Shear capacity of concrete slabs reinforced with glass-fiber ... Journal...of series C slabs. Material properties The normalweight concrete used in this study was ready-mixed concrete

83PCI Journal | Summer 2012

Corrosion of steel in reinforced concrete structures is one of the main factors limiting the service life of bridge decks and parking structures. Chlorides from deicing salts or a marine environment act as catalysts for the corrosion of steel in concrete. Corrosion mitigation requires expensive maintenance, repair, or replacement. The use of glass-fiber-reinforced polymer (GFRP) bars as internal reinforcement is a possible solution to corrosion of steel bars. In addition to their noncorrosive properties, GFRP bars have higher strength than steel bars and are light and easy to handle, which makes them attractive as reinforcement for certain concrete elements, such as slabs. However, GFRP bars have different mechanical properties from steel; GFRP bars behave in a linear elastic manner until rupture, which makes concrete members reinforced with GFRP bars vulnerable to brittle failure.

Considerable research has been undertaken to investigate both flexural and shear performance of GFRP-reinforced concrete structures. Despite the differences in material properties compared with steel bars, the prediction of flexural capacity using the strain compatibility approach is still effective. The behavior of lightweight concrete slabs reinforced with GFRP bars without shear reinforcement is a topic of active research. Prediction of shear capac-

■ This paper reports an experimental investigation of the flexural and shear performance of concrete structures reinforced with glass-fiber-reinforced polymer (GFRP).

■ Simply supported slabs of both normalweight and lightweight concretes with compressive strengths in excess of 8000 psi (55 MPa) were tested.

■ Modified compression field theory first- and second-order equations can provide accurate yet conservative predictions of the behavior of GFRP-reinforced concrete despite the differ-ences in mechanical properties between GFRP and steel.

■ The predictions are less conservative for lightweight than for normalweight concrete.

Shear capacity of concrete slabs reinforced with glass-fiber-reinforced polymer bars using the modified compression field theory

Ruifen Liu and Chris P. Pantelides

Summer 2012 | PCI Journal84

ity is essential in the design of GFRP reinforced concrete members, as Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06)1 recommends that such members be designed as overreinforced, making them vulnerable to shear failure. There is little research available on GFRP-reinforced slabs constructed with high-strength normalweight or light-weight concrete.

The modified compression field theory (MCFT) is an analytical model with 15 equations that produce accurate estimates of shear strength for steel-reinforced concrete members.2 Bentz and Collins3 reduced the MCFT equations to two, which still accurately estimate the shear strength of steel-reinforced concrete members.4 Hoult et al.5 found that crack widths are affected by both a size effect and a strain effect regardless of the type of reinforcement used; they also showed that the two MCFT equations proposed by Bentz and Collins work equally well in predicting the shear capacity of normalweight concrete slabs reinforced with steel or FRP reinforcement.

Sherwood et al.6 demonstrated that the width of a member does not affect the shear stress at failure for steel-rein-forced concrete members, which indicates that the MCFT could be used for both beams and slabs. Bentz et al.7 found that despite the brittle nature of the reinforcement, FRP-reinforced large concrete beams behave similarly in shear to steel-reinforced concrete beams. In this paper, a series of 20 tests is presented to investigate the influence of slab width and depth, slab span, concrete compressive strength, and type of concrete (lightweight versus normalweight) on the shear strength of GFRP-reinforced slabs. The maxi-mum deflection of the slabs under service loads satisfied the American Association of State Highway and Transpor-tation Officials’ AASHTO LRFD Bridge Design Specifica-tions8 in the tests for the slabs designed for flexure accord-ing to ACI 440.1R-06 guidelines (Pantelides et al.9).

Experimental program

Twenty slabs were tested to investigate the behavior of GFRP-reinforced concrete slabs constructed with high-strength normalweight or lightweight concrete. The construction variables included unit weight and compres-sive strength of concrete, slab span and depth, slab width, and reinforcement ratio. Four series of slabs were built with different dimensions or reinforcement ratios. Figure 1 shows the top and bottom reinforcement for series A and B slabs. Series A and B slabs have the same width (2 ft [0.6 m]) but different spans and depths. Series C slabs have the same reinforcement, thickness, and span as series A slabs, but their widths are 6 ft (1.8 m). Series D slabs have the same dimensions as series C slabs, but series D slabs have a GFRP reinforcement ratio approximately half that of series C slabs.

Material properties

The normalweight concrete used in this study was ready-mixed concrete incorporating a 3/4 in. (19 mm) crushed limestone. The specified compressive strength of both normalweight and lightweight concretes was 6000 psi (41 MPa); however, several batches were cast at different times and consequently the concrete compressive strength for the normalweight concrete at the time of testing ranged from 8500 psi (59 MPa) to 12,600 psi (87 MPa) and for lightweight concrete from 8100 psi (56 MPa) to 10,900 psi (75 MPa).

The lightweight concrete used was sand-lightweight con-crete, which had a coarse aggregate (expanded shale) size of 1/2 in. (13 mm). The unit weight of the sand-lightweight concrete used was 123 lb/ft3 (1970 kg/m3).

The GFRP bars used for construction were no. 5 (16M) bars. The tensile strength of the specific lot of GFRP bars used in these tests was 103,700 psi (715 MPa), and the modulus of elasticity was 6280 ksi (43 GPa), as determined from tensile tests of the bars according to ACI 440.3R-04.10

Table 1 shows the concrete compressive strength at the time of testing, the actual reinforcement ratio, and the bal-anced reinforcement ratio.

