1. INTRODUCTION
⌅Concrete, one of the most extensively used construction materials pan world, is under the lens due to the rapid pace at which construction is being undertaken. However, the present spurt of construction activity indicates that adequate care needs to be taken in order to maintain material quality which can sustain the above said growth. The quality of concrete is determined by the mechanical properties it exhibits, therefore in order to ensure product efficacy, the mechanical properties of concrete need to be evaluated with accuracy. Among these, compressive strength (), flexural strength () (modulus of rupture), and modulus of elasticity () are important properties of concrete. In the analysis and design of any type of concrete structures viz., plain, reinforced, or prestressed, these properties need to be well evaluated and incorporated.
Practical assessment of these mechanical
properties with accuracy requires a prolonged duration. However, with
emerging demand for rapid construction, it is the need of hour to have
models for estimating these properties at early stages with accuracy.
The standard guidelines of various countries give the correlation of
compressive strength with the modulus of elasticity and flexural
strength. Table 1 presents the correlations recommended by the design codes of various nations (17(1) BIS, IS. (2000). 456 (2000). Plain and reinforced concrete Code of Practice. Bureau of Indian Standards, New Delhi, India.
(2)
ACI Committee (1999). Building code requirements for structural
concrete: (ACI 31899), and commentary (ACI 318R99). American Concrete
Institute.
(3) Milburn, J.R., Park, R. (1982). Behavior of Reinforced
Concrete Beam Column Joints Designed to NZS 3101. Department of Civil
Engineering, University of Canterbury.
(4) Walraven, J.C. (2008). Eurocode 2: Design of Concrete Structures EN199211 [C]. In Symposium Euro Codes: Background and Applications, Brussels.
(5)
Standard, B. (1985). 8110: Part 1, Structural use of concretecode of
practice for design and construction. British Standards Institute,
London UK, 38.
(6) Canadian Standards Association. (2004). Design of concrete structures. Mississauga. Ont.: Canadian Standards Association.
(7) Turkish Standards. (2000). Requirements for design and construction of reinforced concrete structures. Ankara Turkey.
). However, the values obtained from these correlations are found to be deviating from the experimental values (8(8)
Anbuvelan, K., Subramanian, K. (2014). An empirical relationship
between modulus of elasticity, modulus of rupture and compressive
strength of M60 concrete containing metakaolin. Research Journal of Applied Sciences, Engineering, and Technology, 8(11), 12941298.
,9(9)
Vijayalaxmi, B., Ajay, H., Ranjith, A., Sandya, D. (2015). Experimental
investigation on elastic properties of concrete incorporating GGBFS. International Journal for Research in Applied Science & Engineering Technology, 3(5), 487496.
).
This may be due to the development of technology and extensive
improvement in the quality of ingredients of concrete, especially
cement. Further, the commercially available design software uses the
default values of elastic modulus and flexural strength as stipulated in
standard codes. This leads to incorrect usage of materials, especially
for relatively high strength concrete.
Country  Code of Reference  Modulus of Elasticity  Flexural Strength  Remarks 

American Code  ACI 318 
$Ec=4700\sqrt{fc\text{'}}$

$fr=0.7\sqrt{fc\text{'}}$

$fc\text{'}$ specified 28 days cylinder comp strength 
New Zealand code  NZS 3101 
$Ec=3320\sqrt{fc\text{'}}+6900$

$fcr=0.6\sqrt{fc\text{'}}$

$fc\text{'}$ specified 28 days cylinder comp strength 
Euro Code  EN1992 11 
$Ecm=22000{\left(0.1*fcm\right)}^{0.3}$

$fctm=2.2*\mathrm{l}\mathrm{n}(1+0.1fcm$

$fcm$ Mean value of 28 days concrete cylinder compressive strength 
British Code  BS 8110 
$Ec=20000+0.2*fcu$

$fcr=0.6\sqrt{fcu}$

$fcu$ is the characteristic cube strength at 28 days 
Canadian Code  CSA A23.304 
$Ec=4500\sqrt{fc\text{'}}$

$fr=0.6\sqrt{fc\text{'}}$

$f{c}^{\text{'}}$ specified 28 days cylinder comp strength 
Turkish Code  TS 5002003 
$Ec=3250\sqrt{fck}+14000$

