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Consider the following statements for a simply supported beam subjected to a couple of 10 kN-m at its mid-span.
1. Bending moment is zero at the ends and maximum at the center
2. Bending moment is constant over the entire length of the beam
3. Shear force is constant over the entire length of the beam
4. Shear force is zero over the entire length of the beam Which of the statements given above are correct?
  • a)
    1, 3 and 4
  • b)
    2, 3 and 4
  • c)
    1 and 3
  • d)
    2 and 4
Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements for a simply supported beam subject...
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Consider the following statements for a simply supported beam subject...
1. Bending moment is zero at the ends and maximum at the center:
This statement is correct. For a simply supported beam, the bending moment is zero at the ends because there are no external moments acting on them. At the mid-span, where the couple is applied, the bending moment is maximum. This is because the couple creates a moment that causes the beam to bend, and the maximum bending moment occurs at the point where the beam is most deflected, which is at the center.

2. Bending moment is constant over the entire length of the beam:
This statement is incorrect. The bending moment is not constant over the entire length of the beam. As mentioned earlier, the bending moment is zero at the ends and maximum at the center due to the applied couple. Therefore, the bending moment varies along the length of the beam.

3. Shear force is constant over the entire length of the beam:
This statement is correct. Since there are no external forces acting in the vertical direction, the shear force remains constant throughout the length of the beam. In this case, the shear force would be zero since there are no vertical loads applied to the beam, only the couple which generates bending moment.

4. Shear force is zero over the entire length of the beam:
This statement is incorrect. The shear force is not zero over the entire length of the beam. As mentioned earlier, the shear force is constant throughout the length of the beam, but it is not zero. Although there are no vertical loads applied to the beam in this case, the applied couple induces internal shear forces within the beam.

In conclusion, the correct statements are 1 and 3. The bending moment is zero at the ends and maximum at the center of the beam due to the applied couple, and the shear force is constant (zero in this case) over the entire length of the beam as there are no external vertical loads applied.
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Consider the following statements for a simply supported beam subjected to a couple of 10 kN-m at its mid-span.1. Bending moment is zero at the ends and maximum at the center2. Bending moment is constant over the entire length of the beam3. Shear force is constant over the entire length of the beam4. Shear force is zero over the entire length of the beam Which of the statements given above are correct?a) 1, 3 and 4b) 2, 3 and 4c) 1 and 3d) 2 and 4Correct answer is option 'C'. Can you explain this answer?
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