Fracture Mechanics of Concrete Structures, Proceedings FRAMCOS-2, edited by Folker H. Wittmann, AEDIFICATIO Publishers, D-79104 Freiburg (1995)

HARDENING-SOFTENING BEHAVIOR AND MINIMUM REINFORCEMENT OF RC BEAMS

K. Rokugo, N. Kurihara, T. Ito, Y. Uchida, and W. Koyanagi Department of Civil Engineering, Gifu University, Gifu, Japan

Abstract The flexural failure behavior of RC beams made of different kinds of concrete and reinforcing materials is investigated. High strength concrete (HSC), aramid fiber and steel fiber reinforced concrete (AFRC and SFRC) and continuous fiber reinforced plastic (FRP) grid are included in addition to normal strength concrete (NSC) and ordinary steel bars. The favorable failure modes of RC beams are discussed. In the case of beams reinforced with steel bars, the minimum reinforcement ratios were 0.15% for NSC beams, 0.4% for HSC beams and 1.0% for SFRC beams in the range of this study. High performance non-metallic RC beams could be produced by combining AFRC and FRP grid.

1 Introduction

Fracture Mechanics of Concrete (FMC) covers modeling of fracture behavior of concrete, numerical analysis of fracture behavior of members, applications to structural design, etc.

In addition to conventional structural design methods based on simple

1125

equations load stress estimations, more accurate structural design methods based on actual failure behavior of structural members are needed, which can be calculated through numerical analysis. For the more accurate design methods, FMC can propose constitutive models including softening region and reliable methods to calculate softening, localization and bifurcation behaviors of structures. For the conventional design methods, FMC is helpful to improve accuracy of design equations taking account of knowledge such as size effects. FMC can also give more appropriate explanations of minimum reinforcement relation to hardening-softening behavior.

this test results on the flexural failure behavior of RC beams made of different kinds of concrete and reinforcing materials are presented. strength concrete (HSC), steel fiber and aramid fiber concrete (SFRC and AFRC) and continuous fiber reinforced plastic grid are included in addition to normal strength concrete (NSC) steel reinforcing bars. The distribution deformation beams the hardening condition up to the peak load

the deformation in the softening condition after the peak load are discussed relation to the minimum reinforcement. The favorable modes RC beams are also discussed.

2 mode

To discuss favorable failure modes of members, three types of load­displacement curves A, B and C of beams in flexure are illustrated in Fig. 1 [Rokugo et al. 1993]. The characteristics of curve are superior to those B and C in the following aspects.

" The ultimate is the highest (large load carrying capacity). " The displacement at the ultimate is the largest (large ductility). .. The toughness (area under curve) is the largest (high toughness). " The initial is the largest (high stiffness). " The curve turns at point "a" before the ultimate. This gives

warning of coming ultimate load point (warning of failure). " The beam does not break, and consequently beam portions may not

suddenly (prevention of breaking).

The load and the ductility should be chosen considering the economical aspects, the balance of the performances, etc. The warning through the turning of the curve is not always necessary but is valuable in many cases. prevention of breaking is not essential. This is not necessary when the breaking never occurs because the failure of another part precedes or when the dropping of broken portions does not

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cause serious damage. Moreover, prevention not easy to be achieved the actual cases of large , .... _ ... ...,_.,. ... .._. . ..., ...

own weight. general,

tension

region.

coming ultimate. region but

Moreover, steel (10% or more

strength steel contributes

elongation at strength

regions)

; ;

/Curve C ;

;

/ c Curve B i ,0 ........

// -------x d i,

b

// x :nrieaKmg ~I

Displacement

Fig. 1.

p

Steel

0 ···· .... ~ .. -H·· 0 8

curves

~ Tension

p p .

0 Concrete

Lo.act--ctu;p1::1ce:me:nt curves of specimens

~vz?.~::.nding pc PL p~ Displacement o 8 o 8

Pmm < P < Pbal < P P < Pmm

(c) Load-displacement curves of RC beams

Fig. 2. and softening curves

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3 Failure behavior beams reinforced with FRP grid

reinforced plastic (FRP) rods and grids, which are made of continuous fibers such as aramid, carbon, glass, etc. bound with resin,

potential to be substituted for steel bars in reinforced and prestressed concrete structures. FRP rods and grids are light, strong, and free from corrosion. They are, however, brittle and have no yield

Their elongation at rupture is small and their Young's modulus as compared with steel bars. FRP grids have been used, for

example, instead of steel wire meshes in shotcrete. this chapter, the flexural failure behavior of concrete beams made

kinds of concrete and reinforced with FRP grid is discussed.

