This study investigates the structural response of lightweight non-prismatic beams with linear, quadratic, and trigonometric cross-sectional variation laws under elemental and combined loading conditions. The objective is to identify mechanically interpretable trends that support the preliminary selection of simple geometric parameterizations rather than to obtain an optimized geometry through iterative procedures. Beams restrained at one or both ends, comprising five boundary conditions and seven loading cases, were analyzed under an equal-volume criterion using a Euler-Bernoulli finite element formulation. The model was verified against benchmark solutions for non-prismatic beams, with a maximum relative error of 0.0301%, while the mesh-convergence study produced errors below 0.0034%. The configurations were compared using dimensionless coefficients based on maximum displacement, global displacement, and fundamental natural frequency. All reduced-section beams produced displacement coefficients greater than unity, indicating increased deformation relative to the uncut reference beam; consequently, the preferred parameterization is the one that minimizes this penalty. For beams restrained at one end, the trigonometric cut produced the lowest global displacement coefficient for every elemental and combined load, minimized the maximum displacement in most loading cases, and provided the highest frequency ratios. For beams restrained at both ends, the quadratic cut generally minimized both displacement coefficients and provided the highest frequency ratios for pinned-pinned and rotational spring-rotational spring supports. For fixed-fixed beams, the quadratic cut was generally preferable for displacement control, whereas the trigonometric cut better preserved the fundamental frequency. These trends are explained by the interaction between the spatial distribution of flexural rigidity, the bending-moment distribution, and the location of the removed mass. The results demonstrate that equal-volume section reductions can produce substantially different static and frequency-based responses, providing mechanics-based selection criteria for the preliminary design of lightweight non-prismatic beams.