# Calculation of Arches for the Road and Rail Traffic Act

*Athough the Road and Rail Traffic Act is not a recognised scheme for the relief of unemployment it will certainly have a far reaching effect in this direction. In accordance with the Act, thousands of bridges are to be measured and their carrying capacity calculated. The results obtained will probably entail the reconstruction of a considerable proportion. Included in these bridges are large numbers of masonry arches, many of which were built about a century ago during the development of our roads and canal systems. Owing to the urgency of the work and the large quantity, simple calculations are essential even at the expense of accuracy, providing the error is small. No difficulty will be experienced in finding the axle and vehicle loads for ordinary girder bridges, but with arches it is difficult to get a simple and quick method without making more assumptions besides those used in the mathematical analysis.
These new assumptions will unfortunately have to be based on engineering sense which is always open to argument. The majority of these arches will conform to the segmental or parabolic type and be built of common brick in various thicknesses in lime mortar with an average span of about 15 ft. for those spanning canals. One thing to be remembered is that these arches were built with the idea that the line of thrust would come within the middle third, i.e. there is no tension and in the present calculations this has been considered. It will be soon found that no rule of thumb method or emperical formula can be used to give reasonable results, and that either the elastic theory or the theory of least work will have to be used. The first method is considered the simplest, and can be found in most text books, also an example of a segmental arch is worked out by Mr. A.A. Fordham in a paper on Masonry and Concrete Arches read before the Institution of Structural Engineers on the 25th April, 1929. Most work arises in finding the horizontal thrust and the reactions and it is necessary to make our first assumption, i.e., in finding the horizontal thrust (H) and the reactions (RL and RR) the arch may be considered a parabola using the elastic theory. (See diagram below.)
P.H. Johnson*

Author(s): Johnson, P H

Keywords: arch bridges;masonry;appraising;approximate methods;worked examples