Test setup and procedure

All slabs were tested as simply supported members on two reinforced concrete beams (Fig. 2). Elastomeric pads 6 in. (150 mm) wide and 2 in. (50 mm) thick were placed on the supporting beams so that the slabs could rotate freely near the support without coming into contract with the beams.

The load was applied using a hydraulic actuator through a 10 in. × 20 in. × 1 in. (250 mm × 500 mm × 25 mm) steel bearing plate for all slabs, which simulates the area of a double-tire truck load on a bridge deck.8 The steel bearing plate was placed directly on the concrete surface of the panels. The wider panels are subjected to a combination of one-way shear and punching shear. The load was applied as a series of half-sine downward cycles of increasing am-plitude without stress reversals. The load application was displacement controlled at a constant rate of 0.2 in./min (5 mm/min). The loading scheme was intended to simu-late repeated truck loading applied to the slab of a precast concrete bridge deck.

Test results

During testing, all slabs developed flexural cracks at low loads and additional diagonal cracks as the loads increased. Ultimately, the slabs failed in diagonal tension (Fig. 3). After formation of the critical diagonal crack near one of


the two supports, the concrete crushed on the compression face of the slabs. All slabs failed the same way regard-less of concrete type (normalweight or lightweight), slab dimensions, or amount of reinforcement. In a few tests, a few GFRP bars in the top mat near the outer edges of the slab snapped and sheared off after the ultimate load was reached, shortly before the ultimate deflection (Fig. 3). This occurred after the concrete cover had spalled off and

the bars were exposed, and was the result of the GFRP bars trying to carry the compression forces arising from the applied load. The GFRP bars in the bottom mat did not fracture in any of the tests even though they experienced significant tensile strain and deformation. Table 1 shows the concrete compressive strength at the time of testing, the actual reinforcement ratio, the balanced reinforcement ratio, and the experimental shear capacity.

Figure 1. Dimensions for top and bottom glass-fiber-reinforced polymer reinforcement mat for slabs. Note: no. 5 = 16M; 1 in. = 25.4 mm; 1 ft = 0.305 m.

6 ft

2 ft 8 ft 2 ft

18 N

o. 5

at 4

in.

24 No. 5 at 6 in.

A

2 in

.3 in. 3 in.

2 in

.

A

Support

6 ft

2.12

5 in

.1

in.

4 in.

Cov

er

2 in.

9.25

in.

4 in. Section A-A

Series C slabs

6 ft

2 ft 8 ft 2 ft

8 N

o. 5

at 8

in.

18 No. 5 at 8 in.

A

2 in

. 4 in. 4 in.

2 in

.

A

6 in

.6

in.

Support

6 ft

2.12

5 in

.1

in.

8 in.

Cov

er

5 in. 9.25

in.

8 in.

Section A-A

Series D slabs

2 ft

2 ft 9 ft - 6 in. 2 ft

6 N

o. 5

at 4

in.

27 No. 5 at 6 in.

A

2 in

. 3 in. 3 in.

2 in

.

A

Support

2 ft

2.12

5 in

.1

in.

4 in.

Cov

er

2 in.

10.7

5 in

.

4 in.

Series B slabs

2 ft

2 ft 8 ft 2 ft

6 N

o. 5

at 4

in.

24 No. 5 at 6 in.

A

2 in

. 3 in. 3 in.

2 in

.

A

Support

2 ft

2.12

5 in

.1

in.

4 in.

Cov

er

2 in.

9.25

in.

4 in.

Series A slabs

ITable 1 Slab properties

Dimensions4

Specimen nimber, ;dh3ll

[Thickness Lenh,:psi p,, % Pb, % V, kip V,,,edl, kip

r

IBJW

2 B2NW

3 B2NW

4 B1 LW

5 BitW

6B2LW

7 61 LW*

8 Bi NW

9 B2NW

10 B1LW

11 B2LW

12 B1NUi

13 B2NW

14 B1LW

15 B1tW

16 B21.W

17 B21.W

18 B1NWE

___________

19 B1LWE

20 B2LWE

2 91/4 8 10370 094 095 306 127 171

_______________

‘2j 91/4 8 12650 094 116 302 134 182

2 91/4 8 8760 094 080 276 122 162

2 91/4 8 9090 094 083 25 1 123 164

91/4 8 10930 094 100 229 129 174

2 91/4 8 8700 0 94 0 80 23 0 12 1 122

2 91/4 8 9900 0 94 091 274 15 1 199

2 1 0/4 9 5 11 420 0 79 1 05 23 8 13 0 19 0

______________

2 10I4 95 8840I 081 277 130 175

2 10/4 95 9080 079 083 220 131 177

________________

2L 10I4 95 8700 079 080 233 130 175

________________

6’Ir 91/4 8 12130 096 111 876 393 5296 91/ 8 8510 0 96 0 78 72 7 35 7 47 3

__________________

- 6 91/4 8 9080 0 96 0 83 61 3 36 3 3

6 91/ 8 9080 096 083 648 363 483

6 91/4 8 8250 0 96 0 76 66 8 354 46 9

91/ 8 8060 0 96 0 74 67 6 35 1 46 5

_____________________

— —

__________

91/ 8 12130 054 111 621 — 299 425

6 91/ 8 9080 0 54 0 83 — 55 6 27 7 38 8

6 91/ 8 8060 054 0 74 49 3 26 8 37 4

For this specimen the span was 6 7 ftNote f = specified óöncrete compressive strength MCFT = modified compression field theory V, = experimental shear strength V, = shear force atcritical section for shear a distance daway from maximum moment location V = predicted shear capacity using first order MCFT

