study the performance and the ultimate capacity. Ramirez [1] presented ten repair methods for local or total repair of concrete columns to enhance the low strength of the original concrete columns. Among these methods, steel angles with batten plates were used. Three different techniques were tested to connect the steel cage with the head of the original column. When the connection between the head and steel cage was improved using a special embedded I-section, an enhancement in the strength and general behavior of the tested columns was observed.

At 1997, Ramirez [2] conducted another group of experiments to strengthen defected concrete columns. Four steel plates with four angles at the corners were welded to the plates. Two bonding methods were used to connect the steel plates to the original defected concrete column. In the first group, the gap between the steel plates and concrete was injected using epoxy resin and fine sand. While in the second group, an epoxy adhesive was used to bond steel jacket to the concrete. It was concluded that the steel plate jacket with injection proved to be a more reliable method. Debonding of the plates was observed at low bearing load, and a continuous cracking noise coming from the mastic layer between plate and angle, till reaching a sudden failure at the end of the process. This was related to the low workability and the brittleness of the used adhesion material.

Cirtek [3] conducted a test program consisted of 39 specimens, of dimensions 300 x 300 x 1500 mm. The head and base of each column were shod in order to prevent early failure. The longitudinal reinforcement was welded to the steel shoes. The steel angles of the bandages may be either continuous or non-continuous along the column height. The bandage of a fully banded column had continuous steel angles, while the bandage of a partially banded column has non-continuous ones. One of the main conclusions of this work was that the load-carrying capacity of the columns strengthened with bandage could possibly be increased by almost approximately 55%. Also, a mathematical solution adopting an iterative method was presented but it is a little bit complicated.

Badr [4] studied the experimental behavior of eight rectangular reinforcement concrete columns with low compressive strength concrete (about 200 kg/cm2) which were strengthened by steel jacket. All the specimens were rectangular concrete columns with an aspect ratio equal to two. The steel jacket consisted of four vertical angles placed in the column corners and horizontal strips plates which were distributed along the length of column and welded to the corner angles. The parameters of the study were the size of corner angles, spacing of the strip plates and the usage of anchor bolts in the middle of the long side of the columns. The results of the strengthened columns were plotted and the ultimate loads were compared with the analytical analysis suggested by Wang for confined concrete. The comparison between the results showed a good agreement for the ultimate load of the strengthened columns. It was proved that decreasing the spacing of the horizontal steel strips improved the behavior of the strengthened columns. Also the use of anchor bolts to connect strip at the middle of the long side of the column, raised the strength of the columns by 16%.

Issa et al. [5] conducted an investigation to evaluate the behavior of reinforced concrete columns strengthened externally with steel jacket or fiber composite under axial loads.

This study consisted of two phases, the first phase included the experimental investigations and the second phase included both theoretical and numerical analyses. The experimental program presented in their study included six rectangular reinforced concrete columns with the same cross section of 150 x 200 mm and a height of 1200 mm. The steel jacket consisted of four vertical angles at column corners and horizontal steel plates welded to the corner angles and distributed along column height. The fiber composites consisted of carbon fiber reinforced polymer (CFRP) sheets wrapped around the column cross section. The main parameter was the type of the external strengthening. For the steel jacket the variables were the size of corner angles and the spacing between the steel plates. From the experimental study, it was concluded that increasing the area of corner steel angles and decreasing the spacing between the steel pattern plates of steel jackets increase the ultimate carrying capacity, and ductility of strengthened columns.

Adams et al. [6] performed experiments on axially loaded RC columns strengthened by steel cages as well as numerical models using finite elements method to verify the obtained experimental results. Also, a parametric study was carried out to analyze the influence of each of the parameters on the behavior of RC columns strengthened by steel cages. The study considered these parameters: the size of the angles; the yield stress of the steel of the cage; the compressive strength of the concrete in the column; the size of the strips; the addition of an extra strip at the ends of the cage; and the friction coefficient between the layer of mortar and the steel of the cage. The obtained results of this parametric study were that the slippage between the steel cage and the column can be reduced by increasing the size of the strips due to the greater stiffness of the steel cage in the transverse direction. This improvement in confinement would also result in a better transmission of loads between the cage and the column by the shear stress mechanism.

