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nuts fitted with cast washers. The cross-ties Q, 8 in. wide
by 7 in. deep, are spaced 18 in. between centers and notched
down 1 in. on the stringers. The guard-rail R is 7 in. by
7 in. by 17 ft., and notched down 1 in. on the cross-ties and
bolted to every fourth or fifth cross-tie with ^ in. bolts.
The bridge seat 5 for the stringers is 18 in. deep. The
abutments behind the bridge seat are built up to the top of
the embankment, thus keeping the earth from falling down
upon the bridge seatr The spool M and a device for holding
the strut O in position are shown in detail at T.

In ordinary open culvert masonry the bridge seat and
steps are the only dressed stone used in the structure, the
body of the walls being built of well-scabbled rubble. Large
stones with good beds should compose the bulk of the walls,
and when under-sized stones are used they must be
thoroughly bonded by large ones. The wall plates should
be placed as nearly over the center of the wall as possible, so
that the shock and load of the passing train may be equally
distributed throughout the abutments.

1 467. Arched Culverts. When the volume of water
is too great to be discharged by a double-box culvert with
openings 3x4 feet, an arched culvert is substituted with
a single opening of the required area. In determining
dimensions of culvert openings, the greater danger lies in
making them too small. The volume of surface water ^
discharged from a given area depends on widely differing
conditions, and is often in apparent violation of all pre-
scribed rules. It is not within the province of the engineer
to attempt to meet phenomenal conditions, but he should
meet common extremes, and there is no branch in railroad



construction where he so often blunders as in the matter of

1468. Parts of an Arch. Fig. 387 represents an
arched culvert in which the distance D E is called the span,
OF the rise, the lower boundary line D F E the soffit
or intrados, the upper boundary G B H the back or
extrados. The end of the arch included between the lines

D F E and G B H is called the face. Lines level with D
and E and at right angles to the face of the arch are called
springing lines or springs. The blocks of which the
arch is composed are called arch stones or voussoirs.
The center one B F is the keystone, and the lowest ones
A and C the springers. The parts B G and B H are the
haunches. The spaces B G N K and B H M L are the
spandrels. The material deposited in these spaces is
the spandrel filling. It is sometimes earth and sometimes
masonry or partly of both.

Arches according to their forms have different names.



That in Fig. 387 is a semicircular arch, and is the form
commonly adopted in culvert building. A circular arch
containing an arc of less than 180 is called a segmental
arch (see Fig. 388). The arch shown in Fig. 389, composed

FIG. 388.


of three circular arcs, is called either an elliptical or a
three-centered arch.

1469. To Find the Depth of Keystone. For cut
stone arches, whether circular or elliptic, find the radius O D,
Figs. 387, 388, and 389, which will touch the arch at D, F,
and E.

Rule I. Add together this radius and half the span D E.
Take the square root of the sum. Divide this square root by 4
and add to the quotient T 2 of a foot.

Or, by formula,

depth of keystone in feet =


. + . *f,t.

For second-class work, increase this depth of keystone about
part; for brickwork or fair rubble, about part.

EXAMPLE. The radius O D is 18 feet, the span D "36 feet ; required,
the depth of an arch of cut stone for second-class work and for brick-

SOLUTION. Applying formula 1O3, we have

|/18 + 18
For cut stone, depth of arch = - 7 - +.2 foot = 1.7 feet. Ans.


For second-class work, increase depth of cut stone arch \ = 1,7 -+
frX 1.7 = 1.91 feet. Ans.

For brick or fair rubble, increase depth of cut stone arch \ = 1.7 +
X 1. 7 = 2.12 feet. Ans.

Rankine's formula for depth of keystone in feet is,
depth of keystone in feet \f. 12 radius. (1O4.)

.The latter formula may serve where all conditions are
theoretically perfect, but, under ordinary conditions, the re-
sults given by this formula are too small. The arch stones
of a 36-foot arch should be at least 1 ft. 9 in. in depth, for
considerations of appearance as well as security.

To find the radius O D, Figs. 387, 388, and 380, whether
the arch be circular, segmental, or elliptical:

Rule II. Square half the span; square the wJiole rise ;
add these squares togctlier and divide the sum by twice the
rise. The quotient is the required radius O D.

