TREND LINE ANALYSIS OF WEIGHT VERSUS …ijetie.org/articles/IJETIE_201626004.pdf · statistical procedures of BS EN 13791:2007 on full scale reinforced concrete building frame built

International Journal of Emerging Technology and Innovative Engineering Volume 2, Issue 7, July 2016 (ISSN: 2394 – 6598)

Date of Publication: 07.09.2016

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TREND LINE ANALYSIS OF WEIGHT VERSUS

COMPRESSIVE STRENGTH OF CONCRETE

Sagar Tanwani

Graduate Civil Engineering

Quaid-e-Awam University of Engineering,

Science & Technology

Bashir Ahmed Memon

Professor, Department of Civil Engineering

Quaid-e-Awam University of Engineering,

Science &Technology

ABSTRACT

Concrete is most widely used material in construction industry. To ensure its durability during

service life quality control is ecclesial. 28-day strength of concrete particularly compressive

strength is determined to check and ensure its quality. This requires dedicated equipment and

setup. An alternative to it is the numerical analysis. Therefore, in this research paper relationship

between weight and strength of concrete cylinders is developed using trend line analysis

available in Microsoft excel. For the purpose 240 cylinders using 1:2:4 mix with 0.45 water-

cement ratio are prepared and cured for 28-days. After curing weight of the cylinders is

evaluated first followed by determination of compressive and tensile strength. The obtained

results are then analyzed. It is observed that the trend line fit by power function gives results in

good agreement to experimental observations. Individual equations for relationship between

weight and compressive strength and weight and tensile strength are presented. Then both the

equations are combined in one general equation with separate coefficients for compressive and

tensile strength.

Keywords: compressive strength, tensile strength, weight, tend line analysis.

1. INTRODUCTION

Concrete is most widely used material in

construction industry, mainly due to its

flexibility to be shaped in any desirable

shape, less maintenance cost during service

life. The material is very good in

compression however it has some

limitations in tension. This weakness of

concrete is overcome by using

reinforcement which makes it equally good

in tension. To ensure durability of concrete

during service life it is mandatory to check it

strength during construction. Normally 28-

day strength is required for checking which

on contrary is not only time consuming but

also requires dedicated laboratory setup.

Although early age determination of

concrete strength i.e. 1- day, 3-days and 7-

days strength is in practice and there exist

method of computing projected strength for

28-dyas yet actual 28-day strength is

mandatory by codes of practice. Also in case

if the test result does not confirm the design

strength of concrete then whole process need

to be repeated. It will not only time

consuming but also costly. For each failure

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one has repeat the process to confirm the

required design strength of concrete.

Alternatives to laboratory testing are

nondestructive testing and the numerical

determination of the strength.

Nondestructive testing is normally carried

out in the existing structures. Therefore,

numerical methods may be the suitable

alternative for the purpose. The approach

remained the active area of research since

long among the scholars. Several scholars

have made attempts to develop methods for

the purpose. In the following related

literature is summarized.

Rachna et al[1]

conducted research work to

propose the statistical model for predicting

concrete strength using linear regression

analysis. They used water-binder ratio, fine

aggregate-binder ratio, coarse aggregate-

binder ratio and binder content to conduct

their research work. They used fly ash

variation and curing from 28 to 91 days. For

28-day curing they demonstrated that the

quadratic polynomial with co-efficient of

determination greater than or equal to 0.99

gave results in very good agreement with

reference concrete.

Larrossa et al[2]

in their research work

considered compressive strength of concrete

as variable to ensure conformity control of

port construction work in Brazil. Based on

their results the authors showed variations in

conformity control of concrete from

different places and concluded that there is

need of uniformity in the said area.

Liu et al[3]

in their research work used

nondestructive test (surface hardness

rebound ) value, material design parameters

and regression analysis to increase the

accuracy of strength calculations. They used

166 samples of 738-days age in 146 training

examples. They also used 20 test examples

to estimate concrete compressive strength.

Based on the findings the authors used

regression analysis to establish a

mathematical formula. Their study results

indicatethat the correlation coefficient may

reach 0.9622 which indicates that the

proposed method has

referentialvalue.Therefore, can confidently

be used to compute to determineconcrete

strength.