Other investigators derived mathematical models to simulate the axial load-shortening relationship and to calculate the ultimate load of concrete columns strengthened by steel cage. Montuori et al. [7] presented a rational methodology for analyzing reinforced concrete columns strengthened with angles and battens. The results obtained with such methodology were compared to a set of experimental tests. The different behaviors of the confined and unconfined concrete, the possibility of buckling of the longitudinal bars and the influence of the adopted structural details were explicitly considered. Despite the variability of concrete's resistance, the comparison between the ultimate resistance predicted by means of the proposed model and the one coming from experimental evidence showed a good agreement. In addition, the comparison in terms of moment rotation curves was performed showing a good agreement too. The theoretical model showed a good ability to predict the behavior of columns strengthened with angles and battens, in terms of both deformation and resistance. The strengthening intervention increases the effectively confined area by means of the confining action of angles and battens and modifies the degree of confining action occurring on the concrete that was already confined by hoops before the strengthening intervention. In addition, another important factor was represented by the lateral restraint provided by the cover concrete preventing the buckling of the bars that would arise in the case of unstrengthened columns.

Gimenez et al. [8] conducted full-scale tests on RC columns strengthened with steel cages. The number of strips at the ends of the columns was increased to prevent premature failure occurred in a previous study. With this increase, the ultimate load of the strengthened column was increased. The variables of the study were as follows: unloading the column before applying the strengthening and fitting a capital at the joint between column and beams. It was concluded that the addition of two strips of a smaller size in the sections near the heads considerably improved the ultimate load and ductility of the column.

Calderon et al. [9] presented a new design method of calculating the ultimate load of an axially loaded RC column strengthened by steel caging. The formulation of the new proposal was 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 were 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.

Campione [10] conducted a comparison between the analytical expressions for the prediction of the load carrying capacity of strengthened reinforced concrete (RC) columns with steel angles and strips. The strength contribution due to the confinement effects induced by transverse strips and the strength contribution due to the composite actions of angles and concrete core taking into account that steel angles subjected to combined axial force and bending moment were the main studied parameters. In this study, the obtained theoretical results were compared with good agreement with experimental data available in the literature and with those obtained by using the existing theoretical models.

In the view of the above mentioned discussion, it was found that most research has been concentrated on strengthening columns with low concrete strength (between 15 and 20 N/mm2). Also, the effect of using different types of grout between steel cage and the sides of concrete columns has not been addressed thoroughly. The main objectives of this paper are as follows:

1. To study the efficiency of this strengthening technique in the case of relatively high strength concrete.

2. To study the effect of not connecting the steel angles to the head of the specimens (indirectly loaded case). This to simulate the situation where it is not feasible to connect the vertical angles to the roof slabs and beams.

3. To define the expected failure modes.

4. To compare the available load carrying equations in the literature with the obtained results from the experiments.

2. Experimental program

Ten square columns 150 mm x 150 mm were prepared and casted with two different cube strength values and the total height of the specimens was 1000 mm. All the tested columns were reinforced with the same longitudinal 4 bars of diameter 10 mm and tied with 6 mm mild steel square stirrups spaced at 100 mm along the column height and 50 mm at both ends of the column as demonstrated in Fig. 1. Both the ends of the specimens were protected using 10 mm steel heads where the

150 /-/

О О О

Stirrups

06@5Отт

Stirrups

150 /-/

Sec. И-И

06@ 7 ООтт

Stirrups 06@5Отт

Figure 1 Reinforcement details of the concrete column specimens.

gap between the end of columns and the steel head was filled vertically with a flowable cementitious grout material. Two reference columns were kept un-strengthened; one in each main group. The other eight columns' specimens were strengthened using four longitudinal steel angles and horizontal strips of width equal to 50 mm which were welded to the longitudinal angles at a specific spacing. The spacing between horizontal strips was reduced to 50 mm at both ends close to the steel head to avoid the risk of local failure at these ends and to enforce failure to occur at the middle of the column as shown in Fig. 2. The left gap between the steel angles and strip was vertically filled with grout to fill the 10 mm gap. Table 1 shows the details of the test specimens. The properties of the used grout mortars are given in Table 2 as provided by the manufacturing company. Also the mechanical properties of the steel angles, steel strips, and steel reinforcement are presented in Table 3. The tested columns were divided into two main groups; group 1 was strengthened using four angles 50 50 4.5 mm while in Group 2, columns were strengthened using four vertical angles 30 30 3 mm.

