f beam
or truss design, that is, from the standpoint of stress distribution,
although this "juggling" is limited in practice by economical
considerations.

In a series of beams supported at the ends, bending moments range from
(_w_ _l^{2}_)/8 at the center of each span to zero at the supports, and,
in a series of cantilevers, from zero at the center of the span to (_w_
_l^{2}_)/8 at the supports. Between these two extremes, the designer can
divide, adjust, or juggle them to his heart's content, provided that in
his design he makes the proper provision for the corresponding shifting
of the points of contra-flexure. If that were not the case, how could
ordinary bridge trusses, which have their maximum bending at the center,
compare with those which, like arches, are assumed to have no bending at
that point?

In his tenth point, the author proposes a method of simple designing by
doing away with the complicated formulas which take account of the
actual co-operation of the two materials. He states that an ideal
design can be obtained in the same manner, that is, with the same
formulas, as for ordinary rectangular beams; but, when he does so, he
evidently fails to remember that the neutral axis is not near the center
of a reinforced concrete beam under stress; in fact, with the percentage
of reinforcement ordinarily used in designing--varying between
three-fourths of 1% to 1-1/2%--the neutral axis, when the beam is
loaded, is shifted from 26 to 10% of the beam depth above the center.
Hence, a low percentage of steel reinforcement will produce a great
shifting of the neutral axis, so that a design based on the formulas
advocated by the author would contain either a waste of materials, an
overstress of the concrete, or an understress of the steel; in fact, an
error in the design of from 10 to 26 per cent. Such errors, indeed, are
not to be recommended by good engineers.

The last point which the speaker will discuss is that of the elastic
arch. The theory of the elastic arch is now so well understood, and it
offers such a simple and, it might be said, elegant and self-checking
solution of the arch design, that it has a great many advantages, and
practically none of the disadvantages of other methods.

The author's statement that the segments of an arch could be made up of
loose blocks and afterward cemented together, cannot be endorsed by the
speaker, for, upon such cementing together, a shifting of the lines of
resistanc