Soutsos et al[4]

in their research conducted

in-situ pull out test following standard

statistical procedures of BS EN 13791:2007

on full scale reinforced concrete building

frame built in laboratory. The procedures

account for the uncertainty of the strength

correlation by requiring either the lower95%

confidence limit curve or a curve shifted

downwards by a margin to be used. Based

on their finding they concluded that

conservative estimates of the in-situ

characteristic strength are observed.

Akthem et al[5]


statistical analysis of compressive strength

of lightweight aggregates concrete of the

Benica Martine Bridge in California. They

used specimen of sizes 4x8 in. and 6x12 in

at site and tested in laboratory at 5-years.

The authors used statistical analysis and

probability theory to compare the results

with 35-days test results provided by

California Department of Transportation

Caltrans. The authors observed that although

the dispersion in data from mean strength

was more for specimen of age of 5-years yet

the strength was more by 3.6% than

specimen of age 35-days. They also

observed that the average compressive

strength of 4x8 in. cylinders was more than

the compressive strength of 6x12 in.

cylinders by 2% at 5 years. The probability


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of compressive strength to fall below the

minimum observed strength was

approximately increased 3 times at 5 years

when compared to those observed at 35

days. The probability of compressive

strength to go above the maximum value

was also increased by 1.23% at 5 years.

From the analysis on the compressive

strength data at 35 days and 5 years, it was

concluded that the probability of falling

below the target specified strength

essentially approaches zero, which means

concrete will never fall below its specified

design strength in the life time of the

structure.

Mahmoud[6]

in his research paper presented

statistical model to predict the compressive

strength of concretecontaining different

matrix mixtures at fixed age or at different

age of 1, 3, 7, 28, 56, 90 and180 days. In

this research the author examined effect of

eight different parameters for the matrix

mixture i.e. time, water, cement, metakaolin,

silica fume, sand, aggregateand

superplasticizer, on the compressive strength

of concrete. Based on the research findings

the author concluded that the predicted

model has highcorrelation to the

experimental results for the concrete

compressive strength.

Baji and Ronagh[7]


studied stress-strain block parameters using

statistical analysis. They used database of

experimental results onconcrete equivalent

rectangular stress block parameters. The

authors studied uncertainty involved in the

evaluation of the equivalent

rectangularstress block parameters using

probability-based model errors and

compared with experimental data. Finally,

using Monte Carlo Simulation the authors

studied effect of uncertainty in the concrete

stress block parameters on the ultimate

flexural strengthand curvature. Based on the

results the authors concluded that due to

variations in material and

sectionalproperties, a significantly higher

variability exists in the ultimate curvature of

reinforced concretebeam sections in

comparison to strength and that the ultimate

curvature is sensitive to morerandom

variables comparing to the strength.

Shimizuet al[8]

conducted research to

estimate concrete strength in existing

structures for proper inspection for seismic

resistance and retrofitting of existing

structures in Japan. For the purpose they

used statistical analysis on 10788 cores from

1130 existing buildings. Based on their

findings they concluded that in younger

structures there is less chance of low

strength. Compressive strength showed

changes from floor to floor in a building.

Out of considered buildings significant

number of buildings had low strength.

Jonathan[9]

for his master’s research work

studied the possibility of use of

nanotechnology in the field of cement and

concrete. The author used nanoparticles and

nanofibers & nanotubes in concrete. The

author used Monte Carlo and Bayesian

methods to analyze and compare the results

with those available in literature. Based on

the finding author concluded the use of

statistical prediction to analyze patterns and

trends to set optimal dosage of additives in

concrete.

Kolisho, Hunka and Jung[10] in their

research work performed statistical analysis

of modulus of elasticity and compressive

strength of pre-stresses precast beams. For

the purpose the authors used statistical

analysis between modulus of elasticity and


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compressive strength on 133 test results of

cylinders 150 × 300 mm in size (28-day

curing). Based on their findings the authors

concluded that for this specific case high

skewness is recorded. However, the beta

distribution is better than generally

recommended theoretical distribution for

strength. Moreover, they concluded that

modulus of elasticity is not significantly

affected due to skewness as the mean value

of this parameter is used.

Nowak and Rakoczy[11]

performed research

to develop a statistical model of compressive

strength of lightweight concrete, using new

materialtest data. They used 8000

samplesfrom 8 different sources with

strength ranging from 21 to 50MPa (3000 to

7000 psi). The presented research is focused

on the development of statistical parameters.

