Stiffness

Theory

Stiffness k = F/δ (N/mm), where δ is deflection. It combines material (E) and geometry (second moment of area I, length L): for a cantilever k = 3EI/L³. Unlike E, stiffness is not a material property: it changes when geometry changes. A hollow tube can be stiffer than a solid rod of the same mass because I is larger.

Application

Stiffness, not strength, is often the binding design constraint for precision parts (print beds, robotic arms, precision fixtures). Increasing wall thickness or infill percentage raises stiffness without changing E. Topology optimisation places material where it maximally contributes to I. For FDM, ribs and gussets add stiffness with minimal mass and print time.

Common mistakes

Confusing material stiffness (E, a material property) with structural stiffness (k, a structure property) leads to errors. A stiff part is not necessarily a strong one: high-carbon glass fibre composites are stiff but brittle. Overly stiff parts in assemblies with thermal expansion mismatches generate large internal stresses.

Related terms: Young's Modulus, Elasticity, Bending Moment