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A WORK
ON


BRIDGE


BUILDING:


CONSISTING OF
TWO ESSAYS,
THE ONE ELEMENTARY AND GENERAL, THE OTHER
GIVING


AND
Practical Details
FOR


IRON AND WOODEN BRIDGES.
BY S. WHIPPLE, C. E,
UTICA, N. Y.
H. II. CURTISS, PRINTER, DEVEREUX BLOCK.
1847.




Entered according to the Act of Congress, in the year 1847, by
S. WHIPPLE,
In the Clerk's Office of the District Court of the United States, for the
Northern District of New York.




PREFACE.
THE first part of this work was published in the beginning of the present
year, having been written about a year before. At the time of that publication, the preparation of the subsequent portion of the work, had not
been commenced, nor had its preparation and publication been fully determined on, though an intimation of such a purpose, was therein expressed.
Some fifty or sixty copies of the first Essay were circulated among
friends, and persons who, it was thought, would feel an interest in the subject, for tbe purpose of calling attention to a matter on which I had bestowed a considerable amount of study and investigation, and on whieh I
believed myself in possession of some valuable information.
The encouraging reception which that Essay met with from a number
of engineers and others of high standing, whose opinions on the subject
were worthy of the first consideration, determined me to suspend the distribution of more copies, until I could prepare and publish an additional
part, or Essay, going more into practical detail than had been previously
done, which it was thought, would add greatly to the utility and value
of the work, and render it, in some measure, worthy of the attention of
those interested in the subject treated of.
Under these circumstances, the work does not show that unity of design, and uniformity of plan, which would be expected in a work prepared
and published all at the same time. But, though this may detract a little
from the external appearance of the book, it is believed not to impair its
convenience or utility.
It will be seen that the first part is illustrated by wood-cuts, distributed
through the body of the work, as nearly as might be to where the figures
are respectively described and referred to. It was found not so convenient
to carry out the same plan in the second Essay, and therefore, I have obtained lithographic figures to illustrate that part, which are annexed to the
end of the work. The figures to the last part are distinguished by numbers continued on from those in the first part; and when reference is made
in the last part, to figures in the first, the pages are usually given where
such figures will be found.
The numbers of the articles or sections, also, run from the first part to
the second, in the same system. By the way, the numbers to articles X.




iv.


and XI., are omitted in the print. The former should be on page 9, before
the word " Again," about two-thirds down the page: the latter, before
the word " Discarding," at the second paragraph of page 11. No. XXVII.
is also omitted at the beginning of page 32, and XXVIII. at the first
paragraph from the top, page 33.
Several other trifling typographical errors found way into the first Essay,
none of which, however have been observed, worthy of notice, except, that
ad
in some of the copies, at the end of the 7th line, 9th page, b-1d- occcurs
ad
where it should be -bdw, while in most of the copies, only the accent to
the b is wanting. Also, in the 6th line from the bottom of page 45, the
word pieces should be prices. I may as well in this place, refer to a few
errors that occur in the second Essay, which, as well as the preceding, it
will be well to turn to and correct with a pencil before reading the work.
First, the word and, at the beginning of the 9th line, 58th page, should be
transposed between the figure 10, and the word cylinders, in the same
line. Second, the letter c, (referred to in the 13th line from the bottom of
page 67,) should be on the cross bar nearest to a and b, Fig. 13, P1. I.
Third, in the 7th line of page 77, cb and cd should be ab and cd. The
other errors that have been noticed, are merely mistakes of a letter or
two, which the reader will readily correct as they meet his eye. Further
remarks or explanations are not deemed necessary in this place.
In offering this little work to the Engineering profession, I would not be
suspected of presuming that the subject has been exhausted, or that a want
which has been long and deeply felt in this branch of the profession, is
fully satisfied. I may, however, be allowed to hope, that my labors in the
field will have been the means of effecting one step of advancement towards the attainment of so important a desideratum.




AN
ESSAY
ON
BRIDGE BUILDING:
CONTAINING
ANALYSES AND COMPARISONS
OF TIHE
PRINCIPAL PLANS IN USE,
WITH
INVESTIGATIONS AS TO THE
BEST PLANS AND PROPORTIONS
AND THE
RELATIVE MERITS OF
WOOD AND IRON,
FOR BRIDGES.
BY S. WHIPPLE, C. E.
MATHEMATICAL AND PHILOSOPHICAL INSTRUMENT MAKER.
UTICA, N. Y.
H. H. CURTISS, PRINTER, DEVEREUX BLOCK.
1847.




Entered atccording to Act of Coogres, In Ih er14,b
irn the Clerk's Office ofI the Northiern DisQtrict of New -York.




AN ESSAY


ON
BRIDGE            BUILDING.
I. A Bridge is a structure for sustaining the weights of
carriages and animals in their transit over a stream, gulf,
or valley.
Bridges are built of various plans and dimensions, according to the circumstances and objects of their erection.
My present purpose is, after a few remarks upon the general nature and principles of Bridges, to attempt some
analyses and comparisons of the respective qualities and
merits of various general plans, with a view of deducing
practical results as to a judicious and economical choice
and application of materials in the construction of those
important erections.
II. The force of gravity, on which the weight of bodies
depends, acts in vertical lines, and consequently, a body
can only be prevented friom falling to the earth by a force
equal and opposite to that with which gravity acts on the
body.  This resisting force must not only act vertically
upward, but the line of its action must pass through the
centre of gravity of the body it sustains.  All the forces
in the world, acting parallel witli, or perpendicular to, the
vertical passing through its centre of gravity, could not
prevent an ounce ball, (concentrated to the point of its
centre of gravity,) from falling to the centre of the earth,
unless it were a horizontal force capable of giving the ball
a projection, such that the centrifugal tendency should
equal or exceed gravity: a kind of force which could
never be made available towards preventing people from
falling into the water in crossing rivers, consequently of
no use in bridge building.




4


In fact, nothing but a continuous series of unyielding
material particles, extending from an elevated body downward to the surface of the earth, can hold or sustain that
body above the earth, by vertical and horizontal action
alone, either separately or in combination.
III. Suppose a body, no matter how great or small,
placed above the earth, with an unfathomable abyss, or
an inaccessible space beneath it.  Attach as many cords
to it as you please, strain them much or little, (only horizontally,) the body will fall nevertheless.  Thrust any
number of rods, with whatever force you may, horizontally against it, still the body will fall. Moreover, the
space beneath being inaccessible, there is no foundation
or foothold on which to rest a post or stud, that may directly resist the action of gravity, and the lines of all other
vertical forces or resistances pass by the body without affecting it. In the situation here supposed, the body can
only be prevented from falling by oblique forces, that is,
by forces whose lines of action are neither exactly horizontal, nor exactly vertical.
Attach two cords to the body, draw upon them obliquely upward and outward, in opposite directions, or from
opposite sides of the abyss, with a certain stress, and the
body will be sustained in its position. Apply two rods
to it obliquely upward, of a proper degree of stiflfess, in
the same verticle plane, on opposite sides of the perpendicular, a certain thrust exerted on those rods will prevent
the descent of the body.
IV. Here, then, we have the elementary idea, the grand
fundamental principal in bridge-building.  Whatever
form of structure be adopted, the elementary object to
be accomplished is, to sustain a given weight in a given
position, by a system of oblique forces whose resultant
shall pass through the centre of gravity of the body, in a
vertically upward direction, in circumstances where the
weight cannot be conveniently met by a simple force in
the same line with, and opposite to, that of gravity.




5


To dwell a little on this elementary idea, let us suppose 6.b' [Fig. 1,] to represent the banks of a river, or
the abutments of a bridge, p                  -
and gg' the line of transit.
for carriages, &c.; and sup-     '.."
pose a load of a certain
weight w, to have arrived
at a pointcentrally between
b.b'. The simplest method             i
of sustaining the weight is, perhaps, either to erect two
oblique braces, bw b'w, or suspend two oblique chains,
pw.p'w from fixed supporting points at b.b' or p.p'.
It is not necessary that the weight be exactly at the
angular point w, of the braces or chains, but it may be
sustained by simple suspension at w' below, or simple
support at w", and such obliquity may be given to the
chains or braces, as may be most economical, a consideration which will be taken into account hereafter.
V. Thus we see how a weight may be sustained centrally between the banks of a river, or the extremities of
a bridge. But the structure must not only provide for
the support of the weight at this point, but also at every
other point between b.b' or g.g', and it is obvious that the
same plan and arrangement will apply at any other point
as at the centre, with only the variation of making the
braces or chains of unequal lengths.
This, however, would require as many pairs of braces
or chains as there were points between g.g', a thing, of
course, impracticable. We therefore resort to the lateral
strength and stiffness of beams-phonomena with which
all have some acquaintance, and without digressing in this
place to investigate their principles and causes, I will
merely assume, as a fact sustained by all experience, that
for sustaining weights between two supporting points,
upon nearly the same level, a simple beam affords the
most economical means, until those points exceed a cer2A




tain distance assunder, which distance will vary with circumstances, but in bridge-building will seldom be less
than 10 to 14 feet, where timber beams are employed.
Hence, for bridges of a length of 12 or 14 feet, usually,
nothing better can be employed than a structure supported
by longitudinal beams, with their ends resting on abutments or supports upon the sides of the stream. Of
course, I shall not be understood here, as having any regard to stone or brick arches. For though these are
advantageously used for short spans, and in deep valleys,
where the expense of constructing high abutments for
supporting a lighter superstructure would exceed or approximate to that of constructing the arch, it is my purpose to speak only of those lighter structures, composed
mostly of wood and iron, and supported by abutments
and piers of stone, or by piles, or frames of wood.
Having then, adopted the use of beams for supporting
short distances, it is only necessary on longer stretches, to
provide support for a point once in 10 or 14 feet, by
braces, &c. from the extremities, and for the intermediate points, depend on beams or joists extending from one
to another of the principal points provided for as above.
VI. For a span of 20 or 30 feet, it would seem that
no better plan could be devised, than to support a transverse beam midway between abutments, by two pairs of
braces or suspension chains, one pair on each side of the
road-way; this transverse beam affording support for
longitudinal beams extending therefrom to the abutments.
When suspension chains are used, it is usually called a
suspension bridge. If braces be employed it is termed a
trussed bridge.
VII. Before advancing further, it will be proper to
refer to a fact which has not yet been taken into account,
though one of the utmost importance.
The sustaining of a weight by oblique forces, gives
rise to horizontal forces for which it is necessary to provide counteraction and support, as well as for the weight




7


of the structure and its load. The braces aw and bw, in
supporting the weight w,
[Fig. 2,] act in the directions of their lengths with a
certain force, which bears
the same relation to 4 w as
wa or wb bears to we, and &        C          6
their action at each of the points a and b, is the same as
would be that of a perpendicular force equal to 4 w, and a
ac
horizontal force outward equal to _-w. Therefore the
we
abutments must be calculated to withstand this horizontal
force, or some sort of connection or ligature must be
provided between a and b, capable of withstanding it, in
which case the action upon each abutment is simply a
vertical pressure equal to wu, omitting the weight of the
structure.
This horizontal action is called the horizontal thrust,
and if the abutments be relied on to sustain it, they will
require to be better and more strongly built than when
they only sustain the weight.
This thrust always has place when a weight is sustained
by any means except by a continuous series of solid bodies extending from it directly downward to the earth.
Hence the necessity, in all cases of indirect sustension of
weights, of having, at least, 2 pieces or parts, either inclining in opposite directions, or having unequal inclinations,
that their horizontal actions may neutralize one another;
otherwise the body would move in the direction of the
greater horizontal thrust.
The horizontal thrust has place even in the case of a
simple beam, being exerted by the upper part, and counteracted by the lower.
In the case of suspension bridges, the horizontal action of the chains is inward, and a counteracting outward
thrust is exerted by that portion of the earth between the
points of attachment; or it may be metand opposed by a rigid
body extending from one point of suspension to the other.




8


Whether the horizontal thrust may be more economically sustained by the abutments or otherwise, will depend
ort circumstances, and can more easily be determined in a
subsequent part of the investigation.
VIII. In structures exceeding about 25 feet, or probably 30 feet at most, the length of joist from the centre to
the ends, would require so great a size to give them the
requisite stiffness, that their weight and cost would be
quite objectionable. It becomes expedient, then, in such
cases, to provide support for more than one principal
point, or transverse bearer. A superstructure of from 30
to 40 feet, may be constructed with two cross bearers,
sustained by two trusses, with two pairs of braces each,
as may be seen in Fig. 3, and it will probably be best, in
such short spans, at
least, to provide con-  3..
necting ties between
the feet a.a', of the
braces.  The cross
bearers maybe at b.b'       C       d         a'
or suspended below at c.d. The thrust upon each brace,
will be as the length of the brace divided by the perpendicular Ic or b'd, and the stress upon the tie aa', inversely
as be. Hence the propriety of giving the trusses a considerable elevation.  Unless connected over the top,
however, they become top-heavy, if carried too high, and
are with difficulty sustained in an erect position. They
should, therefore, usually be connected across the top, and
secured by lateral bracing when designed for heavy loads.
IX. The above is the simplest form for a truss to sustain two cross bearers. It is not, however, the most economical. A better, as well as a more common form
of a truss for two bearers is that shewn in Fig. 4.
To compare this form with that in Fig. 3, suppose a
weight, w, placed at each of the points b.b'. In virtue of
those two weights, there will be a vertical pressure equal
to w, exerted at a, through the medium of the brace




9


ba, and a horizontal
thrust equal to, '-   "
and the same at a'.
Similar weights at
bb', in Fig. 3, would       C                 C t
produce the same
ac    ad
vertical pressure, but the thrust would equal --w+A-- wu
be     b(
But ad-2ac and b'd=bc. Hence, by substitution, we
have the horizontal thrust equal to A-w, which is onethird greater than in case of the truss shown in Fig. 4,
having the same general dimensions.
Hence truss [Fig. 3,] requires one third more material
in the tic aa', or one-third more power of abutments to
sustain thrust, than truss [Fig. 4,] and a similar excess
of material in braces; and as an offset, truss 4 requires
the additional braces bd, b'c, possessing about one-third
the strength of the main braces ab,a'b'. This still leaves
the balance in favor of truss 4, aside from the saving of
horizontal thrust. Hence truss 4 is decidedly preferable,
except where the abutments sustain the thrust. For it
will readily be seen that the horizontal thrust of the
braces bd, b'c, in truss 4, cannot act directly on the abutment, whereas the whole thrust of all the braces in truss
3, may be directly sustained by the abutments.
Again, let us suppose two trusses, 5 and 6, of the same
length and height, with four bearing points at equal distances, and loaded at each of these points with a certain
weight w.
In truss 5, let aw, ww. &c. be sub-chords of an arch of
which aa' is the primary chord, and let aa'=5, and consequently ab, be, &c. each=.  Also let the vertical
wb= z, and the vertical wc=h. Now the points a. w. w.
&c. a' are very nearly in a circular arch, and nearly in
equilibrio under the pressure of the weights w.w. &c.The horizontal thrust produced by the weights on this
ab  2w  3w
truss is 2w"-  --
^1  jh   /




10


In truss 6, let each of the weights w.w, &c. be sustained
by an independent pair of braces wa, wa', of the same
VI.  L
height=l. Then each pair of braces will exert a certain
horizontal thrust which will be the same in both directions, and the sum of which, will shew the whole thrust
produced by all the weights, and will be equal to
4 -, 32w?  2 3w  1 4U, 4w
+       --  - -   + - -----w which is - greater than in the
5h   5 k   5    5k A
case of truss 5.
Hence the truss 6 would require more material in about
the same ratio to support the weight with the same proportionate stress, besides that the long braces in truss G
would be unable to bear the same stress in proportion to
their cross section, as the shorter pieces aw, ww, &c., in
truss 5.
But the truss 6 has the advantage of being able to sustain itself when part of the weights are removed, as each
one is sustained independently of the rest; whereas truss
6 would be thrown out of its equilibrium in such a case,
and could not stand without additional support. This
may be afforded by diagonal braces, or ties between each
two of the points w.w, &c., as shewn by the dotted lines,
which will require about one-third as much material as is
required to sustain the horizontal thrust independently of
abutments, or one-th'rd as much as the arch a, w.w, &c.
contains, as will appear further on.




11


Hence, the result of this comparison is analogots
throughout, to that obtained from the comparison of
trusses 3 and 4. And when we take into the account the
disadvantage at which the long braces in truss 6 must act,
and the general practical conveniences of the two plans,
it is probably risking little to assume, as a settled fact,
that the truss containing the arch, and diagonals between
the main points of support, is decidedly preferable to that
in which each cross bearer is sustained by an independent pair of braces.
Discarding, then, the plan of independent bracing, as in
trusses 3 and 5, as inferior to others, I will proceed to a
comparison of the arched truss with another form of
trussing, by a sort of cancel-work, in which each oblique
piece extends from one bearing point to another, between
two parallel horizontal ribs or stringers, bounding the
truss at top and bottom.
Fig. 7 exhibits a canceled truss. In order to analyze and
determine the merits of this kind of truss, I will first consider it to be loaded at each of the bearing points o, n, m,
6, k, i, with a certain weight w. Now, supposiig the
diagonals, except ao and hi, to act by tension, and the
verticals by thrust, it is obvious that the parts in the upper rib between o and i, will act by thrust, and the parts
between a and h, by tension; also, that the diagonals ao
and hi will act by thrust, and of the others, the dotted
ones only, act in this condition of the load, while the
rest are relaxed and useless. In order, then, to ascertain
the stress upon each part, I say firstly, at the point a, we
have an equilibrium between three forces, viz: the thrust
of ao, the tension of ab, and the resistance of the abutment, or support on which the point a rests, which last is
equal to 3w, (not regarding the weight of the truss;) consequently, supposing ab, be, &c., to be each equal to bo,
the tension on ab is manifestly also equal to 3w, and the
thrust on ao is equal to 3w v'2.
Again, at o, we have an equilibrium of four forces, ex



12


erted in the directions of the lines ao, on, ob and oc, of
which ao has just been found equal to 3w V2, and ob is
equal to w, being simply the weight resting at the point
o. Then, extending ao and taking op=ao to represent
' a n'Yr.     m            li p
a      &      c             e      J,/     A
3w V/2, letting fall the perpendicular pq=oob, we have oq,
representing the resultant of ao and ob, which reduces the
forces to 3. Then drawing qr parallel with oc, gr obviously represents the tension of oc, which is equal to 2w V 2,,and or represents the thrust of on, which is equal to 5w.
The tension of bc is 3w, the same as that of ab, since the
parts ob and bn have no action.
Nextly, at the point c, the tension of oc has a horizontal action equal to 2w, which added to the tension of
bc (=3w) gives 5w as the tension of cd. The tension of
or has also an upward action equal 2w, counteracted by
the thrust of cn, which, of course, is also equal to 2w.
One half of this thrust of cn, is counteracted by the
weight w at n, and the other half by the oblique action of
nd, which, of consequence, is equal to w V 2, and exerts a
horizontal force equal to w upon the part nm. But nm is
also acted on in the same direction by the thrust of on, before shewn to be equal to Sw) consequently the thrust of
nm is equal to 6w.
At d, the horizontal action of nd, (=w) in addition to the
tension of cd, (=5w) gives 6w as the tension of dc. The
upward action of nd (=w) just sustains the weight w at m,
through the medium of dm, and the thrust of nm (=6w)
is counteracted by the thrust of ml, which, of course,
must also be equal to 6w.




13


The stress on the remaining parts is the same as on
those analogously situated on the opposite side of the
centre, which we have just determined.
Now, by going through with similar analyses, with the
weights successively removed, beginning at o, and then
by removing from both ends at once, &c., it will be seen
that the maximum stress falls on the horizontal parts, and
upon ao and hi, when the truss is loaded throughout.
That with the weight at o removed, we have the maximum
stress on oc,-=- 5-w L2, and on nc, A-'-w. With the weights
7
removed from o and n, we have the maximum stress on nd,
which is --wJ/2, and on dim, which is --w.
7                        1
The maxmium on me (=fw /2) occurs when the weights
are removed from o.n and m. On /f (=-w,2,) when
o.n.m. and I are unloaded, on k.g, (=-w-/2,) and on
i.g, (=--w) when the point i alone is loaded.
The maximum stress on each part, then, may be arranged
in tabular form, thus:
Acting by Thrust.       Acting by Tension.
Parts.         Mfax. Thrust.  Parts.   Max. Tension.
ao and iki.............3w / 2  ac andfh.............. 3w
on and ki.................5w  cd and ef................5w
nm, ml, and  lk.......... 6w  de................... w
ob and  ig..............  oc and if........... y-w- /2
nc and kf............ 5 w nd and ek.....-.... w V 2
md and el..............o w me and Id............4w/2
If and me............   /2,nb and Ikg.......... wxV 2
Now, multiplying the length of each of these parts by
the maximum stress under all the conditions of the load, it
will give us the means of making a near comparison of
the amount of material required on this plan, with that
required in another plan in which the pieces are similar
in general dimensions, and exposed to like forces as in
this plan.
To simplify the calculation, let ab=ob, and represent
B




14


the unit of length, which will give the length of the
diagonals each= v'2.
Our products then, will be,For parts exposed to a Crushing Force.  For parts exposed to Tension.
ao andih........... 12 w  Parts between a & i...28w
Parts between o &i..28 w  Diagonals............ 20w
Verticals............ 7.42w
Total,... ---........ 48.w
Total,......... 47.42w
XII. There is another modification ofthe cancelled truss,
which dispenses with the vertical pieces, except, perhaps
at the ends, or at the first bearing points from the ends,
and I proceed to give an analysis of the action of its
various parts.
a      6      c      d      e     /       7     A
In Fig. A., let the parts be so arranged and connected,
that the lower stringer ah and the verticals ob and ig,
may act by tension only, ao and ih by thrust only, and the
remaining diagonals by either thrust or tension.
A weight w at o will exert a thrust on ao equal to,w-/2, & on oc, me, kg, & i.h, each, equal to -wV2, and
a tension upon cm and ek equal to -wV/2: also a tension
equal to 1w on ig.
A similar weight at n will exert a thrust=- wV 2 on
nb and oa, and on nd, If, and ih, a thrust=-2wv/2; a tension equal to 4w on ob, and a tension=2=wv/ 2 on dl,
and ft.
A weight w placed at m, will exert a thrust =--wV2 on
mc and oa, and a thrust=,-wV/2 on me, kg, and ih; a
tension=,wV'2 on oc, a tension-=-wV/2 on ek, and one
equal to jw on ig.
The effects of a weight w at 1, will be, a thrust-=-wV2




15


on Id, nb, and oa, and one equal to 4wV 2 on if and ik, a
tension =4w3/2 on dn, one equal to -w on bo, and one
equal to w,/2 on fi.
A weight w at k, will produce a thrust=-w1\/2 on
ke, mc, and oa, and one equal to kw/2 on kg and ih; a
tension =2w/2 on em and co, and one equal to -w on ig.
A weight w at i, will exert a thrust=-4wV2 on ih, one
equal to -w\/2 on if, Id, nb, and oa; a tension=-w/2
onfl and dn, and one equal to -w on bo.
Then, collecting all those partial effects upon the
various parts together in tabular form, representing thrust
by the sign - and tension by +, they will stand in order,
thus:
For oa & ih each (-!- -4---4)w v2C=- 2'w-/2=-3w/2
ob & ig....(5+3      )w      w +1.286w
nb & kg... (-5-3-1 )-wV/2=-       w  2.=-1.286w  2
"/7          19,
mc & If +4w, 2-(4+2)-V 2=      +,142w? 2--,857w/ 2
id & me +wJ2--(3+1)4w     2=- +.286wV'2-,571wV2
ke &nd +(1-3)wV 2-w/12= +,571wv/2-,286wV/2
if&oc +(2+4)w*l1--w\/2=        +,857wv/2-,142?w/2
The quantities with the sign 4 prefixed shew the
maximum tension, a'd those with the sign-the maximum
thrust or crushing force to which these parts respectively
can be exposed, and the differences, the effects produced
by the whole uniform load.
For the action of the horizontal parts, it is manifest
that the tension of ab is equal to horizontal part of the
thrust of oa, that is, equal to 3w. On b.c it is equal to the
same, + the horizontal action of nb, that is,=3w+ 1.286w
=4.286w.
cd sustains this same force, + the horizontal part of
the action of oc and cm under the uniform load, that is,
==(4.286 +,715+,715) w=5.716w.
de sustains the tension of cd+the horizontal action of
nd and dl under the uniform load,= (5.716+571) w=
6.287w.
ef fg, gh, sustain the same forces as cd, be, ab, as just
determined.




