Before getting into the details first know about What is Compressive Strength of Concrete and What is Standard Deviation?

Compressive Strength of Concrete

Compressive strength is the capacity of material or structure to resist or withstand under compression. The Compressive strength of a material is determined by the ability of the material to resist failure in the form of cracks and fissure. The compressive strength of the concrete test is usually done for each batch of mix and calculated separately for different grades of concrete.

What is Standard Deviation?

Standard deviation is evaluated to know the quality of measurements or results.Ā In any real-time experiments, we never consider the single result as the final decision. To achieve the accurate results, the same experimentĀ is repeated at least twice and then the average of these two values is considered as a final result.

In general, The results are never same or equal. There would be at least a slight deviation in the results.

If the repeated samples give different results, we need to know how broadly these results are spread (range of results).Ā Ā Finding this spread helps us to estimate the uncertainty in the measurement and by knowing the range of this spread, and how large this spread is, we can begin to judge the quality of the measurement and set of measurements.

The typical method to evaluate the spread is “Standard deviation”.

In the site, if the quality control is good, the standard deviation is less, and the set of measurements are approximately near or equal to the mean value.

If the quality control is poor on site the set of results will have much variance than the mean value, and ultimately the standard deviation is high.

Standard deviation is denoted as “Ļ”

The formula of Standard Deviation:-

Ļ = Standard DeviationĀ Āµ = Average Strength of Concrete n = Number of Samples x = Crushing value of concrete in N/mm^{2}

Standard Deviation of Compressive strength of concrete:

This can be done in two methods

Method 1: Using the chart specified by IS456

As per IS 456, the assumed Standard deviation values for different grades of concrete are

Grade of concrete

Assumed Standard Deviation

M10

3.5N/mm^{2}

M15

M20

4N/mm^{2}

M25

M30

5N/mm^{2}

Method 2: Calculating the Standard derivation of Compressive strength of concrete accurately:-

As per IS456, one should follow the below set of rules to calculate the accurate standard derivation of compressive strength of concrete

The standard deviation of the concrete cube should be calculated separately for each grade of concrete, for each type of concrete mix and for each batch of mix.

In total 30 No. of samples are considered to calculate the standard deviation.

The below values are real-time results when tested the concrete on site.In the above table, Average StrengthĀ Ī¼ = 744/30 = 24.8 N/mm^{2}

Crushing Value in N/mm^{2} “x”

Average Strength “Āµ”

Deviation (x-Āµ)

(x-Āµ)^{2}

20

24.8

-4.87

23.04

20

24.8

-4.82

23.04

25

24.8

0.21

0.04

26

24.8

1.2

1.44

27

24.8

2.2

4.84

28

24.8

3.2

10.24

29

24.8

4.2

17.64

29

24.8

4.2

17.64

30

24.8

5.23

27.04

20

24.8

-4.8

23.04

25

24.8

0.2

0.04

23

24.8

-1.8

3.24

22

24.8

-2.8

7.84

21

24.8

-3.8

14.44

23

24.8

-1.8

3.24

24

24.8

-0.8

0.64

25

24.8

0.2

0.04

24

24.8

-0.8

0.64

28

24.8

3.2

10.24

26

24.8

1.2

1.44

26

24.8

1.2

1.44

27

24.8

2.2

4.84

744

Total

Total

274.8

n = Number of samples x = Crushing value of concrete inĀ N/mm^{2} Standard Deviation =Ā Ā ā[274.8 (n-1)] = ā(274.8/29) = 3.07N/mm^{2} For above mentioned concrete cubes the standard deviation isĀ 3.07N/mm^{2}

## Admin

This answer was edited.Before getting into the details first know about What is Compressive Strength of Concrete and What is Standard Deviation?

## Compressive Strength of Concrete

Compressive strength is the capacity of material or structure to resist or withstand under compression. The Compressive strength of a material is determined by the ability of the material to resist failure in the form of cracks and fissure.

The compressive strength of the concrete test is usually done for each batch of mix and calculated separately for different grades of concrete.

## What is Standard Deviation?

Standard deviation is evaluated to know the quality of measurements or results.Ā In any real-time experiments, we never consider the single result as the final decision. To achieve the accurate results, the same experimentĀ is repeated at least twice and then the average of these two values is considered as a final result.

In general, The results are never same or equal. There would be at least a slight deviation in the results.

If the repeated samples give different results, we need to know how broadly these results are spread (range of results).Ā Ā Finding this spread helps us to estimate the uncertainty in the measurement and by knowing the range of this spread, and how large this spread is, we can begin to judge the quality of the measurement and set of measurements.

The typical method to evaluate the spread is

“Standard deviation”.In the site, if the quality control is good, the standard deviation is less, and the set of measurements are approximately near or equal to the mean value.

If the quality control is poor on site the set of results will have much variance than the mean value, and ultimately the standard deviation is high.

Standard deviation is denoted as

“Ļ”## The formula of Standard Deviation:-

Ļ = Standard DeviationĀĀµ = Average Strength of Concreten = Number of Samplesx = Crushing value of concrete in N/mm^{2}## Standard Deviation of Compressive strength of concrete:

This can be done in two methods

Method 1: Using the chart specified by IS456As per IS 456, the assumed Standard deviation values for different grades of concrete are

Grade of concreteAssumed Standard Deviation^{2}^{2}^{2}## Method 2: Calculating the Standard derivation of Compressive strength of concrete accurately:-

As per IS456, one should follow the below set of rules to calculate the accurate standard derivation of compressive strength of concrete

The below values are real-time results when tested the concrete on site.In the above table, Average StrengthĀ Ī¼ = 744/30 = 24.8 N/mm

^{2}Crushing Value in N/mm^{2}“x”Average Strength“Āµ”Deviation(x-Āµ)(x-Āµ)^{2}744TotalTotal274.8n = Number of samples

x = Crushing value of concrete inĀ N/mm

^{2}Standard Deviation =Ā Ā ā[274.8 (n-1)] = ā(274.8/29) = 3.07N/mm^{2}For above mentioned concrete cubes the standard deviation isĀ

3.07N/mm^{2}