$fr=0.7\sqrt{fck}$

$fck$ characteristic 28 days cylinder compressive strength 
Indian Code  IS 456 
$Ec=5000\sqrt{fck}$

$fcr=0.7\sqrt{fck}$

$fck$ characteristic 28 days cube compressive strength 
Initially, Li (10(10) Guoqiang, L., Zhao, Y., Pang, S., Li, Y. (1999). Effective Young’s modulus estimation of concrete. Cement and Concrete Research, 29(9), 14551462.
) developed the fourphase sphere model for the theoretical estimation of effective modulus of elasticity. Tomosawa (11(11)
Tomosawa, F., Noguchi, T. (1993). Relationship between compressive
strength and modulus of elasticity of high strength concrete. In Proceedings of the Third International Symposium on Utilization of High Strength Concrete, 2, 12471254.
)
has proposed a practical and universal equation for estimating the
modulus of elasticity, considering the unit weight and type of
aggregates. The mathematical equations for modulus of elasticity with
consideration to different types of aggregates were also developed (12(12)
Noguchi, T., Tomosawa, F., Nemati, K., Chiaia, B., Fantilli, A. (2009).
A practical equation for elastic modulus of concrete. ACI Structural Journal, 106(5), 690.
).
Some researchers gave equations for different mechanical properties of
concrete containing mineral admixtures such as fly ash, silica fume,
metakaolin, and palm kernel shell (7(7) Turkish Standards. (2000). Requirements for design and construction of reinforced concrete structures. Ankara Turkey.
, 8(8)
Anbuvelan, K., Subramanian, K. (2014). An empirical relationship
between modulus of elasticity, modulus of rupture and compressive
strength of M60 concrete containing metakaolin. Research Journal of Applied Sciences, Engineering, and Technology, 8(11), 12941298.
, 13(13)
Pitroda, J., Umrigar, F. (2013). Evaluation of modulus of elasticity of
concrete with partial replacement of cement by thermal industry waste
(fly ash) and paper industry waste (hypo sludge). International Journal of Engineering Science and Innovative Technology, 2(1), 133.
14(14)
Yusuf, I., Jimoh, Y., Salami. W. (2016). An appropriate relationship
between flexural strength and compressive strength of palm kernel shell
concrete. Alexandria Engineering Journal, 55(2), 15531562.
). Liu (15(15) Liu, B., Lv, W., Li, L., Li, P. (2014). Effect of moisture content on static compressive elasticity modulus of concrete. Construction and Building Materials, 69, 133142.
)
reported that the microcracks formed during the curing period have a
significant effect on the elastic modulus. The empirical equation was
proposed to estimate the elastic modulus considering the microcracking
pattern and moisture content. Ahmed (16(16) Ahmed, M., Mallick, J., Hasan, M. (2016). A study of factors affecting the flexural tensile strength of concrete. Journal of King Saud University Engineering Sciences, 28(2), 147156.
)
studied factors like level of stress, age, and confinement ratio, which
have a significant effect on the flexural tensile strength.
Advancements are also made for the development of empirical equations
for freshly compacted concrete (17(17) Nematzadeh, M., Naghipour, M. (2012). Compressive strength and modulus of elasticity of freshly compressed concrete. Construction and Building Materials, 34, 476485.
).
Further,
a study of elastic modulus for sprayed concrete is conducted. It has
been observed that there is a significant difference between the elastic
modulus of plain concrete and sprayed concrete (18(18) Galobardes, I., Cavalaro, S., Aguado, A., Garcia, T. (2014). Estimation of the modulus of elasticity for sprayed concrete. Construction and Building Materials, 53, 4858.
). Equations for mechanical properties of high strength concrete with admixture are also reported (13(13)
Pitroda, J., Umrigar, F. (2013). Evaluation of modulus of elasticity of
concrete with partial replacement of cement by thermal industry waste
(fly ash) and paper industry waste (hypo sludge). International Journal of Engineering Science and Innovative Technology, 2(1), 133.
, 19(19) Gutierrez, P., Canovas, M. (1995). The modulus of elasticity of highperformance concrete. Materials and Structures, 28(10), 559568.
).
However, the models for predicting different mechanical properties for
various mix proportions constituting different commercial grades of
concrete have not been found as reported. In the present study,
extensive experimentation is carried out to determine compressive
strength on cube specimens and cylinder specimens, flexural strength on
beam specimens and modulus of elasticity of concrete. The present
experimental results for flexural strength and modulus of elasticity are
compared with the results obtained using correlations given by
different national codes. Further, the statistical models are developed
using the experimental results to predict the mechanical properties of
concrete. The efficacy of these models is established with some
experimental results as well as the results from the available
literature.
2. EXPERIMENTAL PROCEDURE
⌅Eight basic concrete mixes of varying varieties are used in the present study. Table 2 illustrates the above said mix proportions and corresponding water to cement ratio and aggregate to cement ratio. For different watercement ratios ranging from 0.6 to 0.33, the aggregatecement ratio ranges from 6.9 to 4.9, respectively. Cement content varied from 300 kg/m^{3} [0.0108 lbs/in^{3}] to 420 kg/m^{3} [0.0151 lbs/in^{3}] for different mix proportions.
Mix  Watercement ratio  Aggregate cement ratio  Quantities 1 cu.m of concrete (kg^{#})  