For the purpose the authors presented test

data in form of the cumulative distribution

functions plotted on the normal

probabilitypaper. The shape of the CDF is

an indication of the type of distribution, and

sincethe resulting CDF’s are close to straight

lines, they can be considered as normal

random variables. In addition, the

statisticalparameters are determined by

fitting a straight line to the lower tail of the

CDF. The most important parameters arethe

mean value, bias factor and the coefficient

of variation. The authors observed that the

quality of material and workmanshiphas

been improved over the last 30 years and

this is reflected in reduced coefficients of

variation.

Akcay[12]

in his technical note presented

statistical model and results for the

compressive strength of existing buildings in

potential earthquake risk zone in Istanbul.

He used core samples from 244 structures.

The author presented mean value for a total

of 1,892 characteristic strength values equal

to 22.01 N/mm2 with a standard deviation

value of 9.99 N/mm2. Based on the obtained

results the author concluded that

approximately 42% of all the analyzed

structures were below the required quality.

Das and Chatterjee[13]

conducted research to

develop statistical model using Monte Carlo

simulation technique for self-compacting

and normally compacting concrete. The

authors used and tested concrete cubes at 7,

28, 60, 90, 120 and 150 days after normal

water curing. For each case 10 samples were

tested. The authors introduced a new

concept called ―Root Mean Squared

Spacing (RMSS)to estimate adequate

sample size following the principle of

random walk.Theauthors used MATLAB

software for the analysis. The authors

concluded that new proposed approach

based on simulation technique facilitates to

overcome the problem of low sample size

using Monte Carlo and RMSS methods.

They also concluded that comparative

analysis of test results can provide better

meaningful understanding if systematic

approach is adopted through application of

conventional statistical parameters along

with the new proposed procedure.

Zain et al[14]


non-linear regression equation for prediction

of concrete compressive strength at different

ages. Using the model, the authors obtained

the correlation coefficients equal to 0.995

and 0.994 for the prediction of 7 and28-day

compressive strength respectively. Based on

their results the authors concluded that

proposed model has good correlation with

test results.

Adam[15]

in his research work developed

predictive multiple least square regression


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relationship for concrete strength, elastic

modulus, strain at peak stress, ultimate

strain, and stress-strainbehavior, including

the temperature, aggregate type, test type,

and strength at roomtemperature. The

research results reveals that at high

temperatures both modulus of elasticity and

strength are reduces whereas strain at peak

stress and ultimate strain are increased.

Al-Qadi et al[16]


developed statistical models by considering

influence of key mixture parameter (cement,

water to powder ratio, fly ash andsuper

plasticizer) on hardened properties affecting

the performance of self-compacting cement

concrete. They used thirty-one mixtures to

derive the numerical models. Based on the

results the authors concluded that the models

were valid for a wide range ofmixture

proportioning.

Cecia et al[17]


performed statistical analysis of existing

models for resisting the debonding of FRP

sheets used for strengthening of reinforced

and pre-stressed concrete beams in flexure.

They used 2 different databases for their

work. Based on regression analysis the

authors concluded that there is variation in

different models for calculated loads at

which debonding occurs. They further

concluded that regression analysis helps in

deciding the best model for the purpose.

Yaghi and Hammoud[18] in their research

work developed statistical model based on

modified tolerance based approach for

prediction concrete strength. In their

research article the authors argue that

modified tolerance approach of ACI is based

on normal distribution which has several

draw backs therefore they used reliability

analysis. Also the authors incorporated

lower bound through the use of left

truncated normal distribution. The authors

also compared tolerance factor, modified

tolerance factor and Bartlett and Macgregor

approaches. Based on the results the authors

conclude that the modified tolerance factor

approach givesmore reliable estimates of

equivalent design compressive

strengthespecially for data with high

coefficient of variation.

Novák et al[19]


statistical nonlinear fracture mechanics

analysis to study the size effect of concrete

beams. They used crack band theory based

on fracture energy related in

SBETA/ATENA and introduced statistical

variability of material parameters using

Monte Carlo simulation. They demonstrated

comparison of the results with experimental

data.

Dashrath et al[20]


natural sand, artificial sand, crushed stone

and recycled aggregates to study

compressive and tensile strength of concrete.

Based on the obtained results they

concluded that compressive and tensile

strength reduces with induction of these

aggregates in comparison for reference

concrete. However, they observed that the

reduction in tensile strength is less than

compressive strength. Which shows that

alternative aggregates have promising effect

on strength. However, refined techniques are

required to ensure proper compressive

strength of the resulting material.

