44

CHAPTER 3

STRESS STRAIN BEHAVIOUR OF CONCRETE

CONFINED BY PREFABRICATED CAGE

3.1 SCOPE

The strength and ductility of the structural members can be

enhanced by confining the concrete by transverse reinforcement

commonly in the form of closely spaced steel or hoops (Mohamad Ziara

et. al. 1995, Sharim Sheikh et. al. 1994). At low levels of stress in

concrete, the transverse reinforcement is hardly stressed, hence the

concrete is unconfined. The concrete becomes confined when at stresses

approaching the yield strength, the transverse strains become very high

because of progressive internal cracking and the concrete bears out

against the transverse reinforcement, which then applies a confining

reaction to the concrete. Thus, the transverse reinforcement provides

passive confinement (Esneyder Montoya et. al. 2006, Guney Ozcebe

and Murat Saatcioglu 1987, Sundara Raja Iyengar et. al. 1970). The

confinement of the concrete is provided by arching between adjacent

transverse bars and also to some extent by arching between adjacent

vertical bars (Scott et. al. 1982, Soliman and Yu 1967, Shamim Sheikh

1982).

45

In this study, Prefabricated Cage is used to confine the

concrete in the structural members. Since the use of Prefabricated Cage

for confinement of concrete is a relatively new approach, experimental

and theoretical work in this area is still limited and the models originally

developed for transverse steel reinforcement are not applicable to

Prefabricated Cage reinforcement since the behaviour of concrete

confined with Prefabricated Cage is different from concrete confined

with regular steel reinforcement.

In this chapter, stress-strain behaviour, strength enhancement

and ductility factors of Prefabricated Cage confined concrete cylinders,

including experimental and analytical studies are presented.

3.2 EXPERIMENT PROGRAM

3.2.1 Materials

Cement: Ordinary Portland cement of grade 53, conforming to Indian

Standard Specification IS: 12269 – 1987 was used for preparing the

concrete.

Fine Aggregate: Natural river sand with a maximum size of 4.75mm

conforming Indian Standard Specifications IS: 383 – 1970 was used as a

fine aggregate for making concrete.

Coarse Aggregate: Coarse aggregate passed through 20mm sieve and

retained on 12mm sieve conforming to Indian Standard Specifications

IS: 383 – 1970 was used for concreting. The material properties of the

aggregates are given in Table 3.1.

46

Table 3.1 Properties of Aggregates

Sl.No Properties FineAggregate

CoarseAggregate

1 Fineness Modulus 2.435 2.32 Specific Gravity 2.55 2.83 Density (kg/m3) 1651.6 1623.5

Table 3.2 Properties of Cold-Formed Steel Sheet

ts(mm)

fy(MPa)

Es(MPa)

1.6 260 1.80 x 105

2.0 280 1.81 x 105

2.5 320 2.00 x 105

Cold-Formed Sheet: Cold formed steel sheet of 1.6mm, 2mm and

2.5mm thickness was used as reinforcement cage for a cylinder of

diameter 150mm and height 300mm. The width of Prefabricated Cage

strips used in this study was 15mm and 40mm. The minimum width of

strips that can be cut and bent without undue distortion is 15mm. Hence,

in this study 15mm strips were chosen. To compare the effect of

reinforcement area with same spacing of ties, one series of specimens

with 40mm strips were also cast. To determine the material properties of

the steel sheets, steel coupons were prepared from different parts of the

plate used and tested under tension as per IS: 1608-2005. The properties

obtained from the test are tabulated in Table 3.2.

Water: Potable water was used for mixing concrete and for the curing

of cast specimens.

47

3.2.2 Casting Procedure

Totally 75 cylinders were cast and studied by varying the

parameters like centre to centre spacing of lateral ties, thickness of steel

sheet, width of lateral ties and compressive strength of concrete. The

geometrical details of confined cylinder is summarised in Table 3.3. The

casting of specimens involves two stages namely fabrication of

prefabricated cage and casting of cylinders.

Table 3.3 Geometric Details of Concrete Cylinders

Sl.No.

