Due to wide variation in the characteristics of concrete constituents (sand, coarse aggregates, etc.), concrete is subjected to considerable variation in strength. Also, due to the non-homogenous nature of concrete, specimens taken from the same mix may give different compressive strengths in tests. This variation can be controlled by **strict quality control and quality assurance.**

**Statistically, the variation in concrete strength is studied in terms of standard deviation and the coefficient of variation.**

**Coefficient of Variation = Standard Deviation / Mean Strength**

Experimentally, it is found that the probability distribution of concrete strength **(for a particular concrete mix as determined by compressive strength tests in a laboratory on a large number of specimens)** follows a normal/Gaussian distribution. The coefficient of variation generally varies in the range of **0.01 to 0.02.** With a higher degree of quality control, this variation can be reduced.

Strength of concrete in uniaxial compression is determined by testing a standard cube of **150mm** size and loading it until failure. The cube specimen is tested after 28 days of casting and curing. The strength of the cube is always expressed to the nearest **0.5 N/mm².**

**As per IS 456:2000,** there should be three specimens in a sample. The strength of the sample is expressed as an average of the three specimens of the sample. Individual variation in the strength of cubes should not vary by more **than ±15%** of the average strength, and if the variation is more, then the test result is discarded.

## characteristics compressive strength compliance requirement as per CI.16.1 and 16.3 of IS456:2000

Criteria | Description |

Specified Grade (M) | Minimum characteristic compressive strength at 28 days (N/mm²) |

Individual Test Result | Should be greater than Fck – 4 N/mm² |

Group of 4 Consecutive Test Results (Average) | Should be greater than Fck + 0.825 * Established Standard Deviation (Rounded to nearest 0.5 N/mm²) or Fck + 4 N/mm², whichever is greater |

**characteristics compressive strength compliance requirement as per CI.16.1 and 16.3 of IS456:2000**

# let’s try to understand More about it

## Explanation:

**Individual Test Result:** Each concrete test specimen should have a compressive strength exceeding Fck (specified grade) minus 4 N/mm². This ensures individual test results don’t fall below a minimum acceptable value.

**Group of 4 Consecutive Test Results:** The average strength of a group of four consecutive test results needs to be higher than either of the following:

**Fck + 0.825 *** **Established Standard Deviation (Rounded to nearest 0.5 N/mm²):** This value considers the inherent variation in concrete strength. A higher standard deviation allows for a slightly lower average strength, as long as it stays above this limit.

**Fck + 4 N/mm²:** This is a minimum threshold regardless of the standard deviation.

# Example:

## Let’s consider M20 grade concrete (Fck = 20 N/mm²):

Individual Test Result: The strength of any single test specimen should be greater than 20 N/mm² – 4 N/mm² = 16 N/mm².

**Group of 4 Consecutive Test Results:** The average strength of four consecutive tests needs to be higher than either:

**20 N/mm² + (0.825 * Established Standard Deviation) (rounded to nearest 0.5 N/mm²) – for instance, if the standard deviation is 2 N/mm², the average strength should be greater than 20 N/mm² + (0.825 * 2 N/mm²) = 21.5 N/mm² (rounded to 22 N/mm²).**

**20 N/mm² + 4 N/mm² = 24 N/mm²**

If any individual test result or the average of four consecutive tests falls below these criteria, further investigation or corrective actions might be necessary.

**Why it is needed to define Characteristics Strength of Concrete **

The characteristic strength of concrete plays an important role due to the significant variation in its compressive strength, as tested on concrete cube or cylinder specimens. It is necessary to ensure a minimum guaranteed strength from a given mixture, which also applies to different materials.

The strength of characteristics is defined as the threshold below which the test results are not expected to fall by more than 5%. This parameter is important for maintaining reliability and stability in construction projects, ensuring that structural elements meet specified strength requirements.

It is important to note that the average strength of concrete must be significantly higher than the characteristic strength to accommodate variations and uncertainties in material properties, construction practices, and environmental conditions.

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