CHAPTER 6

STUDIES ON ONE WAY RESTRAINED SLABS

6.1 GENERAL

In this chapter the experimental investigation on one way SFRCC slabs with two short

edges restrained is discussed. Specimens with 0.5%, 0.75% fibres and without fibres

were cast and tested under uniformly distributed load. The influence of fibres in

enhancing load carrying capacity, reducing deflection and crack width, improving

engineering properties like ductility, energy absorption capacity were investigated.

For comparison, similar CVC slabs were also studied. The details of fabrication done

for providing fixity, reinforcement for slabs, casting and testing of slabs are discussed

in the following sections.

6.2 EXPERIMENTAL PROGRAMME

Slabs of 1.66m x 1.00m x 0.06m were cast so as to get an effective span of 1.5m . 6mm

diameter HYSD bars were used as reinforcement. Reinforcement mesh with 6mm

diameter bars at 135mm 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.6.1. Same steel was provided as positive and negative reinforcements.

Two specimens each were cast with 0%, 0.5% and 0.75% of fibres in SCC and two

similar slabs using CVC without fibre. Based on the support condition and fibre

content the slabs are designated and such details are given in Table 6.1.

Table 6.1 Designation of One Way Restrained Slabs

Slab Type of slab % Fibre

FOSCII SCC 0FOSC12 SCCFOSC21 SCC 0.5FOSC22 SCCFOSC31 SCC 0.75FOSC32 SCCFORCI CVC 0FORC2 CVC

133

8o-

" "

1660mm 2( Ommc/c

(a) Plan

---449H-8--T60

r.;=::::;:::::;;;::::=:;=~----------=::::;::==;;::::::::::;;::::::;]

I. ~:::::===~==~o~~==~~==~====~

135mmc/c

6111111 Dia bars a200111m clc 6111111 Dia bars @135mlll clcI 96f-r-G----II

1-----------'16601----------1

(b) Cross Section

Fig. 6.1 Reinforcement Details of Restrained Slabs

For giving fixity, holes of 10mm diameter were provided along two short edges of the

slab for bolting to the loading frame for ensuring fixity at support. A special casting

die is inserted into the mould of slab for providing the holes at the predefined

positions. This die was fabricated by welding steel rod of diameter 16mm and length

100mm on a mild steel plate of width 50mm at predefined positions. During casting

these rods were wound with paper to facilitate easy detachment of the die after

hardening of concrete. This die was placed in the appropriate position and concrete

was poured into the mould and the surface of concrete was levelled. In the case of

134

eve, concrete was placed in two layers and each layer compacted using needle

vibrator. see took less time for casting and had shown a better surface fInish. After

24 hours these specimens were cured by ponding as explained in Chapter 4. Three

control cubes were also cast with each slab. The set up for casting is shown

in Photo 6.1.

Photo 6.1 Casting Arrangement

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

explained in the previous chapter. The plan of loading system is shown in Fig. 6.2.

Slab with restrained edges subjected to uniformly distributed load is shown in Photo

6.2. For providing fixity, the shorter edges ofthe slab was tightened with the loading

frame using 160mm wide and 8mm thick mild steel plates and lOmm diameter bolt

and nut provided at an interval of 200mm. The rotation of the restrained edge was

monitored using dial gauges mounted near the fIxed support. The enlarged diagram

showing the fixed edge of the slab is shown in Fig.6.3. Test set up and

instrumentation are shown in Fig 6.4 and Photo 6.3. Measurements such as fIrst crack

load, deflection, crack width, crack propagation pattern and ultimate load were noted

as explained in the previous chapters.

135

8N

8N

I 8N

8N

Ladrg~tfll-~======~__1~EB>~ ---l

(~dn"a1lias in rml

Fig. 6.2 Loading System

Photo 6.2 One Way Restrained Slab Loaded with Uniformly Distributed Load

136

8mm thick plate

ISLe 150(Loading frame)

10mm dia bolt ~:::-----.-J..l ~

--Supported end ofslab

fi . A.. '..4

Slab

8mm thick plate ---L...,LJ,..:.-----.!.J...-J

Fig. 6.3 Schematic Diagram of Fixity

Photo 6.3 Test Set Up

137

••• of ",

SuPPOtt toLoading Frame

------ Support to Dial e:aug; : •"A :.'...... 0··'

Dial Gauge

support toDial Gauge

Fig. 6.4 Schematic Diagram of Test Set Up

6.3 RESULTS AND DISCUSSION

6.3.1 First Crack Load

The first crack developed at the midspan of the slab parallel to the fixed edge at about

50% of the ultimate load. Both SCC and CVC slabs developed first crack at the same

load. The first crack load for slabs with varying fibre content is given in Table 6.2.

