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The given problem asks to design a square footing using **Working Stress Design (WSD)** for a column with the following details:

- Column dimensions: 18 inches square
- Compressive strength of concrete (\( f'_c \)): 4000 psi
- Reinforcement: 10 bars of #8 diameter with a yield strength (\( f_y \)) of 60 ksi
- Dead load: 250 kips
- Live load: 200 kips
- Allowable soil pressure: 4.5 ksf (kips per square foot)

### Steps to Design the Footing

1. **Calculate the Total Load**  
   Total Load \( P_{total} \) on the footing includes both dead and live loads:  
   \[
   P_{total} = P_{dead} + P_{live} = 250 \text{ kips} + 200 \text{ kips} = 450 \text{ kips}
   \]

2. **Determine the Area of the Footing**  
   Using the allowable soil pressure and the total load, we can determine the required area of the footing. The bearing capacity equation is:
   \[
   A = \frac{P_{total}}{q_{allowable}}
   \]
   where \( q_{allowable} = 4.5 \text{ ksf} \).  
   Converting the total load into ksf units:
   \[
   A = \frac{450 \text{ kips}}{4.5 \text{ ksf}} = 100 \text{ ft}^2
   \]

3. **Determine the Dimensions of the Footing**  
   Since the footing is square, the side length \( L \) is the square root of the area:
   \[
   L = \sqrt{A} = \sqrt{100} = 10 \text{ ft}
   \]
   So, the footing should be a 10 ft by 10 ft square.

### Conclusion
The designed square footing should have dimensions of **10 feet by 10 feet** to support the column with the given loads.

Would you like more details on the reinforcement, or any further clarifications?

### Related Questions:
1. How does the factor of safety affect the design of footings?
2. What are the differences between Working Stress Design (WSD) and Limit State Design (LSD)?
3. How do soil conditions impact the design of footings?
4. What role does concrete's compressive strength (\( f'_c \)) play in footing design?
5. How do you account for eccentric loads in footing design?

### Tip:
In structural design, it's important to verify the actual soil capacity on-site to ensure that the assumed allowable bearing capacity is accurate.

A column 18 in. square, with f'_c = 4000 psi, reinforced with 10# 8Ø of f_y = 60 ksi, supports a dead load of 250 kips and a live load of 200 kips. The allowable soil pressure is 4.5 ksf. Design a square footing using W.S.D.

Learn how to design a square footing for an 18 in. column reinforced with 10# 8Ø bars and supporting 450 kips of total load using Working Stress Design (WSD). The problem involves calculating the footing dimensions based on an allowable soil pressure of 4.5 ksf.

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