EXAMPLE. The span is 30 feet; the rise 10 feet; required, the
radius O D.

SOLUTION. Radius = I = = 16.25 feet. Ans.
20 20

147O. To Proportion the Abutments for a Stone
Arch, whether Circular or Elliptical :

Rule. Find the radius O D, Fig. 387, in feet which will
touch the arch at D, F, and E. Divide this radius by 5. To
the quotient, add ^ of the rise and 2 feet. The sum will be
the thickness D N or E M of each abutment at the springing
line for any abutment wJiosc height E T does not exceed 1%
times its base T U. If of rough rubble, add 6 inches to E M
to insure full thickness in every part.

Or by formula,

Thickness of abut-

ment at spring line in ,. . . . .

, , , . , i radius in feet rise in feet ,
feet, when the height ^ = - J - 1 - - - \-2feef.

does not exceed 1\ | (1O5.)

times the base J

Mark the points J/ and N thus obtained. Next, from the


center O of the span or chord D E, lay off O F(Fig. 387)
equal to ^ of the span, and join F and V. Through the
point M draw the line R U parallel to F V, which will mark
the back of the abutment E T U M. In the same way,
draw the line 5 NX , marking the back of the other abutment.
Now on the lines MR and N S mark the points R and 5, their
height above the line M N being half O B, the full height of
the arch. Produce the line B O, and upon that line as at P
locate a center from which an arc may be described,
passing through S, B, and R. This arc will mark the top of
the masonry rilling above the arch, except when the rise is
about \ of the span or less, in which case the masonry back-
ing must be carried up solid to the level K L of the top of
the arch. Ordinarily, the height E T of the abutment will
not exceed \\ times the base T U. In case the height should
exceed. E T, as E V, make the base Y Z equal to T / in-
creased by % the additional height T Y. Then, from Z draw
a line parallel to U R, which will mark the back line of the
abutment. It is a common practice to give to the faces of
the abutment a batter of from \ inch to 1 inch to the foot,
shown in the dotted line E T' Y' . This considerably in-
creases the base of the abutment, and, proportionately, its
stability. An arc struck from the center /-" with a radius
P' R', R being level with R, will mark the top of the masonry
filling above the arch.

1471. Foundations for Arch. Culverts. As arch
culverts usually require a greater amount of masonry than
box culverts, their foundation must be proportionally
stronger. The general directions given for box culvert
foundations will answer for arch culverts of small span, say
from 4 to 8 feet. For greater spans, unless the natural
foundation is firm and secure, such as hard clay, sand, gravel,
or rock, a deep trench must be dug to receive the founda-
tion. If the soil is soft or marshy, it may be necessary to
drive piles and cut them off at a uniform elevation below
the water-line, and fill between and to the depth of one foot
above tops of piles with concrete made with hydraulic cement.



The trench should extend outside the lines of the founda-
tion at least 12 inches, in order that the pressure of the
superstructure may be sufficiently distributed. The first
course of masonry should project at least 6 inches outside
the majn body of the abutment for the same reason, and
should be composed of much larger stones than those which
form the main body of the superstructure. The paving be-
tween the abutments and curbing at ends of arch should be
of the same dimensions as adopted for box culverts. A
partial section of arch culvert with concrete foundation is
shown in Fig. 390. The stones forming the impost course

FIG. 390.

at A, in a culvert of 16 feet span, should be from 9 inches to
12 inches thick.

1472. Concrete. The concrete for the foundations
should be composed of the following ingredients: Cement,
1 part; sand, 3 parts; broken stone, 5 parts. If the con-
crete is to be deposited below the water level, Portland
cement should invariably be used. If the pit is free from
water at the time of construction, though ordinarily below
water level, Rosendaleor any other good American cement
may be used. The value of concrete depends much upon
the quality of the sand and broken stone used and the man-
ner of mixing. Sand containing loam should never be used,


