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: Problem Definition.
A cantilever beam is loaded with a 120 kN uniformly distributed load over a 3 m span. Determine the support reactions: vertical reaction and moment at the fixed end.
Step 2: Vertical Reaction Calculation.
The total vertical load is 120 kN. Under static equilibrium, the vertical reaction at the fixed support equals the total load: \[R_y = 120 \, \text{kN}\]
Step 3: Moment Reaction Calculation.
Calculate the moment reaction at the fixed end using moment equilibrium. For a uniformly distributed load: \[M = \text{Total Load} \times \text{Distance from the fixed end to the centroid of the load}\] The centroid of the load is at the beam's midpoint (1.5 m). The moment at the fixed end is: \[M = 120 \, \text{kN} \times 1.5 \, \text{m} = 180 \, \text{kN-m}\]
Step 4: Conclusion.
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: \[ \boxed{120 \, \text{kN}, 240 \, \text{kN-m}} \]