Cement content  F.A. 
C.A. 10 mm (0.393 in) 
C.A. 20 mm (0.787 in) 
Water Content  
M1  0.60  6.89  300  684.0  414.0  969.0  180.0 
M2  0.55  6.72  310  688.2  418.5  976.5  170.5 
M3  0.52  6.57  320  694.4  423.0  985.6  166.4 
M4  0.50  6.34  340  707.2  431.1  1016.6  170.0 
M5  0.50  6.07  355  710.0  505.9  939.7  177.5 
M6  0.45  5.85  365  698.6  575.6  861.4  164.3 
M7  0.33  5.08  410  681.0  421.1  982.4  135.3 
M8  0.33  4.96  420  697.6  554.4  831.6  138.6 
*F.A.  Fine Aggregate, C.A.  Coarse Aggregate^{#}1kg = 2.204 lbs
2.1. Materials
⌅The
locally available ingredient materials viz., cement, fine aggregates
(river sand), and coarse aggregate are used for casting of concrete
specimens. Ordinary Portland Cement (OPC) 53 grade, as stipulated in IS
12269 (20(20) IS 12269: 2013, Indian standard specifications for ordinary portland cement, 53 Grade. Bureau of Indian Standards, New Delhi, India.
), is used. The consistency, soundness, and setting time properties of OPC are assessed as per IS 4031 (21(21) IS 4031, Methods of physical tests for hydraulic cement. Bureau of Indian Standards, New Delhi, India.
).
Similarly, the physical properties of fine and coarse aggregates such
as sieve analysis, water absorption, and specific gravity are determined
following IS 2386 (22(22) IS 2386, Methods of test for aggregates for concrete. Bureau of Indian Standards, New Delhi, India.
). Table 3 shows the test results obtained while determining the physical properties of the ingredient materials.
Material  Parameter Assessed  I.S. Code  Test Performed  Result 