CylinderSeries

Thickness(ts) (mm)

Width of Lateralties (b) (mm)

Centre to centre Spacingof Lateral ties (Sv) (mm)

1. A1

1.6 15

Fully confined2. A2 503. A3 1004. A4 1505. A5 - Plain -6. B1

2.0 15

Fully confined7. B2 508. B3 1009. B4 150

10. B5 - Plain -11. C1

2.5 15

Fully confined12. C2 5013. C3 10014. C4 15015. C5 - Plain -16. D1

2.0 40

Fully confined17. D2 5018. D3 10019. D4 13020. D5 - Plain -21. E1

2.0 15

Fully confined22. E2 5023. E3 10024. E4 15025. E5 - Plain -

48

3.2.2.1 Fabrication of Prefabricated Cage for Cylindrical

Specimens

Width of the plate equal to depth and length of the plate which

is equal to the perimeter of the cylinder is taken (Figures 3.1 and 3.2).

The perforations were made to get the centre to centre spacing between

the lateral ties of 50mm, 100mm and 150mm. Then the plates were bent

in the plate bending machine and two ends of the plates were joined by

means of arc welding (Figure 3.3).

Five series of cylinders each consisting of 15 specimens and

hence a total of 75 nos. were cast. Each series consists of one set of fully

confined specimens, three sets of partially confined specimens along

with one set of unconfined specimen.

3.2.2.2 Mixes Adopted

Three mixture proportions were made. Design mix has been

adopted for the test specimen. The mix ratios and water cement ratios

used for the experimental investigation are given in Table 3.4.

Table 3.4 Mix proportions

Beam series Mix ratio W/C ratioA and D 1:1.85:4.87 0.50

B and C 1:1.77:4.65 0.50

E 1:1.69:3.43 0.50

49

3.2.2.3 Casting of Specimens

Within the standard cylinder mould, the fabricated cage was

kept and concrete was poured inside. After 24 hours from casting, the

specimens have been cured in water for 28 days.

Figure 3.1 Schematic View of Slotted Steel Sheet

Figure 3.2 Perforated Steel Sheet before Bending

Figure 3.3 Fabricated Cages for Cylinders

50

Figure 3.4 Test Setup

3.3 TESTING OF SPECIMENS

The specimens were tested using 1000 kN Universal Testing

Machine with auto recording facilities. Uniaxial compression was

applied in a gradual manner. The behaviour of the specimens was keenly

observed from the beginning till it gets collapsed. The appearance of

the first crack, local buckling of the sheet, the development and

propagation of cracks due to increase of load was also recorded. The

loading was continued beyond the maximum until the load was dropped

to about 50% of the maximum value.

3.4 RESULTS AND DISCUSSION

3.4.1 Behaviour of the Test Specimens under Load

The load increased rapidly in the initial stages up to about

80-85% of the peak load and thereafter increased at a slower rate until

the peak load was reached. For all the confined specimens, the test was

continued until the peak load dropped to about 0.5 to 0.75 times the

51

peak load. Beyond the peak load, the strains increased at a rapid rate and

were accompanied by a decrease in the load carrying capacity of the

specimens.

In case specimens confined with Prefabricated Cage, it was

observed that the lateral expansion was small during the initial stages of

loading, resulting in little or no confining stress, which had an

insignificant effect on the stress-strain behaviour of concrete. As the

axial stress increased further, the concrete began to crush and lateral

expansion increased rapidly. As the confining stress at this stage was

very large, the concrete benefited greatly due to the confinement and it

was observed that vertical cracks appeared on the concrete surface at

about 60% of the peak load. On further increase in load, the number of

cracks also increased and the cracks started to widen. Beyond the peak

load, confining steel started to buckle.

In specimens with closely spaced ties, fine vertical cracks

appeared on the concrete surface at about 70% of the peak load. Increase

in the number of cracks and widening of cracks occurred at a reduced

rate on the specimens, with the increase of load.

In case of plain concrete cylinders, the load increased rapidly

up to 70 to 80% of the peak load and thereafter, the rate of increase

became slow. It was observed that the failure of plain cylinders was

sudden and a wide diagonal crack was formed. The crack was steadily

propagated and led to the sudden splitting of specimens as the peak load

was reached.