From the above discussion it is clear that

scholars remained keen to coin out the

methods based on statistical procedure

which can successfully predict the concrete

strength in different cases. In this research

work an attempt is made to develop


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relationship between weight and

compressive strength of concrete cylinders

of standard size. To achieve the target of the

research 1:2:4 mix with water-cement ratio

of 0.45 is used to prepare 240 cylinders.

Ingredients of concrete mix were ordinary

Portland cement, coarse aggregates and hill

sand. These ingredients were proportioned

by weight to prepare 1:2:4 mix followed by

casing of standard size cylinders in standard

manner. Rodding is used for the compacting

of material in molds. After 28-day water

curing first weight of concrete cylinders is

determined then universal load testing

machine was used to evaluate the

compressive and tensile strength of concrete

cylinders. 120 cylinders are selected for

compressive and tensile strength

respectively. The obtained results are then

analyzed using trend line / regression

analysis to develop equations for both

compressive and tensile strength of concrete.

Several methods are studied and will be

discussed in relevant section. The equations

are then used to reevaluate the concrete

strength. The obtained results show very

good agreement between experimental and

numerical results. It is hoped that the work

presented in this article will be very helpful

for practicing engineers to have good idea of

the concrete strength.

2. MATERIAL AND TESTING

To achieve the target of the research work

300 concrete cylinders are prepared using

1:2:4 mix with 0.45 water cement ratio as

per ACI recommendation of concrete mix

design. Ordinary Portland cement, crushed

stone aggregates of maximum 1 inch size

and hill sand are used as the ingredients of

concrete. Mix proportioning is done using

weight method. Mold are prepared and

cylinders are cast using standard procedures.

As the compaction on site is generally made

by rodding therefore the same is adopted for

compaction of the cylinders. As mentioned

earlier 28-day curing is the standard

requirement of curing for the proper strength

of concrete members therefore the cylinders

are then water cured for 28-days. After

curing time weight of all the cylinders is

recorded. The cylinders are then divided

into two batches and each batch is tested

using universal load testing machine for

compressive and tensile strength

respectively. The obtained results of the

strength are then checked for strength

deviation from mean strength. All the

cylinders having strength deviation of 15%

or more are discarded. Finally 120 cylinders

in each batch are selected for further

analysis.

Table 1: Weight and compressive strength of concrete cylinders

# Weight

Compressive

Strength # Weight

Compressive

Strength # Weight

Compressive

Strength

kg psi Kg psi kg psi

1 13.8 3804.50 41 13.6 3761.85 81 13.6 3597.30

2 13.6 3804.95 42 13.6 3742.98 82 13.8 3852.54

3 13.6 3820.75 43 13.8 3780.62 83 13.8 3854.69

4 13.7 3715.25 44 13.8 3810.56 84 13.6 3675.56

5 13.8 3820.50 45 13.7 3762.61 85 13.6 3684.95

6 13.8 3825.75 46 13.7 3755.98 86 13.7 3763.54

7 13.6 3750.25 47 13.7 3745.87 87 13.7 3761.82


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8 13.6 3820.45 48 13.8 3823.69 88 13.8 3844.98