16


In a similar manner we determine the thrust of the
parts between o and i to be, for on and ki equal to 3w+,
714w=3.714w; for nm and bk, equal to 5,28w, and for
rmb, equal to 6.28w.
Now, multiplying the lengths of the different parts by the
maximum stress upon each, we have, for parts exposed to
Thrust,                  Tension.
ao and ih..........12.000w From a to.--......32.290w
From o to i........24.260w Verticals ob & ig... 2.571w
Other diagonals... 12.568w Diagonals......... 7.424w
Total,........ 48,828w  Total,........ 42.285w
Dctuct for parts         Detuct for parts
that act by thrust  1.712?w acting by thrust  1.712w
and tension, prin-  -    and tension, prin -
cipally tension,   47.116 cipally thrust,  40.573iw
This shews a difference of about 8 per cent in favor of
truss A. over truss 7.
But it will be observed that in truss A. the number and
lengths of pieces exposed to thrust are greater, which, in
a measure, will counteract the seeming advantage. This
plan should, doubtless, be preferred in many cases,
especially for wooden bridges.
XIII. Fig. 8 represents an arched truss, of the same
general parts and dimensions, and in the same condition
as to load, &c., as truss Fig 7.
When loaded throughout equally, the arch is supposed
to be in equilibrio without any action of the diagonals.
Now, it is obvious that the three forces meeting at the
point a, viz, the resistance of the support, the thrust of
oa, and the tension of ab, are to one another as ob: oa: ab.
But the first is equal to 3w (neglecting, as in the case of
truss 7, the weight of the structure,) consequently the two
ao       ab
latter are respectively equal to 3w~ and 3wbo      bo
These quantities may be calculated with the utmost
precision by trigonometry. But for practical purposes




17


generally, they may be determined with sufficient accuracy
ao
by geometrical construction, and are found to be 3wbo
ab
6.53w, and 3w--= 5.83w. Hence, making ab=l we have
bo
370           3
--5.S3w and --5.83. Then substituting this value of
bo           bo
3                   ao
Sin the expression 3w, we have the thrust uf ao
bo                   bo
5.S3ao.w.
The number 5.83 is peculiar to this particular proportion
of truss, i.e, having 6 principal bearing points, and md=
Saih.
Now, it is manifest that ah throughout sustains the
same tension as the part ab.
Then, drawing np parallel with ao, the three forces
acting at o, will be as ao (=-p,): on: op. But the thrust of
ao                             on   3
ao=3w-o. Therefore the thrust of on =3w -=   on.w=
bo                             ob oh
5.83onw.
In like manner we find the thrust of nm= 5S3nm.w, and
the thrust of ml= 5.83w.
Now we find by analysis that these quantities represent
the maximum stress upon all the parts of this arch a.o.l,
and the chord ah, in any of the conditions of the load
supposed in relation to truss 7, and multiplying the length
of each part by its maximum stress, the chord a.h, gives a
product 7 x 5.83zo=40,81w.
For the arch we have 5.83w X (ao2 + on2 4 nm2 )2 + 5.83w.
But ao= 1.12 (as determined by geometrical construction,)
on=1.05 and nm=1.01, and substituting these values in
the above expression, we have 5.83w (1 25+1.10.+1.02)2
-5.83w,=45.13w=the sum of the products of the lengths
of the different portions of the arch, multiplied by the
maximum thrust exerted by each respectively.
XIV. In order to ascertain the maximum stress upon
the diagonals and verticals, (the former acting by tensior.
B2




18


and the latter by thrust, as in truss 7,) we commence by
removing the weight from i. The pressure upon the
support at h, then, will be diminished by -w, and upon
the support at a, by 4w, and the former becomes 3w--w
=15w. The three forces acting at A, therefore, will be
15 gh                           15 ih
represented by -uw-- for the tension of gh, and - w7                              7
for the thrust of ih.
Then, taking iq on hi produced, by any scale, to
represent the thrust ih, and drawing qr parallel with /f,
till it meets ik in r, it is obvious that the three forces acting
at i, viz, the thrust of ih and ik, and the tension of if, will
be represented respectively by the sides of the triangle
i, q, r, parallel respectively with the directions of those
forces, and may be measured with scale and dividers, or
calculated trigonometrically; and it will be seen that the
pressure upon the support h, enters as a factor in the
expressions for all these forces.  But this factor is
manifestly the greatest possible in the case here supposed,
except when the whole, or a part of the weight at i were
restored, in which case the part if would obviously be
relieved of the whole, or a part of the stress it sustains
when the whole weight at i is removed. Hence it follows,
that the maximum stress on if, is when all the bearing
points but i have their full load, and the point i is without
load.
Now, taking fs=qr and drawing s.t parallel with gf,
st will represent the horizontal, andft the vertical effect of
the action of fi; the latter effect being counteracted by
the thrust of kf, and the former, in addition to the tension
of fh, is resisted by the tension of ef  Therefore, ft
represents the greatest stress which kf can receive from
ef alone. But it is also liable to the tension of 7f, which
will act in conjunction with if when k is loaded, and i and
I are unloaded, in which case if will have less than its
maximum action. It is founds however, by analysing the
forces under various conditions of the load, that the
maximum action on kf occurs when ifor fl, one or the




19


other, is under a maximum stress, and is nearly the same
in both cases.
XV. If i and k be unloaded,
the pressure on the support at h,
is equal to 2~ow, & the thrust of h
l ow x ih
=-   ---. Taking iq' by the
scale to represent this quantity,
draw q'r' parallel with if, and q'r',
compared with the same scale, will
give the stress of if, from which,
as in the former case, we obtain ft' c
"kto represent the thrust of kf. Also
ir' represents the thrust of ki.
Then, taking kv=ir', on i.k produced, raising the vertical vx=ft',
and joining kx, the line kx will
represent the resultant of the
forces kv and ft', and xy, drawn
parallel with ke, will represent the
tension of ke, which is its maximum C.
strain.  Also, ky represents the.
thrust of kl, and taking ez=xy, and.
drawing za' parallel with ef, we
have ea' to represent the maxi-    -+
mum thrust of el.
By a similar process, removing   '     //
the weight from 1, we obtain db'         /:
and dc' as the maximum action: of
dl and dm, and so of me, nb, &c.  4 -Or the analysis may be commenced at a instead of h, varying
the process as the tyro in dynamics will readily see the circumstances to require; the same results will be obtained, except what may arise from
inaccuracies of construction and measurement.




90


The best plan, perhaps, is to commence the analysis at
both ends. and by the agreement or disagreement on
meeting near the middle, a check will be afforded against
errors.  This method will also prevent errors from
accumulating to the same extent as when the analysis
is pursued throughout the whole length in one direction.
XVI. By this kind of analysis we have the means of
determining, to any necessary degree of accuracy, the
stress upon every part of the truss under any given
circumstances, whereby, knowing the strength of the
material employed, the structure may be judiciously
proportioned in all its parts.
By careful geometrical construction and analysis, in the
manner above explained, I obtain for the maximum strain
of the diagonals as follows: Of bn and cm, 1.1w, of dl,
1.25w, of ek, 1.2w, and of fi, 1.05w; and to obtain the
products of these quantities multiplied by the lengths of
the pieces, it will be sufficiently near, the pieces being
nearly of the same lengths, to multiply the aggregate
length by the mean maximum stress, which gives the
aggregate product=15.07w. For the verticals I obtain
3.70w.
Hence the products for the whole truss will stand,
Exposed to Thrust,       Exposed to Tension.
Arch, (Art. 13).....45.13w. Chord ah......... 40.81w.
Verticals,.......... 3.70w. Diagonals,......... 15.07w.
Total for truss 8,.... 48.83w. Total,............. 55.88w.
Total for truss 7,..47.42w Total for truss 7,...48.00w.
(See Art. 11.)  )
Difference,......... 1.41w. Difference,......... 7.88w.
Shewing that a truss on the plan seen in Fig. 8, will
require about 16 per cent more material to withstand
tension, and nearly 3 per cent more to withstand a crushing
force, than one on the plan shewn in Fig 7.
This is a legitimate mode of comparison generally, as
regards those parts exposed to tension. But with respect
to those exposed to a crushing force, it is only applicable




21


where, as in the present case, the pieces exposed to that
force may be nearly of the same dimensions. Hence the
comparison between trusses Figs. 7 and 8, is more fair and
reliable, than between either of these and truss A.
The verticals may be dispensed with in the arched
truss, by disposing the diagonals so that they may act by
thrust or tension, but I will not stop in this place to
examine into the effects of that modification.
XVII. We have hitherto had regard only to the forces
Sand effects produced by the load, independently of the
Sweight of the structure. For the effects of the latter, it
is sufficient to regard this weight as included in w.w, &c.,
as far as it regards those parts that sustain their maximum
Sstress when the load is uniform throughout. But the
weight of the structure being constant, and not variable
like that of the additional load, its effects are always the
same, and confined to those parts which act under the
Suniform load. Hence, it is proper to calculate the effects
of uniform weights, w'vw', &c., one at each of the bearing
points, where the weight of the structure may be regarded
as concentrated. In this case, w' of course, will be equal
to the quotient of the whole weight of the structure
divided by the number of bearing points+1, the 1 being; added because the two end supports sustain directly a
weight equal to that which acts at each of the bearing
points o, n, m, &c.
The effects of these weights, w'w', &c. on the parts affected by them, added to the maximum effects of the variable
weights vw.,, &c., as above determined, will give the whole
stress to which the various parts will be liable, and which
they should be adequate to sustain, as regards truss 8 and
truss A.
A. There is another effect of the weight of the structure,
as it respects truss 7, which should be taken into account
in practice, though it does not very essentially alter the
result of this general comparison.
The counter diagonals nb, me, If, and kg, [Fig. 7,] can




22


manifestly, only act when the main diagonals oc, &c., to
which they are respectively opposed, are relaxed; i.e, nb,
can only act when the tendency of the variable load is to
produce a greater action upon this part, than the weight
of the structure alone tends to produce on oc, and then,
will only have an action equal to the exccess of the
former tendency above the latter.
Now, we have seen that the tendency of the weight of
the structure is to produce a tension upon oc equal to
2w' /2, and that the maximum action which the variable
load tends to produce on nb, is equal to!wV2. Therefore
the true maximum tension of nb is only equal to (Iw-2w')
V/2, which in practice,will usually be a negative quantity,
and consequently the counter diagonals nb and kg will
usually be of no use in the structure, exceptforappearance,
and may be dispensed with.
In like manner, the maximum action of mc and If is
reduced by the weight of the structure from -wV/2, as
given in Article 11, to (-w--w')V2, which, in some cases,
will be a negative quantity, and the parts may be dispensed
with, especially for common road bridges, which usually
are not liable to be exposed to very large variable
weights.
No analogous modification of effects is produced on
truss 8 by the weight of the structure, since the diagonals
are neutral, or have no action under a uniform load.Hence this fact shews an increased advantage of truss 7
over truss 8.
With regard to truss A, the maximum action of the
parts will be truly expressed by combining, or adding the
effects of the weight of the structure to those of the load,
since the diagonals in the same pannel are not antagonists,
and the increased action of one dose not imply a diminished
action of the other, and the contrary.
XVIII. By recurring to Article 11 where the effects of the
uniform load are determined for truss 7, substituting w'
for w and multiplying by the lengths of the pieces, we




23


Sobtain for the effects produced by the weight of the truss
there represented, the following results:
Products for parts exposed to
Thrust.                  Tension.
End diagonals.......12w' Lower horizontal,.....28w'
Upper horizontal.....28.w' Diagon'lsoc, nd, ek &fi,12w'
Verticals..............6.w'
-        Total,........... 40.w'
Total,...........46.w'
Substituting w' for w in the corresponding products for
Struss 8, shewn in Article 13, we have, for parts exposed
to thrust, 45.13w', and for those exposed to tension, 40.81w;
a result so nearly like that above shewn, that we may
Sregard the two trusses as equal, as to ability, with a given
amount of material, to sustain their own weights and equal
Sloads uniformly distributed.
The balance shewn in Article 16 then, in favor of truss
7, is only applicable to that part of the materials provided
to sustain the variable load, which, in practice, will
probably be from one-half to three-fourths of the whole
for spans of considerable length. Calling, therefore, w=
S3w', the above balances become reduced from 16 to 12 per
cent for tension, and from 3 to 21 per cent for thrust, or
about 7per cent on the whole expense; probably,however,
something more, since a crushing force is generally more
cheaply sustained than a tensile force. Hence the cancelled
truss appears to have from 8 to 10 per cent the advantage
as to economy, considering the two plans to be equally
practicable and convenient.
XIX. With regard to these latter considerations, truss
7 has the advantage as to uniformity in the lengths of
pieces, and in the angles, while truss 8 has more uniformity
in stress, and consequently in the cross sections of pieces
in the same classes, considerations which may be regarded
as nearly balanced.
If the road-way pass over the top, (as we have supposed
in the above computations,) the truss 7 has a decided




24


advantage in presenting the bearing points o, n, m, &c., ii
the same horizontal plane, whereas truss 8 require;
elevated supports for the road-way towards the ends.
XX. If the line of transit be from a to h, the effectf
will be somewhat modified from what has been shewr
above. In truss 7, transferring the weight from o to b
when nb does not act, will produce a tension upon o?
equal to w. Therefore ob and ig will require to be sc
apportioned and connected as to sustain this force. Ai
the points c, d, e, f, the weights would be sustained by
the diagonals, producing exactly the same stress as they
produce when at n, m, &c., through the medium of the
verticals. Therefore the latter would be relieved, each,
of a weight equal to w, without any additional stress on
the other parts. Hence the transfer of the weights from
the upper to the lower level, would have the effect to add
2to to the products for tension, and diminish by 4w those
for thrust; an effect of no great importance, but rather
favorable as far as regards the truss alone.
With respect to truss 8, it was seen (Art. 14) that the
maximum thrust on each vertical, occurred when that
vertical was loaded at the top, and since that thrust, in all
cases was less than w, it follows that a transfer of the
weight to the bottom of the vertical piece, would destroy
all the thrust, and convert the action to one of tension.Still there is a case where the vertical sustains a thrust
which is not destroyed by the weight as in the case just
stated. When i and k [Fig. 8] are unloaded and the other
bearing points loaded, we see that k.f sustains a thrust
represented by ft', which becomes the maximum when
the load is at the bottom of the truss, and for truss 8 it
varies from,35w to 50w. This amount being still farther
reduced by the weight of the road-way, becomes very
small, and the same material necessary to support the
tension, will, in general, be adequate to support the thrust,
if so connected as to be able to resist by both tension and
thrust; for each vertical should possess strength snfficient




25


o sustain the whole weight applied at its lower extremity,
~since the diagonals are supposed to be only capable of
4sustaining the effects of inequality in the load. Therefore
'the transfer of the road-way from the top to the bottom
of the truss, would have the effect to diminish the
representative products for material exposed to thrust by
13.7w (=the amount due to the verticals,) and increase
those for tension by w x the aggregate length of verticals,
jwhich for the truss under consideration is equal to 4.72w,
a change so trifling as not essentially to vary the results
of the former comparisons.
It is proper to remark, that, strictly speaking, the whole
of the weight of the structure can not be regarded as
applied either at o, n, m, &c, or b, c, d, &c. But the
more considerable part of it being where the road-way
is placed, I have considered it sufficient for my present
purpose, to regard it all as concentrated in the main
transverse beams or bearers, whether at o, n, m, &c. or at, c, d, &c.
XXI. To pursue the comparison between truss 7 and,when the road-way is at the bottom, and the trusses are
ot sufficiently high to admit of being tied and secured
cross the top, the cancelled truss being higher (except
n the middle) is somewhat more top-heavy, and may be
ore liable to yield laterally, though this cannot amount
o a serious disadvantage.
The arched truss, moreover, may, by some, be thought
o have a more graceful and agreeable appearance than
he cancelled truss. I will not take upon myself to decide
n this point, except by remarking, that, to a person who
komprehends the principles and properties of different
kinds of structures, in a case where strength is the grand
desideratum, that plan of structure which secures this in
the greatest degree, with the least amount of material and
expense, will generally excite the most pleasing sensations
in the mind.


C




26


XXII. Again, in cases where the truss is sufficiently
high to admit of being secured and braced laterally at
the top, the cancelled truss is better suited to such an
arrangement than the arched truss, which, though high
enough in the middle, will not admit of the lateral security
being extended towards the ends without parts extending
above the arch expressly for that purpose.
XXIII. On the whole, it would seem that the relative
cost of trusses upon the plans shewn in Fig. 7 and 8,
would be nearly proportioned to the amount of material
in each respectively. Hence I conclude, that though for
bridges of moderate length, particularly common road
bridges, and others where the road-way passes near the
lower part of the truss, the arched truss may be preferable,
still, as a general rule, the cancelled truss, as shewn in
Fig. 7, may be constructed to sustain a given weight,
through all the changes to which the load of a bridge is
usually liable, with from five to ten per cent less expense
than the arched truss, and should be preferred for long
spans, especially for rail-roads, and where the track passes
over the top.
With regard to truss A., as compared with truss 7, the
former manifestly has some 8 per cent the advantage in
all cases where the diagonals act by thrust, but otherwise
the advantage will be counteracted, mostly, by the greater
length of some of the parts acting by thrust in truss A.
XXIV. But though I say, judging from the above
examinations and comparisons, such results and advantages,
in the use of the cancelled truss, may be obtained, I am
nevertheless constrained to say, that, though the general
plans and principles of this truss have been extensively
used in bridge building, still, for reasons which I will not,
in this place, undertake to explain, the principles have
never, (to my knowledge or belief,) been applied with
that skill and economy in the proportions of the different
parts of the structure, which are necssary to secure the
advantages above pointed out as practicable.




27


For instance, the bridges built on the plans generally
known as Howe's & Long's plans, are essentially the
same in their general features, as I have shewn in Fig 7.
But instead of being built with each part proportioned to
the maximum stress to which it is liable, the upper and
lower ribs or stringers have been of the same dimensions
throughout, or nearly so; whereas, the stress varies, as
above shewn, some 50 per cent or one-half. The verticals
and diagonals have been made nearly of the same size
throughout, or increased towards the ends to a far less
degree than the comparative stress to whtch they are
subjected in those places, demands.
Now let us suppose the truss Fig. 7 so constructed that
every piece or portion in each class, be of sufficient size
to withstand the maximum stress for any of the parts of
those classes respectively, and the upper rib extending to
the same length as the lower, and the products taken for
each portion into the maximum stress for the class to
which it belongs. We should have
Products for Thrust,      Products for Tension,
Top Rib,.......6 x 7=42.wi Bottom Rib,.........42.0w
Two end Diagonals,... 12.w Six main Diagonals...25.7w
Verticals, nearly -.....13.w Six counter do. J size, 12.8w
Total,............ 67.w   Total,..........80.5w
Or, supposing the diagonals to act by thrust and the
verticals by tension, (Howe's plan,) it will stand,
For Thrust,               For Tension,
Top Rib............ 42.w Bottom Rib,..........42.w
Eight main Diagonals, 48.w Six Verticals, nearly...13.w
Six Counter braces,  18.w
half size,                  Total,...........55.w
Total,...........108.w
Corresponding amounts, if proportioned according to
the stress upon each part, (diagonals acting by thrust,)
For Thrust,               For Tension,
Tob Rib,.............22w Bottom Rib,..........24W
Diagonals............32w Verticals,............. 1Sw
Total,............54w     Total,............42.w




28


Only one-half as much material exposed to thrust, and
a trifle more than three-fourths as much exposed to
tension. This difference is still greater where the length
of the truss has a greater ratio to the height.
The result here shewn is obtained on the supposition that the cross section of each piece may be reduced
in the same ratio as the stress, whether it act by thrust or
tension. With respect to the portion sustaining tension,
this is essentially true. But a piece exposed to a crushing
force in the direction of its length, requires that its length
should not exceed a certain ratio to its diameter, in order
that it may sustain a maximum. But in practice, the
ratio of the length to the diameter is usually much
greater than that which gives the greatest power of
resistance. It follows, then, that in pieces of the same
length, the power of resistance diminishes considerably
faster than the cross section. Consequently the amount
of saving indicated above, could not all be made available
with regard to the parts acting by thrust, though a large
portion of it might.
XXV. Having established the great excellence ofthe cancelled truss, on the plans shewn in Fig. 7 and Fig. A., for
sustaining the weight of bridges & their loads, and pointed
out the proportions which should subsist between its several parts when the general dimensions and proportions
are given, it is proper to endeavor to ascertain the most
economical proportion between the height and length of
the truss, and the most advantageous angle, or inclination
of the diagonals.
The office of the diagonal is, to serve as a medium
through which the resistance of the abutminnt is made to
sustain the weight of bodies not situated over the point of
support; as where ac and bc are made the media through
which the weight of the body w is transmitted to, and
sustained by the two supports a and b, [Fig 9,] situated at
certain equal distances on opposite sides of the vertical




29
passing through w. Now the minimum amount of material required to sustain the weight with a given stress
proportioned to the cross section, is when a c b is a right
angle. To demonstrate this, join
ab, and draw the perpendicular f 9.
cd. Then, the thrust on ac and
bc each, is to -1 w, as the line ac
(or be) is to cd, that is, equal to  A
ac                    a       d      6
0w-, making p=cd. Butmaking
p
ad=ht, ac=,V (ht +p2) and -w   w       2) and this
P         P
multiplied by ac (or V(h2 +p2,) is proportional to the
amount of material required to sustain the weight w, upon
the supposition above laid down, being the stress multiplied by the length of the piece. Therefore, when p has
such a value that the product w (1  )   (h2 +2)=
Izo (-+p,) is a minimum, the least possible amount of
material will support the weight.
h2
Then, differentiating the function - +p in which p is
the variable, and deducing the value of p when the differential 0 we obtain p=-I, and consequently acb is a right
angle, and ac and ch each incline 450 to the horizon.
XXVI. A. But a more important problem is, having
the length and height of the truss given, to determine
the horizontal reach of the diagonal which will give the
greatest degree of economy.
This will present two cases, according as the diagonals
act by tension or thrust. We will first consider them as
acting by tension.
Now, the greatest economy in the use of a given amount
of material in a diagonal acting by tension, is, manifestly,
when the weight it can sustain, multiplied by the horizontal reach, gives the greatest product. This may be called
C2




30


the capacity of the material, and of course, will be
directly as the cross section and the horizontal reach,
and inversely as the rate of strain.
Then, if we make p=the height, and h=-the horizontal
reach, V(h2 -+p2) will be equal to the length of the diagonal, and the amount of material being given, the cross
1
section will be as. Moreover, the rate of strain
S(h 2 ~p2)
will be, manifestly, as  --    or (p being constant,)
P
as V(h +p2)
Hence we have the capacity as   (2        V(h2+p2)
or as --     ), and that value of h which gives the
( A2 +p2 )
maximum value of this expression, is the most advantageous. This is found to be when h=-p, as in the case
above.
Therefore this is the most economical position for the
diagonals in all cases where they act by tension, as far as
depends on those pieces alone.
XXVI. B. For the case of diagonals acting by thrust,
the use of the diagonal or brace, being to carry or transfer
the vertical action of certain weights towards the ends of
the truss from the intermediate points, and the amount of
weights sustained by each diagonal being, in general,
proportioned to the distance of its upper end from the
centre of the truss, it is obvious that the weight sustained
by the brace is essentially the same, according to its distance from the centre, whatever be the number and inclination of the braces. The economy, then, in the use of
material for braces, or diagonals acting by thrust, is
directly as the horizontal reach of the brace (which determines the number,) and inversely as the amount of material in each brace, necessary to sustain the given weight.
Now the amount of material (m) is directly as the acting force or stress, and inversely as the power of resis



31


tance, (r.) But the stress is as the length of the brace,
(being equal to the weight sustained, multiplied by the
length of brace and divided by the height (p) of the
truss,) and the power of resistance is as the cube of the
diameter [d] divided by the square of the length, that is,
dc
as   - +p
If we take then, d' to denote the diameter of the brace
d'3
when -t=0, r becomes r', and is as, andsince the power
p2
of resistance [r] should be as the stress produced by the
weight, we have the following proportion:
d'3  d3
p: J(h7 +p2)::.
Spd3   d'1  (h2 +)2
Whence we have,and p3d3
h2 +4-p      p2
d'3(l2 +p2):. Extracting the cube root of the last equation it becomes pd=d' /(1t2 +p2,) whence d': d::p:
/(h2 +p2). Therefore the diameter should be proportioned to the length of the brace, and the quantity of
material as the cube of the length.
Hence, the greatest economy is when the horizontal
reach, or the base of the triangle, divided by the cube of
the hypothenuse, gives the greatest quotient, i.e, when
Sis at the maximum.
(/62 p2 )I
This is found to occur when h =,75p very nearly. It is
also found by computation, that if h be made equal to p
and.p successively, the economy would be about 9 per
cent less than when h=-p, being about the same in both
cases.
Therefore, other things the same, it is the best economy
to place the diagonals acting by thrust, so that the horizontal reach shall equal - of the perpendicular; but considerable deviations may be made from the rule, when
required by other considerations, without essential detriment to economy in the diagonals.
"* This formula is not fully sustained by experiment, but is, perhaps, sufficient for the
present investigation.




