Statically Determinate Curved Members

Abstract

Chapter 3 dealt with beams, which are straight members subjected to transverse loading. We showed there that transversely loaded beams respond by bending, i.e., they equilibrate the loading by developing internal shear and moment quantities. When the centroidal axis is curved, the behavior of a curved member subjected to transverse loading can undergo a dramatic change from predominately bending action to predominately axial action depending on how the ends are restrained. This characteristic of curved members makes them more efficient than straight members for spanning moderate to large scale openings. A typical application is an arch structure, which is composed of curved members restrained at their ends.

In this chapter, we first develop the general solution for the internal forces existing in a planar curved member and apply it to members having parabolic and circular shapes. Next, we introduce the method of virtual forces specialized for planar curved members and illustrate its application to compute displacements for various geometries. The last section of the chapter deals with the optimal shape for an arch and the analysis of three-hinged arches, a popular form of arch structure. The material presented here also provides the basis for the analysis of statically indeterminate arches treated in Chap. 9.