CICE 2010 - The 5th International Conference on FRP Composites in Civil EngineeringSeptember 27-29, 2010 Beijing, China

Study on the Flexural Capacity of Concrete Beam Hybrid Reinforced with FRP Bars and Steel Bars

Jiwen Zhang (jwzhang@vip.163.com) WenJie Ge & Hang Dai & Yongming Tu College of Civil Engineering, Southeast University, Nanjing, China

Key Laboratory of Concrete and Prestressed Concrete Structure of Ministry of Education, Southeast University, Nanjing, China

ABSTRACT: Two Nominal reinforcement ratios and three failure modes were put forward according to the characteristic of FRP bar and the criterion of appropriate hybrid reinforcement beam was given. Flexural ca-pacity of appropriate hybrid reinforcement beam was analyzed according to the theory of reinforcement con-crete and flexural capacities simplified calculate formula of appropriate hybrid reinforcement beam was pro-posed. three different area ratio of FRP bar to steel bar hybrid reinforced concrete beams, one FRP reinforced concrete beam and one reinforced concrete beam static flexural test were made and the tested results show that the flexural capacities calculate by proposed simplified formula was close to the tested value.

1 INSTUCTION

The fiber reinforced polymer tendons (FRP tendons) as a substitute for steel bars used in concrete struc-ture is an effective method which could resolve the problem of concrete durability aroused by corrupt of steel bars and meet the requirement of special struc-ture such as protecting electromagnetic interference. Recent years, researching about the capability of FRP tendons and concrete structures reinforced with FRP tendons are focus of the civil engineering, new structures are widely used in the coastal structures and the subway engineering. But FRP tendons have characteristics of high strength, low elasticity modulus and linear deformation, these characteris-tics lead to the phenomenon of brittle failure, larger crack width and deflection which restrict the appli-cation of FRP structure in civil engineering. The hybrid reinforced concrete structure combine the advantages of reinforced concrete structure and FRP structure together, it could resolve the problem of the durability of RC structure and brittle failure of FRP structure by laying the FRP tendons in the cor-ner area where concrete easy corrupted, and it still need to keep on loading to up to the ultimate load af-ter the steel bars yield and shows certain safety fac-tor and good ductility. So it is a goodish reinforced format.

2 BASIC ASSUMPTION

1) Plane section assumption, the section keep plane under load and the strain of concrete and bars were linear to its distance to neutral axis. 2) The bars and concrete has good bond behavior, the strain of steel bar was the same with FRP bar in the same place. 3) Neglect concrete tensile force after crack. 4) Constitutive relationships were simplified. Constitutive relationships of steel bar was simplified as two line model, when εs<εy, σs=Esεs, when εy≤εs≤εu, σs=fy. fy yield strength of steel bars, Es elas-tic modulus of steel bars, εu ultimate tensile strain of steel bar and it was consider as 0.001.

Figure.1 Stress-strain curve of steel bar Constitutive relationship of concrete was simplified as follows: εc≤ε0, σc=fc(1-(1-εc/ε0)n) (1)

εc>ε0, σc=fc

ve strain of concrete, consider it as .0033 while it calculate more than 0.0033, fcu,k, haracteristic value of compressive strength of con-

crete cube, n coefficient, consider it as 2.0 while it calculate value more than 2.0.

(2) ε0=0.002+0.5 (fcu,k -50) × 10 -5 (3) εcu=0.0033-(fcu,k -50) × 10 -5

(4) n=2-(f -50)/60 (5ε compressive strain of concrete, σ concrete com-pressive stress corresponding to ε , f axis compres-sive strength of concrete, ε concrete compressive strain while the stress up to f , consider it as 0.002 while the calculate value less than 0.002, ε ulti-mate compressi

cu,k ) c c

c c

0

c

cu

0c

Figure.2 Stress-strain curve of concrete he stress-curve of FRP keep linear, σT f=Efεf, Ef lastic modulus of FRP bars, εfu ultimate strain of

ffu ultimate strength of FRP bar, εfd design strain of FRP bar , ffd design strength of FRP bar.

eFRP bar,

Figure.3 Stress-strain curve of FRP bar

h

einforcement ratio: ρ.

strength: ρ1. ρ1=ρs+ρf ffd / fy

3) Nominal reinforcement ratio conversion by elastic

4 FAILURE MODES OF NORMAL SECTION

Failure modes of normal section could divide into three kinds as following according to the constitu-tive relationships of steel bar and FRP bar.