32


It is now proper to ascertain the comparative effects of
different positions of the diagonal upon the horizontal
parts, and verticals when employed. For that purpose,
take two trusses, [Fig. 10 and 11,] of the same height and
length, but in which the diagonals have different inclinations; and for simplicity, let truss 11 have twice as many
W
F..                  V 1W_
^           w
a d c                                  i
diagonals as 10 Now it is manifest that a given weight
w, on the centre of these trusses, will produce a vertical
pressure =w upon each of the supporting points a and b,
and a horizontal action upon ad, equal to.w -, also that
edb
each diagonal from a to w, will exert the same horizontal
action, the whole amount of which will be sustained by
the different portions of the top and bottom ribs, the
action of which will be increased towards the centre
ad
where it will become equal to -w- Xn, n being the rumed
ber of diagonals affected by w between a and w.
But the length of the truss being the same, n is
of
Inversely as the length of ad, or equal to--, and substia ad            of    af
tuting this value for n, we have Jw.X ~. wL for the
w;d  ad    ed
stress in the centre of the horizontal parts, produced by
the weight w; an expression from which ad has been




33


eliminated, and consequently the distance ad has no effect
upon the stress of the horizontal parts in the centre, and
by the same reasoning it is shewn that the same is true in
relation to any other part of the horizontals, except in
case of Fig. 11, the increments are added at shorter
intervals, and in proportionally smaller quantities, from
the end towards the centre. Hence, in general, there is
no difference in the stress of the horizontal parts, whether
the diagonals have one inclination or another.
With regard to the verticals, that part of their stress
which they receive from the diagonals, is equal to the vertical action of those diagonals, and is the same for a given
weight, whatever be their inclination. On the vertical
uwf the pressure is received directly from the weight.
But on the next adjacent vertical, on either side, one-half
the same pressure is received through the intervening
diagonal, and transmitted to the next, and so on to the end.
Consequently, tle aggregate action of the verticals produced by the weight w, is equal to w+-~iwn, taking n for
the number of verticals receiving their strain through the
medium of the diagonals, and which is equal to the
whole number less 3 when the number is odd, and the
verticals act by thrust, as in Fig. 10 and 11.
Hence, the aggregate stress of verticals increases and
diminishes witli their number; and economy as regards
those parts, would require the diagonals to be inclined to
a less angle with the horizon than that required by economy as regards diagonals.
We have seen, however, (Art. 26 B.) that by placing
the diagonals at 45~ when they act by thrust, we lose
about 9 per cent in the economy of those parts, and we
now see that such an arrangement increases the economy
on verticals to a considerable extent by diminishing their
number, the actual amount depending on the number, and
therefore not deducible by a general rule.
It will, however, be a near approximation to the truth
to assume, that by inclining the diagonals at 450, the loss




34


on diagonals will be very nearly compensated by the gaii
on verticals; hence this would seem to be about the mos
advantageous arrangement for diagonals acting by thrust
in combination with verticals acting by tension.
In case of diagonal ties and vertical struts, a triflin'
saving of material could be effected by increasing th(
horizontal reach of the diagonal beyond an equality witl
the perpendicular, but scarcely sufficient to compensate
for the sacrifice in the simplicity of figure, unless othei
considerations conspire to favor such a departure frorr
simplicity.
XXIX. Nextly, as to the proper height to be given to
the truss, we have seen, [Art. 27,] that the horizontal thrust
produced by the weight w in the centre of the truss, is
equal to.wq, that is, directly as the length and inversely
edn
as the height of the truss. Now this being also true with
respect to all other positions of the weight, it follows that
the horizontal parts have their powers of sustaining the
action of the weights, increased directly as the height.
With regard to the other parts, those which act by tension, remain the same in amount, for though increased in
length, they are diminished in number in the same ratio,
other things the same, as far as it respects the diagonals,
and the stress of the verticals received through the
medium of the diagonals. For illustration the weight w,
[Fig. 12,] will require the same length of diagonals, and
the same stress upon them, to transmit its pressure from
w to a and b, whethe: it be done through the parts w, c, g,
h, i, a, or w, c, h', a, and so of the half transmitted to b.
Also the same length and stress of verticals. But these,
acting by thrust when the diagonals act by tension, have
their power of resistance diminished with increase of
length, and consequently will require an increase of cross
section, such that the cube of the diameter may have a
constant ratio to the square of the length.* If the length


* See Note foot of page 31.




35


be multiplied by a, the diameter must be multiplied by
az, and the cross section by a4-, a factor greater than a.
Moreover, that part of the stress produced by the
weight directly upon the vertical, amounting to about ~
the aggregate maximum stress, manifestly requires an
increase in the   r,cube of the diam- a".
eter proportional
to the increase in
the square of the l
length, with an ad-  \
dition for increase
of weight sus'ain- a    h      C        k
ed proportioned to
the diminution of number. Therefore if the height of truss
be multiplied by a, the diameter must be multiplied by awhich requires the amount of material to be multiplied
by (a-)22X a=-al, a factor greater than the square of a.
Hence, since the verticals, when they act by thrust,
require an increase of material greater than the simple
increase of the height, for one-half, and greater than the
increase in the square of the height for the other half, we
may fairly assume an average increase for those parts,
about as the increase in the square of the height of the
truss.
It will be seen, moreover, that the diagonals at the ends
always act by thrust, and that their aggregate thrust is
equal to the whole weight of load and structure, divided
by the natural sine of the angle those parts make with
the horizon, and when they incline at 450 the above named
sine=1-- /2. Hence the thrust of the parts in question=
the whole weight multiplied by V/2.  Therefore, the
height being multiplied by a, the amount of material in the
endmost braces, will be multiplied by a4, besides what is
compensated by the increased horizontal reach. It will,
therefore, probably, not be too much to assume, both for
verticalsand diagonals throughout, an increase in weight




36


and cost, in the ratio of the increase in height, especially,
taking into account the additional lateral support the high
trusses will require.
Upon this assumption, since the horizontal parts diminish with increase of height, and the verticals and diagonals increase in expense in the same ratio to their respective amounts, the minimum expense of material would
occur when the height were such that the horizontal parts
be equal to all the others.
But in Art. 12, we found that for truss 7, in which the
height is equal to - the length, the representative quantities for horizontals were to those of the other parts, about
as 56 to 40 or as 7 to 5. Therefore if we add 1 to the
height, it becomes 4-+,=- of the length. Then diminishing the horizontals by  we have 56- 5 46-, and increasing the other parts by -I we have 40+ 4-=465.Hence it would seem that the height should be - of the
length.
XXX. This, of course, is not given as a rigorously
demonstrated point. A formula might be deduced, perhaps, by a more elaborate process, which, when comprehended, would be more satisfactory. But to introduce all
the considerations by which the question is affected, would
render any formulas upon the subject necessarily very
complicated, and of comparatively little value in practice.
There are considerations which go to render it quite improbable, that any simple ratio of the height to the length
would be applicable with advantage in all circumstances.
In short spans, where great strength is required, it
would often be found advantageous to carry the height to
- the length, a proportion almost impracticable, and certainly not advisable, in long spans, from the fact that they
would become top-heavy, be more affected by wind, and
other lateral influences and tendencies.
Again, in stretches of moderate length, where less
strength is required, a less height, even as low as i or -1
the length, might be preferable, as having a better appear



37


ance, offering less obstruction to the prospect, &c. But
for a structure of great strength, a height never less than
^ and seldom less than  of the length, can be adopted
without sacrifice of economy,
Another consideration to be taken into account in fixing
the height of the truss is, the distance between bearing
points. In trusses of single cancels, or where the diagonals cross but once, the height must be equal to the
distance between bearing points, or the diagonals must
i cross at oblique angles, which we have seen is unfavorable
to economy in those parts, except that when they act by
tension they may slightly approach the horizontal, and
when by thrust, the perpendicular, without disadvantage.
But if the bearing points be too far apart, it will require
very heavy joists and longitudinal timbers in the road-way,
besides that the top rib will require a greater cross section, being composed of longer pieces.
All these points and considerations will tax the skill
and judgment of the engineer to adjust them properly in
various circumstances, and I do not propose entirely to
supersede his labor, nor will the limits I propose to myself in this essay, allow me to pursue this branch of the
subject further.
XXXI. I have alluded to the plan of sustaining the
horizontal thrust of bridges by the abutments, &c. It
would seem that this might be done to a very great saving
of material. But when a bridge is loaded with a full
load for one-half of its length only, the abutment nearest
to the loaded half sustains about I of the load, and the
other only 4, and the thrust at the two ends is in the same
proportion, as it regards trusses on the plans shewn in
Fig. 7, 8, and A. Now the abutments can only sustain
equal horizontal action from the structure, as they only
act and re-act upon one another through the medium of
Ihe structure. Therefore the difference of thrust, amount"ng to nearly one-half the maximum, must be counteracted
within the superstructure itself. Hence, but little more
D




38


than half the thrust due to the maximum load can be
sustained by the abutment.
Add to this consideration, that of the practical difficulty
of making the abutment act in conjunction with the
means provided within the superstructure, so that the
latter may not at any time be subjected to a strain they
are inadequate to bear, and the apparent advantage of
relying on abutments to sustain thrust, is reduced to a
small amount, if not entirely annihilated.
The principle, however, may be made available for
bridges of light burthens, and for others, some assistance
may be derived by bracing from the abutments. But in
general, for the stronger class of bridges, as rail-road
bridges, &c., it appears proper to adopt the principle,
that the superstructure should be self-sustaining, only
requiring a direct support for its own weight and that of
its load, acting by vertical pressure, from the abutments
and piers.
XXXII. There is a plan, however, as we have already
seen, in which every part of the weight, wherever situated, produces the same thrust at both ends. This is
where each bearing point has an independent pair of
braces extending from it, one to each abutment, as shewn
in Article 11, Fig. 6. The objections to that plan are, that
the amount of thrust is about one-third greater than on
other plans, and the great length of a part of the braces;
faults which very much impair, if not entirely destroy
the value of the plan; at any rate, it is only applicable to
short spans.
XXXIII.   Having decided upon the most suitable
forms and proportions for bridge trusses, I will say a few
words in regard to the material best adapted to the purposes of bridge building. We have seen that the materials
in a bridge truss, are principally subjected to two kinds of
action, that of tension and that of thrust. The lateral action
should always be avoided in the main parts of the truss.




39


It is obvious then, that those materials best calculated to
resist these kinds of force respectively, should, when
practicable, without the sacrifice of economy, be employed in the situations where those forces are respectively exerted.
For instance, when the diagonals act by tension, the
top rib, (or the arch, in case of the arched truss,) and the
verticals, should be composed of the material best adapted
to sustaining a crushing force, while the lower rib or
stringer, and the diagonals, should be of the best material for supporting tension.
Wood and iron, as before remarked, are the only materials that have been employed in bridge building, (I refer
only to the superstructures,) to an extent worthy of notice,
and it seems reasonable to conclude, that on these, we
must place our dependence.
Cast iron will resist a greater crushing force than any
other substance, whose cost will admit of its being used
as a building material. Steel has a greater power of
resistance, but its cost precludes its use as a material for
building. Wrought iron resists nearly equally with cast
iron, but its cost is twice as great, which gives the cast
iron entirely the advantage. On the other hand, wrought
iron resists a tensile force nearly four times as well as cast
iron, and 12 or 15 times as well as wood, bulk for bulk.
Not only are these the strongest materials, but they are
also the most durable. In fact, with proper precautions,
they may be regarded as imperishable.
It would seem, then, that wrought iron for tension, and
cast iron for thrust, were the best materials that could be
employed for building bridges. But wood, though greatly
inferior in strength and durability, is much cheaper and
lighter, so that making up with quantity for its want of
strength, and by frequent renewals for its want of durability, it has hitherto been almost universally used in this
country for bridge building, and in the scarcity of means,
and the unsettled state of things in a new country, where
improvements are necessarily, to a great extent, of a tem



40


porary character, this is undoubtedly the most economical
material for the purpose.
But it is believed that the state of things has now
assumed that degree of settled permanency in many parts
of this country, and available means have accumulated to
that extent which renders it consistent with true economy
to give a character of greater permanence to our improvements, and in the erection of important works, to have
more reference to durability, even at the cost of a greater
present outlay; and in this view of the subject, it seems
highly probable that one of the channels in which this
tendency of things will develope itself, will be in the
extensive employment of iron in the construction of important bridges. With this impression, I proceed to some
general comparisons as to the relative cost and economy
of wood and iron as materials for bridges.
XXXIV. Cast iron resists a crushing force some 20
times as much as wood, consequently it will only require
-9 as much of the former to resist a given force, provided it
can be put into a form in which its liability to flexmre and
yielding laterally, is not greater than that of wood. This
can be accomplished, in part, by giving the iron a hollow
form, so as to make the diameter of the pieces approximate to an equality with twenty times the same amount of
wood, which must generally be used in a simple rectangular or cylindrical form.
Assuming, then, that a cubic foot of cast iron, will do
the same work as 15 cubic feet of wood, (after making
allowance for the necessarily smaller diameter of the iron)
we can institute a comparison which would seem, upon
the surface, to shew the relative economy of the two materials.
A cubic foot of cast iron, manufactured for the work,
will cost about $13,00. 15 cubic feet of wood in a bridge
will cost, say $6,00. Whence it appears that the cast iron
is more than twice as expensive, in the first outlay, for
sustaining a crushing force, as wood.




41


Again, a cubic foot of wrought iron in the work, say
450 lbs. at 71 cts.,-$34.
Wood is about one-fifteenth as strong as iron. But about
one-half of its fibres must be separated, in order that the
other half may be so connected in the structure as to be
available to their full strength by tension. Hence, it will
take some 30 feet to equal one of iron; for which, say it
will cost $12; shewing a difference of a little less than
three to one; the average for both kinds of iron, reckoning
equal quantities of each, being about 2.6 to 1.
To offset against this, we have the superior durability of
the iron, which, as before observed, may be regarded as
per-durable, whereas wood requires frequent renewals, at
a cost each time equal to the first outlay. Now the first
cost of iron is sufficient to provide for the first cost of the
wood, and nearly two renewals. Besides this, money,
though an inanimate substance, is nevertheless, in these
usurious times, made to be exceedingly prolific; insomuch
that with good husbandry, it is found to double itself once
in ten or twelve years, according to the hard face of the
lender, and the hard fortune of the borrower.
Assuming 5 per cent per annum as the net income of
money invested, the term of time in which the 1 ya0 dollars saved in the wooden structure, will require to produce
one dollar for renewal, will shew the time that wood
ought to last, to be equal to iron in economy. 1I. dollars
at compound interest, will yield at 5 per cent, one dollar
in a little less than ten years.
Therefore, if an imperishable iron structure cost 2.6
times as much as one of wood, and the latter last but ten
years, and money will net 5 per cent compound interest,
the two materials are nearly on a par as to economy.
Now experience has shewn that wooden bridges, unprotected by roofing and siding, seldom last with safety,
over eight years, or thereabouts; and the more there be
expended to increase the durability, the less surplus capiD2




42


tal will be left to invest towards renewals. Hence the
iron would seem to have the advantage.
XXXV. But the above comparison is too superficial
and general to be entitled to a great deal of confidence,
except, perhaps, as it regards the sustaining of a given
weight by a simple post, or suspending it by a bar or rod
of iron or wood. In the complicated assemblage of pieces
forming the superstructure of a bridge, there are numerous other facts and considoerations which materially vary
the results. First, there is a diificulty in connecting pieces
of timber in such a manner that every part may be proportioned to the strength required of it, to the same
extent as can be done with iron. Second, it is frequently
necessary to use considerable quantities of iron in bolts
and fastenings, for putting together a structure of wood
requiring great stability. Third, wood soon looses a portion of its strength by partial decay, and consequently
requires additional strength in the beginning, that it may
be safe for a time after decay has commenced.
Hence, but little can be predicated upon the simple general comparison of wood and iron as to strength and cost,
relative to the comparative economy of the two materials
for bridge building.
It is only by comparing the results of actual experience, or, where this has not been had, by comparing
the results of detailed estimates, upon well matured plans,
founded on well established principles, that a satisfactory
conclusion can be arrived at.
With regard to wooden bridges, much experience has
been had, and the reasonable presumption is, that a good
degree of economy has been attained in their construction. But the idea of building iron bridges in this country
is of recent date, and but little has been experimentally proved in relation to their cost and qualities.
XXXVI, This much, however, my own experience
has demonstrated. Having received Letters Patent for
an " Iron Trussed Bridge " upon the general plan of the
arched truss shown in Fig. 8, and constructed two bridges




43
thereon, over the enlarged Erie canal, (72 and 80 feet
span,) one of which has been in use for six years, it may
be regarded as a demonstrated fact, that bridges may be
sustained by iron trusses. Also, that the cost, for the
above class of bridges, is only about 25 per cent more
than the same class of bridges of wood, as heretofore built,
under the most favorable circumstances, on the Erie Canal.
That the iron portion, constituting some - of the whole
as regards expense, in the iron bridge, gives fair promise
of enduring for ages, while the wooden structure can only
be relied on to last 8 or 10 years.
Upon these facts experimentally established, I found
the following comparison:
A common road bridge of 72 feet span, (the usual
length for the enlarged Erie Canal,) will cost, with iron
trusses,
7000 lbs. of cast iron-3 cts.,............$ 210
6000 wrought   do, manufactured for the
work, at 7 cts.,.......................  420
Timber labor and painting,............. 230
Superintendence and profit,..............  80
W hole first cost,......................  940
$175 will renew the perishable part once
in 9 years, to produce which, at 5 per
cent, will require a capital of....... 320
Total for a perpetual maintenance,.......$1260
With wooden trusses fastened with iron,
Timber, labor, paint and profit,.........$ 550
2000 lbs. of iron fastenings,.............  150
Whole first cost...................... $ 700
(Some have cost $1000 or $1200, and
taken 3 to 4000 lbs. of iron.)
To renew $550 worth'of perishable material, once in 9 years at 5 per cent,
compound interest, will require..... 1000
Total for perpetual maintenance,....... $1700




44


Shewing a clear ultimate saving of $440, in favor of
the iron structure.
The reason of the apparent difference between this result and that arrived at (Art. 34) from the general comparison of the cost, &c., of wood and iron, is, that the bridges
here referred to, have been constructed with a very large
amount of iron fastenings, and with large quantities of
casing and painting for protection and appearance.--
Were the comparison confined strictly to the expense of
timber work in the sustaining parts of the trusses, the
result would be found not to differ so essentially fiom
that of the general comparison.
The above estimate of $700 for the first cost of a 72 ft.
wooden bridge, though considerably below the average
cost of canal bridges of that decription, is nevertheless
believed to be greatly above the minimum for which
bridges may be built, dispensing with parts which are not
essential to strength. It is probable that bridges may be
built for $500, as about the minimum, of equal strength
and convenience, and nearly the same durability as those
hitherto built upon the Erie Canal Enlargement at a cost
from 800 to $1000. Upon this supposition, which may
be regarded as an extreme case in favor of wood, the
comparison will stand thus:
First cost of wooden structure,...........  500
Capital invested at 5 per cent to produce
$500 once in 9 years for renewal,.... 909
Total for perpetual maintenance,........$1409
The same for iron structure, as above,.... 1260
Balance in favor of the iron bridge,......$ 149
Finally since theoretical calculation and general comparison shew a probable advantage, for a long term of
time, and experience, as far as it has gone, shows a decided
advantage in favor of iron, it would seem very unwise to
discard the latter, without, at least, a fair trial of its mer



45


its. If in the first essays at iron bridge building, the iron
bridge has competed so successfully with wooden bridges,
improved by the experience of ages, may not the most
satisfactory results be anticipated from an equal degree of
experience in the construction and use of iron bridges 1
XXXVII. Presuming the affirmative to be the only
rational answer to the above question, I have arranged
the details of plans for carrying into practice the preceding principles and suggestions in the construction of railroad bridges of iron.
I have also made careful detailed estimates of the
expense of bridges of different dimensions and in different circumstances, some of the more general results of
which I will here state.
In proportioning the parts of a rail-road bridge, I have
assumed that it may be exposed to a load of 2000 lbs. per
foot run, for the whole or any part of its length, in addition to its own weight, and in case of tension, have allowed
one square inch cross section of wrought iron for every
10,000 lbs. of the maximum strain produced upon every
part by such weights, acting by dead pressure. In case
of thrust, or crushing force, I have allowed one square
inch cross section of cast iron for every 12,000 lbs., acting
on pieces, (mostly in the form of hollow cylinders,) of a
length equal to 18 diameters, and a greater amount of material, where the ratio of the length to the diameter is
greater; always having regard to practicability, as well as
theoretical proportions, in adjusting the dimensions of tho
parts.
My estimates made upon these bases have fully satisfied
me, that a bridge of 100 feet span, with the track sustained
upon the top, will cost about $2000, or $20 per foot, assuming the present pieces of iron, (1846) in ordinary circumstances. If the track pass near the bottom of the
trusses, the expense will be increased two or three dollars
a foot.
For a span of 140 feet, by a liberal detailed estimate,
I make, in round numbers, a cost of $4000. For 70 feet,




46


I make by actual estimate, and liberal allowances for
contingencies, a cost from 900 to $1000, according to circumstances.
Thus it will be seen, that actual estimate makes the cost
of a single stretch of any length, very nearly as the
square of the length, as should be expected from the
nature of the case.
Hence, knowing the cost of a span of any given length,
we readily deduce that of a span of any other length, in
similar circumstances, with reliable certainty.
These estimates of cost provide for superstructures
entirely of iron, except the string timbers to support the
iron rail. By the substitution of wooden cross bearers, a
considerable saving may sometimes be effected without incurring serious inconveniences.
But though my investigations have forced upon me the
conviction, that in general, where strong and durable
bridges are required, iron should be preferred in their
construction, still, there is a multitude of cases where
wooden structures should be preferred, especially in sections of country comparatively new, where timber is
plenty and capital scarce; and where improvements must
necessarily be of a more temporary character. With this
view of the subject, I have given much attention to the
details of wooden bridges, and with a good deal of investigation and experiment, have arranged plans which are
confidently believed to possess important advantages over
the plans generally in use.
1 may therefore be excused the expression of a belief,
that I might be able to render valuable services to those
interested in the construction of important bridges, generally, and with this conviction I make the proffer of my
services, wherever they may be desired, for the purpose of
furnishing plans, superintending the construction of
bridges, either of wood or iron, and of consultation generally, in matters pertaining to this, as well as other subjects in Mechanics aMld Civil Engineering.