[ ] : lOcm grid space

~ JoDf :!~::; ~.·.·.··.~!18[33]

42[92] 8 : mm

3. Sizes of grid

Displacement meter

iE 500 "IE 500 ;.IE 500 >i

Unit: mm

Fig. 4. Loading tests

Table Test conditions of beams reinforced with FRP grid

S ecimen size mm FRP rid Series Concrete

Width Span Depth Bar No. Grid space, mm Moments an PH6 60 PH8 High 80

strength 100 1500 [500] 110 G4 50 concrete 140

180 60

Normal 80 strength 200 1500 [500] 110 G4 100 concrete 140

PN18 180 PF8 Aramid 80 PF14 fiber rein. 100 1500 [500] 140 G6 50 PF23 concrete 230

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3.1 Experimental procedures As indicated in Table 1, thirteen series of concrete beams (two beam specimens in each series) were made using three kinds of concrete (high strength concrete, normal strength concrete and aramid short reinforced concrete (AFRC)) and FRP grid as reinforcement. The depth of beams were varied. FRP grids (bar number: G4 and G6) were made of continuous glass fibers. properties are given in Table 2 their shapes are shown in Fig. 3, where the grid spaces are 50 mm or 100 mm. The thickness of cover concrete was 10 mm. Properties three kinds of concrete are given in Table 3. Properties of short fibers used in AFRC are shown in Table 4. As illustrated in 4, beam specimens were loaded at third points (moment span: 500 The applied load and the displacement (deflection) at loading were recorded.

Table 2. Properties of FRP grids

Tensile Young's Guaranteed Sectional Grid space Bar No. strength modulus maximum load area

kgf/cm2 kgf/cm2 tonf mm2 mm

G4 6000 3.0X 105 0.78 13 50or100

G6 6000 3.0X 105 2.10 35 50

Table 3. Properties of concrete including AFRC

Strength Young's Age at Concrete kgf/cm2 modulus testing

Compression Tension Flexure kgf/cm2 days High strength

766 59.7 96.0 3.85X 105 19 concrete Normal strength

327 27.4 46.4 2.94X 105 11 concrete Aramid fiber

801 (103) 156 3.36X 105 23 reinforced concrete*

* AFRC contains 2% of aramid short fibers

Table 4. Properties of aramid short fibers for AFRC

Size of fiber Specific Tensile Young's Diameter Length gravity strength modulus

mm mm kgf/cm2 kgf/cm2

0.4 30 1.39 3.0X 104 7.0X 105

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I ft = +

beams. crack)

are averaged

I (0.85 + 4.5d I Leh)

1130

account

Table 5. Test results of beams reinforced with FRP grid

Load at first crack, Per, tonf Number Maximum Ultimate

Series Experi- Esti- Esti- of load due to load per

ment ma ti on mation cracks FRP grid, one FRP -1 -2 Pu, tonf bar, tonf

PH6 0.210 0.225 0.246 7 0.341 0.842 PH8 0.355 0.396 0.413 5 0.472 0.869 PHll 0.762 0.757 0.742 1 0.777 0.983 PH14 1.22 1.26 1.18 1 1.03 0.986 PH18 1.94 2.04 1.82 1 1.38 1.03 PN6 0.243 0.195 0.213 5 0.343 0.890 PN8 0.447 0.371 0.385 4 0.510 0.915 PNll 0.727 0.661 0.652 2 0.736 0.968 PN14 1.13 1.14 1.08 1 1.01 1.01 PN18 1.76 1.94 1.74 1 1.24 0.923 PF8 0.400 0.705 - 24 1.51 2.87 PF14 1.20 2.17 - 17 3.50 3.47 PF23 2.87 5.56 - 15 6.58 3.89

2 C.1 1 r 11 1~ r 'SJ sz

I J I s 0.4 li

li li

4-< ~0.4 = 0 0 ..... ..... "t",f0.2 "O~

~ j0.2 3

0 0 0 4 Displacement, mm Displacement, mm

(a) PH6 (b)PH8

sz '5l.. sz sz I i 1

0.8 li li 2S

4-< 1 = 4-< 0 = ..... 0 .....

