Concrete Characteristic Strength
is the strength value which is used to describe the concrete class, and is based on statistical values and the possibility of acquiring lesser strength value than this value is ( TS 500’ de % 10, TS EN 206-1’ de %5 ).
Average Strength ( x ) or ( fcm)
is the arithmetical average strength value of concrete samples taken from a specific class of concrete in a specific time period.
x_{1}+x_{2} +x_{3} +………+xn
X = ____________________ N/mm^{2 } (MPa)
n
X : Average strength
x_{1},x_{2} ,x_{3} ………xn : Each Test Result
n : Number of Sample which is tested
Standard Deviation (S)
is a value which describes to what degree the concrete strength results deviate from the average. If the standard deviation which has a great importance in statistical analysis, is smaller than it points out that average deviation and the risk is fewer.
S = (x_{1}-x)^{2} + (x_{2} – x)^{2} + ………+ (xn –x)^{2} veya = x_{1} + x_{2} + …..+x_{n}
n
If sample number is below 25, instead of (n) , ( n-1) is taken into consideration.
S Standard deviation N/mm^{2} (MPa)
X Average deviation N/mm^{2} (MPa)
x_{1}x_{2}…, x_{n }: Each test results N/mm^{2} (MPa)
n : Test number
Coefficient of Variation (v)
Coefficient of variation, is the ratio of standard deviation to the average strength value and is expressed as %. This value describes the distribution as % instead of numbers. It informs about the concrete control.
V = _S_ .100 (%)
X
V : Coefficient of variation
S : Standard deviation
X : Average strength
Normal Frequency Histogram ( Frequency Distribution)
Belonging to a specific concrete class, is the shape formed of concrete compressive strength in abscissa (x axis), test number or test ratio in ordinate (y axis) . By connecting the upper and middle points of this histogram, normal frequency curve (bell curve) is obtained. If the concrete control is in good form, compressive strength results will be gathered around the average value and bell curve will be long and narrow. As the compressive strength distribution increases, the values will spread, the curve will form a short and broad shape.
Monthly Change Graphics of Concrete Compressive Strength
Arithmetical average of the compressive strength results of a specific concrete class is calculated for each month. Graphics are drawed by showing months in the abscissa, and strengths in the ordinate.
In the graphics, 7 and/or 28 days of compressive strength values and monthly changes are seen.
Same yearly evaluations can be made by the same form.
Difference ( F )
is the difference between the biggest and the smallest strength values. This value is used in calculation of the standard deviation between tests.
Standard Deviation and Coefficient of Variation Between Tests
The distribution measurement of the concrete samples which are taken from sundry places of the same concrete is calculated by the variations which occur within the concrete samples. Calculations are made with the formulas below.
S_{1 }= _1 .F
d_{2}
V_{1} = _S_{1_}. 100
X
S_{1} : Deviation between the tests
1 / d 2 : Constant according to the number of sample in each group
_{ } F : Average difference between the groups
V_{1} : Coefficient of variation between the tests.
X : Average compressive strength
Sample Number |
d_{2} |
1_ |
2 |
1.128 |
0.8865 |
3 |
1.693 |
0.5907 |
4 |
2.059 |
0.4877 |
5 |
2.326 |
0.4299 |
6 |
2.534 |
0.3946 |
7 |
2.704 |
0.3698 |
8 |
2.847 |
0.3512 |
9 |
2.970 |
0.3367 |
10 |
3.078 |
0.3249 |
Numerical Example Concrete Class : C20/25 |
|||||
Test |
Sample 1 |
Sample 2 |
Sample 3 |
Group Average N/mm² |
Difference |
1 |
25 |
24 |
28 |
25.6 |
4 |
2 |
30 |
28 |
26 |
28.0 |
4 |
3 |
24 |
25 |
26 |
25.0 |
2 |
4 |
25 |
29 |
23 |
25.6 |
6 |
5 |
24 |
27 |
26 |
25.6 |
3 |
6 |
30 |
32 |
26 |
29.3 |
8 |
7 |
30 |
30 |
23 |
27.6 |
7 |
8 |
26 |
25 |
23 |
24.6 |
3 |
9 |
25 |
28 |
24 |
25.6 |
4 |
10 |
22 |
22 |
26 |
23.3 |
4 |
11 |
23 |
25 |
26 |
24.6 |
3 |
12 |
25 |
24 |
20 |
23.0 |
5 |
13 |
28 |
27 |
26 |
27.0 |
2 |
14 |
24 |
29 |
26 |
26.3 |
5 |
15 |
23 |
30 |
28 |
27.0 |
7 |
16 |
26 |
22 |
25 |
24.3 |
4 |
n = 48 S1 = 1 / d2 . F = 0.5907. 4.4 = 2.6
x = 25.8
F = 4.4 V1 = S / X . 100 = 2.6 / 25.8 = % 10
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