going dimensions, when subjected to the strains
above mentioned.

=Braces.= The end braces must evidently support the whole weight of
the bridge and load, which for one end of one truss will be 134400
lbs., and as these braces are in pairs,--67200 lbs. will be the strain
vertically on the stick--but as this stick is a diagonal--whose
vertical is 15 ft., and horizontal 10 ft., we shall have for its
length 18 ft. in round numbers, whence the strain along the diagonal
will be found from the proportion 15 : 18 :: 67200 : 80640 lbs.,
whence we have an area of 80 inches required for compression, or a
stick of 8" x 10". Now, to ascertain if this is stiff enough for
flexure, we will substitute these values in the equation

2240 bd cubed
W = --------, and we have
L squared

[TeX: $W = \frac{2240 \times bd^3}{L^2}$]

2240 x 8 x 1000
W = ---------------, or reducing, W=55308 lbs.
324

[TeX: $W = \frac{2240 \times 8 \times 1000}{324} = 55308$]

Now, these proportions will give ample strength for both flexure and
compression, for if we block the two sticks composing the end brace
together, and firmly connect them by bolts, we shall have a built beam

2240 x 24 x 1000
of 24" x 10"--whence W = ---------------- = 165925 lbs.,
324

[TeX: $W = \frac{2240 \times 24 \times 1000}{324} = 165925$]

and as 134400 lbs. was all that the conditions demand, we really have
an excess of strength. The next set of braces supports the weight of
the rectangle included between the upper ends of the braces and the
two chords, and the dimensions of the sticks are calculated in the
same manner. We find, as we approach the centre of the bridge, that
the strains on the braces become less, and consequently their
scantling should be reduced, but in ordinary practice this is seldom
done.

=Rods.= The next thing is to ascertain the dimensions of the various
tie rods. It is evident that the same weight comes upon the first set
of rods, as on the first set of braces--which will give for the rods
at one end of one truss, 134400 lbs.; and as there are two of these
rods, each will sustain a strain of 67200 lbs.--and, at 15,000 lbs.
per square inch, will have an area of 4.48 sq. inches, and, by Vose's
Tables, must have a diameter of 2-1/2 inches. The sizes of the rods in
each set will decrease towards the centre of the bridge as the weight
becomes less.