9 13.6 3821.36 49 13.6 3598.74 89 13.8 3872.66

10 13.8 3754.25 50 13.8 3842.58 90 13.8 3865.74

11 13.7 3678.36 51 13.6 3685.36 91 13.8 3854.65

12 13.8 3845.65 52 13.6 3712.65 92 13.6 3599.87

13 13.7 3655.63 53 13.6 3687.52 93 13.6 3621.54

14 13.7 3687.95 54 13.8 3871.65 94 13.8 3854.96

15 13.7 3750.89 55 13.8 3825.67 95 13.7 3759.68

16 13.6 3726.45 56 13.8 3852.36 96 13.7 3760.51

17 13.6 3765.68 57 13.7 3745.63 97 13.7 3762.43

18 13.7 3755.36 58 13.8 3842.68 98 13.7 3756.82

19 13.8 3838.75 59 13.7 3735.32 99 13.6 3711.97

20 13.8 3780.45 60 13.8 3864.25 100 13.8 3866.98

21 13.7 3756.89 61 13.7 3752.64 101 13.8 3862.78

22 13.7 3779.21 62 13.8 3855.69 102 13.6 3588.96

23 13.7 3563.58 63 13.8 3857.61 103 13.6 3615.87

24 13.7 3598.78 64 13.6 3691.23 104 13.7 3699.87

25 13.6 3524.32 65 13.6 3589.65 105 13.8 3798.99

26 13.6 3598.36 66 13.7 3761.56 106 13.7 3756.93

27 13.6 3496.85 67 13.7 3740.58 107 13.7 3712.85

28 13.8 3452.89 68 13.8 3869.79 108 13.7 3735.68

29 13.8 3476.35 69 13.6 3596.54 109 13.7 3762.59

30 13.7 3682.75 70 13.6 3612.54 110 13.6 3721.54

31 13.6 3679.82 71 13.6 3658.24 111 13.8 3875.12

32 13.8 3742.56 72 13.6 3638.94 112 13.8 3763.21

33 13.8 3752.69 73 13.8 3854.96 113 13.8 3861.23

34 13.6 3685.91 74 13.8 3844.57 114 13.6 3722.65

35 13.7 3812.40 75 13.6 3720.56 115 13.6 3712.36

36 13.7 3761.36 76 13.7 3746.66 116 13.8 3852.65

37 13.8 3785.14 77 13.7 3748.21 117 13.8 3842.86

38 13.6 3764.32 78 13.7 3752.62 118 13.7 3758.71

39 13.8 3719.86 79 13.6 3754.36 119 13.8 3854.36

40 13.6 3754.65 80 13.8 3836.55 120 13.8 3851.26

Table 2: Weight and tensile strength of concrete cylinders

# Weight

Tensile

Strength # Weight

Tensile

Strength # Weight

Tensile

Strength

W1 Psi W1 Psi W1 Psi

1 13.8 422.00 41 13.7 414.00 81 13.7 411.00

2 13.8 424.00 42 13.8 436.00 82 13.8 428.00

3 13.8 435.00 43 13.8 439.00 83 13.8 428.00

4 13.6 388.00 44 13.8 428.00 84 13.8 429.00

5 13.6 392.00 45 13.8 425.00 85 13.6 385.00

6 13.8 432.00 46 13.7 389.00 86 13.6 385.00

7 13.8 438.00 47 13.7 413.00 87 13.7 413.00

8 13.8 439.00 48 13.7 396.00 88 13.7 412.00

9 13.8 436.00 49 13.8 421.00 89 13.7 412.00


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10 13.8 426.00 50 13.8 428.00 90 13.7 398.00

