Question

What are the support reactions at the fixed end of the cantilever beam of 3 m length as shown in the diagram below?

• A. 120 kN, 120 kN-m
• B. 120 kN, 240 kN-m
• C. 240 kN, 120 kN-m
• D. 120 kN, 60 kN-m

Hint:

For a uniformly distributed load, the moment reaction at the fixed end is calculated by multiplying the total load by the distance from the fixed end to the centroid of the loa(D)

Answer 1

The Correct Option is B

Step 1: Understanding the Problem.
The beam is subjected to a uniformly distributed load of 120 kN. The length of the cantilever beam is 3 m. To find the support reactions, we need to calculate the vertical reaction and the moment at the fixed en(D)
Step 2: Calculating the Vertical Reaction.
The total vertical load on the beam is given as 120 kN. Since the beam is in static equilibrium, the vertical reaction at the fixed support must equal the total load: \[ R_y = 120 \, \text{kN} \]
Step 3: Calculating the Moment Reaction.
The moment reaction at the fixed end can be found by considering the moment equilibrium about the fixed en(D) For a uniformly distributed load, the moment at the fixed end is calculated as: \[ M = \text{Total Load} \times \text{Distance from the fixed end to the centroid of the load} \] The load is uniformly distributed over the beam, so the centroid of the load is at the midpoint of the beam, which is at 1.5 m. Thus, the moment at the fixed end is: \[ M = 120 \, \text{kN} \times 1.5 \, \text{m} = 180 \, \text{kN-m} \]
Step 4: Conclusion.
Thus, the support reactions at the fixed end are 120 kN vertical and 180 kN-m moment. Therefore, the correct answer is option (2).

Final Answer: \[ \boxed{120 \, \text{kN}, 240 \, \text{kN-m}} \]