"t",f 0.4 ~ ~0.5 3 j

0 0 0 0 20 Displacement, mm Displacement, mm

(c) PHll (d) PH14

Fig. 5. Behavior of HSC beams reinforced with FRP grid

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Per

0.84 0.71

0.89 0.70 3.78 2.92 2.29

:ZS

2S

40

Then, was determined

PNl 8 series, the measured value the """"'l"·•m,~'I"~,..,.,...._

3.2.4 Ultimate The FRP grid used ultimate tensile maximum compression zone ultimate

~ = 0 .....

0

I t ) 0.8

0

(c) PNll

Fig. 6. Behavior

ZS

two longitudinal bars. was determined

was taken Table 5, the

the maximum value

an decrease in local bending deformation

I 0.6

~ = .s 0.4 "'O ...

Ci::l

30.2

~ = 0 -

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0

0.5

0

l :sz

~ 'Sl.

l ZS ZS

5 1 15

grid

0

8

~1:1 t 1l PF23 ~( t Zi Zi

PF14 I,;: \&.11/lil k II Zi Zi

PF8 ,.}; 111;{\, b,\1? k Zi Zi

beams reinforced grid series)

~ j 0.1

8

3.2.5 Minimum rP1·n"'tr\rl"''"'mPn1" grid displacement

reinforced It is seen from the accompanying plural

4

grid Pu/Per is ;;;;. .. ....,, ...... ...., .. the sectional area is not so

than ratio p=( area .... ~......,........... reinforcement.

seems to be a more reinforcement)/( concrete

and to obtain reliable scatter of and the effects of

be when calculating Per. it should be that the local bending decreases

..,, ....... , ..... i;;.,.,...... of FRP gird. When members are designed using the maximum load FRP grid, an appropriate value Pu/Per,

..... ,, .... 6JL ..... ., ... ..,~ more than should be chosen ductile

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strength concrete, reinforced high strength

Experimental procedures conditions of RC beams are given in Table 6. The properties of

concrete at the age of testing are shown in Table 7. SFRC contained 2% of indented steel short fibers (diameter: 0.6 mm, length: 30 mm, strength: 110 kgf/mm2 (1.08 GPa)). Beams were reinforced with steel bars, DlO (diameter: 9.53 mm, yield strength: 39 kgf/mm2 (382 MPa), tensile strength: 54 kgf/mm2 (530 MPa)). The thickness of cover concrete was 20 mm. For SH series (high strength concrete), the beam

was changed to vary the tension reinforcement ratio. For both SN series (normal strength concrete) and SF series (steel fiber reinforced concrete), the beam depth was changed. RC beams were loaded in same way as described in the previous chapter.

Table 6. conditions of RC beams

Specimen size, mm Tension reinforcement

Series Concrete Span Effective Ratio Width [Moment Depth

depth Bars

% spanl SH18 High 100 lDlO 0.46 (WlO) SH18 strength 145 1500 [500] 180 155 lDlO 0.32

(W14.5) SH18 concrete 200 lDlO 0.23 (W20) SN14 Normal 140 115 lDlO 0.31 SN18 strength 200 1500 [500] 180 155 lDlO 0.23 SN23 concrete 230 205 lDlO 0.17 SN30 300 275 lDlO 0.13 SF14 Steel 140 115 3D10 0.92 SF18 fiber 200 1500 [500] 180 155 3D10 0.68 SF23 reinforced 230 205 3Dl0 0.51 SF30 concrete 300 275 3D10 0.38

Table Properties of concrete including SFRC

Concrete Compression

High strength 863 concrete

Normal stemgth 323 concrete

Steel fiber reinforced 888 concrete*

Strength Young's Age at kgf/cm2 modulus testing

Tension Flexure kgf/cm2 days

88.5 54.3 4.lOX 105 24

49.9 28.9 2.84X 105 11~12

119 89.6 4.05x105 22

* SFRC contains 2% of steel short fibers 1134

results and cns:crnssums results (average two

measured load-displacement curves at the first crack Per

.. ,. ........ ,,. ......... .a............ load due to figures. Since the ...... .11. ..... ., .. .11. .............. ...

at an inflection

Behavior of "'"'"'...,,.,."" seen Fig.

were several new cracks. an •nr• .. o•-.C".O.

are given are shown in Figs.

at steel yielding steel

increased and the ratio Pu/Per r. 0,...,.,...,.,,

0

series, only one crack high strength concrete,

behavior must be greater the case RC beams Fig. when

0.15%,

4.2.2 Behavior of beams load-displacement curves

concrete (SF series) were addition.