11 13.8 428.00 51 13.8 429.00 91 13.8 436.00

12 13.8 432.00 52 13.8 426.00 92 13.8 435.00

13 13.7 405.00 53 13.8 431.00 93 13.6 389.00

14 13.8 438.00 54 13.8 438.00 94 13.8 439.00

15 13.8 439.00 55 13.8 435.00 95 13.7 399.00

16 13.8 437.00 56 13.7 397.00 96 13.7 414.00

17 13.8 439.00 57 13.7 414.00 97 13.8 439.00

18 13.8 428.00 58 13.6 385.00 98 13.8 436.00

19 13.8 438.00 59 13.7 410.00 99 13.8 438.00

20 13.7 409.00 60 13.6 387.00 100 13.7 415.00

21 13.7 405.00 61 13.6 388.00 101 13.6 390.00

22 13.8 429.00 62 13.8 439.00 102 13.6 388.00

23 13.8 430.00 63 13.8 428.00 103 13.6 382.00

24 13.8 436.00 64 13.8 438.00 104 13.8 432.00

25 13.8 438.00 65 13.8 439.00 105 13.8 430.00

26 13.8 432.00 66 13.8 427.00 106 13.8 439.00

27 13.8 431.00 67 13.8 427.00 107 13.8 436.00

28 13.8 426.00 68 13.8 429.00 108 13.8 436.00

29 13.8 429.00 69 13.8 429.00 109 13.7 412.00

30 13.8 432.00 70 13.8 432.00 110 13.7 410.00

31 13.6 387.00 71 13.6 386.00 111 13.7 413.00

32 13.7 398.00 72 13.6 386.00 112 13.8 439.00

33 13.7 402.00 73 13.7 413.00 113 13.8 439.00

34 13.7 413.00 74 13.8 438.00 114 13.8 435.00

35 13.6 386.00 75 13.6 388.00 115 13.6 388.00

36 13.7 411.00 76 13.8 436.00 116 13.8 437.00

37 13.6 388.00 77 13.8 435.00 117 13.8 435.00

38 13.6 389.00 78 13.8 436.00 118 13.8 435.00

39 13.6 382.00 79 13.8 434.00 119 13.8 439.00

40 13.7 410.00 80 13.7 411.00 120 13.8 436.00

Table 3: Basic strength information of all cylinders

Strength Compressive Tensile

Mean strength 3748.48 419

Standard deviation 92.36286 18.73006

Median value 3756.86 428

Maximum strength 3875.12 439

Minimum strength 3452.89 382

Weight and compressive strength of 120

concrete cylinders is given in table 1,

whereas table 2 shows the results of weight

and tensile strength of 120 cylinders. Basic

information of both compressive and tensile

strength is listed in table 3. From this table it

may be observed that mean compressive

strength is 3748.48 psi and mean tensile

strength is recorded as 419 psi. The mean

tensile strength is 11.17% of the


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compressive strength. In addition, deviation

from mean compressive strength is

computed and is recorded as low as 0.01%

and as high as 7.89% which is less than

15%. Similarly, deviation of tensile strength

from mean value is recorded as minimum

equal to 0.33% and maximum equal to

8.96%. The values are well with in the 15%

permissible limit.

3. RESULTS AND DISCUSSION

3.1 Compressive Strength:Weight and

compressive strength results of the cylinders

are then analyzed using in built function of

trend line analysis. The option offers trend

line analysis with linear, polynomial degree

two, exponential, logarithmic and power

functions. All of these functions are used to

analyze the data and the results are plotted in

figure 1. The obtained equations along with

the value of R2 are listed in table 4. The

value of R2 is an important parameter in

regression analysis which gives percentage

of variation of fitted data. Generally high the

value of the parameter represents higher

accuracy of data fit. For our analysis we

obtained about 35% value for R2 which

shows good agreement of fitted data. All

these functions are then used to reevaluate

the compressive strength as function of

weight of the cylinders. The obtained results

are analyzed for basic parameter. Table 5

gives details of minimum, maximum, mean,

median, and standard deviation of

compressive strength of all function

obtained by trend line analysis and

experimental results. This table also gives

details of correlation coefficient of all trend

line functions with respect to experimental

results. It is observed from table 5 that

although there is standard deviation of 92

psi is in the experimental results but

standard deviation of 55 psi is observed in

calculated data using trend line functions.

Also coefficient of correlation of 0.59 is

recorded for all function. Both standard

deviation and coefficient of correlation

shows that the fitted data is in good

agreement with the experimental results.

Table 4: Trend line fit for compressive data

Function Type Polynomial R2

Exponential y = 347.16e0.1736x

0.3411

Linear y = 651.55x - 5181.1 0.3500

Logarithmic y = 8924.5ln(x) - 19613 0.3498

Polynomial Degree 2 y = 1551.9x2 - 41874x + 286132 0.3560

Power y = 7.4231x2.3777

0.3409

Table 5: Statistical parameters of all function versus experimental data (Compressive Strength)

Parameter Experiment Exponential Linear Polynomial

D2 Power Logarithmic

Min 3452.89 3680.29 3679.98 3685.02 3679.60 3680.57

Max 3875.12 3810.31 3810.29 3814.64 3809.57 3810.85


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Mean 3748.48 3748.38 3748.39 3748.41 3747.74 3749.04

Median 3756.86 3744.73 3745.14 3734.31 3744.26 3745.95

Standard

deviation 92.36286 54.53404 54.64331 55.09461 54.50573 54.62948

Correlation

Coefficient - 0.591979 0.591618 0.596642 0.591829 0.591463

After analysis for basic parameters,

experimental data and compressive strength

obtained from trend line function is plotted

in figure 2 for comparison. Although all the

functions are in good agreement with the

experimental data for compressive strength

but it is observed that the power function

gives lowest deviation from mean strength

with minimum error of 0.01% and

maximum error of 10.33%. These error

values are least compared to other functions.

Therefore, power function obtained from

trend line analysis is taken as the standard

function to represent the relationship

between weight and compressive strength of

concrete cylinders and is listed in equation

(1)

y = 7.4231x2.3777

(1)

where x represents weight and y represent

compressive strength of concrete cylinder.

3.2Tensile Strength:

In similar fashion to compressive strength

data, tensile strength data is analyzed. The

results of trend line analysis for all available

functions is plotted in figure 3. The

functions obtained are listed in table 6. The

obtained functions are then used to

reevaluate the tensile strength. Basic

statistical information of the obtained tensile

strength results is given in table 7.

