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  • Print publication year: 2013
  • Online publication date: May 2013

17 - Beam Theory


Beams and Rotor Blades

An adequate blade structural model is essential for the prediction of rotor loads and stability. Rotor blades almost universally have a high structural fineness ratio and thus are well idealized as beams. The complexities of rotation, and now multiple load paths and composite construction, have required extensive and continuing efforts to develop appropriate beam models for the solution of rotor problems. For exposition of beam theory, particularly relevant to rotor blade analyses, see Hodges (2006) and Bauchau (1985).

A beam is a structure that has small cross-section dimensions relative to an axial line. Based on the slender geometry, beam theory develops a one-dimensional model of the three-dimensional structure. The deflection of the structure is described as functions of the axial coordinate, obtained from ordinary differential equations (in the axial coordinate). The equations depend on cross-section properties, including two-dimensional elastic stiffnesses. The three-dimensional stress field is determined from the deflection variables. Beam theory combines kinematic equations relating strain measures to deflection variables, constitutive equations relating stress resultants to strain measures, and equilibrium equations relating stress resultants to applied loads. When inertial loads are included, the motion is described by partial differential equations, in time and the axial coordinate.

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