47
I would add that I design shortly to publish, as a sequel
to what precedes, should circumstances seem to warra.t
it, a set of working plans for bridges of different lengths
and descriptions, both of wood and iron, with details,
specifications, and general remarks.  S. WHIPPLE.








ESSAY N~ II


BRIDGE


BUILDING:


GIVING


PRACTICAL DETAILS
AND
PLANS
FOR


IRON AND WOODEN BRIDGES.
BY S. WHIPPLE, C. E.
UTICA, N. Y.
H. H. CURTISS, PRINTER, DEVEREUX BLOCK.
1847.








ESSAY         NO. II.
In the preceding Essay, to which the following is intended as a supplement or continuation, I have endeavored to give a short and comprehensive general view of
the subject, and to ascertain and point out the best general
plats and proportions for the main longitudinal trusses or
side frames of Bridges, and their several parts.  The
side trusses may be regarded as vastly the most important
parts of the structure; since the strength and sufiiciency of
these being secured, there is little difficulty in arranging
the remaining parts. I propose now to go more into the
details of the matter, and give such practical explanations
and specifications as to the strength of materials, the
methods of joining or connecting the several parts or
pieces, both in the main trusses and the other parts of
the structure, illustrated by the necessary diagrams and
plans, as, it is hoped, will enable the young engineer or
the practical builder to proceed with judgment and confidence in this important branch of the profession.
I will first take up the subject of
Iron Bridges.
XXXVIII. Iron has the power of resisting mechanical
forces in several different ways. It may resist forces that
tend to stretch it asunder, or forces that tend to compress
and crush it; the former producing what is usually called
apositive, and the latter, a negative strain. Or it may be
exposed to and resist forces tending to produce rupture
by extending one side of the piece, and compressing the
opposite side; as where a bar of iron supported at its extremities in a horizontal position, is made to sustain a




52


weight in the middle, which tends to stretch the lower
part and compress the upper. This is called a lateral or
transverse strain.
Iron may also be acted on by forces which tend to force
it asunder laterally, in the manner of the action of a pair
of shears. This kind of strain is less important than
either of the preceding, and especially in bridge building,
it'seldom, if ever, will more than partially have place.
XXXIX. With regard to the simple positive and negative strength of iron, it is only necessary for me to state
in this place, that, as the result of a multitude of experiments, a bar of good wrought iron an inch square will
sustain a positive strain of about 60,000 Ibs. on the average; and a negative strain, in pieces of a length not
exceeding about twice the least diameter, of about 90,000,
and in about the same ratio for greater or less cross
sections.*
Cast iron resists a positive strain equal to from 15,000
to 30,000 lbs. to the square inch, but usually not over
18,000. In fact, it is seldom relied on to sustain this kind
of strain, and its power of resistance in this way is not so
well determined as in the case of wrought iron. But
cast iron resists a negative strain even better than wrought
iron, its power of resistance being from 80,000 to 140,000
lbs.; seldom less than 100,000 to the square inch, for
pieces of a length not exceeding twice the least diameter.
But in pieces of such dimensions as must usually be employed in bridges, fracture would take place by lateral
deflection, with a much smaller force than would crush the
material. It is therefore necessary to take into account
the length and diameter, as well as the area of the cross
section, in order to determine the amount of negative
strain which a piece of cast iron, or any other material,
may be relied on to sustain.
* Wrought iron yields considerably under -,a much less pressure,than*
90,000 lbs. to the square inch; but it becomes hardened by the cornpression, and has its power of resistance increased.




63
XL. The cause of lateral deflection by forces applied
at the ends and tending to crush a long piece, is supposed
to be a want of uniformity in the material, and a want of
such an adjustment of the forces, that the line joining
the centre of pressure at the two ends, may pass through
the centre of resistance.  These elements are liable to
considerable variation, and can not be very closely estirhated' in ariy case.  Thbrefore, the absolute power of
resistance for a piece of considerable length, can not be
deduced by calculation from the simple positive and negative strength of the material, but resort must be had to
direct experiment upon the subject; and even considerable discrepancies should naturally be expected in the
results of experiment, unless the lengths of pieces experimented on be very considerable.
In respect to pieces, however, having their lengths equal
to twenty or more times their diameters, a considerable
degree of uniformity is found in their powers of negative
resistance, and, the following- formula, deduced theoretically, though not fully sustained by experiment, will sometimes be useful in determining the relative powers for pieces of similar cross sections, but different dimensions. The
power of resistance is as the cube of the diameter directly,
d3
and as the square of the length inversely, i. e., R is as -.
12
The manner of obtaining this formula may be readily
illustrated by Fig. B., PI. 1, in which adb represents a post
loaded at a, so as to bend it into a curve, of the half of
which, cd is the versed sine. It is obvious that in this
condition, the convex side of the post is exposed to tension, (or, at least, to less compression than the other,) and
the concave side to compression, and that the effect of the
load at a, towards breaking the post at d, is as the versed
sine cd, which is as the square of ab. But the power of
the post to resist rupture transversely, is manifestly as the
cross section of the post, (i. e. as the square of the diamoe

V




54


ter,) multiplied by the diameter. Hence the power is as
the cube of the diameter. Now, the ability of the post to
sustain the load at a, is directly as the power to resist
rupture just determined, and inversely as the mechanical
advantage with which the load acts, above seen to be as
the square of the length of the post. Hence the formula.
XLI.   The following scanty table of experiments will
give some farther light upon this subject, and may be
worth something in the absence of better data.
TABLE OF EXPERIMII'NTS
On the negative strength of Cast Iron.
No. of 1 11l11 of  I N C H E. Wt. in' Weigkt IBrcak-!  I? EI R K8.
Ex'pts.  p  ce.  Dian. Length  tbs.  borne. ing WtI
1 Cylinder.      9..16  990 1002 Broke jin fiom centre.
2     "       "    "    "   978   90 Proke ý in. from centre.
3   Square.        ".1   803 854 Deflected cornerwise, &
flew out wiliout break4                           914 938 iBroke in Iihalf a minute,
not cornerwise, I inch
froii centret.
5 Cylinder.'      7.1.126 1417 1437 olKe in 3 seconds 40
i nchi from  centre.
S "       "    "    " 13771397 Broke 15 from centre.
T1lie piece was flattened by flask not shutting tirue, anld 1a1( been
straightened with the
hane1111r where it broke
7     "       "   4.5      2580 2580 Broke in 1 minute into
4 pieces of nearly equal
leni'iths. Piece of sanie
as last experirnent.
8                 4.5      3218 3218 BISoke in J minute into
3 pieces, in centre and
1 in. fioni centre.
9   Square..4     4.5.     2813 2838 Broke in 4 niinute, r
Sin. f orn centre; deflection parallel with
sides.
XLII. From experiments 7 and 8 of the above table,
it appears that cast iron will sustain, at the extreme, in
cylindrical pieces, whose lengths equal about 14J diame



ters, a negative strain of from 41,000'to 51,000 lbs. to the
square inch, say an average of 46,000 or more. Square
bars, according to Expt. 9, length equal to 18 times the
width of the side, will sustain about 45,000 to the square
inch.
Now a hollow cylinder, of a thickrness of metal not
exceeding about -j of the diameter of the cyliider, according to calculation, has a transverse strength about 50
per cent greater to, the square inch, than a square bar
whose side equals the diameter of the cylinder. Hence,
a hollow cylinder whose length equals 18 times its diameter, ought to sustain a negative strain of 67,500 lbs. to the
square inch.
It should be observed, however, that direct experiments
upon the lateral strength of the pieces used for arriving at
the results and conclusions above stated as to negative
strength, shewed them to possess uncommon strength
transversely, even to from 30 to 50 per cent greater than
the fair average transverse strength of cast iron, as will
be seen hereafter.
Therefore, I do not consider it proper to estimate the
negative strength of hollow cylinders of the proportions
above statedl, at more than from 40,000 to 50,000 lbs..(say
46,000) to the square inch.
Now, the hollow cylinder being evidently the form best
adapted to sustain a negative strain, or a transverse straiin
in all directions, it would be well worth the while to have
a set of thorough experiments, to determine accurately
their actual strength. This has never, as far as I have
learnt, been done, and therefore I shall assume the above
estimate on the subject, as probably, not very far from the.
truth, subject, however, to correction whenever the facts
and evidences shall be obtained, upon which the correction
can be founded. In the mean time, since we know not
the exact ratio between the greatest safe practical strength
and the absolute strength of iron, and. therefore should,




56


in practice, keep considerably within the limits of probable
safety, it becomes a matter of less importance to know
the exact absolute strength, though this, of course, is desirable.
XLIII. It will be seen moreover, by the table of
experiments, that two cylindrical pieces of 9 inches in
leng-th bore, the one 990 lbs. and the other 978 lbs., giving
a mean of 984 lbs.
d3
Now by the formula, R as -, these same cylinders re12
duced to 4.5 inches in length, should sustain four times as
much, or 3,936 Ibs. But by experiments 7 and S,we see that
they bore only 2,580 and 3,218, giving a mean of 2,899.
Whence it appears that, the diameter being the same, the
strength diminishes faster than the length increases, but
not so fast as the square of the length increases, being
about half way between the two. In fact, if we examine'
the results of these experiments throughout, we find that
the weights borne by pieces of like cross sections, whether
round or square, and of different lengths, were very nearly
the arithmetical mean between the results obtained by
considering them to be inversely as the simple length,
and as the square of the length, successively.
For illustration, take Expts. 1 and 5. If the piece 9'
inches long bore 9901-bs. taking the strength to be inversely as the length, we have this proportion -1: .1: 990:
1,255. Then, takingfthe strength inversely as the square
of the length, we have j,: j:: 990: 1,591. Taking
the mean of these two results, we find (1,255+1,591)-2=
1,423. This is the weight which, according to the rule,
the piece in Expt. 5 should have borne, and it varies only
6 lbs. (less than 4 of one per cent) fiom what it actually
did bear.
Again, take Expts. 1 and 8, in which the lengths were
as 2 to 1. Supposing the weights to be inversely as the
lengths,, and.as the square of.the lengths successively, and




57
taking the mean of the results, we have (1,980+ 3,960)2=-2,970, which is 248 lbs. less than the weight borne in
Expt. 8. But it is also 390 lbs. greater than that borne in
Expt. 7, by a piece of similar dimensions, but an inferior
specimen. It does not seem, therefore, that the rule is
much at fault.
From these facts and others of a similar nature which
have come under my observation, I give the following.
as a good practical rule for determining the negative power of resistance for pieces of similar cross sections, after
knowing from experiment the power of a piece of given
dimensions, and similar cross section. AMiake the power of
D3        D
resistance as -  and as -  successively, and take the mean
L2        L
of the results thus obtained, as the true result; D representingc
the diameter (or side of the square if the cross section be
square,) and L, the length of the piece,
XLIV. This rule will apply to pieces whose lengths
are from 15 to 40 times as great as their diameters, and
perhaps for greater lengths, although in bridge building,
greater lengths will seldom be used.*  But as the length
is reduced to 8 or 10 tim'e's the, diameter, or less, it ia
manifest that the power of resistance increases in a less
ratio than that given in the rule, and even less than inversely as the simple length. For we see by the table of
experiments that a square piece, length equal to 18 diameters, (Expt. 9,) bore at the rate of 45,000 lbs. to the square
inch, which is about one third of the actual crushing
weight for the strongest iron. But according to the rule,
a piece of half the length, or equal to nine diameters,
should sustain 135,000, which is about the maximum for
cast iron, whereas experiment shews that the power og
resistance increases till 'the length is reduced to about 2'
* It is probable that for greater lengths than 40 diameters, the formula
given article 30, would be more nearly sustained than where the length'
is less.




58


diameters. I would therefore apply the rule to square
pieces above 15, and to solid cylindrical, above 12 diameters. From 15 to 10 diameters for square pieces, and
from 12 to 8 for cylinders. I would call the strength as
D, and from those lengths down to 2 diameters, I would
L
add pro rata, according to the differences between the
weights, or resistances determined as above for square
and pieces of 10, cylinders of 8 diameters in length, and
the absolute crushing weight of the iron; i. e., if a square
piece whose length equals 10 diameters bear m pounds,
and the crushing weight for pieces of 2 diameters or less
be n pounds, to obtain the resistance for a piece of 9 diameters, I would call it equal to m+-(n--m)_ 8, and for 8
diameters, 1 would take m+2 (n--n) --8, and so on.
XLV. I havo already observed that in practice, materials should be exposed to much less strain than their absolute strength is capable of sustaining for a short time.
This is a fact well known to every body who has had
experience in building, or has reflected upon the subject,
and the reasons for it are, perhaps, sufficiently obvious,
still, I will mention some of them.
Firstly, there is a great want of uniformity in the quality and strength of materials of the same kind, and no
degree of precaution can always guard against the employment of those containing defective portions, possessing'less than the average strength.
Again; when materials are exposed to a strain, although
it be but a small part of what they can bear, a change is
produced in the arrangement of their particles, whereby
they frequently, if not generally, become weakened, especially if they be frequently exposed to such process.
Hence, it often happens that a piece will break with a less
strain than it has previously borne without apparent
injury.
Now, there are no means of estimating exactly, the




59


allowance necessary to be made for either of these circumstances. Consequently, we can not determine with
certainty how much of any given material may be relied
on with safety, to sustain a given force. We must therefore lean to the safe side, with the greater penchant, in
proportion as the consequences to be apprehended from
a failure are the more disastrous. The failure of a bridge
is liable, in almost all cases, to be a serious affair, even to
the imminent hazzard of life and limb.  They should
therefore, be constructed of such strength as to render
failure quite out of the range of probability, if not absolutely impossible.
It is generally considered that wrought iron of a good
quality may be relied on to sustain a stress equal to one
fourth part of its absolute capacity, with very nearly perfect safety, with reasonable care in selecting, and guarding against defective parts. I have therefore adopted
the rule in practice, of estimating good wrought iron to
be capable of sustaining a positive strain of 15,000 lbs. to
the square inch of cross section.
XLVI. With regard to cast iron, it is not economical
to employ it to sustain tension, and whenever it may be
exposed to that action, I would not rely on it for more
than about 4,000 lbs. to the square inch. I am confidently of opinion, however, that where cast iron is exposed to
a crushing force, in pieces of such length as to be deflected and broken laterally, it may be loaded with safety to
one third of its absolute average capacity. If a piece
exposed to a negative strain have a defective part it does
not diminish its power of resistance to the same extent as
when it acts by tension. The power of negative resistance
being inversely as the flechc or deflection produced by a
given weight, and the fleche depending on the stiffness of
the piece throughout its whole length, the power is manifestly only diminished as the amount of defect multiplied
by the ratio of the length of the defective part, to the whole




60


length; that is, if the piece be defective to the loss of one
fouiurth of its stiffness, for that part of its length to which.is due.one tenth part of the deflection, the deflection will
only:be increased by j x -=9a, and the power of resistance is diminished in the same ratio, whereas the power
of positive resistance would be diminished by -.
The effect of a negative strain, moreover, is believed
not to be so deleterious to the strength of iron, as that of
a positive strain, though I can refer to no particular facts.in corroboration of the opinion.
On the whole, I am induced to estimate the power of
cast iron hollow cylinders of a length equal to 18 diameters, to resist a negative strain, at 15,000 lbs. to the square
inch ofcross section. Solid cylinders, same length, 8,000,
and solid square pieces 10,000.
There is another useful form of cross section for sustaining negative strain, which is that of a cross, thus +.
The power of resistance for this shaped piece, is essentially the same per square inch, as that of the solid square
which will just contain the figure, and may be estimated at
the same rate, calling the side of said square the diameter.
The T formed section will also be sometimes convenient, and possesses about the same power as the x
formed section, and may be estimated as a square of
which the top horizontal, or the perpendicular portion is
the diagonal.
XLVII. The following table, exhibiting the power of
negative resistance to the square inch of cross section, for
hollow and solid cast iron cylinders, and solid square
pieces, under which class may be included the x and T
formed sections, of different lengths, from 2 to 40 diameters, the resistance being estimated at what is considered
safe in practice, will be found convenient in estimating
and proportioning the parts in bridges and other structures
designed to sustain a negative strain.  For Rail Road
bridges, - should be deducted from the quantities in the
table.




61




Power of resistance to the square in. in lbs.
Length in                Sre, X -T
diameters.  Hollow Cyl. Solid Cylinder. Squaeti X   T
2    33333    33333    33333
4    31438    29722    29950
6    29545    26111    26566
8    27652    22500    23183
10    25759    18000    19S00
12    23866    15000    16500
14    20457    11755    14143
16    17900     9562    11953
18    15000     8000    10000
20    12825     6800     8550
22    11156     5955     743S
24     9844     5250     6562
26     8787     4686     5858
28     7921     4224     5280
30     7200     3840     4800
32     6592     3515     4395
34     6072     3238     4048
36     5625     3000     3750
38     5235     2792     3490
40     4833     2610     3262
Lateral or transverse strength.
The transverse strength of bars or beams may be deduced from the positive and negative strength in the
following manner:
Let ab. Fig. C, P1. 1, represent a portion of a rectangular bar projecting from a wall in which it is firmly fixed.
If a weight be applied at w, the uppcr portion will be
stretched and the lower compressed; and where these
portions meet is what is called the neutral plane. Experiment shews that this plane, in rectangular beams, is
central between the upper and lower surfaces, or at least,
very nearly so, for all elastic substances, until they approach rupture. The tendency of the weight at w, then
is to produce rotation about the point c, or the line of
intersection of the neutral plane with the cross section at
c, and the cohesion of the upper portion cd, and the reB




62


pulsion of the lower part cb, tend to resist rotation. Now,
to determine the amount of this resistance, we will first
consider the upper portion; and it is obvious that at every
part of the cross section, the resistance to rotation is as
the resistance to extension, multiplied by the distance of
the part above the neutral plane. But the resistance to
extension is, by the law of elasticity, as the degree or
amount of extension, which is determined by the distance
from the neutral plane. The parts at two inches from
this plane, or the centre of motion, are extended twice as
much as those at one inch, and resist twice as much.
Then, denoting this distance from c by the variable quantity x, the resistance to extension for each part may be
denoted by sx, and the resistance to rotation about c,
by sx2.
Again, representing the horizontal breadth of the beam
by t, t.dx will represent the differential of the section, and
s.t.x2dx the differential of resistance. Then integrating
and making x=cd=-h, we have the whole resistance to
rotation, of the part above the neutral plane = - s.t.h3.
But s.h becomes equal to the positive strength of the material when x=cd-=7, and t.hi = area of the section above
the neutral plane. Therefore, the power of this part to
resist rotation is equal to - the area multiplied by the half
depth of the beam, and the absolute positive strength of
the material, in case the negative strength exceed the
positive.
Now, it is manifest that the part below the neutral plane
exerts exactly the same amount of resistance to rotation
as the part above. Therefore the total resistance to rotation about c, in other words, the resistance to rupture,
is equal to L the whole cross section multiplied by J the
depth of the beam, and by the cohesive strength of the
metal; that is, equal to 4 CtDx~D=4-CtD2, making
D=-db, and C-cohesion, or positive strength of the material.




63


If we wish to determine, then, the greatest weight
which the beam is capable of bearing applied at the point
10, we institute the following equation: TV.L.=- C.tD2,
in which TV=the weight, and L=the length wd. Or, to
make the expression more general, L=the distance from
the centre of motion c, to the line in which the force
(TV) acts.
From the above equation we have TW= C.t.D
6L
XLIX. This formula will enable us to determine the
transverse forces which a rectangular beam will sustain,
when we know the material and dimensions of the beam,
and the lines in which the forces act, are parallel with the
sides of the beam.
In case the positive strength of the material exceed the
negative, the same formula, (W=-- t ), holds true, if
GL
we consider C to represent the negative strength of the
material instead of the positive.
This formula is deduced on the supposition that the
material is perfectly elastic, so as to suffer no permanent
change of shape until the strain produces actual rupture.
There are few substances if any, and certainly wood and
iron are not of the number, that fulfil this condition so
nearly but that considerable discrepancies are found between the deductions of theory and the results of experiment. Indeed, in the case of cast iron, experiment shews
the transverse strength to be fully twice as great as it is
made to appear by the above formula.
C.t.D2
If in the expression C.t., we make L=D, it may be
6L
reduced to - CtD, which shews that the power of the projecting end of a beam to sustain weight at a distance from
the fulcrum equal to the depth of the beam, is only - as
great as the positive, (or negative, in case that be the
smaller,) strength of the beam.




