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TRANSPORTATION
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536
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CHANNEL BRIDGE
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1
PRELIMINARY DESIGNS
OF
MM. SCHNEIDER et Cie
(USINES DU CREUSOT)
AND
H. HERSENT
ENTREPRENEUR DE TRAVAUX PUBLICS, EX-PRÉSIDENT DE LA SOCIÉTÉ DES INGÉNIEURS CIVILS
SIR JOHN FOWLER AND MR. BENJAMIN BAKER, Esqre
CHIEF ENGINEERS OF THE FORTH BRIDGE
CONSULTING ENGINEERS
TEXT
PARIS
IMPRIMERIE ET LIBRAIRIE CENTRALES DES CHEMINS DE FER
IMPRIMERIE CHAIX
SOCIÉTÉ ANONYME AU CAPITAL DE SIX MILLIONS
Rue Bergère, 20.
1889
TRANEPORTATION ESS
UNIV
OF
MICH

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130
$
PROPERTY O
University of
Michigan
Libraries
1817
ARTES SCIENTIA VERITAS
CHANNEL BRIDGE
PRELIMINARY DESIGNS
OF
MM. SCHNEIDER et Cie
(USINES DU Creusot)
AND
H. HERSENT
ENTREPRENEUR DE TRAVAUX PUBLICS, EX-PRÉSIDENT DE LA SOCIÉTÉ DES INGÉNIEURS CIVILS
SIR JOHN FOWLER AND MR. BENJAMIN BAKER, ESQ
CHIEF ENGINEERS OF THE FORTH BRIDGE
CONSULTING ENGINEERS
re
TEXT
PARIS
IMPRIMERIE ET LIBRAIRIE CENTRALES DES CHEMINS DE FER
IMPRIMERIE CHAIX
SOCIÉTÉ ANONYME AJ CAPITAL DE SIX MILLIONS
Rue Bergère, 20
1889
TRANSPORTATION LIBRAR
Transportation
Library
ты
64
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536
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09-28-517 W
Transport.
TABLE OF CONTENTS
PART I
I. Introductory Notice
II. General Description of the Bridge:
§ 1. Placing in Position.
§ 2. Supporting Piers of Masonry
§ 3. Metal Superstructure.
PART II
FOUNDATIONS
H. HERSENT'S PRELIMINARY Design
III. Detailed Description of Foundation Works:
§ 1. Arrangement and Dimensions of Supporting Piers of Masonry
§ 2. Fitting, Transporting, and Placing in Position of Supporting Piers
of Masonry
•
§ 3. Materials and Plant
IV. Cubature, Estimates, Time Required.
PART III
SUPERSTRUCTURE
SCHNEIDER AND CO's PRELIMINARY DESIGN
V. Selection of Systems of Girders.
VI. Arrangement of Metal Superstructure:
§ 1. Spans of 300 and 500m.
§ 2. Spans of 200m and 350™.
§ 3. Spans of 100m and 250m.
VII. Fitting, Transporting, and Erecting Spans:
§ 1. Description.
§ 2. Calculation of Machinery required .
§ 3. Fitting Overhang.
VIII. Estimate of Weights:
§ 1. Spans of 300 and 500™ .
§ 2. Spans of 200m and 350.
§ 3. Spans of 100m and 250m.
§ 4. General Recapitulation.
Page.
7
11
12
14.
19
24
32
35
41
45
48
48
49
31
86
67
3235
60
62
65
4
IX. Calculations of Resistance:
§. 1. Independent Span.
•
1. Longitudinal Beams under Rails.
2, Beams
3. Bracings.
Lower Bracing
Top Bracing.
Cross Bracings.
•
4. Braces and Main Girders
5. Principal Girders
•
§ 2. Central Span and Overhang.
1. Longitudinal Beams under Rails.
2. Beams
•
3. Bracings
•
Lower Bracing.
Cross Bracings
•
Calculations of Effects of Couples
4. Braces and Main Girders .
5. Main Girders
•
§ 3. Metal Columns.
1. Stability when Exposed to Side Wind.
Sockets.
•
Stability on Rollers.
Expansion Slides
•
Circular Supports of Rollers.
Pier Bracings.
Metal Piers
•
Stability at Base of Piers.
Substructure of Piers.
•
Anchor Tubes.
Anchor Bolts .
Stability of Masonry at Level of Tie-Bands
2. Stability when Exposed to Wind Longitudinally
Metal Piers
Stability at Base of Piers.
Stability at Base of Anchor Bolts .
Page.
69
69
70
71
72.
73
74
74
74
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81
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=
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ᏢᎪ Ꭱ Ꭲ I
1
INTRODUCTORY NOTICE
The idea of connecting England with the Continent by a bridge is not
new. It has from the beginning of this century occupied the minds of a
great number of distinguished men, but the labours of M. Thomé de Gamond
particularly contributed to render the idea popular.
Most of the schemes hitherto proposed have been insufficiently worked
out. They have all been found impossible to execute, and for this reason
have each, in succession, sunk into oblivion.
The submarine tunnel was next thought of as the means of communi-
cation between France and England.
The advocates of the bridge, however, have once more given the subject
their attention, and the object of the present paper is to show that the
construction of a bridge between France and England may now he
considered capable of being carried out in practice. We may say that the
problem is at present clearly placed before the technical authorities of both
countries.
However gigantic the undertaking, the many and various improvements
which have been made in the art of bridge-building fully warrant every
hope of success in an attempt to turn out spans of metal 500 metres in
length across the Channel, supported by columns resting.at different depths
on the bottom of the sea.
8
The metal it is proposed to use is steel. The extensive use that has
lately been made of this metal, both in France and abroad, notably in the
Forth Bridge, which is the outcome of the unmistakable progress of
metallurgy, removes every doubt as to the feasibility of dispensing with
about fifty per cent in weight by the use of steel, while ensuring the same
degree of safety.
The preliminary projects submitted by MM. H. Hersent, Schneider and Co.,
and Fowler and Baker, consist of separate reports relating respectively to
the foundations for the piers to be erected in the sea, and to the construction
of the superstructure, as well as of a rational statement of the means for
placing in position the foundations and spans. The authors of these pre-
liminary sketches do not wish to be understood as thinking that no useful
alterations can be made in their work when the time comes for the ultimate
plans to be proceeded with. Whatever opinion may be formed of these
projects, and whatever may be their eventual fate, their authors will at least
have the gratification of having paved the way towards an undertaking of
public interest, and of having furnished data sufficiently minute and correct
to enable the scheme to be submitted to the judgment and criticism of
competent persons whose careful attention they solicit. Among the great
undertakings which present a certain analogy to the proposed Channel
bridge, such as the opening of maritime canals, railways, ports, etc., none
is to the same degree worthy either of the international interest which has
guided the promoters of this great undertaking, or the direct interest of the
two countries, that will not only be called upon to bear the cost, but will
reap the advantages of the project as well. The amount of metal and
machinery to be provided for the construction of a bridge over the Channel
would represent an aggregate weight of about 1,000,000) lons. The assumption
is that each country will have to supply one half of this amount, which on
either side would for a lengthy period give a powerful impulse to the
development of national industry. To estimale as precisely as possible the
expense entailed by the construction of the Channel bridge it would be
necessary to go further into the calculations, and to modify, if necessary
after duly consulting the maritime interests involved in the question, the
number of spans which might have a stretch of 500 metres, as well as of
the spans of shorter length required in various places. In the same way
the extensions to be made in the port of Ambleleuse, and in an English
port situated equally near to the bridge, will have to form the subject of a
more detailed inquiry.
An approximate idea, however, as far as it can be possibly formed by a
rough calculation at first sight, assuming that the distribution of spans shown
"
- 9 -
に
​in Plan I. is adopted, permits the following figures to be given with
reasonable certainty:
Fr. 380,000,000 for masonry supports,
And Fr. 480,000,000 for the metallic superstructure.
In all, Fr. 860,000,000, or £ 34,400,000.
The works for the tunnel and the railways of both countries would have
to be planned later on in agreement with the companies whose lines would
lead up to the bridge. The time required for the completion of the under-
taking may be fixed at about ten years.
-
11 -
GENERAL DESCRIPTION OF THE BRIDGE
§ 1. Situation.
The situation which seems preferable for a bridge connecting England
with the Continent is, as it were, suggested by Nature herself, namely, by
the line stretching over the shallowest parts of the Channel, and connecting
the shores where they are closest to each other. This line commences at a
point near to Cape Grisnez and reaches the coast of England near Folkestone,
passing over the banks of Colbart and Varne. This arrangement has been
adopted in order to enable the existence of these two banks to be taken ad-
vantage of, so as to avoid working in great depths, and thereby to diminish
the height of the piers to be erected.
The banks are situated near the centre of the Channel about six kilo-
metres apart. The depth of the water at that point does not exceed 7 or
8 metres at low water, and they are separated from each other by a depres-
sion about 25 to 27 metres deep. Between the banks of Varne and the British
coast the depth does not exceed 29 metres, but between that of Colbart and
the Cran-aux-Oeufs the bottom sinks somewhat abruptly down to 40 metres;
it then attains 55 metres about midway across, when it begins gradually to
rise. In these parts then the chief difficulties would be encountered in
laying the foundations.
12
The sketch submitted gives about the shortest distance available for the
ready connection of the existing lines of railway in both countries, without
difficulty or an unusual amount of work.
§ 2. Masonry Supports.
PRELIMINARY PROJECT BY H. HERSENT.
In contemplating the construction of the supports, the nature of the
bottom was the first thing that demanded attention, as it was necessary to
ascertain whether its formation and resistance would be sufficient to ensure
the stability of the structure; the next thing to be considered was the form
to be given to the supports, so as to obtain as large a surface as possible at
the base, without causing trouble from the effect of the ebb and flow of the
tides; and lastly, it was found necessary to foresee the difficulties that may
be encountered in an undertaking of this nature in order to determine the
measures to be taken for successfully grappling with them.
The result of repeated experiments is that the ground is found to be suf-
ficiently solid to support very extensive works. In addition, the borings la-
tely made in connection with the proposed Channel tunnel have confirmed
the results of the preceding experiments as to the position and nature of the
bollom, as published by M. Thomé de Gamond. More precise inquiries will
be necessary when. the works are proceeded with, as regards each pier, in
order to be in a position to solve each detail beforehand.
At present, however, there is no doubt that the ground is capable of
supporting a load of from 10 to 12 kilogrammes per square centimetre, as is
often found to be the case on a foundation less solid than that afforded by
the white and blue chalk which everywhere forms the Channel bottom. The
soft parts of the surface in contact with the water and the strata of sediment
and sand that may cover the bottom al certain points, especially near the
shores, will have to be removed in order to lay the piers on more solid
foundation. Each supporting pier will consist of a block of masonry of
good material, set with Portland cement morlar, and laid on the sea bottom;
their surface above high-water level will form the foundation for the metal
columns which serve as direct supports of the spans of the bridge, and will
measure 650 square metres. They will, moreover, have a batter of about
13
1 in 10 up to the foundation caisson, which is flanged in order to increase
the surface of the base in contact with the surface of the ground.
The piers will form a rectangle, 25 metres in length, and their width
will have to be suited to each system of columns. This rectangle will ter-
minate in semicircles, so as to oppose the least possible resistance to the
currents.
Supposing 55 metres, the surface of the base of the piers in contact with
the ground will, be 1604 square metres. Where the depth is less, the surface
will be proportionately smaller. Up to a certain height, the brickwork will
extend over the whole surface of the base, while two recesses will be provided
in order to decrease the load upon the foundation, the sections of the walls
being of sufficient strength to resist any additional loads. The masonry will
be built inside metal caissons similar to those used for ordinary bridge piers,
and forced by compressed air down to the solid ground. These caissons,
which will be surmounted by metal cases surrounding the masonry, will
serve to float the piers until they touch the ground. This will enable the
ground to be carefully cleaned, and promote the application of the concrete
that is to be interposed between the masonry and the bottom, as will be
explained further on.
The caisson will, moreover, be surmounted by a movable dome, which
will be removed when the upper part of the column is completed, so as to
enable the masonry to be carefully finished with squared stones above the
level of low water. Special arrangements will be made for joining the columns
to the masonry so that these joints may be at all times readily inspected to
ascertain whether anything is out of order in each separate portion of the
work. The whole of the pillars will occupy a little over onetwelfth of the
section of the Channel. This reduction of the section of the Channel is not
likely to exercise a notable influence on the erosion of the bottom, or to bring
about an appreciable increase of the speed of the flood and ebb tides. The
distance between the piers, fixed at 500 and 300 metres for the large spans,
will not be less than 200 and 100 metres respectively for the small ones, and
will, at all events, be sufficient to prevent their proving an obstacle to the
free navigation of sailing vessels.
of sailing vessels. As regards
As regards steamships, no such danger is
to be apprehended, as the current, which would certainly become a little faster
in the centre of the open spans, would carry floating bodies, even disabled
vessels, towards that part, and prevent their ever touching the bridge.
It may, therefore, be reasonably admitted that, owing to these distances and
dimensions, the piers would in no way modify the conditions of navigation
in the Channel, and would certainly not constitute an appreciable obstacle
to navigation in general.
-14
$ 3.
The Metallic Superstructure.
PRELIMINARY PROJECT BY MESSRS. SCHNEIDER AND C.
The metal columns are firmly placed upon the platforms of the support-
ing piers of masonry. They are of a distinctly cylindrical shape, and vary
in height between 40 metres and 42,780, and on them will be placed the
main girders of the bridge. There will thus be between the lower part of
the beams, and the level of the sea at low waler, a free space, varying in
height between 61 metres and 63m,780, which height, at high water, will
be reduced to 54 metres and 56m,780 metres respectively. This height is amply
sufficient for the passage of vessels of whatsoever description or tonnage. By
placing the flooring upon vertical cylindrical columns, the space above indi-
cated, of a minimum height of 54 metres, is kept throughout the whole width
of the span a result which has not been achieved in the bridge of similar
dimensions that is now being constructed over the Forth estuary.
In the Forth, in fact, the height at the centre of the structure above
the high-water level is 45m,60 metres, but this height does not extend beyond
the central third of the span. At the twothirds near the ends this space greatly
diminishes, until it is actually reduced to a height of scarcely 15 metres near
the pier.
In order to make the exigencies of navigation agree as far as possible
with the economical carrying out of the preparatory works, three different
lengths of span have been proposed.
No. 1. Alternate spans of 300 and 500 metres.
No. 2.
No. 3.
200
100
350
250
The largest spans correspond to the greatest depths, the smallest to the most
elevated parts of the sea-bottom and to the parts near the shores.
The system of girders to be employed is simple, unlatticed, trussed, so
as to ensure the proper distribution of all stresses. The secondary beams
provided are intended to reduce the length of certain members, to prevent
buckling of braced beams, and to give those employed as struts proportions
suitable to the lengths concerned, whereby it becomes possible to leave the
-
15
co-efficient of compression, which would increase the weight, out of consi-
deration.
The level of the permanent way is 72 metres above the low-water level.
This height might have been reduced by arranging the permanent way in
the lower portion of the bridge, but in that case it would have been neres-
sary to make the cross-beams a great deal larger, and, consequently, heavier.
By raising the permanent way, on the contrary, as it is proposed here
to do, a marked economy is attainable, which will certainly not be absorbed
by increased expenses involved by the necessity of erecting viaducts at both
ends of the bridge.
There will be a double set of rails, and the width of the flooring proper
will be 8 metres.
The whole width of the bridge is variable. The greatest distance between
the axes of the main girders is 25 metres, such a space being necessary to
ensure the stability of the structure under the action of violent gusts of wind.
The roadways are of the ordinary width of 1,50 metres between the axes
of the rails. The latter will be set in grooves to obviate accidents. The
floor, made of ribbed sheet iron, is to cover the bridge throughout its length.
so as to make every part accessible to the men appointed for the supervision
of the bridge. Between and outside the roadways, pavements are provided
for the men to stand on, and thus keep out of the way of passing trains.
Upon the flooring it will be possible to establish « refuges », stations for the
guards, signal-boxes, switches, etc. All these arrangements may be multi-
plied according to the requirements of the traffic, and scattered over any
convenient points and spans. On the piers, lighthouses may be erected, to
indicate obstacles to be avoided. The various kinds of lights used in light-
houses may also serve to indicate to shippers the distance from the Colbart
and Varne banks. It would have been easy to establish a bridge with four
lines of rails instead of two, but the probable development of the traffic did not
appear to warrant any increase of outlay in that direction. The provision of
a road for ordinary vehicles is also superfluous, as goods will always be carried
by rail.
To meet objections from a military point of view, arrangements could
be made for making the span at either end of the bridge unfit for use; the
two end spans notably, which are in contact with the abutments, might be
removable or revolve. The detailed description of the plans and methods of
construction it is proposed to adopt, forms the subject of the following
chapters
PART II
FOUNDATIONS
H. HERSENT'S PRELIMINARY PROJECT
3
19 -
§ 1.
III.
DETAILED DESCRIPTION OF THE FOUNDATION
WORKS.
The Situation and Dimensions of the Brickwork supporting
Columns.
The ground affording sufficient resistance to safely support the piers
when loaded, the surface of the bases has been so calculated that the foundation
should not have a greater load than about 10 kilogrammes to the square cen-
timetre. With regard to the pillars sunk at 55 metres under the low-water
level, the dimensions, the calculations of the masonry sections, and the corres-
ponding weights per centimetre are summed up in the following table :-

