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Let's go through the steps required to solve Question 1 based on the provided details and diagrams.

### Problem Breakdown and Calculation Steps

1. **Apply Load Factors**  
   The load factor is calculated using:
   \[
   wu = 1.2D + 1.6L
   \]
   where:
   - \( D \) is the dead load (40 psf)
   - \( L \) is the live load (20 psf)

   Substituting these values:
   \[
   wu = 1.2 \times 40 + 1.6 \times 20
   \]

2. **Calculate the Load that the Inner Beams Support**  
   The distributed load \( Wu \) on each beam is calculated as:
   \[
   Wu = (wu) \times oc \times L
   \]
   where:
   - \( oc \) is the on-center spacing (20 ft)
   - \( L \) is the span length of each beam (40 ft)

3. **Calculate the Ultimate Moment that the Inner Beams Support**  
   The moment \( Mu \) is given by:
   \[
   Mu = Wu \times L / 8
   \]

4. **Calculate the Nominal Moment**  
   The nominal moment \( Mn \) is derived as:
   \[
   Mn = Mu / 0.9
   \]

5. **Calculate \( Z_{\text{min}} \)**  
   To find the minimum section modulus, \( Z_{\text{min}} \):
   \[
   Z_{\text{min}} = \frac{Mn}{36 \text{ ksi}}
   \]

6. **Determine the Lightest Weight Shape**  
   Using the table provided, find the lightest beam that satisfies the \( Z_{\text{min}} \) requirement. Look for the lightest weight with a \( Z \) value equal to or greater than \( Z_{\text{min}} \).

7. **Calculate the Nominal Moment Capacity and Ensure Adequacy**  
   Calculate the nominal moment capacity using:
   \[
   Mn = M_p - \left( \frac{M_p - M_r}{L_r - L_p} \right) \times (L_b - L_p)
   \]
   Ensure that this moment capacity is greater than the nominal moment calculated in Step 4.

8. **Make the Final Selection**  
   Confirm that the selected beam meets all criteria for load support and adequacy.

Would you like me to go through these calculations step-by-step with the provided data, or are there specific values or further clarification you need? 

---

### Related Questions to Explore Further:
1. How does the on-center spacing affect the load calculations on the beams?
2. What would happen if the dead load were increased to 50 psf?
3. How can beam spacing be adjusted to optimize the design and minimize the weight of the required beam?
4. Why is the factor of 0.9 used in calculating the nominal moment?
5. How does the selection of beam shape impact the structural integrity and cost efficiency?

**Tip:** When working with structural loads, always double-check units to ensure consistency, especially when dealing with pounds per square foot (psf) and other load metrics.

Refer to Figure 1. The A36 wide flange beams given in the figure below have 40 ft span, have 20 ft on center (oc) distance (the panel width of the panels is 10 ft) and are supported by trusses on either end. The beams are braced at every 10 ft (Lb=10 ft). Dead load is 40 psf and live load is 20 psf. Calculate the appropriate beam design.

Learn how to calculate the load factors, moment capacity, and select an appropriate A36 wide flange beam for a truss-supported structure with a 40 ft span. This guide covers steps for applying load factors, calculating the ultimate moment, nominal moment, and selecting the optimal beam shape using an engineering table.

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