64


This is a convenient way of expressing transverse
strength, viz: as equal to a force of so many pounds to
the square inch of cross section, the force being understood as acting on a leverage equal to the breadth of the
beam in the direction of the force. If we call 18,000 lbs.
to the square inch the positive strength of cast iron, we
may call the transverse strength, (according to the above
deduction,) 1 X 18,000 lbs.=3,000 lbs., meaning that a bar
1 inch square will sustain upon its projecting end, 3,000
lbs. at 1 inch from the fulcrum, and proportionally less as
the distance is greater.
Now, experiment shews that it will sustain twice this
amount, and frequently more, so that in reality we may
reckon the transverse strength of cast iron at about 6,000
lbs. to the square inch.
I know of nothing to which to attribute this great discrepancy between theory and experiment, except a want
of complete elasticity in the material.
Cast iron, when exposed to a transverse strain, suffers
extension on one side and compression on the other; and
the power of resistance to both these effects, increases
very nearly as the amount of extension or compression
till they approach a certain point or maximum, and after
passing this point the power diminishes. Now it is reasonable to suppose, in fact, we can hardly suppose the
contrary, that for a certain interval on each side of the
maximum point, the power of resistance remains nearly
stationary. But this stationary interval is reached on the
positive, much sooner than on the negative side, and the
inevitable consequence must be, that the neutral plane is
transferred farther from the positive side, so as to preserve
the equilibrium between the resistance to extension and
the resistance to compression.  Hence, the amount of
resistance on the positive side is increased, both by the
increased area of the cross section of extension, and increased leverage, or distance from the neutral plane.




65


Moreover, a greater portion of the fibres (so to speak) of
extension, act with their full power; since, while the outside portion is passing through what we have called the
stationary interval, successive portions towards the neutral plane, are reaching and approaching that interval.
Hence, some considerable portion of all the fibers of extension, may act with their maximum power, whereas, if
the body were perfectly elastic up to the point of actual
rupture, only the outside fibers, farthest from the neutral
plane, could act with absolute power, and all other parts,
only in the ratio to their respective distances from said
plane. To illustrate, suppose the extreme positive side,
when extended one inch, reach the stationary interval,
which is one inch more. It follows that, when the outside
has passed to the other limit of said interval, one half of
the positive portion of the bar, will be within the range of
that interval, and act with its maximum power, producing
one third more resistance to extension than the same
fibres could afford if the body were perfectly elastic to
the point of rupture.
I know of no more plausible manner of explaining the
observed discrepancy between experiment and calculation
upon this subject.
L. Wrought iron has something more than three times
the positive strength of cast iron, upon the average, and
if we consider its transverse strength to be in the same
ratio to that of cast iron, the following proportion will
give us the transverse strength of wrought iron: 18,000:
6,000:: 60,000: 20,000.
Hence, the projecting end of a bar of wrought iron an
inch square in a horizontal position, should sustain, at one
inch from the fulcrum, a weight of 20,000 lbs. It begins
to bend considerably, however, with about one third of
this strain, and therefore, in practice, it should never,
probably, be exposed to a lateral strain greater than five
thousand pounds to the square inch.
Bi




66


The principal occasions where wrought iron will be
exposed to a transverse strain in bridge builaing, will be
in cylindrical pins for connecting other parts of the work,
in which cases the forces will act with a certain leverage
which can be nearly determined, and denoting by a the
area of the cross section of the pin in square inches, and
by d its diameter in inches, and by b the length between
the centres of bearing at the ends, we shall have 4 X 5,000
ad+l=-the number of pounds the pin will sustain in the
middle with safety. A pin 1 inch in diameter has a cross
section of.785 inches=a, and if 1=6 inches, we have, by
substituting these values in the last formula, 4 X 5,000 X 1
X.785--6=2,620 lbs., which an inch pin will bear in the
middle when supported at 3 inches from the middle each
way.
It will be seen that this formula regards a cylindrical
bar of a given cross section to be capable of bearing the
same force, acting on a leverage equal to its diameter,
that a square bar of the same section can bear on a leverage equal to the width of its side; a supposition which my
experiments on cast iron sustain, though differing from
the result of calculation,
BRIDGE WITH THE ARCHED TRUSS.
LI. For the general plan of this truss, reference may
be had to figures 5 and 8, pages 10 and 19.
The arch is composed of a number of cast iron pieces,
exceeding by one, the number of principal bearing points,
b.c.d. &c., fig. 8, page 19. In this plan I suppose the road
way to be along the chord of the arch, or slightly cambred
according to circumstances, or the taste of the engineer.
The cross section of the ardh pieces may be of various
forms, but there are only two which I would recommend;
the one is the form adopted for my canal bridges, and the
other is that of hollow cylinders, which is more economi



67


cal, in certain cases, as for railroad bridges, requiring
great strength. I will first describe the former.
aonm, Fig. 13, P1. 1. presents a top view of the arch
from the end to the centre, x and y represent enlarged
cross sections at p and q. Each piece consists of two side
portions, of i formed section, connected by 3 or 4 cross
bars of a T formed cross section; those at the ends being
so broad and thick as to possess sufficient transverse
strength to sustain any weight that may be brought upon
the bearing points, and having a semi-circular notch in
each, so as to form around hole where they meet, for the
vertical bolt to pass through.
For a bridge of 72 feet span, in which the arch pieces
are from 11 to 12 feet long, the depth of the section should
be at least six inches, the top cross of the -1 on each side
about 3 inches wide, and the thickness of metal, average
about - of an inch, so as to give about 12 square inches of
cross section. The endmost arch pieces should also have
diagonal bars from 1 to 14- inch square. The mid rib of
the intermediate cross bars of the arch pieces, should have
a depth from 4 to - that of the side portions. The end
cross bars should be from 4 to 6 inches wide, and from 1.
to 2 inches thick in the middle, according to their length;
or greater depth and less width would be better economy.
The cross bar c. should be about a foot from the end,
and the side portions formed into a sort of foot, (see a, Fig
14, PI. 2,) with a shoulder, a. for the chord chain, hereafter to be described, to act against.
The ends of the pieces are beveled according to the radius of the arch, so as to form a fair joint, and one or both
of contiguous ends should have projections lapping by the
joint, to assist in keeping the ends in place.
The width ah, should be a little more than I the
height of the arch, and the width in the centre, should be
not less than fj the length of the piece.
LII. The chord ak, (fig. 8, p. 19,) is a chain composed
of two sets of long links, extending from a to bfrom b to c,




68


&c., and connected by pins or bars, of a length equal to ab
Fig. 13, P1. 1. The cross section of these chains should
contain adout 6 square inches to each truss, for a 72 feet
common road bridge of 16 feet width of way.
In fig. 14, Pl. 2, A represents a top, and B a side view
of the chain, and its connection with the foot of the arch
piece above described. The end links are twisted 90, so
as to have one end open horizontally to receive the arch
piece, and the other vertically to receive the transverse pin,
C is a side view, and D a cross section near the middle of
the transverse pin, shewing the manner in which the vertical and diagonal parts connect with said pilln.
This pin may be formed in this manner. Take a bar
or plate of wrought iron, 6 to 7 inches wide, and - to
thick, of a length about 2 inches shorter than the pin is to
be. Let this be rolled or swedged into the form of a
trough, whose cross-section is shaped as seen at E. Then
take a bar of the same or a little greater length, about 4
inches wide in the middle, and tapering towards the ends;
the section in the middle having a trapezoidal form as at
F. Let this be bent in the form seen at G, and placed in
the trough formed as above, with its convexity upward,
and the ends welded and swedged to a cylindrical form,
(about 21 inches diameter,) to receive, or pass through the
links of the chain. It will readily be seen at C and D,
how the lower or troughed portion is punched for the reception of the diagonals, which cross one another, and are
secured by nuts below, and how the upper part is pierced,
and tapped for the vertical to screw into. This should be
done before welding. The ends of the pin are slightly
headed in the direction of the length of the chain, to keep
the links from slipping off.
LIII. The vertical is a round bar of wrought iron of
about 1- inches in diameter, as 1 have used them in bridges of from 70 to 80 feet span, the lower end screwed
into the transverse pin as just above described, and the
upper end having a thread cut for 9 or 10 inches, with two




69


nuts, from 1 to 11 inch thick, the one to form a shoulder
to hold the upper end of the diagonals, and the other, on
the end to secure it above the cast iron arch.
Fig. 15, P1. 1, is a vertical longitudinal section, showing
the arrangement at the upper end of the vertical and diagonal pieces. Each diagonal has an eye at the upper end,'is
bent so as to allow the vertical to pass directly through, and
prevented from slipping down by the nut below. For this
lower nut, a key, or a solid shoulder may be substituted
with advantage. The diagonals should be of round iron
about 1 inch diameter, for 72 feet span, and enlarged at
the lower end as much as the screw thread cuts away.
LIV. It will be seen that these trusses, having a width
of base equal 1: or more of the height, will support themselves, laterally, without any assistance; wherefore the
flooring, including the cross beams, may be entirely of
wood, and renewed at pleasure without any disturbance of
the iron work.
It is therefore recommended to use wooden cross
beams, which may be formed of two pieces, as by slitting
the beam vertically, and bolting or pinning the parts together, with the vertical bolt passing through the ends.In this manner they may be put on after the trusses are
put together. Between each two cross bearers, and between the endmost ones and the abutments, should be a
pair of diagonal braces, (2 to 3 inches thick by 6 to 10 inches wide,) to prevent lateral swinging of the road way.
Upon the cross beams, longitudinal joists are placed to
support the floor plank, a thing so simple, and so generally understood, that further description is unnecessary
in this place.
More or less casings and finishings of wood work outside of the road way may be added, according to circumstances, or the taste of the builder.
In my 72 feet canal bridge, the height of truss is 9 feet.
But the cord chains and road way have a cambre of 1 foot




70


in the centre, leaving only 8 feet from centre of the arcn
to the chord chains. A greater height, as we have before
seen, would be more economical as regards vertical
strength; but this proportion is thought to have a better
oppearance, and, as the arches have no extraneous support laterally, it is best not to carry them too high, whereby they would be made top-heavy and unsteady. I would
recommend the height of truss on this plan to be from
Sto -' of the length, for road bridges, and a little more for
rail roads; although for rail roads, I prefer the cylindrical
arch pieces, except, perhaps, for spans of 50 feet or less.
Cylindrical Arch Pieces.
LV. I proceed to describe thdse parts of the truss with
the cylindrical arch pieces, which differ from corresponding parts of the truss above described.
The cylinders are cast with a length fiom 15 to 20 times
the diameter, and a thickness from 4 to 1 of the diameter. The ends are beveled to the radius of the arch,
and are about double thickness for 3 or 4 inches from the
joint, with semi-circular notches, so as to form a round
hole at the joint for a horizontal pin to pass through, to
hold the vertical and diagonal parts, passing in by notches
or openings in the under sides of the cylinders at the
joints.
Fig. 16, P1. 2, shews a side view and section of the joint
of the arch, with its pin hole, and the connections of the
verticals and diagonals. The top end of the vertical is
forked, so as to admit the diagonals side by side between
the branches of the fork, thus bringing the action of all
the forces acting on the arch, to meet near the centre of
the cylinders.
The ends of the cylinders resting on the abutments, are
beveled to a horizontal plane, or adapted to foot piece so
beveled, with a large pin hole, by means of which the ends
of the chord chains are connected with the extremeties
of the arch as seen in Fig. 17, P1. 2.




71


This truss otherwise differs little from the preceding,
except that the chain pins are shorter, as the arch pieces
are not expanded towards the ends, or points of connection with the chains, and the end-most links of the chains
do not require the twisting to form said connection.
For estimating the strain upon the different parts of the
arched truss, and proportioning them accordingly, reference may be had to Articles 13, 14 and 15, and to the
tables and remarks upon the strength of iron.
LVI. It will be seen that these trusses, having but
small width of base, will require lateral support to preserve them in a vertical position, which may be afforded
by braces running up from the cross bearers, and by tying
across the top when sufficiently high. In this case, since
the trusses depend for support upon the cross bearers, in
some measure, and since it is desirable that the iron work
form an independent system, capable of sustaining itself
without the aid of any less durable material, I consider it
advisable (although not absolutely necessary) to use iron
cross bearers, in connection with cylindrical arched trusses.
Iron cross bearers may be formed on the same principles as the longitudinal trusses, by combining wrought
and cast iron where each is respectively best suited to
sustain the force it will be subject to.
Fig. 18, P1. 3, shews an iron cross bearer, and the manner of its connections with the verticals and chain pins;
which latter form a sort of nucleus for the connection of
other parts.
The cross bearer has a cast iron arch-like piece standing
with two feet upon two chain pins of the main bearing
trusses. The verticals passing down through said feet,
are screwed into the chain pins. The thrust of the arch
piece is counteracted by a chord chain embracing its feet.
This chain is composed of three links, a little twisted so
as to lie nearly flat wise, when linked together, and long
enough for each of the two connected ends to embrace




72


the vertical bolt as seen at a. The vertical bolts have two
nuts at the lower end, (one above and the other below the
chain and diagonal,) and at the upper end, a countersink,
or a common bolt head, with a key or nut below the arch
piece and the diagonal; the diagonal being.a or - inch
rod with an eye at each end, and bent so as to suffer the
vertical to pass square through.
In case a nut be used under the upper end of the diagonal, the vertical must be enlarged by upsetting or otherwise, where the thread is cut, so that the nut may slip up
from the bottom, or the head at the top must be replaced
by a nut.
The arch piece has a T formed cross section, with such
enlargements where the bolts &c. pass through, as to possess the same strength as at other parts.
The verticals of the main trusses may be of round bolt
iron, with a wrought iron brace as shewn on the right
hand side of the figure, or formed of two flat bars of wrought
iron, (as seen edgewise on the left hand of the figure,)
with a thin cast iron plate edgewise between, forming an
H formed cross section, the two sides wrought, and the
cross, cast iron,broad in the middle and tapering to the ends,
the whole secured together by rivets or bolts passing
through the wrought bars, and either through the cast
iron mid-rib, (transverse holes and extra thickness at the
holes, being cast in it for that purpose,) or on one side
and the other alternately. The lower end of the vertical
should terminate in a round part and screw to pass through
the cross bearer, and enter the chain pin as before stated,
and the upper end, forked and punched to connect with
the arch cylinders of the longitudinal trusses.
When the virtical is formed in this way it will have
more stiffness, and the supporting brace need not connect
so near the top, but may be of wrought or cast iron, connecting with the vertical 3 to 4 feet or more from the bottom, and with the arch piece of the cross bearer, near the
angle where the rail is placed. The brace may be cast
in the same piece with the arch.




73


The sizes of the parts of the cross bearer will depend
on the length and distance asunder. For a single track
rail road bridge, they should be from 14 to 15 feet long
from centre to centre of trusses. The cast iron part should
be about 4 inches broad and deep, and contain about 6
square inches area of cross section, if 12 feet apart, and
more or less, as the distance is greater or less than 12 feet.
The cast iron brace to give lateral support to the main
trusses, should have a cross section of 2; or 3 square
inches. The chord chain should contain 2 square inches
cross section for cross bearers of 3 feet depth and 12 feet
apart, and more, as the depth is less or the distance asunder greater, and vice versa.  The vertical bolts of the
cross bearer should be about 1 inches diameter for 12
feet apart.  The diagonals should be about I inch in
diameter.
LVII. The lateral support necessary to be provided
for the trusses, can not be exactly estimated. It depends
essentially upon the force of the wind (which can not be
very severe, as so little surface is exposed in an iron
bridge,) and upon the centre of resistance in the arch, not
being exactly in the same vertical plane with the centre
of thrust, whereby is produced a tendency to lateral flexure. If we suppose the distance of the axis of thrust from
the axis of resistance, in the middle of the arch, to be ~
the diameter of the arch cylinder, and that the axis of resistance have a circular curve from end to end, which is
probably more than would ever be true in practice, the
tendency to flexure laterally would not exceed the 75th
part of the thrust of the arch, say for a 100 feet truss, about
1,600 lbs. distributed through the whole length of the
truss. A 100 feet truss should have about 8 verticals, and
if each of these possess sufficient stiffness, and be so braced as to afford 200 lbs. of lateral support to the arch, a
failure in that respect would be quite improbable, if not
absolutely impossible.  In using wrought iron braces,
B




74


then, it would be proper to make them of 1 to l1 inch
iron, according to the length.
The depth of tle cross bearer from the arch piece to
the chord tie, should be from 2 to 4 feet; not less than 3
feet when there is sufficient space for such a depth.
LVIII. The lateral swing of the road way, is another
tendency to be guarded against, and this, like the lateral
tendency of the arch, can not be exactly estimated. The
best means of counteracting it is, by horizontal diagonal
tie braces of wrought iron from - to 1- inch diameter,
for 100 feet span, between each two cross bearers, and
these, like the vertical diagonals in the main trusses,
should be larger towards the ends, and smaller in the middle of the span.
These should be fiurnished with swivel nuts for adjustment, (see Fig. 19, P1. 3,) and may be formed as seen at
a, having a head and swivel at one end, and a screw at the
other, with an angle and a hole from one to two feet from
the screw end. Thus formed, it may be interposed between
the cross bearer and the chain pin, so that the hole may
receive the vertical of the main truss, after it has passed
through the foot of the cross bearer, as before described.
String timbers to support the iron rail may be placed
over the upright bolt of the cross bearer. Or, truss-work
resting on the uppermost nut at the lower end of said
bolt, and of such height as to carry the track over the top
of the cross bearer, may be employed, which will give
more stiffness to the track.
The height of the truss for a rail road bridge, should be
from 1 to - the length of span, and no cambre to the chord
chains.
For a span from 40 to 100 feet, (affording from 4 to 8
bearing points, or cross bearers,) this plan is little if any
inferior to any that can be adopted.




Cancelled Truss Bridge.


LIX. For a general view of the truss, see Fig. 7, page 12.
In this plan the part a.o.i.h is composed of hollow cast
iron cylinders, similar to those composing the arch in the
last described truss, but not beveled at the ends, except at
o,i,a, and t. The chains ah also, are formed and connected
in the same manner; but the links of the chains increase
towards the middle of the truss, as shewn to be necessary
in reference to Fig. 7. The verticals act only by thrust
in this plan, and consequently are of cast iron; may be
tubular, or of a x formed cross section, larger in the middle, and tapering towards the ends; the upper end forked,
as in the verticals of the cylindrical arched truss above
described. The lower end may be cast with a wrought
iron screw, and connect with the cross bearer, lateral braces and chain pin, precisely as in the said arched truss, in
case of the cross bearers being placed in that position.
The same manner of securing the trusses laterally, and
preventing lateral swing may be adopted.
The diagonals are connected at both ends in the same
manner as in the cylindrical arched truss, except that the
main diagonals, or those which act when the bridge is loaded uniformly, and which are shewn by the dotted lines in
Fig. 7, are in pairs, (with the counter diagonals between
them,) and larger towards the ends, as the stress increases in those parts. The cross bearers are made in the
same manner as above described for the cylindrical arched trusses.
The cancelled, tapezoidal truss, if rightly proportioned,
is from 5 to 10 per cent cheaper than an arched truss of
the same strength, and for rail road bridges, is generally
to be preferred.
It is decidedly preferable when the track may be placed
on a level with the top of the trusses, in which case, the
distance between trusses need not exceed the 10th part
of the length of span. Hence a considerable amount of




76


material is saved in the construction of the cross bearers,
and in lateral bracing.
The preference to be given to the trapezoidal truss in
this case, is on account of the bearing points, (the joints
of the cylinders,) being in the same horizontal plane, and
not at different elevations as in the arch.
The cross bearer for a track on the top may be as seen
in Fig. 20, P1. 3. The cast iron portion straight, and
formed to fit the cylinders at the ends, where they are
secured by bolts. On the other hand, the wrought iron
part, which acts as a chord chain in the other cross bearer,
acts as a suspension chain in this, having its connections
essentially the same in both cases. The verticals and diagonals, as well as the mode of applying the track timbers,
are also the same as in the case of Fig. 18.
The lateral, or horizontal diagonals, may be as shewn
in Fig. 19, with or without the hole at the angle, and
passing through elongated holes near the ends of the bearer, may be secured by pin or wedge.
The chain pin for trusses sustaining the track on the
top, need not be adapted to receive the vertical by a hole
in the upper side, but may be formed by welding the ends
of 4 square bars, rounding the welded parts to receive
the chain links, and opening the middle portion for the
diagonals to pass through. Fig. 21, P1.3, shews a middle
cross section of a pin formed in this manner, with the diagonals passing through, and the vertical standing on the top.
It will be most economical to make the height of the
truss in this plan, equal to - the length of span, but circumstances may sometimes render it advisable to reduce
it to - or I. The diagonals should incline at 45~, though
a small deviation may be made without great detriment
to economy.
This plan, with the single cancel, as in Fig. 7, is good,
perhaps the best, for any span under 75 feet. If carried
beyond that, it would, perhaps, be best to give more
length without increasing the height, by making more




77


bearing points, to avoid the disadvantage of too long cylinders in the top rib, and long verticals.
LX. From 70 or 80, to 160 feet stretches, should bemade with double cancels, or two crossings of diagonals,
as seen in Fig. 23, P1. 4. The formation and connection
of the parts in this case are precisely as in the above, except as follows: 1st. The end cylinders cb and cd incline
at 600 instead of 450 with the horizon, and must be beveled accordingly. Also, these parts having greater length,
will usually require to be cast in 2 pieces, and will require
the tie and brace f, as well as lateral stiffening, which
may be done as hereafter described for stiffening the verticals. Or, when the track is on the top, by a transverse
bar at c, and diagonals (Fig. 23, PI. 4,) from one truss to
the other, which will also afford lateral support for the
ends of the trusses. If the track be at the bottom, as
from a to d, such an arrangement would interfere with
the passage of the trains, and lateral support must be provided at the ends by braces or guys (gg, Fig. 23,) that
may not produce such interference. With the track at
bottom also, the end-most verticals will act by tension
only, and such materials and connections should be provided as will afford the necessarry resistance.
With the track on the top, the end-most verticals are
useless and unnecessary, if other means than the brace rf
(Fig. 22) be used to stiffen ab, and the two diagonals at
each end represented by dotted lines, are unnecessary to
the strength of the structure in all cases, unless for very
short spans. It is not to be expected however, that the
proportions of a bridge on this plan will be assumed without such an analysis as to determine the amount and kind
of force each part must sustain, which done, it will readily
be seen what parts are necessary, and what proportions
should be given them.
Another modification which the double cancelled truss
requires is, an opening in the middle of the vertical, for
B2




78


the diagonals to pass through. For this purpose, and to
give them the stiffness their great length renders necessary, without too great an expenditure of materials, they
may be formed, when of considerable length, as shewn in
Fig. 24, P1. 4.
The middle or cast iron portion is in two, or may be in
4 pieces, and connected and stiffened by the 4 small bent
wrought iron bolts b.b, &c., (two only appearing in each
view,) passing through flanges formed for that purpose,
and strained out in the middle by a plate as seen at a,
interposed between the two cast iron parts forming the
main body of the vertical. The castings may be tubular,
or of a x formed section; if very long, the tubular form
will be preferable.
The Cancelled Truss without vertical Struts.
(See Fig. A, p. 14.)
LXI. This truss may be constructed of iron, with cast
iron cylinders and horizontal chains, the same as when
the vertical strut is used, and the description relating to
those parts need not be here repeated.
The verticals ob and ig, and the two diagonals oc and if,
(the track being along ah,) should be wrought iron, and
so connected as to act by tension only. Of the other diagonals, those which act mainly by thrust, may be formed
of cast and wrought iron as shewn in Fig. 25, P1. 5. ab is
a view as it would appear when looking lengthwise of the
truss, and cd, when taking a side view. It has a cast iron
portion with a H formed section, a hole in the centre for
the other diagonal, ef, to pass through, and 4 wrought iron
rods, each running fiom the centre (where they receive
the diagonal ef through an eye or loop made for that purpose,) to the end; i. e., two to each end. Those terminating at the upper end b or d, have an eye to receive the
transverse pin connecting the diagonals with the cylinders.
Those terminating at the lower end,pass through the chain
pin, and are secured by screw nuts.




