An isolated footing for a 400 mm × 400 mm column carries a service load of 1600 kN. Safe bearing capacity (SBC) is 200 kN/m2. Self-weight is 10% of service load. The footing area (m2) is
- A7.5
- B8.8Correct
- C9.8
- D10.4
Solution
Concept
Footing area calculation including soil self-weight
Formula
Area = (P + 0.10·P) / SBC
Step-by-step solution
1. Column service load P = 1600 kN. 2. Self-weight of footing = 10% of 1600 kN = 160 kN. 3. Total vertical load transmitted to soil = 1600 + 160 = 1760 kN. 4. Safe bearing capacity (SBC) of soil = 200 kN/m2. 5. Required footing plan area = Total load / SBC = 1760 kN / 200 kN/m2 = 8.8 m2. Answer: B
Explanation
Footing design requires accounting for the column service load plus the self-weight of the foundation (10% of service load). The total load on soil is 1600 + 160 = 1760 kN, requiring an area of 1760 / 200 = 8.8 m2.
Why the other options are wrong
A) 7.5 m2 underestimates required area and overstresses soil. C) 9.8 m2 overestimates self-weight allowance. D) 10.4 m2 uses an incorrect factor of safety.
Shortcut
Area = 1.1 × P / SBC = 1.1 × 1600 / 200 = 1.1 × 8 = 8.8 m2.
Common mistake
Forgetting to add the 10% footing self-weight, which yields 1600 / 200 = 8.0 m2.
Correct answer: B) 8.8