and if none other is available, the sand should be washed in
a slight current of water, which will remove all the loam.
The stone should be broken to a fairly uniform size, and con-
tain no piece which will not pass through a 2^-inch ring.
If suitable stone is not available, hard-burned brickbats,
broken to the requisite size, form an excellent substitute.
For mixing concrete a level platform of rough boards is pre-
pared, convenient to the foundation pit. A suitable quantity
for mixing is the above given proportions in barrels of
material, viz., 1 barrel of cement, 2 barrels of sand, and 5
barrels of broken stone. The broken stone is deposited in
a regular pile, 12 inches in thickness. Upon the same plat-
form the sand and cement are mixed in a dry state, after
which water is added to them and they are worked into a
mortar of uniform consistency. The mortar is then spread
evenly over the stones, and the whole mixed with shovels,
commencing at the outside of the pile and working towards
the middle; which when reached, the shovelers reverse the
movement, working towards the outside and casting the con-
crete towards the middle, so that when the outside of the
pile is reached, the whole will be thoroughly mixed. It is
injurious to work the concrete over repeatedly. Twice
handling with the shovel, if thoroughly done, is sufficient.
The concrete should be deposited in the foundation pit
without delay, before setting commences; and with quick
setting cements, especially in summer weather, the process
is rapid. It is most conveniently handled in wheelbarrows,
and can be deposited directly from them into the pit. In
marshy situations, it is a common practice to confine the
concrete by inclosures of rough boards held together by
stakes driven in the ground. As soon as the concrete is de-
posited from the barrow, it must be spread with hoes or
shovels into uniform layers, the thickness of which will de-
pend upon the depth of concrete to be deposited. If only
12 inches of concrete, it should be deposited in two layers 6f 6
inches each, and each layer well rammed as soon as deposited.
Rammers of about 35 pounds weight, similar to those used
in street paving, are recommended. They are of wood 4


feet long, 6 to 8 inches in diameter at foot, with a lifting
handle. Ramming, when properly done, consolidates the
mass of concrete about 5 or 6 per cent., rendering it less
porous and increasing its strength. Water collecting upon
the surface of the concrete gives evidence of sufficient ram-
ming. The surface of the concrete should be brought to a
uniform level, and sufficient time be allowed for setting
before the abutments are started.

1473. Mortar. Cement mortar should be exclusively
used in the construction of arch culverts, the cement to be
well tested and approved before being allowed to go into the
work. Cement which does not show a tensile strength of
40 pounds to the square inch after remaining in water 24
hours should be rejected. The common American cements,
if of good quality, mixed in the proportion of 1 part of ce-
ment to 2 parts of sand, will afford a mortar suitable for any
ordinary engineering structure. Mortar should never be
mixed in large quantities, lest its strength be impaired by
setting before using. The proper practice is to mix only
such quantities as can be used immediately, thus keeping
the supply perfectly fresh and insuring the highest results.
The cement and sand should always be mixed dry, the water
being added afterwards, and the whole thoroughly worked
with a hoe before using.

The use of cheap brands of cement is false economy.
Ordinary cement will admit of sand in the proportion of two
parts of sand to one of cement. The best Portland cement,
especially for work not requiring rapid setting mortar, will
bear four parts of sand. Hence, the latter may be used
with the same economy as the former, even at twice the cost
per barrel.

1474. Pointing of Joints. Arch culverts for water-
ways are invariably rubble masonry, but of the best of its
kind. Sometimes the corner stones of the abutments, as well
as the arch stones of the faces, are of cut stone. The joints
of these should be left open at the faces until the work is
well advanced or completed, when they should be pointed



with mortar made of the best cement in the proportions of
1 part of cement to 1 part of sand, and neatly dressed with
a pointing tool. The joints of the rubble masonry are
simply struck, i. e., the trowel is pressed against the mortar
and drawn the full length of the joint, forming a water-
shed for each joint. The Joints are struck as the stones
are laid, the same mortar being used at the faces as in the
interior of the walls.

There are two principal methods used in pointing cut
stone, as shown in Figs. 391 and 392. Fig. 391 shows the
form in most general use. It is not so ornamental as that

FIG. 391. FIG. 39^.

shown in Fig. 392, but it is less exposed to the weather, and,
hence, is more enduring and a more certain protection to
the joints. Mortar intended for pointing must be used
immediately after mixing, and the pointing tool repeatedly
run over the joint or bead, under considerable pressure, in
order to compress the mortar and give it a smooth surface
and uniform groove or projection.

