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To solve for the shear force and bending moment in the given beam with the following conditions:

- Beam length \( L = 6 \, \text{m} \)
- Uniformly distributed load \( w = 15 \, \text{kN/m} \)
- The beam is fixed at one end, which makes it a **cantilever beam**.

### Step 1: Shear Force Calculation
The total load on the beam due to the uniformly distributed load is:

\[
P = w \times L = 15 \, \text{kN/m} \times 6 \, \text{m} = 90 \, \text{kN}
\]

For a cantilever beam, the shear force at the fixed end is equal to the total load:

\[
V = P = 90 \, \text{kN}
\]

The shear force is constant along the beam and reduces linearly towards zero at the free end.

### Step 2: Bending Moment Calculation
The maximum bending moment occurs at the fixed support. The formula for the bending moment at the fixed end of a cantilever beam under a uniformly distributed load is:

\[
M = \frac{w L^2}{2}
\]

Substituting the values:

\[
M = \frac{15 \times (6)^2}{2} = \frac{15 \times 36}{2} = 270 \, \text{kNm}
\]

Thus, the maximum bending moment at the fixed end is:

\[
M = 270 \, \text{kNm}
\]

### Summary of Results:
- **Shear force at the fixed end**: \( V = 90 \, \text{kN} \)
- **Maximum bending moment at the fixed end**: \( M = 270 \, \text{kNm} \)

Would you like more details on this solution or the next steps in shear and moment diagram analysis?

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Here are five related questions to deepen your understanding:
1. How does the shear force vary along the length of a cantilever beam?
2. What would happen to the shear and moment values if the load were doubled?
3. How do you calculate the deflection of a cantilever beam under a uniformly distributed load?
4. What is the difference between a simply supported beam and a cantilever beam in terms of load distribution?
5. How would the shear force and moment change if the beam had a point load at the free end instead of a uniform load?

**Tip:** Always consider the boundary conditions of a beam when solving for internal forces.

Solve for shear and moment for a cantilever beam with length 6 m and a uniformly distributed load of 15 kN/m.

This solution calculates the shear force and bending moment for a cantilever beam with a length of 6 meters and a uniformly distributed load of 15 kN/m. Key concepts include shear force, bending moment, and the application of statics to determine these forces. The shear force is constant along the beam, while the bending moment is maximum at the fixed end.

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