Table 6.2 First Crack Load

Slab 0/0 Cube strength First crack load (kN)

designation fibre (N/mm2) Individual Average

FOSCII 0% 46.07 19.62 19.62FOSC12 46.94 19.62

FOSC21 0.5% 48.69 19.62 22.07FOSC22 49.71 24.52

FOSC31 0.75% 52.90 24.52 24.53FOSC32 52.47 24.52

FORCI 0% 46.21 19.62 19.62

FORC2 45.78 19.62

138

Tt may be noted that the first crack load IS enhanced by 10% and 20% respectIvely by

the addition of 0.5% and 0.75% fibres.

6.3.2 Load Deflection Behaviour

Deflections were noted at O.5T (4.91 kN) 1ntervals ofload and the test result 1s plotted

in Fig 6.5 to Fig 6.8. Load deflection curve was linear up to first crack load and non

linear after cracking. Load deflection plot of all the slabs are shown together in

Fig.6.9. It can be observed that addition of fibres improves the stiffuess of slab. Load

deflection pattern was more or less similar for see and eve slabs.

4

6 -

...e:'tJ 3

,g.J

II

• FORC1 I- ... FORC2

I

4036

- -- ------

15 20 26 30Deflection in mm

105

ool

Fig. 6.5 Load Deflection Plot of eve Slabs

ITonne = 9.81kN

139

--+-FOSC11

-.- F0SC12

40353015 20 25

Deflection in mm10

.... -- ....fIII""'-.--­

,.",

/.,/

/"

5

:1I 4

It-&:

'U 3".3

2

1

0

0

Fig. 6.6 Load - Deflection Plot for sec Slab without Fibre

ITonne = 9.81kN

------,-- ---,.-

,...-----7

6

6

...4

l:.-"CI0 3-'

2

1

0

0 10 20 30Deflection in mm

40 60

lI

__ FOS~1

- ..... F0SC22

- - --------------

Fig. 6.7 Load - Deflection Plot for sec Slab with 0.5% Fibre

1Tonne = 9.81kN

140

8

7_-IJt"' ......

6 -l-

S ¥c /' ---.-FOSC31'tJ 4 ~

-Itt- F0SC32" X0..I 3

2

1

0

0 10 20 30 40 60Deflection in mm

Fig. 6.8 Load - Deflection Plot for see Slab with 0.75% Fibre

1Tonne = 9.81kN

8

7

6

5t-c:'C 4IV0...I 3

2

1

0 ~

I

0 10 20 30

Deflection In mm40 50

.. FORC1

- .... FORC2

--.-FOSC11

-+- FOSC12

• FOSC21

--.- FOSC22

--.-FOSC31

-Itt- FOSC32

---- --- -------

Fig. 6.9 Load - Deflection Plot for all Specimens

1TOIUle = 9.81kN141

6.3.3 Crack Width and Propagation of Crack

First crack developed parallel to the fixed edge after a few load increments. Further

loading caused the formation of more number of finer cracks away from midspan

parallel to the first crack and all these cracks extended more or less to the entire

width of slab. The cracks were closely spaced near the midspan and with larger

spacing towards the support of the slab. It has been observed that cracks were

developed on the top surfaces of the slab near the restrained support. Due to technical

difficulties and limitations in the experimental set up the details of these cracks were

not measured.The width of crack at different load levels for slabs with varied fibre

content is given in Fig 6.10. see and eve slabs developed initial crack at same load

and crack widening was also noticed to be similar for both. Significant reduction in

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

crack width was observed higher in the case of slabs without fibre whereas in the case

of slab with fibre multiple cracks were developed with lesser crack width. Specimens

showing the pattern of cracks developed for eve slabs, see slabs with and without

fibre are given in Photos 6.4 to 6.7. Details of the crack pattern at the supports are

shown in Photos 6.8 and 6.9. Development and propagation of cracks at various

stages is shown in Fig. 6.11.

7

6

6

... 4c'0

8 3~""'''''..I

2

--..-FORC1

- .... FORC2

--..-FOSC11

- .... FOSC12_____ FOSC21

-.- FOSC22

---.- FOSC31

-II!- FOSC32

1

3.631 1.6 2 2.6Crack width in mm

0.6

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

o

Fig. 6.10 Load - Crack Width Plot

ITonne = 9.81k:N142

Stage V

Stage IV

Stage III

Stage II

Stage I

\Fig. 6.11 Development of Cracks in FOSCll

143

Photo 6.4 Crack Pattern ofcve Specimen at bottom

Photo 6.S Crack Pattern of see Specimen without Fibre at bottom

Photo 6.6 Crack Pattern of SCC Specimen with 0.5% Fibre at bottom

Photo 6.7 Crack Pattern of sec Specimen with 0.75% Fibre at bottom

14~

Photo 6.8 Crack Pattern at the Restrained Edge

Photo 6.9 Restrained Edge after Failure

6.3.4 Ultimate Load Carrying Capacity

Ultimate load for slab with different volume fraction of fibre is given in Table 6.3.

