Chapter 5Concrete

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 909

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5.1 Grades

The concrete shall be in grades designated as per Table 1.

Table 1 Grade of Concrete(Clauses 5.1, 8.2.2 and 20.1)
Sl No.	Grade Designation	Specified Characteristic Compressive Strength of 150 mm Size Cube at 28 Days $N/mm^2$ (3)
(1)	(2)
i)	M 30	30
ii)	M 35	35
iii)	M 40	40
iv)	M 45	45
v)	M 50	50
vi)	M 55	55
vii)	M 60	60
viii)	M 65	65
ix)	M 70	70
x)	M 75	75
xi)	M 80	80
xii)	M 85	85
xiii)	M 90	90
xiv)	M 95	95
xv)	M 100	100
NOTES1 In the designation of concrete mix M refers to the mix and the number to the specified compressive strength of 150 mm size cube at 28 days, expressed in $N/mm^2$ .2 For pre-tensioned prestressed concrete, the grade of concrete shall be not less than M 40.3 Except where specifically mentioned otherwise, for concrete grade greater than M 60, design parameters given in the Subsection may not be applicable and the values may be obtained from specialized literatures and experimental results.

5.1.1 The characteristic strength of concrete is defined as the strength of the concrete below which not more than 5 percent of the test results are expected to fall.

5.2 Properties of Concrete

5.2.1 Increase in Strength with Age

There is normally a gain of strength beyond 28 days. The quantum of increase depends upon the grade and type of cement, curing and environmental conditions, etc. The design should be based on 28 days characteristic strength of concrete unless there is an evidence to justify a higher strength for a particular structure due to age.

5.2.1.1 The rate of increase of compressive strength with age shall be based on actual investigations.

5.2.2 Tensile Strength of Concrete

The flexural and splitting tensile strength shall be obtained in accordance with accepted standards $[6-5B(10)]$ . When the designer wishes to use an estimate of the flexural tensile strength from the compressive strength, the following formula may be used:

f _ {\mathrm{cr}} = 0. 7 \sqrt {f _ {\mathrm{ck}}}

cr

=

0.7fck

where

$f_{\mathrm{cr}} =$ flexural tensile strength, in $\mathrm{N / mm^2}$ ; and

$f_{ck}$ = characteristic compressive strength of concrete, in N/mm $^{2}$ .

5.2.3 Elastic Deformation

The modulus of elasticity is primarily influenced by the elastic properties of the aggregate and to a lesser extent by the conditions of curing and age of the concrete, the mix proportions and the type of cement. The modulus of elasticity is normally related to the compressive strength of concrete.

5.2.3.1 The modulus of elasticity for concrete may be assumed as follows:

E _ {\mathrm{c}} = 5 0 0 0 \sqrt {f _ {\mathrm{ck}}}

where

$E_{c}$ = short term static modulus of elasticity, in N/mm $^{2}$ ; and

$f_{ck}$ = characteristic compressive strength of concrete, in N/mm $^{2}$ .

Actual measured values may differ by $\pm20$ percent from the values obtained from the above expression.

5.2.4 Shrinkage

The total shrinkage of concrete depends upon the constituents of concrete, size of the member and environmental conditions. For a given humidity and temperature, the total shrinkage of concrete is most influenced by the total amount of water present in the concrete at the time of mixing and, to a lesser extent, by the cement content.

5.2.4.1 The total shrinkage strain is composed of two components, the autogenous shrinkage strain and the drying shrinkage strain.

The value of the total shrinkage strain, $\varepsilon_{\mathrm{cs}}$ is given by:

\varepsilon_ {\mathrm{cs}} = \varepsilon_ {\mathrm{cd}} + \varepsilon_ {\mathrm{ca}}

where

\varepsilon_ {\mathrm{cs}} = \text {total shinkage strain};

\varepsilon_ {\mathrm{cd}} = \text {drying shrinkage strain; and}

\varepsilon_ {\mathrm{ca}} = \text {autogenous shrinkage strain.}

5.2.4.2 The autogenous shrinkage strain develops during hardening of concrete; the major part develops in the early days after casting. Autogenous shrinkage is a linear function of concrete strength. It should be considered specifically when new concrete is cast against hardened concrete.

In the absence of accurate field/laboratory data, the following values may be considered in design:

Grade of Concrete	Autogenous Shrinkage $(\varepsilon_{\text{ca}} \times 10^{6})$
M 30	35
M 35	45
M 45	65
M 50	75
M 60	95

5.2.4.3 The drying shrinkage strain develops slowly, as it is a function of migration of the water through the hardened concrete.