Cement  Soundness  IS 4031  LeChatelier Method  5 mm 
Standard Consistency  Vicats Plunger Test  33%  
Initial Setting Time  33 min  
Final Setting Time  10 hours  
Fine Aggregate  Fineness Modulus  IS 2386  Sieve Analysis  3.01 
Specific Gravity  Pycnometer Bottle Test  2.699  
Water Absorption  Oven Dry Method  1.20%  
Coarse Aggregate  Fineness Modulus  IS 2386  Sieve Analysis  3.62 
Specific Gravity  Wire basket Method  2.99  
Water Absorption  Oven Dry Method  2% 
2.2. Specimen
⌅The concrete specimens are prepared following IS 10086 and IS 516 (23(23) IS 100861982 (1995). Specification for moulds for use in tests of cement and concrete. Bureau of Indian Standards, New Delhi.
, 24(24) IS 516: 1959 (Reaffirmed 2004). Indian standard methods of tests for strength of concrete. Bureau of Indian Standards, New Delhi.
).
The cube specimens (150 mm [5.90 in.]) and cylinder specimens (300 x
150 Φ mm [11.811 x 5.90 in.]) are cast for compressive strength testing.
Beam specimens (150 x 150 x 700 mm [5.90 x 5.90 x 27.56 in.]) are
prepared for flexural testing and an additional set of cylindrical
specimens (300 x 150 Φ mm [11.811 x 5.90 in.]) are cast for determining
the modulus of elasticity. All the above specimens are prepared in each
of the eight mixes. The specimens after casting are kept for initial
setting at room temperature of 28^{°} C [82.4^{°} F] and
relative humidity of 90%. The specimens are demoulded after 24 hours,
and then the specimens are moist cured by ponding in a curing tank for
28 days.
2.3. Testing of specimen
⌅The testing program for all the specimens is conducted as per IS 516 (24(24) IS 516: 1959 (Reaffirmed 2004). Indian standard methods of tests for strength of concrete. Bureau of Indian Standards, New Delhi.
).
All the specimens are tested in Multifunction control console (MCC8)
machine for compression, flexure strength, and modulus of elasticity
following IS 516 (clause 5) (24(24) IS 516: 1959 (Reaffirmed 2004). Indian standard methods of tests for strength of concrete. Bureau of Indian Standards, New Delhi.
).
All the readings of load and deformation are recorded by a calibrated
electronic control system attached to a host PC. Digital linear variable
displacement transducer (LVDT) and extensometer are used to measure the
deformation. The machine is kept in the load control mechanism
throughout the testing program. Care is taken that the vertical axis of
the machine platen coincides with the axis of the specimen.
The
testing surfaces are milled before tests. The specimens are tested in
saturated surface dry conditions. The cube specimens used for
compressive testing are subjected to load on the adjacent side of
casting. However, in the case of cylinder compression testing, the
cylinders are necessarily kept vertical. The load rate used is kept at
0.233 MPa/sec (140 kg/sq.cm/min [1991.27 lbs/sq. in/min]) as recommended
by IS 516 (24(24) IS 516: 1959 (Reaffirmed 2004). Indian standard methods of tests for strength of concrete. Bureau of Indian Standards, New Delhi.
).
The specimens are tested until failure. Four specimens of both cube and
cylinders are tested for a period of 28 days, per mix.
In the
flexural testing of concrete beams, the fourpoint loading mechanism is
used. Two LVDT’s are used for measuring the deflection of the beams. All
the contact surfaces are cleaned to remove loose materials. The
supports are 600 mm [23.62 in.] apart, and loading rollers are 200 mm
[7.874 in.] apart, thereby dividing the beam into three parts of 200 mm
[7.874 in.] each. Figure 1 shows the beam and LVDT arrangement for the flexural test. The load is
applied at the rate of 0.0114 MPa/sec (7 kg/sq.cm/mm) as per IS 516 (24(24) IS 516: 1959 (Reaffirmed 2004). Indian standard methods of tests for strength of concrete. Bureau of Indian Standards, New Delhi.
). The load is increased until the failure of specimens. For every mix, three specimens are tested for the period of 28 days.
Standard cylinders (300 x 150Φmm [11.811 x 5.90 in.]) are used for measuring the modulus of elasticity of concrete. The load is continuously applied at the rate of 0.233 MPa/sec (140 kg/sq.cm/mm [1991.27 lbs/sq. in/min]) as per the guidelines of IS 516 until the average stress of (C+5) kg/sq.cm is obtained, where, C is onethird of the average compressive strength. The load is maintained at this stress value for at least a minute and then gradually unloaded to reach an average stress of 1.5 kg/sq.cm [21.94 lbs/sq.in]. The load is again applied for the second time at the same rate until the average stress of (C+1.5) kg/sq.cm is reached, and unloading is carried out in the same way. The load is further applied for the third time and in ten approximately equal increments of stress reaching up to an average stress of (C+1.5) kg/sq.cm. Two extensometers are diagonally attached to the vertical surface of the specimen for measuring the deformation of specimens at every load change. Figure 2 presents the arrangement of extensometers and the specimen arrangement for the determination of modulus of elasticity test. Three specimens are tested for a period of 28 days per mix proportion.
3. EXPERIMENTAL RESULTS
⌅The testing of concrete specimens is conducted at the age of 28 days after curing. IS 456 (clause 6.2.1) recommends 28 days strength as the characteristic compressive strength to be used for design purposes. Table 4 presents the experimental results for characteristic compressive strength, flexural strength, and modulus of elasticity for all concrete mixes used.
Cube compressive strength (MPa)  

