Overview

This chapter delves into the kinematics of beam deformation, addressing such matters as the strain and velocity fields. Recall that a beam is a structure that has one length dimension much greater than the other two. It is helpful to discuss beam deformation in terms of two geometric features of beams: the reference line and the reference cross-sectional planes at each point along the reference line. The reference line runs along the beam and can be defined in various ways, such as the locus of cross-sectional area centroids, mass centroids, shear centers, and so on, or strictly for convenience, such as a line connecting the corners of the cross-sections of a beam with rectangular cross-sections. A reference cross-section consists of the collection of particles lying in a plane perpendicular to the undeformed beam reference line. When a beam deforms, the deformation can be described in terms of the deflection of the reference line and of the motion and deformation of the reference cross-sectional plane. The motion and deformation of the set of particles that make up the cross-sectional plane of the undeformed beam can be thought of as rigid-body translation and rotation of the reference cross-sectional plane of the undeformed beam plus a relatively small elastic deformation superposed thereon. We group the rigid translation and rotation of the cross-sectional frame with the beam global deformation, whereas the deformation of the cross-section is classified as local deformation or, simply, warping. Contrary to the usual way of thinking about beam deformation,...