The final value of the drying shrinkage strain, $\varepsilon_{cd,\infty}$ may be taken as equal to $k_{h}\cdot\varepsilon_{cd}$ Values of may be taken from the table given below for guidance. These values are expected mean values, with a coefficient of variation of about 30 percent.

f_{ck}

MPa

Unrestrained Drying Shrinkage Values

(\varepsilon_{cd} \times 10^{6})

for Concrete with PortlandCement for Relative Humidity

NOTE — The values for the other designated grades may be obtained by interpolation.

$k_{\mathrm{h}}$ is a coefficient depending on the notional size $h_0$ , as given below:

$h_0$	$k_h$
mm
100	1.0
200	0.85
300	0.75
≥ 500	0.70

5.2.4.4 The development of autogenous shrinkage with time may be taken as:

\varepsilon_ {\mathrm{ca}} (t) = \beta_ {\mathrm{as}} (t). \varepsilon_ {\mathrm{ca}}

where

$\beta_{\mathrm{as}}(t) = 1 - \exp \left(-0.2\sqrt{t}\right)$ where, is in days.

5.2.4.5 The development of the drying shrinkage strain in time may be taken as:

\varepsilon_ {\mathrm{cd}} (t) = \beta_ {\mathrm{ds}} (t, t _ {\mathrm{s}}). k _ {\mathrm{h}}. \varepsilon_ {\mathrm{cd}}

\beta_ {\mathrm{ds}} \left(t, t _ {\mathrm{s}}\right) = \frac {\left(t - t _ {\mathrm{s}}\right)}{\left(t - t _ {\mathrm{s}}\right) + 0 . 0 4 \sqrt {h _ {0} ^ {3}}}

where

$t =$ age of the concrete at the moment considered, in days;

$t_{s} =$ age of the concrete at the beginning of drying shrinkage, in days; normally this is at the end of curing; and

$h_0 =$ notional size of the cross-section, in mm

= $2A_{c}/u$ , where $A_{c}$ is the concrete cross-sectional area and u is the perimeter of that part of the cross-section which is exposed to drying.

5.2.5 Creep

Creep of concrete depends, in addition to the factors listed in 5.2.4 on the stress in the concrete, age at loading and the duration of loading. As long as the stress in concrete does not exceed one-third of characteristic compressive strength, creep may be assumed to be proportional to the stress.

5.2.5.1 The creep coefficient

\phi (t, t _ {0}) = \frac {\varepsilon_ {\mathrm{cc}} (t)}{\varepsilon_ {\mathrm{ci}} (t _ {0})}

where

\varepsilon_ {\mathrm{cc}} (t) = \text {creep strain at time} t > t _ {0},

\varepsilon_ {\mathrm{cl}} (t _ {0}) = \text {initial strain at loading, and}

t _ {0} \quad = \text {initial time of loading.}

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5B PRESTRESSED CONCRETE

The creep coefficient $\phi (t,t_0)$ is given by:

\phi (t, t _ {0}) = \phi_ {0} \beta (t, t _ {0}),

where

$\phi_{0}$ = notional creep coefficient to which the creep co-efficient reaches asymptotically with time (this can be taken as value reached in 70 years), and

$\beta (t,t_0) =$ coefficient describing development of creep with time (see 5.2.5.2).

The notional creep coefficient $\phi_0$ is given by:

\phi_ {0} = \phi_ {\mathrm{RH}} \beta (f _ {\mathrm{cm}}) \beta (t _ {0})

where

$\phi_{\mathrm{RH}} =$ factor to allow for the effect of relative humidity on the notional creep coefficient

\begin{array}{l} = 1 + \frac {1 - \mathrm{RH} / 1 0 0}{0 . 1 \sqrt [ 3 ]{\mathrm{h} _ {0}}} \text {for} f _ {\mathrm{ck}} \leq 4 5 \mathrm{MPa} \\ = \left[ 1 + \frac {1 - \mathrm{RH} / 1 0 0}{0 . 1 \sqrt [ 3 ]{\mathrm{h} _ {0}}} \cdot \alpha_ {1} \right]. \alpha_ {2} \text {for} f _ {\mathrm{ck}} > 4 5 \mathrm{MPa} \end{array}

RH = relative humidity of the ambient environment in percent;

$h_0$ = notional size of the member, in mm;

= 2 A _ {\mathrm{c}} / u;

$A_{\mathrm{c}} =$ cross-sectional area, and

u = perimeter of the member in contact with the atmosphere;

$\beta(f_{\mathrm{cm}})=$ factor to allow for the effect of concrete strength on the notional creep coefficient

= \frac {1 6 . 8}{\sqrt {f _ {\mathrm{ck}} + 8}}

$\beta (t_0) =$ factor to allow for the effect of concrete age at loading on the notional creep coefficient

= \frac {1}{\left(0 . 1 + t _ {0} ^ {0 . 2 0}\right)}

Where end results are not sensitive to precise values calculated as given above, the values given in the table below can be considered as final creep coefficient for design for normal weight concrete of grades between M 30 and M 60, subject to condition that the compressive stress does not exceed $0.36 f_{ck}$ at the age of loading, and mean temperature of concrete is between $10^{\circ}C$ and $20^{\circ}C$ with seasonal variation between and . For temperature greater than the coefficient given may be increased by 10 percent in absence of accurate data.