3 REINFORCEMENT RATIO

Three kinds of reinforcement ratio were put ward for the different elastic modulus and ultimate strengtbetween steel bar and FRP bar 1) Practical rρ=ρs+ρf

(6)

ρs =As /(bh0), ρf =Af /(bh0), As area of steel bars, Af area of FRP bars, b section width, h0 section effec-tive height. 2) Nominal reinforcement ratio conversion by

(7)

modulus: ρ2. ρ2=ρs+ρf Ef /Es (8)

Figure.4 Failure modes of normal section

on rete beam and it was

brittle failure.

-

εs=εf

s: the steel bar had yield and

maximum compressive strain,

Boundary relative neutral axis height could define according to plane section assumption and the given value of εcu. Boundary failure 1: ξnb1=xn1/h0=εcu/(εcu+εy)=1/(1+fy /(Es0.0033)) (9)

1) εc=εcu, 0<εs=εf<εy Failure characteristics: the steel bar has not yield and the stress of FRP bar is small while the concrete up to the ultimate compressive strain, this situatisimilar to the over bar of concnot allowed for its 2) εc=εcu, εy <εs=εf<εfd Failure characteristics: the steel bar had yield and the stress of FRP bar is just a little small than or equal to design stress while the concrete up to the ultimate compressive strain, this situation was ex-pected for its ductile failure. 3)εc<εcu, εfd <Failure characteristicthe stress of FRP bar is more than design stress or the concrete up to thethis situation was not allowed for its brittle failure.

Boundary failure 2: ξnb2=xn2/h0=εcu/(εcu+εfd)=1/(1+εfd /0.0033) (10)

a. boundary state 1 b. boundary state2 Figure.5 Boundary state

Assume the height of neutral axis is xc, h0 section effective height, so boundary relative neutral axis

e 1 oc-cured, when ξnb2≤ξ≤ξ failure mode 2 occured, when ξ<ξnb2 failure m

orce equilibrium:

εfd), for concrete grade less than C50, formula 11 could rewrite as follows according to formula 1-5,

height ξ=xc/h0, when ξ>ξnb1, failure modnb1

ode 3 occurred. According to internal f

cx

0

c s s f fb dx f A f A (11)

xc=εcuh0/(εcu+

00

2c s s3( )cu f

f ff bh f A f A

(12)

For boundary failure 1:

02

3(s f )f c

s y cuE f y

E f

(13)

For boundary failure 2:

02

3( )s fy y cu fdf ffd c

f f

So appropriate reinforcement should

(14)

meet the following requirement simultaneously:

01

2

3( )fd c

s fy y cu

f f

f f

fd

(15)

02

2

3( )f c

s fs y cu y

E f

f

E

(16)

5 APPROPRIATE HYBRID EINFORCEMENT BEAM

In order to calculate convenience, assume k1 ratio of average compressive stress to compressive strength of concrete, k2 ratio of the distance of the compress force point to the compressive edge to the height of compress zone.

1 0( )

n

c n

xk f bx bdy (17)

02

1

( )n

n nc n

xby

k x xk f bx

dy (18)

k1, k2 could obtain according to the for the Constitu-tive relationship of concrete for the maximum com-pressive strain εc.

