Teoria del Contml y vlncuio Sodal

FRP wrapping used in retrofitting concrete columns is considered one of the simplest and most efficient applications, as FRP has excellent material characteristics like high strength to weight ratio and high corrosion resistance FRP behaves elastically, and therefore its confining strength increases proportionally with increasing the force applied. The literature review in this section cares about FRP wrapping only and does not consider the effect of FRP tubes, as the mechanics is different. This section reviews the previous extensive work concerns FRP concrete columns confining chronologically. Hence, the review is classified according to its author/s.

2-2-1 Past Work Review

Fardis and Khalili (1981)

Fardis and Khalili (1981) focused on concentrically loaded short circular columns. They performed short term compression tests on 3 *6 in. and 4*8 in. cylinders and concluded that there is agreement between the strength and the axial stress suggested by Richart et al. (1928) and Newman and Newman equations:

l c

c f f

f = ^'+4.1 2-224

86 . 0

'

' 3.7 





 + 

=

c l l c

c f

f f f

f

2-225

Fardis and Khalili (1982)

Fardis and Khalili (1982) approximated the failure axial strain, using experimental results, in the following form:

57 0005 '

. 0 002 . 0

c f

cu Df

t + E

ε ≈

2-226 And the stress equation can be expressed using a simple hyperbola having initial slope of Ec:







 −

+

=

cu cc cc c

c c c

E f f E

ε ε ε 1 1

2-227 where Ecc is the tangent modulus at failure

Katsumata , Kobatake, Takeda (1988)

Katsumata et al. (1988) tested ten 7.87 * 7.87 in. rectangular specimens wound with carbon fiber. They concluded three outcomes; ultimate displacement and energy dissipation are linearly proportional to carbon fiber quantity, earthquake resistance capacities results from unbinding concrete with carbon fiber do not differ from these of wound concrete directly to carbon fiber and using equivalent quantities of carbon fiber or steel hoops, using effective strength ratio, the earthquake resistance capacity can be correlated.

Ahmed, Khaloo and Irshaid (1991)

Ahmed et al. (1991) tested 33 concrete cylinders confined with fiberglass wire. They concluded that the increase in confined strength decreases with increasing the unconfined concrete strength. And by decreasing the fiber wires spacing, the values of maximum strain at failure and strain at maximum stress increase. Flat or near flat post peak curves can be generated in stress-strain curves by increasing amount of confinement. Ahmed et al. (1991) suggested using the same equations developed for steel spirally reinforced concrete by Ahmed et al. (1982) by replacing f’c and εco by fcc and εcc in the stress equation:

58 over the concrete confined with steel tubes. The specimen used for comparison has diameter of 76.2 mm for steel tubes confining compared to 101.6 mm for fiberglass wiring confinement.

Demers and Neale (1994)

Demers and Neale (1994) conducted experimental work on 20 circular and square columns, fourteen of which were confined with 1-3 plies of FRP, glass and carbon. The circular columns were 152 mm in diameter and 305 mm high. Whereas, the square ones were 152 mm wide and 505 mm high. The results were compared against well known proposed models that were developed for steel hoops and spirals confinement. Demers and Neale (1994) reported that all the models overestimate the ultimate strength except for Cusson et al. (1992). They suggested stress function as follow:

( ) (

^'

)

They suggested conducting more accurate analysis and further tests to generate the function g(E_ft_f,1/f’_c). They also reported that 70 % increase in strength and up to seven times strain at

59

failure can be found for wrapped columns compared to the unconfined ones. It was observed that strength improvement in squared columns is very small compared to the rounded ones.

Taniguchi, Mutsuyoshi, Kita and Machida (1993)

Taniguchi et al. adapted Sakai (1991) equation for concrete confined with lateral steel to fit the FRP behavior as follow:

( )

lateral steel and FRP. However no FRP parameters showed in the proposed equations.

