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This question sheet involves analyzing two structural mechanics problems:

1. **Question 1 (Beam Analysis)** - Involves calculating the reactions at supports \( B \) and \( D \) for a loaded overhanging beam, determining the shear force at critical points, calculating the bending moment along the beam, and identifying points of contraflexure.

   **Steps for Solution**:
   - **Reactions at \( B \) and \( D \)**: Use equilibrium equations to find vertical and horizontal reactions.
   - **Shear Force**: Calculate the shear force at each segment between loads.
   - **Bending Moment**: Integrate shear force to find the bending moment distribution.
   - **Contraflexure Points**: Find where the bending moment changes sign along the beam.

2. **Question 2 (Pin-Jointed Truss Analysis)** - Requires calculating forces in all members of a pin-jointed plane frame using the method of joint resolution.

   **Steps for Solution**:
   - **Joint Resolution**: Start from joints with only two unknowns, typically beginning with joints at supports (points \( A \) and \( C \)), then move to joint \( B \) where the external load is applied.
   - **Equilibrium of Forces**: Use equilibrium equations (\( \sum F_x = 0 \) and \( \sum F_y = 0 \)) to solve for forces in each member systematically.

Would you like detailed step-by-step solutions for these problems or clarification on any particular part? 

Here are some follow-up questions to deepen understanding:

1. How does one determine the points of contraflexure in a beam?
2. What are the key steps in analyzing a beam with multiple types of loads (point loads and distributed loads)?
3. How does the method of joint resolution work for determining forces in truss members?
4. What role does equilibrium play in calculating reactions at supports?
5. How do bending moment and shear force diagrams help in structural analysis?

**Tip**: For truss analysis, always start with joints that have the least number of unknowns for easier calculations.

Figure 1 shows a loaded overhanging beam. Determine:
(a) the reactions at B and D;
(b) shear force at critical points along the beam;
(c) bending moment along the beam and
(d) points of contraflexure from supports B and D.

Figure 2 shows a loaded pin-jointed plane frame. Determine the forces in all the members using the method of joint resolution.

Solve structural analysis problems involving a loaded overhanging beam and a pin-jointed plane frame. Learn how to determine reactions, shear forces, bending moments, and points of contraflexure in beams, as well as member forces in trusses using joint resolution. Suitable for undergraduate engineering students.

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