EFFECT OF CORNER RADIUS ON THE BEHAVIOR OF STRENGTHENED RC COLUMNS WITH DIFFERENT HEIGHTS EMAD E. ETMAN AND ABDEL-HAKIM A. KHALIL Department of Structural Engineering, Tanta University, Tanta, Egypt,
[email protected]
ABSTRACT Efficiency of confining square or rectangular columns, using fiber reinforced polymers - FRP, has been proven to be less than confining columns with circular sections. This loss of efficiency may be due to the inability of the FRP to reach its ultimate tensile strain and the concrete section is not uniformly confined by the FRP jacket. For square or rectangular columns, increasing the efficiency of FRP confinement may be achieved by rounding column corners before wrapping. Also, the column height affects the enhancement of the load carrying capacity and ductility of columns. In this paper, an extensive experimental program consisting of twenty four reinforced concrete, RC, columns, strengthened using Carbon Fiber Reinforced Polymers sheets, CFRP, divided into six groups was conducted to investigate the effect of different heights and corner radius. The experimental results showed that there is a certain effect of the roundness ratio and column heights on the behavior of the strengthened reinforced concrete columns. Analytical modeling of the stress strain relation of the strengthened RC columns considering the effect of column heights and corner radius was proposed. Verification was made using available experimental data. The proposed model showed a good agreement with the experimental results. Keywords: FRP; RC Columns; Strengthening; Confinement; column height; corner radius.
INTRODUCTION The deficiencies of RC Columns may include, but not limited, incapability of carrying the service load due to a substandard detailing or change in the use of building. Other reasons such as deterioration of concrete under severe environmental attack, and structural damage due to fire or earthquakes should not be ignored. Traditional conventional methods like concrete or steel jacketing were used for repair, strengthening, or providing a lateral confinement for the RC columns,١,٢,٣. Over the last few years, there has been a worldwide increase in the use of composite materials for strengthening and rehabilitation of deficient RC structures. One important application of this composite strengthening technology is the use of FRP jackets to provide external confinement for RC columns. This technology still in its emerging stage and more researches are still needed, ٤,٥,٦,٧. Investigation of internal confinement, external confinement, ductility and strength of axially loaded short, circular or rectangular, columns were thoroughly investigated by so many researchers, ٨,٩,.,.,.,١٩,٢٠. From their work, they concluded that confining a circular column greatly enhanced the column capacity and ductility while sharp edged rectangular or square columns showed a little enhancement. One possibility to increase the effectiveness of FRP confinement of
sharp edged square or rectangular columns is to modify the column section from sharp edges to rounded corners. Researchers٢١,٢٢,٢٣, made a comparative study between circular and rectangular columns strengthened using FRP and explored the best treatment for the sharp edge problem in rectangular columns and they concluded that corner radius plays an important role on the efficiency of confinement. Others٢٤, presented a linear finite element method analysis and concluded that larger confining stresses developed at sharp corners. Slender columns and the effect of columns heights on their behavior did not take the proper attention. However, the results of testing long columns as well as analytical modeling to establish slenderness limit in concrete filled fiber-reinforced polymer tubes similar to those developed for conventional RC columns was reported.,٢٥. Others,٢٦, studied the behavior of FRP jacketed concrete columns under eccentric loading with geometrical limitations and reported that further researches are needed in the area of the effect of various cross-section shapes on retrofitting. The efficiency of strengthening RC columns with different slenderness ratios using CFRP wraps was investigated by٢٧, and it was concluded that the increase of slenderness ratios for strengthened columns, reduces the ultimate strength and strain. In this paper, an extensive experimental program was conducted to study the effect of corner radius and column heights on the stress strain behavior, strength, ductility and modes of failure. Along with the experimental program, an analytical was proposed taking into consideration the effect of both corner radius and column height. The model was verified against experimental results and other published analytical models.
EXPERIMENTAL PROGRAM Test Specimens A total of twenty four columns, divided into six groups according to their slenderness ratios,(h/b), where h is the column height and b is the column width, was tested. The slenderness ratio ranged between ٥ and ١٦. Each group consisted of four specimens having different cross sections. The first section was square, the second and third were originally square modified with rounded corners at radii of ٣٠ mm and ٦٠ mm, respectively, and the fourth was circular. All specimens are longitudinally reinforced with four twelve mm diameter high tensile steel bars and transversally by eight mm normal mild steel stirrups spaced at ٢٠٠mm over the column height. Stirrups were spaced at ٥٠mm for a distance ١٥٠mm from both column ends. As shown in figure١.
