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).