Pure bending occurs when a beam is subjected to a bending moment without any axial force or shear force. In pure bending, the beam experiences a combination of compressive and tensile stresses on its cross-section, resulting in bending deformation.

Here are the reasons why option A is the correct answer:

Shear force is constant throughout the span:
- In pure bending, the shear force is constant along the entire span of the beam. This means that the shear force does not vary from one section of the beam to another.
- The constant shear force is a result of the equilibrium of the applied loads, where the sum of the vertical forces is zero.
- When the shear force is constant, it implies that there is no change in the internal forces acting on the beam, and the beam is only experiencing bending moments.

Load is applied as UDL throughout the span:
- When a uniform distributed load (UDL) is applied to a beam, it results in a linearly varying shear force along the span, which contradicts the condition of pure bending.
- The varying shear force indicates that there are additional internal forces acting on the beam, such as axial forces or additional transverse loads, which are not present in pure bending.

Load is applied at the mid-span only:
- If the load is applied at the mid-span only, it leads to a concentrated load, which generates a non-uniform shear force along the span of the beam.
- The non-uniform shear force again indicates the presence of additional internal forces, making it different from the condition of pure bending.

None of the above:
- This option states that none of the given conditions represents pure bending.
- Since options B and C have already been discussed and found to be inconsistent with pure bending, this statement is true.

In summary, pure bending occurs when the shear force is constant throughout the span of the beam. This condition ensures that the beam is only experiencing bending moments without any axial forces or varying shear forces.