HISTORY OF BRIDGE BUILDING

[Illustration: FIG. 3.--Ponte Salario.]

4. _Roman Bridges_.--The first bridge known to have been constructed at

Rome over the Tiber was the timber Pons Sublicius, the bridge defended by

Horatius. The Pons Milvius, now Ponte Molle, was reconstructed in stone by

M. Aemilius Scaurus in 109 B.C., and some portions of the old bridge are

believed to exist in the present structure. The arches vary from 51 to 79

ft. span. The Pons Fabricius (mod. Ponte dei Quattro Capi), of about 62

B.C., is practically intact; and the Pons Cestius, built probably in 46

B.C., retains much of the original masonry. The Pons Aelius, built by

Hadrian A.D. 134 and repaired by Pope Nicholas II. and Clement IX., is now

the bridge of St Angelo. It had eight arches, the greatest span being 62

ft.[1] Dio Cassius mentions a bridge, possibly 3000 to 4000 ft. in length,

built by Trajan over the Danube in A.D. 104. Some piers are said still to

exist. A bas-relief on the Trajan column shows this bridge with masonry

piers and timber arches, but the representation is probably conventional

(fig. 1). Trajan also constructed the bridge of Alcantara in Spain (fig.

2), of a total length of 670 ft., at 210 ft. above the stream. This had six

arches and was built of stone blocks without cement. The bridge of Narses,

built in the 6th century (fig. 3), carried the Via Salaria over the Anio.

It was destroyed in 1867, during the approach of Garibaldi to Rome. It had

a fortification such as became usual in later bridges for defence or for

the enforcement of tolls. The great lines of aqueducts built by Roman

engineers, and dating from 300 B.C. onwards, where they are carried above

ground, are arched bridge structures of remarkable magnitude (see

AQUEDUCTS, § _Roman_). They are generally of brick and concrete.

[Illustration: FIG. 4.--First Span of Schaffhausen Bridge.]

5. _Medieval and other Early Bridges_.--Bridges with stone piers and timber

superstructures were no doubt constructed from Roman times onward, but they

have perished. Fig. 4 shows a timber bridge erected by the brothers

Grubenmann at Schaffhausen about the middle of the 18th century. It had

spans of 172 and 193 ft., and may be taken as a representative type of

bridges of this kind. The Wittingen bridge by the same engineers had a span

of 390 ft., probably the longest timber [v.04 p.0535] span ever

constructed. Of stone bridges in Great Britain, the earliest were the

cyclopean bridges still existing on Dartmoor, consisting of stone piers

bridged by stone slabs. The bridge over the East Dart near Tavistock had

three piers, with slabs 15 ft. by 6 ft. (Smiles, _Lives of the Engineers,_

ii. 43). It is reputed to have lasted for 2000 years.

[Illustration: FIG. 5.--Crowland Bridge.]

The curious bridge at Crowland near Peterborough (fig. 5) which now spans

roadways, the streams which formerly flowed under it having been diverted,

is one of the earliest known stone bridges in England. It is referred to in

a charter of the year 943. It was probably built by the abbots. The first

bridges over the Thames at London were no doubt of timber. William of

Malmesbury mentions the existence of a bridge in 994. J. Stow (_Survey of

the Cities of London and Westminster_) describes the building of the first

stone bridge commonly called Old London Bridge: "About the year 1176, the

stone bridge was begun to be founded by Peter of Colechurch, near unto the

bridge of timber, but more towards the west." It carried timber houses

(fig. 6) which were frequently burned down, yet the main structure existed

till the beginning of the 19th century. The span of the arches ranged from

10 to 33 ft., and the total waterway was only 337 ft. The waterway of the

present London Bridge is 690 ft., and the removal of the obstruction caused

by the old bridge caused a lowering of the low-water level by 5 ft., and a

considerable deepening of the river-bed. (See Smiles, _Lives of the

Engineers_, "Rennie.")

[Illustration: FIG. 6.--Old London Bridge, A.D. 1600. From a Drawing in the

Pepysian Library Magdalene College, Cambridge.

From J. R Green's _A Short History of the English People_, by permission of

Macmillan & Co., Ltd.]

The architects of the Renaissance showed great boldness in their designs. A

granite arch built in 1377 over the Adda at Trezzo had a span at low water

of 251 ft. This noble bridge was destroyed for military reasons by

Carmagnola in 1416. The Rialto bridge at Venice, with a span of 91 ft., was

built in 1588 by Antonio da Ponte. Fig. 7 shows the beautiful Ponte dellà

Trinità erected at Florence in 1566 from the design of B. Ammanati.

6. _Modern Bridges._--(a) _Timber._--In England timber bridges of

considerable span, either braced trusses or laminated arches (_i.e._ arches

of planks bolted together), were built for some of the earlier railways,

particularly the Great Western and the Manchester, Sheffield &

Lincolnshire. They have mostly been replaced, decay having taken place at

the joints. Timber bridges of large span were constructed in America

between the end of the 18th and the middle of the 19th century. The

Amoskeag bridge over the Merrimac at Manchester, N.H., U.S.A., built in

1792, had 6 spans of 92 ft. The Bellows Falls bridge over the Connecticut

(built 1785-1792) had 2 spans of 184 ft. The singular Colossus bridge,

built in 1812 over the Schuylkill, a kind of flat arched truss, had a span

of 340 ft. Some of these timber bridges are said to have lasted ninety

years with ordinary repairs, but they were road bridges not heavily loaded.

From 1840, trusses, chiefly of timber but with wrought-iron tension-rods

and cast-iron shoes, were adopted in America. The Howe truss of 1830 and

the Pratt truss of 1844 are examples. The Howe truss had timber chords and

a lattice of timber struts, with vertical iron ties. In the Pratt truss the

struts were vertical and the ties inclined. Down to 1850 such bridges were

generally limited to 150 ft. span. The timber was white pine. As railway

loads increased and greater spans were demanded, the Howe truss was

stiffened by timber arches on each side of each girder. Such a composite

structure is, however, fundamentally defective, the distribution of loading

to the two independent systems being indeterminate. Remarkably high timber

piers were built. The Genesee viaduct, 800 ft. in length, built in

1851-1852 in 10 spans, had timber trestle piers 190 ft. in height. (See

Mosse, "American Timber Bridges," _Proc. Inst. C.E._ xxii. p. 305, and for

more modern examples, cxlii. p. 409; and clv. p. 382; Cooper, "American

Railroad Bridges," _Trans. Am. Soc. C.E._ vol. xxi pp. 1-28.) These timber

framed structures served as models for the earlier metal trusses which

began to be used soon after 1850, and which, except in a few localities

where iron is costly, have quite superseded them.

[Illustration: FIG. 7.--Ponte della Trinità, Florence.]

7. (b) _Masonry._--The present London Bridge, begun in 1824 and completed

in 1831, is as fine an example of a masonry arch structure as can be found

(figs. 8 and 9). The design was made by John Rennie the elder, and the

acting engineer was his son, Sir John Rennie. The semi-elliptical shape of

the arches the variation of span, the slight curvature of the roadway, and

the simple yet bold architectural details, combine to make it a singularly

beautiful bridge. The centre arch has a span of 152 ft., and rises 29 ft. 6

in above Trinity high-water mark; the arches on each side of the centre

have a span of 140 ft. and the abutment arches 130 ft. The total length of

the bridge is 1005 ft., its width from outside to outside 56 ft., and

height above low [v.04 p.0536] water 60 ft. The two centre piers are 24 ft.

thick, the exterior stones are granite, the interior, half Bramley Fall and

half from Painshaw, Derbyshire. The voussoirs of the centre arch (all of

granite) are 4 ft. 9 in. deep at the crown, and increase to not less than 9

ft. at the springing. The general depth at which the foundations are laid

is about 29 ft. 6 in. below low water. The total cost was £1,458,311, but

the contractor's tender for the bridge alone was £425,081.

[Illustration: FIG. 8.--London New Bridge.]

Since 1867 it had been recognized that London Bridge was inadequate to

carry the traffic passing over it, and a scheme for widening it was adopted

in 1900. This was carried out in 1902-1904, the footways being carried on

granite corbels, on which are mounted cornices and open parapets. The width

between parapets is now 65 ft., giving a roadway of 35 ft. and two footways

of 15 ft. each. The architect was Andrew Murray and the engineer, G. E. W.

Cruttwell. (Cole, _Proc. Inst. C.E._ clxi. p. 290.)

The largest masonry arch is the Adolphe bridge in Luxemburg, erected in

1900-1903. This has a span of 278 ft., 138 ft. rise above the river, and

102 ft. from foundation to crown. The thickness of the arch is 4 ft. 8 in.

at the crown and 7 ft. 2 in. where it joins the spandrel masonry. The

roadway is 52 ft. 6 in. wide. The bridge is not continuous in width, there

are arch rings on each face, each 16.4 ft. wide with a space between of

19.7 ft. This space is filled with a flooring of reinforced concrete,

resting on the two arches, and carrying the central roadway. By the method

adopted the total masonry has been reduced one-third. One centering was

used for the two arch rings, supported on dwarf walls which formed a

slipway, along which it was moved after the first was built.

[Illustration: FIG. 9.--Half Elevation and Half Section of Arch of London

Bridge.]

Till near the end of the 19th century bridges of masonry or brickwork were

so constructed that they had to be treated as rigid blockwork structures.

The stability of such structures depends on the position of the line of

pressure relatively to the intrados and extrados of the arch ring.

