The shape of SFD for a cantilever beam subjected to a couple at its free end?

Question

Answer

Shape of SFD for Cantilever Beam Subjected to a Couple at its Free End

Introduction

When a cantilever beam is subjected to a couple at its free end, the shear force and bending moment diagrams will have a specific shape.

Shear Force Diagram (SFD)

The shear force diagram for a cantilever beam subjected to a couple at its free end will have the following shape:

The shear force will be zero at the fixed end of the beam

The shear force will be constant between the fixed end and the point of application of the couple

The shear force will change linearly from the point of application of the couple to the free end of the beam

The shear force will be equal to the magnitude of the couple at the free end of the beam

Bending Moment Diagram (BMD)

The bending moment diagram for a cantilever beam subjected to a couple at its free end will have the following shape:

The bending moment will be zero at the fixed end of the beam

The bending moment will change linearly between the fixed end and the point of application of the couple

The bending moment will be constant from the point of application of the couple to the free end of the beam

The bending moment will be equal to the product of the magnitude of the couple and the length of the beam at the free end

Conclusion

In conclusion, the shear force and bending moment diagrams for a cantilever beam subjected to a couple at its free end will have a specific shape. It is important to understand this shape in order to design and analyze structures that are subjected to this type of loading.

Answer

No shear force in any part of the beam

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