= predicted shear capacity using second order MCFT Pb = fiber reinforced polymer reinforcement ratio producing balanced strain conditions

pf= FRP reinforcement ratio 1 in = 25 4 mm 1 ft = 0 305 m 1 kip = 4 448 kN 1 psi = 6 895 kPa

--

*1

L- -- - - - -

-LoadframeLoad cell

earing plate

I GFRP panel I -Elastomenc pad

- - -

Concrete beam-r6 in

12 ft8ft

I Bearing platee[•-..

-

- Elastomeric pad

ElevatiOn:

ccL

-0

c..J

4, Traffic directionPLAN


lower the ultimate shear strength will be; the size effect is influenced by the aggregate size. For lightweight concrete and high-strength normalweight concrete, the cement matrix is stronger than the aggregate, and the cracks go through the aggregate, thus eliminating any aggregate interlock. Two simplified equations were used for shear ca-pacity predictions. The first equation is a first-order linear approximation, which was initially developed for steel-reinforced concrete sections with the longitudinal strain at middepth at shear failure x being less than 0.1% as shown in Eq. (1), which is expressed in SI units as derived.5

Shear strength prediction using the MCFT

The MCFT is used to predict the shear strength of the slabs. The MCFT assumes that the ultimate shear strength of concrete members is related to the crack width at shear failure, which is controlled by the strain effect and the size effect. Because of the strain effect, the larger the longitudi-nal strain, the wider the cracks and the lower the ultimate shear strength. The size effect means that if two geo-metrically similar beams or slabs with different depths are subjected to the same shear stresses, the deeper the beam the wider the crack width will be and, consequently, the

Figure 3. Slab performance.

Shear failure mode

Snapping and shearing off of top GFRP bars

Figure 4. Shear cracks pass through the aggregate.

0.40 ir 1300II I[(1 ÷ 1500E ) I + S )j

qf;b,,dx

where

V,, = predicted shear strength

5re = effective crack spacing (mm)

4 = specified concrete compressive strength (MPa)

b, = web width (mm)

= effective shear depth to be taken as 0.9d (mm)

d = distance from extreme compression fiber to themiddle of the bottom FRP bar

The size effect term for members without stirrups is givenby Hoult et al. as Eq. (2) expressed in SI units.

where

Sxe31.5d

0.77d16 + a

ag = maximum aggregate size (mm)

For normaiweight concrete with compressive strengthabove 10,000 psi (70 MPa) or for lightweight concrete, theaggregate size should be taken as zero because the crackstend to pass through the aggregate particles. This wasconfirmed in the present tests. To avoid a discontinuity instrength predictions, for normaiweight concrete Hoult etal.5 suggested that the aggregate size be linearly reducedfrom the specified size to zero as the actual concretestrength increases from 8700 psi (60 MPa) to 10,000 psi(70 MPa).

A,. = area of the longitudinal reinforcement (mm2)

When FRP reinforcement is used, typically higher longitudinal strains will be developed compared with steel reinforcement. A second-order approximation to the MCFT

(2) theoretical diagonal crack width calculation leads to theshear capacity prediction equation as Eq. (4) expressed inSI units.5

0.30 1300 FV= 0.7 lf”A (4)

0.5+(l000ç.+0.15) 000+Sj

The experimental shear strengths of the specimens werecompared with Eq. (1) and Eq. (4). Figure 4 shows theshear cracks passing through the coarse aggregate eventhough some of the normaiweight concrete compressivestrength was slightly less than 10,000 psi (70 MPa); thus,the aggregate size was considered to be zero in the shearprediction equations for all specimens. Table 1 shows thepredicted shear capacity of the slabs using the first-orderEq. (1) VPdl and the second-order Eq. (4) Vd2.Figures 5

Normalweight concrete slab Lightweight concrete slab

The strain effect is included via the strain term E,.. For(1) members not subjected to axial load that are not pre

stressed, the strain term is given by Hoult et al. as Eq. (3)expressed in SI units.

M Id +V‘ (3)

2EAr r

where

Mf = bending moment at the critical section for shear

Ar = shear force at the critical section for shear, which isevaluated at a distance d from the maximum momentlocation

Er = elastic modulus of the reinforcement (GPa)

Summer 2012 PCI Journal


Figure 5. Normalized shear strength versus concrete compressive strength using the first-order modified compression field theory Eq. (1). Note: 1 psi = 6.895 kPa.

1.0

1.5

2.0

2.5

7,000 8,000 9,000 10,000 11,000 12,000 13,000

Nor

mal

ized

she

ar s

treng

th V

c/E

q.(1

)

Concrete compressive strength, psi

Normalweight concrete

Lightweight concrete

Figure 6. Normalized shear strength versus concrete compressive strength using the second-order modified compression field theory Eq. (4). Note: 1 psi = 6.895 kPa.