Specimen  M1  M2  M3  M4  M5  M6  M7  M8 
#1  28.21  35.99  40.31  48.83  51.59  58.40  61.30  63.91 
#2  28.03  39.19  39.25  44.31  54.69  49.93  58.93  67.98 
#3  29.52  36.67  41.95  47.54  52.60  54.83  60.68  65.24 
#4  29.33  38.75  41.35  46.67  54.39  58.06  60.24  65.07 
Average  28.77  37.65  40.71  46.83  53.31  55.30  60.28  65.55 
C.O.V. (%)  3%  4%  3%  4%  3%  7%  2%  3% 
Cylinder compressive strength (MPa)  
M1  M2  M3  M4  M5  M6  M7  M8  
#1  20.43  23.83  30.76  34.51  40.18  41.25  46.47  49.02 
#2  21.36  26.53  32.25  36.89  36.99  45.23  47.10  55.78 
#3  21.02  25.25  31.22  35.67  38.60  42.45  44.02  51.10 
#4  20.52  24.51  31.70  36.25  39.54  44.35  46.29  53.41 
Average  20.83  25.03  31.48  35.83  38.83  43.32  45.97  52.33 
C.O.V. (%)  2%  5%  2%  3%  4%  4%  3%  6% 
Flexural Strength (MPa)  
M1  M2  M3  M4  M5  M6  M7  M8  
#1  3.69  4.05  4.58  4.41  5.12  5.50  5.66  6.45 
#2  3.72  4.39  4.65  4.68  4.96  5.185  5.78  5.91 
#3  3.76  4.55  4.71  4.77  5.09  5.21  5.68  6.31 
Average  3.72  4.33  4.65  4.62  5.06  5.30  5.71  6.22 
C.O.V. (%)  1%  6%  1%  4%  2%  3%  1%  5% 
Modulus of Elasticity (MPa)  
M1  M2  M3  M4  M5  M6  M7  M8  
#1  27349.37  26997.30  34814.22  35813.57  38952.44  37388.81  43701.64  45885.27 
#2  24458.12  30964.60  32594.59  34694.70  35837.58  38952.44  42287.62  48733.77 
#3  25889.93  28743.32  33861.41  34744.69  37043.47  38426.51  43034.65  46757.12 
Average  25899.14  28901.74  33756.74  35084.32  37277.83  38255.92  43007.97  47125.39 
C.O.V. (%)  6%  7%  3%  2%  4%  2%  2%  3% 
The compressive strength, flexural strength and modulus of elasticity are important parameters considered in designing the structural concrete members. It is necessary to validate the correlation proposed by various codes with experimental results. Figure 3 compares the experimental value of flexural strength of concrete mixes tested after 28 days with the empirical correlation given by standard codes of different countries. Figure 4 similarly compares the modulus of elasticity of the eight concrete mixtures to correlation stipulated by standard codes. Regardless of the type of concrete, the modulus of rupture at 28 days has a variation of more than 15% in most of the cases. The ACI318 and EN 199211, regardless of the compressive strength of concrete, conservatively estimates the modulus of rupture almost by 20%. Similar observations were made for modulus of elasticity at 28 days. The ACI318 regardless of concretes underestimates the modulus of elasticity by 20%.
4. ANALYTICAL INVESTIGATION
⌅In the present investigation, multiple linear regression analysis of experimental data is performed to develop predictive models for the estimation of compressive strength, flexural strength, and modulus of elasticity. For statistical modeling, multiple linear regression analysis was carried out using IBMSPSS Statistics (version 23). The coefficient of correlation, i.e., Pearson’s R, a parameter indicating the strength of correlation of dependent and independent variables, is also obtained for all the proposed models. Pearson’s Rvalue in the proximity of unity signifies the efficiency of the prediction model.
Further, the linear curve fit is plotted between the predicted value and the experimental value. The R^{2} value, i.e., the coefficient of determination, is obtained for this linear curve. R^{2} value approaching closer to unity is indicative of a higher efficacy of the predictive model.
4.1. Prediction of cube compressive strength
⌅In developing a model through SPSS, compressive strength is used as a dependent, and the quantity of cement, fine aggregate, coarse aggregate, and water in 1 cu.m of concrete are used as variables. The model is developed with SPSS software (version 23) using the experimental data generated during testing of cube compressive strength as presented by Eq. 1. Out of the available 32 strength values, 17 have been used to generate the model, while the remaining 15 strength values have been used to validate the proposed model.
where $fck$ is the compressive strength of cube specimen (MPa) at the age of 28 days, C, FA, CA, and W are the quantities of the cement, fine aggregate, coarse aggregate, and water respectively in kg/m^{3} of concrete mix.
Pearson’s
R for the aboveproposed model is found as 0.98, indicating the
effectiveness of the proposed model. It is worth noting here that the
coefficient of water quantity is obtained to be negative, indicating
that compressive strength is inversely proportional to the quantity of
water added to the concrete mix. The generated predictive models from
the available test data, as detailed in the previous section, are
validated from the remaining test results. Table 5 presents actual experimental values of the compressive strength of cube
that are obtained from a test program conducted and the predicted
values that are obtained from the proposed model [1].
The table also depicts the percentage deviation in the predicted values
of compressive strength. It can be seen that in all cases, the
percentage deviation is less than 5% except for one value, which is
deviating by 9.98%, still less than 10%, and hence well acceptable.
These show the effectiveness of the proposed model in predicting the
cube compressive strength of the concrete. The efficacy of the present
model is further checked with the results available in literature (8(8)
Anbuvelan, K., Subramanian, K. (2014). An empirical relationship
between modulus of elasticity, modulus of rupture and compressive
strength of M60 concrete containing metakaolin. Research Journal of Applied Sciences, Engineering, and Technology, 8(11), 12941298.
, 25(25) Shelke, N.L., Gadve, S. (2016). Prediction of compressive strength of concrete based on accelerated strength. Structural Engineering and Mechanics: An International Journal, 58(6), 989999.
). It can be seen that these experimental values are also in good agreement with the results obtained from the models.
Author  Experimental Values (MPa*)  Predicted Values (MPa)  Deviation (%) 

