CHAPTER 7

STUDIES ON TWO WAY RESTRAINED SLABS

7.1 GENERAL

In this chapter the investigation on two way SFRSee slabs with all edges retrained

against rotation is discussed. SCC slabs with 0.5%, 0.75% fibres and without fibres

were cast and tested under uniformly distributed load. eve slabs were also tested for

comparison. The details of fabrication done for casting, reinforcement for slabs,

casting and testing of slabs are discussed in the following sections.

7.2 EXPERIMENTAL PROGRAMME

Slabs of 1.66m x 1.16m x 0.06m were cast so as to get an effective size of

1.5m x l.OOm. Reinforcement cage with 6mm diameter HYSD bars at 150mm c/c

along the longer direction and 200mm c/c along the shorter direction was placed at the

bottom over cover blocks of thickness 12mm as shown in Fig. 7.1. Same area of steel

was provided as positive and negative reinforcements. Two specimens each were cast

with 0%, 0.5% and 0.75% of fibres in see and two cast with eve without fibre.

Based on the support condition and fibre content the slabs are designated and the

details furnished in Table 7.1.

Table 7.1 Designation of Fixed Two Way Slabs

SlabType

%designation Fibre

FTSel1 see 0FTsel2 see

FTse21 see 0.5FTse22 see

FISC31 see 0.75FIse32 see

FIRe1 eve 0FIRC2 eve

154

Fixity was provided as explained in restrained one way slabs (section 7.2) The

reinforcement cage and arrangement of the mould for casting is shown in Photo 7.1

I

" ... ...

I

200mm c/e

1660mm ISOmmc/c

Fig. 7.1 Reinforcement Details

Photo 7.1 Casting Arrangement

155

The slab is loaded with a uniformly distributed load by using the loading system

shown in Fig. 7.2.

:m 3D :m :m :roI I I I I

gN

ooN

ooN

ooN

ooN

1Em

(.All drrersicrs in~

Fig. 7.2 Loading System

All edges of the slab was fixed with the loading frame using mild steel plates and

tightened using nut and bolt at an interval of 200 mm for providing fixity. The

rotation of the restrained edge was monitored using dial gauges. Details of the test set

up of the slab with all edges restrained subjected to uniformly distributed load is

shown in Photo 7.2. Measurements such as first crack load, deflection and crack width

at each load increment, crack propagation pattern and ultimate load were noted as

explained in the previous chapters.

156

Photo 7.2 Test Set Up

7.3 RESULTS AND DISCUSSION

7.3.1 First Cra~kLoad

The first crack developed at the midspan of the slab parallel to the longer edge as in

simply supported case. Both sce and evc slabs developed first crack almost at the

same load. The first crack load fOT slabs with varied fibre content is shown in

Table 7.2.

Table 7.2 First Crack Load

Slab Cube %tibre First crack load (kN)designation strength

Individual AverageFTSCll 45.34 0 53.95 51.50

FTSC12 42.51 49.05

FTSC21 53.63 0.5 63.76 66.22

FTSC22 47.31 68.67

FTSC31 57.12 0.75 68.67 68.67

FTSC32 52.76 68.67

FTRCI 46.00 0 58.86 56.41

FTRC2 47.52 53.95

157

It may be noted that the first crack load is enhanced by about 30% and 35%

respectively by the addition of 0.5% and 0.75% fibres.

7.3.2 Load Deflection Behaviour

Mid span deflections were noted at O.5T intervals of load and is plotted in Fig. 7.3 to

Fig 7.6. As in all other case load deflection curve was linear up to first crack load and

non linear thereafter. Fig 7.7 shows the load deflection plot of all the slabs. It can be

observed that addition of fibre improves the stiffness of slab. Load deflection pattem

was more or less similar for see and eve slabs. Ultimate load could not be reached

in the two way restrained slabs due to the limitation ofthe testing frame.

