Civil Engineering Reference
In-Depth Information
so that it passes through the three hinges, Figure 17.2 (d). The thrust at the arch
springings and the compression at any point along the arch may then be calculated by
simple statics. The bending moment at any point of the arch may also be calculated
by taking moments about that point, or by measuring the distance between the line of
thrust and the neutral axis of the arch.
If the arch has less than three hinges, and is consequently indeterminate, the line
of thrust may not be drawn precisely without elastic analysis. Thus, for a fi xed-ended
arch, the line of thrust will not pass through the springings, where there will be a
moment in the arch, Figure 17.2 (e). However, the line of thrust will always be a 'best
fi t' to the shape of the arch neutral axis, and so can be drawn approximately, allowing
an early rough estimation of the bending moments in the arch, and also allowing a fi rst
approximation to the best shape for the arch.
The correct shape for an arch carrying a uniformly distributed vertical load is a
parabola. For an arch of constant thickness carrying only its self weight, the correct
shape is a catenary (which is very close to a parabola). For an arch carrying its self
weight and external loads, the best shape is a compromise between a catenary and the
funicular diagram of the loads.
17.3 Unreinforced concrete and masonry arches
The stability of a masonry arch is given principally by its shape and its thickness. When
the shape of the line of thrust differs from the shape of the arch, the arch ring needs a
fi nite thickness to contain it, Figure 17.3. Where the line of thrust is within the middle
Figure 17.3
Masonry arch with external loads