79


These rods being strained out by short screw struts as
seen at g.g, give stiffness to the piece between the centre
and the ends, and being wedged, or otherwise made fast
to the crossing diagonal ef, in the centre, are in a condition
to resist a crushing force to advantage.  The wrought
iron rods should be sufficient to sustain whatever tension
the piece may be exposed to.
Those diagonals which act slightly by thrust, but principally by tension, may be of round wrought iron rods, of
sufficient size to sustain any force that may act upon them,
and should be so connected as to act by either tension or
thrust, without play or motion in changing from thrust to
tension, and the contrary; and for this purpose the eye at
the upper end should be made snug to the connecting
pin by wedging, if necessary, and the lower end, passing
through the chain pin, should have a nut on both sides.
These pieces passing through those above described, in
the centre, are secured at that point, and thus, the better
enabled to stand the small thrust they are liable to.
Before constructing a bridge on this plan, it should be
considered whether the track is to be at the top or bottom.
Then the kind and amount of stress upon each part, due
to the weight of the structure, should be ascertained, and
these forces added to, or subtracted from (according as the
signs are like or unlike,) the maximum effects due to the
variable load, will shiew the forces each part must be capable of sustaining, and the construction may be proceeded
in with confidence.
These trusses may be used with either wood or iron
cross bearers, and when not high enough to be connected
across the top, must be supported laterally, by braces or
guy rods from the cross bearers to the cylinders. When
the track is on the top, the same arrangements for lateral
support may be used as in the case of the truss with vertical struts.
The preceding details, it is hoped, will be found sufficient to enable the advantages and excellencies previously




80


pointed out as appertaining to the three general plans of
trussing, (viz., the arched truss, and the cancelled, trapezoidal truss, with and without the verticals,) to be made
easily available, in the construction of iron bridges for
rail roads, for all spans under 160 or 180 feet. The modifications required to adapt the same to the purposes of
common travel will readily suggest themselves to the
practical engineer and skillful mechanic.
It is not expected that these details are so full and
clear as to leave no necessity for the exercise of ability,
skill, and judgment in carrying them into practice. The
plan and purpose of this work would not admit of such
minuteness of detail, if the time, experience and ability
were not wanting to accomplish the object. Neither is it
presumed that some of the details that have been given,
may not be susceptible of material improvement. Still, I
do entertain the fullest confidence that nothing is here
given but that is highly feasible, and worthy of being used
as a guide, where better plans and modes are not known.
LXII. I have not yet spoken of stretches of more than
180 feet; not that this length forms a limit beyond which
it would be impracticable to construct bridges on these
general principles. But for greater spans than what is here
mentioned, I would suggest the following modification
of the truss Fig. 7, p. 12.
It is desirable that a transverse bearer should be contained in the structure, at least, once in 12 or 15 feet.
Hence, in long stretches the verticals and diagonals
become very numerous, and the former being very long,
and acting by thrust, must necessarily act to a great disadvantage. It is proposed therefore, to form a simple truss
as in Fig. 7, of a height of from - to  the length, containing from 5 to 7 full length verticals, (or from 3 to 5, dispensing with the end ones,) and between each two of
these, make use of suspension chains and 2 or more short
verticals, when the track is to be on the top, or sub-arches




81


and short verticals when the track is to be at the bottom,
Fig. 26, P1. 5, shews this arrangement, one half with
the track at the top, and the other with the track at the
bottom.   When the track is below, small suspension
chains will be required to sustain the weight of the cylinders between the main bearing points, as shewn in the
figure.  Or there may be independent trusses, or
bridges extending from one of the main bearing points to
another.
I have not perfected the details of such an arrangement,
but have so far considered the subject as to be satisfied of
the feasibility of it, even for spans of 400 or 500 feet, not
to say more. This plan admits of using wire cables to
advantage.
It has been proposed by an eminent English engineer,
(Mr. Stevenson,) to construct a tubular, or box bridge over
the Menai Straights, out of plates or sheets of wrought
iron about 1 inch thick; the box to be 15 feet wide, 30
feet high, and 450 feet long, and weighing upwards of
1,500,000 Ibs, and it is doubted, even by the projector,
whether this will be sufficient for the purpose.
Now, I have estimated, with considerable care, the probable amount of iron that would be required for a bridge
of 450 feet on the plan shewn in Figure 26. In this estimate I have reckoned the safe load of wrought iron at 12,000 lbs. to the square inch, which is about 15,000 lbs. for
that portion which sustains the dead weight of the structure, and 10,000 for that which supports the moveable
load, instead of 10,000 lbs. for the whole, as I have adopted
the rule of estimating for rail road bridges of ordinary
lengths, for reasons to be explained hereafter.  This
course seems warrantable in the present case, since, besides that so large a portion of the strength of the material goes to support the dead weight, whatever effects may
be due to the motion of the additional load, will be proportionately much less, acting on such a mass of material,




82


than upon a short bridge of only a few tons weight.
My estimate shews a gross amount of about 560,000 lbs.
in about equal portions of wrought and cast iron, to sustain
900,000 lbs. besides the weiglit of the structure. We may
put this amount, in round numbers, at 600,000 lbs., and the
tubular bridge, as above described will require at least
two and a half times as much iron, all wrought, to sustain
the same load, in addition to its own weight, with the same
stress on the material.
As a corollary to what precedes, it may be remarked
that, as a 450 feet bridge will support twice and a half its
weight, one of 900 feet will weigh four times as much,
and sustain twice as much, or will sustain 25 per cent.
more than its own weight, with the same stress of material.
Hence, no good reason appears against the practicability
of making a trussed bridge of 900 feet long, (by 150 feet
high,) that would be safe for ordinary travel, but not for
a rail way, (unless the truss be proportionally higher.) It
is probable, however, that fiom 4 to 5 hundred feet would
form a limit, practically, beyond which it would scarcely
be advisable to undertake the construction of a trussed
bridge.
Effects of rapid motion of Trains, and remarks upon
the forces to which Bridges may be exposed.
LXIII. I have given one fourth the absolute positive
strength, and one third the negative strength, as the safe
practical strength of iron, beyond which it is not prudent
to load that material. This has reference to dead forces,
and not, of course, to forces brought instantaneously to
act on the material.
It is well known that, on an elastic material like iron, a
given force will produce twice as much effect when instantaneously applied, as when brought gradually to act.
Any one can illustrate this by taking a pound weight,
holding it in contact with the dish of a spring balance,
and letting it go suddenly,'when it will be found to move




83
the pointer to the two pound mark, after which it will settle and remain on the one pound mark.
Now, upon a bridge for common travel the maximum
forces to be provided for are, the weight of the materials
in the structure, and a crowd of men or other animals, all
of which acts principally as so much dead weight. Hence,
for such bridges, it is proper to consider the whole area
of the road way, covered with men, which is about 100 lbs.
to the square foot, as the greatest load to which the bridge
can be exposed. The effects of such a load, upon the
whole or any part of the platform, added to those of the
weight of the structure, are the forces which the bridge
should be calculated to sustain; and for that purpose, it
is sufficient to provide in each part, 1 square inch cross
section of good wrought iron to every 15,000 Ibs. of tension to be sustained, and for thrust, to provide cast (or
wrought) iron, according to the table for the safe practical strength of cast iron.
The methods of estimating the stress of the several
parts of the structure, were given in full in the first part
of this work.
In regard to rail road bridges, the enquiry naturally
suggests itself, whether the ponderous engines and trains
dashing over with lightning velocity, do not produce effects
approximating to those of forces instantaneously applied
Doubtless some greater effect is produced upon some
parts of a bridge by the rapid, than by the slow transit of
a train. But with respect to the horizontal parts, (and
the arch, in case of the arched truss,) which suffer their
maximum strain under the full load of the bridge, sufficient time elapses between the first and the last portions
of weight added, to obviate any tendency to mischief
from the sudden application of force. With regard to
the diagonals and the verticals, it is doubtful whether the
same remark would not hold essentially true.
"When the equilibrium of an elastic body is disturbed,




84


it vibrates about the point of equilibrium, with longer or
shorter times of vibration, according to distance of the motion and the mass of the vibrating body. If a weight be instantly left to act upon the lower end of a suspended iron
rod, it will stretch the rod twice as far, abating what is
due to atmospheric resistance and want of perfect elasticity, as it is capable of holding it at for any length of
time. The elasticity of the rod will then preponderate,
and will raise the weight nearly to its original position.
The weight again will preponderate in turn, and thus the
vibration will be kept up, till the want of perfect elasticity
in the iron, and the resistance of the air, shall finally induce a state of rest. Now, we know that these vibrations
are extremely short, as to duration of time, as well as extent of motion; quite inappreciable to the senses, unless
the rod be very long; and if the weight be applied so
gradually that a space of time equal to several of these
vibrations, elapses from the incipiency to the end of the
application, the vibration must be reduced to almost nothing, if not entirely destroyed. With regard, then, to the
diagonal of a bridge, the weight has to traverse a space
of 10 or 12 feet from the time it begins to act, until it
comes to produce its full action, requiring, at a velocity of
60 ft. in a second, or - of a mile in a minute,  part of a
second of time; a space greater than many of the vibrations above spoken of.
I conclude then, that theoretically, no allowance need
be made for the rapidity of the passage of rail road
trains, and, that if the rail be perfectly straight and even,
and the motion true and equable, there is no more danger
to a bridge friom a rapid than a moderate transit.
But practically, this perfection in the adjustment of the
rail and the movement, can not be secured; and consequently it is reasonable to suppose there is, in reality some
more liability to failure by the quick passage of a rail
road train, than by the same load at rest on the bridge.




Again, the adoption of iron bridges for rail roads, is a
new thing, which many regard in the light of an " experiment," about which many wise doubts are entertained;
and to reduce the chances of failure in this incipient
stage of the matter, which would serve to weaken confidence, and delay the introduction of the change, as well
as be attended with disastrous consequences to life and
limb, perhaps; I have thought proper to provide bountifully of the means for sustaining all the forces, both actual and contingent, that can ever come to act in the premises.
For that purpose, I have adopted the general rule for
R. R. bridges, of estimating wrought iron to sustain only
10,000 lbs. positive strain to the square inch, (only onesixth the absolute capacity,) and cast iron hollow cylinders, of a length equal to J 8 diameters, from 10 to 12,000
negative strain, or about a fourth part of the actual capacity; and in like proportion for other forms and dimensions of pieces. Consequently, in estimating for R. R.
bridges, I diminish the quantities given in the table for
the practical strength of cast iron by about one quarter.
As to the gross load for a R. R. bridge, the heavy engines now used in this country, comprise about 20 tons
of weight within as many feet of length.  The heavy
freight trains weigh, in general, not over 1000 lbs. to the
foot run. But I have thought proper to estimate bridges
as liable to a load of 2000 lbs. to every foot, upon the
whole or any part of their length.
The providing of abundant strength seems the more
proper, as the tendency has been and still is, to increase
the weight of engines and loads to the utmost capacity of
the track, and hence an iron bridge, intended as a durable structure, should be proportioned with reference to
such changes and tendencies.
I have now given such details of the plans I propose
for the construction of Iron Truss Bridges, as appeared to
D




86


me necessary to guide the skillful builder in the erection of
bridges, for rail roads or common roads, of all lengths
which will be likely to be undertaken upon the Truss
principle. I will, therefore, leave this part of the subject
for the present.
Suspension Bridges.
The general principle of Suspension Bridges was
briefly alluded to in Article 6. It is not my purpose to
go much into particulars with respect to this kind of
bridges. My object is not to compile from works already
before the public, but to give such results of my own
labors and investigations, as are believed to possess originality and value. Not having given a large share of attention to the details of Suspension Bridges, I shall have but
little to offer.
The longest spans ever built, have been on the suspension plan. In fact, this plan has advantages for very long
spans, which render it practicable to construct longer
stretches upon this than upon the truss principle. In the
truss bridge, a large portion of the material does nothing
towards directly sustaining the weight of the bridge and
load. The horizontal portions, for instance, in trusses Fig.
7 and Fig. A do not directly sustain a pound of weight.
They simply act and react upon one another through the
medium of the oblique parts, and are essential to enable
the latter to perform their functions. The chord chains also,
in the. arched truss, only sustain the horizontal action of
the arch.
Now, all of these parts add to the weight of the structure, and proportionally to the necessary amount of material.
In the suspension bridge also, the oblique action of
the suspension chains gives rise to horizontal forces which
must be counteracted. But the material by which this
counteraction is produced, is situated outside of the piers or
abutments supporting the spans, and consequently, do not




87


add to the weight to be sustained between said piers or
abutments. Therefore, a less proportion of the strength
of the material is exhausted in sustaining the structure itself.
But we have seen that the weight of a bridge increases
in the duplicate ratio of the increase in length, while its
power of sustaining weight, only increases in the simple
ratio of increase in length; and the limit of the practicable length of span is, when the weight becomes equal
to the whole power of the material to sustain.
It is manifest, then, that the trussed bridge will sooner
reach that limit than the suspension bridge, the latter
containing a less amount of material in proportion to its
strength, or power of sustension.
If the trussed bridge require fifty per cent more material for a given length to sustain a given weight, than a
suspension bridge, the latter will sustain its own weight
till the square of its length is fifty per cent. greater than
the square of the greatest length at which the former can
sustain itself.
This advantage of the suspension principle, renders it
worthy of some consideration for very long stretches,
where the weight of the structure forms so large an item
in the whole amount of weight to be supported.
Suspension bridges have been used with tolerable success for common travel, where the moving load is trifling,
compared with the weight of the structure itself. The
most important one now in use in this country, is that
over the Schuylkill, near Philadelphia, being 343 feet
long, and 27 feet wide. It is sustained by wire cables
passing over towers at the corners of the bridge, the ends
of the cables carried down obliquely and anchored into
the ground outside of the towers, and the central portions
hanging in a catenarean curve between the towers. The
road-way or platform is suspended from these curved
cables. This is the general plan of constructing suspen

*




88


sion bridges, using sometimes wire cables, and sometimes
chains formed by connecting bars of iron. Much longer
ones have been constructed in Europe, even two or three
times as long as the Schuylkill bridge, some of which
have endured, while others have failed.
A serious difficulty in the use of suspension bridges is,
the want of fixedness or stability among the parts. The
curve of the chains being left to find its own equilibrium,
yields to every force that tends to disturb that equilibrium,
and hence arises an undulatory motion, whenever the
bridge is exposed to the passage of heavy loads, or to the
action of strong winds, which is frequently attended with
disastrous consequences. This quality renders these
bridges utterly unfit for rail road purposes, as they are
usually constructed. No plan has yet, as I believe, been
devised and successfully executed, to obviate the difficulty. Similar obstacles are encountered, to those alluded
to in speaking of the feasibility of sustaining the horizontal thrust of truss bridges by the action of abutments and
piers.
I have a plan which is believed to be original, and
which is certain to obviate the difficulties of undulation,
and render the suspension bridge as applicable to rail
roads as to common roads. It is not, however, to be
expected, that a bridge can be built that will sustain a rail
road train of hundreds of tons, at so small an expense as
will suffice for a common road bridge, seldom required to
support more than a few thousand pounds.
LXV. This is my plan. Divide the stretch into a convenient number of parts, of 25 or 50 feet, or any convenient length; as by the points b.c.d.ef., Fig. D., P1. 5. At
each of these points is to be provided support for a
weight, say of one ton to each foot between each two of
these points, in addition to the weight of a proportionate
part of the structure. The former of these weights may
be represented by w, and the latter by w', and their sum
by W.




89


Now, from a to b, let there be an inverted arched truss,
the horizontal and vertical parts being of cast iron, (the
former, hollow cylinders,) and the rest of wrought iron.
Let the end b, of this truss, be sustained by a chain or
cable hb, descending obliquely from the top of the supporting tower ah. If ab=ah, which we will suppose for the
present, the chain hb must be sufficient to sustain a
stress= WT/2 and the horizontal hollow cylinders ab, must
sustain a negative strain or thrust equal to W+the action
produced by the extreme tension of the curve chain akb.
We have now provided, (considering the points a and I
to be fixed,) support for the point b, and for the space ah.
For the point c, let fall two chains, lc and ic, the former
(hc) being capable of sustaining a stress equal to  T/5,
and ic, capable of sustaining a stress equal to - WT/17.
For the point d, the two chains hd and id, each capable
of sustaining J WV 10, will be sufficient.
The points e and f are provided for in the same manner as b and c. It is obvious that any other number of
points might be assumed, the same principle being applied
to support them.
If the distances bc, cd, &c., be greater than can be
economically spanned by simple beams, truss-work may
be employed to advantage, either of wood or iron, upon
some of the general plans, previously, or hereafter to be
described in this work.
Similar provisions by bracing, &c., must be resorted to
to guard against lateral swing, as is made use of in the
case of truss-bridges.
In order to secure the permanency of the point A, and
prevent the tower from being drawn inward by the tension
of hb, hc, &c., a guy chain hl, descends obliquely, with
an inclination equal to that of the resultant of all the
antagonist forces, and of a strength equal to the aggregate of those forces, (or their resultant, according to the
mode of arrangement.)
n2




90


The chains hb, hc, hd, &c., should, be supported at suitable intervals, to prevent them from assuming a curved
form, by which they would, in a measure, be liable to the
same difficulties from undulating motion as the common
suspension bridge; though to a much less degree. This
support may be given to- the chains by vertical rods or
studs running up from the platform, or by a curved chain
himni, from which those below may be suspended, and
those above, supported by stiff rods. Whatever may be
supported by this curved chain, will leave so much less
to be sustained by other parts of the structure, and the
latter may be proportionally smaller.
To estimate the quantity of iron in this structure, let us
assume ag=450, and ah=75 feet=ab. Now, the material in each part, is as the stress multiplied by the length
of the part. But the stress is as the weight sustained,
multiplied by the length, therefore, the material is as the
weight, multiplied by the square of the length.
Making ab=l, lib will be equal to /2 and ib2=2.
But the weight sustained by hb,= TV. Hence the material in hb may be represented by hb2 W=2W.
Again, hclc2=a2+ c2-12 +22 -5, and the weight sustained by he, being - WI, the material will be represented
by  TVWx5=--W.
In like manner, the material in lid, may be represented
by - Wx 10-=5 W, and the material in le, by - W17= - W.
Adding these amounts together, we have 16W to represent the material in hb, ch, hd, and he, and 32 W for the
same, together with the corresponding chains ci, di, &c.
Now, the unit in this expression=75 feet, and W=150,000 Ibs. plus I the weight of the structure between piers,
which we will assume at 66,000 lbs., making W- 216,000
Ibs.
To sustain this weight at 12,0001bs.to the square inch,will
require 18 square inches cross section of iron, or about
60 lbs. to the foot. This multiplied by 75, gives 4500 lbs.,
which substituted for W  in the expression 32 TW,




91
gives 144,000 lbs., as the weight of material in the parts
in question.
The tension of the guy hl, will be about 51 W and the
length, say 250 feet=31 ab. Therefore the material in
lh, will be represented by 18 W, and a like amount for
the opposite end, making 36- W, whieh gives 165,000
lbs. as the weight of material, making a total of 309,000
lbs. for main suspension chains or cables. To this should
be added, probably, 20 per cent for vertical support to
chains, extra weight at joints, or connections, making
371,000 lbs.
We now want 5 heavy cross bearers at b.c.d. &c., for
which say............ 12,000 lbs. cast, & 8,000 wrought,
6 truss bridges of 75 ft., 48,000 "  "  48,000  "
Cast iron saddles on
towers, &c.,........  12,000  "  "
Horizontal guys and diagonals to prevent
lateral swing, say................  10,000  "
Add amount fr'm above............. 371,000  "
Total,...........  72,000...... 427,000
This makes the weight of iron, in round numbers, 500,000 lbs., of which, say 300,000, are between piers. Adding to this 70,000 lbs. for rail track, makes 370,000 lbs., as
the weight of that part of structure between piers. Now,
the structure is calculated to sustain 6 1V=1,296,000 lbs.,
from which, deducting 370,000, leaves 926,000 as the effective strength of the bridge.
In a preceding article, (62) I made the amount of iron
in a 450 feet truss-bridge, by liberal estimate, about
600,000 Ibs, and the effective strengh 900,000 lbs.:
from which it appears that the truss bridge requires about
100,000 lbs. more iron to sustain the same weight, than
the suspension bridge.  But it does not follow that the
expense would be in the same proportion. On the con



92


trary, the suspension bridge would cost considerably
more, in consequence of being mostly of wrought iron,
while the truss-bridge is composed of one half cast iron,
which does not cost more than half as much for the same
quantity.
Besides this, the towers to support the suspension
bridge, and the pits for securing the guys, add greatly'to
the expense.
I conclude then, that unless some better and more economical plan can be devised for adapting suspension
bridges to R. R. purposes than I have yet met with, the
truss bridge is decidedly preferable for any thing less
than 500 feet, unless it be in very peculiar circumstances,
and such as have never come within my observation. If
cases should occur warranting attempts to construct R. R.
bridges of greater stretch than 500 feet, the suspension
might deserve a preference.  But such will occur so
rarely, if at all, that I choose to leave them for the special
investigation of those into whose hands their management may fall, rather than devote to them, in this work,
the time and space which I consider would be more
profitably occupied in matters more within the range of
ordinary practical bridge building.
I will here make one remark in reference to the proposed " Niagara Suspension Bridge."
I have seen it stated that the plan proposed is, " the
combination of the suspension chains, (or cables,) with a
heavy cast iron arch," which, it is thought, will obviate
the difficulties of undulation.
How much or how little this may differ from a truss
bridge, I can not judge, without a more full description
of the plan than I have yet seen. I will hazard the opinion, however, that the modification of the truss shewn in
Fig. 26, is better suited to the purpose than any combination of arches and suspension chains that can be devised,
The banks of the river being very high, the bridge
would be so placed as to have the rail track on the top.




