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To determine the plank, beam, and column reactions for the single-bay, post-and-beam deck illustrated, we'll analyze the given dataTo determine the plank, beam, and column reactions for the single-bay, post-and-beam deck illustrated, we'll analyze the given 

### Given Information:
1. **Loads:**
   - **Live Load:** 60 lb/ft²
   - **Dead Load:** 8 lb/ft²
   - **Beam Self-Weight:** 10 lb/ft for a 12 ft beam
   - **Column Self-Weight:** 100 lb

2. **Dimensions:**
   - Plank span (length) is 8 ft.
   - Beam span (length) is 12 ft.
   - The deck is 8 ft by 12 ft in area.

### Step-by-Step Solution:

#### 1. **Calculate the Uniform Load on the Plank:**
The total load per unit area on the plank is the sum of the live load and dead load:

\[
w_{total} = 60 \, \text{lb/ft}^2 + 8 \, \text{lb/ft}^2 = 68 \, \text{lb/ft}^2
\]

The planks have a tributary width of 1 ft, so the total uniform load per linear foot on the plank is:

\[
w_{plank} = 68 \, \text{lb/ft}^2 \times 1 \, \text{ft} = 68 \, \text{lb/ft}
\]

#### 2. **Determine Reactions at the Ends of the Plank:**
The plank acts as a simply supported beam of length \( L = 8 \, \text{ft} \) with a uniform load \( w_{plank} = 68 \, \text{lb/ft} \).

The reactions at both ends (let's call them \( R_{beam} \)) are equal and can be calculated using:

\[
R_{beam} = \frac{w_{plank} \times L}{2} = \frac{68 \, \text{lb/ft} \times 8 \, \text{ft}}{2} = 272 \, \text{lb}
\]

#### 3. **Calculate the Load on the Beam:**
Each beam receives load from a series of planks. Given the width of the deck (8 ft), there are 8 planks (1 ft wide each). Each plank exerts a reaction force of \( R_{beam} = 272 \, \text{lb} \) on the beam.

The total uniform load on each beam is:

\[
w_{beam} = R_{beam} \times \text{number of planks} = 272 \, \text{lb} \times 8 = 2176 \, \text{lb}
\]

Convert this to a uniform load per linear foot:

\[
w_{beam} = \frac{2176 \, \text{lb}}{12 \, \text{ft}} \approx 181.33 \, \text{lb/ft}
\]

#### 4. **Determine Reactions at the Ends of the Beam:**
The beam is simply supported with a uniform load of \( w_{beam} = 181.33 \, \text{lb/ft} \) over a length of \( L = 12 \, \text{ft} \).

Reactions at both ends (let's call them \( R_{col} \)):

\[
R_{col} = \frac{w_{beam} \times L}{2} = \frac{181.33 \, \text{lb/ft} \times 12 \, \text{ft}}{2} = 1088 \, \text{lb}
\]

#### 5. **Calculate Column Reactions Including Column Self-Weight:**
Each column supports the reaction from the beam and its own weight:

\[
R_{column} = R_{col} + \text{column self-weight}
\]

\[
R_{column} = 1088 \, \text{lb} + 100 \, \text{lb} = 1188 \, \text{lb}
\]

### Summary of Results:
- **Plank Reaction (at each end):** \( R_{beam} = 272 \, \text{lb} \)
- **Beam Reaction (at each end):** \( R_{col} = 1088 \, \text{lb} \)
- **Column Reaction (including self-weight):** \( R_{column} = 1188 \, \text{lb} \)

Would you like more details or have any specific questions about this calculation?

### Related Questions:
1. How would the reactions change if the live load increased to 80 lb/ft²?
2. What is the maximum bending moment in the beam?
3. How would the analysis differ if the beam was continuous over multiple spans?
4. How does the deflection of the beam change with different materials?
5. What are the safety factors typically used in this type of structural analysis?

### Tip:
Always verify units throughout your calculations to ensure consistency and accuracy!

Determine the plank, beam, and column reactions for the single-bay, post-and-beam deck illustrated. The loads are: 60 lb/ft² live load, 8 lb/ft² dead load, 10 lb/ft self-weight of 12' beams, and 100 lb self-weight of columns.

This guide explains how to calculate plank, beam, and column reactions for a post-and-beam deck with live and dead loads. Step-by-step instructions include key calculations for load distribution and equilibrium of forces.

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