DESIGNATIONS
SIZE
and
VOLUME
REMARKS
Length: at base.
$7,00
at low-water level.
47⁰⁰,50
above the cornice
42¹,00
Width at base.
32m,00
at low-water level.
22m,50
above the cornice.
17m,00
Surface at base.
1.604m2
•
at low-water level.
above the cornice .
960m2
631ma
Volume (exterior).
86.000m3
of the recess
28.000ms
of the masonry
57.200m³
Loads:
to be supported per square centimetre
at base on ground.
9k,80
at low-water level.
at base of columns .
5,75
On the masonry.
8*,20
On hewn granite.
20
The resistances offer every appearance of safety, alike as regards the
ground, the ordinary masonry, the body of the pillar, and the granite blocks
supporting the metal columns. The base appears to be sufficient to resist
the different transverse and longitudinal stresses (of which wind is the most
important cause) that may tend to overturn the pillars.
The length of the spans supported by the columns is 400 metres.
The surface exposed to the action of the wind on this distance is about
7,590 square metres.
The surface exposed to the action of the wind on the metal columns,
622 square metres.
The surface exposed on the 20-metre sub-basement, 370 square metres.
The surface exposed on the lower part of the piers, 1,570 square metres.
Assuming that the force of the wind and the strength of the pressure
exercised by the currents attain altogether 270 kilos per square metre, the
stresses produced upon each of these surfaces will be as follows: -
7.590m2 × 270k
2.049.300 kilos
622m² × 270k
167.940
370m2 × 270k
99.900
1.570m2 270k
423.900
And the moments of overturn will be :
2.049.300h 137", 1280.959.030 kilogrammetres.
X
167.940k × 95,4
X
16.021.476
99.900 × 66m
6.593.400
423.900 X 28m
11.869.200
Total moment of overturn at the
base of the piers.
One length of span of 400 metres weighs.
Two metal columns.
315.443.106 kilogrammetres.
Kos
One masonry pier.
1.164.000
2.010.000
148.675.000
TOTAL WEIGHT
•
Kos. 157.849.000
The points of the emergence of the resultant x from the centre of the
pillar is
x =
315.443.106
157.849.000
1m,99.
The surface of a column is 1604 square metres. The moment of inertia
of s in relation to the small axis of the column is 355,346.
Hence r² =
355,346
1,604
221,5.
*
21
One-half length n of the columns is 28m,5.
зов
Hence = d
d =
Ն
221,5
28,5
7m,77.
The co-efficient of stability, that is, the ratio of the moment of overturn
at the base of the piers, as compared with the momentum that would be
produced by a compression equal to zero upon the extreme edge of the
leeway will be
d
7.77
3.90.
X
1.99
Each pier is to consist of a block of good material, in which two
recesses or walls are cut out in order to diminish their weight at the base.
The particular portion upon which the metal columns rest will be the same
in all pillars, but the lower portion will increase in surface in proportion to
the height to which the structure is to be immersed in water.
The external walls will have a batter of 0,10 per metre, and the lower
parl, which will be taken up by a metal caisson, will project over the external
face of the wall as shown in the plan.
Caisson. The metal caisson of each pillar will correspond in external
shape and dimensions to the contemplated depth of the foundations. It will
consist of two distinct parts. The lower part will be 2 metres high and
open at the base, while the upper one, the exterior of which will surround
the masonry of the body of the pier, will form one single chamber, extend-
ing over the whole surface of the caisson. Special frames and cross-pieces
will serve to maintain the sheet-iron casings in position, and in a state of
rigidity.
The lower portion, intended for the use of compressed air, and for
fixing the structure to the ground, will consist of an external metallic
casing limiting the periphery, and of vertical walls, dividing the horizontal
surface into compartments of from 50 to 60 square metres each-these com-
partments, capable of being used and expanded either separately or together,
each provided with compressed air, and intended for clearing the ground of
foreign matter, or simply to level it, and to effect the final filling at the
junction of the structure with the ground. Each of these compartments of
the base will be provided with air sluices arranged at the bottom, and with
special devices for facilitating access and inspection, for removing excavated
matter, and for filling up the excavations with concrete from outside.
The first piers on each shore may be constructed without necessitating
any alteration in the means ordinarily employed for this kind of structure.
The experience acquired in sinking these first piers will thus enable improved
22
methods to be adopted for the thorough clearance of the soil, the filling of
the compartments, and, in short, the completion of the whole base in the
case of depths exceeding from 20 to 25 metres below the surface of the
water. In exceptional cases they reached 30 and above 35 metres, but at
such depths accidents have sometimes occurred, which appear to have been
the result of excessive fatigue on the part of the men employed, and of the
want of proper provisions for compression and expansion.
Divers going down in search of sponges and corals descend to a depth
of 50 metres, and thus experience the effects of the compression and expan-
sion which would be obtained in using compressed air al such a depth.
It will not be too much, therefore, to say that the ground will be capable
of being
inspected under all the piers before the concrete is filled in at
the base.
It may also be taken for granted that the bottom can be cleared before-
hand by means of special apparatus, enabling compressed air to be dispensed
with, and that the filling of the compartments and air chambers can be
effected, either outside or inside the pillars, without its being necessary for
the men to perform any important work below.
In considering the matter from this point of view, the question arises
as to what would happen if the 120 cubic metres of concrete required for
filling one compartment were conveyed down through a funnel pipe. It was
found that if the water contained in the lower working chamber can be
ejected to make room for the concrete, the filling of such chamber can
be satisfactorily completed, and the concrete will in no way be inferior to
any of the other methods used for ordinary depths. This method of carrying
down concrete through one continuous pipe is far preferable to the use of
cases, which are liable to give off rather considerable quantities of grout.
From these remarks it may be inferred that if each compartment was filled
in specially and separately from the others, the satisfactory completion of
the works would be assured, and that, should any of the compartments not
prove quite faultless in some respects, the whole of the works would not on
that account be impaired.
These arrangements contemplated for the filling of the compartments
have made it possible to determine the shape of the lower portion of the
caissons of the piers, and the lines of resistance of the staging. The cais-
sons would have to consist of one externally inclined wall, and of vertical
walls strengthened by strong frames at the portion that is in contact with
the ground, and terminating in the form of declivities. All these vertical
walls should join the metal roof that separates the lower compartments from
the upper portion, and correspond to the upper beams, whose resistance
they will thus increase. When the load is sufficiently heavy the declivities
23
will touch the ground, and this contact, at the time of low tide, taken in
conjunction with the normal oscillation, will probably be sufficient to break
off fragments, which the currents of the sea will remove when high tide
sets in. The chances are that the levelling of the ground can be done without
any considerable expenditure of labour; but the cutters will have to be of
rather considerable size, in determining which the experience acquired by
the sinking of the first caissons near the shore will have to be taken into
account. The levelling apparatus used in the ports of Brest and Cherbourg
has already furnished valuable hints on this point.
The portion of the caisson situated above the roof will serve to contain
the masonry, and to protect the same from immediate contact with the
water, while at the same time it will enable the men employed in the
works to operate in a dry place as the structure advances downwards.
This part of each caisson will be formed of a water-tight metal case.
supported by horizontal framings, provided for preserving the external form.
All these framings will be enclosed in the masonry, which, in the possible
event of the decay of the iron, would remain still unaffected.
The portion of each caisson situated above the level of low water will
be movable, and can be utilised successively for several piers, which will
consist of a sort of dome composed of metal plates suitably fitted to each
other. These will cover the structure of the pier and enable the lower
ends to be sunk to the sea bottom in such a way that the masonry, although
floating, can be completed as if it were erected on land. This has been
successfully achieved in building the dry docks at Saïgon and Missiessy, at
Toulon, where 45,000 cubic metres of brickwork, representing a weight of
100,000 tons, were kept afloat in the caissons for several months.
The piers, at a depth of 55 metres, would have to support the load of
12,000 tons at their juncture with the ground, which is by no means
an unheard-of achievement.
Plans 3, 4, and 5 illustrate the general arrangement of the caissons;
they show, indeed, the lower portion, or concrete chamber, the central
portion containing the ballast masonry, and the top or dome that is to
surmount the whole.
Masonry. The masonry of which the body of each pier is to consist
should be composed of good homogeneous calcareous materials from Marquise,
Boulogne, etc., of which there is a great quantity in the neighbourhood of
Gris-nez. They can be carried to the spot either from Ambleteuse, Boulogne,
or Calais, and will cause no trouble.
The morlar required for the whole structure will consist of Portland
cement, in the proportion of 500 kilogrammes per cubic metre of silicious
24
or granitic sand.
Calcareous or schistose sand must be avoided as liable
to decomposition. Upon the roof of the caissons a layer of concrete 1,50 to
2 metres thick shall be formed to protect the iron beams, and above that the
ordinary masonry shall be made of rough quarry stones, which shall rise
up to the low-water level. Two caissons being provided externally, which
will render the structure lighter, will greatly facilitate the work on the
lower portion, when it is required to fill the chambers of the masonry and
the bodies of the piers. At each successive height of about 4 metres, two
courses of cut stones will be placed, which will have the effect of better
distributing the load, and rendering the tendency to settle down more
uniform. The level surface of the lower portion below the low-water level
should also consist of rough stones. From the low-water level upwards,
the recesses before mentioned will gradually be made narrower, and terminate
in two caps, surmounted by funnels, giving access for purposes of inspection
and for anchoring the supports of the bridge. The masonry and the upper
portion below the low-water level should be fitted with granite stone walls,
so as to offer a considerable resistance to the crushing stress and to atmos-
pheric destructive agencies. The platform upon which the metal columns
and supports of the bridge are to rest would consist of a number of
successive courses of granite stones, which should distribute the weight and
the loads equally over the surface of the piers, and they will be provided
with the necessary holes for anchoring the metal columns to the pillars.
Round the platform a metal balustrade should be erected to protect the
persons employed in supervision and repairs.
§ 2.
The Construction, Conveyance, and Fitting into Position of the
Supporting Columns.
The Port. The size of the pillars, and the considerable amount of mate-
rial required, will necessitate the establishment of a port at a point nearest to
the spot where the works are begun on either coast. On the French coast,
a great construction of that sort would probably have to be provided for in
the Bay of Ambleleuse, although part of the traffic will still have to be left
to the ports of Boulogne and Calais. On the English coast, Folkestone
would form the centre of operations. The port of Ambletcuse might be
established in the free part of the valley, and protected by means of two
piers or jellies. The west pier would point to the north at an angle of
25
45 degrees to the coast, and the north one would form an incline southwards.
The entrance would be 250 metres wide, and 7 or 8 metres deep at low
water.
A channel 150 metres wide, protected by a stockade of wood forming
a quay for the vessels to come alongside, would give ready access to the
port, which would practically consist of the existing port deepened and
extended.
This port, dug 6 metres deep below the low-water level, would be
700 metres long and 350 metres wide, so as to admit of the plant necessary
for the simultaneous construction of a number of girders. The bottom would
be utilised for constructing the foundation of the caissons. Several docks
would have to be provided in the port at half-tide level or somewhat lower,
which would be isolated from each other, and separated from the sea by
floating dams, just like a sort of floating docks, that would have to be ope-
rated whenever the caisson is taken out, so as to simplify this operation as
much as possible. Besides the port a tidal dock would have to be construc-
ted, with quays, bridges, and all necessary arrangements for facilitating
the embarking of men and goods, and for insuring the safety of the floating
stock. The Northern railway lines will have to lead up to the quays and
to any other points that may be deemed desirable, so as to enable all the
material and machinery to be carried from place to place by railway, and
in order to facilitating the loading, unloading, and storage of same.
The dwellings of the workmen will be established at a short distance,
but it is very probable that the steamship traffic will permit the employment
of workmen residing in Calais or Boulogne, especially to the works to be
performed in the offing. It is, moreover, very likely that important quan-
tities of material will have to be conveyed by these ports. This division
of labour on the French coast will benefit the whole of the operations, and
prevent obstruction of any point of the district occupied by the works. On
the coast of England the port of Folkestone and others will be made use of
for similar purposes. A network of telephonic cables will connect the diffe-
rent loading stations between them, and also with the yards on land and
in the offing, so as to ensure that unity of action which is absolutely neces-
sary in the execution of great undertakings such as this. The first portion
of the foundation caissons, which includes the lower chambers, and the
cross beams up to a height of 3,50 to 4 metres, will be constructed in
a closed basin, as has been done with the caissons built in Toulon, Ant-
werp, and Saigun. They will be put afloat by opening the doors at the
spring-tide, so that they may be brought up to the outer harbour, where
the work will be continued.
In the outer harbour, then, the erection of metal walls and the caissons
4
26
will be carried on until a height of from 12 to 15 metres above the base is
reached. At the same time the ballasting, by means of a layer of concrete
from 2 metres to 2m,50 thick, will be commenced, being inten led to insure
the necessary stability for conveyance through deep water. This latter ope-
ration can be carried out by means of tugs when the caisson is sunk 10 or
12 metres deep, that being the maximum weight that can be charged, lest
it should make it difficult to leave the port. The caisson will then, with
ils ballast of masonry, be brought to the place it will have to occupy, where
it will be fixed by the means hereinafter described. The ground will be
dug by the ordinary methods, with the aid of compressed air and other sui-
table means, until the base is firmly established upon a sufficiently firm
foundation. The chambers on the roof will be filled with concrete, and the
upper masonry will thus gradually rise until its completion. As regards
the pillars to be sunk at a depth of less than 10 or 12 metres below low-
water level, the operation will be as described, but beyond that depth the
caisson, when it leaves the port, will be brought up to the pillar that is
already placed in position, and the ballasting will be continued up to the
time that it has to be taken to the place of its immersion, so as to concen-
trate as far as possible, at one and the same place, the whole work to be
performed in the sea, and thus facilitate surveillance and measures of pre-
caution that cannot be dispensed with in such operations.
By thus proceeding step by step, the necessary experience will be acqui-
red as the work goes on for venturing down to lower depths, the work
being perfectly regular, and one may say even normal, since it is supported
by precedent.
Putting in Position. The most important and perhaps the most delicate
operation in this great undertaking is the placing of piers, while still afloat,
into the positions they are eventually to occupy, with sufficient precision,
so that the length of each span of the superstructure may be about equal.
Great precautions must evidently be taken, and the effects of bad weather
avoided, until sufficient experience is acquired.
For the first operations, il will always be necessary to work in fair weather
and at low water, preferably slack water, so as to be able to touch the ground
and fix the construction in a short time. If, after inspection, it should be
found that the place where they ground is not the right one, the piers are
to be raised, and the whole process to be gone through over again until the
column is in its proper place. In fact, the method to be adopted is very
similar to that which we used with M. Castor for putting in place the piers
of the Arles bridge over the Rhone.
At a distance of from 200 to 300 metres, strong anchors would be run
27
out on chains corresponding to as many barges arranged for supporting and
raising them. These barges will be connected with the caisson of the pier by
sufficiently strong moorings to enable it to be retained in place, to perform
the lining out, and to determine the distances, all operations requiring the
attendance of very experienced engineers, capable of taking duly into account
the deviations due to the action of the tides. The putting into line and fixing
the distances may be effected when the edge of the caisson is at a short dis-
tance from the ground (say from 0m,50 to 1 metre). It will thus be possible to
admit into the chambers in the lower portion of the masonry an amount of
water that will give the caissons sufficient weight to enable them to touch
the ground, and to insure stability, which will make it more easy to ascer-
tain whether they are placed in the right position, and are perfectly vertical.
Whenever it might be found that the pier was not in its proper position,
it would be necessary, in order to get it afloat again, to let the water out,
to replace it by compressed air in the roof, and to begin the same operation
afresh. If, on the contrary, the operation proved successful, it will be suffi-
cient, to ensure the stability of the caisson, to add to the load a certain amount
of masonry, and to withdraw the water or compressed air which had been
provisionally used during the ballasting, preliminary to putting in position.
The position of a column being sunk in the midst of anchored barges,
and attached by the necessary moorings, will be very similar to that of a
spider in the middle of its web.
it
By reason of the particular position which each column is to take up,
will probably be necessary to strengthen some of the moorings, and to run
out several more anchors.
The barges used for that purpose will have to be provided with the
necessary steam-engines and winches, so as to operate with the necessary
amount of safety and power. The same winches can also be used for lifting
the anchors.
The barges will form a sort of protecting belt to the pier they surround
at the moment of its immersion, and will serve to moderate the height and
strength of the waves. It will be possible even to increase this effect of allay-
ing the waves by using open rafts, moored to the barges, which would
cover a comparatively large surface of water on the weather side.
The employment of oil, as has been pointed out by M. Admiral Cloué,
has the effect of stopping the breakers, and it is very probable that, after a
few experiments, we might, in this way, succeed in obtaining sufficiently
smooth water around the piers to enable materials to be put into position
under almost any conditions of weather.
The experience hitherto obtained of the new means of protection against
the action of the sea, shows that one may succeed in working, almost without
28
interruption, at floating caissons, as if they were situated on a small island.
Such is the impression which has been deeply engraved upon the memory
of all those who witnessed the works carried out in constructing the docks
in the port of Toulon. When the moorings are thus arranged near the posi-
tion of the columns, the masonry of the pier will be built up, the leakings
being at the same time tightened, in order to prevent having too much to
do at the last moment. The laying of the masonry will compel the conti-
nuous raising of the metallic walls of the caisson up to the level of the sea
at low water.
For the purpose of protecting the masonry, after getting each column
into position, and bringing the upper portions of the masonry into correct
line, the caisson will be surmounted by a movable metal structure, which we
may call a dome, on account of its being contracted towards the top.
This dome, which will be about 14 metres in height above the fixed
portions of the caisson, will be composed of metal plates, one upon the other,
and bolted together to the top wall of the caisson, in order to permit of sub-
sequent taking to pieces. The tightness of the joints will be produced by
layers of caoutchouc, as is usually done with dams 80 to 100 metres square
surface, weighing 18 to 20 tons, employed in foundation caissons. The
mounting and taking to pieces of this dome will be managed by means of
a floating derrick, capable of lifting a weight of from 40 to 50 tons.
The lower part of the dome will be furnished with a gallery, or hori-
zontal platform, which will be used at the same time for the purpose of
increasing the main resistance. In the middle portion would be another
platform or gallery, above high-water mark, for receiving the cranes necessary
for lifting the materials required for the masonry, after the caisson has been
finally placed in position.
Levelling the Ground. - Before the caissons are put in place, it will
be easy to ascertain, by preliminary boring, the nature of the ground upon
which the pier would have to rest, and to see whether it is perfectly hori-
zontal or not. These experiments will also permit of making sure that the
ground has sufficient resistance to sustain the piers, or whether it is
necessary to prepare a special bed for them. Such levelling of the formation
of the bed will probably be requisite in the case of piers near the coast, but
owing to the small depth of the sea in those parts, compressed air may be
used without any difficulty. For depths of from 20 to 35 metres, which
hitherto have only been obtained in exceptional cases, no uneasiness need
be fell with regard to the applicability of compressed air, inasmuch as
experience will show the practical improvements that may be made in the
methods and means already employed
29
1
About twenty-four piers will have to be erected in portions of the
ground lying at a depth exceeding 35 metres. For these twenty-four piers,
the experience previously acquired cannot fail to prove a safe guide as to
the improvements that may be made in the methods of operation, and to
give practical value to works which hitherto have only been attempted in
cases of exceptional difficulty.
Should it so happen, in levelling the ground for the piers that are to
descend to the maximum depth, that any danger were to be apprehended
from the use of compressed air, there will be no necessity nevertheless to
remain inactive, for owing to its rotary structure the ground can be acted
upon by means of rotating machinery that can be set in motion from the
platform, or it may be cleared and levelled beforehand by means of special
machinery. The clearing of all matter rejected in the levelling operation can
be performed by means of force-pumps of considerable power, or compressed
air engines, whereby the ground operated upon would be divided into a
number of sections, to enable the currents to carry away the fragments.
Experience will probably show that the action of the water column under
pressure will alone be sufficient to clear the ground, and especially to remove
all on the surface.
The filling of the working chambers with concrete will be effected by
means of compressed air, in the case of all the piers that will enable compressed
air to be used. There is no doubt that this very important operation will
itself suggest various improvements that can be made in the processes now
employed, and will meet all requirements in the sinking of most of the
piers.
Filling in the Concrete Base. It is thought that by repeating the
experiments made in the construction of the Kehl Bridge, it will be possible.
in the case of great depths, to convey the concrete down to the lower portions
of the working chambers by the simple use of free air, and to obtain very
satisfactory results. One method that is to be thought of in this connection,
consists in the filling of one of the compartments, having a surface of about
60 metres, by one uninterrupted operation, allowing the water and grout
that will be produced, or any slime that may be made and left on the ground
to escape through a special orifice placed at the top of the chamber.
To obtain this result a great funnel will have to be used, made of steel
sheets, and having a sufficient diameter to allow the concrete to pass through
it without too much impediment (0,75 appear from trials hitherto made
to be a diameter that will answer this purpose).
This funnel or tube will have to be filled in with concrete up to the
top, and closed at the foot by a self-closing valve. " That would have to
"(
30
be opened, so as to permit the immediate passage of enough concrete to fill
one of the compartments.
The introduction of the concrete will occupy from fifteen to twenty
minutes, so that when the compartment is filled the funnel should still retain
a sufficient quantity of it to form a head and thus to prevent the water from
entering the funnel during the operation. In operating in this manner, and
in the case of each of the compartments of the lower part of the caisson, it
will appear beyond doubt that the foundation leaves nothing to be desired in
respect of strength, since the identical operation is gone through for each sepa-
rate portion. In fact, the whole of the work will consist in repeating partial
operations such as these, for which, therefore, suitable machinery will have
to be provided, and it may be considered certain that the normal pressure.
exercised by the concrete remaining in the funnels will be sufficient for the
removal of the slime and groul. The test of such practical data as are avail-
able in this kind of work justifies the choice of this mode of operation. The
only objection that occurs to the mind is, that it is unlikely for 120 cubic
metres of concrete to be got ready in the space of from fifteen to twenty mi-
nules. It does not appear impossible, however, to obtain such a supply, nor
even difficult, seeing the enormous quantity of concrete that will be required,
and the very powerful machinery that must necessarily be employed. Each
pile, when immersed and placed on the ground, will comprise, for a depth
of 55 metres below the low-water level, the following components:-
Displacement of water (al low water).
Difference of tide
Volume of the pier
•
Space of the recesses
Volume of masonry .
Weight of masonry
caissons.
•
(at high
Load sustained by the ground
70.5133
)
75.970m³
5.460m3
86.000m³
28.800m3
57.200m³
1.160t
148.870
150.030
1.604m2
Load expressed in kilogrammes per square centi-
metre .
Weight of metal columns
•
flooring.
9,3k
2.010t
7.164¹
Total load supported by the ground
Total load expressed in kilogrammes par square
157.850
9,8k
Surface of piers at the base.
centimetre.
•
•
31
Upper Levelling. Whenever a pier is titted in position, it becomes
necessary to raise the masonry from the lower waterlevel up to the base of the
metal portion, that is, a distance of 20 metres, and up to a height of 15 metres
above the highest waterlevel, so as to protect the base of the metal columns
as far as possible from the action of the breakers. This work, which is not
inconsiderable, since it represents 12,000 cubic metres of masonry, will, du-
ring the first half of the operation, be sheltered by the upper dome, while the
last half of the work will have to be carried on after the dome is removed.
The masonry of the upper portion is to be provided with walls of hewn gra-
nite stones similar to those composing the upper courses. The body will be
an ordinary filling in" work. Ladders, and even flights of steps, will be
provided to facilitate the access of the workmen, or their escape in case of
accident. These ladders and steps will also enable the works to be inspected
and observed after they are completed.
66
Erosion at the Base. If any fear was entertained as to the liability of
the ground at the foot of the piers to become eroded by the currents of the
sea, and thus to become less strong and reliable, it will be necessary to
protect them by means of sacks filled with concrete, and so piled up, one
above the other, as to form a sort of slope round each pier. Such a result
could only be obtained by lowering the sacks of concrete with the aid of win-
ches, as they could not be thrown down. A good result may also be attai-
ned by forming stone packings around the base of the piers, composed of
bulky pieces of rock discharged through special doors or gates (as isolated
stones would not descend vertically), the probabilities being that no devia-
tion will take place when they are discharged in one bulk through a door. The
compression of ground resulting from such rock packing round the piers
will even add to its resistance, if that be desirable.
Special Considerations. No construction has been attempted up to the
present time unless by means of stones sunk to the bottom, which get dis-
placed or broken above the sea. The sea, in fact, often destroys even piers
constructed by rocks, so that the safely of vessel in ports is rather jeopar-
dised. It must be recognised, however, that while formerly there was no pre-
cedent to assist those employed in the solution of these questions, the expe-
rience acquired since has given mankind a great many useful hints by which
we ought to profil, and which we must not leave out of sight even when a
totally new step has to be taken in the same direction.
Taking for granted that the works will be sufficiently protected against
the action of the tops of the breakers, and that it will even be possible to
shelter them against the less powerful action of the swell, the undulations
32
of which cannot cover more than 100 metres distance from the top of one
wave to that of another, or measure more than 2,50 from top to bottom,
it may be inferred that, in the case of a pier 57 metres long, such a pier will
not be thrown out of the perpendicular by any rocking motion to which it may
be subjected, and which will only represent a fraction of that sometimes expe-
rienced by ships situated near the pier. Piers sunk deep into the water, and
forming a considerable bulk, will only undergo part of the effects consequent
upon the surface being thrown out of the level, and will present, as already
mentioned (even while afloat), the appearance of small islands in regard to
the ships that may approach them, while the vessels car. ying materials will
in most cases follow the undulations of the surface of the sea. The work
here contemplated has a certain analogy with the erection of a number of
isolated lighthouses upon rocks, which have always caused a considerable expen-
diture of labour and capital. These works, difficult as they were, did great
honour to the able and skilled engineers who had devoted themselves to suc-
cessfully carrying them out, but it is plain that an immense amount of trouble
and labour would have been saved had these very structures been built upon
a metal caisson placed upon the bottom of the sea, in the season when that
is practicable. The lighthouses in the estuary of the Oder may be mentioned
as an instance illustrating this statement, resting, as they do, upon a metal
caisson.
§ 3. Materials and Machinery required for the Completion of the
Works.
The usefulness of a special port for the construction of the caisson, the
fitting of the girders, and the sailing and floating stock has been sufficiently
dealt with above. Such ports, as before stated, would have to be situated as
nearly as possible to the point at which the works are begun upon either coast.
Each of these ports would have to answer the immediate and special
requirements of the work, and have docks or basins enabling four caissons
to be formed at the same time, and two more caissons loaded. Each will
also contain buildings for storing up the iron and the cement, and the work-
rooms for the manufacture of the metal fittings. In fact, it will amount to
an extensive works, that will supply all that is necessary for the construction
of the bridge.
The port will also have to be provided with suitable shunting arrange-
33
ments, as well as with all that is necessary to keep the floating stock in good
repair, which stock would have to be rather considerable to assist in the
erection of the masonry in the offing.
Nothing less than the number of vessels enumerated in the following list
will be sufficient :-
Five steamboats of 250 H.P., carrying ballast and various compressed air engi-
nes, with the proper fitting.
Ten steamboats of 300 H.P. and 10,000 tons capacity for conveying the work-
ing material to the spot. Each one of these vessels will be divided
so as to be able to hold convenient proportions of the different categories
of materials that are to be employed, and will also be fitted with the
necessary machinery for loading and unloading, for manufacture of
mortar and production of the electric light.
Twenty-five anchoring barges for mooring, provided each with a machine
and a winch for mooring and lifting the anchors.
Five tugs or lighters for keeping the various materials in reach of the works
in the offing.
Two barges with masts, yards, etc., for putting up and taking down the
domes of from fifty to sixty tons each.
Thirty unsinkable barges for the port traffic, and for the conveyance of
accessories.
The gangways will be arranged in such a manner as to receive the goods
as they come from the interior of the country from the railway station direct.
The quays will be provided with cranes of various degrees of power, corres-
ponding to the weight of the pieces they have to lift.
20
5
35
IV
CUBING, ESTIMATES, AND TIMES REQUIRED FOR
COMPLETION OF WORKS
The following table shows in a condensed form the importance and the
number of the piers to be constructed, such construction requiring about
four million cubic metres of masonry and about seventy-six thousand tons of
metal.
Table of the Work to be Performed for the Construction of the Piers

