TABLE OF CONTENTS Curved beams and shells are often preferable to straight beams and plates, as exemplified by most vegetable, animal and even mineral creations, as well as by a large variety of human architectural and engineering works. Amongst several other reasons convenience, streamlining and aesthetics among them, the basic advantage of curved geometry is to provide the structural elements with a highly improved resistance to external loads for the same quantity of material required. This is because, in a curved structure, most of the transverse load is often balanced by tensile or compressive stresses. This can be conveniently emphasized by considering first simplified arch and shell models where bending and torsion terms are entirely discarded. They extend to the curved geometry, the models used to describe the longitudinal motion of straight beams and the in-plane motion of plates. Though the range of validity of such models is clearly limited to certain load conditions, it is appropriate to present and discuss them in a rather detailed manner, for sake of clarity at least, before embarking on the more elaborate models presented in the next chapter, which account for string or membrane stresses as well as for bending and torsion stresses.
As pointed out in Chapter 3 in connection with beam assemblies, there is a large difference between the flexure and the longitudinal stiffness scale factors of a straight beam element, the ratio being given by:
where ? stands for...