Generally, so far as could be ascertained, the line of pressure lies within

the middle half of the depth of the voussoirs. In finding the abutment

reactions some principle such as the principle of least action must be

used, and some assumptions of doubtful validity made. But if hinges are

introduced at crown and springings, the calculation of the stresses in the

arch ring becomes simple, as the line of pressures must pass through the

hinges. Such hinges have been used not only for metal arches, but in a

modified form for masonry and concrete arches. Three cases therefore arise:

(a) The arch is rigid at crown and springings; (b) the arch is two-hinged

(hinges at springings); (c) the arch is three-hinged (hinges at crown and

springings). For an elementary account of the theory of arches, hinged or

not, reference may be made to a paper by H. M. Martin (_Proc. Inst. C. E._

vol. xciii. p. 462); and for that of the elastic arch, to a paper by

A.E.Young (_Proc. Inst. C.E._ vol. cxxxi. p. 323).

In Germany and America two- and three-hinged arches of masonry and concrete

have been built, up to 150 ft. span, with much economy, and the

calculations being simple, an engineer can venture to work closely to the

dimensions required by theory. For hinges, Leibbrand, of Stuttgart, uses

sheets of lead about 1 in. thick extending over the middle third of the

depth of the voussoir joints, the rest of the joints being left open. As

the lead is plastic this construction is virtually an articulation. If the

pressure on the lead is uniformly varying, the centre of pressure must be

within the middle third of the width of the lead; that is, it cannot

deviate from the centre of the voussoir joint by more than one-eighteenth

of its depth. In any case the position of the line of pressures is confined

at the lead articulations within very narrow limits, and ambiguity as to

the stresses is greatly diminished. The restricted area on which the

pressure acts at the lead joints involves greater intensity of stress than

has been usual in arched bridges. In the Württemberg hinged arches a limit

of stress of 110 tons per sq. ft. was allowed, while in the unhinged arches

at Cologne and Coblentz the limit was 50 to 60 tons per sq. ft. (_Annales

des Fonts et Chaussées_, 1891). At Rechtenstein a bridge of two concrete

arches has been constructed, span 75½ ft., with lead articulations: width

of arch 11 ft.; depth of arch at crown and springing 2.1 and 2.96 ft.

respectively. The stresses were calculated to be 15, 17 and 12 tons per sq.

ft. at crown, joint of rupture, and springing respectively. At Cincinnati a

concrete arch of 70 ft. span has been built, with a rise of 10 ft. The

concrete is reinforced by eleven 9-in. steel-rolled joists, spaced 3 ft.

apart and supported by a cross-channel joist at each springing. The arch is

15 in. thick at the crown and 4 ft. at the abutments. The concrete

consisted of 1 cement, 2 sand and 3 to 4 broken stone. An important series

of experiments on the strength of masonry, brick and concrete structures

will be found in the _Zeitschr. des österreichen Ing. und Arch. Vereines_

(1895).

The thermal coefficient of expansion of steel and concrete is nearly the

same, otherwise changes of temperature would cause shearing stress at the

junction of the two materials. If the two materials are disposed

symmetrically, the amount of load carried by each would be in direct

proportion to the coefficient of elasticity and inversely as the moment of

inertia of the cross section. But it is usual in many cases to provide a

sufficient section of steel to carry all the tension. For concrete the

coefficient of elasticity E varies with the amount of stress and diminishes

as the ratio of sand and stone to cement increases. Its value is generally

taken at 1,500,000 to 3,000,000 lb per sq. in. For steel E = 28,000,000 to

30,000,000, or on the average about twelve times its value for concrete.

The maximum compressive working stress on the concrete may be 500 lb per

sq. in., the tensile working stress 50 lb per sq. in., and the working

shearing stress 75 lb per sq. in. The tensile stress on the steel may be

16,000 lb per sq. in. The amount of steel in the structure may vary from

0.75 to 1.5%. The concrete not only affords much of the strength to resist

compression, but effectively protects the steel from corrosion.

8. (c) _Suspension Bridges._--A suspension bridge consists of two or more

chains, constructed of links connected by pins, or of twisted wire strands,

or of wires laid parallel. The chains pass over lofty piers on which they

usually rest on saddles carried by rollers, and are led down on either side

to anchorages in rock chambers. A level platform is hung from the chains by

suspension rods. In the suspension bridge iron or steel can be used in its

strongest form, namely hard-drawn wire. Iron suspension bridges began to be

used at the end of the 18th century for road bridges with spans

unattainable at that time in any other system. In 1819 T. Telford began the

construction of the Menai bridge (fig. 10), the span being 570 ft. and the

dip 43 ft. This bridge suffered some injury in a storm, but it is still in

good condition and one of the most graceful of bridges. Other bridges built

soon after were the Fribourg bridge of 870 ft. span, the Hammersmith bridge

of 422 ft. span, and the Pest bridge of 666 ft. span. The merit of the

simple suspension bridge is its cheapness, and its defect is its

flexibility. This last becomes less [v.04 p.0537] serious as the dead

weight of the structure becomes large in proportion to the live or

temporary load. It is, therefore, a type specially suited for great spans.

Some suspension bridges have broken down in consequence of the oscillations

produced by bodies of men marching in step. In 1850 a suspension bridge at

Angers gave way when 487 soldiers were marching over it, and 226 were

killed.

[Illustration: FIG. 10.--Menai Suspension Bridge.]

To obtain greater stiffness various plans have been adopted. In the Ordish

system a certain number of intermediate points in the span are supported by

oblique chains, on which girders rest. The Ordish bridge built at Prague in

1868 had oblique chains supporting the stiffening girders at intermediate

points of the span. A curved chain supported the oblique chains and kept

them straight. In 1860 a bridge was erected over the Danube canal at

Vienna, of 264 ft. span which had two parallel chains one above the other

and 4 ft. apart on each side of the bridge. The chains of each pair were

connected by bracing so that they formed a stiff inverted arch resisting

deformation under unequal loading. The bridge carried a railway, but it

proved weak owing to errors of calculation, and it was taken down in 1884.

The principle was sound and has been proposed at various times. About 1850

it was perceived that a bridge stiff enough to carry railway trains could

be constructed by combining supporting chains with stiffening girders

suspended from them. W. J. M. Rankine proved (_Applied Mechanics_, p. 370)

that the necessary strength of a stiffening girder would be only

one-seventh part of that of an independent girder of the same span as the

bridge, suited to carry the same moving load (not including the dead weight

of the girder which is supported by the chain). (See "Suspension Bridge

with Stiffened Roadway," by Sir G. Airy, and the discussion, _Proc. Inst,

C.E._, 1867, xxvi. p. 258; also "Suspension Bridges with Stiffening

Girders," by Max am Ende, _Proc. Inst. C.E._ cxxxvii. p. 306.)

[Illustration: FIG. 11.--Niagara Suspension Bridge.]

The most remarkable bridge constructed on this system was the Niagara

bridge built by J. A. Roebling in 1852-1855 (fig. 11). The span was 821

ft., much the largest of any railway bridge at that time, and the height

above the river 245 ft. There were four suspension cables, each 10 in. in

diameter; each was composed of seven strands, containing 520 parallel

wires, or 3640 wires in each cable. Each cable was carried on a separate

saddle on rollers on each pier. The stiffening girder, constructed chiefly

of timber, was a box-shaped braced girder 18 ft. deep and 25 ft. wide,

carrying the railway on top and a roadway within. After various repairs and

strengthenings, including the replacement of the timber girder by an iron

one in 1880, this bridge in 1896-1897 was taken down and a steel arch built

in its place. It was not strong enough to deal with the increasing weight

of railway traffic. In 1836 I. K. Brunei constructed the towers and

abutments for a suspension bridge of 702 ft. span at Clifton over the Avon,

but the project was not then carried further; in 1860, however, the link

chains of the Hungerford suspension bridge which was being taken down were

available at small cost, and these were used to complete the bridge. There

are three chains on each side, of one and two links alternately, and these

support wrought iron stiffening girders. There are wrought iron saddles and

steel rollers on the piers. At 196 ft. on either side from the towers the

chains are carried over similar saddles without rollers, and thence at 45°

with the horizontal down to the anchorages. Each chain has an anchor plate

5 ft. by 6 ft. The links are 24 ft. long at the centre of the bridge, and

longer as they are more inclined, so that their horizontal projection is 24

ft. The chains are so arranged that there is a suspending rod at each 8

ft., attached at the joint of one of the three chains. For erection a

suspended platform was constructed on eight wire ropes, on which the chains

were laid out and connected. Another wire rope with a travelling carriage

took out the links. The sectional area of the chains is 481 sq. in. at the

piers and 440 sq. in. at the centre. The two stiffening girders are plate

girders 3 ft. deep with flanges of 11 sq. in. area. In addition, the hand

railing on each side forms a girder 4 ft. 9 in. deep, with flanges 4½ sq.

in. area.

[Illustration: FIG. 12.--Williamsburg Suspension Bridge.]

Of later bridges of great span, perhaps the bridges over the East river at

New York are the most remarkable. The Brooklyn bridge, begun in 1872, has a

centre span of 1595½ and side spans of 930 ft. The Brooklyn approach being

971 ft., and the New York approach 1562½ ft., the total length of the

bridge is 5989 ft. There are four cables which carry a promenade, a roadway

and an electric railway. The stiffening girders of the main span are 40 ft.

deep and 67 ft. apart. The saddles for the chains are 329 ft. above high

water. The cables are 15¾ in. in diameter. Each cable has 19 strands of 278

parallel steel wires, 7 B.W.G. Each wire is taken separately across the

river and its length adjusted. Roebling preferred parallel wires as 10 %

stronger than twisted wires. Each strand when made up and clamped was

lowered to its position. The Williamsburg bridge (fig. 12), begun in 1897

and opened for traffic in 1903, has a span of 1600 ft., a versed sine of

176 ft., and a width of 118 ft. It has two decks, and carries two elevated

railway tracks, four electric tramcar lines, two carriageways, two footways

and two [v.04 p.0538] bicycle paths. There are four cables, one on each

side of the two main trusses or stiffening girders. These girders are

supported by the cables over the centre span but not in the side spans.