52

Table 3.5 gives the test results of cylinders, which represent

the average of three test specimens. Referring to Table 3.5, it can be

seen that the values of the ultimate load of the confined cylinders were

higher than the unconfined cylinders which was cast from the same pour

of concrete.

Table 3.5 Details of the Experimental Results

ID.Mark

ts(mm)

SpacingSv

(mm)

UltimateCompressiveStrength, fcc

(N/mm2)

Increase inCompressive

Strength(%)

Strains Increase inUltimate

Strain at fcc(%)

@ peak @0.85peak

A1

1.6

CFT 45.86 224.10 0.0233 0.0385 606.06A2 50 23.21 64.03 0.0100 0.0259 203.03A3 100 20.95 48.06 0.0083 0.0167 151.52A4 150 19.25 36.04 0.0067 0.0127 103.032A5 PLAIN 14.15 - 0.0033 - -B1

2.0

CFT 49.27 148.59 0.0267 0.0545 709.09B2 50 31.71 59.99 0.0117 0.0252 254.55B3 100 29.44 48.54 0.0100 0.0150 203.035B4 150 25.48 28.56 0.0067 0.0121 103.0303B5 PLAIN 19.82 - 0.0033 - -C1

2.5

CFT 48.12 149.97 0.0283 0.0619 757.58C2 50 35.67 85.30 0.0167 0.0300 406.06C3 100 32.84 70.60 0.0117 0.0253 254.55C4 150 27.74 44.10 0.0083 0.0222 151.52C5 PLAIN 19.25 - 0.0033 - -D1

2.0

CFT 47.57 211.12 0.0281 0.0583 680.56D2 50 44.22 189.21 0.0267 0.0810 641.67D3 100 30.06 96.60 0.0220 0.0667 511.11D4 130 27.74 81.43 0.0120 0.0523 233.33D5 PLAIN 15.29 - 0.0036 - -E1

2.0

0 49.82 108.98 0.0167 0.0667 317.50E2 50 35.10 47.23 0.0100 0.0227 150.00E3 100 31.71 33.01 0.0083 0.0128 107.50E4 150 27.18 14.01 0.0067 0.0102 67.50E5 PLAIN 23.84 - 0.0040 - -

53

3.4.2 Mechanics of the Action of Steel Ties

The increase in compressive strength and the deformation of

confined concrete is due to the resistance offered to the lateral bulging

of concrete by the surrounding lateral ties of Prefabricated Cage. As the

longitudinal stress increases on a specimen with lateral ties, the lateral

pressure offered by the ties increases. This continues until the

maximum load is reached and the confined concrete is held in a sort of

plastic equilibrium between the longitudinal stress and lateral pressure.

Beyond this stage, there is no further increase in longitudinal stress

because the lateral binding medium starts yielding plastically for

additional lateral deformations. Also, after the maximum load is

reached, the strain energy released by the machine is absorbed in

deforming the confining steel further, and so the descending branch of

the stress-strain curve can be obtained in the usual testing machine.

3.4.3 Stress-Strain Behaviour

The stress-strain curves of the concrete confined by different

centre to centre spacing are illustrated in Figures 3.5(a) - 3.5(e) for

Group A, B, C, D and E.

When the concrete cylinder is confined by Prefabricated Cage,

its ultimate compressive strength is higher than the unconfined cylinder.

The compressive stress-strain curve is highly dependent on the centre to

centre distance of lateral ties and thickness of Prefabricated Cage. The

stress-strain curves from the experimental result shows that the

transverse ties of Prefabricated Cage can offer more confinement when

54

the spacing is less. An increase in the plastic plateau is observed in the

stress-strain curve of specimens confined with Prefabricated Cage when

compared to the unconfined specimens. Specimens with 50mm spacing

of lateral ties showed a higher increase in the confined strength than the

higher spacing specimens. Whereas the effect of confinement is small in

confined cylinders with 150mm spacing lateral ties which is consistent

with the predictions of Sundararaja Iyengar et. al. (1970).

During the ascending part of loading, confinement has little or

no effect and the concrete is visually free of cracks up to the first peak.

