To solve for the forces in each member of the king post truss with an 8 m span, we'll follow the structured approach outlined below.

### 1. Break Down the Problem
1. Identify the geometry of the truss and the locations of applied loads.
2. Determine the support reactions due to the applied loads.
3. Use methods such as the method of joints or method of sections to find the force in each member.

### 2. Relevant Concepts
1. **Equilibrium of Forces:** The sum of vertical forces and the sum of horizontal forces must equal zero.
2. **Moment Equilibrium:** The sum of moments around any point must equal zero.
3. **Truss Member Force Calculation:** Assuming members are pin-jointed, we can analyze one joint at a time.

### 3. Analysis and Detail
Assuming a simple case where we have joint loads (like P at the center) and that the truss is symmetric, the following would apply:

1. **Calculate Support Reactions:**
- Let $ R_A $ and $ R_B $ be the reactions at supports A and B respectively.
- Using the equilibrium equations:
$$
\sum F_y = 0: R_A + R_B - P = 0
$$
$$
\sum M_A = 0: R_B \cdot 8 m - P \cdot 4 m = 0
$$
From these, you can solve for $ R_A $ and $ R_B $.

2. **Force Distribution in Members:**
- Start at joint A:
$$
\sum F_y = 0: T_{AC} - R_A = 0 \implies T_{AC} = R_A
$$
$ T_{AC} $ is the force in the member AC.

- Move to joint C:
$$
\sum F_x = 0: T_{AC} - T_{BC}\cos(\theta) = 0
$$
$$
\sum F_y = 0: T_{BC}\sin(\theta) - T_{AD} = 0
$$
where $ \theta $ is the angle between member BC and the horizontal.

3. **Continue analyzing other joints** (D, B, etc.) using similar equilibrium equations until all member forces are calculated.

### 4. Verify and Summarize
1. Check calculations for consistency (do the forces balance out when summing at each joint?).
2. Present the forces in a tabular format once calculations are verified.

### Final Answer
Here’s an example of how the forces might be presented, assuming values from calculation:

| Member | Force (kN) |
|----------|------------|
| AC | $ T_{AC} $ |
| AD | $ T_{AD} $ |
| BC | $ T_{BC} $ |
| BD | $ T_{BD} $ |

Note that exact force values depend on the specific loading and geometry detailed in Fig. 33, which was not provided. To perform these calculations, you would need to substitute values into the equations based on that diagram.

Question

To solve for the forces in each member of the king post truss with an 8 m span, we'll follow the structured approach outlined below.

### 1. Break Down the Problem
1. Identify the geometry of the truss and the locations of applied loads.
2. Determine the support reactions due to the applied loads.
3. Use methods such as the method of joints or method of sections to find the force in each member.

### 2. Relevant Concepts
1. **Equilibrium of Forces:** The sum of vertical forces and the sum of horizontal forces must equal zero.
2. **Moment Equilibrium:** The sum of moments around any point must equal zero.
3. **Truss Member Force Calculation:** Assuming members are pin-jointed, we can analyze one joint at a time.

### 3. Analysis and Detail
Assuming a simple case where we have joint loads (like P at the center) and that the truss is symmetric, the following would apply:

1. **Calculate Support Reactions:**
   - Let $ R_A $ and $ R_B $ be the reactions at supports A and B respectively.
   - Using the equilibrium equations:
     $$
     \sum F_y = 0: R_A + R_B - P = 0
     $$
     $$
     \sum M_A = 0: R_B \cdot 8 m - P \cdot 4 m = 0
     $$
     From these, you can solve for $ R_A $ and $ R_B $.

2. **Force Distribution in Members:**
   - Start at joint A:
     $$
     \sum F_y = 0: T_{AC} - R_A = 0 \implies T_{AC} = R_A
     $$
     $ T_{AC} $ is the force in the member AC.
  
   - Move to joint C:
     $$
     \sum F_x = 0: T_{AC} - T_{BC}\cos(\theta) = 0
     $$
     $$
     \sum F_y = 0: T_{BC}\sin(\theta) - T_{AD} = 0
     $$
     where $ \theta $ is the angle between member BC and the horizontal.

3. **Continue analyzing other joints** (D, B, etc.) using similar equilibrium equations until all member forces are calculated.

### 4. Verify and Summarize
1. Check calculations for consistency (do the forces balance out when summing at each joint?).
2. Present the forces in a tabular format once calculations are verified.

### Final Answer
Here’s an example of how the forces might be presented, assuming values from calculation:

| Member   | Force (kN) |
|----------|------------|
| AC       | $ T_{AC} $ |
| AD       | $ T_{AD} $ |
| BC       | $ T_{BC} $ |
| BD       | $ T_{BD} $ |

Note that exact force values depend on the specific loading and geometry detailed in Fig. 33, which was not provided. To perform these calculations, you would need to substitute values into the equations based on that diagram.

Knowee AI · Accepted Answer