MASONRY
CAISSONS
DESIGNATIONS
Breadth
of
Piers
Cubic
Metres
per Pie s
Total in
Cubic
Metres
Weight
of
Caisson
REMARKS
Total
Weight
m3
m3
hos
Los
Piers at under Low Waters
14
17.300
10
6 20.500
15
сс
242.200 311.000 4.354.000
123.000 386.300 2.317.800
24.500 196.000 466.800 3.734.400
20
18 28.600
25
30
31.900
30
504.000
957 000
601.600
561.600 10.108.800
618.600 18.558.000
35
40
6 43.400
45
4 48.000
50
55
4 52.600
10 57.200
118
3.939.600
16 37.600
୬ 40.500
81.000 790.200 1.580.400
260.400 873.800 3.242.800
192.000 966.400 3.865.600
210.400 1.058.200 4.232.800
572.000 1.163.20011.163.200
76.309.800
697.000 11.152.000
If it be desired to complete the whole of the works within a period of
ten years, which does not seem at all impossible, about two years would
have to be devoted to preparatory works for establishing of working yards
36
and buildings, so that the whole time, with this preparatory period included,
would extend over twelve years. In such a case the foundation-work would
have to be completed one year before the superstructure is begun, but it
might be commenced even a little before the first year has quite elapsed.
Thus ten years may be considered as necessary for the foundation-works and
the superstructure.
The labour would have to be divided between two working yards situated
on either coast, so that each yard would have to turn out two million cubic
metres of masonry, concrete, and caissons, to the amount of 40,000 tons
each in a year, with the amount of 200,000 cubic metres of masonry, and
4,000 tons of iron caissons. The iron would be supplied from existing works,
so that no difficulty would be encountered in this respect, except that to
the annual 4,000 tons will have to be added the iron necessary for the
superstructure. The plant required, however, for this demand exists, and
this is the main point.
As regards the masonry, there are some difficulties that would have to
be contended with, not on account of the quantity of 200,000 cubic metres
that must be turned out every year, but owing to drawbacks inherent
to any work to be performed in the sea, as well as to the inconvience
attending the conveyance of men to the spot, and the loading and unloading
of materials.
In the maritime works performed in the port of Antwerp 600 cubic
metres of brickwork or of concrete have been turned out every day, and in
the construction of docks at Missiessy 200 cubic metres of masonry for each
caisson were easily supplied. At Boulogne and Calais the condition of the
sea enables work to be carried on by dredging inachines from 200 to 250 days
per year, which goes to show that if in the Channel bridge a better adapted
and stronger material be used, the works can be carried on from 40 to
50 days longer, i.e., from 250 to 300 days a year, or, on an average, for
275 lays per annum. Deducting the holidays, however, the work will not be
continued for more than 250 days, so that it will be necessary to turn out each
200.000
250
day
800 cubic metres of masonry.
It does not appear to be possible to put more than 100 cubic metres of
masonry per diem into one pier caisson, so that to obtain the total quantity
of work required it woult be necessary to operate on eight caissons at
once, and, besides, perform the preparatory and supplemental operations
separately.
In estimating the time that would probably be required to perform each
of these operations, one can at once form an idea of the number of columns
that will have to be operated upon at the same time.
37

AVERAGE COLUMN WITH BASE AT 30 METRES
BELOW THE LOW-WATER LEVEL
Construction of caissons.
•
•
Loading same before moving
Conveying same to place of sinking
Masonry to be erected before sinking.
Clearing the ground (?) under the edge.
Fitting in place and final clearing of ground.
Application of concrete
Timelost through bad weather and holidays
•
QUANTITIES
TIME
REMARKS
697.000k
60 days
2.200m2 10 >>>
2
>>
17.500m3
175
>>
30
བ
>>
20
>>
2.400m3 20
160
>>
2
>>
477 days
The supply of the immense quantity of necessary material does not
appear to offer any very great difficulties. As regards the concrete and the
rough bricks and stones, the chalk quarries situated near Marquise may easily
be taken advantage of, and they will probably suffice to supply all that is
necessary in this respect with the assistance of a railway line.
The shipping of such materials may be divided among the ports of Calais,
Boulogne, and Ambleteuse proportionately to the 'facilities which each of
those ports offers. The unloading on the spot where the work is carried on
will be effected by labourers, assisted by special machinery, and no compli-
cations are to be feared in this connection except such as may arise from the
unsatisfactory condition of the sea, which may be guarded against in the
manner indicated in the preceding chapter.
The sand required for making the mortar will be supplied by the beach.
Cement is manufactured in considerable quantities all around Boulogne,
from whence 50,000 tons per annum can be easily obtained. The granite for
the capping of the piers may be derived from the quarries of Chausey, Fla-
manville, etc., situated on the coast, and placed beforehand in a condition
suitable for the purpose.
PART III
SUPERSTRUCTURE
PRELIMINARY PROJECT OF MESSRS. SCHNEIDER & C°
41
V
CHOICE OF SYSTEMS OF GIRDERS
The idea of placing non-continuous girders upon piers erected at regular
intervals of 500 metres must be rejected at once. It is true that this system
would offer the unquestionable advantage of considerably reducing the number
of piers that might constitute obstruction to the navigation; but it would,
on the other hand, be attended by the drawback of increasing the weight of
the bridge extremely, for it is well known that the weight of a girder with
two points of support increases much more rapidly in proportion to the span
than a girder arranged in cantilever system.
It would seem advisable to form large cantilever spans, but such an
arrangement requires that between the points of support of the same girder
a sufficient length is left for ensuring the stability of the work during cons-
truction, and to make up for the varying distribution of the overcharge, as
well as to meet the emergency of excessive gusts of wind.
It will be understood that, from the standpoint of economy, it would be
desirable to reduce this length as much as possible - 100 metres, for instance,
would be a satisfactory length; but then it may be objected that, in many
cases, these lengths of 100 metres would interfere with navigation, especially
with that of sailing-vessels. It would, therefore, be necessary, to avoid multi-
plying such obstacles, to increase the distance between the piers. This dis-
tance has consequently been fixed at 300 metres at the deepest part of the
sea, where the spans, arranged so as to form cantilevers, would therefore
attain 500 metres. It has been stated before that, in addition to the alternate
spans of 300 and of 500 metres, there would also be spans of 200 and 350
metres, and another set of spans of 100 and 250 metres respectively, to be
placed ad the points corresponding to the elevated portions of the ground
and in the vicinity of the coast.
In considering the spans of 300 and 500 metres, the first idea that occurs
is to form the spans of girders extending over the whole length of 300 metres,
6
12
and extending on either side in the form of cantilevers of 250 metres, so
that the junction of two cantilevers should constitute a span of 500 metres
in all. The accompanying sketch shows this arrangement.