The tested parameters are as follows:

1. Strength of concrete.

2. Type of grout material injected between column and the steel cage.

3. Spacing of the horizontal strips.

4. The size of the longitudinal angles.

5. The existence of connection between the steel cage and both heads of the specimens.

The details of the tested columns are shown in Figs. 1 and 2. 3. Instrumentation and test setup

Tests were carried out with specimens placed vertically. All the test specimens were tested using 3000 kN hydraulic machine

PL2 î 0*210*1 Omm

4PLs 190*100*1 Omm

Steel head

4150*50*4.5 Steel strip

Concrete column

welded to head Steel head

A- Specimen SCI

PL210*210*1 Omm

4PLs 190*100*1 Omm

Steel head

4L30*30*5

Steel strips

Corldreie column

welded to head Steel head

c- Specimen SCW2

PL210*210*1 Omm

4PLs190*100*1 Omm Steel head

No connection

4L50*50*4.5 Concrete column

Steel head

- Specimen SCN1

PL210*210*1 Omm

4PLs 190*

Steel head

Concrete column \

-welded to head Steel head

d- Specimen SE2

Steel angle

—a^--—

f " \ ^ Steel strip

I \ « Grout

/ 150 /

Cross section of the strengthened column

Figure 2 Details of some strengthened specimens.

Table 1 Details of the test specimens.

Specimen Group Spacing of strips (mm) Corner angles Grout type Angle-head connection fcu (N/mm2)

N1 (reference) 1 N.A. N.A. N.A. N.A. 57.80

SC1 1 170.00 4L50*50*4.5 Cement Connected 57.80

SCN1 1 170.00 4L50*50*4.5 Cement Not connected 57.80

SCW1 1 260.00 4L50*50*4.5 Cement Connected 57.80

SE1 1 170.00 4L50*50*4.5 Epoxy Connected 57.80

N2 (reference) 2 N.A. N.A. N.A. N.A. 47.50

SC2 2 170.00 4L30*30*3 Cement Connected 47.50

SCN2 2 170.00 4L30*30*3 Cement Not connected 47.50

SCW2 2 260.00 4L30*30*3 Cement Connected 47.50

SE2 2 170.00 4L30*30*3 Epoxy Connected 47.50

N.A. not available.

Table 2 Mechanical properties of the used grout mortars according to the manufacturer.

Grout material Compressive strength Flexural strength

(after 24 h) (N/mm2) (N/mm2)

Cementitious mortar 18-20 6.95

Epoxy Grout 100 40

Table 3 Mechanical properties of steel angles, strips, and steel reinforcement.

Item Type fy (N/mm2) fu (N/mm2)

10 mm Reinforcement 420.0 -

L 50*50*4.5 Corner angle 415.0 540.0

L 30*30*3 Corner angle 485.0 699.0

fy: Yield stress. fu: Maximum stress.

4. Failure modes

For reference columns, N1 and N2 the behavior was similar. The axial shortening increased in a linear manner till failure. A sudden failure occurred when parts of the concrete cover spalled-off and buckling of the longitudinal reinforcement bars was observed as shown in Fig. 4. During failure of column N2, the lock of one stirrup started to open outside the section during failure stage.

In the case of the strengthened columns, the relation between load and axial shortening was almost linear till about 75% of the failure load followed by some nonlinear increase in the axial shortening. The failure in these specimens started with the buckling of the one or more of the vertical angles followed by the buckling of the reinforcement steel bars and eventually a crushing of concrete section near these bars as shown in Fig. 5. In some specimens, it was noted that the weld between the horizontal strip and vertical angle was broken, most probably after the occurrence of buckling of the vertical angles as it is obvious from the buckling shape of the angles as demonstrated in Fig. 6.

and the load was applied with a small increment of loads equal to 100 kN. The instrumentation consisted of two dial gauges mounted on two opposite faces of each specimen to measure the axial shortening of the specimens as shown in Fig. 3. In all strengthened specimens, two strain gauges were placed on two different vertical angles at the midheight of the column. Also, two strain gauges were placed on the middle of two perpendicular horizontal strips to record strain values at different loading stages to help to investigate the efficiency of these steel elements in improving the behavior of the strengthened concrete columns. The age of concrete in the course of the tests varied from 60 to 180 days.