93


while a passage-way for carriages and common travel
could be arranged underneath, perfectly secure from all
danger, except, perhaps, that of frightening horses by the
passage of trains overhead. It would probably be best,
however, not to suffer horses to go on to the bridge when
trains were in hearing.
WOODEN BRIDGES.
Preliminary Remarks upon the Strength of Timber, &c.
LXVI. The qualities of wood as a building material,
have been extensively treated of by authors, with whose
works the public have long been familiar, with a degree
of ability and research to which I can make no pretensions. I shall therefore only simply state the conclusions
I have arrived at, from reading and observation, with respect to the average absolute strength, (positive, negative,
transverse, and to resist splitting, in certain cases,) of the
timbers principally in use for building purposes, as also,
the forces they will bear with safety in various circumstances. At the same time, I shall, of course, leave it to
others to adopt my conclusions for their own practice, or
to modify or correct them, according as their greater
experience or better judgment may dictate.
Pine timber in this section of country, is perhaps to be
ranked as the most valuable timber for building, in use.White oak and some other varieties are preferred for
some purposes, as being harder and somewhat stronger,
and especially better calculated to bear a negative or
crushing force, whether acting parallel with, or at right
angles to their fibres. But in what follows, I shall principally have reference to the ordinary white pine of this
country.
Some writers and experimenters estimate the absolute
positive strength of pine, at 10,000 lbs. to the square inch.
of cross section, and the safe practical strength at one



94


fifth of this amount, or 2000 lbs. to the square inch. I am
not in possession of facts that would warrant the conclusion that this estimate for the absolute strength is too
high. But I have been induced to adopt the rule for
practice, of not relying on pine to sustain more than 1000
lbs. to the inch, for that portion of the piece not cut or
separated to form connections with the rest of the structure.
The negative strength of pine is not over about half the
positive strength. But I consider it reliable under a
crushing force, (parallel with its fibres) of 1000 lbs. to the
square inch, in pieces of a length not more than five or
six times the diameter. And for pieces of the length of
18 times the diameter (or side of the square) I would
trust it with 700 lbs. to the square inch.
From a length of 18 down to 6 diameters, I would add
pro rata of the difference between 700 and 1000 lbs., and
from 18 diameters upward, make use of the rule given in
regard to the negative strength of iron.
The following table, giving the lengths of pieces in
terms of the sides of their cross-sections, or their diameters in the directions in which they are liable to be deflected, and the number of pounds to the square inch which
they may be relied on to sustain with safety, may be of
utility in practice. For lengths above 40 diameters, the
strength is reckoned as the cube of the diameter divided
by the square of the length.
Length.  Pounds.;.rve th.  Pounds.  Lecngrth.  Pounds.
6   1000 i 24    460    50    143
8    950   26    410    55    118
10    900 i28     370    60    100
12    850   30    336
1 4   800   32    307
16    750   34    283
18    700 i 36    263
20    600 i 40    229
22    520   45    176
S.....................................




95


Transverse Strength of Wood.
XLVII. Pine will bear a transverse strain of 1500 lbs.
to the square inch of cross section; i. e., the projecting end
of abeam will sustain, at a distance from the fulcrum equal
to the depth of the beam, 1500 lbs. for each square inch in
its cross section. Or what amounts to the same, a beam 1
inch square upon supports 2 inches apart, will sustain in
the middle, a weight of 3000 lbs.
I have therefore, adopted 250 lbs. to the square inch, as
the safe load for pine when acting transversely; and to
calculate the safe load for a projecting beam, this quantity must be multiplied by the cross section and the depth,
and divided by the distance of the load from the fulcrum.
For the safe load in the middle of a beam supported at
the ends, take four times the above amount, or 1000 lbs.,
multiply by the cross section and the depth, and divide by
the length between supports.
In order that a piece of timber may act by tension, it
is necessary to cut off a portion of the fibres, so as to form
a head, or shoulder reversed from the end, for the stretching force to act against; and that the strength of the piece
may be made available for as great a portion of the
length as may be without having the shoulder split off, it
is important to know the power of the material to resist
that kind of action.
Let ab, Fig. 27, P1. 6, represent a shoulder by means of
which the stick is made to act by tension. The area ab
should contain about 1 square inch for every thousand
pounds to beapplied to it. Now if ab be too nigh the end
of the stick, the part abcd will be split and thrust off from
the end. I find by experiment, that, to produce this effect
upon straight grained pine, requires a force of nearly 600
lbs. to the square inch in the area of cleavage, efcb. I
would therefore, in practice, allow 1 square inch for every 100 lbs., which would require ef to be equal to 10 ae.
If the shoulder be in the central part of the stick, as




96


by a mortice or pin-hole, two cleavages must be made
from the hole to the end in order to force the part out,
consequently, the distance from the hole to the end, need
be only five times the width of the hole; i. e., an inch hole
should be 5 inches, and a two inch hole, 10 inches from
the end.
Timber is sometimes liable to be crushed by forces acting transversely to its fibres. If the pressure be applied
to the whole side of a piece, the pressure should not
exceed 150, or at most 200 lbs. to the square inch, in practice. If the pressure act on one-half or less of the surface, it will bear from 300 to 500 lbs. to the inch without
yielding so as to endanger the work. Hard timbers will
bear from 20 to 50 per cent. more.
From what has been said, it follows that for a piece to
act to the best advantage by tension, if the connection be
made all at the same point in the length, the piece must
be cut half off, so as to form an area of shoulder equal to
the cross section of the remaining part of the stick. But
if several shoulders be made, a less number of the fibres
will require to be separated.
If, on a piece 4 inches thick, instead of a shoulder of 2
inches; at 20 inches from the end, we make two of 1 inch
each, one at 10 and the other at 20 inches from the end,
we have the same area of shoulder, and fifty per cent.
more fibres to act by tension, which may be made available by cutting another shoulder at 30 inches from the end.
Thus a greater portion of the fibers, but a less portion of
the length is made available.
In the same manner, if a piece be connected by pinning, requiring two pins of 2 inches diameter, at 10 inches
from the end, four 1 inch pins, two at 5 and two at 10
inches, (if stiff enough,) will give the same shoulder surface, and require the cutting of only half as many fibres;
and two more pins, at 15 inches from the end, will give
three-fourths of the whole amount of fibres available. In
case the smaller pins are not stiff enough, they may be
of an oblong section in the direction of the strain.




97


A still further reduction of the depth of shoulder, or
width of pin, will make a still larger portion of the fibres
available, but not so much length, and experience and
judgment, with a little calculation, will dictate the proper
medium in this respect. The limit in theory, is, when the
shoulders are infinitely small, in which case the whole
amount of fibres becomes available. But in practice, I
would only estimate from one-half to two-thirds as available for tension. This reduces the safe load for pieces acting by tension, to from 500 to 700 lbs., (I usually take the
former,) to the square inch, for the whole cross section.
I shall not, perhaps, find a more suitable place to make
a few general remarks upon the merits and use of pins
for connecting pieces of timber. I am much in favor of
the use of iron pins and bolts for this purpose, especially
for connecting pieces that cross, or meet one another at
an angle.  Wooden pins in such cases, do not possess
sufficient strength in proportion to the surface, unless
made so large as to cut the timber too much. Moreover,
the action on the pin tends to crush it laterally, in which
direction the hardest timbers do no! offer so much resistence as the ends of the fibres to which they are opposed.
Where pieces are connected with their fibres parallel,
wooden pins or keys with the cross sections elongated
in the direction of the grain, to give them the necessary
strength, may be employed without too much cutting of
the timber; but as just remarked, the key is liable to yield
before the ends of the fibres cut, are taxed to their full
capacity, and consequently is poorly adapted to the purpose in any case where the utmost strength is required.But when the grain runs in different directions, the hole
can not be elongated without too much cutting of at least
one of the pieces. Suppose a piece to be connected by
a pin between two others. The pin should be strong
enough to bear as much strain as the opposed surface can
sustain. Now, this can scarcely be accomplished by
wooden pins, as has just been remarked. But,74f suffiE




98


ciently stiff, the pin may yield somewhat without injury
to its strength. The transverse strength of pin timber
may be taken at about 300 lbs. to the inch. The formula
4 x 300ad--, (a=-cross section, and d=diameter of pin,)
gives the amount that the pin will bear in the middle.Now 1, in this case, is equal to 11 the thickness (t) of the
middle piece of timber, and the effect of the force exerted
by said middle piece, is two-thirds of what the same force
would produce if concentrated in the middle of the pin.
We have, then, 4 x 1 X 300ad-1- 1t, =1200ad--t=strength
of the pin.
But the opposed surface will bear 1000td.
Putting this expression equal to the former, and deducing the value of d, in terms of t, it will shew the smallest
diameter of a wooden pin strong enough to bear as much
as the opposed surface.
This gives d a trifle (about 2j per cent,) larger than i.
In the same manner, 4 x 1 x 5000ad-11t, represents
the strength of an iron pin in the same circumstances;
and putting this equal to 1000td gives the most economical diameter of an iron pin-,252t, and the length=2t.
Since the pieces a and c, [Fig. 28,] require each half
the thickness of the piece b, and since the diameter of
the pin should be about 1t, it will be equal to ~ the thickness of a or c. Hence, when a piece is fastened on by
spiking, the spike should have a diameter equal to 1, and
a length from 3 to 4 times the thickness of the piece
spiked on, in order to secure the greatest effect, for the
amount of material cut off by the spike hole.
When the end bearings of the pin act transversly to
the grain, they require at least 50 per cent more extent
of bearing, which increases the value of I in the formula
to 1it, and the effect of the force upon the middle portion
to 4 of the effect of the same force acting all at the centre.
The equation for the proper diameter of the pin, then,
will be 4XlX 1 x 5000ad  lt=1000td, whence d=,283t,
and the length, 21t.




99


Splicing.
This is an important operation, and may properly
claim consideration in this place.
Fig. 29, P1. 6, is a form of splicing in which - of the
fibres are made available; the depth of the locking
being equal to - the thickness of the stick. The length
of the lap should be 10 times the depth of locking each
way, or 20--3 -69 of the thickness of the stick.*
By two lockings, as in Fig. 30, PI. 6, one-half the fibres
are available, with a lap of 10 times the thickness of the
stick.
With three lockings, on the same principle, - of the
fibres are available, with of a lap of 12 times the thickness, and by lapping 13- times the thickness, we make -
of the fibres available. Finally, by a lap of 20 times the
thickness, and an infinite number of lockings, the whole
amount of fibres would be available.
But this, of course, is a limit not attainable in practice.
From - to a, say -, on an average, is as much as can be
reckoned on, and this is as much as can usually be made
available at the end connections.
Splicing may be done by lapping with a plain scarf, as
in Fig. 31, P1. 6, and bolting, pinning and spiking the
parts together.  If the pins and spikes be properly
arranged and proportioned, a strong splice may be
formed in this way, with a less lap than on the preceding
plan. But the expense will usually be greater, and on
the whole, the locked splice is generally entitled to a
preference.
Timbers may also be connected by iron straps and bolts,
either with or without a lap. The aggregate cross section of straps should be about 1 inch for every 10 to
15,000 lbs. strain which the splice is intended to bear.
The diameter of the bolts fastening the straps, should
* In this splice, the power being applied at the reversed shoulder, out of the
line of the unbroken fibres which resist the power, the tendency is to throw
the ends outward, and produce a degree of lateral action, which somewhat
weakens the timber beyond the proportion to the fibres cut.




100


be from - to I the thickness of the timber, to secure the
greatest effect according to the fibres cut by the bolt hole.
To connect two sticks twelve inches square, so as to
make half the fibres available, take 6 straps, two feet long
from hole to hole, (three straps on a side,) and six 2 inch
bolts, as shewn in the figure 32, P1. 6. The straps should
contain each, 1 square inch cross section, or a little more,
in all parts.
This will take, say 150 lbs. of iron at 8 cents,...$12,00.
To form a splice with 2 lockings, 10 ft. lap
will cost, for 10c.ft. timber at 30 cts.,.....$3,00
40 lbs. iron  at 8 cents,................  3,20
Extra labor,.....................  1,00
-   7,20
Difference,................ 8 4,80
The splice with iron straps will cost near $5,00, or 68
per cent more, for a 12 inch timber, than the lap and lock
splice. The same proportion may not hold for all sizes
of timber, but there can be little doubt that the lap and
lock plan is the better and more economical mode of
splicing.
I will now proceed to the application of the preceding
general facts and deductions to the construction of
bridges.
It is not necessary to allude to bridges of less than 12
or 15 feet, simple beams being sufficient for such cases.
Plan of a 20 ft. Bridge for Rail Roads,
Applicable for Stretches from 15 to 25 ft.-[See Fig. 33, P1. 7.]
In this plan, A represents a side, and B, an end view of
one truss; and C, a top view of the bridge. The scale is
distorted, in order to shew the details more distinctly,
without making the figure of an inconvenient size. The
lengths of pieces are on a scale of 1 to 100, and the widths
or diameters, 1 to 30. The angles are in their true proportions.




101


The truss is composed of a horizontal stringer, 5 inches
deep by 6 inches wide, two main braces 6 X 5, 2 pieces of
hard wood plank 6 X 2, and about 23- feet long, spiked
on to the lower side of the stringer at the ends; 2 bolts
I inch, to secure the lower ends of the braces, with clips,
or washer plates under the heads and nuts; and 2 bolts,
1 inch diameter, passing from the vertex of the braces,
divergently down through the transverse beam, as seen at
B. Under the heads of these bolts at the vertex, is a
plate fitted to the wood, about 4 inch thick, and at least 24
square inches in area. Between the two nuts and the
lower side of the beam, are plates of the same thickness
and same aggregate area, to prevent the nuts from bedding into the timber.
The lower ends of the braces toe into the horizontal
stringer, by two shoulders; the extreme one, I of an
inch deep, and the other 14 inches deep, and at least 20
inches from the end of the stringer.
The bolts supporting the transverse beam, diverge
each at least 50 from the perpendicular, to secure the
upright position of the truss, and equal tension of the
bolts.
The trusses should be about 14 feet apart in the clear,
and the cross beam 12 inches wide by 14 deep; or greater
depth and less width, when practicable. It should be
secured by bolting, spiking or other means, to the lower
side of the stringer. Or, in some cases, it may be above
the stringer with advantage.
For the horizontal braces shewn at C, 2 by 6 inch stuff is
sufficient; and they should be spiked to the under side of
the rail timbers.
The rail timbers should be at least 10 X 12 inches.
Bed pieces 3 X 12, on the abutments, under the ends of
the trusses, may or may not be used.
This bridge will take a trifle less than 100 cubic feet of
timber, including, or 55 ft. without the rail timbers; and
about 135 lbs. of iron.
E2




102


To adapt this plan to a greater or less span than 20 ft.,
the cross section of parts acting by tension should be
varied in the same ratio as the length of span. Those
acting by thrust, should be varied at a rate between the
simple and the duplicate ratio of the variation in length.
I prefer a reference to general facts and principles, to
rules and formule, the reasons for which can not be
taken in at a view. I have given illustrations of the
modes of determining the maximum forces of every kind
to which each piece in the truss is liable; also, the power
of resistence of the material in the various circumstances
in which it may be placed. I will here add the following
general directions, which, if attended to in arranging the
proportions of a bridge, will be pretty likely to ensure its
sufficiency for the purpose it is intended for.
Estimate the kind and amount of force to which each
piece is liable. If it be tension, see that there be at least
1 square inch of unbroken fibres, for every 1000 lbs. of
tension. If a negative or crushing force, parallel with
the fibres, consider the length between supported points,
and the least diameter of the piece, and then see whether
the strain per square inch, is greater than the amount
given in the table of safe negative resistence of timber,
for pieces of such proportions, and if necessary, change
the dimensions accordingly. See that the pressure upon
the end of the grain, be not more than 1000 lbs. to the
square inch, and at right angles with the grain, from 150 to
500 lbs., according as the pressure is upon the whole, or
only a small portion of the surface.
As a piece can only be made to act with tension, by
cutting a portion of its fibres, and applying the force to
the reversed ends, be sure that at least an inch area of
fibres thus cut, for every 1000 lbs. of tension, be opposed
to the pressure of the straining force.
Where an iron pin secures one piece between two others, acting in the directions of the fibres throughout, see
that the diameter of the pin be about 4 the thickness of




103


the middle piece, and extend into each of the out side
pieces to the length of ~ the thickness of the middle
piece. If the action of the pin be transversly to the
fibres, give it at least 50 per cent more bearing surface for
the same pressure, than where it acts on the ends of the
fibres, and make the diameter not less than,28 the thickness
the middle piece. Where pressure acts on the reversed
ends of fibres, tending to force them out or off from the
end of the stick, be sure that the amount of cleavage, be
not less than one square inch for each 100 lbs. of force.
See that the transverse strain of timber, and the positive
stress of iron, are in all parts within the limits of safety.
Finally, see that every force that tends to break or
derange the structure, have an adequate counteracting
force opposed to it, and attend to such minor details as
cannot fail to suggest themselves while attending to the
above enumerated points, and the chance of failure must
be exceedingly small, if failure be even possible.
"24 to 36 ft. Span.
For this range, probably no better general form of
truss can be adopted, than that shewn in Fig. 4, page 9.
The principal details are the same as in the above
described plan of a 20 ft. bridge. The foot of the braces
are secured in the same manner, the amount of bearing
surface being increased to correspond with the increased
pressure. The upper ends of the braces should be made
square, and the upper horizontal piece, beveled so as to
fit the braces. The small cross braces toe into the upper
and lower horizontals, the one being 3 X 7 inches, (for a
30 feet bridge,) and edgewise to view, the other 3 X 5, flatwise to view, and passing through a mortice in the centre
of the former.
The transverse bearers are the same size, and sustained
in the same manner by bolts diverging downward, as in
the 20 feet bridge.  Also, the horizontal braces are




104


arranged the same, but should be a little larger, except
the middle pair; say 21 by 6 inches.
The dimensions of the parts of the truss for a 30 feet
bridge, should be, for the lower stringer, about 6 inches
deep by 7 wide. The braces and top piece, 7 inches
square. The sizes of the cross braces have been already
given. The bolts at the feet of the braces, i or 1 inch in
diameter. The suspension bolts, about 1- inches diameter.
The truss should be about 7 feet from top to bottom,
for the proportions of parts above given.
A 30 feet rail road bridge will require 180 cubic feet of
timber, (including 64 cubic ft. of rail timbers,) and about
375 lbs. of iron.
Plan for a 40 Feet Bridge,
Applicable for any length between 36 and 48 feet, and not confined within
those limits.-[Sec Fig. 34, P1. 8.]
Scale for lengths of timbers, 1 to 100; other dimensions, 1 to 30.
In this truss, the upper and lower horizontal stringers
a and b, are each composed of two pieces, 6 inches deep
by 4 inches thick, and placed 6 inches apart.
The brace c, is 6  14, edgewise to view, with 6
inches cut out of the middle, at the upper end, to make
room for d and e. At the lower end, it is fitted into a boxing of 1 inch depth upon the upper and inner sides of
the stringers a, while the middle portion, 6 inches in
thickness, runs down to the abutment, being beveled off
even with the lower side of a.
The vertical, d, consists of 2 planks, 8 x 21, placed 3
inches apart, to receive the upper end of e, and a 3 inch
tenon formed on the lower end off, between.
There is a boxing 1 inch deep at each end to let in the
upper and lower stringer pieces, and the vertical pieces
should extend at least 6 inches beyond the boxing. There
is also a boxing in d, just above the stringer a, an inch
deep, in the edge, to receive the cross bearer, and the




105


cross bearer is boxed 4 or 5 inches deep, to receive the
verticals d.
The diagonals ff, 3 x 7 inches, are locked or tenoned together at the upper end, and fitted into a half inch
boxing on the inside of the upper stringer b. In the center is a mortice 3 x 7 inches for the piece e to pass through.
The lower end is reduced to 3 inches wide between the
pieces d, and 4 inches at the end, having a head, or
reversed shoulder fitting a triangular boxing inside of d,
shown by dotted lines.
The diagonals e.e, are secured each by 2 bolts of 14
inches diameter, and a few spikes at the upper end; and
at the lower end, they are halved and locked together,
with a piece of 2 inch plank, 24 feet long. locked, bolted,
and spiked onto each, and extending across the other to
the end. These short pieces, being reduced to 14 inches
thick, except for 6 inches at the upper end, which forms
the locking, they just fill the 6 inch space between the
stringer pieces. Two bolts of 11 inch iron, through
stringer and diagonals, with a few spike, complete the
arrangement at this point.
To secure the vertical position of the truss, a brace and
tie runs up from a point in each cross beam, about 24 feet
from the centre of the truss, to or near the top stringer,
being secured at each end so as to act by either tension
or thrust, with a force of some 2000 lbs. each. Perhaps
the best arrangement for this purpose is, to use a 3 inch
square, or 3 x 4 scantling for the brace, with a 1 iron rod
running beside it for the tension. These are not shewn
in Fig. 34.
If the lower stringers can not be obtained of the whole
length, they may be spliced by a two-lock splice between
cross beams, with a piece of 2 inch plank about 6 feet
long, which will extend 16 inches beyond the lap each
way, well spiked on to the inside. Six inch pressed
spike, (- inch iron,) the points drawn about an inch for




106
clenching, with a portion of five inch spike, may be used
to advantage in this splice.
But the splicing at best, adds considerably to the
expense, and it is better, when practicable, to obtain
stringers of the full length, even at a considerable extra
cost per foot.
The amount of materials for a 40 feet railroad bridge
on this plan, is estimated at 306 cubic feet of timber, and
400 lbs. of iron.
Plan of a 60 Feet Rail Road Bridge,
APPLICABLE FROM 48 TO 72 FEET WITH ADVANTAGE.
Scale for Length of Pieces, 1 to 100; other Dimensions, 1 to 30.
LXIX. Figure 35, P1. 9, shews a side view from one
end past the centre.
The lower stringer a, is composed, as in the preceding
plan, of two portions, each 9 inches deep by 5 wide, with
a space of 11 inches between, from the end to the point
a, about three feet from the second cross-beam from the
end. Thence, a 21 inch plank extending to within the
same distance of the opposite end, is added to the inside
of each portion, reducing the width of the space to six
inches. These plank are well spiked at the ends, say
with 3 spike, - square by 7 inches long, at each end of
each plank, two being placed six inches apart, and 3 or
3j from the end, and the other in the centre, and 7 or 8
inches from the end. It would be better, perhaps, that
one or two of these, should be A or - screw bolts.
The 5 x9 part of the stringer may be spliced by the
double lock splice, centrally opposite the second bearing
point, or any where between the second and fourth. If
spliced at the bearing point, the transverse bolts which
secure the diagonals, will strengthen the splice at the same
time. The splice, of course, should be farther assisted by
spike and small bolts, and these should in general, be at




107


least five times their diameter from the lockings, or from
the ends of the pieces.
The top stringer is composed of two 5 x 8 portions, 9
inches apart, with a 2 inch plank on the inside of each,
extending from the second to the fourth connecting point,
or half the length of the stringer. The parts in the top
stringer may be in two or more pieces, meeting by square
ends, or lapped a few inches and halved, without locking.
The end braces are each composed of two pieces, 8
inches deep by 7 wide, and 5 inches apart, with a block
at the lower end and the centre; the latter having a k
bolt passing through it, and thus connecting the two portions of the brace. The block at the lower end is secured
by the main bolt connecting the brace with the ends of the
stringer pieces.
The lower end of the brace is fitted into a 11 inch
triangular boxing on the inside, and a 1 inch boxing on
the upper side of the stringer pieces, as shewn by the dotted lines in the figure; the boxing on the upper side,only
extending to within one inch of the outside of the stringer; the lower stringer being two inches wider from out.
side to outside, than the brace and the upper stringer.
The brace meets the end of the upper stringer by a
bevel joint bisecting the angle formed by the two; the
brace pieces being cut away upon the inside, where they
interfere with the vertical.
The vertical, v, is composed of two pieces of 8 x4, with
a space of 4 inches, to admit the diagonals b and c between. Each part of the vertical has a 1l inch boxing at
the upper end, to receive the inside of the upper stringer
and main brace pieces, with two 11 inch bolts passing
through the whole. There are also at this point, two *
inch iron pins, passing through the vertical pieces and the
diagonal b, but not through the stringer or brace pieces.
These pins should be, one directly under each of the bolts,
but not cutting the same fibres in b, as are cut by the bolt
holes.  The vertical should extend about nine inches




