The point load carrying capacity of a 0.3 m diameter circular pile resting in a layer of saturated clay having undrained cohesion of 200 kPa is
- A162 kN
- B127.2 kNCorrect
- C95.2 kN
- DNone of these
Solution
Concept
Point Bearing Capacity of Piles in Clay
Formula
Qp = Nc × cu × Ap
Step-by-step solution
1. Identify given values: Nc = 9, cu = 200 kPa, diameter d = 0.3 m. 2. Calculate tip area (Ap): Ap = (π/4) \* (0.3)² ≈ 0.0707 m². 3. Apply formula: Qp = 9 \* 200 \* 0.0707 = 127.2 kN.
Explanation
To find the point load carrying capacity (Qp) of a pile in saturated clay, the formula used is Qp = Nc × cu × Ap.1. Bearing capacity factor (Nc) for pile tip in clay is 9. 2. Undrained cohesion (cu) = 200 kPa. 3. Cross-sectional area of the circular pile (Ap) = (π / 4) \* d² = (π / 4) \* (0.3)² ≈ 0.0707 m².Calculating the point load carrying capacity: Qp = 9 \* 200 \* 0.0707 ≈ 127.2 kN. Thus, 127.2 kN (Option B) is the correct answer.
Shortcut
Use the quick formula Qp ≈ 7.07 × cu × d² (since Nc × π/4 = 9 × 0.785 ≈ 7.07). For d = 0.3 m: Qp ≈ 7.07 × 200 × 0.09 ≈ 127.2 kN.
Common mistake
Students often forget to apply the circular cross-sectional area formula (π/4 × d²) and instead calculate area as d², resulting in 162 kN (Option A). Another common error is using an incorrect bearing capacity factor (Nc) or confusing point load capacity with skin friction resistance.
Correct answer: B) 127.2 kN