Intermediate piers support the trusses in the side spans. The cables are

18¾ in. in diameter; each weighs about 1116 tons, and has a nominal

breaking strength of 22,320 tons, the actual breaking strength being

probably greater. The saddles are 332 ft. above the water. The four cables

support a dead load of 7140 tons and a live load of 4017 tons. Each cable

is composed of 37 strands of 208 wires, or 7696 parallel steel wires, No. 8

B.W.G., or about 3/16 in. in diameter. The wire was required to have a

tensile strength of 89 tons per sq. in., and 2½% elongation in 5 ft. and 5%

in 8 in. Cast steel clamps hold the cable together, and to these the

suspending rods are attached. The cables are wrapped in cotton duck soaked

in oxidized oil and varnish, and are sheathed in sheet iron. A later

bridge, the Manhattan, is designed to carry four railway tracks and four

tramway lines, with a wide roadway and footpaths, supported by cables 21¼

in. in diameter, each composed of 9472 galvanized steel wires 3/16 in. in

diameter.

[Illustration: FIG. 13.--Tower Bridge, London.]

The Tower Bridge, London (fig. 13), is a suspension bridge with a secondary

bascule bridge in the centre span to permit the passage of ships. Two main

towers in the river and two towers on the shore abutments carry the

suspension chains. The opening bridge between the river towers consists of

two leaves or bascules, pivoted near the faces of the piers and rotating in

a vertical plane. When raised, the width of 200 ft. between the main river

piers is unobstructed up to the high-level foot-bridge, which is 141 ft.

above Trinity H.W. The clear width of the two shore spans is 270 ft. The

total length of the bridge is 940 ft., and that of the approaches 1260 ft.

on the north and 780 ft. on the south. The width of the bridge between

parapets is 60 ft., except across the centre span, where it is 49 ft. The

main towers consist of a skeleton of steel, enclosed in a facing of granite

and Portland stone, backed with brickwork. There are two high-level

footways for use when the bascules are raised, the main girders of which

are of the cantilever and suspended girder type. The cantilevers are fixed

to the shore side of the towers. The middle girders are 120 ft. in length

and attached to the cantilevers by links. The main suspension chains are

carried across the centre span in the form of horizontal ties resting on

the high-level footway girders. These ties are jointed to the hanging

chains by pins 20 in. in diameter with a ring in halves surrounding it 5

in. thick. One half ring is rigidly attached to the tie and one to the

hanging chain, so that the wear due to any movement is distributed over the

length of the pin. A rocker bearing under these pins transmits the load at

the joint to the steel columns of the towers. The abutment towers are

similar to the river towers. On the abutment towers the chains are

connected by horizontal links, carried on rockers, to anchor ties. The

suspension chains are constructed in the form of braced girders, so that

they are stiff against unsymmetrical loading. Each chain over a shore span

consists of two segments, the longer attached to the tie at the top of the

river tower, the shorter to the link at the top of the abutment tower, and

the two jointed together at the lowest point. Transverse girders are hung

from the chains at distances of 18 ft. There are fifteen main transverse

girders to each shore span, with nine longitudinal girders between each

pair. The trough flooring, 3/8 in. thick and 6 in. deep, is riveted to the

longitudinals. The anchor ties are connected to girders embedded in large

concrete blocks in the foundations of the approach viaducts.

The two bascules are each constructed with four main girders. Over the

river these are lattice girders, with transverse girders 12 ft. apart, and

longitudinal and subsidiary transverse girders dividing the floor into

rectangles 3 ft. by 3½ ft. covered with buckled plates. The roadway is of

pine blocks dowelled. The bascules rotate through an angle of 82°, and

their rear ends in the bascule chambers of the piers carry 365 tons of

counterweight, the total weight of each being 1070 tons. They rotate on

steel shafts 21 in. in diameter and 48 ft. long, and the bascules can be

lifted or lowered in one minute, but usually the time taken is one and a

half minutes. They are worked by hydraulic machinery.

9. (d) _Iron and Steel Girder Bridges._--The main supporting members are

two or more horizontal beams, girders or trusses. The girders carry a floor

or platform either on top (_deck_ bridges) or near the bottom (_through_

bridges). The platform is variously constructed. For railway bridges it

commonly consists of cross girders, attached to or resting on the main

girders, and longitudinal rail girders or stringers carried by the cross

girders and directly supporting the sleepers and rails. For spans over 75

ft., expansion due to change of temperature is provided for by carrying one

end of each chain girder on rollers placed between the bearing-plate on the

girder and the bed-plate on the pier or abutment.

Fig. 14 shows the roller bed of a girder of the Kuilenburg bridge of 490

ft. span. It will be seen that the girder directly rests on a cylindrical

pin or rocker so placed as to distribute the load uniformly to all the

rollers. The pressure on the rollers is limited to about p = 600 d in lb

per in. length of roller, where d is the diameter of the roller in inches.

[Illustration: FIG. 14.--Roller Bed of a Girder.]

In the girders of bridges the horizontal girder is almost exclusively

subjected to vertical loading forces. Investigation of the internal

stresses, which balance the external forces, shows that most of the

material should be arranged in a top flange, boom or chord, subjected to

compression, and a bottom flange or chord, subjected to tension. (See

STRENGTH OF MATERIALS.) Connecting the flanges is a vertical web which may

be a solid plate or a system of bracing bars. In any case, though the exact

form of cross section of girders varies very much, it is virtually an I

section (fig. 15). The function of the flanges is to resist a horizontal

tension and compression distributed practically uniformly on their cross

sections. The web resists forces equivalent [v.04 p.0539] to a shear on

vertical and horizontal planes. The inclined tensions and compressions in

the bars of a braced web are equivalent to this shear. The horizontal

stresses in the flanges are greatest at the centre of a span. The stresses

in the web are greatest at the ends of the span. In the most numerous cases

the flanges or chords are parallel. But girders may have curved chords and

then the stresses in the web are diminished.

[Illustration: FIG. 15.--Flanged Girder.]

At first girders had solid or plate webs, but for spans over 100 ft. the

web always now consists of bracing bars. In some girder bridges the members

are connected entirely by riveting, in others the principal members are

connected by pin joints. The pin system of connexion used in the Chepstow,

Saltash, Newark Dyke and other early English bridges is now rarely used in

Europe. But it is so commonly used in America as to be regarded as a

distinctive American feature. With pin connexions some weight is saved in

the girders, and erection is a little easier. In early pin bridges

insufficient bearing area was allowed between the pins and parts connected,

and they worked loose. In some cases riveted covers had to be substituted

for the pins. The proportions are now better understood. Nevertheless the

tendency is to use riveted connexions in preference to pins, and in any

case to use pins for tension members only.

On the first English railways cast iron girder bridges for spans of 20 to

66 ft. were used, and in some cases these were trussed with wrought iron.

When in 1845 the plans for carrying the Chester and Holyhead railway over

the Menai Straits were considered, the conditions imposed by the admiralty

in the interests of navigation involved the adoption of a new type of

bridge. There was an idea of using suspension chains combined with a

girder, and in fact the tower piers were built so as to accommodate chains.

But the theory of such a combined structure could not be formulated at that

time, and it was proved, partly by experiment, that a simple tubular girder

of wrought iron was strong enough to carry the railway. The Britannia

bridge (fig. 16) has two spans of 460 and two of 230 ft. at 104 ft. above

high water. It consists of a pair of tubular girders with solid or plate

sides stiffened by angle irons, one line of rails passing through each

tube. Each girder is 1511 ft. long and weighs 4680 tons. In cross section

(fig. 17), it is 15 ft. wide and varies in depth from 23 ft. at the ends to

30 ft. at the centre. Partly to counteract any tendency to buckling under

compression and partly for convenience in assembling a great mass of

plates, the top and bottom were made cellular, the cells being just large

enough to permit passage for painting. The total area of the cellular top

flange of the large-span girders is 648 sq. in., and of the bottom 585 sq.

in. As no scaffolding could be used for the centre spans, the girders were

built on shore, floated out and raised by hydraulic presses. The credit for

the success of the Conway and Britannia bridges must be divided between the

engineers. Robert Stephenson and William Fairbairn, and Eaton Hodgkinson,

who assisted in the experimental tests and in formulating the imperfect

theory then available. The Conway bridge was first completed, and the first

train passed through the Britannia bridge in 1850. Though each girder has

been made continuous over the four spans it has not quite the proportions

over the piers which a continuous girder should have, and must be regarded

as an imperfectly continuous girder. The spans were in fact designed as

independent girders, the advantage of continuity being at that time

imperfectly known. The vertical sides of the girders are stiffened so that

they amount to 40% of the whole weight. This was partly necessary to meet

the uncertain conditions in floating when the distribution of supporting

forces was unknown and there were chances of distortion.

[Illustration: FIG. 16.--Britannia Bridge.]

[Illustration: FIG. 17.--Britannia Bridge (Cross Section of Tubular

Girder).]

Wrought iron and, later, steel plate web girders were largely used for

railway bridges in England after the construction of the Conway and Menai

bridges, and it was in the discussions arising during their design that the

proper function of the vertical web between the top and bottom flanges of a

girder first came to be understood. The proportion of depth to span in the

Britannia bridge was 1/16. But so far as the flanges are concerned the

stress [v.04 p.0540] to be resisted varies inversely as the depth of the

girder. It would be economical, therefore, to make the girder very deep.

