Estimating Stresses and Displacements in Arches
In this chapter we develop analytical estimates of the behavior exhibited by curved, arch-like structures under centrally directed and gravitational line loads. We will see that the behavior ranges from elementary beam bending at one end to a state of pure compression at the other, and that we can track that behavior through an arch rise parameter that is a function of the arch’s semivertex angle, radius, and thickness. Our principal results are useful estimates of the dependence of the major displacements and stress resultants on the arch rise parameter. We will also show that these results are obtained for three different curvature expressions, and we will delineate some differences between curved beam and arch theories. Finally, we will offer some insight into the assumptions underlying the very famous arch designs of the Swiss architect Robert Maillart.