In the last decades, developments in manufacturing engineering and material sciences have enabled the possibility of realizing complex beam-like structures with variable cross-section via 3D printing, to achieve enhanced mechanical properties. In this context, Triply Periodic Minimal Surfaces (TPMS) represent a fascinating family of structures that can be precisely described by trigonometric equations in the space R^3. Among the available TPMS we focus on the Gyroid. In particular, we examine beams made of the repetition of gyroid cells along one direction, and we investigate numerically the buckling response of such beams. Based on a finite element formulation, we perform analyses considering the Reissner planar beam theory and an approximate theory for inextensible beams and we explore the buckling load of planar beams with a sinusoidal inertia along the axis. As expected, we observe that the position of the maximums/minimums of the inertia with respect to the constrains has a strong impact on the critical load, and when the number of oscillations of the inertia grows, the critical load reaches a plateau value. However, both planar beam theories are not able to capture the buckling load of a complex gyroid-based beam, even if we consider the same variation of inertia: local and boundary effects have a considerable impact on the solution and therefore a study of the in-plane response of such a beam is needed to solve the problem.