1
1
*-
250 m
300 m
500 m
It is a well-known fact that in the Forth Bridge the two large spans
are not completely covered by the cantilevers, the latter being connected by
an ordinary independent span.
It therefore becomes necessary to ascertain whether the addition of
such an independent span would result in diminishing the weight. The
nature of this paper does not enable us here to reproduce the calculations
to which this inquiry has conducted us, but it may be stated that these
calculations have shown that the addition of an independent span is advi-
sable, and that, supposing the distance between the points of support to be
500 metres, the space comprised between one-third and one-fourth of the
distance between the points of support is the best indication of the length
to be given to the same, for by this means a saving of about 17 per cent.
is realised on each overhanging portion of the cantilever. The accompanying
sketch shows the arrangements adopted for the three types of spans.

1- Type
187m5
211 Type
Турс
130
3 Type
9275
300!!!
500
m
18 - 15
125 m
18- 15
200
m
350 m
130m
-20m
130m
100
250"
-925
65
ܵܐ
J.
9.2!!!5
43
It now remains to determine what arrangement is to be adopted with
regard to the main girders of the bridge. The best girder will be the one
that will necessitate the employment of least weight while offering sufficient
resistance to vertical loads and presenting the least surface to the action of
the wind.
Many types of girders of the same height, and presenting about the
same intervals between the lower apices, have been examined, it being
desirable to avoid taking into consideration the weight of the beams and of
the sleepers under the rails.
Warren compound girder.
Post girder.
Warren laced girders.
AA

W
Warren simple girder.


W


Prall girder.
The following table shows the weight of the different girders as compa-
red with the weight of the Warren's compound girder:

WARREN'S WARREN'S WARREN'S
POST
PRATT
LAGED
COMPOUND
SIMPLE
Weight to resist vertical strain
>>
>>
wind.
1.000 0,957 1,063 0,956 1,190
1.000 1,137 1,241 1,350 1,080
Proportional average. 1.000
1,047
1,143 1,133 1,141
44
9
11
This proportional average has been calculated on the assumption that
the weight necessary to resist the wind represented of the weight suffi-
cient to withstand vertical strain. The question has been carefully inquired
into, and the present report is the result.
It will be seen that the Warren compound girder offers most advantages,
and therefore this type of girder has been selected. The same girder has
also been adopted for the independent spans connecting the consecutive can-
tilevers.
45
VI
(1)
ARRANGEMENT OF METALLIC SUPERSTRUCTURE "")
§ 1.
Spans of 300 and 500 metres.
It is proposed to provide the bridge with two lines of way situated
at 1,50 apart. The upper level of the rails will be 72 metres above the
low-water level, the lowermost portion of the bridge being 61 metres above
the low-water level throughout the extent of the spans of 300 metres, while
in the centre of the spans of 500 metres, that portion is 66,50 above the
low-water level (see sheets 6, 7, 8 and 9).
Central Span and Cantilever Arms. — The metal flooring of the bridge
is formed of two girders resting upon two piers 300 metres apart, and length-
ened on either side to the extent of 187 metres, the arms of the cantilevers
being 500 metres apart. These girders are 11 metres high at the ends of
the overhanging portions, and 65 metres high almost throughout the span
of 300 metres. Each girder consists of two members or chords connected
by bracings forming isosceles triangles. The lower flanges of the two
girders have a distance of 25 metres between their axes in the central
span of 300 metres, and an interval of 10 metres at the ends. They are
(1) The segments and calculations relating to the superstructure for the contemplated Channel bridge
were conducted by M. J. B. Pradel, managing engineer of the Chantier du Creusot at Chalon-sur-Saône.
46
horizontal in the central span, but are raised to a height of 5 metres at
the ends of the cantilevers. The upper chords are connected in the largest
portion of the central span, but diverge at a certain point, so as to be
10 metres apart at the ends, and this is also the case with the lower
chords; in the cantilevers they assume the shape of polygons inscribed in
a circle of 650 metres radius.
All the principal members of each girder, such as the chords and braces,
are formed of plate and section iron divided into four segments. The
secondary bars are of simple sections.
The lower chords are square. They are 2 metres high at the central
span, but decrease in weight towards the ends of the cantilevers down to
1 metre. The upper chords have the same width as the lower ones, but as
the segments of which they are composed are longer, their height varies
between 3 metres and 1,50. The braces are square, and their size is
variable, according to the open length. The distance between the principal
lower apices of each girder varies between 50 metres and 6.50, so as to
make up as far as possible for the difference of diction of the braces.
The lower chords are connected by cross-shaped bracings, the bars of
which are of hollow circular section. Cross bracings between struts of
the two main girders give additional strength to those girders and increase
their resistance to the wind.
Independent Span.
The independent span of 150 metres is formed
of two girders resting upon the ends of the cantilevers. Their height is
11 metres on the supports and 20 metres in the centre, their central spans
being 10 metres apart. Each girder consists of two flanges or chords, the
lower one being horizontal and the upper one assuming the shape of a
polygon inscribed in a circle, both being connected by web, forming
isosceles triangles.
The two flanges are formed of sheet and section iron divided into
four segments of identical shape. Their common height varies from
1 metre (at the ends) to 1,50 (in the centre of the span). The web is of
the same type. The secondary bars are of simple section.
The lower and upper numbers of the main girders are connected by
cross-shaped bracings, the bars of which are of caisson section. Here also
there are cross-bracings corresponding to the struts of the two girders.
The Flooring Proper. The two lines of rails are supported by four
rows of longitudinal beams disposed parallel with the rails. These beams
are latticed. Their height and span are unequal, and their dimensions
vary according to the stress they are to resist.

The Channel Bridge & Railway Company, C.
TELEGRAPHIC
REGISTERED ADDRESS
"PINOS"
TELEPHONE NO 1748.
derata;
and am
ii Paris
I have
sendu
so
information
110. Cannon Street.
London.
your
E.C

29 July 1892



Post Card
f yesterday
came to the Lecretary
give you
he e
that be
you
ean
desire.
farther futh.
the

+

Edwarda
20. Alfred
Street
Liverpool B.

The Channel Bridge & Railway Company, L
TELEGRAPHIC
REGISTERED ADDRESS
"PINOS"
TELEPHONE N° 1748 -
B.
110.
Dear Sir,
1
Mr. Cannon Street.
London.
1
за
EC
td
Aug 1892

Monst Que Palland the
Du
Secretary of this Company
me to send
has asked
u
some papers connected
with the enterprise which I am doing
by this days post, they consist of
(1) The Articles of Association of
Company.
(2) Two Books
of the p
of
а
Booke slowing
project.
the
the position
(3) A Report of the proceedings
held at the General Meeting
26th ult: and,
on
(4) A Plan skewing the connection
of the proposed Bridge with
Consmental and other railway systems
A book is in course

-ion which will
carry
of publicat.
the proceedings
by
to a later period than that covered
the two prints sent, but this will not
be re
ready
for
{"
another six weeks or so.
"As regards shares, the bompany
has been only issuing these as money
is wanted!. There are no
вного
regular forms
of application, but should you wish to
subscribe for shares and will let me
I will see that the application is laid
before the Directors
The £ 4 share has
been I understand as high as £10 on
the Paris Bourse; but owing to the recent
financial depression is now I believe
about par again.
Yours fouthfully
Sal
J. Edwards boq
вод
47
The rails are to be embedded in a groove to avoid accidents. The
plates are formed of ribbed iron 8 millimetres thick, weighing 50 kilo-
grammes per square metre. They rest upon 1-shaped irons.
The footways are provided with balustrades fixed upon the overhanging
ledges attached to the external beams. The horizontal beams under the
rails are carried by transverse pieces, each of which connects two of the
lower apices of the main girders. All these pieces assume the shape of a
Warren girder with three bays. Their weight is variable, and the bars of
which they are composed are of hollow tubular section.
Piers. The metal portion of the piers comprises two columns of
34,900 high. Each column is formed of two cylindrical cores having
a common axis, and
and a diameler of 4m 600 and 6m,400 respectively,
twelve such cores arranged in a precisely vertical plane serve to con-
nect the others, and by their prolongation form external and internal
stiffeners.
The interior stiffeners have a free space of 3 metres, which is
invariable troughout the height of the column. The outer stiffeners give
the body of the pier an apparent diameter of 8 metres, which gradually
increases to 12 metres towards the base.
The inner cylindrical core is provided with a prolongation of 14 metres
forming an anchoring lube of 4 metres in diameter, but as it would be
insufficient in case of a longitudinal action of the wind, and also to provide
for expansion, twelve anchor bolts have been added forming the bed of
each column. These bolts have a diameler of 0,250 and their action
extends over a height of 14 metres of masonry.
The two columns of the same pier are connected by bracings which
enable them generally to resist the transverse action of the wind.
The piers terminate at the top in ledges carrying the balustrade.
A circular plate 6,200 in diameter, and 1.400 in height, covers each
column, and is formed of sheet iron, serving to receive the supporting
apparatus with a fixed or expanding fool.
The expansion gear comprises six rails, 0,600 in diameter and 3 metres
in length.
The load is transmitted from the floors to the piers by sockels, hence
it is distributed all over the sheet iron plates and angle irons, braced toge-
ther so as to prevent overturning under the action of the wind.
The columns of the pier are fixed, while the columns of the next pier
have expansion gear. The effect of the expansion or the contraction of a
floor results in a corresponding reduction, or augmentation, of the play
between the overhanging portions of the cantilever and the ends of the
48
independent span. The span rests on one side upon fixed supports, on the
other on rolling gear.
§ 2.
The Spans of 200 and 350 metres.
The upper level of the rails is 72 metres above low-water level. The
lower portion of the bridge is supposed to be at 62,680 above the low-
water level throughout the whole extent of the spans of 200 metres, while
in the centre of the spans of 350 metres the height above the low-water
level is 66m,497.
The whole of the spans of 200 metres and 350 metres being similar to
the spans of 300 metres and 500 metres, it will suffice, after what has been
said in the preceding paragraph, to refer to sheets 10, 11, 12 and 13 of the
plans to comprehend the arrangement adopted with regard to this type of
spans.
$ 3. The Spans of 100 metres and 250 metres.
The upper level of the rails is always 72 metres above low-water
level.
The lower portion of the bridge is quoted as being at 63,780 above
low-water level throughout the spans of 100 metres, while in the centre
of the spans of 250 metres the height above the low-water level is 66,497.
To comprehend the arrangement adopted in the case of this latter type of
span, it is sufficient to refer to sheels 14, 15, 16 and 17.
49
VII
CONSTRUCTION, TRANSPORT, AND PUTTING IN
POSITION OF THE METAL SPANS.
cas
1. Description.
The important work of putting down a complete fitting-up plant will
have to be carried out upon the coast in the vicinity of the abutment of the
bridge. The small port of Ambleteuse, sufficiently sheltered from the winds
of the offing and the effects of breakers, seems to be best adapted for this
plant, which, as described on page 24, consists of two quays provided with
suitably arranged jetties. These are intended to sustain the weight of the
whole metal framework, and therefore constitute an essential part of the
plant. The quays are to connect these jetties. They are supplemented by
a channel of sufficient width ant depth to allow each loaded span to wait
for a favourable moment to be placed on the piers by means of tugs.
Upon the quays scaffolding will be erected, supplied with powerful and
improved machinery, such as cranes, steam winches, and hydraulic lifting
machines.
The various parts of the bridge will reach the working-yard in as com-
plete a condition as possible. A greater or less number of works may be
applied to manufacture these different parts, in order to avoid the neces-
sity of rapidly calling into existence a regular industrial town on a desert
part of the coast, and thus obviate any disorder that may result from so
doing, either while the works are proceeding or after their abrupt completion.
The fitting together of all the pieces can be mainly done in the workyards,
as regards the central spans and the overhanging cantilever arms. Once
fitted up, each span will have to be freed from all the supports except those
7
50 -
upon which it is supposed finally to rest. The must then be sufficiently
shifted along the jetties to enable them to be placed on the barges provided.
for carrying them to their ultimate position (see sheet 22).
The power required for hoisting the bridge is not such as to be above
the capacity of hydraulic cranes. Let us, in fact, consider the case in which
the difficulty appears to be most serious, namely, that of the central span
of 300 metres, with 50 metres in overhanging portions on either side, wei-
ghing 9,580 tons. Supposing the coefficient of friction to be 0,10, it will be
seen that the effort necessary will only amount to 958 tons. Particular
attention is to be paid to the arrangement of the slides.
As the bridge, indeed, must be able to remain upon the scaffoldings
for a certain time, means must be provided for turning it round. The sup-
porting surface is to be formed by the base of a cone carrying the turning
socket. Thus, in the case of the heaviest span, a surface of 15 square
metres will be obtained for 4,790 tons, which amounts to 32 kilogrammes
per square centimetre.
The slides will have to be strongly fixed to the masonry. To avoid
their breaking under the strain they will have to undergo, they must be able
to support about 500 tons at the transverse section, their width being 2,50.
They evidently must be about 20 millimetres thick. They will rest upon
wooden crossbars, lest, in consequence of some difficulty in the execution
of the work, an excessive pressure per unit of surface should result
in any given point, the consequence of which would be a crushing of the
metal.
The loading will be effected at high water. The barges will be brought
under the bridge before the tide, and will raise it when the tide sets in.
The whole will then be disengaged by transverse traction by means of
winches.
There may be three barges in the case of the heaviest span. The craft
must therefore have a nominal capacity of about 3,200 tons, and a displace-
ment of about 5,500 tons when fully loaded, including the weight of the
scaffoldings provided for supporting the span.
Barges 22 metres wide, 70 metres long, and drawing 6m,50, will answer
the purpose.
They will also fully insure the stability of the whole. The bridge may
then sustain a considerable transverse pressure of wind without rendering
the resulting inclination dangerous.
•
The various barges will be connected between them by steel cables strel-
ched crosswise, as is sometimes done in the case of bridges over rivers for
the passage of artillery in times of war.
The barges shall be provided with compartments that can be filled with
- 51 -
water by means of sluice valves, so as to second the action of the tide
during the discharging operations. It will thus become unnecessary to
follow all the small movements of the sea, while nothing will prevent fair
weather from being taken advantage of.
The whole of the bridge and barges will be tugged by a large steamer
by means of crowfoot lashings, which is preferable to using several tugs
which might not act with the desirable uniformity.
It will be understood that whenever the distance from fixed points either
on the shore or at the piers makes it possible, it will be best to use direct
traction and sufficiently powerful steam winches. Upon the piers it will
be necessary, at the point where the girders are to be laid down, to
provide sufficiently powerful buffers to intercept the shocks due to the
movement of the sea.
When the bridge has reached the position it is to occupy, and is brought
to rest in four points on the piers of masonry, the raising of it by means
of hydraulic presses, arranged inside the rings which form the base of the
metallic piers, shall be proceeded with.
The bridge shall then be raised to the required height to enable the
following four elements of the piers being placed in position. The presses
will afterwards be withdrawn and the operation may continue in the same
way until the span assumes its ultimate position.
By adding to the weight to be thus raised the strain produced by the
wind, it will be seen that each of the presses placed within the metal piers
should be endowed with an effective power of 2,900 tons.
It has been stated before that the large spans were not to be quite
completed on the shore. As regards the two overhanging portions, they
will be placed in position by a process of free erection similar to that used
by the Creusot Company in 1865, for the bridge across the river El Cinca
(Spain). As to the separate spans, they may be completed in the yard.
They can then, by means of barges, be brought under the two overhanging
portions which they are to connect, and there raised to their ultimate
position by means of sufficiently powerful lifting apparatus.
အာ
§ 2.
Calculation of the Machinery employed in Fitting Up.
Buffers.
The momentum to be deadened in case the buffers should
be called upon to operate by movements of the sea occurring at the time of
disembarking on to the piers, may be regarded as practically equal to half
52
the mass of the bridge, multiplied by half the square of the speed acquired
PV2
by the end imparting the shock, viz., In taking this figure for a
29
startingpoint, one may be certain the real amount is exceeded, for, supposing
the bridge rotates about its centre, the sum of the momenta would still be
below that figure.
Suppose, now, that the shock is to be relieved by twelve buffers of
the railway type, arranged within each of the piers, the strongest of
these buffers are capable of moving a distance of 0,10 and of carrying a
load of eight tons. The available labour, therefore, can be set down as
8 × 12 × 0,1
practically equal to
,
which quantity must be equal to half the
2
momentum, viz., to
2400
19,62
v³.
Therefore v equals 0,198 per second.
Now, a swell sufficiently long to influence the barges, corresponds,
as is well known, to a time of oscillation of about 3". Thus the average
velocity, as worked out above, would correspond, in a similar oscillation, to
a rise of the sea of 0,594 per second.
This, however, is an amount of lifting which may be avoided in effec-
ting the discharge, especially in the summer.
A more precise calculation can be made by taking the force of inertia
into account, but it seems unnecessary to dwell further on this point. It will
can be easily seen that there will be no difficulty in deadening the impact
due to the velocity imparted by the waves.
Barges. The case more particularly considered here is that of the
heaviest span, it being the one attended by most difficulties.
The first condition to be fulfilled as regards the barges is to make it
impossible for them to capsize, and to insure their stability. This object can
be attained by placing the centre of gravity of the whole below the longitu-
dinal meta-centrum. It can be taken for granted that the centre of gravity
of the empty hulls of the barges will be 1 metre above the floating-line of
the load, since they will be surmounted by a superstructure rising up to
20 metres above the floating-line, and since they will, when fully charged,
rise to 4,15 above the water, their draught being 6,50.
This being so, the bridge weighing 3,200 tons per barge, and having its
centre of gravity 49 metres above the water, the general centre of gravity
according to the calculation of weight will be -
3.200 × 49m + 2.300 × 1m
5.500
29 metres
53
the draught of the barges being 6,50, the minimum height of the longitu-
dinal meta-centrum, above the centre of the keel, will be about 32 metres.
Now, supposing that barges are used measuring 22 metres in width,
and 70 in length, the height of the meta-centrum, with a displacement of
5,500 tons, will be about 40 metres. Thus stability will be amply provided
for, and the distance of the centre of gravity from the meta-centrum will
be 8 metres.
This distance is sufficient, as will be shown further on, to insure stabi-
lity under a wind coming transversely upon the bridge with a considerable.
pressure.
The surface the bridge will offer to the wind in that direction will be
8.750 square metres, and the centre of pressure is situaded 21",35 above the
girders, that is 46,85 above the surface of the water.
If p be the pressure of the wind square metre, the momentum of the
wind in relation to the floating line will be
8.750 46,85 × p.
If 0 is the incline assumed by the barges, then P (R
A) sin 0 =
- A being
8.750 46,85 p. P being the total displacement, and R
the distance of the centre of gravity from the melacentrum, this distance we
have assumed to amount to 8 metres, and P is 16.500.000.
Now, it is desirable that the immersed end should not go down deeper
2,5
than 2m,50:- sin A must no exceed
35
It follows that the pressure per unit of surface which the whole struc-
ture will be able to sustain will be equal to
Ρ
16.500.000 × 8 × 2,5
8.750 × 46,85 × 35
23 K.
Thus even a violent storm could not possibly capsize the barges.
But, granting that this point has been sufficiently illustrated, it may be
questioned whether the bridge will not run the risk of being deformed
under the strains it will be subjected to by the barges themselves during its
transport, especially if the operation it nos carried out in perfectly fair weather.
It is obvious that if there is but little sea running, so that the waves are
insufficient to influence the barges themselves, the whole operation will
proceed as if they floated upon a perfectly smooth sea, so that no anomalous
strains would ensue.
As to traction, or those strains that will result from gyration, it will be
readily seen that they will be of no great importance, if all the operations
are performed slowly -e. g., the towing power necessary to tug the bridge
at a speed of eight knots will not exceed 150 tons, even if a very sharp wind
54
happens to add to the resistance proper, such wind exercising a pressure of
10 kilogrammes per square metre, the towing power need not exceed 160 tons.
Now, the bridge has been calculated to resist more considerable transverse
strains than that.
While one may reasonably depend on having fairly good weather in the
Channel during the summer, it may happen, nevertheless, that the barges,
upon leaving the port, may encounter a considerable swell, at least in length,
which, although not very noticeable, may exercise on a girder more powerful
strains than those provided for in the preceding calculations.
Thus, it may happen that the swell exercises on one of the barges a lifting
strain that will be transmitted to the bridge. This strain will be equal to
the floating surface of the barge, multiplied by the distance between the
ordinary floating line and the medium floating line, determined by the section
of the wave. Now as the floating surface extends over about 1,000 square
metres, it will be seen that a wave that would cause the floating line to rise
0,50, would cause a thrust of 500 tons. Such a wave, however, would have
a lifting power considerably above 0,50 inasmuch as its section is never a
horizontal line. One may set it down at 0,75 in the least favourable case.
This strain of 500 tons, however, would not in itself prove dangerous,
considering the sections of the girders and the use of lashings. It will thus
be seen that, from this point of view also, the transport would be by no
means impossible.
We have hitherto considered only those stresses from which the girders
are naturally protected, such strains acting in the same way as those which
the girder is originally destined to withstand; but the girders will be
exposed, besides, to another kind of strain, the torsion strain, which they will
sustain whenever the barges that carry them tend to take up positions at
different angles to the perpendicular, in consequence of the varying inclines
of the waves.
These are the stresses that require special attention. Let us then
consider the portion of a girder comprised between the two floats. They will
assume a certain relative position, corresponding to an angle of torsion of the
bridge 0, and will assume the inclines 0' and o" respectively, in relation to
the liquid surface upon which they float. If we call a the angle formed by
the two floating surfaces, we obtain
01
α₁ = 0₂+0' — 0″.
-
On the other hand, the moment of stability of the first barge is P (R—A) 0′,
that of the second P (RA), and the couple which counterbalances the
twisting strain is
(a
P (R — A) (0′
A) (0' 0"), or P (RA) (α — 0¸).
55
It is equal to a moment of torsion of
1
/ I, G
I, G = P (R — A) (α, — 0₁) ·
0₁).
But, on the other hand, if be the effect of the strain upon the fibre
Ꮎ ;
supporting the heaviest load, this effect is proportionate to
αι
i.e., to
P (R
A) α,
I, G + IP (R — A)
I, G
P (R A)
+1
From this expression we cannot yet obtain the value of; but we may
infer from it that it is desirable, within certain limits, to multiply the num-
ber of barges.
Supposing, in effect, that they are uniformly divided, the displacement
P of each will be proportionate to the distance between them, as I and
Р
= c.
Let h be the distance of the centre of gravity from the remotest fibre;
we obtain
σ = Gh
= Gh
X1
P
P (R
I G
A)
+1
P
Ip G
+1
lc (R
A)
The value of 1, corresponding to the maximum of is
G
I, G
Ip
c (R — A)
By this formula a far greater length than that of the girder will be found.
As I diminishes, decreases too; thus it will be seen that it is desirable
to increase as far as practicable the number of barges.
The necessity for the girder to rest upon parts capable of a local resis-
tance, leads to the adoption of the number three for every 9.580 tons. Less
than this cannot be taken in the case of the other spans.
Given a distance between the barges 1, and the angle a₁, of the floating
surfaces of two consecutive barges, the corresponding value may be calculated
from 。. But an easier method is to find out at what angle a₁, equals a tor-
sion of 6 kilogrammes per square millimetre.
It will then be found that a should be equal to something more than 200°;
we are therefore justified in concluding that the torsion produced, even by
very powerful waves, will only cause perfectly insignificant strains.
All the preceding calculations are naturally only approximate; they
nevertheless permit the inference that the transport of the spans is quite
possible.
56
t
§ 3. - The Fitting of the Cantilever Arms.
We here treat of a method of putting into position the central spans
and overhanging trusses, so as to avoid the employment of hydraulic cranes,
which have hitherto been indispensable.
The necessity of raising the bridge by hydraulic cranes each time one
places a ring of the columns into position necessitales a series of alternative
manipulation, requiring a great deal of time and trouble. It is easy enough,
on the contrary, to mount the columns separately by small sections by the
aid of hoisting gear of less power; but as the carriage of the spans on floating
barges is not to be thought of, it being too difficult to thus bring them into
a position that will permit them to be raised to the place they are to occupy,
the result is that it is necessary to fit up these spans at the required height
straight away. The idea might at first sight suggest itself that the piers
already constructed should be used as supports. For, by surmounting them
each separately by a platform of sufficient size to insure slability, it would
be possible to fit the spans by free erection on either side of each pier.
The junction of the two sections of a girder would then have to be made in
the centre of the central span; but whatever care is taken in carrying out
this operation, it would leave serious doubts as to the continuity of the
girders, such as is assumed in the calculations.
It is by far preferable to commence the mounting in the centre of the
central span with the aid of auxiliary and removable piers interposed between
the piers that are to be left standing permanently.
In the case of the larger spans two piers might be arranged, as shown
in the following sketch.
A A A A