This peak corresponds to load at first crack of concrete. After that,

concrete axial stress loses 10-15% of its maximum value due to the

sudden cracking of concrete. At this stage, lateral concrete strain

increases significantly and as a result of which the passive confinement

becomes very significant. The concrete core gains strength due to the

lateral confining pressure. Generally, the stress-strain curves show a

slight strength gain and a plastic plateau after the peak load.

The stress-strain curves for unconfined concrete cylinders are

shown in Figure 3.5(f). The unconfined specimens suddenly failed when

they reached their ultimate load carrying capacity. Because of this, the

descending branch of the stress-strain curve of unconfined specimens

could not be determined. As the ascending portion of the stress-strain

curves of unconfined specimens merge with that of confined specimens,

it is shown separately in Figure 3.5(f).

55

Figure 3.5(a) Stress-Strain Curves of the Confined Concrete forSeries A

Figure 3.5(b) Stress-Strain Curves of the Confined Concrete forSeries B

0

5

10

15

20

25

30

35

40

45

50

0 0.01 0.02 0.03 0.04 0.05

Strain

t – 1.6 mmB – 15 mmfck - 14.15MPa

CFT

50 mm

100 mm150 mm

0

10

20

30

40

50

60

0 0.02 0.04 0.06 0.08

Strain

t – 2 mmfck – 19.82MPaB – 15 mm

CFT

50 mm

100 mm

150 mm

56

Figure 3.5(c) Stress-Strain Curves of the Confined Concrete forSeries C

Figure 3.5(d) Stress-Strain Curves of the Confined Concrete forSeries D

0

10

20

30

40

50

60

0 0.01 0.02 0.03 0.04 0.05 0.06

Strain

t – 2.5 mmfck – 19.25MPaB – 15 mm

CFT

50 mm

100 mm

150 mm

50mm

100mm130mm

57

Figure 3.5(e) Stress-Strain Curves of the Confined Concrete forSeries E

Figure 3.5(f) Stress-Strain Curves of the Unconfined Concrete

0

10

20

30

40

50

60

0 0.01 0.02 0.03 0.04 0.05 0.06

Strain

t – 2 mmfck – 23.84MPaB – 15 mm

CFT

100 mm

150 mm

50 mm

58

3.4.4 Strength Enhancement Factor

The confinement effect corresponding to each variable was

analyzed by calculating and comparing the loads carried by the core

concrete. The parametrical study was preceded by measuring the

strength enhancement factor defined as,

= (3.1)

where,

is the maximum compressive strength of confined concrete

is the compressive strength of the concrete cylinder.

Strength enhancement factor of cylinders confined by

Prefabricated Cage is listed in Table 3.5.

3.4.5 Ductility Index

The ductility of the confined member depends greatly on the

confinement degree of the core concrete. This study measured the

ductility of the specimen by utilizing the definition of the ductility ratio

provided by Razvi and Saatcioglu (1999). The ductility ratio (µ ), which

is the ratio of the core concrete strain ( ) corresponding to the stress

0.85 to an assumed strain (0.004), is given by,

= (3.2)

59

Ductility Index of cylinders confined by Prefabricated Cage is

listed in Table 3.6.

Table 3.6 Strength Enhancement Factor and Ductility Index ofCylinders confined by Prefabricated Cage

ID.Mark

SpacingSv

(mm)

Compressivestrength ofConfinedConcrete

fcc(N/mm2)

Compressivestrength ofunconfined

concretef’

c(N/mm2)

StrengthEnhancement

FactorKs

0.85Ductility

Ratio ( )

A2 50 23.2114.15

1.64 0.0259 6.475A3 100 20.95 1.50 0.0167 4.175A4 150 19.25 1.36 0.0127 3.175B2 50 31.71

19.821.60 0.0252 6.300

B3 100 29.44 1.49 0.0150 3.750B4 150 25.48 1.29 0.0121 3.025C2 50 35.67

19.251.85 0.0300 7.500

C3 100 32.84 1.71 0.0253 6.325C4 150 27.74 1.44 0.0222 5.550D2 50 44.22

15.292.89 0.0810 20.250

D3 100 30.06 1.97 0.0667 16.675D4 130 27.74 1.81 0.0523 13.075E2 50 35.10

23.841.47 0.0227 5.675

E3 100 31.71 1.33 0.0128 3.200E4 150 27.18 1.14 0.0102 2.550

3.4.6 Effect of Concrete Strength

As the axial loads increase from the initial stages of loading,

the concrete cylinder is longitudinally contracted and laterally expanded

with internal micro cracks. The lateral concrete pressure increases with

the increase of axial loads. At this time, the ties resist the high expansion

60

pressure and the effective confinement by lateral ties leads to the

enhancement of the axial load carrying capacity. Figures 3.6 (a) - 3.6 (d)

shows some of the tested specimens.