5. Load-axial shortening behavior

The relationships between applied axial load and column axial shortening of the tested specimens are presented in Figs. 7 and 8. Also, the ratio of the ultimate load of each column to that of the reference column of the same group is shown in Figs. 9 and 10 respectively. Generally, the ultimate axial load and the maximum vertical deformations are higher in Group 1 than those of Group 2 due to the higher concrete compressive strength of Group 1 and the use of smaller angle section to

Figure 3 General views of the test setup showing the measurement instruments.

Figure 4 Failure mechanism of the reference columns.

Figure 5 Failure shape of the strengthened columns.

Figure 6 Fracture of the weld between horizontal strips and the vertical angle in some strengthened columns.

* 2000

g 1500

•= 1000 S.

--N1 refer —SCNl snce column

/ —SE1

0.5 1 1.5 2

Axial shortening, mm

Figure 7 Axial load versus axial shortening of Group 1.

strengthen columns in Group 2. Figs. 7 and 8 show that the initial stiffness of the strengthened specimens is higher than that of the reference column of the same group. Generally, all the strengthened columns achieved higher maximum axial shortenings than those of the reference columns without steel cages. This indicates the gain of more ductility when steel cage was added. Also, strengthened specimens with steel cage connected to the head achieved higher ultimate loads than those without connections (SCW1 and SCW2) in the two groups. This is due to the difference in the load transfer mechanism of the two cases. When steel cage is not connected to the head,

m 1000

—*—N2, reference column —o—SC2 —x—SCN2 —o—SCW2 —o—SE2

0.0 0.5 1.0 1.5 2.0

Axial shortening, mm

Figure 8 Axial load versus axial shortening of Group 2. Group 1

N1 SCI SCN1 SCW1 SE1 Figure 9 Ultimate load ratio of group 1.

Group 2

2.5 2.0

•s 1.5

a.3 1.0

0.5 0.0

N2 SC2 SCN2 SCW2 SE2 Figure 10 Ultimate load ratio of group 2.

load is transferred to vertical angle from the column body through adhesion between them, while direct load is transferred from the head to the steel angle in addition to the adhesion between the two elements. When spacing between horizontal steel strips is relatively wide (as in specimens SCW1, and SCW2), the ultimate axial load as well as the maximum axial shortenings were less than those corresponding to columns having smaller spacing between strips. It can be observed that the increased spacing between horizontal strip, accelerated the action of buckling of the vertical angles and this led to the relatively quick failure of these columns. Using epoxy grout to fill the gap between the steel cage and the concrete columns slightly enhanced the general behavior of these strengthened columns (Specimen SE1) because the ultimate axial load and the maximum vertical deformations were higher than those with cement grout (specimen SC1). This is related to higher bond strength of epoxy grout which delayed the separation between steel angles and surface of concrete column. To normalize the axial loads of the specimens, a normalized load ratio, is obtained using the following equation:

p - J-J a)

J cu c

Table 4 Main results of the tested columns.

Specimen Group fcu (MPa) Pfailure (kN) Max. axial shortening (mm) Max. axial strain P --P- PoU ~ fcuAc Pfailure

N1 (reference) 1 57.80 1475.00 0.67 0.0017 1.13 1.00

SC1 1 57.80 2570.00 0.99 0.0025 1.98 1.74

SCN1 1 57.80 1990.00 1.00 0.0025 1.46 1.35

SCW1 1 57.80 2310.00 0.83 0.0021 1.77 1.57

SE1 1 57.80 2600.00 1.64 0.0041 2.00 1.76

N2 (reference) 2 47.50 1050.00 0.69 0.0017 0.98 1.00

SC2 2 47.50 2190.00 1.06 0.0027 2.01 2.08

SCN2 2 47.50 2000.00 1.17 0.0029 1.87 1.90

SCW2 2 47.50 2050.00 0.93 0.0023 2.00 1.95

SE2 2 47.50 2090.00 1.04 0.0026 1.96 1.99

Pr„, is the normalized ultimate axial load.

where Ac is the gross concrete sectional area, fcu is the average concrete cube strength. Table 4 shows the values of the normalized load ratio at failure, Pou. It is clear that all the strengthened specimens reached a value more than 150% of those of the unstrengthened columns with the expected exception of columns SCN1, and SCN2 in which, vertical angles were not connected to the head.

