Q5 Draw the influence line for (a) the moment at B, (b) the shear at C, and (c) the vertical reaction at B. Solve this problem using the basic method. Hint: The support at A resists only a horizontal force and a bending moment. Solution (a) MB 8 12 ·x(m) -4 4m C 4m B 4 m

Structural Analysis
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Chapter2: Loads On Structures
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Explain in depth how to come about the solutions provide for this problem. I’m confused on how to draw the graphs and how to come about the numbers on the graphs. If you could explain in detail step by step so I can understand the process and concept.
**Q5 Explanation and Solution:**

**Problem:**  
Draw the influence line for:
(a) The moment at \( B \).  
(b) The shear at \( C \).  
(c) The vertical reaction at \( B \).  
Solve this problem using the basic method.

**Hint:**  
The support at \( A \) resists only a horizontal force and a bending moment.

---

**Solution:**

The diagram (top right) depicts a beam with supports and a load application. The beam is divided into three segments, each 4 meters in length, totaling 12 meters from point \( A \) to point \( B \).

**(a) Moment at \( B \), \( M_B \):**

- The graph shows the influence line for the moment at \( B \).
- The x-axis represents the position along the beam in meters (\( x(m) \)).
- The line decreases linearly from 0 to -4 between \( x = 8 \) meters to \( x = 12 \) meters.

**(b) Shear at \( C \), \( V_C \):**

- The graph shows the influence line for the shear at \( C \).
- The influence line is constant at -1 from \( x = 0 \) to \( x = 4 \).
- It returns to 0 from \( x = 4 \) to \( x = 12 \).

**(c) Vertical Reaction at \( B \), \( B_y \):**

- The graph illustrates the influence line for the vertical reaction at \( B \).
- The influence line is constant at 1 from the beginning (\( x = 0 \)) to the end (\( x = 12 \)) of the beam.

These influence lines are useful for determining how moving loads affect the structure at specific points, aiding in the design and analysis of the beam.
Transcribed Image Text:**Q5 Explanation and Solution:** **Problem:** Draw the influence line for: (a) The moment at \( B \). (b) The shear at \( C \). (c) The vertical reaction at \( B \). Solve this problem using the basic method. **Hint:** The support at \( A \) resists only a horizontal force and a bending moment. --- **Solution:** The diagram (top right) depicts a beam with supports and a load application. The beam is divided into three segments, each 4 meters in length, totaling 12 meters from point \( A \) to point \( B \). **(a) Moment at \( B \), \( M_B \):** - The graph shows the influence line for the moment at \( B \). - The x-axis represents the position along the beam in meters (\( x(m) \)). - The line decreases linearly from 0 to -4 between \( x = 8 \) meters to \( x = 12 \) meters. **(b) Shear at \( C \), \( V_C \):** - The graph shows the influence line for the shear at \( C \). - The influence line is constant at -1 from \( x = 0 \) to \( x = 4 \). - It returns to 0 from \( x = 4 \) to \( x = 12 \). **(c) Vertical Reaction at \( B \), \( B_y \):** - The graph illustrates the influence line for the vertical reaction at \( B \). - The influence line is constant at 1 from the beginning (\( x = 0 \)) to the end (\( x = 12 \)) of the beam. These influence lines are useful for determining how moving loads affect the structure at specific points, aiding in the design and analysis of the beam.
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