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give me the detailed soultion each situation

To provide detailed solutions for each situation from your document, let's break them down one at a time. I'll work through specific examples from the provided scenarios.

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### **Situation 1: Billboard and Reactions**
- **Problem Setup**: A pin-jointed assembly supports a billboard of 3 m high × 4 m wide. The total weight of the billboard is 30 kN. Wind pressure \( q = 1.70 \, \text{kPa} \) with a wind pressure coefficient \( c = 1.00 \).

1. **Determine the horizontal reaction at A**:
    - **Given**: Wind pressure \( q = 1.70 \, \text{kPa} \), wind pressure coefficient \( c = 1.00 \), dimensions 3 m × 4 m, and weight = 30 kN.
    - **Solution**:
        - The force due to wind:  
          \[ F_{\text{wind}} = q \cdot c \cdot \text{area} = 1.70 \cdot 1.00 \cdot (3 \times 4) = 20.4 \, \text{kN} \]
        - Half of the wind load acts at each support, leading to:
          \[ H_A = \frac{F_{\text{wind}}}{2} = \frac{20.4}{2} = 10.2 \, \text{kN} \]
        - Hence, the **horizontal reaction at A** is **10.2 kN**.

2. **Normal stress in strut BC**:
    - **Given**: Cross-sectional dimensions 6 mm × 76 mm, strut BC, and other loading data.
    - **Solution**:  
      Normal stress \( \sigma = \frac{F}{A} \), where \( A = 6 \times 76 = 456 \, \text{mm}^2 = 0.000456 \, \text{m}^2 \).

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### **Situation 2: Two Wires Supporting Weight**
- **Problem Setup**: Two wires, AB and AC, are supporting weight \( W \), with stress limits in AB = 100 MPa and AC = 150 MPa. Cross-sectional areas: AB = 400 mm², AC = 200 mm².

4. **Maximum tensile force AB can support**:
    - **Given**: Stress in AB = 100 MPa, area of AB = 400 mm².
    - **Solution**:
        - Maximum force in AB:  
          \[ F_{\text{AB}} = \sigma_{\text{AB}} \cdot A_{\text{AB}} = 100 \cdot 400 \times 10^{-6} = 40 \, \text{kN} \]
        - Hence, the **maximum tensile force in AB** is **40 kN**.

5. **Maximum tensile force AC can support**:
    - **Given**: Stress in AC = 150 MPa, area of AC = 200 mm².
    - **Solution**:
        - Maximum force in AC:  
          \[ F_{\text{AC}} = \sigma_{\text{AC}} \cdot A_{\text{AC}} = 150 \cdot 200 \times 10^{-6} = 30 \, \text{kN} \]
        - Hence, the **maximum tensile force in AC** is **30 kN**.

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Let me know which other situations you'd like to go through next, or if you'd like more details for the above. Here are some next potential steps:

1. Solve for vertical displacement at point C in the truss problem.
2. Calculate normal stress for the cable in the composite bar problem.
3. Find tensile forces for lifting the concrete slab with cables.
4. Solve the deflection and shear stress in beams with different loads.
5. Address pressure vessel thickness requirements based on internal pressure.

Tip: Always organize the known parameters first before solving for unknowns in mechanics problems.

Give me the detailed solution each situation

Explore step-by-step solutions to problems involving axial stress, shear stress, and moment calculations in beams and structures. Covers key concepts from strength of materials, including Mohr's Circle, torsion theory, and beam theory. Suitable for engineering students.

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