This, however, involves a much heavier web, and therefore for any type of

girder there must be a ratio of depth to span which is most economical. In

the case of the plate web there must be a considerable excess of material,

partly to stiffen it against buckling and partly because an excess of

thickness must be provided to reduce the effect of corrosion. It was soon

found that with plate webs the ratio of depth to span could not be

economically increased beyond 1/15 to 1/12. On the other hand a framed or

braced web afforded opportunity for much better arrangement of material,

and it very soon became apparent that open web or lattice or braced girders

were more economical of material than solid web girders, except for small

spans. In America such girders were used from the first and naturally

followed the general design of the earlier timber bridges. Now plate web

girders are only used for spans of less than 100 ft.

Three types of bracing for the web very early developed--the Warren type in

which the bracing bars form equilateral triangles, the Whipple Murphy in

which the struts are vertical and the ties inclined, and the lattice in

which both struts and ties are inclined at equal angles, usually 45° with

the horizontal. The earliest published theoretical investigations of the

stresses in bracing bars were perhaps those in the paper by W.T. Doyne and

W.B. Blood (_Proc. Inst. C.E._, 1851, xi. p. 1), and the paper by J.

Barton, "On the economic distribution of material in the sides of wrought

iron beams" (_Proc. Inst. C.E._, 1855, xiv. p. 443).

[Illustration: FIG. 18.--Span of Saltash Bridge.]

The Boyne bridge, constructed by Barton in Ireland, in 1854-1855, was a

remarkable example of the confidence with which engineers began to apply

theory in design. It was a bridge for two lines of railway with lattice

girders continuous over three spans. The centre span was 264 ft., and the

side spans 138 ft. 8 in.; depth 22 ft. 6 in. Not only were the bracing bars

designed to calculated stresses, and the continuity of the girders taken

into account, but the validity of the calculations was tested by a

verification on the actual bridge of the position of the points of contrary

flexure of the centre span. At the calculated position of one of the points

of contrary flexure all the rivets of the top boom were cut out, and by

lowering the end of the girder over the side span one inch, the joint was

opened 1/32 in. Then the rivets were cut out similarly at the other point

of contrary flexure and the joint opened. The girder held its position with

both joints severed, proving that, as should be the case, there was no

stress in the boom where the bending moment changes sign.

[Illustration: FIG. 19.--Newark Dyke Bridge and Section of Newark Dyke

Bridge.]

By curving the top boom of a girder to form an arch and the bottom boom to

form a suspension chain, the need of web except for non-uniform loading is

obviated. I.K. Brunel adopted this principle for the Saltash bridge near

Plymouth, built soon after the Britannia bridge. It has two spans of 455

ft. and seventeen smaller spans, the roadway being 100 ft. above high

water. The top boom of each girder is an elliptical wrought iron tube 17

ft. wide by 12 ft. deep. The lower boom is a pair of chains, of

wrought-iron links, 14 in each chain, of 7 in. by 1 in. section, the links

being connected by pins. The suspending rods and cross bracing are very

light. The depth of the girder at the centre is about one-eighth of the

span.

[Illustration: FIG. 20.--Fink Truss.]

In both England and America in early braced bridges cast iron, generally in

the form of tubes circular or octagonal in section, was used for

compression members, and wrought iron for the tension members. Fig. 19

shows the Newark Dyke bridge on the Great Northern railway over the Trent.

It was a pin-jointed Warren girder bridge erected from designs by C.M. Wild

in 1851-1853. The span between supports was 259 ft., the clear span 240½

ft.; depth between joint pins 16 ft. There were four girders, two to each

line of way. The top flange consisted of cast iron hollow castings butted

end to end, and the struts were of cast iron. The lower flange and ties

were flat wrought iron links. This bridge has now been replaced by a

stronger bridge to carry the greater loads imposed by modern traffic. Fig.

20 shows a Fink truss, a characteristic early American type, with cast iron

compression and wrought iron tension members. The bridge is a deck bridge,

the railway being carried on top. The transfer of the loads to the ends of

the bridge by [v.04 p.0541] long ties is uneconomical, and this type has

disappeared. The Warren type, either with two sets of bracing bars or with

intermediate verticals, affords convenient means of supporting the floor

girders. In 1869 a bridge of 390 ft. span was built on this system at

Louisville.

Amongst remarkable American girder bridges may be mentioned the Ohio bridge

on the Cincinnati & Covington railway, which is probably the largest girder

span constructed. The centre span is 550 ft. and the side spans 490

ft.--centre to centre of piers. The girders are independent polygonal

girders. The centre girder has a length of 545 ft. and a depth of 84 ft.

between pin centres. It is 67 ft. between parapets, and carries two lines

of railway, two carriageways, and two footways. The cross girders,

stringers and wind-bracing are wrought iron, the rest of mild steel. The

bridge was constructed in 1888 by the Phoenix Bridge Company, and was

erected on staging. The total weight of iron and steel in three spans was

about 5000 tons.

[Illustration: FIG. 21.--Typical Cantilever Bridge.]

[Illustration: FIG. 22.]

10. (e) _Cantilever Bridges._--It has been stated that if in a girder

bridge of three or more spans, the girders were made continuous there would

be an important economy of material, but that the danger of settlement of

the supports, which would seriously alter the points of contrary flexure or

points where the bending moment changes sign, and therefore the magnitude

and distribution of the stresses, generally prevents the adoption of

continuity. If, however, hinges or joints are introduced at the points of

contrary flexure, they become necessarily points where the bending moment

is zero and ambiguity as to the stresses vanishes. The exceptional local

conditions at the site of the Forth bridge led to the adoption there of the

cantilever system, till then little considered. Now it is well understood

that in many positions this system is the simplest and most economical

method of bridging. It is available for spans greater than those

practicable with independent girders; in fact, on this system the spans are

virtually reduced to smaller spans so far as the stresses are concerned.

There is another advantage which in many cases is of the highest

importance. The cantilevers can be built out from the piers, member by

member, without any temporary scaffolding below, so that navigation is not

interrupted, the cost of scaffolding is saved, and the difficulty of

building in deep water is obviated. The centre girder may be built on the

cantilevers and rolled into place or lifted from the water-level. Fig. 21

shows a typical cantilever bridge of American design. In this case the

shore ends of the cantilevers are anchored to the abutments. J.A.L. Waddell

has shown that, in some cases, it is convenient to erect simple independent

spans, by building them out as cantilevers and converting them into

independent girders after erection. Fig. 22 shows girders erected in this

way, the dotted lines being temporary members during erection, which are

removed afterwards. The side spans are erected first on staging and

anchored to the piers. From these, by the aid of the temporary members, the

centre span is built out from both sides. The most important cantilever

bridges so far erected or projected are as follows:--

[Illustration: FIG. 23.--Forth Bridge.]

(1) The Forth bridge (fig. 23). The original design was for a stiffened

suspension bridge, but after the fall of the Tay bridge in 1879 this was

abandoned. The bridge, which was begun in 1882 and completed in 1889, is at

the only narrowing of the Forth in a distance of 50 m., at a point where

the channel, about a mile in width, is divided by the island of Inchgarvie.

The length of the cantilever bridge is 5330 ft., made up thus: central

tower on Inchgarvie 260 ft.; Fife and Queensferry piers each 145 ft.; two

central girders between cantilevers each 350 ft.; and six cantilevers each

680 ft. The two main spans are each 1710 ft. The clear headway is 157 ft.,

and the extreme height of the towers above high water 361 ft. The outer

ends of the shore cantilevers are loaded to balance half the weight of the

central girder, the rolling load, and 200 tons in addition. An internal

viaduct of lattice girders carries a double line of rails. Provision is

made for longitudinal expansion due to change of temperature, for

distortion due to the sun acting on one side of the structure, and for the

wind acting on one side of the bridge. The amount of steel used was 38,000

tons exclusive of approach viaducts. (See _The Forth Bridge_, by W.

Westhofen; _Reports of the British Association_ (1884 and 1885); _Die Forth

Brücke_, von G. Barkhausen (Berlin, 1889); _The Forth Bridge_, by Philip

Phillips (1890); Vernon Harcourt, _Proc. Inst. C.E._ cxxi. p. 309.)

(2) The Niagara bridge of a total length of 910 ft., for two lines of

railway. Clear span between towers 495 ft. Completed in 1883, and more

recently strengthened (_Proc. Inst. C.E._ cvii. p. 18, and cxliv. p. 331).

[Illustration: FIG. 24.--Lansdowne Bridge.]

(3) The Lansdowne bridge (completed 1889) at Sukkur, over the Indus. The

clear span is 790 ft., and the suspended girder 200 ft. in length. The span

to the centres of the end uprights is 820 ft.; width between centres of

main uprights at bed-plate 100 ft., and between centres of main members at

end of cantilevers 20 ft. The bridge is for a single line of railway of 5

ft. 6 in. gauge. The back guys are the most heavily strained part of the

structure, the stress provided for being 1200 tons. This is due to the half

weight of centre girder, the weight of the cantilever itself, the rolling

load on half the bridge, and the wind pressure. The anchors are built up of

steel plates and angle, bars, and are buried in a large mass of concrete.

The area of each anchor plate, normal to the line of stress, is 32 ft. by

12 ft. The bridge was designed by Sir A. Rendel, the consulting engineer to

the Indian government (_Proc. Inst. C.E._ ciii. p. 123).

(4) The Red Rock cantilever bridge over the Colorado river, with a centre

span of 660 ft.

(5) The Poughkeepsie bridge over the Hudson, built 1886-1887. There are

five river and two shore spans. The girders over the second and fourth

spans are extended as cantilevers over the adjoining spans. The shore piers

carry cantilevers projecting one way over the river openings and the other

way over a shore span where it is secured to an anchorage. The girder spans

are 525 ft., the cantilever spans 547 ft., and the shore spans 201 ft.