Present Study  29.33  29.48  0.51 
28.13  29.48  4.80  
36.37  34.61  4.83  
38.45  34.61  9.98  
41.35  39.62  4.17  
40.54  39.62  2.26  
47.54  48.64  2.32  
46.67  48.64  4.23  
52.60  51.64  1.82  
54.35  51.64  4.98  
54.83  52.25  4.71  
58.04  52.25  9.98  
60.68  60.08  0.99  
60.24  60.08  0.27  
59.26  60.08  1.38  
Anbuvelan (2014) (8(8)
Anbuvelan, K., Subramanian, K. (2014). An empirical relationship
between modulus of elasticity, modulus of rupture and compressive
strength of M60 concrete containing metakaolin. Research Journal of Applied Sciences, Engineering, and Technology, 8(11), 12941298. ) 
62.44  68.77  10.15 
Shelke N. (2006) (25(25) Shelke, N.L., Gadve, S. (2016). Prediction of compressive strength of concrete based on accelerated strength. Structural Engineering and Mechanics: An International Journal, 58(6), 989999. ) 
50.46  44.66  11.49 
52.47  46.07  12.20  
56.07  50.05  10.75 
*1MPa = 145.04 lbs/sq.in
Additionally, to assess the efficacy of the proposed model [1], predicted values are plotted against experimental values, as shown in Figure 5, for which the R^{2} value is found to be 0.97. It is observed that linear fit of the predicted values plotted against experimental values obtained from available literature lies within the 95% prediction band. This indicates that predicted values are in consonance with experimental values. All the predicted values obtained from the model lies in the 95% prediction band.
4.2. Prediction of cylinder compressive strength
⌅According to the standard code guidelines of some of the nations such as America (ACI318), New Zealand (NZS3101), and Europe (EN 199211), the compressive strength is measured on cylindrical specimens of standard size, generally 300 mm x 150 mm for the purpose of designing. Hence, a model for prediction of cylinder compressive strength is also developed on the same lines as cube compressive strength as stated in [2].
Where $fck\text{'}$ is the compressive strength of cylinder (MPa) at the age of 28 days.
For
the above model, the correlating coefficient is obtained as 0.98, which
alludes to the effectiveness of the model. The comparison of the
compressive strength of the cylinder across different mixes is as shown
in Table 6. From the testing program, experimental values are obtained and the proposed model [2]
is used to predict the corresponding values. The percentage deviation
in predicted value from experimental value is also shown in Table 6.
In no case, the percentage deviation is more than 5% except in one
instance where it is 9.09%. These figures clearly indicate the closeness
of the proposed model to the experimental results. The efficiency of
the developed model is further checked with the results available in
literature (8(8)
Anbuvelan, K., Subramanian, K. (2014). An empirical relationship
between modulus of elasticity, modulus of rupture and compressive
strength of M60 concrete containing metakaolin. Research Journal of Applied Sciences, Engineering, and Technology, 8(11), 12941298.
, 16(16) Ahmed, M., Mallick, J., Hasan, M. (2016). A study of factors affecting the flexural tensile strength of concrete. Journal of King Saud University Engineering Sciences, 28(2), 147156.
, 26(26)
Ashour, S.A. (2000). Effect of compressive strength and tensile
reinforcement ratio on flexural behavior of highstrength concrete
beams. Engineering Structures, 22(5), 413423.
). These experimental values imply to be in good agreement with the results obtained from the models.
Author  Experimental Values (MPa)  Predicted Values (MPa)  Deviation (%) 

