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.