١٥٠mm
١٥٠mm ٢
١٢ mm
٥
٨ mm/m´
٢
١٢ mm
R٢=٣٠m m ١٥٠mm
R٣=٦٠m m١٥٠mm
١٥٠mm
Fig. ١ Different cross sections and details of reinforcement All specimens were wrapped with one ply of unidirectional CFRP sheets having virtual thickness of ٠.١١٣mm, elastic modulus of ١٥٠Gpa and ١.٥% maximum strain. All specimens were tested under axial load. Details of specimen cross sections, concrete compressive strength, slenderness ratios and specimen notations are listed in table ١.
Table ١: Details of model column specimens Concrete Roundness compressive Cross section of strengthened Group Specimen h/b ratio strength specimen Ri/Rc fco (MPa) S١ ٠.٠ Square R١=٠ S٢ ٠.٤ Square; rounded corners R٢=٣٠mm. ١ ٥ ٢٨.٨ S٣ ٠.٨ Square; rounded corners R٣=٦٠mm. S٤ ١.٠ Circular R٤=٧٥mm S٥ ٠.٠ Square R١=٠ S٦ ٠.٤ Square; rounded corners R٢=٣٠mm. ٢ ٧ ٢٩.٥ S٧ ٠.٨ Square; rounded corners R٣=٦٠mm. S٨ ١.٠ Circular R٤=٧٥mm S٩ ٠.٠ Square R١=٠ S١٠ ٠.٤ Square; rounded corners R٢=٣٠mm. ٣ ٩ ٣٠.٢ S١١ ٠.٨ Square; rounded corners R٣=٦٠mm. S١٢ ١.٠ Circular R٤=٧٥mm S١٣ ٠.٠ Square R١=٠ S١٤ ٠.٤ Square; rounded corners R٢=٣٠mm. ٤ ١١ ٢٩.٢ S١٥ ٠.٨ Square; rounded corners R٣=٦٠mm. S١٦ ١.٠ Circular R٤=٧٥mm S١٧ ٠.٠ Square R١=٠ S١٨ ٠.٤ Square; rounded corners R٢=٣٠mm. ٥ ١٣ ٣٠.٠ S١٩ ٠.٨ Square; rounded corners R٣=٦٠mm. S٢٠ ١.٠ Circular R٤=٧٥mm S٢١ ٠.٠ Square R١=٠ S٢٢ ٠.٤ Square; rounded corners R٢=٣٠mm. ٦ ١٦ ٢٨.٩ S٢٣ ٠.٨ Square; rounded corners R٣=٦٠mm. S٢٤ ١.٠ Circular R٤=٧٥mm h= Height of column, b= Width of column, Ri = corner radius, Rc= radius of largest circle that could be drawn inside the square section
Test Setup and Instrumentation The specimens were tested under an axial compression under the same condition in a loading frame as shown in Fig. ٢. The vertical longitudinal strain, for the square specimens, was measured using four, ٣٠ mm gauge length, mechanical dial gauges fixed to specimen nominally on ٤٠٠ mm gauge length. Only two mechanical dial gauges were used for the circular specimen. Lateral strains were measured on the concrete face at mid height using four electrical strain gauges. For specimens wrapped with CFRP sheets, the lateral strain was also measured at the same level. Buckling of columns with height to width ratios (h/b), ٩, ١٣ and ١٦ was monitored using two mechanical dial gauges fixed against two perpendicular sides. Finally, the axial load was recorded using a load cell. All mechanical instrumentation’s were removed at about ٩٠% of the ultimate load as it was very dangerous to get near to specimens to read them. In a late stage, two steel caps were used to prevent premature failure of the specimens and to guarantee that failure occur at middle third of the specimen.
Loading frame Strain Gauge
Dial Gauge
jack load cell Steel cap Dial Gauge
Cross section Frame base
Fig. ٢ Test setup and instrumentation TEST RESULTS AND DISCUSSION Strength Enhancement and Failure Loads The strength enhancement ratio (fcc/fco), where fco, is the unconfined compressive strength of concrete and fcc is the confined compressive strength of concrete for different slenderness ratios is presented in this paragraph. From figure ٣, it was concluded that there is a clear effect of the shape of the column cross section. The less strength enhancement was noted for the square cross section columns. The strength enhancement increased due to the increase of the corner radius reaching to its maximum enhancement for the circular section. This was noted as a trend for different slenderness ratios. On the other hand, with the increase in slenderness ratio, (h/b), an over all reduction in strength enhancement was observed for each sections geometry.
