What is the stiffness factor (k) equation?

The stiffness factor (k) equation, represented as ( K = \frac{E \cdot A}{L} ), reflects the relationship between the material properties and geometry of a structural element. In this equation, ( E ) denotes the modulus of elasticity of the material, ( A ) is the cross-sectional area, and ( L ) is the length of the element.

This formula indicates that the stiffness of a structural element increases with a larger cross-sectional area and a higher modulus of elasticity, while it decreases with an increase in length. Essentially, a material that is stiffer (higher ( E )) or has a larger cross-sectional area provides greater resistance to deformation under axial loads. Conversely, a longer element tends to be less stiff, as its added length allows for greater deflection under the same load conditions.

The other variations presented in the choices don't properly represent the stiffness factor for axial loading scenarios. They manipulate the relationships between the parameters in ways that do not align with the principles of material mechanics and structural behavior, hence not yielding the effective stiffness of a structural element.