If characteristic compressivestrength of concrete fck is definedas strength below which not morethan 95% of the test result areexpected to fall, the expression offck in term of mean strength fm andstandard deviation andsigma; would bea)fm - 1.656b)fm + 1.656c)fmd)fm + 0.1656Correct answer is option 'B'. Can you explain this answer?

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If characteristic compressive strength of concrete fck is defined as strength below which not more than 95% of the test result are expected to fall, the expression of f_ck in term of mean strength f_m and standard deviation σ would be

a)
f_m - 1.656
b)
f_m + 1.656
c)
f_m
d)
f_m + 0.1656

Correct answer is option 'B'. Can you explain this answer?

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If characteristic compressivestrength of concrete fck is definedas str...

S can be given by:

fck = fm - 1.65s

where:

- fck is the characteristic compressive strength of concrete
- fm is the mean strength of concrete
- s is the standard deviation of concrete strength
- 1.65 is a constant value representing the number of standard deviations from the mean required to obtain a 95% confidence level.

This equation is commonly used to estimate the characteristic strength of concrete based on the results of compressive strength tests. It allows engineers to determine the minimum strength required for a particular application, such as building design or structural analysis.

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If characteristic compressivestrength of concrete fck is definedas str...

The characteristic compressive strength of concrete, denoted

f_{ck}

, is defined as the strength below which no more than 5% of the test results are expected to fall. In statistical terms, this is the strength corresponding to the 5th percentile of the strength distribution.

In most cases, the compressive strength of concrete follows a normal distribution. The relationship between the characteristic strength

f_{ck}

, the mean strength

f_m

, and the standard deviation

\sigma

can be derived from the properties of the normal distribution.

Step 1: Understanding the Concept

The characteristic strength

f_{ck}

is defined such that only 5% of the test results fall below it. This corresponds to the 5th percentile of the normal distribution.

For a normal distribution:

The mean strength is
$f_m$
.
The standard deviation is
$\sigma$
.
The 5th percentile is located at a value corresponding to
$z$
-score = -1.645 (this value is obtained from standard normal distribution tables for a cumulative probability of 5%).

Step 2: Relation between

f_{ck}

f_m

, and

\sigma

The general equation for a normal distribution is:

f_{ck} = f_m - 1.645 \cdot \sigma

This equation means that the characteristic strength

f_{ck}

is the mean strength

f_m

minus 1.645 times the standard deviation

\sigma

Final Expression:

Thus, the expression for the characteristic compressive strength

f_{ck}

in terms of the mean strength

f_m

and the standard deviation

\sigma

is:

f_{ck} = f_m - 1.645 \cdot \sigma

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If characteristic compressivestrength of concrete fck is definedas strength below which not morethan 95% of the test result areexpected to fall, the expression offck in term of mean strength fm andstandard deviation σ would bea)fm - 1.656b)fm + 1.656c)fmd)fm + 0.1656Correct answer is option 'B'. Can you explain this answer?

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If characteristic compressivestrength of concrete fck is definedas strength below which not morethan 95% of the test result areexpected to fall, the expression offck in term of mean strength fm andstandard deviation σ would bea)fm - 1.656b)fm + 1.656c)fmd)fm + 0.1656Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If characteristic compressivestrength of concrete fck is definedas strength below which not morethan 95% of the test result areexpected to fall, the expression offck in term of mean strength fm andstandard deviation σ would bea)fm - 1.656b)fm + 1.656c)fmd)fm + 0.1656Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If characteristic compressivestrength of concrete fck is definedas strength below which not morethan 95% of the test result areexpected to fall, the expression offck in term of mean strength fm andstandard deviation σ would bea)fm - 1.656b)fm + 1.656c)fmd)fm + 0.1656Correct answer is option 'B'. Can you explain this answer?.

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