Credit: giatecscientific.com
Standard deviation denotes the deviation of a set of variables from the mean value. It is the method to determine the reliability of concrete compressive strength results of a batch concrete.
In the design mix of concrete, the target strength should be equal to the characteristic strength plus 1.65 times the standard deviation.
The concrete was produced from a certain mixture of different material and those all are having different properties.
In the design mix, the concrete was calculated by weight method so mistakes may happen. If so standard deviation value was added in concrete design mix for safer side.
As per IS 456 follow the below rule to calculate the standard deviation of concrete cubes.
| Sample No | Crushing Value in N/Sqmm (X) | Average Strength (M) | Deviation X-M | (X-M)2 |
| 1 | 20 | 24.8 | -4.8 | 23.04 |
| 2 | 20 | 24.8 | -4.8 | 23.04 |
| 3 | 25 | 24.8 | 0.2 | 0.04 |
| 4 | 26 | 24.8 | 1.2 | 1.44 |
| 5 | 27 | 24.8 | 2.2 | 4.84 |
| 6 | 28 | 24.8 | 3.2 | 10.24 |
| 7 | 29 | 24.8 | 4.2 | 17.64 |
| 8 | 29 | 24.8 | 4.2 | 17.64 |
| 9 | 30 | 24.8 | 5.2 | 27.04 |
| 10 | 20 | 24.8 | -4.8 | 23.04 |
| 11 | 25 | 24.8 | 0.2 | 0.04 |
| 12 | 23 | 24.8 | -1.8 | 3.24 |
| 13 | 22 | 24.8 | -2.8 | 7.84 |
| 14 | 21 | 24.8 | -3.8 | 14.44 |
| 15 | 23 | 24.8 | -1.8 | 3.24 |
| 16 | 24 | 24.8 | -0.8 | 0.64 |
| 17 | 25 | 24.8 | 0.2 | 0.04 |
| 18 | 24 | 24.8 | -0.8 | 0.64 |
| 19 | 28 | 24.8 | 3.2 | 10.24 |
| 20 | 26 | 24.8 | 1.2 | 1.44 |
| 21 | 26 | 24.8 | 1.2 | 1.44 |
| 22 | 27 | 24.8 | 2.2 | 4.84 |
| 23 | 21 | 24.8 | -3.8 | 14.44 |
| 24 | 22 | 24.8 | -2.8 | 7.84 |
| 25 | 23 | 24.8 | -1.8 | 3.24 |
| 26 | 24 | 24.8 | -0.8 | 0.64 |
| 27 | 29 | 24.8 | 4.2 | 17.64 |
| 28 | 30 | 24.8 | 5.2 | 27.04 |
| 29 | 22 | 24.8 | -2.8 | 7.84 |
| 30 | 25 | 24.8 | 0.2 | 0.04 |
| Total | 744 | Total | 274.8 |
Average Strength μ = 744/30 = 24.8 N/Sqmm
n = Number of sample
Std Deviation = √[274.8 (n-1)] = √(274.8/29) = 3.07 N/sqmm
Hence the Standard Deviation of above concrete cube test results – 3.07 N/Sqmm.
As per IS 456, the assumed standard deviation value has mentioned from past records for a similar grade of concrete.
| Grade of Concrete | Assumed Std Deviation (N/Sq.mm) |
| M10 | 3.5 |
| M15 | 3.5 |
| M20 | 4 |
| M25 | 4 |
| M30 | 5 |
| M35 | 5 |
| M40 | 5 |
| M45 | 5 |
| M50 | 5 |
Before starting any civil engineering work, regardless of branches, horizontal, vertical, and angular measurements of…
The data measurements gathered from surveying helps establish the plan and design of all civil…
Surveying is the art and science of civil engineering that determines the relative (comparable) position…
The formation of cracks on the concrete surface may lead to reduce the durability of…
Understanding the different levels of structure seems a bit of a daunting task. Don’t worry…
We knew that pipes are used to transport gas or liquid substance from one place…
View Comments
WHAT HAPPENS IF STANDARD DEVIATION FOR M50 IS MORE THAN 5 AND HOW WE CAN RECTIFY THE ISSUE AND WHAT IS THE SOLUTION?
the SD for M50 concrete being greater than 5MPa is not in itself a matter of very serious concern. the value of 5MPA for M50 grade concrete is assumed for design purpose for assuming the Target strength =1.65 *Characteristic strength ie the strength assumed for structural design purpose. the value 5 is used for initial estimation purpose in the absence of actual test results, and hence is on the conservative size, and hence exceeding 5 indicates something amiss in the quality control . with a standard deviation >5 a Larger target strength has to be aimed for so that the probability of any sample being lower in strength than the Characteristic strength is statistically insignificant. however to address the specific question , a better control on the quantities of the inputs, as also uniformity in their quality would help in the matter.