6. Load-concrete axial strain behavior

From load and axial concrete strain relationships shown in Figs. 11 and 12, it is clear that the maximum axial strain is higher in the strengthened columns than those without steel cage. This indicates that ductility of the strengthened columns has been raised by about 50% in most of the strengthened cases.

7. Load-vertical steel angle strain behavior

The average axial strain records were obtained from the average readings of the strain indicator and plotted versus the axial load for each group as shown in Figs. 13 and 14 respectively. It is clear that indirectly loaded steel angles in columns (SCN1, and SCN2) showed the least strain values in the two test groups throughout the whole test when compared with the other specimens and the maximum strain in these angles is less than the yield value. This is due to the mechanism of load transfer available in this kind of specimens as previously mentioned. On the other hand, specimens grouted using epoxy grout showed

higher strain value at each load step especially in the case specimen, SE2. This is due to the adhesive effect of the epoxy grout which is more efficient than that of the cement grout.

As a trial to monitor the axial load carried by both the concrete column including the longitudinal reinforcement and the vertical angles, the values of the average vertical strain measured on steel angles were used to obtain the axial stress and the axial load carried by the angles. The obtained results are given in Table 5. From this table, it is clear that the strength of the concrete columns in Group 2 was enhanced due to the use of the steel cage more than those of Group 1 because the ratio of the confining stress to concrete strength is higher in this group.

8. Horizontal strip behavior

The main function of the steel strips is to prevent the premature buckling of the vertical angles and to reduce the horizontal expansion of the concrete section which will result in confining the concrete section. Figs. 15 and 16 show the measured stain values on the horizontal strips. Also it should be mentioned that no strain reading could be obtained during testing column SCW1 due to problems in the strain gauges. All the measured values are less than the yield strain of the strips (about 0.00196). Strain values of columns grouted using epoxy grout are the highest ones comparing with other samples due to better adhesion as mentioned before. Also, the maximum strain values of Group 2 are higher than those of Group

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 Axial concrete strain

Figure 12 Normalized load ratio versus axial concrete strain for Group 2.

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 Axial concrete strain

Figure 11 Normalized load ratio versus axial concrete strain for Group 1.

z JC 2000

A O 1500

3 1000

jr*^ -K-SC1

' -e-scNi -•-SCWl

—A—SEl -Yield strain

0.0000 0.0010 0.0020 0.0030

Vertical angle strain

0.0040

Figure 13 Axial load versus vertical steel angle strain of Group 1.

-4 SC2 -*-SCN2 —+- SCW2 -6 SE2 -Yield strain

0.0000 0.0010 0.0020 0.0030

Vertical steel angle strain

0.0040

Figure 14 Axial load versus vertical steel angle strain of Group 2.

1. This is due to the higher strength of the vertical angles in Group 2 and this indicates that the confining effect is higher in Group 2 than that of Group 1 except for column SE1 where epoxy grout was used.

9. Comparison of the available analytical models

According to Eurocode No. 4 [11], the ultimate load of composite columns can be expressed by the following equation:

N„,Rd = Aafylya + Ac(0.85/ck/yc)+ AJJys

tural steel, the concrete, and the reinforcement, respectively, fy, fck and fsk are their characteristic strengths and ya, yc, and ys are partial safety factors at the ultimate limit states. If all the

0.00000 0.00020 0.00040 0.00060 0.00080 0.00100 Horizontal strip strain

Figure 15 Axial load versus axial strain of horizontal steel strip of Group 1.

.X 2000

n o 1500

13 1000

SCN2 SCW2 -SE2 -

0.0000 0.0002 0.0004 0.0006 0.0008 Horizontal strip strain

0.0010

Figure 16 Axial load versus axial strain of horizontal steel strip of Group 2.

partial safety factors are considered equal to unity for the sake of comparison with the experimental results, Eq. (2) will be reduced to:

= A/y + Ac(0.85/Ck)+ Af

On the other hand, many investigators tried to obtain an accurate equation for the load-carrying equation of reinforced concrete column strengthened by steel angles and horizontal strips. The main factor implemented in these investigations was the confining effect of both vertical angles placed in the corner of the concrete columns as well as the horizontal strips. The main dimensions of the strengthened concrete column used in these equations are given in Fig. 17. Campione [10] reported an analytical expression for the prediction of the load carrying capacity of strengthened reinforced concrete columns with steel angles and strips. The ultimate load capacity is given by:

PuCampoine na ' Aafy ^ Ac ■ fcc + Asfsk (4)

where fcc is compressive strength of confined concrete, and na is a dimensionless ratio of the maximum axial force available in

where Aa, Ac and As are the cross-sectional areas of the struc-

Table 5 Values of calculated ultimate axial loads of steel angles and corresponding concrete column.