Strength Enhancemen fcc/fco %
240 Square rounded corners,30 mm radius rounded corners, 60 mm radius Circular
200 160 120 80 40 0 h/b=5
h/b=7
h/b=9 h/b=11 Slenderness Ratio
h/b=13
h/b=16
Figure ٣: Strength enhancement for different slenderness ratios
In figure ٤, a relation showing the failure load against roundness ratio (Ri/Rc) at different slenderness ratios (h/b) ranged from ٥ to ١٦ is presented. It was observed that, increasing of roundness ratio leads to increase of the failure load of the tested specimens.
Failure Load kN
850 h/b=5 h/b=7 h/b=9 h/b=11 h/b=13 h/b=16
750
650
550 0
0.2
0.4
0.6
0.8
1
R i /R c Figure ٤: Effect of roundness ratio on the failure loads The relation between the slenderness ratio and failure load is shown in figure ٥. Deterioration in the load capacity of all tested strengthened RC columns was noted as a characteristic criterion with the increase in slenderness ratio. 900 Square 60mm corner radius
30mm corner radius Circular
Failure Load kN
800
700
600
500 3
5
7
9
11
13
15
17
h/b
Figure ٥: Effect of slenderness ratio on the failure loads
19
Modes of Failure Typical failure of CFRP wrapped concrete columns with either different corner radii or heights are shown in figure ٦.
S٢٠
Figure ٦: Example of modes of failure All the specimens in this investigation, strengthened with CFRP wraps, failed by rupture of the CFRP followed by crushing of concrete core as shown in figure ٧. In specimens tested with steel caps, the failure occurred at the middle third. Other specimens the failure took place at the upper or lower third of the specimen.
Figure ٧:
a.)Rupture of CFRP
b.)Crushing of concrete after CFRP rupture
Ductility Behavior Increase in ductility of the strengthened columns with either rounded corners or circular sections relative to the strengthened square section was clearly noticed. While the percentage of the increase in ductility, compared to square sections, for sections with slenderness ratio h/b=٥ was between ٤٠% and ٥٥% it dropped to values between ٨% and ٢٨% for h/b=١٦. This could be a result of the effect of slenderness ratio, as the enhancement in ductility decreases as the slenderness ratios increase. This is shown in figure ٨.
160
h/b=5
h/b=7
h/b=9
h/b=11
h/b=13
h/b=16
140
Circular
80
60mm corner radius
100
30mm corner radius
120
Square
% increase in ductility compared to square section
180
60 Specimen cross section
Figure ٨: specimen cross section versus increase in ductility
Stress-Strain Behavior For each group, typical stress strain curves were plotted as shown in Figure ٩-a and ٩-b. Figure ٩-a shows the relations for groups ١,٢ and ٣, while results for groups ٤,٥ and ٦ are shown in figure ٩b.The curves to the right represents the plots of axial stress versus axial strain, whereas, the curves to the left show the plots of axial stress versus lateral strains. For all groups, there was a noticeable trend of the increase in stiffness. The square strengthened columns, generally, showed a less increase in stiffness compared to the rounded corners columns as a result of the effect of corner radius in enhancing the strengthened column stiffness. The columns with the circular sections showed the highest stiffness except in group ١ of h/b=٥ as some specimens of this group failed prematurely before using the steel caps. Also, it was observed for all specimens that for the same stress level, specimens with higher slenderness ratios showed increase in both vertical and lateral strain values than specimens with the lower slenderness ratios.
