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The shear stress on a beam section is maximum:-
- a)On the extreme bottom surface fibres
- b)At the neutral axis of the section
- c)At the free edges
- d)On the extreme top surface fibres
Correct answer is option 'B'. Can you explain this answer?
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The shear stress on a beam section is maximum:-a)On the extreme bottom...
Shown below is a rectangular beam in pure bending. As shown above, shear stresses vary quadratically with the distance y1 from the neutral axis. The maximum shear stress occurs at the neutral axis and is zero at both the top and bottom surface of the beam. Shear flow has the units of force per unit distance.
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The shear stress on a beam section is maximum:-a)On the extreme bottom...
Shear stress on a beam section is maximum at the neutral axis of the section. This can be explained by the following points:
Definition of neutral axis:
The neutral axis of a beam is an imaginary line passing through the centroid of the cross-section, where the shear stress is zero. It is also known as the axis of zero stress.
Shear stress distribution:
When a beam is subjected to transverse loading, shear stress is induced on the cross-section. The distribution of shear stress is not uniform across the section, but it varies linearly from maximum value at the extreme fibres to zero at the neutral axis.
Shear stress equation:
The shear stress at any point on the cross-section can be calculated by using the following equation:
τ = VQ/Ib
where τ is shear stress, V is the shear force, Q is the first moment of area about the neutral axis, I is the moment of inertia of the cross-section about the neutral axis, and b is the width of the section.
From the above equation, it can be observed that shear stress is directly proportional to the distance from the neutral axis. Therefore, the maximum shear stress occurs at the extreme fibres, whereas it is zero at the neutral axis.
Conclusion:
Hence, it is concluded that the shear stress on a beam section is maximum at the extreme fibres and zero at the neutral axis. Therefore, the correct option is B.
Definition of neutral axis:
The neutral axis of a beam is an imaginary line passing through the centroid of the cross-section, where the shear stress is zero. It is also known as the axis of zero stress.
Shear stress distribution:
When a beam is subjected to transverse loading, shear stress is induced on the cross-section. The distribution of shear stress is not uniform across the section, but it varies linearly from maximum value at the extreme fibres to zero at the neutral axis.
Shear stress equation:
The shear stress at any point on the cross-section can be calculated by using the following equation:
τ = VQ/Ib
where τ is shear stress, V is the shear force, Q is the first moment of area about the neutral axis, I is the moment of inertia of the cross-section about the neutral axis, and b is the width of the section.
From the above equation, it can be observed that shear stress is directly proportional to the distance from the neutral axis. Therefore, the maximum shear stress occurs at the extreme fibres, whereas it is zero at the neutral axis.
Conclusion:
Hence, it is concluded that the shear stress on a beam section is maximum at the extreme fibres and zero at the neutral axis. Therefore, the correct option is B.
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The shear stress on a beam section is maximum:-a)On the extreme bottom surface fibresb)At the neutral axis of the sectionc)At the free edgesd)On the extreme top surface fibresCorrect answer is option 'B'. Can you explain this answer?
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