Wing Bending Calculations

Nomenclature L y spanwise coordinate q net beam loading S shear M bending moment θ deflection angle (= dw/dx) w deflection κ local beam curvature ′ lift/span distribution ′ S η normalized spanwise coordinate (= 2y/b) c local wing chord wing wing area b wing span λ taper ratio E Young's modulus δ tip deflection N load factor m wing mass/span distribution I bending inertia i spanwise station index n last station index at tip L lift W weight g gravitational acceleration () o quantity at wing root Loading and Deflection Relations The net wing beam load distribution along the span is given by ′ ′ q(y) = L (y) − N g m (y) (1) where m ′ (y) is the local mass/span of the wing, and N is the load factor. In steady level flight we have N = 1. The net loading q(y) produces shear S(y) and bending moment M(y) in the beam structure. This resultant distribution produces a deflection angle θ(y), and deflection w(y) of the beam, as sketched in Figure 1. net loading q(y) = L'(y) − N g m'(y) L'(y) − N g m'(y) aero loading θ y gravity + inertial w loading q S M y y y y y 0 b/2 Figure 1: Aerodynamic and mass loadings, and resulting structural loads and deflection.