therefore, when W is 112 lbs., we calculate that the force on A B is
124 lbs., and on C B 168 lbs. A B would require about 300 lbs. to
crush it, and C B about 2,000 lbs. to tear it asunder, consequently
the tie and strut can support 1 cwt. with ease. If, however, W were
increased to about 270 lbs., the force on A B would become too great,
and fracture would arise from the collapse of this strut.
421. When a structure is loaded up to the breaking point of one part,
it is proper for economy that all the other parts should be so designed
that they shall be as near as possible to their breaking points. In
fact, since nothing is stronger than its weakest part, any additional
strength which the remaining parts may possess adds no strength to the
whole, and is only so much material wasted. Hence our structure would
be just as strong, and would be more properly designed if the section
of B C were reduced to one-fifth, for the tie would then break when the
tension upon it amounted to 400 lbs. When W is 270 lbs. the compression
on A B is 300 lbs., and the tension on B C is 405 lbs., so that both
tie and strut attain their breaking loads together. The principle of
duly apportioning the strength of each piece to the load it has to
carry, involves the essence of sound engineering. In that greatest of
mechanical feats, the construction of a mighty railway bridge across a
wide span, attention to this principle is of vital importance. Such a
bridge has to bear the occasional load of a passing train, but it has
always to support the far greater load of the bridge materials. There
is thus every inducement to make the weight of each part of the bridge
as light as may be consistent with safety.