Which of the following shows the CORRECT expression for the target mean strength (fm) of concrete if the characteristic strength and standard deviation are fck and σ respectively?
Try it first: pick an option, then read the explanation.
Correct answer: A. fm = fck + 1.65σ
Target Mean Strength Formula
IS 10262 requires concrete to be designed to a target mean strength higher than the characteristic strength, to ensure only 5% of test results fall below fck. The formula is:
fm = fck + 1.65σwhere 1.65 is the factor corresponding to the 5% tail of the standard normal distribution, and σ is the standard deviation of the test results. Adding 1.65σ ensures the design has the required statistical margin above the characteristic value.
fm = fck + 1.65σ — option A.
Key takeaway
Target mean = characteristic + safety margin. The “+” sign is critical: options B, C, D all subtract, which would give a lower target — that’s wrong.