[Illustration: FIG. 25.--Quebec Bridge (original design)]

(6) The Quebec bridge (fig. 25) over the St Lawrence, which collapsed while

in course of construction in 1907. This bridge, connecting very important

railway systems, was designed to carry two lines of rails, a highway and

electric railway on each side, all between the main trusses. Length between

abutments 3240 ft.; [v.04 p.0542] channel span 1800 ft.; suspended span 675

ft.; shore spans 562½ ft. Total weight of metal about 32,000 tons.

[Illustration: FIG. 26.--Jubilee Bridge over the Hugli.]

(7) The Jubilee bridge over the Hugli, designed by Sir Bradford Leslie, is

a cantilever bridge of another type (fig. 26). The girders are of the

Whipple Murphy type, but with curved top booms. The bridge carries a double

line of railway, between the main girders. The central double cantilever is

360 ft. long. The two side span girders are 420 ft long. The cantilever

rests on two river piers 120 ft. apart, centre to centre. The side girders

rest on the cantilevers on 15 in. pins, in pendulum links suspended from

similar pins in saddles 9 ft. high.

[Illustration: FIG. 27.--Coalbrookdale Bridge.]

11. (f) _Metal Arch Bridges._--The first iron bridge erected was

constructed by John Wilkinson (1728-1808) and Abraham Darby (1750-1791) in

1773-1779 at Coalbrookdale over the Severn (fig. 27). It had five cast iron

arched ribs with a centre span of 100 ft. This curious bridge is still in

use. Sir B. Baker stated that it had required patching for ninety years,

because the arch and the high side arches would not work together.

Expansion and contraction broke the high arch and the connexions between

the arches. When it broke they fished it. Then the bolts sheared or the

ironwork broke in a new place. He advised that there was nothing unsafe; it

was perfectly strong and the stress in vital parts moderate. All that

needed to be done was to fish the fractured ribs of the high arches, put

oval holes in the fishes, and not screw up the bolts too tight.

Cast iron arches of considerable span were constructed late in the 18th and

early in the 19th century. The difficulty of casting heavy arch ribs led to

the construction of cast iron arches of cast voussoirs, somewhat like the

voussoirs of masonry bridges. Such a bridge was the Wearmouth bridge,

designed by Rowland Burdon and erected in 1793-1796, with a span of 235 ft.

Southwark bridge over the Thames, designed by John Rennie with cast iron

ribs and erected in 1814-1819, has a centre span of 240 ft. and a rise of

24 ft. In Paris the Austerlitz (1800-1806) and Carrousel (1834-1836)

bridges had cast iron arches. In 1858 an aqueduct bridge was erected at

Washington by M.C. Meigs (1816-1892). This had two arched ribs formed by

the cast iron pipes through which the water passed. The pipes were 4 ft. in

diameter inside, 1½ in. thick, and were lined with staves of pine 3 in.

thick to prevent freezing. The span was 200 ft.

[Illustration: FIG. 28.--Arch of Bridge at Coblenz]

Fig. 28 shows one of the wrought iron arches of a bridge over the Rhine at

Coblenz. The bridge consists of three spans of about 315 ft. each.

[Illustration: FIG. 29.--St Louis Bridge.]

Of large-span bridges with steel arches, one of the most important is the

St Louis bridge over the Mississippi, completed in 1874 (fig. 29). The

river at St Louis is confined to a single channel, 1600 ft. wide, and in a

freshet in 1870 the scour reached a depth of 51 ft. Captain J.B. Eads, the

engineer, determined to establish the piers and abutments on rock at a

depth for the east pier and east abutment of 136 ft. below high water. This

was effected by caissons with air chambers and air locks, a feat

unprecedented in the annals of engineering. The bridge has three spans,

each formed of arches of cast steel. The centre span is 520 ft. and the

side spans 502 ft. in the clear. The rise of the centre arch is 47½ ft.,

and that of the side arches 46 ft. Each span has four steel double ribs of

steel tubes butted and clasped by wrought iron couplings. The vertical

bracing between the upper and lower members of each rib, which are 12 ft.

apart, centre to centre, consolidates them into a single arch. The arches

carry a double railway track and above this a roadway 54 ft. wide.

The St Louis bridge is not hinged, but later bridges have been constructed

with hinges at the springings and sometimes with hinges at the crown also.

The Alexander III. bridge over the Seine has fifteen steel ribs hinged at

crown and springings with a span of 353 ft. between centres of hinges and

358 ft. between abutments. The rise from side to centre hinges is 20 ft. 7

in. The roadway is 65½ ft. wide and footways 33 ft. (_Proc. Inst. C.E._

cxxx. p. 335).

[Illustration: FIG. 30.--Viaur Viaduct.]

The largest three-hinged-arch bridge constructed is the Viaur viaduct in

the south of France (fig. 30). The central span is 721 ft. 9 in. and the

height of the rails above the valley 380 ft. It has a very fine appearance,

especially when seen in perspective and not merely in elevation.

[Illustration: FIG. 31.--Douro Viaduct.]

Fig. 31 shows the Douro viaduct of a total length of 1158 ft. carrying a

railway 200 ft. above the water. The span of the central opening is 525 ft.

The principal rib is crescent-shaped 32.8 ft. deep [v.04 p.0543] at the

crown. Rolling load taken at 1.2 ton per ft. Weight of centre span 727

tons. The Luiz I. bridge is another arched bridge over the Douro, also

designed by T. Seyrig. This has a span of 566 ft. There are an upper and

lower roadway, 164 ft. apart vertically. The arch rests on rollers and is

narrowest at the crown. The reason given for this change of form was that

it more conveniently allowed the lower road to pass between the springings

and ensured the transmission of the wind stresses to the abutments without

interrupting the cross-bracing. Wire cables were used in the erection, by

which the members were lifted from barges and assembled, the operations

being conducted from the side piers.

[Illustration: FIG. 32.--Niagara Falls and Clifton Bridge.]

The Niagara Falls and Clifton steel arch (fig. 32) replaces the older

Roebling suspension bridge. The centre span is a two-hinged parabolic

braced rib arch, and there are side spans of 190 and 210 ft. The bridge

carries two electric-car tracks, two roadways and two footways. The main

span weighed 1629 tons, the side spans 154 and 166 tons (Buck, _Proc. Inst.

C.E._ cxliv. p. 70). Prof. Claxton Fidler, speaking of the arrangement

adopted for putting initial stress on the top chord, stated that this

bridge marked the furthest advance yet made in this type of construction.

When such a rib is erected on centering without initial stress, the

subsequent compression of the arch under its weight inflicts a bending

stress and excess of compression in the upper member at the crown. But the

bold expedients adopted by the engineer annulled the bending action.

The Garabit viaduct carries the railway near St Flour, in the Cantal

department, France, at 420 ft. above low water. The deepest part of the

valley is crossed by an arch of 541 ft. span, and 213 ft. rise. The bridge

is similar to that at Oporto, also designed by Seyrig. It is formed by a

crescent-shaped arch, continued on one side by four, on the other side by

two lattice girder spans, on iron piers. The arch is formed by two lattice

ribs hinged at the abutments. Its depth at the crown is 33 ft., and its

centre line follows nearly the parabolic line of pressures. The two arch

ribs are 65½ ft. apart at the springings and 20½ ft. at the crown. The

roadway girders are lattice, 17 ft. deep, supported from the arch ribs at

four points. The total length of the viaduct is 1715 ft. The lattice

girders of the side spans were first rolled into place, so as to project

some distance beyond the piers, and then the arch ribs were built out,

being partly supported by wire-rope cables from the lattice girders above.

The total weight of ironwork was 3200 tons and the cost £124,000 (_Annales

des travaux publiques_, 1884).

The Victoria Falls bridge over the Zambezi, designed by Sir Douglas Fox,

and completed in 1905, is a combination of girder and arch having a total

length of 650 ft. The centre arch is 500 ft. span, the rise of the crown 90

ft., and depth at crown 15 ft. The width between centres of ribs of main

arch is 27½ ft. at crown and 53 ft. 9 in at springings. The curve of the

main arch is a parabola. The bridge has a roadway of 30 ft. for two lines

of rails. Each half arch was supported by cables till joined at the centre.

An electric cableway of 900 ft. span capable of carrying 10 tons was used

in erection.

12. (g) _Movable Bridges_ can be closed to carry a road or railway or in

some cases an aqueduct, but can be opened to give free passage to

navigation. They are of several types:--

[Illustration: FIG. 33.]

(1) _Lifting Bridges._--The bridge with its platform is suspended from

girders above by chains and counterweights at the four corners (fig. 33 a).

It is lifted vertically to the required height when opened. Bridges of this

type are not very numerous or important.

(2) _Rolling Bridges._--The girders are longer than the span and the part

overhanging the abutment is counter-weighted so that the centre of gravity

is over the abutment when the bridge is rolled forward (fig. 33 b). To fill

the gap in the approaches when the bridge is rolled forward a frame

carrying that part of the road is moved into place sideways. At Sunderland,

the bridge is first lifted by a hydraulic press so as to clear the roadway

behind, and is then rolled back.

(3) _Draw or Bascule Bridges._--The fortress draw-bridge is the original

type, in which a single leaf, or bascule, turns round a horizontal hinge at

one abutment. The bridge when closed is supported on abutments at each end.

It is raised by chains and counterweights. A more common type is a bridge

with two leaves or bascules, one hinged at each abutment. When closed [v.04

p.0544] the bascules are locked at the centre (see fig. 13). In these

bridges each bascule is prolonged backwards beyond the hinge so as to

balance at the hinge, the prolongation sinking into the piers when the

bridge is opened.