Present Study  21.02  21.05  0.16 
20.52  21.05  2.60  
25.25  25.65  1.60  
24.51  25.65  4.67  
31.22  29.93  4.14  
31.49  29.93  4.96  
35.67  37.20  4.30  
36.25  37.20  2.63  
38.60  39.29  1.79  
39.54  39.29  0.63  
42.42  40.32  4.96  
44.35  40.32  9.09  
44.02  47.76  8.49  
46.29  47.76  3.17  
51.10  52.01  1.79  
53.41  52.01  2.61  
Anbuvelan (2014) (8(8)
Anbuvelan, K., Subramanian, K. (2014). An empirical relationship
between modulus of elasticity, modulus of rupture and compressive
strength of M60 concrete containing metakaolin. Research Journal of Applied Sciences, Engineering, and Technology, 8(11), 12941298. ) 
49.95  53.37  6.84 
Ahmed (2016) (16(16) Ahmed, M., Mallick, J., Hasan, M. (2016). A study of factors affecting the flexural tensile strength of concrete. Journal of King Saud University Engineering Sciences, 28(2), 147156. ) 
31.80  36.42  14.15 
78.2  76.06  2.73  
Ashour (2000) (26(26)
Ashour, S.A. (2000). Effect of compressive strength and tensile
reinforcement ratio on flexural behavior of highstrength concrete
beams. Engineering Structures, 22(5), 413423. ) 
48.00  43.67  9.02 
78.00  77.13  1.12 
Moreover, when plotted, the R^{2} value for predicted values against experimental values is 0.97. This indicates the higher efficacy of the prediction model. Also, as seen in Figure 6, almost all values lie in the 95% prediction band. The linear fit of the predicted values plotted against experimental values obtained from available literature lies close to prediction band. This signifies the effectiveness of the proposed model.
4.3. Prediction of flexural strength
⌅The tensile strength of concrete is most commonly attributed to flexural strength (modulus of rupture). Almost all structural components are subjected to significant flexure stresses. Several structural components viz., slabs, beams, road pavements are designed basically for the flexural loads. In the investigation of flexural strength according to standard codes, it is revealed that the process involves tedious experimentation. Therefore, the standard guidelines of different countries have given an empirical equation for estimating the flexural strength of concrete correlating to compressive strength. However, compressive strength also needs aout 28 days of experimentation. Hence, for estimating the flexural strength at an early age with accuracy, a predictive model is developed as given in [3].
where, $fcr$ is the flexural tensile strength of concrete (MPa).
Pearson’s R, obtained after multiple regression analyses for the above mentioned model, is 0.96. Table 7 shows the deviation of experimental values acquired from the test
program for flexural tensile strength and predicted values obtained from
the proposed model [3].
It is witnessed that the predicted values have a percentage deviation
of less than 9%. These indicate that the proposed model gives value in
the vicinity of experimental values. The effectiveness of the developed
model is further validated by comparing it to reported results (27(27)
Khayat, K.H., Bickley, J.A., Hooton, R.D. (1995). Highstrength
concrete properties derived from compressive strength values. Cement, Concrete and Aggregates, 17(2), 126133.
). The results obtained from the models are consistent with these experimental values.
Author  Experimental Values (MPa)  Predicted Values (MPa)  Deviation (%) 

