Strength of concrete is directly proportional to ……………..
Correct Answer: A. Cement water ratio
📚 Detailed Explanation: Strength and the Cement-Water Ratio
While Abrams' Law is typically stated as an inverse relationship (strength ∝ 1/w/c), it is equivalent to say that strength is directly proportional to the cement-water ratio (c/w), which is the reciprocal of w/c.
Why A (Cement water ratio) is correct: c/w ratio = 1 / (w/c ratio). As c/w increases (more cement per unit water), the w/c ratio decreases, and compressive strength increases. This is a direct (not inverse) proportionality — exactly what the question asks. Option B (sand-cement ratio) affects mix leanness/richness but is not the direct determinant of strength; at constant w/c, increasing sand-cement ratio lowers strength somewhat. Option C (water-aggregate ratio) is not a standard mix design parameter.
Equivalent Statements of Abrams' Law
| Form | Proportionality |
|---|---|
| Abrams' original form | Strength ∝ 1 / w/c ratio (inverse) |
| Equivalent form | Strength ∝ c/w ratio (direct) |
| Powers' form | Strength ∝ gel-space ratio cubed |
Key Concepts for Students
- Strength is directly proportional to the cement-water (c/w) ratio — the inverse of w/c.
- Doubling the cement-water ratio (halving w/c) does not double strength due to the exponential nature of Abrams' Law, but strength does increase substantially.
- This form is useful in mix design charts where c/w is plotted on the x-axis and 28-day strength on the y-axis.