(a) Linear function (b) Polynomial degree two


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(c) Exponential function (d) Logarithmic function

(e) Power function

Figure 1: Trend line fit for compressive strength data


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Figure 2: Experimental results along with all trend line functions (Compressive Strength)

Table 6: Trend line fit for all tensile strength data

Function Type Polynomial R2

Exponential y = 0.162e0.5718x

0.9251

Linear y = 235.4x - 2815.6 0.9221

Log y = 3226.6ln(x) - 8035.9 0.9219

Polynomial D-2 y = 227.16x2 - 5992.8x + 39873 0.9244

Power y = 5*10-07

x7.8381

0.9249

For the comparison purpose all tensile

strength values versus experimental results

are plotted in figure 4. It may be visualized

from this figure that almost all the functions

give results in good agreement with

experimental values. It is noted that both

standard deviation of tensile strength given

by power function is less compared to other

type of functions. and coefficient of

correlation for power function. Although the

correlation coefficient for power function

.001 remained than that of the exponential

functions but the mean error of power

function is less compared to other functions.

Therefore, power function is taken as the

best fit of the experimental data for tensile

strength and is reproduced as under.

y = 5*10-07

x7.8381

(2)


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(a) Linear Function (b) Polynomial Degree two

(c) Exponential Function (d) Logarithmic Function

(e) Power Function

Figure 3: Trend line fit for tensile strength data


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Figure 4: Experimental results along with all trend line functions (Tensile Strength)

Table 7: Statistical parameters of all function versus experimental data (Tensile Strength)

Parameter Experiment Exponential Linear Log Polynomial

Degree 2 Power

Min 382.00 382.01 387.20 385.75 386.43 383.50

Max 439.00 428.22 434.30 432.86 432.71 429.99

Mean 419.59 414.97 420.96 419.53 419.07 416.68

Median 428.00 428.22 434.30 432.86 432.71 429.99

Standard deviation 18.73006 17.745 17.993 17.983 18.005 17.840

Correlation Coefficient - 0.961 0.960 0.960 0.961 0.961

Combining both equations (1) and (2) in one general equation it may be written as

𝑦 = 𝛼𝑥𝛽 (3)

Where 𝑥 represents weight of cylinders and

𝑦 represent concrete strength with 𝛼 equal to

7.4231 for compressive strength and 5x10-7

for tensile strength. Similarly, 𝛽 equals to

2.3777 for compressive strength and 7.8381

for tensile strength.


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4. CONCLUSION

Quality control of concrete require

determination of its strength particularly

compressive strength of cylinders / cubes

cured for 28-days. This require dedicated

laboratory setup. An alternative of it is the

numerical analysis. This research paper

presents relationship between weigh and

concrete strength (both compressive and

tensile) using trend line analysis. All of the

inbuilt options of trend line analysis of excel

are evaluated for compressive and tensile

strength data of 120 cylinders each. These

cylinders are prepared using 1:2:4 mix with

0.45 water-cement ratio and cured for 28-

days. It is observed that power function

gives results in best agreement to

experimental values. First separate equations

for relationship between weight and

compressive strength and weight and tensile

strength are presented then combined into

one equation by stating coefficients for

compressive and tensile strength evaluation.

It is hoped that the work presented in this

research paper will not only improve the

literature on the topic but also help the

practicing engineers to have good insight of

concrete strength from weight on site.

5. REFERENCES

[1] Rachna A, Maneek K, Sharma R K, and

Sharma M K, “Predicting Compressive

Strength of Concrete”, International

Journal of Applied Science and

Engineering, Vol. 13, No. 2, pp: 171 –

185, 2015.

[2] Larrossa M C, Real M V, Dias C R R

and MagalhaesF C, “Statistical analysis

and conformity testing of concretein

port construction work”, IBRACON

Structures and Material Journal, Vol. 7,

No. 3, pp: 468 – 497, 2014.

[3] Liu JC, Sue MLand Kou CH,

“Estimating the Strength of Concrete

UsingSurface Rebound Value and

Design Parameters ofConcrete

Material”Tamkang Journal of Science

and Engineering, Vol. 12, No. 1, pp: 17,

2009.

[4] SoutsosM, BungeyJ, Long A and

Tickell G, “Interpretation of in-situ

concrete strength test results”,

NDTCE’09, Non-Destructive Testing in

Civil Engineering, Nantes, France, June

30th – July 3rd

, 2009.

