e also
provides strength to resist a pressure of 50 lb per sq. ft. on twice the
vertical projection of one truss, no train being supposed to be on the
bridge.

19. _Stresses Permitted._--For a long time engineers held the convenient
opinion that, if the total dead and live load stress on any section of a
structure (of iron) did not exceed 5 tons per sq. in., ample safety was
secured. It is no longer possible to design by so simple a rule. In an
interesting address to the British Association in 1885, Sir B. Baker
described the condition of opinion as to the safe limits of stress as
chaotic. "The old foundations," he said, "are shaken, and engineers have
not come to an agreement respecting the rebuilding of the structure. The
variance in the strength of existing bridges is such as to be apparent to
the educated eye without any calculation. In the present day engineers are
in accord as to the principles of estimating the magnitude of the stresses
on the members of a structure, but not so in proportioning the members to
resist those stresses. The practical result is that a bridge which would be
passed by the English Board of Trade would require to be strengthened 5% in
some parts and 60% in others, before it would be accepted by the German
government, or by any of the leading railway companies in America." Sir B.
Baker then described the results of experiments on repetition of stress,
and added that "hundreds of existing bridges which carry twenty trains a
day with perfect safety would break down quickly under twenty trains an
hour. This fact was forced on my attention nearly twenty-five years ago by
the fracture of a number of girders of ordinary strength under a
five-minutes' train service."

Practical experience taught engineers that though 5 tons per sq. in. for
iron, or 61/2 tons per sq. in. for steel, was safe or more than safe for long
bridges with large ratio of dead to live load, it was not safe for short
ones in which the stresses are mainly due to live load, the weight of the
bridge being small. The experiments of A. Woehler, repeated by Johann
Bauschinger, Sir B. Baker and others, show that the breaking stress of a
bar is not a fixed quantity, but depends on the range of variation of
stress to which it is subjected, if that variation is repeated a very large
number of times. Let K be the breaking strength of a bar per unit of
section, when it is loaded once gradually to breaking. This may be termed
the statical