Let's analyze and the problem step-step. --- Problem Breakdown **Load carried the column** \( P =120\, \{kN} \) **Support condition**: Supported on 1 m deep, square footing- **Soil bearing capacity** \( 20\, \text{k/m}^2 \) - **Coefficient of safety (FOS)**: 3.5 - **Footing dimensions**: \( \text{Depth} = 1\, \text{m} \) --- # Step 1: Calculate the **allowable soil bearing pressure** \[ q_{allow} = \frac{\text{Soil bearing capacity}}{\text{Factor of Safety}} = \frac{20\, \text{kN/m}^2}{3.5} \approx 5.714\, \text{kN/m}^2 \] --- # Step 2: Find the **area of footing** required to safely support the load \[ A = \frac{P}{q_{allow}} = \frac{120\, \text{kN}}{5.714\, \text{kN/m}^2} \approx 210\, \text{m}^2 \] --- # Step 3: Determine the **size of the footing** Since the footing is square, let the side length be \( L \): \[ L = \sqrt{A} = \sqrt{210} \approx 14.49\, \text{m} \] **Note:** The problem states the footing has a **depth of 1 m**, so the footing's **thickness** is 1 m, but the width (length of footing sides) is approximately 14.49 m. --- # Final Answer: | **Footing size** | **Approximately 14.5 meters** on each side | --- # Additional notes: - The footing should be designed with a width of approximately 14.5 m to safely carry the vertical load considering the soil bearing capacity and safety factor. - Ensure all dimensions include practical considerations and code requirements in actual design. --- **Summary:** The footing should be roughly **14.5 m x 14.5 m** square to safely support the load of 120 kN with the given soil and safety considerations.