1 475. Centers for Arches. A center is a temporary
wooden structure for supporting an arch while it is being
built. Centers are built lying flat on a fixed platform, to a
full-sized drawing, and vary widely in design, according to
the type and dimensions of the arch. The different parts of
a center are given in Fig. 393, which is a standard type of
centering for all arches of moderate span, say from 6 to 16 feet.



The frames A, A are made of ribs of 1^-inch plank and
united as shown in the figure, breaking joints and fastened
together with spikes. The ribs are fitted to the drawing as
the frames are built. The ribs are 4 ft. 1 in. in length, 8 in.
in width at ends, and 10 in. in width at middle, the edge
being trimmed down to fit the curve of the arch. The chord
B is composed of two planks, each 1 in. thick by 10 in. in
width and 10 ft. in length, spiked securely to the frames.
The upright strut C is 3 in. thick by 10 in. in width, placed

directly under the crown of the arch and fastened to the
frame by two cleats D securely spiked to both frame and
strut. Its foot passes between the planks forming the chord
to which it is spiked. The brace E is fastened at top to the
strut with spikes. Its foot passes between the chord planks
and is shaped to abut against the rib at the spring line,
being securely spiked to the chord. The frames are spaced
3 feet from center to center, and rest on G in. by in. caps
/ which are supported by 6 in. by in. posts G. These posts
rest on 4 in. by G in. ground sills H which rest on the stone
paving. On the caps directly under each frame are striking
or lowering wedges K, by means of which the frames are
raised in case any of the posts should settle.


1476. Striking Centers. Upon the completion of
the masonry, the lowering wedges are removed, which per-
mits of the removal of the centering. This process is called
striking the centers. There is great difference of opinion as
to the length of time which should elapse after the comple-
tion of the masonry before the centers are struck. In the
case of brick and rubble arches where the mortar forms a
considerable part of the mass, a period of two or three
months should elapse before the centers are struck. This
will allow the mortar to harden and prevent undue com-
pression of the joints and consequent settlement of the arch.

1477. General Directions for the Building of an
Arch. All arch stones must be laid with beds in radial
lines. The joints at the intrados, or soffit, will, therefore,
be thinner than at the extrados, or back. All rough pro-
jections must be removed from the beds of the stones, and
the stones laid in firm beds with broken joints. Until the
arch is half built, the backing need not be started, as an ex-
cess of weight on the haunches is liable to cause a lifting of
the crown. In arches of large span it is a common practice
to load the centering at the crown until 45 of the arch
above the springing line is completed. When the 45 line is
passed and the pressure on the centering becomes more
nearly vertical, the backing must be carried up to take the
pressure. The continuance of the centering will be no
hindrance to traffic over the bridge.

1478. Wing Walls. Wing walls are generally built
with faces diverging at an angle of 120 from the face of the
arch. Their foundations are prepared at the same time as
the abutment foundations, and varied to suit the different
heights of wall above them. Abutments and wing walls are
carried up together, the stones of both walls interbonding so
as to form one solid mass of masonry. The thickness^f the
wing walls at foundation line should ordinarily be f 4 ^ of the
full height of the wall at that point, with faces battered from
1 to 1 inches to the foot and having a thickness of 2 feet
at the top.


When T 4 of the height of the wall (allowing a batter of
1 inch to the foot) does not give a thickness of 2 feet at
the top, the thickness of foundation must be sufficiently in-
creased to insure that thickness at the top. Where wing
walls attain a height of 12 feet and over, make the thickness
of the foundation of the height. Sometimes the slope of
the back of the wall is broken up into steps instead of being
uniform. Some advantage is gained from such treatment,
as the weight of the back filling bears directly upon the pro-
jecting stones. Any attempt to give the back a smooth,
uniform slope should be avoided. It adds nothing to the
appearance of the work, as it is covered by the embankment,
and lessens the friction of the filling against the back of the
wall, which tends to prevent its overturning. It is far
better to increase the size of the stones, allowing their rough
edges to project from the rear face. The large stones act
as binders for the smaller ones, greatly increasing the sta-
bility of the wall, and the projections afford the necessary
friction to the filling. A general plan of a semicircular arch
culvert, including parapet and wing walls, is given in
Fig. 394.