Figure 3.6(a) Tested Specimens –Failure Pattern for Sv-50mm c/c

Figure 3.6(b) Tested Specimens –Failure Pattern for Sv-100mm c/c

61

Figure 3.6(c) Tested Specimens –Failure Pattern for Sv-150mm c/c

Figure 3.6(d) Tested Specimens –Failure Pattern for CFT

Figure 3.7 gives the variation of strength enhancement factor

and ductility index of confined cylinders according to the compressive

strength of concrete cylinder. It is shown that the magnitude of the

strength and ductility of confined concrete decreases with the increase of

concrete strength because of its more brittle property.

62

Figure 3.7 Variations of Ks and µ According to Concrete Strength

3.4.7 Effect of Tie Spacing

Smaller tie spacing increases the confined concrete area

resulting in higher confinement. The concrete cylinder confined by the

smaller tie spacing can resist the larger stress due to the improved

confinement and they can resist the high-axial loads and high lateral

pressure. Figure 3.8 gives the variation of the factors Ks and of the

confined cylinders according to the tie spacing. It is observed that the

closely spaced ties lead to improved strength and ductility, due to the

increase of the effectively confined area of concrete for carrying the

loads. The cylinders with tie spacing of 50mm (D1/3) exhibit the large

increase in strength and ductility, but the cylinders with tie spacing of

150mm (D1) show minimum increase. It is desirable to sustain the tie

spacing below D for maintaining proper strength and ductility.

In addition, the tie spacing controls the buckling of

longitudinal braces. In A series specimens, the strength enhancement is

64%, 50% and 36% corresponding to tie spacing that is equal to 50mm,

1.1

1.2

1.3

1.4

1.5

1.6

1.7

12 17 22 27

fc' (Mpa)

1.1

2.1

3.1

4.1

5.1

6.1

7.1

12 17 22 27fc' (Mpa)

63

100mm and 150mm respectively. Whereas in B series specimens, 60%

to 29% increase in strength enhancement is observed. When compared

to B series specimens, C series specimens show more strength due to the

increase in lateral confining pressure i.e., using higher thickness lateral

ties.

Strength enhancement factor and ductility index of the D series

specimens are higher than all other series due to more confinement

provided by increase in width of lateral ties. When compared to B series,

E series specimens show a lesser enhancement in strength. This could be

attributed due to the fact the strength enhancement is inversely

proportional to the compressive strength of concrete.

Figure 3.8 Variations of Ks and µ According to Tie Spacing

3.5 CONFINING MODELS FOR CONFINED CONCRETE

In recent years, different research groups suggested different

confining models and equations for concrete confined with steel spirals

or ties. In the following section, equations are proposed to estimate the

1.11.31.51.71.92.12.32.52.72.93.1

0 100 200Tie Spacing (mm)

A SeriesB SeriesC SeriesD SeriesE Series

1.1

6.1

11.1

16.1

21.1

26.1

0 50 100 150 200Tie Spacing (mm)

A Series

B SeriesC SeriesD Series

E Series

64

ultimate stress and strain of concrete confined by Prefabricated Cage

based on the investigations by Richart et.al. (1928).

3.5.1 Ultimate Compressive Strength

Most empirical expressions for predicting the strength of

confined concrete (fcc) take the form of Richart et. al. (1928).

(3.3)

where,

fl is the lateral stress that produces confinement,

= (3.4)

is the strength of unconfined concrete cylinder

k1 is the confinement effectiveness coefficient

Equation (3.3) has been used by most researchers to estimate

the ultimate stress of confined concrete (fcc) assuming that the failure of

the system occurs when the confined pressure reaches its maximum.

