Dynamic pile formula (Engineering News): A drop hammer weighs 1,800 kg and falls freely through 1.00 m onto a pile. If the penetration under the last blow is 5 mm, estimate the allowable load from the Engineering News formula.

Introduction / Context:
Dynamic formulae offer quick estimates of pile capacity from driving data. The classic Engineering News (EN) formula relates hammer energy per blow to allowable load using an empirical set-up term to account for losses and uncertainties, especially for drop hammers.

Given Data / Assumptions:

• Hammer weight W = 1,800 kg ≈ 1.8 tonnes.
• Free fall H = 1.00 m ≈ 3.28 ft.
• Final set s = 5 mm ≈ 0.197 in.
• Drop hammer (use EN constant c = 1 inch in the denominator; W in tons, H in feet, s in inches).

Concept / Approach:
Engineering News (imperial form for drop hammers):
Q_allow (tons) = (2 * W * H) / (s + 1)where W is in tons, H in feet, s in inches. Convert given metric quantities to these units and substitute.

Step-by-Step Solution:

Verification / Alternative check:
Different national adaptations exist (metric forms using kN and mm with constants like 2.5). Using the classic EN (drop hammer) form produces a result near 10 tons, matching the provided options.

Why Other Options Are Wrong:

• 100 or 50 tonnes: Far too large for the given modest hammer and set.
• 20 tonnes: Double the computed value; inconsistent with EN formula.

Common Pitfalls:
Mixing units; using the steam/air hammer constant instead of the drop-hammer constant; forgetting that the EN value is an allowable (already conservative) estimate.

Final Answer:
10 tonnes