A simply supported beam of length 1 m is subjected to a uniformly distributed bending moment of 1 N m per meter throughout the length as shown in the figure. The bending moment at the mid-point of the beam is __________N m (rounded off to the nearest integer).
Show Hint
For simply supported beams subjected to a uniformly distributed bending moment, the bending moment is the same throughout the length of the beam, including at the mid-point.
Step 1: Understanding the problem setup.
The beam is simply supported, and a uniformly distributed bending moment of 1 N m per meter is applied throughout the length of the beam. The question asks for the bending moment at the mid-point of the beam.
Step 2: Formula for bending moment in a simply supported beam.
In this case, the bending moment at any point along the beam is related to the distance from the left support. However, for a uniformly distributed bending moment, the bending moment is constant throughout the beam. That means the moment at the mid-point is the same as the moment at any other point along the length of the beam.
\[
M(x) = M_0
\]
where \( M_0 = 1 \, \text{N m} \) is the uniformly distributed bending moment per unit length. Since the beam is simply supported and the distributed moment does not vary, the moment at the mid-point remains \( 0 \, \text{N m} \) because there is no additional external moment applied at the mid-point.
Step 3: Conclusion.
The bending moment at the mid-point of the beam is \( 0 \, \text{N m} \).
