--- title: "Characteristic strength from test results" subject: "Concrete Technology and Masonry Structure" chapter: 5 key: "semester_5/concrete_technology_and_masonry_structure:characteristic-strength-30-28" source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/characteristic-strength-30-28 site: BCT Engineering --- # Characteristic strength from test results Concrete Technology and Masonry Structure · Chapter 5: Testing of concrete and quality control - Asked in: 2068 Chaitra, 8 marks - Video: [Characteristic Strength and Target Mean Strength of Concrete| Interview Question #10](https://www.youtube.com/watch?v=gWIUBuEFU-U) — Engineering Academy - 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-30-28 - Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-5 ## Question Define characteristic strength of concrete. The test results of a compressive strength test are given as follows: 30, 28, 25, 27, 23, 29, 31, 30, 30, 32 (MPa). What will be the characteristic strength of the concrete? Make necessary assumptions. ## Short answer Mean of 10 results = 28.50 N/mm², standard deviation s = 2.799 N/mm². Characteristic strength at 95% confidence is f_ck = 28.50 – 1.65×2.799 = 23.88 N/mm² (≈23.9 N/mm²). ## Answer **Definition:** the characteristic strength of concrete is the value of the compressive strength of 150 mm cubes at 28 days below which not more than 5% of the test results are expected to fall (IS 456, Terminology). With a normal distribution, $f_{ck} = f_m - 1.65\,s$. #### Calculation **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. $n = 10$, $\sum x = 285$, mean $f_m = 285/10 = 28.50$ N/mm$^2$. | No. | $x$ | $x - f_m$ | $(x-f_m)^2$ | |---|---|---|---| | 1 | 30 | +1.50 | 2.25 | | 2 | 28 | -0.50 | 0.25 | | 3 | 25 | -3.50 | 12.25 | | 4 | 27 | -1.50 | 2.25 | | 5 | 23 | -5.50 | 30.25 | | 6 | 29 | +0.50 | 0.25 | | 7 | 31 | +2.50 | 6.25 | | 8 | 30 | +1.50 | 2.25 | | 9 | 30 | +1.50 | 2.25 | | 10 | 32 | +3.50 | 12.25 | | | | Sum | 70.50 | $$ \begin{aligned} s &= \sqrt{\frac{70.50}{10-1}} = 2.799\ \text{N/mm}^2 \\ f_{ck} &= 28.50 - 1.65\times2.799 = 23.88\ \text{N/mm}^2 \end{aligned} $$ **Answer: characteristic strength $f_{ck} \approx$ 23.9 N/mm$^2$.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the characteristic strength of concrete? A. Average 7-day strength B. 28-day strength of 150 mm cubes below which not more than 5% of results fall C. Maximum cube strength D. Strength below which 95% fall Answer: B. It is the 5% fractile of 28-day cube strength. (Key point: Definition) 2. What is the mean of the results? A. 30.0 N/mm2 B. 27.0 N/mm2 C. 28.50 N/mm2 D. 25.0 N/mm2 Answer: C. 285/10 = 28.5. (Key point: Mean) 3. What is s? A. 7.05 N/mm2 B. 2.50 N/mm2 C. 0.28 N/mm2 D. 2.80 N/mm2 Answer: D. sqrt(70.5/9) = 2.799. (Key point: Std dev) 4. What is fck? A. 23.9 N/mm2 B. 28.5 N/mm2 C. 33.1 N/mm2 D. 26.2 N/mm2 Answer: A. 28.5 - 1.65 x 2.799 = 23.88. 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