(4) _Swing or Turning Bridges._--The largest movable bridges revolve about

a vertical axis. The bridge is carried on a circular base plate with a

central pivot and a circular track for a live ring and conical rollers. A

circular revolving platform rests on the pivot and rollers. A toothed arc

fixed to the revolving platform or to the live ring serves to give motion

to the bridge. The main girders rest on the revolving platform, and the

ends of the bridge are circular arcs fitting the fixed roadway. Three

arrangements are found: (a) the axis of rotation is on a pier at the centre

of the river and the bridge is equal armed (fig. 33 c), so that two

navigation passages are opened simultaneously. (b) The axis of rotation is

on one abutment, and the bridge is then usually unequal armed (fig. 33 d),

the shorter arm being over the land. (c) In some small bridges the shorter

arm is vertical and the bridge turns on a kind of vertical crane post at

the abutment (fig. 33 e).

(5) _Floating Bridges_, the roadway being carried on pontoons moored in the

stream.

The movable bridge in its closed position must be proportioned like a fixed

bridge, but it has also other conditions to fulfil. If it revolves about a

vertical axis its centre of gravity must always lie in that axis; if it

rolls the centre of gravity must always lie over the abutment. It must have

strength to support safely its own overhanging weight when moving.

At Konigsberg there is a road bridge of two fixed spans of 39 ft., and a

central span of 60 ft. between bearings, or 41 ft. clear, with balanced

bascules over the centre span. Each bascule consists of two main girders

with cross girders and stringers. The main girders are hung at each side on

a horizontal shaft 8-5/8 in. in diameter, and are 6 ft. deep at the hinge,

diminishing to 1 ft. 7 in. at the centre of the span. The counterweight is

a depressed cantilever arm 12 ft. long, overlapped by the fixed platform

which sinks into a recess in the masonry when the bridge opens. In closed

position the main girders rest on a bed plate on the face of the pier 4 ft.

3 in. beyond the shaft bearings. The bridge is worked by hydraulic power,

an accumulator with a load of 34 tons supplying pressure water at 630 lb

per sq. in. The bridge opens in 15 seconds and closes in 25 seconds.

At the opening span of the Tower bridge (fig. 13) there are four main

girders in each bascule. They project 100 ft. beyond and 62 ft. 6 in.

within the face of the piers. Transverse girders and bracings are inserted

between the main girders at 12 ft. intervals. The floor is of buckled

plates paved with wood blocks. The arc of rotation is 82°, and the axis of

rotation is 13 ft. 3 in. inside the face of the piers, and 5 ft. 7 in.

below the roadway. The weight of ballast in the short arms of the bascules

is 365 tons. The weight of each leaf including ballast is about 1070 tons.

The axis is of forged steel 21 in. in diameter and 48 ft. long. The axis

has eight bearings, consisting of rings of live rollers 4-7/16 in. in

diameter and 22 in. long. The bascules are rotated by pinions driven by

hydraulic engines working in steel sectors 42 ft. radius (_Proc. Inst.

C.E._ cxxvii. p. 35).

As an example of a swing bridge, that between Duluth and Superior at the

head of Lake Superior over the St Louis river may be described. The centre

opening is 500 ft., spanned by a turning bridge, 58 ft. wide. The girders

weighing 2000 tons carry a double track for trains between the girders and

on each side on cantilevers a trolley track, roadway and footway. The

bridge can be opened in 2 minutes, and is operated by two large electric

motors. These have a speed reduction from armature shaft to bridge column

of 1500 to 1, through four intermediate spur gears and a worm gear. The end

lifts which transfer the weight of the bridge to the piers when the span is

closed consist of massive eccentrics having a throw of 4 in. The clearance

is 2 in., so that the ends are lifted 2 in. This gives a load of 50 tons

per eccentric. One motor is placed at each end of the span to operate the

eccentrics and also to release the latches and raise the rails of the steam

track.

At Riga there is a floating pontoon bridge over the Duna. It consists of

fourteen rafts, 105 ft. in length, each supported by two pontoons placed 64

ft. apart. The pairs of rafts are joined by three baulks 15 ft. long laid

in parallel grooves in the framing. Two spans are arranged for opening

easily. The total length is 1720 ft. and the width 46 ft. The pontoons are

of iron, 85½ ft. in length, and their section is elliptical, 10½ ft.

horizontal and 12 ft. vertical. The displacement of each pontoon is 180

tons and its weight 22 tons. The mooring chains, weighing 22 lb per ft.,

are taken from the upstream end of each pontoon to a downstream screw pile

mooring and from the downstream end to an upstream screw pile.

13. _Transporter Bridges._--This new type of bridge consists of a high

level bridge from which is suspended a car at a low level. The car receives

the traffic and conveys it across the river, being caused to travel by

electric machinery on the high level bridge. Bridges of this type have been

erected at Portugalete, Bizerta, Rouen, Rochefort and more recently across

the Mersey between the towns of Widnes and Runcorn.

[Illustration: FIG. 34.--Widnes and Runcorn Transporter Bridge.]

The Runcorn bridge crosses the Manchester Ship Canal and the Mersey in one

span of 1000 ft., and four approach spans of 55½ ft. on one side and one

span on the other. The low-level approach roadways are 35 ft. wide with

footpaths 6 ft. wide on each side. The supporting structure is a cable

suspension bridge with stiffening girders. A car is suspended from the

bridge, carried by a trolley running on the underside of the stiffening

girders, the car being [v.04 p.0545] propelled electrically from one side

to the other. The underside of the stiffening girder is 82 ft. above the

river. The car is 55 ft. long by 24½ ft. wide. The electric motors are

under the control of the driver in a cabin on the car. The trolley is an

articulated frame 77 ft. long in five sections coupled together with pins.

To this are fixed the bearings of the running wheels, fourteen on each

side. There are two steel-clad series-wound motors of 36 B.H.P. For a test

load of 120 tons the tractive force is 70 lb per ton, which is sufficient

for acceleration, and maintaining speed against wind pressure. The brakes

are magnetic, with auxiliary handbrakes. Electricity is obtained by two gas

engines (one spare) each of 75 B.H.P.

On the opening day passengers were taken across at the rate of more than

2000 per hour in addition to a number of vehicles. The time of crossing is

3 or 4 minutes. The total cost of the structure was £133,000.

14. In the United States few railway companies design or build their own

bridges. General specifications as to span, loading, &c., are furnished to

bridge-building companies, which make the design under the direction of

engineers who are experts in this kind of work. The design, with strain

sheets and detail drawings, is submitted to the railway engineer with

estimates. The result is that American bridges are generally of

well-settled types and their members of uniform design, carefully

considered with reference to convenient and accurate manufacture. Standard

patterns of details are largely adopted, and more system is introduced in

the workshop than is possible where the designs are more varied. Riveted

plate girders are used up to 50 ft. span, riveted braced girders for spans

of 50 ft. to 75 ft., and pin-connected girders for longer spans. Since the

erection of the Forth bridge, cantilever bridges have been extensively

used, and some remarkable steel arch and suspension bridges have also been

constructed. Overhead railways are virtually continuous bridge

constructions, and much attention has been given to a study of the special

conditions appertaining to that case.

_Substructure._

15. The substructure of a bridge comprises the piers, abutments and

foundations. These portions usually consist of masonry in some form,

including under that general head stone masonry, brickwork and concrete.

Occasionally metal work or woodwork is used for intermediate piers.

When girders form the superstructure, the resultant pressure on the piers

or abutments is vertical, and the dimensions of these are simply regulated

by the sufficiency to bear this vertical load.

When arches form the superstructure, the abutment must be so designed as to

transmit the resultant thrust to the foundation in a safe direction, and so

distributed that no part may be unduly compressed. The intermediate piers

should also have considerable stability, so as to counterbalance the thrust

arising when one arch is loaded while the other is free from load.

For suspension bridges the abutment forming the anchorage must be so

designed as to be thoroughly stable under the greatest pull which the

chains can exert. The piers require to be carried above the platform, and

their design must be modified according to the type of suspension bridge

adopted. When the resultant pressure is not vertical on the piers these

must be constructed to meet the inclined pressure. In any stiffened

suspension bridge the action of the pier will be analogous to that of a

pier between two arches.

_Concrete in a shell_ is a name which might be applied to all the methods

of founding a pier which depend on the very valuable property which strong

hydraulic concrete possesses of setting into a solid mass under water. The

required space is enclosed by a wooden or iron shell; the soil inside the

shell is removed by dredging, or some form of mechanical excavator, until

the formation is reached which is to support the pier; the concrete is then

shot into the enclosed space from a height of about 10 ft., and rammed down

in layers about 1 ft. thick; it soon consolidates into a permanent

artificial stone.

_Piles_ are used as foundations in compressible or loose soil. The heads of

the piles are sawn off, and a platform of timber or concrete rests on them.

Cast iron and concrete reinforced piles are now used. _Screw piles_ are

cast iron piles which are screwed into the soil instead of being driven in.

At their end is fixed a blade of cast iron from two to eight times the

diameter of the shaft of the pile; the pitch of the screw varies from

one-half to one-fourth of the external diameter of the blade.

_Disk piles_ have been used in sand. These piles have a flat flange at the

bottom, and water is pumped in at the top of the pile, which is weighted to

prevent it from rising. Sand is thus blown or pumped from below the piles,

which are thus easily lowered in ground which baffles all attempts to drive

in piles by blows. In ground which is of the nature of quicksand, piles

will often slowly rise to their original position after each blow.

_Wells._--In some soils foundations may be obtained by the device of

building a masonry casing like that of a well and excavating the soil

inside; the casing gradually sinks and the masonry is continued at the

surface. This method is applicable in running sands. The interior of the

well is generally filled up with concrete or brick when the required depth

has been reached.

_Piers and Abutments._--Piers and abutments are of masonry, brickwork, or

cast or wrought iron. In the last case they consist of any number of hollow

cylindrical pillars, vertical or raking, turned and planed at the ends and

united by a projection or socket and by flanges and bolts. The pillars are

strengthened against lateral yielding by horizontal and diagonal bracing.

