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Consider the following statements :
A simply-supported beamish subjected to a couple somewhere in the span. It would produce
1. A rectangular SF diagram
2. parabolic BM diagrams
3. both + ve and - ve BMs are maximum at the point of application of the couple.
Of these statements
- a)1, 2, and 3 are correct
- b)1 and 2 are correct
- c)2 and 3 are correct
- d)1 and 3 are correct
Correct answer is option 'D'. Can you explain this answer?
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Consider the following statements :A simply-supported beamish subject...
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Consider the following statements :A simply-supported beamish subject...
Statement 1: A simply-supported beam subjected to a couple somewhere in the span would produce a rectangular Shear Force (SF) diagram.
The shear force diagram represents the variation of the shear force along the length of the beam. In this case, since the beam is subjected to a couple, the shear force will be constant throughout the span. This means that the shear force diagram will be a rectangular shape, with the same magnitude of shear force at all points along the beam.
Statement 2: A simply-supported beam subjected to a couple somewhere in the span would produce parabolic Bending Moment (BM) diagrams.
The bending moment diagram represents the variation of the bending moment along the length of the beam. When a beam is subjected to a couple, it induces bending in the beam. The bending moment will be maximum at the point of application of the couple and gradually decrease towards the supports. This variation in bending moment is represented by a parabolic shape in the bending moment diagram.
Statement 3: Both positive and negative bending moments are maximum at the point of application of the couple.
When a beam is subjected to a couple, it causes bending in the beam. The bending moment can be either positive or negative, depending on the direction of the couple. At the point of application of the couple, the bending moment will be maximum, regardless of whether it is positive or negative. This is because the moment arm from the point of application to any other point along the beam is maximum at the point of application.
Conclusion:
From the explanations above, we can conclude that statements 1 and 3 are correct.
- Statement 1 states that a simply-supported beam subjected to a couple produces a rectangular shear force diagram, which is true.
- Statement 2 states that a simply-supported beam subjected to a couple produces parabolic bending moment diagrams, which is also true.
- Statement 3 states that both positive and negative bending moments are maximum at the point of application of the couple, which is true.
Therefore, the correct answer is option D, as both statements 1 and 3 are correct.
The shear force diagram represents the variation of the shear force along the length of the beam. In this case, since the beam is subjected to a couple, the shear force will be constant throughout the span. This means that the shear force diagram will be a rectangular shape, with the same magnitude of shear force at all points along the beam.
Statement 2: A simply-supported beam subjected to a couple somewhere in the span would produce parabolic Bending Moment (BM) diagrams.
The bending moment diagram represents the variation of the bending moment along the length of the beam. When a beam is subjected to a couple, it induces bending in the beam. The bending moment will be maximum at the point of application of the couple and gradually decrease towards the supports. This variation in bending moment is represented by a parabolic shape in the bending moment diagram.
Statement 3: Both positive and negative bending moments are maximum at the point of application of the couple.
When a beam is subjected to a couple, it causes bending in the beam. The bending moment can be either positive or negative, depending on the direction of the couple. At the point of application of the couple, the bending moment will be maximum, regardless of whether it is positive or negative. This is because the moment arm from the point of application to any other point along the beam is maximum at the point of application.
Conclusion:
From the explanations above, we can conclude that statements 1 and 3 are correct.
- Statement 1 states that a simply-supported beam subjected to a couple produces a rectangular shear force diagram, which is true.
- Statement 2 states that a simply-supported beam subjected to a couple produces parabolic bending moment diagrams, which is also true.
- Statement 3 states that both positive and negative bending moments are maximum at the point of application of the couple, which is true.
Therefore, the correct answer is option D, as both statements 1 and 3 are correct.
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Consider the following statements :A simply-supported beamish subjected to a couple somewhere in the span. It would produce1. A rectangular SF diagram2. parabolic BM diagrams3. both + ve and - ve BMs are maximum at the point of application of the couple.Of these statementsa)1, 2, and 3 are correctb)1 and 2 are correctc)2 and 3 are correctd)1 and 3 are correctCorrect answer is option 'D'. Can you explain this answer?
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