290.)

The largest masonry arch is the Adolphe bridge in Luxemburg, erected in
1900-1903. This has a span of 278 ft., 138 ft. rise above the river, and
102 ft. from foundation to crown. The thickness of the arch is 4 ft. 8 in.
at the crown and 7 ft. 2 in. where it joins the spandrel masonry. The
roadway is 52 ft. 6 in. wide. The bridge is not continuous in width, there
are arch rings on each face, each 16.4 ft. wide with a space between of
19.7 ft. This space is filled with a flooring of reinforced concrete,
resting on the two arches, and carrying the central roadway. By the method
adopted the total masonry has been reduced one-third. One centering was
used for the two arch rings, supported on dwarf walls which formed a
slipway, along which it was moved after the first was built.

[Illustration: FIG. 9.--Half Elevation and Half Section of Arch of London
Bridge.]

Till near the end of the 19th century bridges of masonry or brickwork were
so constructed that they had to be treated as rigid blockwork structures.
The stability of such structures depends on the position of the line of
pressure relatively to the intrados and extrados of the arch ring.
Generally, so far as could be ascertained, the line of pressure lies within
the middle half of the depth of the voussoirs. In finding the abutment
reactions some principle such as the principle of least action must be
used, and some assumptions of doubtful validity made. But if hinges are
introduced at crown and springings, the calculation of the stresses in the
arch ring becomes simple, as the line of pressures must pass through the
hinges. Such hinges have been used not only for metal arches, but in a
modified form for masonry and concrete arches. Three cases therefore arise:
(a) The arch is rigid at crown and springings; (b) the arch is two-hinged
(hinges at springings); (c) the arch is three-hinged (hinges at crown and
springings). For an elementary account of the theory of arches, hinged or
not, reference may be made to a paper by H. M. Martin (_Proc. Inst. C. E._
vol. xciii. p. 462); and for that of the elastic arch, to a paper by
A.E.Young (_Proc. Inst. C.E._ vol. cxxxi. p. 323).

In Germany and America two- and three-hinged arches of masonry and concrete
have been built, up to 150 ft. span, with much economy, and the
calculations being simple, an engineer can venture to work closely to the
dimensions required by theory. For hinges, Leibbrand, of Stuttgart, uses
sheet