TABLE OF CONTENTS In a straight beam having either a constant cross section or a cross section which changes gradually along the length of the beam, the neutral surface is defined as the longitudinal surface of zero fiber stress when the member is subjected to pure bending. It contains the neutral axis of every section, and these neutral axes pass through the centroids of the respective sections. In this section on bending in the plane of the curve, the use of the many formulas is restricted to those members for which that axis passing through the centroid of a given section and directed normal to the plane of bending of the member is a principal axis. The one exception to this requirement is for a condition equivalent to the beam being constrained to remain in its original plane of curvature such as by frictionless external guides.
To determine the stresses and deformations in curved beams satisfying the restrictions given above, one first identifies several cross sections and then locates the centroids of each. From these centroidal locations the curved centroidal surface can be defined. For bending in the plane of the curve there will be at each section (1) a force N normal to the cross section and taken to act through the centroid, (2) a shear force V parallel to the cross section in a radial direction, and (3) a bending couple M in the plane of the curve. In addition...
