<p>Parasitic Bending Moments in Truss Structures with Small Bending Stiffness</p>

Truss structures are commonly idealized as assemblies of axially loaded members connected by perfectly hinged joints. In practice, however, finite joint rigidity, member bending stiffness, and unavoidable eccentricities generate small but systematic (parasitic) bending moments that are not captured by classical truss theory. Although modern finite-element tools can model these effects directly, there remains a need for simple and mechanically transparent methods that clarify their origin, scaling, and limitations of common design approximations. <div> This paper proposes an asymptotic approach for estimating parasitic joint moments in planar trusses with slender members and small bending stiffness. The method shows that the response of a truss with rigid joints can be approximated through the analysis of two simpler auxiliary systems: (i) a purely hinged truss governing the leading-order axial-force distribution and chord rotations, and (ii) a fixed rigid truss subjected to equivalent nodal moments derived from these rotations. A further virtual loading applied to the hinged truss provides consistent first-order corrections to nodal displacements and axial forces. </div> <div> A central result is that parasitic moments are governed by member chord rotations rather than by stiffness-proportional apportioning of nodal moments. Consequently, simplified rules that distribute eccentricity-induced moments in proportion to member bending stiffness, as adopted in some standards, are shown to systematically overestimate bending effects and are not asymptotically consistent with the small-bending-stiffness regime. A numerical example demonstrates that the proposed method accurately reproduces axial forces, bending moments, and deformations of the fully rigid truss while retaining the simplicity and insight of truss-based analyses. </div>