Specimen Group P/ailure (kN) Pangie in steel angles (kN) PConCrete load in concrete column (kN) Pangles (%) Pconcrete

N1 (reference) 1 1475 0 1475 0.00 100.00

SC1 1 2570 747.00 1823.00 50.64 123.59

SCN1 1 1990 538.65 1451.35 36.52 98.40

SCW1 1 2310 747.00 1563.00 50.64 105.97

SE1 1 2600 747.00 1853.00 50.64 125.63

N2 (reference) 2 1050 0 1050 0.00 100.00

SC2 2 2190 347.76 1842.24 33.12 175.45

SCN2 2 2000 347.76 1652.24 33.12 157.36

SCW2 2 2150 383.76 1766.24 36.55 168.21

SE2 2 2150 349.20 1800.80 33.26 171.50

' ----1|

Vertical angles

Concrete column Strip

i/JCiJ

Section plan

Figure 17 Details and dimensions of the steel cage.

the vertical angles. The confined concrete of Mander et al. [14] was used to find the stress of the confined concrete,

fcc = fo 1 + 4.74

where JL is the average confining stress due to existence of the steel cage and can be obtained according to the yielding of the horizontal strips or the vertical angles. If the horizontal strip yields first the,

fystrip ' , e(

where S is the spacing between strips, t2 is the thickness of the strip, b is the column width, L2 is the width of the strip, and Jy strip is the yield stress of the strip. But if the vertical angles yields; which is the case in this paper; then:

16M„\/l

fck b(s - L2)

where Mp is the plastic moment of one of the angles related to the existing axial load in the angle. This moment value can be obtained by plastic analysis of the angle. Campoine [12] reported the following equations to evaluate both the plastic axial load and plastic moment as:

Np = 2Ll ' tl ' fya

Mp = ~L~Y~~fya

16 ' fya ' tl

The evaluation of the plastic moment according to the last equation is iterative. The factor na is evaluated using the following equation using the confining stress:

^tfya(t1 'fya ' L2 - ^

2L1 ' t1 ' fya

where qmax is the equivalent confining resultant imposed by each vertical angle which is given by:

qmax = -c 16 ,2 Mp (11)

Is - L2)

As observed by Calderon et al. [9] the behavior of RC columns strengthened by steel caging depends on the determination of the maximum confinement pressures can be governed at rupture by yielding of the angles or by yielding of strips. Two different values of confinement pressures were deduced. The application of this method to determine the load carrying capacity requires an iterative procedure. The values of maximum confinement pressures related to the yielding of steel angles or steel strips are shown below. In this case, the ultimate load carrying capacity is obtained as:

PuCalderon = Ac(0.85fck) + AJ^ + 2.5.Ac 'fL + Nl

where Ac is the area of concrete section, Jl is the equivalent confinement pressures related to the yielding of steel strips or steel angles (can be obtained by the same equation presented in Campoine model) and NL the axial load supported by the cage at the end of a strip and can be obtained by:

Nl = N0 '(1 - e

-mL2 \

where L2 is the width of steel strip, No is the load carried by concrete and m is defined by:

" 2î2El

where 1 is the friction between steel and concrete (taken = 0.50), yc is the concrete Poisson's ratio ( = 0.20), Ec is the concrete elastic modulus, EL is the steel elastic modulus, b is the column width, and t2 is the thickness of the horizontal strip.

It was noted that the coefficient m, in the previous equation was obtained assuming a continuous steel jacket around the body of the column which is different from the case of column strengthened by steel cage where strips are put at a specific distance. Also, the only difference between the two previous models is the way the force in the vertical angles is evaluated.