[5] Akthem A, Nadeem M S, Magenti

R,Lee P, “Strength Unit Weight and

Elasticity of ConcreteCylinders for the

Benicia Martinez Bridge”, Final Report

(CA 10-1862) submitted to the

California Department of

Transportation (Caltrans) under

Contract No. 59A0682, March 2011.

[6] Mahmoud SA, “Statistical Modelling

and Prediction of CompressiveStrength

of Concrete”, Concrete Research

Letters, Vol. 3, No. 2, June 2012.

[7] Baji H and Ronagh H R, “Statistical

Analysis of the Concrete Rectangular

Stress Block Parameters”, The 2013

World Congress on Advances in

Structural Engineering and Mechanics

Korea, September 8 – 12, 2013.

[8] Shimizu Y, HirosawaM, and Zhou J D,

“Statistical Analysis of Concrete

Strength in ExistingReinforced

Concrete Buildings in Japan”,

12WCEE, 2000.

[9] Jonathan G, “Nanotechnology in

Concrete:Critical Review and Statistical

Analysis”, A Master’s Thesis Submitted

to the Faculty ofthe College of

Engineering and Computer Science,

Florida Atlantic University, May 2013.


360

COPYRIGHT TO IJETIE

[10] Kolisho J, Hunka P and Jung K, “A

Statistical Analysis of the Modulus of

Elasticity andCompressive Strength of

Concrete C45/55 forPre-Stressed

Precast Beams”,Journal of Civil

Engineering and Architecture,Vol. 6,

No. 11, pp. 1571–1576, 2012.

[11] Nowak A S, and RakoczyAM,

“Statistical Model for Compressive

Strength of Lightweight Concrete”,

Architecture – Civil Engineering

Environment, Si Lesian University of

Technology, No. 4, 2011.

[12] Akcay B, “Variation of In-Place

Concrete Core Strengthin Structures

from Istanbul Area: StatisticalAnalysis

of Concrete Core Data”, Technical

Notes, DOI: 10.1061/(ASCE)0899-

1561, 16:5(507), 2004.

[13] Das D, AND Chatterjee A, “A Proposed

Statistical Procedure for Assessment of

Strength of Concrete from Low Sample

Size Using Monte Carlo Simulation”,

International Journal of Engineering

Science and Innovative Technology,

Vol. 2, Issue 4, July 2013.

[14] ZainM F M, Suhad M A, Sopian K,

JamilM, and Che-Ani AI,

“Mathematical Regression Model for

the Prediction ofConcrete Strength”,

Proceedings of the 10th WSEAS international

conference on Mathematical methods,

computational techniques and intelligent

systems (MAMECTIS'08), pp: 396-402, 2008.

[15] Adam MK, Yahya C K, and David J K,

“Stress-Strain Properties of Concreteat

Elevated Temperatures”, Structural

Engineering Research Report#NDSE-

09-01, Department of Civil Engineering

and Geological Sciences, University of

Notre Dame, April 2009.

[16] Al-Qadi A NS, Kamal NB M, Hashem

AM, and Qahir NS A, “Statistical

Models for Hardened Properties of Self-

Compacting Concrete”, American J. of

Engineering and Applied Sciences, Vol.

2, No. 4, pp: 764-770, 2009.

[17] CeciaA M, Casas J R, and Michel G,

“Statistical Analysis of Existing Models

for Flexural Strengthening ofConcrete

Bridge Beams using FRP Sheets”,

Construction and Building Materials,

Vol. 27, Issue 1, pp: 490–520, 2012.

[18] Yaghi K and HammoudH,” Estimation

of the Design Concrete Strength

fromCore Tests: Modified Tolerance

Factor Approach”, International Journal

of Engineering Research & Technology,

Vol. 5, Issue 01, 2016.

[19] NovákD, VořechovskýM, PuklR and

Červenka V, “Statistical nonlinear

analysis - size effect of concrete

beams”, International Journal of

Fracture, Vol. 108, pp: 43 – 61, 2001.

[20] Dashrath K B, Kulkarni V P, Kandekar

S B, Mehetre A J, “Compression and

Split Tensile Strength of Concrete

Containing Different Aggregates”,

International Journal of Engineering

Research & Technology (IJERT), Vol.

3 Issue 3, March – 2014.

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