Present Study  3.72  3.63  2.20 
3.66  3.63  0.60  
4.35  4.01  7.82  
4.37  4.01  8.24  
4.60  4.31  6.25  
4.67  4.31  7.66  
4.53  4.67  3.25  
4.73  4.67  1.11  
5.09  4.75  6.67  
4.99  4.75  4.80  
5.21  4.90  5.83  
5.34  4.90  8.12  
5.68  5.66  0.32  
6.31  6.05  4.03  
Khayat (2015) (27(27)
Khayat, K.H., Bickley, J.A., Hooton, R.D. (1995). Highstrength
concrete properties derived from compressive strength values. Cement, Concrete and Aggregates, 17(2), 126133. ) 
5.5  6.21  12.84 
Figure 7 shows the curve fit obtained from the linear regression analysis. The R^{2} value or coefficient of determination is obtained as 0.94. In addition to this, it can be seen from the curve that all experimental values are in the 95% prediction band. The predicted values plotted against experimental values obtained from available literature lies in to prediction band. This indicates the efficiency of the proposed model.
4.4. Prediction of modulus of elasticity
⌅The modulus of elasticity is the valuable mechanical property used in the analysis and designing of concrete structures. The modulus of elasticity is the measure of flexibility of the material. The deflection pattern of materials is governed by its modulus of elasticity and hence defines the serviceability of the material. The existing standard guidelines give the correlation of modulus of elasticity with compressive strength. In addition to this, standard experimental procedures are also prescribed for its determination. However, this process requires a longer duration of time. Hence for prompt analysis of elastic property of the designed concrete, the predictive model is articulated. [4] gives the prediction model for modulus of elasticity of concrete.
where, Ec is the modulus of elasticity of concrete (MPa).
Also,
after performing statistical analysis, Pearson’s Rvalue obtained is
0.976. The predicted values obtained from the proposed model [4]
are compared with the experimental values of modulus of elasticity. It
is apparent that none of the predicted values have a percentage
deviation of more than 4.5%, as shown in Table 8.
This indicates that the proposed model give values, which are very
close to the experimental values. The effectiveness of the developed
model is further examined with the results available in literature (9(9)
Vijayalaxmi, B., Ajay, H., Ranjith, A., Sandya, D. (2015). Experimental
investigation on elastic properties of concrete incorporating GGBFS. International Journal for Research in Applied Science & Engineering Technology, 3(5), 487496.
, 26(26)
Ashour, S.A. (2000). Effect of compressive strength and tensile
reinforcement ratio on flexural behavior of highstrength concrete
beams. Engineering Structures, 22(5), 413423.
). It is apparent that these experimental values are also in good agreement with the results obtained from the models.
Author  42,898 mm  Predicted Values (MPa)  Deviation (%) 

Present Study  25889.93  26114.25  0.87 
28743.32  29527.52  2.73  
30723.71  29527.52  3.89  
33861.41  32462.65  4.13  
34744.69  36300.24  4.48  
37043.47  37070.69  0.07  
37423.2  37070.69  0.94  
38426.51  37717.53  1.85  
43034.65  43086.99  0.12  
46757.12  47430.35  1.44  
48439.49  47430.35  2.08  
Vijaylaxmi (2014) (9(9)
Vijayalaxmi, B., Ajay, H., Ranjith, A., Sandya, D. (2015). Experimental
investigation on elastic properties of concrete incorporating GGBFS. International Journal for Research in Applied Science & Engineering Technology, 3(5), 487496. ) 
25998.43  27818.96  7.00 
Ashour (2000) (26(26)
Ashour, S.A. (2000). Effect of compressive strength and tensile
reinforcement ratio on flexural behavior of highstrength concrete
beams. Engineering Structures, 22(5), 413423. ) 
24612.00  27489.00  11.69 
Additionally, a curve fit with a 95% prediction band is also developed, as shown in Figure 8. The efficacy of the above model can be seen from the R^{2} value, which is obtained as 0.98. The predicted values plotted against experimental values obtained from available literature fall within the prediction band. This demonstrate the efficacy of the proposed model.
5. CONCLUSION
⌅In this study, mechanical properties of concrete are investigated for eight commercial concrete mixes. The models are proposed for predicting compressive strength of cube and cylinder specimens, flexural strength, and modulus of elasticity. It can be concluded that

The predicted values obtained from the proposed models are closer to the experimental values. Hence, the present approach provides a practical and generalized tool that can be adopted by the industry. This tool can be used to give results at a very early stage without much delay.

The developed models shows a negative coefficient of water quantity, which indicates that the mechanical properties are inversely related to the quantity of water added to the concrete mix.