50.0
Stress N/mm2
S1 S3
h/b=5
40.0 30.0 20.0 10.0
Lateral strain
0.0 -0.004
-0.002
Vertical strain
0.000 0.002 Strain
Stress N/mm2
50.0
S5 S7
h/b=7
40.0
0.004
0.006
S6 S8
30.0 20.0 10.0
Lateral strain
0.0 -0.004
-0.002
Vertical strain
0.000 0.002 Strain
50.0 h/b=9
Stress N/mm2
S2 S4
40.0
0.004
0.006
S9 S11
S10 S12
30.0 20.0 10.0
Lateral strain
0.0 -0.004
-0.002
Vertical strain
0.000
0.002 Strain
0.004
Figure ٩-a: Stress strain relationships for groups ١,٢ and ٣
0.006
Stress N/mm2
50.0 S13 S14 S15
h/b=11
40.0 30.0 20.0
Vertical strain
Lateral strain
10.0 0.0 -0.004
-0.002
0.000
0.002 Strain
0.004
0.006
Stress N/mm2
50.0 h/b=13
40.0
S17 S19
S18 S20
30.0 20.0 10.0
Lateral strain
0.0 -0.004
-0.002
Vertical strain
0.000 0.002 Strain
0.004
0.006
Stress N/mm2
50.0 h/b=16
40.0
S21 S23
S22 S24
30.0 20.0 Lateral strain
10.0 0.0 -0.004
-0.002
Vertical strain
0.000 0.002 Strain
0.004
Figure ٩-b: Stress strain relationships for groups ٤,٥ and ٦
0.006
ANALYTICAL MODELING The strengthening of RC columns using FRP wrapping is based on the well-established fact that lateral confinement of concrete can substantially enhance its axial compressive strength and ductility. Pioneers ٢٨,٢٩, defined a strength enhancement model that all researchers after them followed the same basic concept, that was mainly derived for specimens with circular cross section; the model took the following general formulation
f cc¢ f = 1 + k1 l . f co¢ f co¢ In which
f cc¢
and
concrete respectively,
f co¢ fl
(١)
are the compressive strengthens of the confined and the unconfined is the lateral confining pressure defined by equation ٢, and k١ is the
confinement effectiveness coefficient.
fl = In which
2 f frpt frp d
(٢)
f frp is the tensile strength of the FRP, t frp is the virtual thickness of the fibers and
d is the diameter of the confined concrete section. In the previous model the confinement effectiveness coefficient depended on the type of confining material and is mainly dedicated for confined circular specimens and is just applicable in predicting the strength gain in concrete in circular RC columns. However, this needs to be adjusted to work for the noncircular concrete columns in which the concrete is not uniformly confined. As a result of the nonuniform confining pressure, the effectiveness of confinement is greatly reduced٣٠,٣١. A model for the stress strain behavior of square or rectangular cross section columns was presented٣٢.
s c = Ec e c and
( Ec - E 2 ) 2 2 e c for 0 £ e c £ e co 4 f co¢
s c = f co¢ + E2e c
for
e c ³ e co
(٣)
(٤)
where Ec is the modulus of Elasticity of unconfined Concrete
ec
is the peak axial strain.
E٢ is the slope of the linear second portion and is given by equation ٤.
E2 = In which
e cc
is the confined concrete strain.
2 fl
e cc
(٥)
Previous models were, basically, derived either for circular or noncircular, (square or rectangular), section. The effect of corner radius was considered by some of the authors, however, a comparison between the existing models٣١,٣٢ and the experimental data showed that these models overestimate the section capacity especially for long columns. For this reason, a new factor for the corner radius of the specimen was proposed. On the other hand, the effect of specimen height was not fully established in the literature. In this paper a new proposed factor to show the effect of specimen height, based on experimental results, is concluded. The two new factors are stated in the following.
Effect of specimen height The effect of specimen height and slenderness ratio was found to reduce the stress capacity of the section. Therefore, a new factor, k٢, to account for the effect of slenderness ratio was proposed as follow:
æ æ e - ec ö ö ç C1 - C1 ç co ÷÷ ÷ ç e 3 ç co è ø ÷ h ´ 10 for 0 £ e £ e k2 = ç ÷ c co A ç ÷b ç ÷ è ø
(٦)
In which C١ = constant = ١١.١٨ , A, = Cross section of Column, and h/b = slenderness ratio
k2 =
3 C1 h ´ ´ 10 for e c ³ e co A b
(٧)
Effect of Corner Radius The effect of corner radii is proposed as a new factor, k٣, this factor is represented by the following formulation. 2
æR ö æR ö k 3 = 98.5 ´ çç i ÷÷ + 23.3 ´ çç i ÷÷ è Rc ø è Rc ø In which
(٨)
æ Ri ö çç ÷÷ is the roundness ratio of the section è Rc ø
Final Form of Proposed Model Based on the above discussion, the final form of the proposed model can be expressed as follows:
æ ( Ec - E 2 ) 2 2 ö s c = çç Ec e c e c ÷÷ ´ (1 + k 3 ) - k 2 for 0 £ e c £ e co 4 f co¢ è ø and
(٩)
s c = ( f co¢ + E2e c ) ´ (1 + k 3 ) - k 2
for
e c ³ e co
(١٠)
All units are in mm and Newton.