Age at Loading $t_0$ (days)	Creep Coefficient $\phi_o$ (70 yr, $t_0$ ) of an Ordinary Structural Concrete after 70 Years of Loading

5.2.5.2 The development of creep with time may be taken as $\phi(t,t_{0})=\beta(t,t_{0})\phi_{0}$

\left| \beta \left(t, t _ {0}\right) = \left[ \frac {t - t _ {0}}{\beta_ {\mathrm{H}} + \left(t - t _ {0}\right)} \right] ^ {0. 3} \right|

where

$t$ = age of concrete in days at the moment considered;

$t_0$ = age of concrete at loading, in days;

$(t - t_0) =$ duration of loading, in days; and

$\beta_{H}$ = a coefficient depending on the relative humidity (RH in percent) and the notional member size ( $h_{0}$ in mm).

\left| \begin{array}{l} = 1. 5 \left[ 1 + \left(1. 2 \frac {\mathrm{RH}}{\mathrm{RH} _ {0}}\right) ^ {1 8} \right] h _ {0} + 2 5 0 \leq 1 5 0 0 \\ \text {for} f _ {\mathrm{ck}} \leq 4 5 \mathrm{MPa} \\ = 1. 5 \left[ 1 + \left(1. 2 \frac {\mathrm{RH}}{\mathrm{RH} _ {0}}\right) ^ {1 8} \right] h _ {0} + 2 5 0 \alpha_ {3} \leq 1 5 0 0 \alpha_ {3} \\ \text {for} f _ {\mathrm{ck}} > 4 5 \mathrm{MPa} \end{array} \right|

where

RH = relative humidity expressed as percent.

$RH_{0}$ = 100 (that is, 100 percent relative humidity).

$\alpha_{1}, \alpha_{2}, \alpha_{3} =$ coefficients to consider the influence of the concrete strength,

\alpha_ {1} = \left[ \frac {4 5}{f _ {\mathrm{ck}} + 8} \right] ^ {0. 7}, \alpha_ {2} = \left[ \frac {4 5}{f _ {\mathrm{ck}} + 8} \right] ^ {0. 2}, \alpha_ {3} = \left[ \frac {4 5}{f _ {\mathrm{ck}} + 8} \right] ^ {0. 5}

5.2.6 Thermal Expansion

The coefficient of thermal expansion depends on nature of cement, the aggregate, the cement content, the relative humidity and the size of sections. The values of coefficient of thermal expansion for concrete with different aggregates may be taken as given below:

Type of Aggregate	Coefficient of Thermal Expansion for Concrete / °C
Quartzite	$1.2 \text{ to } 1.3 \times 10^{-5}$
Sandstone	$0.9 \text{ to } 1.2 \times 10^{-5}$
Granite	$0.7 \text{ to } 0.95 \times 10^{-5}$
Basalt	$0.8 \text{ to } 0.95 \times 10^{-5}$
Limestone	$0.6 \text{ to } 0.9 \times 10^{-5}$

6 WORKABILITY OF CONCRETE

The concrete mix proportions chosen should be such that the concrete is of adequate workability for the placing conditions of the concrete and can properly be compacted with the means available. Suggested ranges of values of workability of concrete are given in Part 6 'Structural Design, Section 5 Concrete, Subsection 5A Plain and Reinforced Concrete' of the Code.

\varepsilon_{cd}

6

)

ca

)

t

s

)

.

kh

.

εcd

(t−ts)+0.04h03(t−ts)

)

,

β

(

t0

)

0.13h01−RH/100

for

fck

≤

45

MPa

=[1+0.13h01−RH/100⋅α1].α2forfck>45MPa

16.8

∘

C

-20^{\circ}C

40^{\circ}C

40^{\circ}C

[

βH+(t−t0)t−t0

]

0.3

=1.5[1+(1.2RH0RH)18]h0+250≤1500forfck≤45MPa=1.5[1+(1.2RH0RH)18]hforfck>45MPa

ck

+

8

45

]

0.7

,

α2

=

[fck+845]0.2,α3=

[fck+845]0.5

0

+

250

α3

≤

1500

α3