Concrete Mix Design MCQ with answer and solution

Concept

Statistical target mean strength in concrete

Formula

f_m = f_ck + 1.65 × s

Step-by-step solution

1. Concrete manufacturing is subject to statistical variations in cement properties, aggregate grading, moisture contents, and workmanship. 2. The statistical factor of safety (design margin) explicitly accounts for this material variability; statement (i) is true. 3. To ensure that 95% of field test results equal or exceed the characteristic strength (fck), the mix is designed for a target mean strength fm = fck + 1.65 × s; statement (ii) is true. 4. Hence, both statements (i) and (ii) are true. Answer: C

Explanation

Mix design incorporates statistical margins of safety to compensate for inherent variations in material properties, moisture contents, batching accuracy, and field workmanship. By applying a standard deviation margin (1.65 σ in IS 456), the target mean compressive strength is engineered substantially above the specified characteristic strength so that no more than 5% of tests fall below the design threshold.

Why the other options are wrong

A) Statement (ii) is also true as target mean strength is intentionally designed above characteristic strength. B) Statement (i) is also true because the margin directly accommodates statistical variability in batching and materials. D) Both statements correctly describe the statistical basis of concrete mix proportioning in IS 10262 and IS 456.

Shortcut

Target mean strength fm = fck + 1.65·s (accounts for variability and ensures not more than 5% fall below fck).

Common mistake

Confusing structural safety factors (partial safety factor on strength) with statistical mix design margins.