suspend the
points B and D from them, and start the braces B b and D b--and, if
the truss were longer, would continue on in the same manner as far as
needful. To prevent the. truss from altering its form, as shown by the
dotted lines A' b C', and A E C, by any passing load, we insert the
counter braces marked R.

The braces A a and C c, must support all of the weight of the bridge
and its load within the parallelogram B a c D--and the next set of
braces, B b and D b, sustain that part of the load which comes over
the centre of the bridge. Consequently the braces must increase in
size from the centre towards the abutments. The rods resist the same
pressure in amount as their braces--but being vertical, do not need
the increase, given to the braces on account of their inclination--but
increase simply with the strain upon them, from the centre to the ends
of the truss.

There are many forms of small bridges differing from those enumerated,
in various minor details, but sufficient has been said to give the
reader a fair idea of the strains upon the different parts, and how to
arrange and proportion the materials to resist them.

PRACTICAL RULES AND EXAMPLES IN WOODEN BRIDGE BUILDING.

In any case that may arise, we must determine approximately the gross
weight of the bridge and its load--as a basis, and then we can proceed
as follows--in case of a Howe, Pratt, or Arch Brace Truss.

=To find the dimensions of the Lower Chord.=

The tension at the centre of the Lower Chord is found by _dividing the_
_product of the weight of the whole bridge and load by the span_, by
sight times the height--or letting T=tension in lbs., W=weight of
bridge and load in lbs., S=span in feet, and h=rise or height--we have

W x S
T = ----- --.
8 h

[TeX: $T = \frac{W \times S}{8 h}$]

In this case we have taken the rise at 1/8 of the span, which is
evidently the best ratio between those dimensions, as it equalizes
the vertical and horizontal forces. As to the proportions of the
_bays_ or _panels_, (or that portion of the truss bounded by two
adjacent verticals, as struts or ties, and the chords,) the ratio of
the rise (or the vertical distance between the centre lines of the two
chords,) and the length on the chord should be such, that the diagonal
truss members may make an angle of about 50 deg. with the chords; as the
size of the timbers is increased by decreasing the angle, and, if the
angle is increased,