471. Where a great span is required, the suspension bridge possesses
many advantages. It is lighter than a girder bridge of the same span,
and consequently cheaper, while its singular elegance contrasts very
favourably with the appearance of more solid structures. On the other
hand, a suspension bridge is not so well suited for railway traffic as
the lattice girder.
472. The mechanical character of the suspension bridge is simple. If
a rope or a chain be suspended from two points to which its ends are
attached, the chain hangs in a certain curve known to mathematicians
as the _catenary_. The form of the _catenary_ varies with the length
of the rope, but it would not be possible to make the chain lie in a
straight line between the two points of support, for reasons pointed
out in Art. 20. No matter how great be the force applied, it will
still be concave. When the chain is stretched until the depression
in the middle is small compared with the distance between the points
of support, the curve though always a catenary, has a very close
resemblance to the _parabola_.
473. In Fig. 65 a model of a suspension bridge is shown. The two chains
are fixed one on each side at the points E and F; they then pass over
the piers A, D, and bridge a span of nine feet. The vertical line
at the centre B C shows the greatest amount by which the chain has
deflected from the horizontal A D. When the deflection of the middle of
the chain is about one-tenth part of A D, the curve A C D becomes for
all practical purposes a parabola. The roadway is suspended by slender
iron rods from the chains, the lengths of the suspension rods being so
regulated as to make it nearly horizontal.
474. The roadway in the model is laden with 8 stone weights. We have
distributed them in this manner in order to represent the permanent
load which a great suspension bridge has to carry. The series of
weights thus arranged produces substantially the same effect as if
it were actually distributed uniformly along the length. In a real
suspension bridge the weight of the chain itself adds greatly to the
tension.
475. We assume that the chain hangs in the form of a parabola, and that
the load is uniformly ranged along the bridge. The tension upon the
chains is greatest at their highest points, and least at their lowest
points, though the difference is small. The amount of the tension can
be calculated when the load, span, and deflection are known. We cannot
give the steps of the calculation, but we shall enunciate the result.
[Illustration: FIG. 65.]
476. The magnitude of the tension at the lowest point C of each chain
is found by multiplying the total weight (including chains, suspension
rods, and roadway) by the span, and dividing the product by sixteen
times the deflection.
The tension of the chain at the highest point A exceeds that at the
lowest point C, by a weight found by multiplying the total load by the
deflection, and dividing the product by twice the span.
477. The total weight of roadway, chains, and load in the model is
120 lbs.; the deflection is 10", the span 108"; the product of the
weight and span is 12,960; sixteen times the deflection is 160; and,
therefore, the tension at the point C is found, by dividing 12,960 by
160, to be 81 lbs.
To find the tension at the point A, we multiply 120 by 10, and divide
the product by 216; the quotient is nearly 6. This added to 81 lbs.
gives 87 lbs. for the tension on the chain at A.
478. One chain of the model is attached to a spring balance at A; by
reference to the scale we see the tension indicated to be 90 lbs.: a
sufficiently close approximation to the calculated tension of 87 lbs.
479. A large suspension bridge has its chains strained by an enormous
force. It is therefore necessary that the ends of these chains be very
firmly secured. A good attachment is obtained by anchoring the chain to
a large iron anchor imbedded in solid rock.
480. In Art. 45 we have pointed out how the dimensions of the tie rod
could be determined when the tension was known. Similar considerations
will enable us to calculate the size of the chain necessary for a
suspension bridge when we have ascertained the tension to which it will
be subjected.
481. We can easily determine by trial what effect is produced on the
tension of the chain, by placing a weight upon the bridge in addition
to the permanent load. Thus an additional stone weight in the centre
raises the tension of the spring balance to 100 lbs.; of course the
tension in the other chain is the same: and thus we find a weight of
14 lbs. has produced additional tensions of 10 lbs. each in the two
chains. With a weight of 28 lbs. at the centre we find a strain of 110
lbs. on the chain.
482. These additional weights may be regarded as analogous to the
weights of the vehicles which the suspension bridge is required to
carry. In a large suspension bridge the tension produced by the passing
loads is only a small fraction of the permanent load.
LECTURE XV.
_THE MOTION OF A FALLING BODY._
Introduction.—The First Law of Motion.—The Experiment
of Galileo from the Tower of Pisa.—The Space
is proportional to the Square of the Time.—A
Body falls 16' in the First Second.—The Action
of Gravity is independent of the Motion of the
Body.—How the Force of Gravity is defined.—The
Path of a Projectile is a Parabola.