1.0

1.5

2.0

7,000 8,000 9,000 10,000 11,000 12,000 13,000

Nor

mal

ized

she

ar s

treng

th V

c/E

q. (4

)




9,000 10,000 11,000


• Normaiweight concrete


Figure 7 Normalized shear strength versus concrete compressive strength using actual strain and the first order niodi1fied compression field theory Eq 1)

Note 1 psi = 6 895 kPa

and 6 show comparisons of the ratios of tested-to-predictedshear strength versus concrete compressive strength for thefirst-order and second-order MCFT predictions, respectively.

The average ratio of experimental shear strength—to—predicted shear strength is 1.97, with a coefficient of variationCOV of 10.6% (Fig. 5). The average ratio of experimentalshear strength—to—predicted shear strength is 1.46, with aCOy of 10.7% (Fig. 6). The results show that both equations conservatively estimate the shear strength. The second-order equation estimates are closer to the experimentally obtained shear capacity. This is expected because ofthe higher longitudinal strain in the GFRP bars comparedwith steel bars. However, the ratio of experimental shearstrength—to—predicted shear strength for both the first-order Eq. (1) and the second-order Eq. (4) is 43% and 27%higher, respectively, than the beams or slabs in the study byHoult et al. This may be caused by the high compressivestrength of the concrete and the fact that the steel bearing plate was placed directly on the concrete surface, thusreducing the shear span. In addition, only GFRP reinforcedconcrete specimens were included in this research, whereasthe study by Hoult et al. considered steel, GFRP, carbonFRE and aramid FRP reinforced specimens.

Normaiweight concrete slabs generally had higher ratiosof experimental shear strength—to—predicted shear strength

—Summer 2012 PCIJournal

than lightweight concrete slabs (Fig. 5 and 6). For thefirst-order expression, the average ratio of experimental-to-predicted shear strength for normaiweight concrete slabs is2.14, with a COV of 9.2%; the average ratio for lightweightconcrete slabs is 1.86, with a COVof 6.1% (Fig. 5). Forthe second-order expression, the average ratio for normalweight concrete slabs is 1.58 with a COV of 9.9%; theaverage ratio for lightweight concrete slabs is 1.38 with aCOV of 8.1% (Fig. 6). In both the first-order and second-order MCFT predictions, the lightweight concrete slabshad an experimental-to-predicted shear strength ratio equalto 87% of the normalweight concrete slabs. This showsthat even though the predictions are conservative for lightweight concrete, they are less conservative than the predictions for normalweight concrete. Thus, the unit weight ofthe concrete in addition to compressive strength needs tobe considered in predictions for shear strength.

Figures 7 and 8 show the experimental shear strengthnormalized by the shear predictions of Eq. (1) and Eq. (4),respectively, using the actual strain in the GFRP barsmeasured during the tests. The strain in the GFRP barswas measured using strain gauges applied to the bars ofthe bottom reinforcing mat at midspan. For the first-orderMCFT expression, the average ratio for normalweightconcrete slabs is 3.05, with a COVof 17.3%; the averageratio for lightweight concrete slabs is 2.54, with a COV of12.0% (Fig. 7). For the second-order MCFT expression,

7,000 8,000 12,000 13,000


accurately the middepth strain than the first-order equation. Both the first-order and second-order equations predict similar strains for normalweight and lightweight concrete. Strain predictions using the MCFT equations ignore ten-sion stiffening, which might help explain the variance between measured and predicted strains.

Shear design using the MCFT

It is interesting to examine the conservatism of the two MCFT equations from the designer’s perspective. The assumptions used in the design of normalweight and light-weight concrete slabs are as follows: the design concrete compressive strength is 6000 psi (40 MPa), the GFRP bar modulus of elasticity is 5920 ksi (40.8 GPa), and its ultimate tensile strength is 95,000 psi (655 MPa). Using the design approach recommended by Hoult et al. with strain compatibility analysis, the predicted shear strength of the concrete slabs is conservative. The resulting average experimental-to-predicted shear strength ratio is 3.57 and 3.54 for normalweight and lightweight concrete slabs, respectively, when using the first-order MCFT prediction. The COV is 10% and 7.4% for normalweight and light-weight concrete slabs, respectively. Using the second-order MCFT prediction, the ratio of experimental to predicted shear strength is 1.86 and 1.85 for normalweight and light-weight concrete slabs, respectively. The COV is 11.3% and

the average ratio for normalweight concrete slabs is 1.62 with a COV of 15.7%. The average ratio for lightweight concrete slabs is 1.37 with a COV of 9.7% (Fig. 8). In both the first-order and second-order MCFT predictions, the lightweight concrete slabs had a shear ratio of 83% to 85% of the normalweight concrete slabs, respectively. Compar-ing the results of Fig. 5 to Fig. 7 and Fig. 6 to Fig. 8, the different ratios of experimental shear strength to predicted shear strength demonstrate that Eq. (3) slightly underpre-dicts the actual strain of the tested concrete slabs in this research.

Table 2 shows the measured and predicted strain using the first-order pred1 and second-order pred2 approximations at the middepth of the slabs. The measured middepth strain is defined as the maximum strain measured at the bottom longitudinal GFRP bars divided by two. The overall aver-age ratio of the first-order MCFT expression predicted-to-measured strain is 60.5% for normalweight concrete slabs and 61.6% for lightweight concrete slabs. In addition, the measured-to-predicted strain ratio is higher for slabs with a longer span (series B) and slabs with a smaller reinforce-ment ratio (series D) for both the first-order and second-or-der equations. The overall average ratio of the second-order MCFT expression predicted to measured strain is 82.0% for normalweight concrete slabs and 83.1% for lightweight concrete slabs. The second-order equation predicts more

Figure 8. Normalized shear strength versus concrete compressive strength using actual strain and the second-order modified compression field theory Eq. (4). Note: 1 psi = 6.895 kPa.

