Concrete exhibits inherently low ductility and tensile strength despite its high compressive strength. Typically, it must be reinforced with steel rebars, yet it still suffers from potential corrosion issues. This work proposes and examines a new method for improving the bending stiffness of cementitious beams by reinforcing with 3D printed plastic TPMS-Primitive scaffolds. Three concrete beams of the same size - including non-reinforced, reinforced with one-layer, and two-layer bioinspired thin-walled molds - are designed and fabricated for three-point bending tests and comparisons. The simulation is found to be in good agreement with the experiment in terms of stress-strain curves and crack propagation. Results show the improved load-bearing capacity of the concrete beam reinforced with 3D-printed TPMS-Primitive shells. The peak load of the two-layer TPMS-Primitive reinforced beam is 35% and 125% higher than that of the one-layer reinforced beam and the non-reinforced concrete beam, respectively. Furthermore, the TPMS-Primitive reinforced concrete beams reveal a smooth softening behavior in bending and increase ductility as well. The scalable and sustainable production of such beams for construction applications could be realized by a combination of 3D printing techniques and recycled plastic.