_e__FTRC1

- .... -FTRC2

6040302010

2

Ow__-------r-------,r-----,-----.-------,

oDeflection in mm

Fig. 7.3 Load - Deflection Plot orcvc Slabs

1 T=9.81 kN

158

20

18

16

14

I- 12 jc

"': 1"'0

~

6

4

2

0

0 10 20 30 40 50

--+-FTSC11

- ........ -FTSC12

60

Deflection in mm

Fig. 7.4 Load - Deflection Plot for sec Slab without Fibre

IT = 9.81 kN

5040

25 l

20 j ......I- 15c ___ FTSC21

"0 - ___ - FTSC22

"'0

10 1..J

5

Deflection in mm

Fig. 7.5 Load - Deflection Plot for see Slab with 0.5% Fibre

IT=9.81 kN

159

25

l20

~ 15

1c:: --.-- FTSC31

" - -.- - FTSC32CIS

10 j0...J

5

403530252015105

O-E---,-------,------,--,-------,-----,---..,-----.,

oDeflection in mm

Fig. 7.6 Load m Deflection Plot for see Slab with 0.75% Fibre

IT=9.81 kN

-..-F1RC1

--+--FTRC2

-+--FTSC11

- ..... -FTSC12

~FTSC21

- ..... -FTSC22

--.--FTSC31

- ..... -FTSC32

605040302010

Ot;i'-----..,-------r-----r------,-----r-----,

o

Deflection In mm

Fig. 7.7 Load - Deflection Plot for all Specimens

1T =9.81 kN

160

7.3.3 Crack Width and Propagation of Crack

First crack on the bottom side developed parallel to the longer edge after a few load

increments. On further loading, the cracks extended to the edges as in the case of two

way simply supported slabs. More number of finer cracks developed in the slabs with

fibres. Cracks were developed at the top surface of the slab at the restrained edges

also. But measurements were not taken on these cracks due to the limitations of the

experimental set up.

The width of crack at different load levels for two way restrained slabs is given in

Fig 7.8. see and eve developed initial crack at same load and the pattern of

widening was also similar in nature. A significant reduction in crack width was

observed for see slabs with fibre. The rate of development in crack width was

observed higher in the case of slabs without fibre. Crack pattern of two way slabs

having varying content of fibres are given in Photos 7.3 to 7.6 and crack propagation

pattern is shown in Fig. 7.9.

20 ~18

16

14

1.... 12 1c~ 10 i10

oS 8

6

4

2

0

0 1 2 3 4

• FTRC1

-.- FTRC2

• FTSC11

- .... FTSC12

-----FTSC21---. FTSC22

--.-FTSC31

-It- FTSC32

crack width in mm

Fig. 7.8 Load - Crack Width Plot

IT=9.81 kN

161

Stage V

Stage IV

Stage III

Stage II

Stage I

ks' FTSC12F ' 7 9 Development of Crac III19. • .162

Photo 7.3 Crack Pattern ofCVC Specimen at bottom

Photo 7.4 Crack Pattern ofsec Specimen without Fibre at bottom

Photo 7.5 Crack Pattern ofsee Specimen with 0.5% Fibre at bottom

Photo 7.6 Crack Pattern ofsec Specimen with 0.75% Fibre at bottom

163

7.4 ANALYSIS OF TEST RESULTS

7.4.1 Prediction of Deflection

Various researchers have proposed methods for prediction of deflection for restrained

slabs as explained in Chapter 2. The equation proposed by Desayi and l\'luthu

(1979) for deflection of two way restrained slabs as given in Eq(2.21) to Eq(2.25)

was studied and is plotted against the test results in Fig 7.10 to Fig 7.B.The details of

calculation are given in Appendix D. It can be seen that there is no general agreement

between the theoretical and experimental values. Scanlon and Thompson (1990)

have observed that the determination of the first crack load based on modulus of

rupture obtained from small beam specimens does not account for the restraint

stresses in slabs due to the presence of reinforcement and attachment to rigid supports.