1.0

1.5

2.0

7,000 8,000 9,000 10,000 11,000 12,000 13,000

Nor

mal

ized

she

ar s

treng

th V

c/E

q. (4

)




8B1LNW-

9 B2NWi*R •tL-2’ -

r10Bitwvfr

12 B1NW

13 82NW

14EtLW

1581LW

it 821W

18 B1NWE

19 B1LWE

20 B2LWE-

0.51

0.46

0.46

0.49

061 036 059 - 079

060 - 038 063 ;r 085

_______

,Ic - -- -

- 059 034 059 078

nd—

035 nd nd

059 — -037 1 062 084

060 034 057 - 076

nd 031 nd nd

055 039 072 j 054 098 —

066 - 037 056 050 075

________________

-‘ 056j 037 066 050 089 J055 037 r 066 r 039 089

079 - 037 047 050 063

________________

-

— _ga- - - - -- -‘- -

058 034 058 — 045— 078

070 034 049 - 046 065

060 034 057 046 076/ - -.

045 033 • 074 044 098•

- r ‘063 033 053 044 070

072 051 070 072 - 100

079 047 060 065 084

—

_________

064 ‘r046 072 - 064 1L

100

For this specimen the span was 67 ft. —Note MCFT = modified compression field theory n d = no data 6ma = average longitudinal strain at middepth at shear failure ç,1 = predicted

longitudinal strain at middepth at shear failure using first order MCFT = predicted longitudinal strain at middepth at shear failure using second

order MCFT 1 ft = 0 305 m-- •••- i;-. --

8.1%, respectively. The conservatism of the second-orderMCFT in the design process is greater than the experimental predicted ratios observed in the tests. However, this isdesirable in actual design, and thus the design approachrecommended by Hoult et al. produces acceptable results.

To compare the results of the GFRP reinforced slabstested in the present study, in particular those cast withlightweight cQncrete, with existing data for normalweightconcrete slabs reinforced with GFRP bars, a comparison ismade of the present test results with the database providedin Hoult et al., which includes studies found in other references.11-20Additional studies of normalweight concretespecimens reinforced with GFRP bars7’2123 were includedin the present study to create an updated database. Allspecimens in the updated database are normaiweight con-

tB1NW .:

I3B2NW

crete beams or slabs reinforced with GFRP bars withoutany transverse reinforcement that failed in one-way shear.Figures 9 and 10 show the strain effect using the first-order and second-order MCFT equations for the GFRP-reinforced members using the updated database, respectively.The longitudinal strain at middepth is the strain predictedusing the MCFT, and the shear strength is normalized soonly the strain effect is shown. Figures 9 and 10 show thatlightweight concrete slabs follow the same trend as normalweight concrete beams or slabs, which indicates thatthe strain effect is unchanged and could be predicted usingthe MCFT for lightweight concrete slabs.

Figure 11 shows the size effect for normaiweight andlightweight concrete members reinforced with GFRP bars.The size effect is derived using the tested shear strength


Figure 9. Strain effect: normalweight concrete versus lightweight concrete slabs for first-order modified compression field theory Eq. (1). Note: Vc = predicted shear strength; εx = longitudinal strain at middepth at predicted shear failure.

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

0

10

20

30

40

50

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Longitudinal strain at mid-depth, mm/mm

Nor

mal

ized

she

ar s

tress

, psi

Nor

mal

ized

she

ar s

tress

, MP

a

Longitudinal strain at mid-depth, in./in.

Updated database

Present normalweight concrete

Present lightweight concrete

0.41 1500c x

v =+

Figure 10. Strain effect: normalweight concrete versus lightweight concrete slabs for second-order modified compression field theory Eq. (4). Note: Vc = predicted shear strength; εx = longitudinal strain at middepth at predicted shear failure.

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Longitudinal strain at mid-depth, mm/mm

Nor

mal

ized

she

ar s

tres,

psi

root

s

Nor

mal

ized

she

ar s

tress

, MP

a ro

ots

Longitudinal strain at mid-depth, in./in.

Updated atabase



)0.70.3

0.5 1000 0.15c xv =

(+ +

2.5

2.0

CoC0)ECa)a 1.5CoVa,(0a,

0

1.0

a)a,N

Cl)

0.5

0.0

Effective crack spacing, mm

800

Figure 11 Size effect normaiweight concrete versus lightweight concrete slabs for second order modified compression field theory Eq (4) Note S = effective

crackspacing.

normalized by the strain effect and the quantity bj4.Figure 11 shows that lightweight concrete slabs followthe same trend as normalweight concrete beams or slabs,which indicates that the size effect is unchanged and couldbe predicted using the MCFT for lightweight concreteslabs.