100
IV
H
35m
6m
80m
25m
300 m
ترجل
60
35m
52 m
I

57
These piers are formed of two columns, each 51 metres high, and
6 metres in external diameter, braced together in a transverse direction,
and resting upon a caisson, the form of which, in horizontal section, is that
of a rectangle terminating in a semicircle, so that it should oppose the least
possible resistance to the currents.
At the top the caisson is 35 metres long and 10 metres wide, and at the
base 60 metres long and 5 metres wide. Its height is 65 metres for the
maximum depths. The two piers he:e considered are so situated that there
is a distance of 80 metres between their axes, and they are connected by a
superstructure forming a platform 100 metres long by 35 metres wide.
It is on this platform that the fitting up of the different parts of the bridge
will be effected, just as if it was in an ordinary workyard on land, whereu-
pon the construction of it will be continued, by means of free erection,
until on either side the permanent pier is reached, which will then have to
be completed so as to be able to receive the girders. When once the span is
set down upon the piers, the mounting operation can be continued with the
assistance of the auxiliary piers. The superstructure can then be removed as
well as the columns, and both can be used together, with the caissons, in the
fitting in place of the next span.
Each caisson being of dimensions comparable to those of the caissons.
provided for in the case of the brickwork surrounding the columns, it will
be possible to set it afloat and ground it, after being provided with the
compartments necessary for receiving the ballast of sand. Its cubical volume
being about 51.000 cubic metres, it will be necessary to fill a little over
one-half of it with sand ot make it ground. With the caisson in position, it
may still be found, even after the same be loaded with the columns, the
superstructure, and the portions of the bridge then in course of completion,
that infiltrations should take place at its base which would give a thrust
equivalent to 43.500 tons. This being so, a ballast of about 8,000 cubic
metres of sand will have to be added, in order to insure the stability of the
whole under the action of wind at the time that the bridge girders are about
to be placed upon the piers intended to support them.
For the fitting up of the intermediate spans, two auxiliary piers seem
necessary.
As to the small spans, where the piers of the bridge are 100 metres
apart, one single auxiliary pier will be sufficient, if it be connected with
the permanent pier by a platform.
8
59
VIII
ESTIMATES OF WEIGHT
The following weights have been obtained by adding to those found by
calculations 18 per cent., to provide for additional pieces that will be
employed in fitting and rivetting. Taking all parts together, the limit of
stress is assumed to be 12 kilogrammes per sectional square millimetre, the
rivet bolts not being subtracted.
This limit, howerer, may be considered as a very high one, for it has
never been reached hitherto in all the steel structures that have been built;
but, nevertheless, after carefully examining the conditions involved in the
question, it will be found that the assumption of such a limit is not
unjustified.
8
11
In the present case the permanent load represents of the total load.
From the formulas deduced from the experiments of Wöhler, it appears that
the limit of stress of 12 kilogrammes offers the same guarantees of safety as
a limit of 10,5 in the case where the permanent load and the additional
load have equal influences.
In the case of such pieces as the longitudinals under the rails and the
beams, where the additional load greatly exceeds the permanent load, it may
be said that the addition of 18 per cent. is certainly excessive
in fact,
that it surpasses any figure suggested by a lengthy experience. Even as
regards the other parts of the bridge, this figure may be regarded as exag-
gerated, owing to the use of sheet iron and section irons that can attain
12 metres in length, which would notably reduce the importance of the
fittings. It must be added that in calculating these pieces, very liberal
allowance has been made for any unforeseen excess of weight, since instead
of calculating their rcal length, the distance between their axes has been
taken into account.
To simplify calculations, the same coefficient (12 kilogrammes) has been
admitted as applying to all the members of the bridge. In a final project,
however, it will be necessary to examine whether it is not more rational to
attribute to each piece a coefficient of resistance varying with the size and
the direction of the stress to which that particular part is subjected.
60
! Δ
B
I. SPANS OF 300 METRES AND 500 METRES
d
1º Central Span and Cantilever Arms.
C'

D'
9
E
F
G
AMAMA
2
H'
E
E 2
Fi F2
G2 H1 H2 I
Ꭰ .
B 2
2
187m 5
LOWER
members
150m

CENTRAL SPAN
UPPER
members
BARS
LOWER
members
CANTILEVER ARMS
UPPER
members
BARS
A,
C₁
شکی سے تھے تے تے
76T,093
A'
45T,088
a
221,839
D,
137,231
D'
172T,280
I
125T,527
78, 010 Β'
96, 293
b
28, 658|| D₂
D₂
2
127,
127, 419
E'
106, 670
h
108, 914
B₁
92, 230
C
121, 117
C
59, 267|| E₁
77, 251
F'
59, 976
ї
64, 494
B₁₂
98, 059
d
74, 950 E.,
70,487
G'
33, 340
i
56, 578
126, 814
e
122, 537
F₁
40, 198
H'
16, 320
k
30, 756
C₂ 136, 820
f 166, 146
F₂
2
35, 972
I'
4, 528
し
​28, 261
G₁
18, 702
M
14, 338
G₁₂
15, 950
n
14, 706
2
H₁
H₂
2
I
1
5,992
6, 913
3,833
0
7,167
ק
9.485
9
5, 238
608,026
262T, 498
474,397
539T,948
393T,114
465™,464

NAMES OF PIECES
ONE CENTRAL SPAN
TWO OVERHANGING PIECES
of 300 metres
of 187,5 each
Main girders.
5.379⁰, 684
5.594", 104
Secondary bars of the main girders
67, 336
55, 632
Footplates, rails, footways, and bracings of sleepers .
411, 732
501, 560
Longitudinals under rails.
335, 040
380, 680
Beams
106, 824
97, 002
Lower bracing
270, 468
431, 144
Cross bracing.
45, 584
41, 006
6.616", 668
7.101T. 128
SUM TOTAL.
13.717,796
61
Y
K'
J
2° Independant Span of 125 metres.
7)
L'

W
J Ki K2
I 1
L2
Mi
625
LOWER CHORDS
62m:5
125 m
UPPER CHORDS
BARS
J
2T,353
J'
3T,827
9T.968
Y
་་
་་
2,880
K'
7,409
2,715
2,327
L'
11,911
S
2,839
2
1
2,464
3,977
И
1,158
ورا
4, 375
4”
1,857
N
M.
5,812
W
0.571
217,724
23T,147
217,572
Main girders.
Secondary bars of principal girders.
Plates, rails, footways, bracings of sleepers
Longitudinals under rails .
Beams.
Lower bracing
Upper bracing
Cross bracing
•
#

265™ 772
11,790
162,584
102,720
24,114
16,864
13,488
8,862
TOTAL.
606⁰,194
- 62
1
!
3° Two Metal Piers.
Interior framing of lower numbers of floor girders.
Supporting contrivance
Metal columns
•
Bracing of columns.
Anchor tubes.
Anchor bolts.
Metal flooring (1º ÷ 2º).
Piers (3).
60 tonnes.
764
2.268
332
240
360
TOTAL.
4.024 tonnes.
Summary.
TOTAL.
Weight per metre of column:
18.348
800
= about 23 tons.
14.324 tonnes.
4.024
18.348 tonnes.
§ 2. SPANS OF 200 METRES AND 350 METRES
1. Central Span and Cantilever Arms.
A 2
A'
B

AA
B 1
B2
700
m
D'
E
F
G
h
m
C₁
C2
D1
D2
E 1
E2
Fi
F2
130 m
G1 G₂ Hi
1
63

CENTRAL SPAN
LOWER
Members
UPPER
Members
BARS
LOWER
Members
CANTILEVER ARMS
UPPER
Members
BARS
A.
38T,708
A'
46⁰,020
a
13T,338
D₁
59,025
C
74T,248
f
50T.989
B₁
42, 419
Β'
53, 078
b
18, 139|| D₂
53, 881
D'
44,507
I
44, 228
B₂
44, 611
C
25, 339|| E₁
30, 702
E'
23, 020
h
24, 638
2
C₁
54, 816
d
41, 695 E
27.611
F'
10, 623
i
22, 353
C₁₂
59, 052
¿
63, 399|| F₁
14, 002
G'
2, 769
11, 317
F₂
12. 175
11, 108
G₁
4, 724
し
​5, 048
G₂
3, 800
m
6, 475
H₁
1, 947
N
3, 689
239¹,606
99⁰,098
161,930
207T,867
155T,169
179,845
ONE CENTRAL SPAN
TWO OVERHANGING TRUSSES
NAMES OF PIECES
of 200 metres
of 130 Metres each
Main girders.
2.002™, 536
2.171⁰, 324
Secondary bars of main girders
40, 000
30, 300
Plates, rails, footways, bracings of sleepers .
268, 752
344, 384
Longitudinals under rails .
207, 320
263, 400
Beams.
67, 920
66, 396
Lower bracings
67, 840
154, 454
Cross bracings.
33, 300
29, 192
2.687T, 868
3.059⁰, 650
SUM TOTAL
5.747,518
y
2. Independent Span of 90 Metres.
I'
H'
ť

AA
L
12
J
J3
4.5m
45m
Hz
*
90m
64

LOWER CHORDS
UPPER CHORDS
BARS
11 2
1',067
I'
1,874
Y
0T,868
1,
1,538
I'
3,899
0
2,715
I
1,263
J'
2,411
p
1,711
2
2,381
1,680
1
J
2,472
"'
0,338
2
S
0,902
8",743
8T,184
8T,214
Main girders.
Secondary bars of main girders.
100.56/T
8.431
Footplates, rails, footways, bracings of girders
116.776
Longitudinals under rails.
84.944
Beams.
19.184
Lower bracing.
9.990
Upper bracing.
7.984
Cross bracing .
5.442
TOTAL.
353.315™
3. Two Metal Piers.
Inner framings of lower members of floor girders.
Supporting machinery.
Metal columns.
Bracings of columns.
Anchor lubes .
Anchor bolts
28T
428,8
1.625,2
248
180
340
TOTAL.
2.844™
63
Metal flooring (1° + 2º)
•
Piers (3º).
Summary.
6.601'
3.844
8.945
TOTAL.
Weight per running metre:
8.945
500
about 16,3 tons.
Α'
§ 3. SPANS OF 100 METRES AND 250 METRES
1. Central Span and Cantilever Arms.

b
B'
e
D'
E
Aa
Bi
B2
C₁
Co
Di
D2
E'
Es
F
50m
.92" 5

CENTRAL SPAN
CANTILEVER ARMS
LOWER CHORDS
UPPER CHORDS
BARS
LOWER CHORDS
UPPER CHORDS
BARS
A,
27,232
A'
32T,598
a
4,681
C₁
27,836
B'
B, 28, 718
b
11, 117
C₁₂
24, 764
C'
35T,698
20, 562
d
27,712
(
B,
29, 972
C
21, 394
D₁
13, 406
D₂
11, 632
E
R =
D'
9, 476
ľ
2, 250
g
E₁
4, 616
h
E2
3, 683
21, 596
11, 635
10, 665
1, 730
3, 660
F
1, 287
j
2,753
85¹,972
32T,598
37",195
86,974
67,983
81T 781
9
66

NAMES OF PIECES
Main girders.
Secondary bars of main girders
Plates, rails, footways, bracing of sleepers
Longitudinals under rails
Beams.
Lower bracing
Cross bracings.
•
SUM TOTAL
ONE CENTRAL SPAN
TWO CANTILEVER ARMS
of 100 metres
of 92.5 Metres each
623T,060
946T,844
12, 900
15, 164
•
133, 500
243, 340
101, 184
176, 280
27, 600
42, 952
16, 326
69, 040
22. 000
15, 000
936, 570
1.508T,620
•
•
•
9.4427,190
2. Independent Span of 65 Metres.
Y
K
G'

X A
F2
G
G2
H
32m5
65"!