The confinement effectiveness coefficient k1 is also a variable

with respect to the confining pressure. Using a regression analysis of the

experimental data with a correlation factor of 93 percent, an equation for

k1 can be calculated as,

= 2.742 (3.5)

65

3.5.2 Ultimate Axial Strain

Cylinder failure occurs when the lateral strain reaches the

ultimate strain of the lateral ties. Therefore, for identifying the ultimate

axial strain, any model should consider the effect of the lateral strain.

Ultimate longitudinal strain ( cc) proposed by Richart et.al. is

given as,

1 + (3.6)

where,

fl is the lateral stress that produces confinement

is the strength of unconfined concrete

k2 is the effectiveness coefficient

is the ultimate strain of unconfined concrete

Using a regression analysis of the experimental data with a

correlation factor of 92 percent, an equation for k2 can be calculated as,

= 13.90 (3.7)

66

3.5.3 Comparison between Predicted and Experimental Results

The experimental test results obtained in this study were

compared to the analytical data obtained by the proposed equations. The

analytical model was also compared to the model available in the

literature (Mander et. al.1988).

Confinement model proposed by Mander et. al. (1988),

1.25 + 2.25 1 + (3.8)

1 + 5 (3.9)

Comparisons between the experimental and predicted values

of the ultimate strengths and failure strains of concrete confined by

Prefabricated Cage are presented in Tables 3.7 and 3.8, respectively.

The equations proposed in this study perform the best as compared to

Mander’s equations. Table 3.7 shows that the ultimate strength of

Prefabricated Cage confined concrete specimens suits well with the

proposed equation, whereas Mander’s equation underestimates the

strength. Table 3.8 also shows that the failure strains of Prefabricated

Cage encased concrete specimens compare satisfactorily with the

proposed equation, whereas the Mander’s equation underestimates the

failure strain.

67

Table 3.7 Comparison of Prediction Equations for CompressiveStrength of Concrete Cylinders Confined byPrefabricated Cage

ID.Mark

fl(N/mm2)

ExperimentalStrength

fcc(N/mm2)

Proposed Equation Mander’sEquation

fcc(N/mm2)

Error,Percent

fcc(N/mm2)

Error,Percent

A2 1.664 23.21 23.79 -2.50 23.26 -0.22A3 0.832 20.95 20.08 4.15 19.21 8.31A4 0.556 19.25 18.64 3.17 17.67 8.21B2 2.240 31.71 32.96 -3.94 32.17 -1.45B3 1.130 29.44 27.96 5.03 26.66 9.44B4 0.746 25.48 25.89 -1.61 24.55 3.65C2 3.196 35.67 35.96 -0.81 35.50 0.48C3 1.600 32.84 29.55 10.02 28.54 13.09C4 1.066 27.74 27.01 2.63 25.77 7.10

D2 5.972 44.22 45.15 -2.10 38.61 12.69

D3 2.986 30.06 30.16 -0.33 29.86 0.67

D4 2.296 27.74 27.66 0.29 27.23 1.84

E2 2.322 35.10 35.45 -1.00 36.99 -5.38

E3 1.166 31.71 32.74 -3.25 31.07 2.02

E4 0.772 27.18 27.70 -2.00 28.80 -5.96

68

Table 3.8 Comparison of Prediction Equations for Ultimate Strainof Concrete Cylinders Confined by Prefabricated Cage

ID.Mark

flExperimental

Strain

Proposed Equation

Mander’sEquation

cc Error,Percent

cc Error,Percent

A2 1.664 0.0100 0.0113 -13.48 0.0084 15.97A3 0.832 0.0083 0.0086 -3.18 0.0068 18.00A4 0.556 0.0067 0.0073 -9.18 0.0056 16.35B2 2.240 0.0117 0.0111 4.76 0.0080 31.63B3 1.130 0.0100 0.0084 15.50 0.0069 31.46B4 0.746 0.0067 0.0072 -8.13 0.0049 27.53C2 3.196 0.0167 0.0131 21.41 0.0105 36.95C3 1.600 0.0117 0.0098 16.13 0.0091 22.57C4 1.066 0.0083 0.0083 -0.40 0.0064 22.77D2 5.972 0.0267 0.0192 28.01 0.0209 21.64D3 2.986 0.0220 0.0141 36.01 0.0117 47.00D4 2.296 0.0120 0.0126 -4.70 0.0101 15.48E2 2.322 0.0100 0.0105 -4.59 0.0067 32.77E3 1.166 0.0083 0.0078 5.48 0.0053 36.13E4 0.772 0.0067 0.0068 -1.56 0.0034 49.24