As a simplification of the above mentioned analytical models, a simple model is proposed in this study to capture all the main characteristics of the strengthened column behavior. The following assumptions are used:

Axially loaded square columns sections are studied. The obtained model can be adjusted to rectangular sections.

Strain values in concrete and directly loaded angles are equal.

Buckling in vertical angles does not occur until yielding starts.

Confining effect due to stirrups is neglected.

The axial strength of the grout between steel angles and

concrete column is neglected.

The vertical angles in the corners are assumed to be rigid in the transverse directions and as a result they do not have any bending deformations. The confining stresses are evaluated in a similar way to that derived by Calderon et al. [9]. The lateral strain is obtained by:

n„ =

where ex, ey, and ez are strain values in X, Y, and Z directions and (ex = ey for symmetry), ox, oy, and oz are stress in X, Y, and Z directions respectively, Ec is the modulus of elasticity of concrete and yc is the Poisson's ratio of concrete (taken = 0.2 in this study). Also we have:

Ox = Oy = —l (16)

And = -^-2 (17)

where fl is the confining stress, Nc is the axial load carried by concrete, and b is the column width. Equation of the strain can be rewritten as:

/i, /i , Nc f,

"EC + EVc + b^TVc - E(mc

The axial stress carried by the horizontal strip can be expressed as:

' 2ht2

where S is the spacing of the strips, l2 is the width of the strip, and t2 is the strip thickness. The axial strain of the strip is: a.

estrip

By ensuring deformation compatibility between the concrete column and the cage (from Eq. (18) and Eq. (20)), we obtain:

/ibs = / (m

2l2 ¿2 Es Ec

b2 Ec c

Therefore the average confining stress in X and Y directions is:

■/i — TT ' i b2 1

2l2 t2 E,

As obtained by Badalamenti et al. [13] the maximum compres-sive strength of the confined concrete is:

where Jco is the unconfined strength of concrete. The confining stress is variable with the increase in the axial load of the

column. Also, the strain corresponding to the maximum concrete stress is defined according to Mander et al. model [14] and given by:

The stress-strain relationship of the confined concrete is modeled as a second degree curve up to the maximum stress point followed by a straight line till failure. The axial strength contribution of the vertical angles is due to the axial shortening of the column if they are directly loaded or due to friction if they are not connected to the head of the column (indirectly loaded angles) and the axial force of one angle evaluated as:

Na - 2 ■ lj ■ ij ■ /s for directly loaded angle

(18) Na — V2 ■ / ■ b ■ S ■ i For indireclty loaded angle

where 1 is friction coefficient (taken = 0.5 as suggested by Badalamenti et al. [13]).

The stress-strain curve for directly loaded steel angles is expresses as:

{Eses if es 6 ey

{/y if e, > ey

where Jy is the yield stress and es is the axial strain in steel angles. It should be remembered that the axial strain of steel is equal to that of concrete to ensure strain compatibility.

For each tested column, the suggested analytical model was applied. The axial strain was increased in a step wise procedure while the transverse strains, the confining stress, the forces in concrete, reinforcement steel and vertical angles were obtained. This procedure was continued till reaching the maximum confined concrete stress and the corresponding axial strain. The obtained maximum load and corresponding maximum strain values are given in Table 6. Also the analytical results are shown in the same table.

It is clear that all the experimental ultimate loads are higher than those obtained by the analytical model. Also the estimation in the case of Group 1 is more accurate than those of Group 2. Also obtained analytical strain values corresponding to the maximum confined stress is higher than the experimental values. This is due to the load control nature of the used testing machine. As a comparison, the results obtained from three available analytical models were calculated and presented in Table 7. It is clear that both the proposed model and the model

Table 6 Comparison between experimental and analytical results.

Group Specimen /cu (MPa) Experimental Analytical

Pu (kN) Maximum axial strain Pu (kN) pe M ximum xi l str in

1 N1 57.8 1475 0.0017 1337.29 0.91 0.0020

1 SC1 57.8 2570 0.0025 2194.60 0.85 0.0043

1 SCN1 57.8 1990 0.0025 1590.58 0.80 0.0043

1 SCW1 57.8 2310 0.0021 2115.48 0.92 0.0036

1 SE1 57.8 2600 0.0041 2194.60 0.84 0.0043

2 N2 47.5 1050 0.0017 1008.34 0.96 0.0020

2 SC2 47.5 2190 0.0027 1562.34 0.71 0.0043

2 SCN2 47.5 2000 0.0029 1330.64 0.67 0.0043

2 SCW2 47.5 2150 0.0023 1497.32 0.70 0.0036

2 SE2 47.5 2150 0.0026 1562.34 0.73 0.0043

Table 7 Comparison between experimental and available analytical model results.

