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In a simply supported beam carrying a uniformly distributed load ‘w’ per unit length, the point of contraflexure
- a)Lies in the centre of the beam
- b)Lies at the ends of the beam
- c)Depends upon the length of the beam
- d)Does not exist
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a simply supported beam carrying a uniformly distributed load ‘w’ ...
Contra-flexure = contra (opposite) + flexure (bending)
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In a bending beam, a point is known as a point of contra flexure if it is a location at which no bending occurs. In a bending moment diagram, it is the point at which the bending moment curve intersects with the zero line. In other words, where the bending moment changes its sign from negative to positive or vice versa. It occurs in the overhanging beam.
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In a simply supported beam carrying a uniformly distributed load ‘w’ ...
Point of Contraflexure in a Simply Supported Beam with Uniformly Distributed Load
Simply supported beam is a type of beam that is supported at two points with one end fixed and the other end free. A uniformly distributed load is a load that is spread evenly across the beam. The point of contraflexure is a point in the beam where the bending moment changes sign. It is the point where the beam changes from being concave upwards to being concave downwards or vice versa.
Does not Exist
The correct answer to the given question is option 'D', which states that the point of contraflexure does not exist in a simply supported beam carrying a uniformly distributed load. This is because the bending moment is constant throughout the beam, and there is no change in sign of the bending moment.
Explanation
The bending moment in a simply supported beam with a uniformly distributed load is given by the equation:
M(x) = wLx/2 - w(x^2/2)
where M(x) is the bending moment at a distance 'x' from one end of the beam, w is the uniformly distributed load per unit length, and L is the length of the beam.
The bending moment is maximum at the supports and zero at the center of the beam. The shear force is constant throughout the beam and is equal to the total load on the beam. Therefore, there is no point in the beam where the bending moment changes sign, and hence, the point of contraflexure does not exist.
Conclusion
In conclusion, the point of contraflexure does not exist in a simply supported beam carrying a uniformly distributed load. This is because the bending moment is constant throughout the beam, and there is no change in sign of the bending moment.
Simply supported beam is a type of beam that is supported at two points with one end fixed and the other end free. A uniformly distributed load is a load that is spread evenly across the beam. The point of contraflexure is a point in the beam where the bending moment changes sign. It is the point where the beam changes from being concave upwards to being concave downwards or vice versa.
Does not Exist
The correct answer to the given question is option 'D', which states that the point of contraflexure does not exist in a simply supported beam carrying a uniformly distributed load. This is because the bending moment is constant throughout the beam, and there is no change in sign of the bending moment.
Explanation
The bending moment in a simply supported beam with a uniformly distributed load is given by the equation:
M(x) = wLx/2 - w(x^2/2)
where M(x) is the bending moment at a distance 'x' from one end of the beam, w is the uniformly distributed load per unit length, and L is the length of the beam.
The bending moment is maximum at the supports and zero at the center of the beam. The shear force is constant throughout the beam and is equal to the total load on the beam. Therefore, there is no point in the beam where the bending moment changes sign, and hence, the point of contraflexure does not exist.
Conclusion
In conclusion, the point of contraflexure does not exist in a simply supported beam carrying a uniformly distributed load. This is because the bending moment is constant throughout the beam, and there is no change in sign of the bending moment.
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In a simply supported beam carrying a uniformly distributed load ‘w’ per unit length, the point of contraflexurea)Lies in the centre of the beamb)Lies at the ends of the beamc)Depends upon the length of the beamd)Does not existCorrect answer is option 'D'. Can you explain this answer?
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