LOWER MEMBERS
UPPER MEMBERS
BARS
F₂
0T,628
F'
1T,101
y
0T,564
G₁
0, 792
G'
2, 121
た
​1, 312
G2
0, 773
0, 938
H₁
2, 283
m
1, 001
1
忆
​0, 202
4T,476
3T,222
4º,017
67
Main girders
46.860™
Secondary bars of main girders.
5.770
Footplates, rails, footways, bracing of sleepers
84.336
Longitudinals under rails.
57.696
Beams. .
15.648
Lower bracing.
7.650
Upper bracing.
5.71h
Cross bracing
5 442
TOTAL.
229.116™
3. Two Metal Columns.
Inner framings of lower members of floor-girders.
Supporting contrivance.
12T
240
Metal piers.
•
Bracings of piers.
Anchor tubes
Anchor bolts .
1.448
140
112
220
TOTAL.
2.172T
Summary.
Metal flooring (1° 2°)
2.674T
Piers (3).
2.172
Weight of the running metre:
TOTAL.
4.846
350
4.846T
13,8, approximately.
NUMBER
of Spans
for the
whole
of the
Bridge
$ 4. GENERAL SUMMARY

DESCRIPTION OF SPANS
LENGTHS
UNITS
WEIGHTS
LENGTHS
TOTALS
WEIGHTS
32
Spans of 300 and 500m.
800M
18.348™
25.600
M
587.136T
13
>>
200 and 350m .
550
8.945
7.150
116.283
14
100 and 250m.
350
4.846
4.900
67.844
TOTALS for whole bridge.
37.650
771.265T
Average weight per linear metre of bridge:
771.265
37.650
= 20',5.
69
IX
CALCULATIONS OF RESISTANCE
The calculations relating to the large spans of 300 and 500 metres will
alone be here reproduced, the same method having been followed for the
three other types of spans.
§ 1. — THE INDEPENDENT SPAN
1. Sleepers under Rails,
The two lines of rails are carried by four rows of sleepers laid parallel
to the rails.
Their length varies from 6m,50 to 14 metres.
The loads comprise:
The weight of the rails, of the foolplates, of the footways, and the bra-
cings of the sleepers;
The weight of the sleepers proper is supposed to vary with the weight
under consideration;
одход
одход
And the additional load due to passing trains.
470x10
10
ΟΙ
10
LO
O
et 200×19
500 et 560
1 mooo et
m 200
250
et 320
250
et 320
This additional load is assumed to be uniformly
distributed according to the regulations of the 9th
July 1877.
All the longitudinal beams are latticed.
The accompanying sketch shows their shape in
cross section.
The bars of the lattice work are formed of T
100 X 60
100 × 61
and of
8×8
9 × 8
irons of
The results of the calculations of the longitudinal
beams underlying the rails are contained in the fol-
lowing table. They have been arrived at on the as-
sumption that the beams will be supported at the
ends only: -
70 -

NUMBER
FOOTPLATES, RAILS,ETC.
LENGTH
WEIGHT
WEIGHT
WEIGHT
OF
BEAMS
WEIGHT
of
of
in
per running metre
of
of
BEDPLATES
of
a Row
BEAMS
BEAM
BEAM
under rails, etc.
BEAMS
24
6m,50
324,37
1.402k
4.217k
2.804k
9, 25
324, 37
1.842
12.002
7.368
4
11, 75
324, 37
2.148
15.245
8.592
2
14, 00
327,94
3.458
9.182
6.916
TOTAL per row of beams.
40.646k
25.680k
Thus, for the four rows of the whole bridge, the weights are as follows :—
Bed-plates, rails, footways, bracings of beams.
Beams under rails .
162T,584
102, 720
2. Beams.
The beams or bridge pieces are the immediate support of the sleepers
underlying the rails.
They assume the shape of Warren girders with three panels; their height
varies between 3m,60 and 5m, 40 metres, and their length of span between
9 metres and 8m,50.
Leaving out of consideration the weight of the beams proper, it will be
found that they will only have to support those distinct loads which will be
transmitted to them through the medium of the sleepers underlying the rails.
Thus there is, in the first place, the load given through the bed-plates,
rails, etc., and that of the sleepers themselves The table given enables these
loads to be determined. As to the weight of the trains, it will vary accord-
ing to their position and nature.
Let us call any given beam 7, the two adjacent ones ẞ and 8, and sup-
pose that the moving roads comprised between 3 and are 1, 2, 3, 4, 5.
B
5
Y
I
~
M. Bertrand de Fonviolant
8 has shown that if ß, Y,
I
and y, d, be considered
as two disconnected gir-
ders, the position of the
train to which the maxi-

mum of reaction of support y corresponds, is the same as that which produces
the maximum moment of flexure under section y of the beam sustaining the
same loads and resting upon the two supports ẞ and only.
71-
P.H
Applying, therefore, Weyrauch's construction, one is enabled immedia-
tely to find the more unfavorable position of the train, whether of simple
or double traction, and to calculate the load transmitted to the beam. The
results of such calculation are as follows:-

62m5
*-
6,5 9,25 9,25 11,75 11,75
14
W
MAXIMUM
STRESS
BEAMS
(for each
Weight.)
a
LB & E ← -e
CASE IN WHICH
THE MAXIMUM
Stress is exercised.
42T
Simple traction train.
43
dº
47
dº
50
d°
54
do
55
dº
59
do
Supposing all the piers supported by each beam concentrated on its two
upper apices, the science of statics enables us to determine the strains
that will be developed in each of these elements, and the corresponding
weights.
The following figures will thus be arrived at:-
Weight of one beam .
1.629 kilog.
1.622
ب
1.746
2.022
W
á
2.016
B'
1.968
1.054
12.057 kilog.
1/2 Y
TOTAL.
Hence the weight of all the beams of one whole span may be expressed
thus
2 × 12,057 = 24,114.
3. Bracings.
To determine the stresses due to the action of wind, it has been assumed
that the pressures exercised upon all the parts of the superstructure would
be transmitted to the upper and lower apices of the main girders.
To calculate these pressures all those surfaces of the girder exposed to
the wind, considered as plain, the surface of the sleepers and of the train
72
(in the case of the bridge being loaded), and the surface of the web ef the
girder exposed to the wind, less the portion concealed by the sleeper and
the train, have been considered, and it has moreover been assumed that the
wind may attain a force of 170 kilogrammes per square metre at a time
when the span is loaded, and 270 kilogrammes per square metre when the
span is free from any load.
By these means loads have been obtained for the different apices for
half of a span.
21
231

17 18
19
20
21
23
23


LOWER
SPAN
SPAN
UPPER
SPAN
SPAN
APICES
LOADED
UNLOADED
APICES
LOADED
UNLOADED
17
4T,989
5T,507
17'
6T,211
112,180
18
12, 917
14, 707
19'
14.037
24, 742
19
11, 708
11, 102
21'
21, 564
36, 116
20
20, 596
26, 386
23'
13, 217
21, 966
21
15, 645
15, 404
22
27, 484
35, 334
23
9, 979
10, 238
Lower Bracing. The whole of the lower chords of the principal gir-
ders and of the cross-shaped bracings which connect them form a girder
sustaining the strains transmitted to the lower apices. This girder may be
considered as imbedded into a recess at both ends. Plan 20 shows how the
moments of flexure and of shearing stress have been determined.
From these the stresses developed in the chords and in the bars of the
bracings as well as the corresponding weights can be worked out.
73


CHORDS
STRESS
in
LENGTH
of
ONE CHORD ONE CHORD
WEIGHT
of
PANELS
including
ONE CHORD
THE BARS
STRESS
on the
TWO BARS
LENGTH
OF ONE BAR
WEIGHT
of
TWO BARS
J
220T,5
154, 5
6,50
1T 099
(17,18)
142T, 2
11,927
1T,301
K₂
76, 5
20 20
9, 23
1, 096
(18,19)
155, 0
13, 623
1, 620
9, 25
0, 343
(19,20)
134, 8
13, 623
1, 409
L₁₁
55, 5
11, 73
0, 500
(20,21)
135, 0
15, 431
1,598
Liz
99, 6
11, 75
0.898
(21,22)
100, 0
15, 431
1, 184
M₁
114, O
14, 00
1, 224
(22,23)
100, 0
17, 205
1. 320
TOTAL.
5,360
TOTAL.
8T,432
The following weights will thus be obtained for the whole span :
Weight of the lower chords.
Weight of the lower bracing.
Top Bracing.
4 X 5,360 21,440
2 X 8,432 =
16,861
The girder formed of the upper chords and braces should
also be considered as embedded in recesses at the ends. The web is or flat
surface, but it is subject to the normal strains consistent with its form in
horizontal sections.
This point has been inquired into by M. Maurice Lévy, and the drawing
on Sheet 18 was based on the formula of the analytic theory he had propo-
sed. This theory gives the moments of flexure and torsion and the shearing
stresses, determined according to the directions of the braces.
The following tables summarise the results arrived at:


CHORDS
STRAIN
upon
LENGTH
of
ONE CHORD ONE CHORD
WEIGHT
of
PANEL
including
STRESS
upon the
LENGTH
of
WEIGHT
of
ONE CHORD
BRACES
TWO BRACES
ONE BAR
TWO BARS
J'
K'
161T,4
98, 4
16⁰⁰,269
27,014
(17',19′)
21, 288
1, 607
(19',21)
1567,8
133, 5
18m.651
2T,243
23, 260
2, 382
L'
156, O
25, 798
3, 087
(21',23')
100, 0
27.624
2, 119
TOTAL.
6º,708
TOTAL.
6T,744
The following weights, therefore, apply to the whole span:
Weight of the top chord. .
Weight of the top bracing.
4 X 6,708
26¹,832
X
2 × 6,7!!
13,488
10
74
Cross Bracings. When once the moments of torsion are known, it beco-
mes possible to determine the stresses in the bars of the cross bracings. The
torsion stress, however, being very insignificant, the weights thus found
with regard to the bars are inadmissible. Supposing these bars are of a size
compatible with their shape, their total weight will be 8.862 tons.
4. Secondary Bars (Braces of Main Girders).
The secondary bars, with a portion of the main bars, form heavier girders
with three bays. A simple application of statics is therefore sufficient to
enable the stresses to be determined which these bars will have to with-
stand, supposing that the loads they will have to support directly are known.
The weight of the secondary girders throughout the span will therefore
be 11.790 tons.
5. Main Girders.
The length of each main girder is 125 metres. The load they have to
support is formed of the weight of the girders themselves, the weight of the
metal flooring, and of additionnal loads. A variety of experiments show that
these loads may be regarded as uniformly distributed and applied to the
lower portion of the girders.
Let
p be the total per square metre of the main girder.
P the weight of a girder such as it should be to resist vertical strains.
p' the weight per running metre of girder for all parts under conside-
ration; and
p" the overcharge per running metre of girder.
We then obtain-
p =
PL
+ p' + p²
(1).
Or let
t be the tension or compression of one girder bar per unit of load and
per running metre.
I the length of the bar.
the density of the metal.
R the co-efficient of resistance per unit of surface.
The weight of a bar will then be :-
元
​1,18
R ptl
78
The factor 1,18 being allowed for rivetings, joints, and fittings, the
weight of one girder will then be :-
P = 1,18
R
1,18 ᾗ ρ Σα
Ꭱ p
(2).
Eliminating p between formula (1) and (2), we find:
P
1,18 π Χ
L
RL
(p' + pˆ) Σ tl
1,18 Π Σ 1
(3).
Calculation of (p' + p). If we summarise the weights of all the pieces
known, we obtain :
Bedplates, rails, footways, etc.
Sleepers under rails.
Beams
•
Bars of lower bracing
•
Tons.
162.584
102.720
24.114
16.864
Bars of upper bracing
13.488
Bars of inclined bracings.
8.862
Secondary bars of main girders.
11.790
Weight of chords required to enable them to resist the
action of the wind.
48.272
388.694
The weight per metre throughout will be:
p' =
388¹,694
2 × 125
1,555.
The overcharge (p") per metre throughout of girder = 3 tons. Hence :
p' + p = 1,555 + 3 = 4,555.
Calculation ofl. The configuration of a girder being strictly inde-
formable, the stresses acting upon each bar may be determined by a figure
forming a counterpart of such configuration.
The tracing on Sheet 18 is based on the assumption of a load of one ton
per metre throughout.
bar:
The following table gives the figures of t, of, and of tl, for each
76

CHORDS
t
し
​tl
BARS
t
tl
J
55,2
6m,50
358,800
y
62,5
5m,72
357,500
K
55,2
18, 50
1.021,200
2'
60,8
12, 78
777,024
L
84,7
23, 50
1.990, 450
S
46,1
17, 63
812,743
M
93,8
14, 00
1.313,200
t
40,0
17, 63
705,200
J'
31,9
16, 27
319,013
И
15,1
21, 96
331,596
K'
78,0
21, 29
1.660,620
V
24,2
21, 96
531,432
L'
97,9
25, 80
2.525,820
ш
6,7
24, 41
163,547
Total..
9.389,103
Total..
3.679,042
Thus for one whole girder we obtain :
Σll = 2 × (9.389,103 + 3.679,042) = 26.136.
By these means all the quantities are known that are included in the
second number of formula (3), namely :-
hence:
T
p
+ p
4¹,555
ΣΗ
Σ tl = 26.136
R = 12 × 106
II
7.800
L
125
P
= 0,87
L
The weight of the two girders, necessary to enable them to withstand
vertical strains, is therefore :
2 × 125 × 0¹,87
=
217",500
Adding to it the weight necessary to withstand the action of the wind,
we obtain:
217,500 + 48,272 265¹,772
دیک
§ 2.
CENTRAL SPAN AND CANTILEVER ARMS
1. Longitudinal Beams under Rails.
The length of span of the sleepers varies from 7,50 to 25 metres.
Their arrangement being the same as that of the corresponding pieces
of the independent span, the results only of the calculations will be here
indicated.
-
77 -

DESCRIPTION
NUMBER
LENGTH
BEDPLATES
WEIGHT
WEIGHT
WEIGHT
of
of sleepers in a
of
rails, etc.,
weight per
of one
of bedplates,
of
span
row
sleepers
average metre
of sleeper
sleeper
rails, etc.
sleepers
Central span.
12
25m,00
343,11
6.980k
102.933k
83.760k
Total for one row of sleepers.
102.933k
83.760k
4
25,00
343k, 11
6.980k
34.311k
27.920k
4
21, 50
335, 94
3.825
28.891
23.300
企
​18, 00
333, 74
4.434
24.029
17.736
Overhanging
4
14, 50
327, 94
3.349
19.021
13.396
portion
4
11, 00
324, 37
2.431
14.272
9 724
7, 30
324, 37
1.547
4.866
3.094
Total for one row of sleepers.
125.390k
95.170k
For the four rows of sleepers we shall thus have :-

DESCRIPTION
Bedplates, rails, foolway, and bracings of longitudinals.
Longitudinals underlying rails.
2. Beams.
CENTRAL SPAN
TWO CANTILEVER ARMS
of 300 metres
of 187,5 each
411,732
501T,560
335, 040
380, 680
The beams of the central span and of the cantilever arms assume the
same shape as those of the independent span.
Their length varies between 23 and 9 metres, and their height from
7⁰⁰,60 to 3m,60.
The loads due to the bedplates, rails, etc., and the weight of the slee-
pers are found with the assistance of the following tables.
As regards the strain due to the passing trains, the sketch below
indicates the maximum attained in the case of each train.
25
-25...
a
25..
21,5....
21,5-----
IS
18...
18
14,5.... 144,5.
14,5 --x---11.
1.
75x