In some cases the piers are cast iron cylinders 10 ft. or more in diameter

filled with concrete.

[Illustration: FIG. 35.--Cylinder, Charing Cross Bridge.]

_Cylinder Foundations._--Formerly when bridge piers had to be placed where

a firm bearing stratum could only be reached at a considerable depth, a

timber cofferdam was used in which piles were driven down to the firm

stratum. On the piles the masonry piers were built. Many bridges so

constructed have stood for centuries. A great change of method arose when

iron cylinders and in some cases brick cylinders or wells were adopted for

foundations. These can be sunk to almost any depth or brought up to any

height, and are filled with Portland cement concrete. They are sometimes

excavated by grabs. Sometimes they are closed in and kept free of water by

compressed air so that excavation work can be carried on inside them (fig.

35). Sometimes in silty river beds they are sunk 100 ft. or more, for [v.04

p.0546] security against deep scouring of the river-bed in floods. In the

case of the Empress bridge over the Sutlej each pier consisted of three

brick wells, 19 ft. in diameter, sunk 110 ft. The piers of the Benares

bridge were single iron caissons, 65 ft. by 28 ft., sunk about 100 ft.,

lined with brick and filled with concrete. At the Forth bridge iron

caissons 70 ft. in diameter were sunk about 40 ft. into the bed of the

Forth. In this case the compressed air process was used.

16. _Erection._--Consideration of the local conditions affecting the

erection of bridges is always important, and sometimes becomes a

controlling factor in the determination of the design. The methods of

erection may be classed as--(1) erection on staging or falsework; (2)

floating to the site and raising; (3) rolling out from one abutment; (4)

building out member by member, the completed part forming the stage from

which additions are handled.

(1) In erection on staging, the materials available determine the character

of the staging; stacks of timber, earth banks, or built-up staging of piles

and trestles have all been employed, also iron staging, which can be

rapidly erected and moved from site to site. The most ordinary type of

staging consists of timber piles at nearly equal distances of 20 ft. to 30

ft., carrying a timber platform, on which the bridge is erected. Sometimes

a wide space is left for navigation, and the platform at this part is

carried by a timber and iron truss. When the headway is great or the river

deep, timber-braced piers or clusters of piles at distances of 50 ft. to

100 ft. may be used. These carry temporary trusses of timber or steel. The

Kuilenburg bridge in Holland, which has a span of 492 ft., was erected on a

timber staging of this kind, containing 81,000 cub. ft. of timber and 5

tons of bolts. The bridge superstructure weighed 2150 tons, so that 38 cub.

ft. of timber were used per ton of superstructure.

(2) The Britannia and Conway bridges were built on staging on shore, lifted

by pontoons, floated out to their position between the piers, and lastly

lifted into place by hydraulic presses. The Moerdyk bridge in Holland, with

14 spans of 328 ft., was erected in a similar way. The convenience of

erecting girders on shore is very great, but there is some risk in the

floating operations and a good deal of hauling plant is required.

(3) If a bridge consists of girders continuous over two or more spans, it

may be put together on the embankment at one end and rolled over the piers.

In some cases hauling tackle is used, in others power is applied by levers

and ratchets to the rollers on which the girders travel. In such rolling

operations the girder is subjected to straining actions different from

those which it is intended to resist, and parts intended for tension may be

in compression; hence it may need to be stiffened by timber during rolling.

The bending action on the bottom boom in passing over the rollers is also

severe. Modifications of the system have been adopted for bridges with

discontinuous spans. In narrow ravines a bridge of one span may be rolled

out, if the projecting end is supported on a temporary suspension cable

anchored on each side. The free end is slung to a block running on the

cable. If the bridge is erected when the river is nearly dry a travelling

stage may be constructed to carry the projecting end of the girder while it

is hauled across, the other end resting on one abutment. Sometimes a girder

is rolled out about one-third of its length, and then supported on a

floating pontoon.

(4) Some types of bridge can be built out from the abutments, the completed

part forming an erecting stage on which lifting appliances are fixed.

Generally, in addition, wire cables are stretched across the span, from

which lifting tackle is suspended. In bridges so erected the straining

action during erection must be studied, and material must be added to

resist erecting stresses. In the case of the St Louis bridge, half arches

were built out on either side of each pier, so that the load balanced.

Skeleton towers on the piers supported chains attached to the arched ribs

at suitable points. In spite of careful provision, much difficulty was

experienced in making the connexion at the crown, from the expansion due to

temperature changes. The Douro bridge was similarly erected. The girders of

the side spans were rolled out so as to overhang the great span by 105 ft.,

and formed a platform from which parts of the arch could be suspended.

Dwarf towers, built on the arch ring at the fifth panel from either side,

helped to support the girder above, in erecting the centre part of the arch

(Seyrig, _Proc. Inst. C.E._ lxiii. p. 177). The great cantilever bridges

have been erected in the same way, and they are specially adapted for

erection by building out.

_Straining Actions and Working Stresses._

17. In metal bridges wrought iron has been replaced by mild steel--a

stronger, tougher and better material. Ingot metal or mild steel was

sometimes treacherous when first introduced, and accidents occurred, the

causes of which were obscure. In fact, small differences of composition or

variations in thermal treatment during manufacture involve relatively large

differences of quality. Now it is understood that care must be taken in

specifying the exact quality and in testing the material supplied.

Structural wrought iron has a tenacity of 20 to 22½ tons per sq. in. in the

direction of rolling, and an ultimate elongation of 8 or 10% in 8 in.

Across the direction of rolling the tenacity is about 18 tons per sq. in.,

and the elongation 3% in 8 in. Steel has only a small difference of quality

in different directions. There is still controversy as to what degree of

hardness, or (which is nearly the same thing) what percentage of carbon,

can be permitted with safety in steel for structures.

The qualities of steel used may be classified as follows:--(a) Soft steel,

having a tenacity of 22½ to 26 tons per sq. in., and an elongation of 32 to

24% in 8 in. (b) Medium steel, having a tenacity of 26 to 34 tons per sq.

in., and 28 to 25% elongation. (c) Moderately hard steel, having a tenacity

of 34 to 37 tons per sq. in., and 17% elongation, (d) Hard steel, having a

tenacity of 37 to 40 tons per sq. in., and 10% elongation. Soft steel is

used for rivets always, and sometimes for the whole superstructure of a

bridge, but medium steel more generally for the plates, angle bars, &c.,

the weight of the bridge being then reduced by about 7% for a given factor

of safety. Moderately hard steel has been used for the larger members of

long-span bridges. Hard steel, if used at all, is used only for compression

members, in which there is less risk of flaws extending than in tension

members. With medium or moderately hard steel all rivet holes should be

drilled, or punched 1/8 in. less in diameter than the rivet and reamed out,

so as to remove the ring of material strained by the punch.

In the specification for bridge material, drawn up by the British

Engineering Standards Committee, it is provided that the steel shall be

acid or basic open-hearth steel, containing not more than 0.06% of sulphur

or phosphorus. Plates, angles and bars, other than rivet bars, must have a

tensile strength of 28 to 32 tons per sq. in., with an elevation of 20% in

8 in. Rivet bars tested on a gauge length eight times the diameter must

have a tensile strength of 26 to 30 tons per sq. in. and an elongation of

25%.

18. _Straining Actions._--The external forces acting on a bridge may be

classified as follows:--

(1) The _live_ or _temporary load_, for road bridges the weight of a dense

crowd uniformly distributed, or the weight of a heavy wagon or traction

engine; for railway bridges the weight of the heaviest train likely to come

on the bridge. (2) An allowance is sometimes made for _impact_, that is the

dynamical action of the live load due to want of vertical balance in the

moving parts of locomotives, to irregularities of the permanent way, or to

yielding of the structure. (3) The _dead load_ comprises the weight of the

main girders, flooring and wind bracing, or the total weight of the

superstructure exclusive of any part directly carried by the piers. This is

usually treated as uniformly distributed over the span. (4) The _horizontal

pressure_ due to a wind blowing transversely to the span, which becomes of

importance in long and high bridges. (5) The _longitudinal drag_ due to the

friction of a train when braked, about one-seventh of the weight of the

train. (6) On a curved bridge the _centrifugal load_ due to the radical

acceleration of the train. If w is the weight of a locomotive in tons, r

the radius of curvature of the track, v the velocity in feet per sec.; then

the horizontal force exerted on the bridge is wv^2/gr tons. (7) In some

cases, especially in arch and suspension bridges, changes of temperature

set up stresses equivalent to those produced by an external load. In Europe

a variation of temperature of 70° C. or 126° F. is commonly assumed. For

this the expansion is about 1 in. in 100 ft. Generally a structure should

be anchored at one point and free to move if possible in other directions.

Roughly, if expansion is prevented, a stress of one ton per sq. in. is set

up in steel structures for each 12° change of temperature.

i. _Live Load on Road Bridges._--A dense crowd of people may be taken as a

uniform load of 80 to 120 lb per sq. ft. But in recent times the weight of

traction engines and wagons which pass over bridges has increased, and this

kind of load generally produces greater straining action than a crowd of

people. In manufacturing districts and near large towns loads of 30 tons

may come on road bridges, and county and borough authorities insist on

provision being made for such loads. In Switzerland roads are divided into

three classes according to their importance, and the following loads are

prescribed, the designer having to provide sufficient strength either for a

uniformly distributed crowd, or for a heavy wagon anywhere on the

roadway:-- [v.04 p.0547]

| Crowd, | Wagon,

| lb per sq. ft. | tons per axle.

| |

Main Roads ....... | 92 | 10 with 13 ft. wheel base

Secondary Roads .. | 72 | 6 " 10 " "

Other Roads ...... | 51 | 3 " 8 " "

In England still larger loads are now provided for. J.C. Inglis (_Proc.

