s of lead about 1 in. thick extending over the middle third of the
depth of the voussoir joints, the rest of the joints being left open. As
the lead is plastic this construction is virtually an articulation. If the
pressure on the lead is uniformly varying, the centre of pressure must be
within the middle third of the width of the lead; that is, it cannot
deviate from the centre of the voussoir joint by more than one-eighteenth
of its depth. In any case the position of the line of pressures is confined
at the lead articulations within very narrow limits, and ambiguity as to
the stresses is greatly diminished. The restricted area on which the
pressure acts at the lead joints involves greater intensity of stress than
has been usual in arched bridges. In the Wuerttemberg hinged arches a limit
of stress of 110 tons per sq. ft. was allowed, while in the unhinged arches
at Cologne and Coblentz the limit was 50 to 60 tons per sq. ft. (_Annales
des Fonts et Chaussees_, 1891). At Rechtenstein a bridge of two concrete
arches has been constructed, span 751/2 ft., with lead articulations: width
of arch 11 ft.; depth of arch at crown and springing 2.1 and 2.96 ft.
respectively. The stresses were calculated to be 15, 17 and 12 tons per sq.
ft. at crown, joint of rupture, and springing respectively. At Cincinnati a
concrete arch of 70 ft. span has been built, with a rise of 10 ft. The
concrete is reinforced by eleven 9-in. steel-rolled joists, spaced 3 ft.
apart and supported by a cross-channel joist at each springing. The arch is
15 in. thick at the crown and 4 ft. at the abutments. The concrete
consisted of 1 cement, 2 sand and 3 to 4 broken stone. An important series
of experiments on the strength of masonry, brick and concrete structures
will be found in the _Zeitschr. des oesterreichen Ing. und Arch. Vereines_
(1895).

The thermal coefficient of expansion of steel and concrete is nearly the
same, otherwise changes of temperature would cause shearing stress at the
junction of the two materials. If the two materials are disposed
symmetrically, the amount of load carried by each would be in direct
proportion to the coefficient of elasticity and inversely as the moment of
inertia of the cross section. But it is usual in many cases to provide a
sufficient section of steel to carry all the tension. For concrete the
coefficient of elasticity E varies with the amount of stress and diminishes
as the ratio of sand and stone to cement increas