108


above the top of the stringer, and the diagonal b, 9 or 10
inches beyond the bolt holes. The vertical recieves the
lower stringer pieces into a - inch boxing, and also recieves between its two parts, a 4 inch tenon upon the lower end of the diagonal c, which is 4 X 9 inches, and stands
edgewise to view. There is also an inch boxing on the
edge of the vertical, just above the stringer, to receive the
cross bearer; which latter is boxed 5 inches deep to receive
the vertical, as in the case of the last plan. It is desirable
that the centre of the beam should be brought nearer to
the centre of the vertical, but a good plan for effecting it
has not occurred to me. The arrangement here adopted
can not, however, be very objectionable.
The vertical pieces extend 5 or 6 inches below the bottom of the stringer. Two 1- inch bolts placed diagonally
about 7 inches from centre to centre, and passing through
stringer, vertical and diagonal pieces, as shewn in the figure, complete the connection at this point.
The diagonal b, (being 10X4 inches,) passes through a
mortice in the centre of c, and also through a mortice near
the lower end of the diagonal e. The latter piece being
7 x 4 inches, has an oblique shoulder of ~ an inch on each
side, fitting into a triangular boxing of corresponding depth
on the inside of the stringer. Two 1- inch bolts pass
through the whole, and a 1- inch pin, 7 inches long,
passes through h about midway of its width and close to
the under side of e, with a - inch plate, 3 inches long
by 2 inches wide, for each end of the pin to bear on.
The cross bearer at this point is boxed on, so as to bear
upon both the diagonals and the stringer pieces.
At the upper end of c, is a mortice 3 X 9 inches for the
end of d to pass through; d being also 3X9. On each
side of c, is a shoulder of 1 inch, oblique to the piece, but
in a vertical line, acting against the ends of the inner
plank of the top stringer; one inch of the ends of the
plank being halved off, to let the piece c pass by with a
width of 7 inches. A 1l inch bolt passes through the




109


stringer, and through the centre of c and d. There are
also two 1- inch iron pins, 7 inches long, passing through
d on the upper side of c, 41 inches from centre to centre,
with two - inch plates 2 x 7 inches, for the ends of the pin
to bear on. These bearing plates should have nail holes
at the ends.  The pieces in all cases, should extend beyond the bolt or pin holes, not less than five times the diameter of said holes.
The diagonal e, is halved and locked with its mate at
the upper end, and fitting an x formed boxing 1 inch
deep, inside of the stringer pieces, is secured by a 11 inch
bolt through the whole.
The piece d is halved and locked with its mate at the
lower end, with a piece of 2 inch plank, 21 feet long,
locked, bolted and spiked on to each, as in the corresponding case in the preceding plan. Two 1~ inch bolts are
used at this point, each in the centre of the stringer.
The horizontal bracing is the same in this as in the preceding plan, the braces being a little larger towards the
ends. 3 x 6 braces will be sufficient, or 3 X 6 at the ends
and 21 X 6 in the middle. They may be halved together
at the crossing point, and spiked to the under side of the
rail timbers, or one may be placed sufficiently below the
other to pass without cutting either.
The bracing and tying to preserve the vertical position
of the trusses, is the same as in the 40 ft. plan. In this,
as well as that, the braces may be on the outside of the
truss, the cross bearers extending some three feet from
the centre of the truss, to support the brace and tie.These braces are not shewn in the figure.
It is advisable in all these plans where the erect position of the truss depends on its connections with the cross
beams, that the latter should be trussed, in all cases where
they would not thereby occupy too much space vertically,
as the spring of the beam communicates motion to the
truss. This is, perhaps, less detrimental in a rail road,
F




110


than a common bridge, since the steady motion of cars
has not that tendency to produce vibration, which arises
from the trotting of horses. Still, it is an object to secure
stiffness in the cross beams in all cases.
Fig. 36, PI. 7, shews a good form for a trussed cross
bearer for a rail road bridge.  All except the two short
braces is 8 x 8 inch stuff. The two short braces 3 X 3 inch
stuff. The long and short bolts, - or 1 inch iron, according to the distance of the cross bearers asunder. The
truss should be not much less than 3 feet deep in the middle, and the line of the centre of the main braces, should
meet that of the bottom timber, at the centre of the main
trusses of the bridge. The boxings at the foot of the
brace should be about 1I inches deep, for the extreme one,
and about 3 inches for the other. The upper end of the main
braces should be made square, and the necessary bevel all
made upon the top piece.  This truss, if 3 feet deep, is
good for about 16 tons.
The 60 feet bridge estimates at 600 cubic feet of timber, and 1,000 lbs. of iron.
An 80 feet Bridge.
LXX. On the preceding plan, a truss of 70 feet in
the clear, requires a height of 12 feet from centre to centre
of the stringers. For trusses exceeding this height, it is
very desirable that they should be connected at the top,
as it is somewhat troublesome to support them independently in a vertical position. By adding one or two to the
number of pannels, the length maybe increased to near a
hundred feet with a height of about 12 feet. This would
answer a tolerable purpose for common roads, and even
for rail roads, they are frequently built of no greater
height. But we have seen that there is a loss of economy
when the length of the truss exceeds about six times its
height.
Rail road bridges require about 15 feet in the clear,
above the top ef the rail, which takes about 18 feet




111


height of truss, with the cross beams on the top of the
lower stringers. By suspending the beams below the
stringers, 16 feet trusses will give sufficient space. I
propose the following plan, Fig. 37, P1. 10, for an 80 feet
bridge, which, by diminishing or increasing the length or
number of pannels, or bearing points, may be suited to
any span from 70 to 150, or perhaps 200 feet, with probably as good economy, to say the least, as any plan in use.
The scale of this plan is the same as that of the preceding,
1 to 100 for length, and 1 to 30 for other dimensions.
This I call a double-cancelled truss; there being two
crossings of the diagonals in the centre of each pannel, or
between each two consecutive bearing points.
The lower stringer is formed mainly as in the preceding plan, being 21 inches in width horizontally, and 9
inches deep. From the end to within a foot of the first
cross beam, the space between the two portions of the
stringer is 13 inches. Thence, to about midway between
the 2d and 3d beam, the space is 9 inches; and thence to
the centre, 5 inches; and so for the other half. The outside courses are 4 inches thick for the whole length, spliced with the double-lock splice. Opposite the 9 inch space,
a 2 inch plank is added, and opposite the 5 inch space, a
4 inch piece, locked by a single lock on to the 2 inch
plank just mentioned, as seen in the figure.
The upper stringer is 19 inches from outside to outside,
and 9 inches deep. Each half is composed of a 5 inch
course on the outside throughout, with a 2 inch course on
the inside, between the points over the second cross beam
from each end.
The end braces h, are in two pieces of 9X 6 inches,
with a 7 inch space between; the lower end fitted into an
inch boxing inside, and a 11 inch boxing on the top of the
stringer pieces; the end resting on the abutment. Between the two pieces at the foot, passes the diagonal e;
being reduced at the end, to a width corresponding with
the space that receives it. This piece also extends down




112


to the abutment. At the top, b forms a bevel joint with
the top stringer.
The vertical d, is 12 x 3 inches; passes through e in the
middle, and h at the lower end, where d and h are both
secured to the stringer by two 11 inch bolts. The cross
beam at this point may be let into the edge of d, 3 inches,
and boxed, so as to bring the centre of the beam within
4 inches of the centre of d. At the upper end, d terminates in two pieces of 2 inch plank, 5 feet long, one on
each side; locked I or - inch deep, bolted and spiked, so
as to occupy a space of 6 inches from out to out, and cut
away on the inside, so as to make room for g, which is
3 x 12 inches.
The oblique piece f, 9 x 4 inches, passes through e, k,
and k; being secured at the lower end by two 1I inch
bolts, and a 1- inch pin, 9 inches long, with bearing plates,
2 or 2 X 3 X  inch, on the under side of k. At the upper
end, f has 2 pieces of 3 X 12 inch plank about 7 feet long,
locked on 3 inch deep, and spreading so as to be 11 inches
from out to out at the end; boxed 1 inch on each outside,
to receive the top stringer and the brace b; and cut away
inside, making a space of 6 inches for d. The piecef
should extend 9 or 10 inches above the stringer. Two 1 -inch bolts through the whole, and two 1- inch iron pins
through all but the stringer and brace, will be sufficient
for this point.
The diagonal e, 4 x 9 inches, at the upper end, has a
shoulder of 1 inch on each side, cut vertically, and acting
against the end of the inner plank of the top stringer. It
has a 1~ inch. bolt and 2 iron pins, 1- inch, and 7 inches
long, through i, on the upper side of e, with bearing plates
under the ends of the pins.
The diagonal h, (3J X 9 inches,) and the top stringer,
are each boxed 1 inch, to let in the width of the other;
with two 11 inch bolts. h has 5 mortices, including those
at the ends, as have also the other diagonals that stand
edgewise to view in the plan.




113


The diagonal k (3x9 inches) is boxed in the same manner as A, at the upper end, and has one 1 inch bolt.
The piece n, is 3j X 7 inches except about 8 feet of its
upper end, which is reduced to 3. inches wide; and passes through its fellow m, and through k. m is also reduced
to 3ý inches at the upper end, and at the lower, fits a boxing of 1 inch in the lower stringer,but has no shouldering;
has two 11 inch bolts and a ~ inch spike through, and two
1 inch pins with bearing plates on the under side, through g.
The diagonals i (9 x 3,) and its antagonist (7 X 3,) at the
lower end, halve and lock, with lap pieces locked, bolted
and spiked, as in the case of d.d, in the preceding plan,
making up a thickness of 6 inches, which, of course, requires a ~ inch boxing on the inside of the stringer pieces.
This point has two 1~ inch bolts. The diagonals generally, should have ~ inch spike at the crossings; or perhaps a round iron pin from. to 1 inch diameter would be
cheaper and better.
The cross beams for this stretch, being 9 feet apart,
should be 10 X 14 or 12 X 12 inches and put on as in preceding plans. The horizontal braces may be from 3 x 5
in the middle, to 3 X 7 at the ends of the span.
Across the top are light tie beams, say 5 X 7 inches,
fitted on to the top stringer, similarly to the fitting of the
bearing beams below; secured with small bolts or spike,
with diagonal horizontal braces, 3 X 4, or 4 X 4 inches. At
the ends should be lateral supporters, running down from
near the upper end of the main end braces b, diverging
from 1 in 6 to 1 in 4 outward, to the abutment, or a bed
timber lying on the abutment; and properly secured at
both ends.   These braces should be about 6 inches
square, with perhaps a steadying block and small bolt
midway.
The truss in this plan is proportionally higher than is
thought advisable for long spans, the height being to the
length, as 1 to 4.. It is not certain whether this proportion
for an 80 or 90 feet span is more or less economical than
P2




114


a less height, independently of affording room for the
locomotive. But taking in that consideration, there can
be no doubt of the propriety of giving to an 80 feet stretch,
this height of truss.
Reducing the height of truss I foot, and the space between bearing points I a foot, will afford a stretch of
about 75 feet, and still afford room for the engine, by a
proper arrangement of track, &c.
It is not necessary that the height of truss be exactly
once, twice, or thrice the space between bearing points
or cross beams; even with the uniform rectangular crossings of the diagonals or cancels. The height may be once
and a half, or twice and a half the length of said space.
Hence, the skillful engineer will find little difficulty in
arranging the proportionate height of truss, and preserving
the distance between bearers within such limits as to
secure economy in the use of rail timbers, &c.
The estimate for an 80 feet bridge is, 920 cubic feet of
timber, and 1250 lbs. of iron.
LXXT. It is hoped that enough of detail and specification have already been given, to make the peculiarities
of the plans I recommend, intelligible to those conversant
with the subject, or to those desirous of acquiring a knowledge thereof. I will therefore, after some remarks upon
the adaptation of these plans to sustaining the load on the
top of the trusses, and to the use of common roads, dismiss the consideration of the subject for the present.
It will appear obvious enough, that all these trusses in
the preceding plans, are equally well, and even better
calculated to sustain the weight on the top, than at the
bottom, as they have been regarded to do in what precedes. Some difference would take place, on making the
transfer of weight, in the action of some of the parts. The
amount of tension would be increased in some places,
and thrust in others, and vice versa. This is necessary to
be taken into account in apportioning the dimensions,




115


and arranging the connections of the parts, and sufficient
directions and illustrations have already been given, to
enable this to be done, and the plan arranged with facility.
When the track passes over the top, the abutments or
piers should be built with offsets or recesses to support
the ends of the trusses, and a thin wall carried up to support the ends of the rail timbers; or, a bent of wood may
be made to answer the purpose.
With this arrangement of the track, the distance between
trusses need not exceed the tenth part of the length of
span, by which means a considerable saving may be effected in the length and size of cross bearers.
Horizontal bracing, of course, will be requisite at the
top, but not at the bottom of the trusses; as the constant
tension on the lower stringers, will counteract sufficiently
any tendency to swing, unless the sides be boarded up,
so as to take the severe action of the wind; in which case
some bracing may be necessary.
On the whole, it is manifest, that when practicable,
there is a decided advantage in point of economy, in arranging the plan for the track to pass over the top.
Common Road Bridges.
LXXII. If we allow 16 ft. width of road-way, which
will admit the passage of two carriages, and reckon 100
11s. to the square foot for the maximum load of a common
road bridge, the trusses for the latter would require only
about three-fourths the strength that we have estimated for
rail road bridges, aside from what supports the structure
itself.
But the flooring of the common road bridge is heavier
than the rail track, though the load of 100 lbs. to the
square foot is more, probably, than one bridge in a thousand is ever exposed to. It is therefore probable, that
the trusses for common road bridges do not, in general,
require more than three-quarters the strength of a rail




116


road bridge. Even much less strength, in many case's,
would be entirely safe.
But it is well to lean always towards safety, and rather
make a structure unnecessarily strong than too weak.--
Enough, however, has perhaps been said on this head.
I would make no difference in the general plan of
trusses for rail road or common bridges. Sometimes a
less proportionate height will be admissable, if thought to
possess any advantages in the way of appearance, or for
any other consideration. I would seldom, however,
make the height less than one-eighth the length of span.
A height from 12 to 14 ft. on a common road, will admit
of ties across the top, and in such cases they should
always be employed, with suitable horizontal bracing, and
in all cases sufficient security should be provided to preserve the erect position of the trusses; for if their erectness be lost, their strength is very much impaired, and
they are not only dangerous, but very unpleasant to the
eye.
The flooring may be formed with longitudinal joists,
upon the cross bearers, and cross planking upon the joists,
or by making the bottom stringer a little larger, particularly deeper, diminishing the horizontal thickness of the
cross bearers, and increasing their number, so as to leave
spaces of only 2A or 3 ft. between them, and laying the
plank lengthwise or diagonally. Horizontal braces may
be spiked on the lower side of the cross beams or joists,
in the manner of what is sometimes called stay-lathing.
An advantage of planking lengthwise is, the more
steady motion of carriages, producing less shaking of the
structure; also, the less wearing of plank by toe corks.
The disadvantage if any, is the liability of the wheels to
wear at the joints of the plank. It would seem that this
might be obviated by inclining the plank more or less out
of the direct line of the wheel track. The longitudinal
planking is the cheaper method, as one set of timbers, (the
joists,) is dispensed with, without any considerable increase in the expense of the cross timbers. On the whole,




117


I am at a loss for the reason of this plan of planking on
bridges, not having been more extensively used.
Roofing and Siding.
LXXIII. As to the propriety of roofing and siding
bridges, it may be remarked, that it no doubt adds considerably to the durability of the structure; but it also
increases the weight, and consequently the requisite
strength of the trusses; thereby enhancing the first cost
to a considerable degree. They are much more liable to
injury by the action of the wind, when roofed and sided,
which is another somewhat important consideration.
If a bridge costing $1000 without covering, will last
nine years, an additional investment of $1818 at 5 per
cent., compound interest, will produce the means of renewal as often as necessary, so that $2818, will provide
for a perpetual maintenance.
Again, supposing that the same bridge protected by
roofing and siding, will last thirty years and cost $1500,
including repairs in keeping on boards, &c., it will require
an investment of only about $500 to provide for renewal,
or $2000 for perpetual maintenance.
This shews decidedly in favor of roofing and siding, and
I am inclined to think not too favorably, though the estimate of cost has been rather roughly made. For short
stretches, the comparison would shew a different result
up to a certain limit. The cost of roofing and siding,
particularly the former, is about the same per foot run,
for long or short stretches; while the cost of the supporting trusses, per foot, is nearly proportional to the length
of stretches.
A 30 ft. bridge for instance, would cost about double,
with roof and siding, that it would without; and allowing
the former to cost $200 and the latter $100, the comparison would be about $280 for the perpetual maintenance of
the uncovered bridge, against about $266 for the covered
one. Hence, this must be near the dividing point; and it
may be put down as highly probable, if not a decided




point, that below 30 ft. there is no economy in covering
bridges; but above that limit, or something near that,
there is a decided advantage in " protection," increasing
with the length of stretch.
Many bridges are annually swept away in this country
by floods aud freshets. Where the permanency of the
structure is doubtful, prudence would rather dictate that
the structure be made as cheap as possible, consistently
with strength and safety.
These remarks upon covering, have more particular
reference to common bridges. As to rail road bridges,
there is more liability to accident by fire in covered, than
uncovered bridges, and the policy may be somewhat more
doubtful, unless for considerable stretches.
In the construction of bridges not designed to be covered, it is believed to be worthy of recommendation to
saturate the joints, and points of contact of the different
pieces of timber, with oil-paint, pitch, or some other substance that may serve to harden the timber, as well as preserve it by excluding water. Those parts are liable to
decay much sooner than in other places, as well as being
usually the weakest parts, where the timber is cut most to
form the connections.
Length of Stretch.
There are cases where the length of the stretches for a
bridge is optional, and may be regulated as economy in
construction may dictate. For instance, in crossing a
broad stream or valley, where piers are not objectionable,
as obstructing the current, &c. In such cases it is desirable to know what length of stretch is most favorable to
economy.
It may be assumed in the first place, that the cost of a
pier is nearly the same to support a short, as a long span.
Hence the cost of piers will be as their number; or inversely as the length of stretches. Therefore the minimum cost for both piers and superstructure, (for a bridge
of indefinite length,) will occur when the cost of a pier is
just equal to that of one stretch of the superstructure,




119


The Dee Bridge.
A considerable degree of excitement has been caused within a few
months in England, by the failure of a bridge over the river Dee, near
Chester, (England,) during the passage of a rail road train, by which accident several lives were lost.
As the facts of the case may afford an instructive lesson upon the subject treated of in the preceding pages, I am inclined to state the most important of them, with a few accompanying remarks, before taking leave of
the subject.
The bridge in question, was upon the plan called the " Cast Iron Girder
Bridge."
In this plan, each track, or pair of ways, is supported by two cast iron
Girders, or beams, with their ends resting on abutments and piers, which,
in the case of the Dee Bridge, are 98 feet apart. The form of the Girders, is essentially that of the common railway bars, known as the.i or,
rail; the vertical "' web" being two and one-eighth inches thick, by about
three and one-half feet deep; the lower flange, twenty-four and one-half
inches wide by two and a half thick, and the top flange, about seven and
a half inches wide, by a little less than two inches thick; the whole cross
section containiug 160 square inches, and the whole depth being 45 inches.
In addition to this, are wrought iron suspension bars, containing 60
square inches of cross section, running obliquely downward from a connection at the ends, about 3 ft. above the upper flance, (there being a
rising portion at the ends to which such connection is made,) to the lower
flange, at the joints of the cast iron part, 36 ft., or one third the length of
the girder, from the ends; the casting being in three pieces, connected by
bolting through flanges, and by strengthening pieces at the points. Between
the two joints, the suspension bars run horizontally, just above the lower
flange of the girder.
One effect of these suspension bars is, to throw a great amount of thrust,
or crushing force upon the top flange, in so much that the engineers who
examined and testified upon the subject, upon the inquest held in relation
to the lives lost by the accident, generally concurred in the opinion that
they rather weakened than strengthened the girder. Adopting that conclusion upon this point, which appears to be corroborated by experiment,
let us examine whether the failure of the bridge, in connection with the
other facts of the case, should inspire distrust, or confidence in the use of
iron bridges for rail roads.
By calculation according to formulm deduced from experiment, a pair
of girders is estimated to be able to sustain at the extreme or breaking point, 148 tons in the centre, or 296 tons distributed uniformly over
their length. In this estimate, the testifying engineers concur with little or
no variation. Now, the weight of a pair of girders, is about 70 tons, or,
with other parts of the structure, about 90 tons. Mr. H. Robertson, (en



120


gineer,) estimates the effects of the engine and tender as " equivalent to
32 tons in the centre," which is equal to 64 tons distributed. Add to
these, " 25 tons of ballast," which was put on to the bridge just before the
accident, and we see there was 90~ 64+ 25 =179 tons upon the bridge,
which was more than six-tenths of the actual breaking weight, supposing
it all at rest, and acting equally on the two girders. But the action of the
engine, and the vibration of the girders, (which must be considerable for a
length between supports equal to 26 times the depth,) must be very important, though not capable of exact estimation. It is therefore riot improbable that the girder was taxed to more than two-thirds ofits extreme capacity under favorable circumstances.
Now, from one-quarter to one-third of the actual breaking strain, is all
that any practical engineer estimates it safe to rely on cast iron to bear;
whereas, in case of the Dee bridge, we see it exposed to a load of more
than six-tenths of the ordinary capacity, besides the effects of motion,
vibration, &c. It certainly cannot be surprising, then, that a failure took
place. And so far from this failure amounting to evidence, or even an
argument, against the safety of iron bridges, the fact that this is the first
and only failure that has yet taken place, among 1" upwards of 100 similar
bridges either in use or in the course of construction, in England," some of
which are doubtlessly, often exposed to strains exceeding half their absolute capacity to bear, seems calculated to inspire the fullest confidence,
that, properly proportioned, so as never to be exposed to a stress of more than
one-fifth or one-quarter of the average strength of the metal, iron bridges
may be relied on with the utmost confidence.
We see that the Dee bridge contained some 70 tons or more of iron in
the girders, for a single track of 98 feet stretch,* besides 20 tons in the
other work, which is nearly one-third of the actual breaking weight of the
girders; and as much or more than they ever should or could with safety
be exposed to.
The English engineers seem to me to have erred, in deducting the
weight of the structure from the breaking weight, instead of the safe loac
of the girders, to obtain the effective strength.
- Now, that the most eminent engineers, of a most scientific nation
should be obliged to avail themselves of the extensive employment of suci
a plan of structure as that, is evidence enough of a prevalent want o
more light upon the subject of Bridges. And whether my labors in th4
field will have aided essentially towards supplying the deficiency, it is un
necessary for me to give a more direct expression of opinion, than will b
afforded by respectfully offering these humble essays to the attention of th.
engineering profession.
* I estimate the amount of iron for a like stretch upon my plans, at about 15 tons.














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