https://file.aiquickdraw.com/mathbot/file/1728051101894pbbcixg6.jpg

To show the deflected shape of the beam in the given diagram, let's analyze the loading and support conditions:

### Analysis of the Beam:
1. **Beam Type**: The beam is supported by two fixed supports at points \( A \) and \( D \).
2. **Loading Conditions**:
   - A counter-clockwise moment of \( 5 \, \text{kN-m} \) is applied at point \( B \).
   - A vertical point load of \( 8 \, \text{kN} \) is applied downwards at point \( C \).

### Deflection Shape:
- Due to the **moment at \( B \)**, the beam will tend to **rotate** counter-clockwise, causing the portion of the beam from \( A \) to \( C \) to curve downwards.
- The **point load at \( C \)** causes a **downward deflection** starting from that point, making the beam bend further downwards.
- At **fixed supports \( A \) and \( D \)**, the deflection is zero, and the slope of the beam is constrained (no rotation).

### Deflected Shape Description:
- The left portion \( A \)-\( B \) will curve **slightly upwards** near \( A \), then **deflect downwards** as it approaches \( B \).
- Between \( B \) and \( C \), the beam will **deflect downwards** more prominently.
- The segment from \( C \) to \( D \) will continue to deflect downwards but with a steeper curvature due to the applied point load.
  
The overall deflected shape will resemble a curve starting from \( A \), dipping at \( B \), and sagging significantly at \( C \) before trying to return to zero deflection at \( D \).

Let me know if you need a visual representation of this, or have any further questions!

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**Further Questions:**

1. How do fixed supports impact the deflection and slope at the ends?
2. What are the key differences in deflection shape for point loads versus applied moments?
3. How does the location of the applied moment affect the beam’s deflection profile?
4. What are the common deflected shapes for various beam loading scenarios?
5. How can we calculate the maximum deflection and bending moment in the beam?

**Tip:** When dealing with deflections, it's essential to consider both the boundary conditions and the type of loads applied, as they significantly influence the final shape.

Show the deflected shape of the beam in the provided diagram.

Analyze the deflected shape of a beam with fixed supports under the influence of a 5 kN-m moment at point B and an 8 kN point load at point C. This structural analysis problem applies key beam deflection concepts and the moment-area theorem.

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