Verification of The Proposed Model To verify the proposed model, it was compared with Teng model٣٢, as one of the latest verified models, and then both models were plotted against the experimental data obtained within this research program. Figure ١٠ shows a comparison between Teng et-al model, which does not consider the specimen height, and the proposed model. From the figure, it is clear that the effect of the specimen height is rational and very well represented. As the slenderness ratio, (specimen height), increases, the stress required to produce the same strain decreases. These results coincide rationally with the experimental obtained data.
40
Stress N/mm2
30
20
Teng et-al,2002,circular h/b=5, circular h/b=7, circular h/b=9, circular h/b=11, circular h/b=13, circular h/b=16, circular
10
0 0
0.002
0.004
0.006
Strain Figure ١٠: Stress Strain Relationships; Teng et-al model versus the new proposed model. Figures ١١ to ١٤, represents the relationships between the experimental stress and strain versus the theoretical values based on Teng model as well as the proposed model. The figures were chosen to represent short columns, (h/b=٧ and h/b=٩), and long column, (h/b=١٣ and h/b=١٦). From figures ١١ and ١٢, it could be noticed, for short columns, that there is a close agreement between Teng model, proposed model and experimental results for circular sections and sections with Ri/Rc = ٠.٨. From figures ١٣ and ١٤, generally the proposed model showed better agreement
with the experimental results. However, considering that Teng model represents short columns, the comparison showed that this model is over estimating the behavior of the slender columns.
h/b=7 40
Stress N/mm
2
30
Theoretical,Circular Theoretical,60 mm Theoretical,30mm Theoretical,Square Exprimental,S8◌ُ Exprimental,S7 Exprimental,S6 Exprimental,S5 Teng et-al model
20
10
0 0
0.002
0.004
0.006
Strain Figure ١١: Verification of proposed model at h/b=٧
h/b=9 40
Stress N/mm
2
30
Theoretical,Circular Theoretical,60 mm Theoretical,30mm Theoretical,Square Exprimental,S12 Exprimental,S11 Exprimental,S10 Exprimental,S9 Teng et-al model
20
10
0 0
0.002
0.004 Strain
Figure ١٢: Verification of proposed model at h/b=٩
0.006
h/b=13 40
Stress N/mm
2
30
20
Theoretical,Circular Theoretical,60 mm Theoretical,30mm Theoretical,Square Experimental,S20 Experimental,S19 Experimental,S18 Experimental,S17 Teng et-al model
10
0 0
0.002
0.004
0.006
Strain Figure ١٣: Verification of proposed model at h/b=١٣
40 h/b=16
Stress N/mm
2
30
20 Theoretical,Circular Theoretical,60 mm Theoretical,30mm Theoretical,Square Experimental,S24 Experimental,S23 Experimental,S22 Experimental,S21 Teng et-al model
10
0 0
0.002
0.004 Strain
Figure ١٤: Verification of proposed model at h/b=١٦
0.006
CONCLUSIONS The experiental and analytical investigations on the effect of roundness ratio, Ri/Rc, , and slenderness ratio, h/b, on the behavior of RC strengthened columns yielded the following conclusions: (١) The less strength enhancement was noted for the square cross section columns. (٢) Icreasing of roundness ratio leads to increase of the failure load of the tested specimens. (٣) Deterioration in the load capacity of all tested strengthened RC columns was noted as a characteristic criterion with the increase in slenderness ratio. (٤) Circular or rounded corners sections of strengthened RC columns exhibited higher ductility than the strengthened square ones. (٥) The enhancement in ductility for short columns was higher than that of the long columns. For sections with slenderness ratio h/b=٥ , the enhancement in ductility ranged between ٤٠% and ٥٥%, however, it dropped to values between ٨% and ٢٨% for h/b=١٦. (٦) The increases in roundness ratio lead to increase in specimens’ stiffness. (٧) Stress and strain models based on tests of short columns cannot be applied for long (slender) column without slenderness ratio modification. The proposed model, which took into consideration the roundness ratio and slenderness ratio, showed a very good agreement with the experimental results. The model also showed a reasonable agreement with Teng model, thought; it was made for short columns.
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