From this study, it can be inferred that the ultimate load carrying capacity was

enhanced by about 15% and 30% by the addition of 0.5% and 0.75% fibres. Average

load carrying capacity was found to be same for see and eve slabs.

145

Table 6.3 Ultimate Load

Slab 0/0Cube Ultimate load (l<N)

designation fibrestrength

Individual Average(N/mm2)

FOSCll 0% 46.07 50.03 48.07FOSC12 46.94 46.11

FOSC21 0.5% 48.69 50.03 55.43FOSC22 49.71 60.82

FOSC31 0.75% 52.90 58.86 62.78FOSC32 52.47 66.70

FORCI 0% 46.21 50.03 48.07FORC2 45.78 46.11

6.4 ANALYSIS OF TEST RESULTS

6.4.1 Energy Absorption Capacity

Energy absorption capacity calculated as the area under p-a curve was enhanced by

the addition of fibres as in the case of simply supported slab. On addition of 0.5%

and 0.75% fibres the energy absorbed was enhanced by 14% and 46% respectively.

Energy absorption capacity of SCC and CVC were similar. The energy absorption

capacities of slabs with varying content of fibres is shown in Table 6.4

Table 6.4 Energy Absorption Capacity

Slab Energy absorption capacity (l<Nmm)

designation Individual Average Relative

FOSCll 1314.54 1275.30 1

FOSC12 1236.06

FOSC21 1461.69 1456.79 1.142

FOSC22 1451.88

FOSC31 1697.13 1858.99 1.458

FOSC32 2020.86

FORCI 1294.92 1221.35 0.958FORC2 1147.77

146

6.4.2 Toughness Index

Is and 110 were determined for all the specimens as explained in section 4.5.2 and the

result is shown in Table 6.5. It can be seen that toughness index of SFRSee slabs is

more or less similar to that of see slabs without fibre. Whereas, toughness index of

cve and see are found to be comparable.

Table 6.5 Toughness Index

SlabDeflection at Area up to Tou2hness indexfirst crack

designation<>t (mm) <>t 3<>t 5.5<>t Is Ave. Is 110 Ave. 110

FOSC11 5.20 294.30 1731.46 4434.12 5.88 5.69 15.07 14.52

FOSC12 5.20 309.01 1703.99 4312.47 5.51 13.96

FOSC21 4.55 269.77 1520.55 3831.78 5.63 5.65 14.20 14.55

FOSC22 5.40 405.15 2297.50 6033.15 5.67 14.89

FOSC31 6.40 530.72 2787.02 6839.53 5.25 5.59 12.89 13.76

FOSC32 3.92 279.58 1656.90 4086.84 5.93 14.62

FORC1 2.92 179.52 887.805 2198.42 4.95 5.03 12.24 12.46

FORC2 5.60 368.85 1886.46 4676.42 5.11 12.68

6.4.3 Ductility Factor

Ductility factor calculated for the slabs is given in Table 6.6. The ductility factor for

slabs with 0.5% and 0.75% are 35% and 65% higher than those without fibre. When

SCC and CVC are compared, ductility factor for CVC slabs are 37% higher.

Table 6.6 Ductility Factor

Yield Deflection Ductility factor (011 )Slab

Ultimateload (mm) Oy

load P udesignation P(kN) y AtPu AtPy Gain

(liN)Ou Oy

Individual Averagefactor

FOSe11 50.03 34.33 35.10 10.5 3.343.52 1

FOSC12 46.10 26.48 37.00 10.0 3.70

FOSC21 50.03 27.46 39.66 7.5 5.294.74 1.35

FOSC22 60.82 30.41 35.60 8.5 4.19

FOSC31 58.86 28.44 40.85 7.5 5.445.82 1.65

FOSC32 66.70 35.31 46.52 7.5 6.20

FORC1 50.03 27.46 34.50 7.5 4.604.58 1.37

FORC2 46.10 21.58 35.52 7.8 4.55

147

(6.1)

6.4.4 Prediction of Collapse Load

Collapse load based on yield line theory as explained in section 2.6.2 was computed

for all the specimen and is given in Table 6.7. The details of computation is given in

Appendix C. Collapse load of SFRSCC slabs were higher than that of SCC slabs

without fibre. It can be noted that the experimental collapse load were higher than the

computed values. This can be due to the development of membrane forces as

explained in Chapter 2. The maximum enhancement was 29%, observed in SCC slabs

with 0.75% fibres.

