Which of the following laws states that the compressive strength of hardened concrete is inversely proportional to the water-cement ratio, when the concrete mix is of workable consistency?
Correct Answer: B. Abram’s Law
📚 Detailed Explanation: Abrams' Law
Duff Abrams (1919) established the foundational relationship between concrete strength and the water-cement ratio, which remains the most important equation in concrete mix design today.
Why B (Abrams' Law) is correct: Abrams' Law states: “The strength of a fully compacted concrete mix is dependent only upon the water-cement ratio, provided the mix is of workable consistency.” The mathematical form is f'c = A/B(w/c), where A and B are empirical constants depending on the cement type and age. This produces a hyperbolic decrease: as w/c rises, strength falls. The other laws (Archimedes — buoyancy; Avogadro — gas moles; Coulomb — electrostatic force) have no relevance to concrete strength.
Abrams' Law Summary
| Parameter | Value / Description |
|---|---|
| Stated by | Duff Abrams, 1919 (Portland Cement Association, USA) |
| Formula | f'c = A / B(w/c) |
| Relationship | Strength inversely proportional to w/c |
| Valid range | Workable concrete (w/c 0.35–0.70) |
| Graph shape | Hyperbolic decreasing curve |
Key Concepts for Students
- Higher w/c = more pores in hardened cement paste = lower strength — the physical basis of Abrams' Law.
- The law applies only to fully compacted concrete of workable consistency; segregated or unworkable mixes do not follow it.
- Abrams' Law is the foundation of IS 10262 mix design: target w/c is selected from strength requirements.