The size effect and the strain effect do not exhibit significant differences between normalweight concrete and lightweight concrete beams or slabs. This is also verified bycomparing the predicted and experimental shear strengthresults of all beams or slabs in the updated experimentaldatabase. For the first-order MCFT equation, the averageexperimental-to-predicted shear strength ratio is 1.59 and1.84 for normaiweight concrete and lightweight concretemembers, respectively. The COV is 35.0% and 5.9% fornormalweight and lightweight concrete members, respectively. Figure 12 shows the nonnalized shear strengthversus concrete compressive strength using the second-order MCFT. For the second-order MCFT equation, theaverage ratio of experimental shear strength to predictedshear strength is 1.27 and 1.37, and the COVis 27.2% and5.8% for normalweight and lightweight concrete members,respectively. The ratio of experimental-to-predicted shearstrength is lower for normalweight concrete beams or slabs

than the ratio for lightweight concrete slabs when the ratiosare compared with the updated database. These results arethe opposite of what was found for the specimens testedin the present study. However, when the slabs and beamsare distinguished,.it is observed that this is caused by themember depth effect.

The yellow diamonds in Fig. 12 represent only slabspecimens collected from other research. Comparing theexperimental-to-predicted shear strength ratio, slab specimens have a higher ratio than beams. Considering only theslabs collected from other research and the slabs from thepresent research, the average experimental ratio for normalweight concrete is 1.56, and for lightweight concreteit is 1.37 using the second-order equation. Lightweightconcrete slabs have a ratio 88% of normalweight concreteslabs, which follows the same trend as the slabs tested inthe present research. The comparisons carried out indicatethat a reduction factor is needed for the use of lightweightconcrete members reinforced with GFRP bars. Because alllightweight slabs come from the present study, it is likelythat differences in bearing plate details are systematic forsuch tests but not for the normalweight slabs from otherstudies. This can also be a factor in the variability of lightweight versus normaiweight concrete results.

200 400 600

(0

00

0

1000 1200 1400

0

0 0

0 Updated database

0

0

• Present normaiweight concrete

0 lightweight concrete

.

.

.

.0 •

0

$000

0 00000

Is00 0$0 0

0

B0

0

0 00

1300

1000+ S0

0

0

10 20 30 40 50

Effective crack spacing, in.

___

- —

-

— WL, es4WE Summer 2012 PCI Journal Jf’4P - AS1Ufl


and Eq. (4) could be used for both steel and FRP reinforce-ment, and the experimental-to-predicted shear strength ra-tio improved only slightly using Eq. (5). This indicates that even if the strain achieved in GFRP-reinforced concrete members is higher than that in steel reinforced concrete members, the size effect factor in Eq. (1) and Eq. (4) is sufficiently accurate for predicting the shear capacity of GFRP-reinforced concrete members.

Conclusion

This paper presents experimental results for 20 GFRP reinforced concrete slabs cast with either normalweight or lightweight concrete and compares the shear strength obtained in the tests with predictions using MCFT. The following conclusions were drawn:

• The second-order MCFT equation accurately predicts the shear strength of normalweight and lightweight concrete slabs reinforced with GFRP bars. The first-order MCFT equation is more conservative compared with the second-order equation. Lightweight concrete slabs, which failed in one-way shear, show the same size and strain effects as normalweight concrete slabs or beams reinforced with GFRP bars.

The size effect factor used in Eq. (1) and Eq. (4) was developed based on steel reinforced concrete members, which have a maximum strain at middepth of the mem-ber of 0.001.3 The measured average strain in the bottom GFRP bars in the present research at midspan is 0.012; thus the middepth strain is 0.006. The measured strain in the tested slabs is six times the maximum strain used to develop the size effect factor. Figure 9 in Bentz and Col-lins3 was redeveloped, and higher strain data curves were added (Fig. 13). Six of the curves in Fig. 13 represent the assumed middepth strain from 0.001 to 0.006. A new curve shown in Fig. 13 was chosen to compare with the one in the MCFT. This curve lies close to the middle of the data from the MCFT analyses across the size range and is similar to the size factor used in Eq. (1) and Eq. (4). The size effect factor intended to compare with the MCFT is obtained from Eq. (5) in SI units.

1450

1000 1 5+ . Sxe (5)

Using Eq. (5) to replace the size effect factor in Eq. (1) and Eq. (4), Table 3 shows the prediction results. Table 3 shows that Eq. (5) gave predictions closer to the experi-mental results. However, the size effect factor in Eq. (1)

Figure 12. Normalized shear strength versus concrete compressive strength using second-order modified compression field theory Eq. (4) for the updated database. Note: Vc = predicted shear strength.1 psi = 6.895 kPa.

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

Nor

mal

ized

she

ar s

treng

th V

c/E

q. (4

)


Updated database (beam)

Updated database (slab)



Summer 2012 | PCI Journal96

• Using the strains from flexural design for the first-order and second-order MCFT equations results in conservative designs because the actual concrete compressive strength and guaranteed GFRP properties are generally higher than the design values.

• The ratio of experimental to predicted shear strength from MCFT theory is lower for lightweight than for normalweight concrete slabs reinforced with GFRP

• The average predicted-to-measured middepth strain ratio was 60% for both normalweight and lightweight concrete slabs using the first-order MCFT equation. The average ratio was 82% for both normalweight and lightweight concrete slabs using the second-order MCFT equation. Strain predictions using the MCFT equations ignore tension stiffening, which might help explain the variance between measured and predicted strains.

Figure 13. Size effect factor for middepth strain. Note: MCFT = modified compression field theory.

0 10 20 30 40 50 60 70 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 0 200 400 600 800 1000 1200 1400 1600 1800 2000

Effective cracking spacing parameter Sxe, in.

Siz

e ef

fect

fact

or

Effective cracking spacing parameter Sxe, mm

MCFT

0.001 in./in.

0.002 in./in.

0.003 in./in.

0.004 in./in.