人
​Cantilever arms
(n
Central span ·
78

MAXIMUM
CASE
BEAMS
strain
in which the maximum
BEAMS
strain
MAXIMUM
in which the maximum
CASE
(for one line)
may be attained.
(for one line)
is attained
n
हे ४
89T
Double traction train.
n
66T
Simple traction train.
89
dº
Ө
60
dº
ß
உ
83
dº
λ
58
dº
710
81
do
ૐ.
52
do
76
do
<
48
dº
(1)
71
do
Q
42
do
In addition to this, the beams will have to sustain two kinds of strains
the one due to the action produced by the wind upon the train and the
sleepers, and the other caused by the incline of the main girders, which
will be more amply referred to farther on.
The weights attained in this connection are recorded in the following
table:

WEIGHT
NUMBER
TOTAL
DESCRIPTION OF SPANS
BEAMS
ON EACH BEAM
OF BEAMS
WEIGHT
Central span of 300 metres.
n'
8.902K
TOTAL.
12
106T,824
106,824
n'
8.902K
1
8¹,902
α
7.838
B
6.776
Y
6.070
5.114
Ε
4.182
Two cantilever arms of 187,5
η
3.500
A
2.814
each
λ
2.402
इ >
2.138
1.718
1.498
2 2 2 2 2 2 2 2 2 2 2
15,676
13, 552
12, 140
10,228
8,364
7,000
5,628
4,804
4,276
3,436
Р
TOTAL.
2,996
97T.002
79
3. Bracings.
The surfaces exposed to the action of the wind have been determined in
the same way as in the case of the independent span, and the force of the
wind has been supposed to be the same.
It has been assumed that the pressures at each apex are due to the
braces that are there united to the chord or flange. Thus the different apices
would have to sustain the following pressures: -

A
B'
A A A A A
Ꮽ
Ez
F
10
2
2
F1
11'
G'
15
H'
15'
I
1
n
F2 Gi G2 HɅ/H₂
12
13 14 15 16 17

TOP APICES
CASE OF LOADED BRIDGE
CASE OF UNLOADED BRIDGE
1'
60T, 182
3'
60, 182
95T,583
95, 583
5'
59, 978
93, 978
7'
59, 300
93, 000
9'
58, 752
92, 359
11'
52, 569
90, 432
13'
38, 203
61, 656
15'
24, 428
40, 702
17'
9, 123
10, 290
80

LOWER
CASE OF BRIDGE LOADED
CASE OF BRIDGE NOT LOADED
LOADS
APICES
applied direct
sleepers and trains
LOADS DUE
to
LOADS DUR
LOADS
applied direct
to
sleepers
0
40T,768
11,050
66T,962
7T,425
1
26, 908
22, 100
34, 506
14, 850
2
81, 534
22, 100
133, 926
14, 850
5
6
0 + 20 CO
3
26, 908
22, 100
34, 506
14, 850
4
81, 534
22, 100
133, 926
14, 850
26, 908
22, 100
34, 506
14, 850
70, 473
22, 100
125, 506
14, 850
7
24, 557
22, 100
40, 666
14, 850
62, 118
20, 188
99, 810
13, 220
9
17, 816
18, 275
29, 713
11, 610
10
41, 331
16, 329
72, 130
9, 936
11
12, 723
14,382
21, 250
8, 262
12
27, 622
12, 614
49, 393
6, 872
13
8,887
10, 846
14, 426
5, 481
14
18, 595
9, 350
32, 171
4, 523
15
6, 091
7,854
9, 628
3, 564
16
11, 298
6, 650
16, 002
2, 997
17
2, 798
2,878
4, 712
1, 215
Owing to the absence of bracings at the upper portion of the girders,
it is the lower bracing that will have to resist the action of the wind.
The stresses due to the trains and to the sleepers, as well as those
applied to the top apices, will therefore have to be transmitted to the lower
apices.
But in order to obtain a system of forces equivalent to the first system, it
will be necessary to add to these forces conveyed to the lower nodes such
couples as will equal the moments of such forces about their new points of
application.
The effects of such couples will be these: -
The strains due to the sleepers under the rails and to the train are trans-
mitted to the lower apices by means of braces.
This transmission develops in the web of the beams, tensions, and
compressions which have been taken into account in calculating their
weights.
Let Ph be the intensity of one couple due to the action of the wind upon
the sleepers and the train.
If I be the distance of the measurements of the lower girders it will
81 -
be seen that the couple Ph will load one of the girders with a quantity
equal to
Ph
ī
while the second girder will be relieved of the same quantity.
As to the stress on the top apices, it has been supposed that they are
transmitted to the lower apices by the rigid structure composed of the com-
pressed bars of the girders and the cross bracings connecting the bars by
pairs.
8
1
人
​Let us suppose, for example, that the force P' is
applied to apex 9'. From the foregoing considerations
it is clear that it will be transmitted to apex 8 by
bars i of the two girders and by the braces connec-
ting these two bars.
This couple is equal to the product of P' mul-
tiplied by the distance between the nodes 9' and 8.
It will be seen that it can be decomposed into two
other couples.

P'h'
The one P'h' loading one of the girders with and the other P' pro-
ducing in the members a tension and a compression equal to
P'λ
Lower Bracing. The whole of the lower chords or flanges of the
principal girders, the lower bars of the beams and cross-shaped bracings,
gives the form of girder which is to sustain the stresses transmitted to the
lower apices (see sheet 20).
It has been shown just now what stresses would act upon each of the lower
apices. To these must be added the effect of wind upon the independent span
of 125 metres.
These effects are, 158',347 when the bridge is loaded,
and 212,682
free.
They must be applied to apex 17, that is, to the end of the overhanging
portion of the cantilever.
To these effects we must further add couples similar to those mentioned
above. The effect of these couples is to load vertically the main girders with
a weight equal to-
124,698, when the bridge is loaded,
and 167,545
free
11
82
APICES
These, however, will only have to be considered in calculations referring
to the larger trains.
In the case of the lower bracing there will have to be considered at the
end of the cantilever arm a moment of flexure equal to and acting in the
opposite direction to the moment at the junctions of the lower bracing of the
independent span.

CASE OF BRIDGE LOADED
CASE OF BRIDGE FREE
STRESSES
applied
Direct
STRESSES
due to
Trains
and
Sleepers.
STRESSES
STRESSES
of
TOTALS
Top
Apices.
applied
Direct.
STRESSES
due to
Sleepers.
STRESSES
of
Top
Apices
TOTALS
0
40T,768
11,050
1
26,908
22, 100
51,818
49,008
66T,962
7T,425
74,387
34,306
14, 850
2
81, 534
59, 356
22, 100
60T,182 163, 816
133, 926
14, 830
3
26,908
957,583 244, 359
22, 100
49,008
34,506
14, 850
4
81, 534
59, 356
22, 100
60, 182
163, 816
133, 926
14, 830
5
95, 583 244, 359
26, 908
22,100
49,008
34,506
14, 850
6
70,473
59, 356
22, 100 | 119, 278
211, 851
123, 506
7
24, 557
14, 850 186, 978 327, 334
22,100
46,657
40, 666
14,850
55, 516
8
62, 118
20, 188
38, 752
141, 058
99, 810
13, 220
92, 359 205, 389
9
17,816
18,275
36, 091
29, 713
11, 610
41, 323
10
41, 331
16, 329
52.569
110, 229
72, 130
9,936
90, 432
172,498
11
12, 723
14,382
27, 105
21, 250
8, 262
29, 512
12
27,622
12, 614
38, 203
78, 439
49,393
6, 872
61, 656 117, 921
13
8,887
10, 846
19, 733
14,426
5, 481
19,907
14
18, 595
9, 350
24, 428
52, 373
32, 171
4,523
40, 702
77, 396
15
6,091
7, 834
13,945
9,628
3,564
13, 192
16
11, 298
6, 650
9, 125
27,073
16, 002
2,997
10, 290
29, 289
2,898
2, 678
17
5,876
158, 347
4, 712
1,213
5,927
212,682
On Sheet 20 the diagrams will be found which serve to determine the
moment of flexion and the strains along the bars of the bracings.
The results of these calculations are embodied in the following tables :-
83

MEMBERS
CASE OF BRIDGE LOADED
CASE OF BRIDGE FREE
LENGTH
of
MEMBERS
STRESSES
WEIGHT
STRESSES
WEIGHTS
A₁
B₁
B₂
ت کی تو ھے تے تے
25,000
1.308T
28T,916
2.665T
51,101
A₂
25, 000
1.608
30, 833
2.720
52, 156
25, 000
1.884
36, 126
3.020
37, 909
25, 000
2.188
41, 955
3.380
64, 812
25,
000
2.680
31, 389
3.980
76, 317
C₂
25, 000
3.200
61, 395
4.660
89, 356
D₁
23, 029
3.200
61, 395
4.660
89, 459
Ꭰ,
D2
25, 029
2.687
51, 583
3.915
73, 157
E₁
21, 525
2.152, 4
35, 534
3.120
51, 511
E₂
21, 525
1.742, 7
28, 770
2.490
41, 110
F₁
18, 021
1.298, 4
17, 946
1.835
25, 640
1
F₂
18, 021
992, 6
13, 720
1.365
18, 867
G₁
14, 517
654
7,282
817
9, 097
ངརུག
14, 517
406, 8
4, 530
518
5, 768
H₁
11, 013
145, 6
1, 230
164
1, 385
H₂
11, 013
254, 7
2, 151
354
2, 990
2
I
7, 309
382
2, 200
523
3, 012
DESCRIPTION
or SIDES
DESCRIPTION OF SPANS
TOTAL
STRAINS
LENGTII
including
on the Two
or EACH BAR
THE BARS
BARS
WEIGHT
OF EACH BAR
(0,1)
175T
35, 355
1¹,745
(1,2)
495
35, 355
13, 423
Central span.
(2,3)
572
35, 355
'S, 311
(3,4)
765
35, 355
20, 745
(4,5)
842
35, 355
22, 833
(5,6)
2.138
35, 355
57.977
TOTAL for one half Span
135¹,234
(6,7)
2.332T
34m,300
61.708
(7,8)
1.455
33, 250
37, 107
(8,9)
1.262
29, 350
28, 410
(9,10)
1.103
28. 250
23, 943
Cantilever arms.
(10,11)
998
24, 150
18, 486
(11,12)
782
23, 750.
14, 246
(12,13)
675
20, 100
10, 407
(13,14)
548
19. 300
8, 112
(14,15)
465
16, 030
5, 724
(15,16)
370
15, 650
4, 442
(16,17)
309
12, 600
2,987
TOTAL for one cantilever arm.
215T,572
- 84
Aggregate weight of all the bars of the lower bracings:
In a central span of 300 metres..
In two cantilever arms of 187,500.
270¹,468
431,144
Cross Bracings. The cross bracings which connect twos-and-twos the
struts of the main girders must be capable of transmitting to the lower apices
those stresses acting on the top apices.
The tensions and the compressions of the bars of these bracings may be
determined by simple diagrams such as are used in statics.
Stresses are also developed in the central bars.
The following tables give the results :-


MAIN BARS
WEIGHT
WEIGHT
CORRESPONDING
of
of
BARS
GIRDERS
BRIDGE LOADED
BRIDGE FREE
CROSS BRACINGS
a
9º,170
14T,600
a
5T,698
9, 170
14, 600
b.
5, 698
d
9, 170
d
14, 600
5, 698
f
5, 698
f
9, 170
14, 600
9
5, 377
g
8, 294
13, 000
i
5, 717
i
6, 969
10, 900
k
4, 897
k
4, 686
m
8, 100
3, 807
0
0, 335
m
2, 217
3, 580
q
0, 370
0, 746
1, 250
q
0, 311
0, 350
TOTAL. .
43º,295
Total weight of the cross bracings:
In the central span of 300 metres.
457584
In the two cantilever arms of 187.5 metres, each. 41006
Calculation of Effects due to Couples.
The nature of these effects
having been indicated above, the results of the calculations will alone be
here stated.
85


VERTICAL STRAINS DUE TO COUPLES
Ph and P'h'
WEIGHTS OF CHORDS
necessary to enable them to withstand couples P'x
APICES
loaded
BRIDGE LOADED
BRIDGE FREE
CHORDS
BRIDGE LOADED
BRIDGE FREE
0
4T,6
2T,6
A₁
0T,956
1T,911
1 2 3 →→ 20 co
9, 2
5, 3
A₂
0,956
1, 911
165,
7
253, 8
B₁₁
2, 110
3, 744
9, 2
5, 3
B₂
2, 110
3, 744
4
165, 7
253, 8
C₁
3, 264
5, 576
9, 2
5, 3
C₂
3, 264
6
306, 7
471, 7
D₁
3, 264
7
9,4
5, 4
D₂
3, 264
2020 20
5, 576
5, 601
5, 601
8
150, O
226, 9
E₁
1, 978
3, 255
9
9, 1
4, 3
Ez
1, 978
3, 255
10
126, 6
208, 7
F₁
0, 912
1, 444
11
6, 9
3, 2
F
0, 912
1,444
12
81, 7
124, 5
G₁
0, 141
0, 485
13
5, 6
2,2
G₁₂
0, 141
0, 485
14
42, 8
64,8
H₁
0, 055
0,062
15
4,
4.4
1, 5
H₂
0, 053
0, 062
16
13, 3
12, 0
I
>>
17
1, 6
0,5
4. The Secondary Bars of the Main Girders.
The same methods of calculation are here adopted as in the case of the
independent span. The results are as follows:

CORRESPONDING
apices
WEIGHT
of
SECONDARY BARS
1
4T,828
3
5, 412
5
6, 593
7
6, 332
9
3, 784
11
2, 134
13
1, 116
15
0, 541
86
5. Main Girders.
Each main girder comprises a central span of 300 metres, and the two
adjacent overhanging portions of 187,500 each.
What has now to be determined is the weight that will enable each
girder to resist vertical strains. Such strains are due to a variety of causes :-
To the weight of the bed-plates, rails, etc.
To the weight of the sleepers under the rails.
To the weight of the beams.
To the weight of the bars of the lower bracings.
To the weight of the bars of the cross bracing.
To the weight of the chords and bars, which is necessary to enable
them to withstand the effects of the wind.
To the vertical stresses due to the wind.
To the weight of the secondary bars of the girders.
To the effects due to the independent span of 125 metres.
To the additional load due to trains (assumed to be at the rate of 3 tons
per metre of girder); and lastly.
To the weight of the girders themselves.
With the assistance of the preceding tables, the strains that can be
applied to each main apex of the girder may be readily determined.
Owing to the method of construction of the girder, the weights of the
lower chords and of the bars of the girder may be regarded as transmitted
to the lower apices; the top apices only being loaded with the weight of
the top chords.
The following table indicates the strains that are known, as applied to
the apices of half of a girder :—
APICES
CASE OF BRIDGE LOADED
CASE OF BRIDGE FREE
024
170º,234
498, 214
105,037
484, 020
539, 346
531, 195
6
743, 027
823, 004
8
506, 144
486, 451
10
386, 766
371, 655
12
266, 622
218, 074
14
170, 439
115, 351
16
83. 908
38, 026
17
483, 187
326, 760
87
The inspection of this table shows that the case of the bridge being load -
ed is the most unfavourable one. We will, therefore, take the figures of the
second column for the calculations of the girders.
Assuming that the approximale weight of the members of the girder is
found by any convenient method, such weight will have to be distributed
among the different apices, and by adding it to the figures of the foregoing
table we will obtain a fresh series of loads that may serve as a base for a
second approximale estimate of the weight.
By repeating the same process a third approximate figure can be obtained,
and the calculation may thus be continued until two consecutive approxima-
tions represent as nearly as possible the weight of a semi-girder. The stresses
developed in each member of the girder have been represented statically.
In a diagram on sheet 19 the final approximations are given. The results
are as follows:

CENTRAL SPAN
WEIGHT OF CHORDS
CANTILEVER ARMS
WEIGHT OF BARS
WEIGHT or CHORDS
WEIGHT OF BARS
I
1T,633
q
4T,927
C
144,321
f
H
9, 413
Ρ
9, 485
B
107, 987
e
136,976
122. 337
G
22, 558
0
6, 421
A
92, 442
d
63, 780
F
43, 679
N
14, 706
C'
121, 117
C
59, 267
E
79, 477
m
12, 121
B'
96, 293
b
19, 488
D
145, 143
し
​28, 261
Α'
45, 088
a
13, 669
I'
4, 528
k
26, 070
H'
16, 320
j
56, 578
G'
33, 340
i
57, 525
F'
59, 976
h
108, 914
E'
106, 670
g
117, 233
D'
172, 280
These are the weights necessary to resist vertical strains.
To determine the real weights, the stresses due to the action of wind
should be added.
Thus the total weights of the two main girders are as follows:
In one central span of 300 metres . .
For the two cantilever arms of 187,5 each .
5 379',684
3.594,104
88
The diagrams on Sheet 19 show that owing to the incline of the girders
the compression stresses are developed in the lower bars of the beams; it has
been ascertained that they are capable of sustaining these stresses.
§ 3. -
METAL COLUMNS.
In determining the stability of the metal columns the following two cases
have been considered :—
1. When the wind acts horizontally and at right angles to the longitudinal
axis of the bridge, or transversely to the bridge; and
2. When the wind acts horizontally, and in the direction of the longi-
tudinal axis of the bridge.
In these two cases the thrust at the head of the columns due to expan-
sion is added to the effects of the wind.
In the first case, the surfaces exposed to the wind are, with regard to
the flooring, those which have been determined by the calculations of the
bracings of the main girders; and in regard to the metal columns, they
represent the sum of the diametrical surfaces of the piers, which are considered
as invariable throughout their height.
In the second case, the vertical projections of the chords of the girders
of the lower and upper bracings (supposed to be flat for a distance equal
to the heights of the sums of the girder braces) and the sum of the vertical
projections of all the remaining bars, beams, etc., have been taken into
account in dealing with the floor.
Considering that all these members are comparatively close to each other,
il is amply sufficient to take half of the total surfaces. In the case of the
metal column the sum of the superficial diameters of the two piers and of
the five rows of pier bracings has been taken (Sheet 21).
The wind pressures are the same as those assumed in the calculations
of the floor, that is to say, 270 kilogrammes per square metre in the case
of the floor being free from any load, and 170 kilogrammes when the floor
is loaded by trains.
89

FLOOR
Free
TRANSVERSE
WIND
LONGITUDINAL
FLOOR
Loaded
I LOOR
Free
Strain of wind pressure upon 400 metres of
flooring in connection with a metal column.
Height of the centre of pressure above the axis
of the lower rib
2.030™
1.455T
767T
20m, 1
19m.4
24m,3
Weight of 400 metres of flooring connected
with the metal column .
7.162T
7.162T
7.162T
Inner framings of the lower braces on the
right of the supports.
Overcharge of 6 tons per running metre of
bridge.
30T
30T
30T
2.400T
TOTAL.
7.192T
9.392T
7.162T
Weight acting on one pillar.
3.596T
4.796T
3.396T
1. Stability under the Action of Transverse Wind.
Sockets. -The greatest load supported by a socket in that which results
at the time when the bridge is subjected to additional load.
The distance between the base of a socket and the axis of the lower base
is 1,4.
The load is expressed by the following formula :
M
C = P+
Weight due to the floor.
Weight due to the socket and accessories.
P 4.802 tons.
4.796 tons
6
M, being the moment of overturn under the action of the wind, is equal
to 1.455 tons (19m,4 + 1,4) 30.264 Tm
, being the distance of the columns, equals 25 mètres.
C = 6,012,6.
The surface of support for the socket is 2m × 0,m5
1 in 2
The crushing stress is equal to -
R = 6 per square millimetre.
12
90 -
Stability above the rollers.
JL JL J L JL JL
3,5
90
I
2,1
Axis of the lower member.