Specimen Group fcu Pu experimental P (analytical) Pu (Eurocode4) Pu (Campoine) Pu (Calderon)

(MPa) (kN) (kN) (kN) (kN) (kN)

N1 1 57.8 1475.0 1337.3 1038.3 1198.3 1033.6

(reference)

SC1 1 57.8 2570.0 2194.6 1785.3 2133.9 1580.4

SCN1 1 57.8 1990.0 1590.6 1785.3 2133.9 1580.4

SCW1 1 57.8 2310.0 2115.5 1785.3 2016.1 1330.9

SE1 1 57.8 2600.0 2194.6 1785.3 2133.9 1580.4

N2 2 47.5 1050.0 1008.3 876.8 1008.3 876.8

(reference)

SC2 2 47.5 2190.0 1562.3 1226.0 1577.3 1126.8

SCN2 2 47.5 2000.0 1330.6 1226.0 1577.3 1126.8

SCW2 2 47.5 2150.0 1497.3 1226.0 1462.5 994.2

SE2 2 47.5 2150.0 1562.3 1226.0 1577.3 1126.8

of Campoine [10] recognize the load sharing of indirectly loaded vertical angles as they are loaded by friction between concrete and steel. Also, Calderon et al.'s model [9] gives the least results as this model evaluates the contribution of the vertical angles through strain compatibility and friction and not based on direct loading case.

10. Summary and conclusions

In this study, an experimental program was conducted on ten axially loaded column's specimens till failure. The main objectives of this paper were to study the behavior and the efficiency of reinforced concrete square columns strengthened by steel angles and strips (steel cage). Size of the steel angle, strip spacing, grout material between column sides and steel angles, and the connection between the steel cage to the specimen head, were the main studied parameters in this paper. The behavior of the tested columns, axial deformation, axial strain of vertical angles and horizontal strips were obtained and analyzed. Also, an analytical model was developed in this study using the simple mechanics and strain compatibility to obtain the ultimate loads of the strengthened columns. The effect of the confining stress due to the steel cage and forces in the vertical angles were calculated considering both directly and indirectly connected angles.

From the obtained results, it was concluded the following:

1. Using vertical angles welded to horizontal spaced strips in order to strengthen concrete column is very efficient and the gain in the axial load capacity of the strengthened columns was very promising. The increase in axial load is between 2.1 and 1.35 of those of the unstrength-ened columns. This gain is due to the confinement effect of the external steel cage, and the ability of the steel angle to resist a part of the applied axial load even in the case of indirectly connected angles. The failure in most of the strengthened specimens was due to the buckling of the steel angle followed by crushing of the concrete columns. Also, it was noticed that axial ductility of the strengthened column increased by 50% in most cases comparing to that of the unstrength-ened columns.

2. In all tested strengthened columns, failure was initiated by the buckling of the vertical angles after their yielding in most cases. No yielding of the horizontal strip was observed. This is due to the relatively large size of the horizontal strips with respect to the vertical angles.

3. Using epoxy grout instead of cement grout slightly enhanced the behavior of the strengthened column. Therefore, it may be economical to use cement grout to fill the gap between the steel cage and concrete column due the higher cost of epoxy grout comparing with that of cement grout.

4. Directly connected vertical angles to the head of the column enables to transfer load directly to the angle. All angles connected in this manner showed yielding before failure of the strengthened column. On the other hand, load was transferred to indirectly connected angles by friction, and the angles did not reach yielding in this case. Nevertheless, the ultimate load capacity of columns with indirectly load angles was between 1.35 and 1.90 of those of the unstrengthened columns.

5. The proposed analytical model predicted the ultimate strength including the confining effect of the outer steel cage. The results obtained by the analytical model showed fairly good agreement with the experimental results.

Acknowledgment

The authors would like to express their gratitude to Mr. Reda

Abu-Elnaga for his help in preparing the test specimens.

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