Page 5 - ICJ-November-2019

TECHNICAL PAPER

The value of dynamic Poisson’s ratio is always higher than the suggested the following expression
static Poisson’s ratio; an average value is about 0.24 . Leslie E c=1.04E d - 4.1 (9)
[4]
[5]
and Cheesman used the value of Poisson’s ratio of 0.24 for the
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concretes having a density in excess of 2240 kg/m and found For normal density concretes, Popovics suggested the
[12]
good results. following relationship in terms of density of concrete
In general, the modulus of elasticity increases with the E c=446.09E d ρ -1 (10)
1.4
compressive strength of concrete. However, the modulus of
[13]
elasticity of aggregates and hydrated cement paste affect Nematzadeh and Naghipour provided an interesting solution
the modulus of elasticity of concretes. The static modulus to enhance the compressive strength and elastic modulus of
[14]
of elasticity of concrete, recommended by IS 456 , can be concrete. Krizova and Hela described the influence of various
[1]
assumed as factors on elasticity modulus of concrete. Authors presented
that the results of the elastic modulus of concrete are mainly
E c=5.0 f ck (2) influenced by water coefficient and the size of the maximum
[15]
The actual measured values may differ by ±20% from the values fraction of the aggregate. Kulkarni et al. investigated
obtained from Eqn. (2). The relationship for the secant modulus the modulus of elasticity of concrete, made with recycled
[6]
of elasticity, recommended by ACI 318 is aggregates. Authors found that elastic modulus decreases
when the percentage replacement of recycled aggregates is
[16]
E c=4.73 f ck (3) increased. Lee et al. evaluated the dynamic elastic modulus
For concretes with compressive strength up to 83 MPa, ACI 363R of three different concretes with target compressive strengths of
[7]
quotes 30, 35 and 40 MPa using the shear-wave velocity measurements.
E c=3.32 f ck +6.9 (4) The aim of the study is to provide some relevant data on
dynamic modulus of elasticity; in which the properties of
In the range of compressive strength between 80 to 140
[8]
MPa, Kakizaki et al. found that the modulus of elasticity is concretes are the main subject of investigation. In order to
approximately related to compressive strength by compare the low strength concrete with the medium strength
concrete several testing were performed in the laboratory,
E c=3.65 f ck (5) conforming to the relevant Indian standards. UPV of the
concretes were experimentally obtained and the dynamic
The density of concrete is increased when the density of
aggregates increases. However, the normal weight aggregates modulus of elasticity of concretes are calculated with the
have a higher density than the hydrated cement paste and as a assumed value of Poisson’s ratio. The results are presented with
result, higher modulus of elasticity of concrete is obtained for the correlation of the predicted models by regression analysis.
a given compressive strength. When the density of concrete is
between 2320 and 2480 kg/m , the modulus of elasticity was 2. eXPeRIMeNtAL stUDY
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given by ACI 318 as 2.1 Material Properties
[6]
E c=4.3ρ 1.5 f ck ×10 -5 (6) Concrete is produced by homogenous mixing of suitable
proportions of cement, water, and aggregates. The physical
The ratio of static to dynamic modulus is always smaller than
unity. The ratio is increased with the age and is higher for high properties of materials, which were obtained experimentally in
strength of concrete. Various relationships were proposed by the laboratory, are described in the following sections.
different researchers. The simplest of these, proposed by Lydon
and Balendran was 2.1.1 Cement
[9]
Pozzolana Portland cement is normally used in concrete
(7)
E c=0.83E d
technology nowadays and it is used in various quantities to
The British testing standard BS8100 Part 2 provided the obtain a wider range of mixtures of low and medium strength
[10]
following empirical equation concretes. PPC, conforming to IS 1489 was used in this
[17]
E c=1.25E d -19 (8) investigation in preparing the concrete mixtures. The tests were
performed in the laboratory to determine the physical and
However, Eqn. (8) does not apply for the concretes that contain mechanical properties of cement and the obtained values are
more than 500 kg/m of cement. Swamy and Bandyopadhyay presented in Table 1.
[11]
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8 The IndIan ConCreTe Journal | november 2019