Stresses in Inclined Arches of Multiple-Arch Dams

The paper here presented contains the derivation of analytical formulas for moments, thrusts, and shears in the inclined circular arches of multiple-arch dams. All the equations were derived by integration through application of the theorem of Castigliano, and they include the internal elastic work due to shear. As they are all necessarily long and cumber some, coefficients for obtaining moments, thrusts, and shears were computed, and curves representing these coefficients are presented for the convenience of the designing engineer. The water load on the arch may be divided into two parts, the first being the uniform water load due to the head measured from the free water surface to the arch crown, and the second, the variable water load which results from the inclination of the arch. In addition to the water load, the dead weight of the arch and the temperature stresses must be considered, and the moments, thrusts, and shears of all these influences must be combined algebraically to determine maximum stresses.