Question

A column transmits a load of \(225\ \text{kN}\) to a square footing. The safe bearing capacity of the soil is \(100\ \text{kN/m}^2\). The minimum length (in m) of the side of this safe square footing is (rounded off to one decimal place).

Hint:

Find the footing area from load divided by safe bearing capacity, then take the square root to get the side of a square footing.

Answer 1

Correct Answer: 1.5

Step 1: Understanding the Question:
A column carries a load of \(225\ \text{kN}\) down onto a square footing. The soil under the footing can safely take a bearing pressure of \(100\ \text{kN/m}^2\). We need to find the minimum side length of the square footing, rounded to one decimal place.

Step 2: Key Formula or Approach:
A footing is sized so that the bearing pressure it applies on the soil never goes over the soil's safe bearing capacity. Bearing pressure is load divided by the footing's base area, so the minimum required area is
\[ A_{\text{req}} = \frac{\text{Load}}{\text{Safe Bearing Capacity}} \]
For a square footing of side \(L\), the area is \(A = L^2\), so once \(A_{\text{req}}\) is known, \(L = \sqrt{A_{\text{req}}}\).

Step 3: Calculating the required area:
\[ A_{\text{req}} = \frac{225\ \text{kN}}{100\ \text{kN/m}^2} = 2.25\ \text{m}^2 \]

Step 4: Calculating the side length:
\[ L = \sqrt{2.25} = 1.5\ \text{m} \]
This value is already exact to one decimal place, so no further rounding is needed.

Step 5: Final Answer:
The minimum side length of the square footing that keeps the bearing pressure within the soil's safe capacity is \(1.5\ \text{m}\).
\[ \boxed{L = 1.5\ \text{m}} \]