Question

The characteristic compressive strength of concrete at 28 days is 25 N/mm$^2$ and the standard deviation is 4.0 N/mm$^2$. The target strength for concrete mix at 28 days is

• A. 25.0 MPa
• B. 29.0 MPa
• C. 31.6 MPa
• D. 33.0 MPa

Hint:

The formula $f_m = f_{ck} + 1.65 \sigma$ is fundamental to concrete mix design.
The term $1.65 \sigma$ is the "margin" added to the characteristic strength to ensure that most of the concrete produced on site will meet the required strength specification.
Always remember this formula.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to calculate the target mean strength for a concrete mix design, given the characteristic strength and the standard deviation.

Step 2: Key Formula or Approach:
In concrete mix design, the

target mean strength ($f_m$) is the average compressive strength that the mix is designed to achieve in the lab. It is set higher than the specified

characteristic strength ($f_{ck}$) to account for the expected variability in concrete quality on site.
According to IS 456:2000, the relationship is:
\[ f_m = f_{ck} + 1.65 \sigma \] where:
$f_m$ = Target mean compressive strength
$f_{ck}$ = Characteristic compressive strength (the strength below which not more than 5% of test results are expected to fall)
$\sigma$ = Standard deviation of the test results
The factor 1.65 corresponds to a 5% probability of failure in a normal distribution.

Step 3: Detailed Explanation:
We are given:
- Characteristic strength ($f_{ck}$) = 25 N/mm$^2$ (which is 25 MPa)
- Standard deviation ($\sigma$) = 4.0 N/mm$^2$
Substitute these values into the formula:
\[ f_m = 25 + 1.65 \times 4.0 \] \[ f_m = 25 + 6.6 \] \[ f_m = 31.6 \text{ N/mm}^2 \text{ or } 31.6 \text{ MPa} \]

Step 4: Final Answer:
The target strength for the concrete mix at 28 days is 31.6 MPa.