Design of Symmetrical Concrete Arches

The method of analysis here given is believed to be considerably simpler than any accurate method of applyi11g the elastic theory to symmetrical arches heretofore published.

The formulas are derived by actual integration and the results are therefore even more exact than those obtained by the usual method of dividing the arch rib into finite lengths. In order that the integration could be performed, it was necessary to express the arch axis and the thickness of rib mathematically. An equation has been derived which, for different values of the ratio of the loading per unit length of rib at the springing line to that at the crown, gives a curve that has been found to coincide almost exactly with the dead load pressure line for practical bridge arches. Another equation defines very satisfactorily the variation of thickness of the rib from springing line to crown between any desired limits. By substituting these equations in the general elastic equations for symmetrical arches, definite formulas for reactions have been obtained.