0.005 in./in.

0.006 in./in.

Eq. (5)

Table 3. Comparison results for different size effect factor

Size effect factor Concrete type Vexp /Vpred 1 COV1 Vexp /Vpred 2 COV2

1300

1000 + SxeEq. (1)

Normalweight 1.59 0.35 1.27 0.27

Lightweight 1.84 0.06 1.37 0.06

1450

1000 + 1.5Sxe Eq. (5)

Normalweight 1.52 0.20 1.22 0.20

Lightweight 1.70 0.06 1.29 0.06

Normalweight(5)/Normalweight(1) 0.95 0.57 0.96 0.62

Lightweight(5)/Lightweight(1) 0.92 0.97 0.94 1.01

Note: COV1 = coefficient of variation for first-order MCFT; COV2 = coefficient of variation for second-order MCFT; MCFT = modified compression field theory; Sxe = effective crack spacing; Vexp = experimental shear strength; Vpred1 = predicted shear capacity using first-order MCFT; Vpred 2 = predicted shear capacity using second-order MCFT.


6. Sherwood, E. G., A. S. Lubell, E. C. Bentz, and M. P. Collins. 2006. “One-Way Shear Strength of Thick Slabs and Wide Beams.” ACI Structural Journal 103 (6): 794–802.

7. Bentz, E. C., L. Massam, and M. P. Collins. 2010. “Shear Strength of Large Concrete Members with FRP Reinforcement.” Journal of Composites for Con-struction 14 (6): 637–646.

8. AASHTO (American Association of State Highway and Transportation Officials). 2007. AASHTO LRFD Bridge Design Specifications. 4th ed. Washington, DC: AASHTO.

9. Pantelides, C. P., R. Liu, and L. D. Reaveley. 2011. “Lightweight Concrete Bridge Deck Precast Panels Reinforced with GFRP Bars.” ACI Structural Journal 275 (3): 1–18.

10. ACI 440.3R. 2004. Guide Test Methods for Fiber-Re-inforced Polymers (FRPs) for Reinforcing or Strength-ening Concrete Structures. Farmington Hills, MI: ACI.

11. Alkhrdaji, T., M. A. Wideman, A. Belarbi, and A. Nanni. 2001. “Shear Strength of GFRP RC Beams and Slabs.” In Proceedings CCC 2001 Composites in Construction, Porto, Portugal, October 10–12, 2001, 409–414. Leiden, the Netherlands: A. A. Balkema.

12. Ashour, A. F. 2006. “Flexural and Shear Capacities of Concrete Beams Reinforced with GFRP Bars.” Con-struction and Building Materials 20 (10): 1005–1015.

13. Deitz, D. H., I. E. Harik, and H. Gersund. 1999. “One-Way Slabs Reinforced with Glass Fiber Reinforced Polymer Reinforcing Bars.” In Proceedings, 4th Inter-national Symposium Fiber-Reinforced Polymer (FRP) Reinforcement for Concrete Structures, FRPRCS4, 279–286. Farmington Hills, MI: American Concrete Institute.

14. El-Sayed, A. K., E. El-Salakawy, and B. Benmokrane. 2005. “Shear Strength of One-Way Concrete Slabs Reinforced with Fiber-Reinforced Polymer Composite Bars.” Journal of Composites for Construction 9 (2): 147–157.

15. El-Sayed, A. K., E. El-Salakawy, and B. Benmokrane. 2006. “Shear Strength of FRP-Reinforced Concrete Beams Without Transverse Reinforcement.” ACI Structural Journal 103 (2): 235–243.

16. El-Sayed, A. K., E. El-Salakawy, and B. Benmokrane. 2006. “Shear Capacity of High-Strength Concrete Beams Reinforced with FRP Bars.” ACI Structural Journal 103 (3): 383–389.

bars. A reduction factor is required for the design of lightweight concrete slabs when GFRP bars are used as reinforcement.

• Although the size effect factor in the original MCFT was developed based on strains in steel-reinforced concrete members, it is still accurate for the shear pre-diction of GFRP-reinforced concrete members, which achieve higher strains.

• Both normalweight and lightweight concrete slabs tested in this study were constructed with concrete having measured compressive strengths in excess of 8000 psi (55 MPa). Additional results for normal-strength lightweight concrete slabs are required to validate the findings of the present study.

Acknowledgments

The research reported in this paper was supported by the Utah Department of Transportation and the Expanded Shale, Clay and Slate Institute. The authors acknowledge the contribution of Hughes Bros Inc., Utelite Corp., and Hanson Structural Precast. The authors acknowledge the assistance of L. D. Reaveley, professor; M. Bryant; B. T. Besser; and C. A. Burningham of the University of Utah in the experimental portion of the research. The authors are grateful to N. A. Hoult, professor, of Queen’s University and E. C. Bentz, professor, of the University of Toronto for making their database available to the authors.

References

1. ACI (American Concrete Institute) 440.1R-06. 2006. Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars. Farmington Hills, MI: ACI.

2. Vecchio, F. J., and M. P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” ACI Structural Journal 83 (2): 219–231.

3. Bentz, E. C., and M. P. Collins. 2006. “Development of the 2004 CSA A23.3 Shear Provisions for Rein-forced Concrete.” Canadian Journal of Civil Engineer-ing 33 (5): 521–534.