The span A B is 16 feet, and the rise CD 8 feet. The
thickness of arch D E is found by applying formula 1O3,
Art. 1469,

i/ 'radius -4- half span
depth of keystone in feet = -~- '- - + . 2 foot.

4/8 feet + 8 feet
Substituting given dimensions, we have - - f-

.2 foot = 1.2 feet, which is the depth of key given for cut
stone. As the rule calls for ^ greater depth for arches
of rubble, which is the material supposed to be used in the

arch under consideration, = .3 foot; 1.2 + .3 = 1.5

feet required depth of keystone. The length of the soffit
A D F is equal to half the circumference of a circle whose
diameter is 1G feet. Its length is, therefore, 25.13 feet.
The number of stones in an arch should always be an odd
number, which will place the keystone in the center of the



arch and give an equal number of arch stones on both sides
of the key. If now we make the thickness of the arch
stones 12 inches from center to center of joint on the soffit,
the arch will contain 12 such stones on each side of the key
and leave 13^- inches for the thickness of the keystone.
The height of the abutments F F' we take at 6 feet. The

thickness F G of the abutments at spring line we find by
applying formula 1O5, Art. 147O.
Thickness of abut- "1

me nt at spring line in

. . i i j. / radius in feet rise in feet . a - .
feet, when height of r - = - 1 - - -^ - \-1fcct.

abutment does not ex-
ceed 1\ times its base J

Substituting given dimensions, we have thickness of abut-

ment at spring line in feet = ' -j- -
5 10

2 ft. = 4.4 feet.



This thickness of abutment is for first-class masonry. As
our structure is of rubble, we add % foot to 4.4 feet, which
gives 4.9 feet. We further increase the thickness of the abut-
ments to 5.0 feet, which will insure perfect stability without
any excess of masonry. We give to the back of the abut-
ment wall a batter of 1 inch to the foot, making the thick-
ness of the abutments at the ground line X Y 5 feet 6
inches. The height of the points L and M above the spring
line is 4 feet and 9 inches, equal to one-half the full height
C E of the arch. The arc L E M which limits the top of
the backing or spandrel filling is struck with the radius
W L, 18 feet 9 inches in length, found by trial. The wing
walls O and Pare shown in plan at Q and R. A section of
wing wall at S T is shown in full at U. The top N of the
parapet is 1 foot 9 inches above top of arch. The parapet
and wing walls have a coping of dressed stone 6 in. in

1479. General Directions for Building Rubble
"Walls. Small stones, excepting for back filling, should not
be used, provided those of suitable size can be had at
reasonable cost. Stones of too great size are equally
objectionable unless they have
full beds and reach from face to
face of wall. Many rubble walls
are built, as shown in Fig. 395,
of large stones showing on one
face, but extending only a short
distance into the wall, while the
back and body of the wall are
composed of small stones. The
back of the wall, having so much
greater proportion of mortar than
the front, will in high walls settle
considerably more than the front, producing cracks in the
masonry. The almost total lack of binders is an even
greater source of weakness. Such a wall is objectionable in
any situation, but when serving as a retaining wall for a

1 I















I 1







FIG. 396.



railroad embankment where the back filling is subjected to
the constant vibrations caused by passing trains, its ultimate
failure is almost certain.

A full proportion of large stones should show on both
front and back and extend well into the wall, binding the
wall compactly together, as shown in Fig. 396.


148O. A retaining -wall is one for sustaining the
pressure of earth, sand, rock, or any other substance
deposited behind it after it is built. The material deposited
is called filling or backing. Retaining walls are much
used in railroad construction, especially in sections where
the natural slope of the ground approaches closely to that

h 3'-4

of the angle of ordinary earth filling, viz., 1% horizontal to
1 vertical. Railway tracks entering towns, especially where
they cross or crowd other lines, terminal grounds, etc.,
invariably require retaining walls. The pressure exerted
by the backing will vary greatly, depending upon the slope
of the ground behind the wall, the nature of the material
composing the backing, and the manner of depositing it; but
chiefly depending upon the height of the backing. The
usual form of retaining wall is shown in Fig. 397. There is



no invariable rule for determining the dimensions of retain -
ing walls, and the rules of various authors differ widely.
The following rule by Trautwine is based upon careful
experiments and is widely adopted. The back of the

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