yielding of steel bars. extended and the beam It is seen from the results ratio should be greater greater than which yielding and the final ~ ... ...,..., ....... ...,..., ...... ...,....... n.0.,...,-.,...,,,.,,,c

Crack load of crack

two ways described values of estimation-2,

account, were estimation-1, especially

The yield loads Py of fibers and were roughly <:>cT11 m1J,.,..,,r1

= Psy + 0.7Pcy

where Psy is the yield resistance of concrete

to is

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· Table 8. Test results of RC beams

Load at first crack, Per, tonf

Series Experi- Esti- Esti-

SH18 (WlO) SH18

(W14.5) SH18 (W20)

SN14 SN18 SN23 SN30 SF14 SF18 SF23 SF30

3 :ZS

0

0

ment, ma ti on mation -1 -2

1.94 1.94 1.72

2.54 2.76 2.46

3.53 3.88 3.46

1.22 1.29 1.21 2.02 2.15 1.92 2.63 3.43 2.93 4.82 6.06 4.92 1.96 3.15 -3.85 5.25 -6.27 8.39 -9.36 14.3 -

Displacement, mm (a) SH18 (WlO)

1 Displacement, mm (c) SH18 (W20)

Yield load, Py, tonf Maximum Number

Experi-ment

1.75

1.74

1.79

0.98 1.72 2.30 3.43 5.76 8.17 11.7 19.0

Esti-mation

--

-

----

5.84 8.70 12.6 19.1

3 Zi

0

load due to of Pu -steel bars, cracks Per Pu, tonf

2.15 3 1.11

2.39 2 0.94

2.47 1 0.70

1.71 5 1.40 2.36 4 1.17 3.16 3 1.20 4.41 1 0.91

(5.51) 9 (2.81) (7.53) 8 (1.96) (9.94) 8 (1.59) (14.5) 9 (1.55)

:ZS

4 Displacement, mm

(b) SH18 (W14.5)

Fig. 9. Behavior of HSC beams reinforced with steel bars (SH series)

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Pu Py

1.23

1.37

1.38

1.74 1.37 1.37 1.29

(0.96) (0.92) (0.85) (0.76)

without steel bars, which is the value of estimation-1 Table 8.

4.2.4 Minimum reinforcement for RC beams As is known, the two conditions of Pu>Pcr and Pu>Py must be satisfied in order that the beams behave in a ductile failure mode with

ZS

0

4 ZS

0

1 ? I

Displacement, mm (a) SN14

60 Displacement, mm

(c) SN23

ZS

ZS

I 3 ZS

4-4 i:: 0 ......

"'O" C'd

31

0

I 6 2l

0

'\]

( [ \J

~ 2l

Displacement, mm (b) SN18 sz

! 2

ZS

1 0 Displacement, mm

(d) SN30

Fig. 10. Behavior of NSC beams reinforced with steel bars (SN series)

SF30 J1\1~ I~ ZS ZS

c...,. sz '\l i::

SF23 .(.. 'i \(1( \\ 0 y. ...... "'1 2l &

~ \~ .1': < 3 SF18 il5

SF14 h 2l

sz g 0 SF14 I l{n11d 1<b\ /1

Displacement, 2l 2l mm

Fig. 11. Behavior of SFRC beams reinforced with steel bars (SF series)

1137

loads Per, and be of beam depth on the crack

account deeper beams. In the case of SFRC, the effect of steel addition on the yield load Py must

5

m ..................... ,,,.,, reinforcement ratios for the ductile behavior were 0.15% series and 1.0% SF .., ...... , ...... ..,.

materials are investigated reinforcement. is

beams fail in a

reinforced with FRP grid, .................... ,.., ....... of FRP grid should be known

sectional area FRP grid is not so is more suitable than the area ratio to

must

High performance non-metallic concrete '"' ......... u. ..... .,.,"''U by combining AFRC and FRP

beams, the minimum reinforcement ratios were 0.15% for NSC beams, 0.4% for beams

SFRC beams the range of this study. SFRC order to adequately evaluate the yield load Py, resistance

must be taken into account. The size effect beam load was not negligible for deeper beams.

modes of beams are discussed. features such as of failure and prevention of are 1n1n11n1"<=•rl out.

6

and Koyanagi, W. {l 993a) design of concrete members

reinforcing materials. Proc. of Symp. on Advanced Design and Fabrication of Composite

(In press).

and Koyanagi, W. (1992) Application effect on flexural strength of concrete.

20, 87-97.

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