Inst. C.E._ cxli. p. 35) has considered two cases--(a) a traction engine

and boiler trolley, and (b) a traction engine and trucks loaded with

granite. He has calculated the equivalent load per foot of span which would

produce the same maximum bending moments. The following are some of the

results:--

Span Ft. |10. |20. |30. |40. |50. |

| | | | | |

Equivalent load in tons per ft. run, | | | | | |

Case a ............................. |1.75|0.95|0.70|0.73|0.72|

Do. Case b ......................... |3.25|1.7 |1.3 |1.2 |1.15|

Large as these loads are on short spans, they are not more than must often

be provided for.

_Live Load on Railway Bridges._--The live load is the weight of the

heaviest train which can come on the bridge. In the earlier girder bridges

the live load was taken to be equivalent to a uniform load of 1 ton per

foot run for each line of way. At that time locomotives on railways of 4

ft. 8½ in. gauge weighed at most 35 to 45 tons, and their length between

buffers was such that the average load did not exceed 1 ton per foot run.

Trains of wagons did not weigh more than three-quarters of a ton per foot

run when most heavily loaded. The weights of engines and wagons are now

greater, and in addition it is recognized that the concentration of the

loading at the axles gives rise to greater straining action, especially in

short bridges, than the same load uniformly distributed along the span.

Hence many of the earlier bridges have had to be strengthened to carry

modern traffic. The following examples of some of the heaviest locomotives

on English railways is given by W.B. Farr (_Proc. Inst. C.E._ cxli. p.

12):--

_Passenger Engines._

Total weights, tons ......... 84.35 | 98.90 | 91.90 | 85.48

Tons per ft. over all ....... 1.58 | 1.71 | 1.62 | 1.61

Tons per ft. of wheel base .. 1.92 | 2.04 | 1.97 | 1.95

Maximum axle load, tons ..... 19.00 | 16.00 | 18.70 | 18.50

_Goods Engines._

Total weight, tons .......... 77.90 | 78.80 | 76.46 | 75.65

Tons per ft. over all ....... 1.54 | 1.50 | 1.54 | 1.51

Tons per ft. of wheel base .. 2.02 | 2.02 | 2.03 | 2.00

Maximum axle load, tons ..... 15.90 | 16.00 | 13.65 | 15.50

_Tank Engines._

Total weight, tons .......... 53.80 | 58.61 | 60.80 | 47.00

Tons per ft. over all ....... 1.60 | 1.68 | 1.70 | 1.55

Tons per ft. of wheel base .. 2.45 | 2.52 | 2.23 | 3.03

Maximum axle load, tons ..... 17.54 | 15.29 | 17.10 | 15.77

Farr has drawn diagrams of bending moment for forty different very heavy

locomotives on different spans, and has determined for each case a uniform

load which at every point would produce as great a bending moment as the

actual wheel loads. The following short abstract gives the equivalent

uniform load which produces bending moments as great as those of any of the

engines calculated:--

Span in Ft. | Load per ft. run equivalent

| to actual Wheel Loads in Tons,

| for each Track.

|

5.0 | 7.6

10.0 | 4.85

20.0 | 3.20

30.0 | 2.63

50.0 | 2.24

100.0 | 1.97

Fig. 36 gives the loads per axle and the distribution of loads in some

exceptionally heavy modern British locomotives.

[Illustration: Express Passenger Engine, G.N. Ry.]

[Illustration: Goods Engine, L. & Y. Ry.]

[Illustration: Passenger Engine, Cal. Ry.

FIG. 36.]

[v.04 p.0548] In Austria the official regulations require that railway

bridges shall be designed for at least the following live loads per foot

run and per track:--

| Span. | Live Load in Tons. |

| - - - - - - - -|- - - - - - - - - - - - - - - -|

|Metres. | Ft. | Per metre run. | Per ft. run. |

| | | | |

| 1 | 3.3 | 20 | 6.1 |

| 2 | 6.6 | 15 | 4.6 |

| 5 | 16.4 | 10 | 3.1 |

| 20 | 65.6 | 5 | 1.5 |

| 30 | 98.4 | 4 | 1.2 |

It would be simpler and more convenient in designing short bridges if,

instead of assuming an equivalent uniform rolling load, agreement could be

come to as to a typical heavy locomotive which would produce stresses as

great as any existing locomotive on each class of railway. Bridges would

then be designed for these selected loads, and the process would be safer

in dealing with flooring girders and shearing forces than the assumption of

a uniform load.

Some American locomotives are very heavy. Thus a consolidation engine may

weigh 126 tons with a length over buffers of 57 ft., corresponding to an

average load of 2.55 tons per ft. run. Also long ore wagons are used which

weigh loaded two tons per ft. run. J.A.L. Waddell (_De Pontibus_, New York,

1898) proposes to arrange railways in seven classes, according to the live

loads which may be expected from the character of their traffic, and to

construct bridges in accordance with this classification. For the lightest

class, he takes a locomotive and tender of 93.5 tons, 52 ft. between

buffers (average load 1.8 tons per ft. run), and for the heaviest a

locomotive and tender weighing 144.5 tons, 52 ft. between buffers (average

load 2.77 tons per ft. run). Wagons he assumes to weigh for the lightest

class 1.3 tons per ft. run and for the heaviest 1.9 tons. He takes as the

live load for a bridge two such engines, followed by a train of wagons

covering the span. Waddell's tons are short tons of 2000 lb.

ii. _Impact._--If a vertical load is imposed suddenly, but without

velocity, work is done during deflection, and the deformation and stress

are momentarily double those due to the same load at rest on the structure.

No load of exactly this kind is ever applied to a bridge. But if a load is

so applied that the deflection increases with speed, the stress is greater

than that due to a very gradually applied load, and vibrations about a mean

position are set up. The rails not being absolutely straight and smooth,

centrifugal and lurching actions occur which alter the distribution of the

loading. Again, rapidly changing forces, due to the moving parts of the

engine which are unbalanced vertically, act on the bridge; and, lastly,

inequalities of level at the rail ends give rise to shocks. For all these

reasons the stresses due to the live load are greater than those due to the

same load resting quietly on the bridge. This increment is larger on the

flooring girders than on the main ones, and on short main girders than on

long ones. The impact stresses depend so much on local conditions that it

is difficult to fix what allowance should be made. E.H. Stone (_Trans. Am.

Soc. of C.E._ xli. p. 467) collated some measurements of deflection taken

during official trials of Indian bridges, and found the increment of

deflection due to impact to depend on the ratio of dead to live load. By

plotting and averaging he obtained the following results:--

_Excess of Deflection and straining Action of a moving Load over that due

to a resting Load._

Dead load in per cent | | | | | | | |

of total load .... | 10 | 20 | 30 | 40 | 50 | 70 | 90 |

Live load in per cent | | | | | | | |

of total load .... | 90 | 80 | 70 | 60 | 50 | 30 | 10 |

Ratio of live to dead | | | | | | | |

load ............. | 9 | 4 |2.3 |1.5 |1.0 |0.43|0.10|

Excess of deflection | | | | | | | |

and stress due to | | | | | | | |

moving load | | | | | | | |

per cent ......... | 23 | 13 | 8 |5.5 |4.0 |1.6 |0.3 |

These results are for the centre deflections of main girders, but Stone

infers that the augmentation of stress for any member, due to causes

included in impact allowance, will be the same percentage for the same

ratios of live to dead load stresses. Valuable measurements of the

deformations of girders and tension members due to moving trains have been

made by S.W. Robinson (_Trans. Am. Soc. C.E._ xvi.) and by F.E. Turneaure

(_Trans. Am. Soc. C.E._ xli.). The latter used a recording deflectometer

and two recording extensometers. The observations are difficult, and the

inertia of the instrument is liable to cause error, but much care was

taken. The most striking conclusions from the results are that the

locomotive balance weights have a large effect in causing vibration, and

next, that in certain cases the vibrations are cumulative, reaching a value

greater than that due to any single impact action. Generally: (1) At speeds

less than 25 m. an hour there is not much vibration. (2) The increase of

deflection due to impact at 40 or 50 m. an hour is likely to reach 40 to

50% for girder spans of less than 50 ft. (3) This percentage decreases

rapidly for longer spans, becoming about 25% for 75-ft. spans. (4) The

increase per cent of boom stresses due to impact is about the same as that

of deflection; that in web bracing bars is rather greater. (5) Speed of

train produces no effect on the mean deflection, but only on the magnitude

of the vibrations.

A purely empirical allowance for impact stresses has been proposed,

amounting to 20% of the live load stresses for floor stringers; 15% for

floor cross girders; and for main girders, 10% for 40-ft. spans, and 5% for

100-ft. spans. These percentages are added to the live load stresses.

iii. _Dead Load._--The dead load consists of the weight of main girders,

flooring and wind-bracing. It is generally reckoned to be uniformly

distributed, but in large spans the distribution of weight in the main

girders should be calculated and taken into account. The weight of the

bridge flooring depends on the type adopted. Road bridges vary so much in

the character of the flooring that no general rule can be given. In railway

bridges the weight of sleepers, rails, &c., is 0.2 to 0.25 tons per ft. run

for each line of way, while the rail girders, cross girders, &c., weigh

0.15 to 0.2 tons. If a footway is added about 0.4 ton per ft. run may be

allowed for this. The weight of main girders increases with the span, and

there is for any type of bridge a limiting span beyond which the dead load

stresses exceed the assigned limit of working stress.

Let W_l be the total live load, W_f the total flooring load on a bridge of

span l, both being considered for the present purpose to be uniform per ft.

run. Let k(W_l+W_f) be the weight of main girders designed to carry

W_l+W_f, but not their own weight in addition. Then