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A simply supported beam has equal overhanging lengths and carries equal concentrated loads P at ends. Bending moment over the length between the supports
  • a)
    is zero
  • b)
    is a non-zero constant
  • c)
    varies uniformly from one support to the other
  • d)
    is maximum at mid-span
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A simply supported beam has equal overhanging lengths and carries equa...
Explanation:

- The given simply supported beam has equal overhanging lengths and carries equal concentrated loads P at ends.
- Let the length of the beam be L and the overhanging length be x.
- The total length of the beam is 2x + L.
- Due to symmetry, the reactions at the supports will be equal and half of the total load P each.
- Let the reaction at each support be R and the load at each end be P/2.
- The bending moment at any section of the beam is the algebraic sum of the moments caused by the loads on either side of the section.
- Consider a section at a distance x from the left support. The bending moment at this section can be calculated as follows:
- The moment caused by the load P/2 at the left end is P/2 * x.
- The moment caused by the reaction R at the left support is R * (2x + L - x) = R * (x + L).
- The moment caused by the load P/2 at the right end is P/2 * (L - x).
- The moment caused by the reaction R at the right support is R * (2x + L - (L - x)) = R * (x + L).
- The bending moment at the section is the algebraic sum of these moments, which is given by:
M = P/2 * x + R * (x + L) - P/2 * (L - x) - R * (x + L)
- Simplifying this expression, we get:
M = P * x/2 - R * x
- As the load P and the span L are constant, the bending moment at any section of the beam varies linearly with the distance x from the left support.
- The bending moment is zero at the left support (x = 0) and maximum at the right support (x = L/2).
- Therefore, the bending moment over the length between the supports is a non-zero constant, which is equal to P/4.
- Hence, the correct answer is option 'B' - the bending moment over the length between the supports is a non-zero constant.
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