2 m 75
275
1,2
1,2

BRIDGE FREE BRIDGE LOADED
BRIDGE LOADED
Wind on floor. .
V
Height of centre of pressure.
g
2.030T
23m,6
1.455T
22m 9
Moment of overturn .
vg = m
48.380Tm
33.320™m
Wind on expansion slides.
び
​Weight of floor.
Total Weight.
Height of centre of pressure.
Moment of overturn
Total moment of overturn.
Total pressure of wind
•
Weight of pieces above rollers.
A half distance between columns.
Moment of stability.
Coefficient of safety.
Relation of stress of wind to the weigh.
g'
v' g′ = m'
m+m' = M,
v + v = V
ᏮᎢ
1m,03
6™m
48.386™m
3T,8
1,05
4Tm
33.324™m
2.056™
1.458⁰,8
p
p'
p+p' = P
1
7.192T
9.592T
134T
134T
7.326T
9.726T
•
10
12m,5
12m,5
PS Ms
91.575Tm
121.575™m
| > |
Ms
Mr
1,89
3,65
V
P
0,28
0,15
91
*
Expansion Slides.
The slide which is to support the heaviest load is
situated under the beam exposed to the wind when the bridge is loaded. It
is subject to the action of the rollers, which is equal to —
M
PX
C
P, being the load supported by the column
9.726
2
4.863 tons.
M, being the moment of overturn = 33,324™m
, being the distance between the columns=25".
The effect above the rollers equals 6.196 tons.
Supposing that all the rollers support the same load, the centre effect
on either side the axis of the socket is at a distance of 1,2, and the moment
of deflexion at the centre of the slide is equal to-
6.196T
2
× 1,2 = 3.717,6.
I
The section of the slide is a value of
0,323610.
12
The maximum strain per square millimetre of section is equal to 11¹,48.
Rollers. The greatest reaction of rollers determined for the expansion
slides equals 6.196 tons. The weight of an apparatus of ten rollers is 45 tons.
Each roller supports at its base a load of
6.19645
10
624T,1.
The strain per unit of surface, according to M. Contamin, is—
R being the stress to be determined.
E the modulus of elasticity
Q weight of a roller
I length of a roller
r radius of a roller
R³
9 EQ²
64 12.2
22,5 X 10.
624.100k.
3m.
R = 11,51 per "/
m/m².
2
The strain whereby the rollers are set in motion, which shall be consi-
dered farther on, is equal to -
a being the width of the deformed portion.
F
21
Q for each roller,
3
1
2r
2
24 Q
E lr
=
0,000529 Q.
92
Circular Roller Supports.
The supports rest upon columns by means
of a circular support 2",75 in radius. They are formed of two circular plates
of 60 millimetres thickness, the inner distance between them being 1m,28.
They are strengthened by ribs and crowns of sheet-iron, and by angle irons.
The total pressure sustained by the rollers is 6.241 tons. The rectangle
formed by the end rollers has a surface of-
4™,2 × 3m = 12m²,6.
The pressure per square metre is equal to-
6241
12,6
496 tons.
Supposing that the load is the same throughout the surface of the plate,
the maximum stress, according to the formula of MM. Lévy, would be
R = Ρ h2
p being the pressure per square metre
a being the radius of support
h being the external height
h, being the internal height
α
h₁²
2
496,000 kilos.
2⁰,75.
1m, 40.
1,28.
2
R 11,7 par m/m².
Pier Bracings. The bracings that connect the piers are five in number,
and are arranged parallel to each other. They sustain the greatest strains
when the bridge is free, assuming that the wind has an intensity of 250 kilo-
grammes per square metre.
The system of bracings being double, the pressures are supposed to be
equally divided between the two halves, one half of the pressure being
sustained by the joints of the windward piers, and the other half by those
of the leeward piers. The section of the bars will enable them to bear a strain
of 12 kilogrammes per square millimetre.
Metal Piers. The piers carry the aggregate weight of all the metal
parts, and they resist at the same time the action of transverse wind and the
flexure produced by a stress capable of setting into motion the expansion rollers.
For any pier section we must have
P
p'
Mn
R =
+
S
S
+ 15 +
S
Sr2
R being the strain per unit of section
limetre.
12 kilogrammes per square mil-
P weight of all the known metal parts acting above the section under
consideration.
P' stress in component of pier, due to wind, through the medium of the
bracing.
93
p weight of the component of pier, which is here unknown.
M the moment due to thrust of expanding stress.
n distance of the remotest web from the centre of gravity of the section.
2 is the square of the radius of the gyration of the section under consi-
deration.
S section of the component, the value of which is
S =
p
1,18 II l
The co-efficient 1,18 is the allowance made for the fittings and rivetings.
being the specific gravity of the steel
7.8.
being the length of the segment of pier under consideration.
These two expressions will give :
Ρ
P+ P+
R
1,18 II Z
Mn
p2
1
Thus it is this formula which serves to determine the weight of the seg-
ment of the pier. The weight is less than that indicated in the case of a
longitudinal action of the wind, and it is only mentioned here in passing.
Stability at the Base of the Piers. -The conditions of stability under
the action of transverse wind are indicated in the following table:

Wind on flooring
Height of centre of pressure.
Moment of overturn .
Wind upon expansion slides.
Height of centre of pressure.
Moment of overturn
Wind on piers. .
Height of centre of pressure.
Moment of overturn
Total amount of overturn.
Total stress of wind at base.
Weight of metal flooring .
Weight of supporting apparatus and
metal columns.
Total weight.
Half distance between the piers
Moment of stability.
Ratio of moments
Relation of the stress of the wind to
the weight
BRIDGE FREE BRIDGE LOADED
g
2.030T
61,1
1.455T
vg = m
125.255TD
Tm
V'
6T
38m 55
v' g'
= m'
روح
g"
231 Tu,3
162T
18m.75
3.037™m 3
18,73
1.912™m 5
60 m.4
87.882™m
>
3,8
38 m,55
146™,5
102T
v" g"
=m"
m+m'+m"=M,
128.323™m.8
89.941™m
v + v + v″ = V
2.218T
1.560 T,8
Ρ
7.192T
9.592T
p'
1
2
~ 2 - | | |-
1.982T
1.982T
p+p' = P
9.174T
11.574T
♡
12m3
12m,5
Ms
114.675™m
144.675™m
Ms
0.89
1,6
V
0,24
0,13
P
94
Substructure of Piers.
The substructure of the piers produces maximum
pressures on the masonry in the case of wind acting longitudinally. The
calculations in this connection are reproduced farther on.
Anchor Tubes.
When the bridge is not loaded the stability at the
base of the piers can only be ensured by means of anchorings.
The pull on these pieces is represented by this formula:
M
T =
P
CO
M being the moment of overturn at the base of the piers
à the distance between the piers 25 m.
128.523,8.
P the weight acting on the base of the piers
9.174
2
4.587T
T = 554¹.
The section of the centre tube alone is 0m2,3237 square metre.
The strain at the anchorings, therefore, is insignificant.
Anchor Bolts. By the effect of expansion the tubes are caused to oppose
little resistance to the overturning strain, being situated in the centre of the
piers, but here the anchoring bolts have to be considered. They have a
maximum stress to sustain in the case of longitudinal wind. We will refer
to them farther on.
Stability of the Masonries at the Level of the Tie-Bands.
The height
of the masonry that is subject to the effects of anchoring must be such as to
prevent lifting.
The maximum and minimum pressures may be represented by this for-
mula:
C
P + P Mn
+
S
I
The quantities expressed in this formula are indicated in the following
table :
Weight of metal parts
P
9.174T
Height of anchoring .
h
14T
Surface at the top of the masonry.
S
625m²,8
Weight of masonry without the sloping por-
tion.
Total weight at level of tie-bands.
P + P
at
21.028™
30.202⁰
Moment of overturn at level of substructures
M
128.523™,8
Stress of wind at level of substructures .
Moment of overturn .
21
2.218™
vh
- m'
31.052TI
95
Stress of wind upon masonry.
Moment of overturn.
Total moment of overturn .
Value of n
v
647,4
T
1
h
=m"
450™m,8
2
m+m'+m"=M 160.026TH,6
n
21m
Value of I
Pressure upon masonry on the windward side
C
leeward side .
C
Total pressure of wind.
v + v
V
I
77.991,6
m
2
0k,5 par c/
9k,1 par c/m²
2.282¹,4
V
Relation of wind to the weight.
0,075
P+ P
The expansion which tends to overturn the column in the direction of
the length of the bridge does not to an appreciable extent alter the results
indicated above.
2. Stability under the Action of Longitudinal Wind.
When the action of wind is longitudinal, the thrust felt at the head of
the piers joins the strain due to expansion. The piers which support the
rollers cannot exercise a resistance more powerful than is the strain which is
capable of setting such rollers in motion. The consequence is that the
difference is transmitted to the piers with fixed supports. The greatest
overturning strain further acts upon the piers on the leeward side provide
with fixed supports when the bridge is not loaded.
M
The vertical strain that acts above the rollers is equal to P = d
The values of this formula are indicated in the following table: —
Weight of metal parts on pier.
•
Pressure of wind upon 800 metres of girder.
Height of centre of pressure above the rollers.
Moment of overturn
Distance of piers.
•
Vertical stress upon rollers (windward piers)
Vertical stress upon leeward piers.
Load upon one roller
3.592T+45T
10
Co-efficient of rolling friction according to
the formula found before, namely,
0,000.529 Q
3
Strain required to set the rollers in motion.
P
3.663™
V
767T
H
VH = M
27m,8
21.322™™,6
d
300m
3.592T
3.734T
Q
363.700k
K
0,038
3.637 × 0,038
138',2
96
Method of Determining the Strains at the Head of the Pillars above
the Level of the Rollers.

35927
Rollers
138T,2
0
138T,2
Wind 767 T
3734™

Contraction
Wind
Resultant
Fixed
138T,2
767⁰
628¹,8=
Thus the pillars at their heads have to sustain a maximum strain of
628T,8.
Metal Piers.
The piers support the weight of all the metal parts, and
at the same time resist the action of longitudinal wind and the flexure
produced by the horizontal stress at the heads, which is 628,8, being due
to the combined effects of the wind and the expansion of the floor.
Taking any desired section of the pier, we must have
R =
P
N
Р
+ + (M + m + m')
S S Sr2
R being tho strain sustained by the metal per unit of section 12 kilo-
grammes per square millimetre.
P weight of the known metallic parts.
p weight of the pier segment under consideration (the value of this has
to be determined).
M moment due to the horizontal stress at the head of the pier.
m moment due to the stress of wind acting upon the bracings, such
stress being centred upon each apex.
m' moment of force of the wind upon the pier.
n distance of web farthest from the centre of gravity of the section.
2 the section of the radius of gyration of the section under consideration.
S' section of pier segment of a value of
S
p
1,18 II 7
1,18 being the co-efficient which makes allowance for the fittings and
rivetings.
II specific gravity of steel 7,8.
7 length of the pier segment under consideration.
97
From these two expressions the following formula results:
1
1
P
n
P+ (M + m + m')
r2
R
1,18ΠΙ
1
The weight of the pier segments has been determined with the assistance
of this formula. The minimum thickness of 10 millimetres has been main-
tained with regard to all the samples of steel of which the sections are com-
posed.
Stability at Base of Pillars.
The stability at the base of a pillar cannot
be given unless by taking into account the anchor bolts. The foundation-
plate in contact with the masonry presents a circular surface with recesses.
The maximum pressures of this plate upon the masonry are expressed by
the following formula:
P
C =
=
S
H
Mn
Sp2
"
the values of which appear in the following table:
Vertical load above rollers
Weight of the parts of the pier situated above
p
3.734
T
the upper level of the rollers .
p'
ལ
Total vertical load upon superstructure of pier.
Surface of foundation-plate
p + p = P
924T
4.658T
S
69m²,68
Effect upon the masonry from direct compres-
P
sion per square centimetre.
Horizontal stress on head of pier
S
Alas
6k .7
F
628⁰,8
Height of centre of action above the substructure.
H
37m,5
Wind upon bracings.
Moment of overturn .
Height of centre of pressure.
Moment of overturn .
Effect of wind on pier.
FH = m
23.580™m
υ
74,6
h
17,8
vh = m'
Tm
1.327™m,9
V
82,5
Height of centre of pressure.
h'
18m,75
Moment of overturn
v'h'm"
1.546™,9
Total moment of overturn
m+m+m" =M
26.454Tm ,8
External radius of the foundation-plate
n
6 .2
Square of the radius of gyration.
1-2
10,97
Effect on masonry from flexure per square
Mn
21,5
centimetre
Sr2
13
98
Maximum compression on the leeward side
per square centimetre
Maximum compression on the windward side
C
28,2
per square centimetre
C
14k8
Horizontal stress at level of substructure.
F + v + v
785⁰,9
Relation of horizontal stress to vertical load
F+v+v
Р
0,17
The anchor bolts oppose the overturning tendency. Their maximum
tension is assumed to be —
1
Mn
t:
S
p2
P).
The values of this formula are as follow:
Diameter of bolt
Sum of sections of 12 bolts.
Moment of overturn .
Radius of circle of bolts, virtual value
Square of radius of gyration.
Vertical loads.
Maximum tension per square millimetre.
0m,25
0m²,589
26.454™,8
22 P
5m,55
15,4
Р
4.658T
t
8k .26
Stability at Base of Anchor Bolts.
The maximum and minimum
pressures felt in the masonry at the level of the tie-bands is expressed in
the following formula:
C
P+ P
S
Mn
+
9.316T
14m
625m²,8
21.028T
the different values of which are indicated in the following table:
Weight of metal parts for two piers.
Height of anchors.
Surface of masonry at top
·
P
h
is a
at
Weight of masonry without the sloping portion
Total weight at level of tie-bands.
P+P
Moment of overturn at level of substructures
of the two piers.
Horizontal stress at level of substructures
Moment of overturn. .
Stress of wind upon masonry.
Moment of overturn.
Total moment of overturn.
m
F
.Fh m'
30.344T
52.909™,6
1.571⁰ ,8
22.005™, 2
158T 8
1
v + 5 h = m"
1.111™,6
•m+m' + m”—M] 76.026™,4
99
Value
14
I
of the surface of the masonry.
Direct compression per square centimetre
=|=
ก
P + P
1.683,6
4k,8
S
Mn
Maximum flexure per square centimetre
4k,5
I
Minimum pressure on windward masonry per
square centimetre.
C
Ok,3
Maximum pressure on leeward masonry per
square centimetre.
C
9k,3
Horizontal stress at level of tie-bands.
F + v
1.730⁰,6
F + v
Relation of horizontal strains to weight. .
0,057
P+P
RAILWAYS' Central prinTING-OFFICE. CHAIX, PRINTER. rue bergère, 20. PARIS. 27558-12-9 300

UNIVERSITY OF MICHIGAN
3 9015 02122 8815
Transportation
Library
TG
64
.E58
S36
Schneider et cie
Le Creusot, France.
Channel bridge
Text
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