4. Sherwood, E. G., E. C. Bentz, and M.P. Collins. 2007. “The Effect of Aggregate Size on the Beam-Shear Strength of Thick Slabs.” ACI Structural Journal 104 (2): 180–190.

5. Hoult, N. A., E. G. Sherwood, E. C. Bentz, and M. P. Collins. 2008. “Does the Use of FRP Reinforcement Change the One-Way Shear Behavior of Reinforced Concrete Slabs?” Journal of Composites for Construc-tion 12 (2): 125–133.

17. Gross, S. P., J. R. Yost, D. W. Dinehart, E. Svensen, COV2 = coefficient of variation for second-order modified

and N. Liu. 2001. “Shear Strength of Normal and compression field theory

High Strength Concrete Beams Reinforced with GFRPBars.” In Proceedings, International Conference on d = distance from extreme compression fiber to middle

High Performance Materials in Bridges, 426—437. of bottom fiber-reinforced-polymer bar

Reston, VA: American Society of Civil Engineers.d = effective shear depth to be taken as 0.9d

18. Tariq, M., and J. P. Newhook. 2003. “Shear Testing ofFRP Reinforced Concrete without Transverse Rein- Er = elastic modulus of reinforcement

forcement.” In Proceedings, Annual Conference of theCanadian Societyfor Civil Engineering, 1330—1339. 4 = specified concrete compressive strengthMontreal, QC, Canada: Canadian Society of CivilEngineering. M1 = bending moment at critical section for shear, a

distance d away from maximum moment location

19. Tureyen, A., and R. J. Frosch. 2002. “Shear Tests ofFRP-Reinforced Beams Without Stirrups.” ACI Struc- = effective crack spacing

tural Journal 99 (4): 427—434.V = predicted shear strength

20. Yost, J. R., S. P. Gross, and D. W. Dinehart. 2001.“Shear Strength of Normal Strength Concrete Beams l’, experimental shear strength

Reinforced with Deformed GFRP Bars.” Journal ofComposites for Construction 5 (4): 268—275. = shear force at critical section for shear, a distance

d away from maximum moment location

21. Alam, M. S., and A. Hussein. 2009. “Shear Strength ofConcrete Beams Reinforced with Glass Fibre Rein- = predicted shear capacity using first-order MCFT

forced Polymer (GFRP) Bars.” In Proceedings of 9thInternational Symposium on Fiber Reinforced Polymer Vpre = predicted shear capacity using second-order

Reinforcement for Concrete Structures, FRPRCS-9. MCFT

Adelaide, Australia: ICE Australia.Em=e = average longitudinal strain at middepth at shear

22. Jang, H., M. Kim, I. Cho, and C. Kim. 2009. “Con- failure

crete Shear Strength of Beams Reinforced with FRPBars According to Flexural Reinforcement Ratio and = predicted longitudinal strain at middepth at shear

Shear Span to Depth Ratio.” In Proceedings of 9th failure using first-order MCFT

International Symposium on Fiber Reinforced PolymerReinforcementfor Concrete Structures, FRPRCS-9. = predicted longitudinal strain at middepth at shear

Adelaide, Australia: ICE Australia. failure using second-order MCFI

23. Swamy, N., and M. Aburawi. 1997. “Structural 1mph- = longitudinal strain at middepth at predicted shear

cations of Using GFRP Bars as Concrete Reinforce- failure

ment.” In Proceedings of 3rd International Symposium, FRPRCS-3, Non-Metallic (FRP) Reinforcement Pb = fiber-reinforced-polymer reinforcement ratio pro-

for Concrete Structures, Vol. 2, 503—510. Tokyo, ducing balanced strain conditions

Japan: Japan Concrete Institute.Pf = fiber-reinforced-polymer reinforcement ratio

Notation

ag = maximum aggregate size in millimeters

A,. = area of the longitudinal reinforcement - - ;- -

= web width ‘ - -

COV = coefficient of variation -, S

COy1 = coefficient of variation for first order modified - -, ‘-

compression field theory — -

Summer 2012 PCI Journal


About the authors

Ruifen Liu is a PhD candidate in the Civil and Environmental Engineering Department of the University of Utah. She received her bachelor’s degree and MS from Beijing Jiaotong University. Her research interests include

design and construction of structural normalweight and lightweight concrete reinforced with fiber-reinforced-polymer bars.

Chris P. Pantelides is a professor in the Civil and Environmental Engineering Department of the University of Utah. He received his bachelor’s degree at the American University of Beirut and his MS and PhD from the

University of Missouri–Rolla. His research interests include seismic design and rehabilitation of reinforced concrete buildings and bridges.

Abstract

The ultimate shear capacity of slabs reinforced with glass-fiber-reinforced polymer (GFRP) bars is com-pared with the shear strength predicted using the modified compression field theory (MCFT). This paper uses the results of 20 tests of GFRP-reinforced slabs with either lightweight or normalweight concrete with measured strengths in excess of 8000 psi (55 MPa). Several parameters were examined, including slab width, span, thickness, and reinforcement ratio of GFRP bars. It is shown that the MCFT can accurately predict shear strength for both normalweight and light-weight concrete slabs reinforced with GFRP bars.

Keywords

Bar, GFRP, glass-fiber-reinforced polymer, lightweight concrete, normalweight concrete, shear strength.

Review policy

This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute’s peer-review process.

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Shear capacity of concrete slabs reinforced with glass-fiber ... Journal...of series C slabs. Material properties The normalweight concrete used in this study was ready-mixed concrete

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