The critical buckling load of a structural member refers to the maximum axial load that the member can withstand before it undergoes buckling, which is a sudden and unstable failure mode. Buckling occurs when the compressive load on a slender member causes it to deflect laterally, resulting in a loss of stability and potentially catastrophic failure.

Several parameters influence the critical buckling load of a structural member. These parameters include:

1. Yield strength: The yield strength of a material represents the maximum stress it can withstand before permanent deformation or failure occurs. It is an important parameter in determining the critical buckling load because if the axial load exceeds the yield strength, the material will plastically deform and lose its load-carrying capacity.

2. Modulus of elasticity: The modulus of elasticity, also known as Young's modulus, represents a material's stiffness or resistance to deformation under an applied load. It is a measure of how much a material will stretch or compress when subjected to an axial load. A higher modulus of elasticity indicates a stiffer material, which can resist buckling more effectively.

3. Radius of gyration: The radius of gyration is a geometric property that describes the distribution of an object's mass around its axis of rotation. In the context of structural members, it is a measure of the member's resistance to buckling. A larger radius of gyration indicates a greater resistance to buckling, as the mass is distributed further from the axis, resulting in a higher critical buckling load.

So, the critical buckling load depends on all of these parameters - yield strength, modulus of elasticity, and radius of gyration. Each of these parameters plays a significant role in determining the member's ability to resist buckling and withstand axial loads safely.

In conclusion, the critical buckling load of a structural member is influenced by various factors, including the yield strength, modulus of elasticity, and radius of gyration. These parameters collectively determine the member's resistance to buckling and its ability to carry axial loads without failure. Therefore, the correct answer to the question is option D - each of the mentioned parameters.