According to Power's formula the theoretical compressive strength of a sample of concrete with gel-space ratio 0.59 is:
Correct Answer: B. 49.29 MPa
📚 Detailed Explanation: Powers' Formula Calculation (Q31)
This is a direct numerical application of T.C. Powers' (1958) formula for theoretical concrete strength based on the gel-space ratio.
Why B (49.29 MPa) is correct:
Powers' Formula: f'c = 240 × x³
Given: x = 0.59
Step 1: x² = 0.59 × 0.59 = 0.3481
Step 2: x³ = 0.3481 × 0.59 = 0.205379
Step 3: f'c = 240 × 0.205379 = 49.29 MPa
Powers' Formula: f'c = 240 × x³
Given: x = 0.59
Step 1: x² = 0.59 × 0.59 = 0.3481
Step 2: x³ = 0.3481 × 0.59 = 0.205379
Step 3: f'c = 240 × 0.205379 = 49.29 MPa
Note: Q20 had x = 0.589 → 49.04 N/mm²; this question has x = 0.59 → 49.29 MPa. The small difference confirms different gel-space ratios give slightly different strengths. Option A (78.84): would require x = 0.69; option C (97.24): x ~0.74; option D (57.2): x ~0.62 — none match 0.59.
Calculation Summary
| Step | Value |
|---|---|
| Gel-space ratio (x) | 0.59 |
| x² | 0.3481 |
| x³ | 0.20538 |
| f'c = 240 × x³ | 49.29 MPa |
Key Concepts for Students
- f'c = 240 x³ — memorise and apply directly. The cube exponent means small x changes cause large strength differences.
- 240 MPa is the theoretical intrinsic strength of pure C-S-H gel with zero capillary pores (x=1).
- Typical structural concrete has x = 0.55–0.75, giving f'c = 40–100 MPa range.