Table 6.7 Collapse Load

SlabCollapse load (kN)

designation Theoretical Experimental Exp/the

FOSCII 46.241 50.031 1.081

FOSC12 46.263 46.107 0.996

FOSC21 49.924 50.031 1.002

FOSC22 49.945 60.822 1.217

FOSC31 51.756 58.860 1.137

FOSC32 51.749 66.708 1.289

FORCI 46.244 50.031 1.081

FORC2 46.233 46.107 0.997

Average 1.1

6.4.5 Prediction of Deflection

Maximum elastic deflection of a homogeneous beam subjected to uniformly

distributed load is given by :

fJpi 4

0=-E1

where

fJ

P

i

£1

_1_ for restrained beam384

load per unit length

span of the beam

flexural rigidity of the beam

148

(6.2)

The equation for beam is extended to one way restrained slabs and the deflection is

predicted in two stages. In the first stage up to first crack load (Pcr )

I =Igr

Deflection (8cr ) at Pcr is

8 =_I_PerI4

er 384 EIgr

pcr load at first crack per unit area

In the second stage up to the Johansen's collapse load (Pj ) :

I = Ieff

Deflection (8j ) at Pj is

8 =8 +_I_(Pi - Per)J er 384 E I

e er(6.3)

Theoretical deflection (8j) at Pjwith Ie.ff= Icr is calculated and is shown in Fig. 6.12 to

6.15.

Since the prediction is not satisfactory, a modification is proposed which is similar to

the one adopted by Muthu et a1. for the effective moment of inertia:

(6.4)

(6.5)

a is found for all slabs without fibre and a regression analysis was done, as given in

Fig. 6.12 based onfek

149

0.26 Y=-o.0296x + 1.6269

•0.2

•0.16 -

IS • •0.1

0.05

4746.846,646A46.24646.8

O+----.------.------r----r---~--~--~

46.6

fckin N/mm2

Fig. 6.12 Variation of a with Strength ofConcrete

a = -O.0295kk + 1.5269

where fck is in N/ mm2

The values of deflection computed based on modified effective moment of inertia is

plotted against load and is found to be in good agreement with experimental results

and is shown in Fig. 6.13 to 6.16.

150

6

5

4f0­e:; 3tISo.J

2

1

_6(lhe}

-.-6 (exp)

~ 6 (proposed)

5040302010

oa----.,.------,-------,,..------,------,o

Deflection in rnm

Fig. 6.13 Comparison of Experimental, Theoretical and Proposed Deflection at

Midspan of FOSCll

IT=9.81k.N

40353015 20 25Deflection in rnm

105

5

4.5

4

3.5

f- 3e:; 2.5ta.3 2

1.5

1

0.5

O __--,.----r---.,-----,----.------,--.,-----.,

o

Fig. 6.14 Comparison of Experimental, Theoretical and Proposed Deflection at

Midspan of FOSC12

IT=9.81kN

151

6

5

4l­I:.- 3'i.s

2

1

-0(the)

_0 (8l(p)

-.-0 (proposed)

403020Deflection in mm

100 .....------.-------,------..,.------.,

o

Fig. 6.15 Comparison of Experimental, Theoretical and Proposed Deflection at

~fidspanof FORC1

5

4.5

4

3.5

- 3c:i 2.50

2...1.5

1

0.5

0

0 10 20 30Deflection in mm

40

-6(Ihe)

_0 (exp)

_ 0 (proposed)

Fig. 6.16 Comparison ofExperimental, Theoretical and Proposed Deflection at

Midspan ofFORC2

IT =9.81 kN

152

6.4.6 Evaluation of Load Factor

Load factor with respect to a short term deflection of 2mm and crack width of O.3mm

are tabulated and is shown in Table 6.8. As in the case of simply supported slabs, load

factor with respect to deflection is found to be much higher than that with respect to

cracking. It may also be noted that load factor with respect to limit state of cracking is

around 1.5. Hence deflection governs the design of restrained one way slabs.

Table 6.8 Load Factor

Service load (kN)Slab Ultimate Load factor

designation load Load at Load at w.r.t.limit state w.r.t. limit(kN) oj=2mm wcr =O.3mm of deflection state of

cracking

FOSCll 50.03 10.00 39.24 5.00 1.28

FOSC12 46.10 10.20 30.31 4.52 1.52

FORCl 50.03 16.18 44.92 3.09 1.11

FORC2 46.10 12.55 29.43 3.69 1.57

6.5 SUMMARY

This chapter summarizes the behaviour of SCC, CVC and SFRSCC under uniformly

distributed load. The load carrying capacity, development and propagation of cracks,

deflection and cracking behaviour of restrained one way slabs cast using sce and

eve were found to be similar. Engineering properties like ductility, energy

absorption were improved by the addition of fibres. Theoretical method for prediction

of collapse load was found to underestimate ultimate load and need modification.

Prediction of deflection by classical method was not satisfactory. The same method

based on modified effective moment of inertia was found to predict the deflection of

one way restrained slabs satisfactorily.

153