3.5.4 Influence of Confinement on Ultimate Strength and Strain

When the load on the confined specimen reached a maximum

value Richart et. al. (1928) concluded that the steel had reached a point

far beyond its limit of proportionality. Hence, in studying the effect of

confinement on ultimate strength, the stress in the confining steel is

taken to be equal to its yield stress. To take into account the influence on

the physical properties of confining steel and confined concrete on the

69

effect of confinement, the confinement factor is defined as b x (fy/fc’).

Where fy is the yield strength of the lateral ties, fc’ is the compressive

strength of unconfined concrete cylinder and b is the volumetric ratio

taken as the ratio of volume of braces to the volume of confined

concrete.

The variation of strains cc and 0.85 at ultimate stress and

0.85 times ultimate stress in the descending portion of the curve are

studied with respect to confinement factor. The ratio of the strains is

plotted against confinement factor (Figures 3.9 and 3.10) for the values

in the Table 3.5. From the plot, it is observed that the ( cc co) and

0.85 co) varied linearly with the confinement factor.

Figure 3.9 Variations of Confinement Factor with Enhancement inStrain ( cc co)

cc co = 0.08 b.fy /fc' + 1.190R² = 0.91

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100

Confinement Factor, b.fy/fc'

70

The equation for enhancement in strain at ultimate stress with

confinement factor is given by,

= 0.08 + 1.19 (3.10)

Figure 3.10 Variations of Confinement Factor with Enhancement inStrain ( 0.85 co )

The equation for enhancement in strain at 0.85 times ultimate

stress in the descending portion of the stress-strain curve is given by,

= 0.287 + 0.646 (3.11)

0.85 co = 0.287 b.fy/fc' + 0.646R² = 0.928

0

5

10

15

20

25

0 20 40 60 80 100

Confinement Factor, s.fy/fc'

71

3.6 KEY FINDINGS

The influence of confinement on the ultimate strength,

ultimate strain and stress-strain characteristics have been studied

through an experimental investigation.

By performing a series of compression tests on confined

and unconfined cylinders of different compressive

strength of concrete, thickness of steel sheet and centre to

centre spacing of lateral ties, it is demonstrated that

confined cylinders with smaller tie spacing has good

confinement and enhanced strength.

Confinement provided by Prefabricated Cage increases

both strength and deformation capacity of concrete in

compression. The increase in the strain capacity is

considerably greater than the increase in the strength. For

instance, in B2 specimens, the strength of concrete is

increased by 1.6 times whereas, the strain at maximum

stress is increased by about 3.5 times when a lateral tie

spacing of 50mm centre to centre is used for confinement.

The ultimate compressive strength of the concrete

confined by Prefabricated Cage is increased by 47 – 85%

in specimens with 50mm spacing of lateral ties, whereas,

in specimens with 100mm spacing lateral ties, it varies

from 33% - 71% depending upon the cross sectional area

of lateral ties.

72

An increase in the thickness of the Prefabricated Cage,

i.e., increase in the lateral confining stress can increase

the ultimate strength and strain of confined concrete.

The effect of confinement is small when the pitch of the

binder is equal to the least lateral dimension of the

specimen. This is because concrete under compressive

load fails at 45° plane which meet the sides of the

specimen over a depth equal to the least lateral dimension

of the specimen.

The ultimate strength and strains of confined concrete are

found to increase linearly with confinement factor within

the limits of variables studied in this investigation.

Strength enhancement factor and ductility factor

decreases with increase in the compressive strength of

concrete, area of lateral ties and decrease with increase in

lateral tie spacing.

Equations proposed to estimate the ultimate stresses and

ultimate strains produce satisfactory predictions as

compared to the model proposed by Mander et. al. (1988).