Question

Compression test on 4 samples of $150$ $mm$ cubes of concrete gave following results:
$25$ $MPa$, $28$ $MPa$, $32$ $MPa$, $31$ $MPa$
The characteristic strength of concrete (in MPa, rounded off to two decimal places) is _____.

• A. 23.6

Answer 1

The correct option is A 23.6
Number of cubes $\left(n\right)=4$
Mean strength, $f_m=\frac{25+28+32+31}{4}=29$ $MPa$
Here, individual variation is with in $\pm 15$ % of average.
Hence, okay
Standard deviation, $\sigma =\sqrt{\frac{\Sigma (f_m-f_i{)}^2}{n-1}}$
$\sigma =\sqrt{\frac{(29-25{)}^2+(29-28{)}^2+(29-32{)}^2+(29-31{)}^2}{3}}=3.16MPa$
Characteristic strength of concrete$=f_m-1.65\sigma$
$=29-(1.65\times 3.16)$
$=23.78$ $MPa$