00 1 2

0 0

1 / 4, (1 ),

3 3 /c c c

cc

k k0

19) (

20

0 1 20

6 ( / ), 1 ,

3 12 4( /c c

cc

k k

0 )

(20)

Concrete compressive stress figure was transferred into equal rectangle stress figure. The height of rec-tangle is γ1xc, the compressive stress is γ2fc, keeping the force and its location unchanged, γ1=2k2, γ2=2k2/k1, when εc>0.003, εc has no obvious effect on γ1 and γ2, taken the ultimate concrete compres-sive strain as 0.0033 could obtain γ1=0.823, γ2=1.03, consider γ1=0.8, γ2=1.0 for simplified. So boundary relative neutral axis height could obtain ξb1=0.8ξnb1, ξb2=0.8ξnb2, according to internal force equilibrium:

c y s f f ff bx f A E A (21)

0.0033(0.8 / 1)f (22)

to equation 21 and assume Taken equation 22

y s

c

fA

f

,

0.0033 f fEB

cf

, so flexural capacity of

plify calculate as following: 2

0 (1 / 2)u cM f bh

appropriate hybrid reinforcement beam could sim-

(23) 2( ) 3.2B

2

A B A B

(24)

ERIMENTAL VERIFICATION

Three different area ratios of BFRP tendons to steel

able1 Mechanical performance of BFRP bar and steel bars a

6 EXP

bars hybrid reinforced concrete beams, one BFRP reinforced concrete beam and one RC beam static bending test were made. The size of the member was b×h×l=200 mm×300 mm×2500 mm, C35 fine aggre-gate concrete was used and the concrete cover was 23 mm, BFRP tendons of diameter 8 mm and steel bars of diameter 10 mm were used as the longitudi-nal main bar, steel bar of diameter 8 mm was used as stirrup bars. Mechanical performance of concrete was list in table 1, mechanical performance of BFRP bar and steel bars was list in table 2 and test set-up was show in figure. 1. T

Bar Diameter/mm Ef /GPa fy /MPa fu /MP

Steel 10 180 360 533 Steel 8 180 423 585 BFRP 8 55 — 880

* The Steel bars surface form of diameter 8 m nd 10 s

ft

m a mm iscrewed; the surface form of BFRP bar is screwed.

able 2 Mechanical performance of concrete (MPa) Tfcu Ec fc 42 3.3 4 28.1 2×10 .4

Figure. 1 Test set-up

able 3 Comparison of theory value and tested value of flex-

Mu,e/Mu,

T

ural capacity

Specimen FRP bar Steel bar Mu,t Mu,e

t

FS1 4 6 68.9 74.4 1.08

FS2 5 5 68.8 73.5 1.07

FS3 6 4 68.7 72.8 1.06

F1 0 9 66.5 67.6 1.02

S1 10 0 69.8 67.9 0.97 * Unit of Mu,t and Mu,e is kN·m.

Flexural capacity Mu,t calculate by proposed simpli-fied formula using the measured strength of bars and concrete and ultimate bearing capacity Mu,e meas-ured by the test were list in table 3. As can be seem from the table, average value of Mu,t / Mu,e u=1.04, coefficient of variation δ=0.002.

7 CONCLUSIONS

Based on the constitutive relationships of materials, two Nominal reinforcement ratios, three failure modes were put forward and the criterion of appro-priate hybrid reinforcement beam was given. Flex-ural capacity of appropriate hybrid reinforcement beam was analyzed and simplified calculate formula was proposed. three different area ratio of FRP bar to steel bar hybrid reinforced concrete beams, one FRP reinforced concrete beam and one reinforced concrete beam static flexural test were made and the tested results show that the flexural capacities calcu-

late by proposed simplified formula was close to the tested value.

8 ACKNOWLEDGEMENTS

This work is supported by the National Natural Sci-ence Foundation of China (50808039), the Chinese National High Technology Research and Develop-ment Program (2007AA03Z550), the Natural Sci-ence Foundation of Jiangsu Province, China (BK2008148, SBK200921303), the Doctoral Foun-dation of Ministry of Education, China (20070286095), and the State Key Laboratory of Subtropical Building Science, South China Univer-sity Of Technology, China (2008KB24).

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