As a result service load moments are usually of the same order as the calculated

cracking moment. They have suggested O.32fi! MPa as modulus of rupture for

deflection calculations. When this was applied to the equation proposed by Desayi

and l\futhu , it could predict the deflection at an assumed working load equal to two

third of Johansen's load (~Wj) reasonably well. The computed deflection based on3

equation proposed by Desayi and Mutbu and modified equation after introducing

the values of modulus of rupture = 0.32.J7: are plotted against the experimental

results and are shown in Fig. 7.10 to 7.13.

60

_6 (exp)

_6(08Ay! and MUlhu)

_6 (modifil!d)

5020 30 40

Defl.ection in mm

10

6

4

2

o.-----.---~---.----~--...----..

0.

20.

18

16

14

to- 12c.- 10'g.3 8

Fig. 7.10 Comparison of Theoretical, Experimental and Modified Deflection of

FTSCll (IT=9.81 kN)

164

50

_ll(exp)

-.-0 (Desayi and Muthu)

-.-0 (modified)

40302010

20]

18 i

:: j... 12 j~ 10 ~«I

.3 8

6

4

2

o ~------r-------r------r-----.-------,o

Deflection in mm

Fig. 7.11 Comparison of Theoretical, Experimental and Modified Deflection of

FTSC12( 1T=9.81 kN)

-+-6 (exp)

-.- 0(Oesayi and MutI1u)

........ {) (modified)

20 -,

:: j14 ~

t- 12 1c:0 10ClI

j 8

6

4

2

o ._-----,-----,-----,-----,-------,o 10 20 30 40 50

Deflection in mm

Fig. 7.12 Comparison of Theoretical, Experimental and Modified Deflection of

FTRCI ( 1T=9.81kN)

165

20

18

16

14

I- 12c:; 10I'll

S 8

6

4

2

oo

r

10

r - r

20 30

Deflection in mm

T

40

_0 (exp)

~o (Desayi and Muthu)

-.-0 (modified)

-,

50

Fig. 7.13 Comparison of Theoretical, Experimental and J\'Iodified Deflection of

FTRC2

1T=9.81 kN

7.4.2 Prediction of Crack Width

Based on Nawy's equation, the possible crack width which may develop in a

restrained slab is predicted by :

WC7 = kf3f.~M, (7.1)

where

Wcr crack width at face ofconcrete caused by flexural load (in)

k fracture coefficient; having a value of k =2.8x 10-5 for uniformly

loaded, restrained two way action square slabs and plates; unit of k is

in in2llb,

Jl ratio of the distance from the neutral axis to the tensile face of the slab

to the distance from the neutral axis to the centroid of reinforcement

grid (to simplifY calculations use p= 1.25, although it varies from 1.2

to 1.35, (Edward Nawy, 2005)

166

(7.2)

Is actual average service load stress level or 40% ofthe design yield

strength in ksi

I direction of the reinforcement closest to the outer concrete fibres; this

is the direction for which crack control check is to be made.

db1 diameter of the reinforcement in direction 1 closest to the concrete

outer fibre (in)

c1 concrete cover to centroid of reinforcement (in)

s1 spacing of the reinforcement in direction 1

S2 spacing of reinforcement in perpendicular direction 2

Q active steel ratio ( = area of steel per foot width/ 12(dbl +2Cl) in

direction 1 )

C1 clear concrete cover measured from the tensile face of the concrete to

the nearest edge of reinforcing bar in direction 1

wcr :: kf3f,~MI =0.3727 mm (7.3) .

Experimental crack width at yield load was found from Fig. 7.8 and is about 0.35mm

which is close to the predicted crack width of 0.3727mm. Thus the Nawy's equation

is able to predict the crack width of two way restrained slabs reasonably well.

7.5 SUMMARY

The strength and behaviour of see, eve and SFRSCC two way restrained slabs

were studied in this chapter. Fibre inclusion was observed to improve ultimate strength,

ductility and energy absorption capacity of slabs. see and eve slabs were found to exhibit

similar deflection and cracking behaviour. A modified method for computing deflection was

proposed incorporating the equation for modulus of rupture as given by Scanlon and

Thompson and was found to compare satisfactorily with experimental results. The equation of

Edward. G. Nawy was found to predict the crack width in the case of two way restrained

see and eve slabs reasonably well.

167