60

Hoppel, Bogetti, Gillespie Jr, Howie and Karbhari (1994)

Hoppel et al. (1994) related the hydrostatic pressure of concrete wrapped with composite to the axial stress:

c f f

DE E P t

P=σ( =0)υ

2-237

where P is the hydrostatic pressure, σ(P=0) is the concrete compressive failure strength at atmospheric pressure,

Saadatmantesh, Ehsani and Li (1994)

Saadatmanesh et al. (1994) utilized Mander et al. model (1988) that was originally generated for concrete confined with steel hoops or spirals, in developing a computer program that calculates the ultimate moment and curvature at failure for columns. Interaction diagrams for different cases were plotted and compared to the unconfined case from Chai et al. (1991).

However, no evidence of the proposed procedure accuracy was conducted.

Nanni and Bradford (1995)

Nanni and Bradford (1995) tested 150 * 300 cm fifty one cylinder specimen of unconfined concrete and confined with FRP. Aramid FRP tape, glass filament winding and glass aramid pre formed shells are the three types used in confining. Nanni and Bradford (1994) reported that unconfined specimens and specimens confined with Aramid FRP tape with spacing of 50 mm had shear cone failure mode. Whereas the one with less than 50 mm spacing and glass filament wound specimens failed by shell rupture. And finally specimen confined with glass aramid pre-formed shells had joint failure. They showed that the models; Mander model (1988)

61

and Fardis and Khalili (1982) are correlated and accurate in predicting the ultimate strength.

However, they underestimated the ultimate strain and did not represent the stress strain curves shape. They also suggested bilinear stress strain curve with a bend over point at unconfined strength and 0.003 for strain.

Howie and Karbhari (1995)

Howie and Karbhari (1995) concluded through testing study that setting plies in the hoop direction gives the largest increase in strength.

Harmon, Slattery and Ramakrishnan (1995)

Harmon et al (1995) developed a new model for stress-strain prediction based on linear elastic deformation and shear slip. Although the void collapse was mentioned as one of the parameter that influences the stress strain behavior, it was disregarded due to its possible small effect by having a well compacted concrete mix. Harmon et al. (1995) defined the confinement efficiency ratio as follow:

t r

z c

f f

be R f

+ +

=

'

5 . 4

2-238

(

/1000

)

^0.25

5 . 0 6 .

0 k_s

b= +

2-239

( )

^{/ 2}

2 .

0 f b

z =− σ_r + _t 2-240

where ks is the secant stiffness ft is the split cylinder strength and fr is the radial stress. It was observed that stress strain curves plotted using the proposed model were having bilinear pattern.

62 Mirmiran and Shahawy (1995)

Mirmiran and Shahawy (1995) introduced a model developed specifically for concrete wrapped with FRP that considers concrete lateral expansion and the fiber composite non ductile behavior. They utilized Madas and Elnashai (1992) equation that relates the axial and radial strain to predict the radial strain. Consequently the calculated radial strain is used to find the lateral pressure as follow:

r

where εr is the radial strain.Finally the lateral pressure f_l was used to find the equivelant stress using Mander model (1988).

Hosotani , Kawashima and Hoshikuma (1997)

Hosotani et al (1997) conducted experimental work on 10 cylinder specimens and 12 square specimen that are 600 mm high and 200 mm wide. The stress strain model proposed by idealizing the experimental stress strain curves as follow:

1

63

The proposed model compared well with the experimental work done by the same researchers.

They noted that ρ f becomes effective for values more than 1%.

Miyauchi, Nishibayashi and Inoue (1997)

Miyauchi et al (1997) tested cylindrical specimens ( 10 cm wide * 20 cm heigh and 15 cm * 30 cm heigh) wrapped with one, two and three carbon fiber sheets. They found that

64

compressive strength and corresponding strain improve with increasing the number of FRP sheets. The proposed ultimate compressive strength equation was adapted from Richart model as follow :

And the proposed stress equations are as follow:



65

( ) ( ( ) )

2

2 1 2 ' 2 '

' '

' 4 2 2

2

co

co c co cu c cu c c c

cu

c f f f f

f

ε

ε ε

ε ε

ε ε λ



 



− − + − +

=

2-264

The proposed model (Figure (2-19)) was well correlated to the experimental work done by Miyauchi et al (1997)

f

^cu

ε

^cu

ε '

^t

f'

^t

A x ia l S tr es s

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