---
title: "Characteristic strength at 95% confidence"
subject: "Concrete Technology and Masonry Structure"
chapter: 5
key: "semester_5/concrete_technology_and_masonry_structure:characteristic-strength-16-17"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/characteristic-strength-16-17
site: BCT Engineering
---

# Characteristic strength at 95% confidence

Concrete Technology and Masonry Structure · Chapter 5: Testing of concrete and quality control

- Asked in: 2068 Baisakh (old course), 5 marks
- Video: [Concrete Cube Test Explained: Complete Procedure, Theory, Calculation & Real M15 Result](https://www.youtube.com/watch?v=3jxlPHn9v_s) — Cipher Spectrum
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/characteristic-strength-16-17
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-5

## Question

The compressive strength test results of a concrete specimen were found as 16; 17; 19; 21; 22; 25; 26; 27; 28 and 15 N/mm$^2$. Calculate the characteristic strength of the test result at 95% confidence level.

## Short answer

Mean of 10 results = 21.60 N/mm², sample standard deviation s = 4.766 N/mm². Characteristic strength f_ck = f_m – 1.65s = 21.60 – 1.65×4.766 = 13.74 N/mm² (≈13.7 N/mm²), assuming normal distribution.

## Answer

Characteristic strength is the value of strength below which not more than 5% of the test results are expected to fall (IS 456, Terminology).

**Formula:** characteristic strength (95% confidence) $f_{ck} = f_m - 1.65\,s$, with the sample standard deviation $s = \sqrt{\sum(x-f_m)^2/(n-1)}$. The factor 1.65 comes from the normal distribution (the same factor is used in mix design, $f_{target} = f_{ck} + 1.65\,s$, IS 10262). Assumptions: the results follow the normal distribution, and the sample standard deviation ($n-1$) is used.

$n = 10$, $\sum x = 216$, mean $f_m = 216/10 = 21.60$ N/mm$^2$.

| No. | $x$ | $x - f_m$ | $(x-f_m)^2$ |
|---|---|---|---|
| 1 | 16 | -5.60 | 31.36 |
| 2 | 17 | -4.60 | 21.16 |
| 3 | 19 | -2.60 | 6.76 |
| 4 | 21 | -0.60 | 0.36 |
| 5 | 22 | +0.40 | 0.16 |
| 6 | 25 | +3.40 | 11.56 |
| 7 | 26 | +4.40 | 19.36 |
| 8 | 27 | +5.40 | 29.16 |
| 9 | 28 | +6.40 | 40.96 |
| 10 | 15 | -6.60 | 43.56 |
| | | Sum | 204.40 |

$$
\begin{aligned} s &= \sqrt{\frac{204.40}{10-1}} = 4.766\ \text{N/mm}^2 \\ f_{ck} &= 21.60 - 1.65\times4.766 = 13.74\ \text{N/mm}^2 \end{aligned}
$$

**Answer: characteristic strength $f_{ck} \approx$ 13.7 N/mm$^2$.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does characteristic strength mean?
   A. Mean strength
   B. Value below which not more than 5% of results fall
   C. Maximum strength
   D. Value below which 50% fall
   Answer: B. IS 456 defines it at the 5% fractile. (Key point: Definition)

2. Which formula gives characteristic strength?
   A. fck = fm + 1.65 s
   B. fck = fm - s
   C. fck = fm - 1.65 s
   D. fck = fm/1.65
   Answer: C. fck = fm - 1.65 s. (Key point: Formula)

3. What is the mean of the ten results?
   A. 20.0 N/mm2
   B. 24.0 N/mm2
   C. 21.6 kN
   D. 21.60 N/mm2
   Answer: D. Sum 216 over 10 gives 21.60. (Key point: Mean)

4. What is the characteristic strength?
   A. 13.7 N/mm2
   B. 21.6 N/mm2
   C. 18.4 N/mm2
   D. 15.0 N/mm2
   Answer: A. 21.60 - 1.65 x 4.766 = 13.74. (Key point: Result)

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