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to Rope. The common practice of driving with hammer
attached to rope is to be condemned. The force necessary
to uncoil the rope from the drum and the friction of rope on
hoisting sheave rob the blow of at least one-fourth of its
force. In an actual case in practice, a pile penetrated 0.5
foot with a 40-foot fall of a 2,470 pound hammer with line
attached to hammer and slacked on drum ; it penetrated
0.7 foot when hammer was allowed to fall free, the gain in
penetration from a free fall of hammer being 40 per cent,
greater than when the hammer was attached to a rope.

1578. Pile Shoes. In cases where piles are to be
driven through a stratum of boulders, old cribwork, or any
substance offering great resistance to driving, resort
is frequently had to shoeing the piles with either cast or
wrought iron. Common forms of shoes are shown in Figs. 474
and 475. The shoe in Fig. 474 is of wrought iron, the point





FIG. 474. FIG. 475.



FIG. 476.



being fastened to the pile by spikes through the strap s. The
shoe in Fig. 475 is an inverted cone of cast iron. The bolt



1006 RAILROAD CONSTRUCTION.

, which fastens the shoe to the pile, is of wrought iron, the
cone being cast around it. The flat base of the cone affords
a good bearing for the foot of the pile. The practice of
shoeing piles has of late years fallen into disuse. In a great
many instances where shoes have failed, piles cut off square
have driven fairly well. Shod or pointed piles are liable to
cant or drive at an angle. In average ground a pile cut off
square at the point will drive better, truer, and almost as
rapidly as when pointed. There are, however, situations
where either shoeing or pointing is absolutely necessary.

1 579. Pile Hoops. To prevent the pile from splitting
while driving, the head is surrounded by an iron hoop from
one-half to one inch thick and from 1 to 3 inches wide,
as shown in Fig. 476. They are, however, an uncertain
security, especially in hard driving, when often the pile
splits below the hoop and bulges to such an extent that it
must be cut off before the driving can be continued.

1580. Slight Penetration Often Indicates Poor
Driving. When the penetration caused by a high fall of
a heavy hammer is less than one-fourth inch with oak or
one-half inch with soft wood piles, there is danger of over
driving. A common mode of failure is shown in Fig. 477.

1581. Spacing Piles. Bearing Piles, i. e., those
used for foundations, should not be spaced less than three
feet center to center; those spaced less than 2 feet are
worse than wasted. Where piles are overcrowded, the soil
either becomes churned to a liquid mass or so compressed
that those already driven are forced upwards while others
are being driven. This effect sometimes occurs where the
surface soil is underlaid with quicksand or soil of a buoyant
nature, even where there is no overcrowding. A remedy
for this trouble is often found in driving piles with the large
end or top downwards. Where a considerable area is to be
piled, those at the center should be driven first, then
working towards the outside of the area. Where the reverse
order is used, the soil of the enclosed area often becomes so
compressed that piles can not penetrate it.



RAILROAD CONSTRUCTION.



1007



1582. Computing Loads. Calling the average
weight of masonry two tons per cubic yard, piles spaced
three feet center to center will carry a wall of masonry from
50 to 75 feet in height. Piles spaced 2 feet center to
center will support a wall of masonry from 75 to 100 feet in
height. Greater loads are not warranted by good practice.
Where a greater mass of masonry is required, the founda-
tions should be stepped out so as to admit another row of
piles, thus distributing the pressure over a greater surface.

EXAMPLE. A double row of foundation piles carries an 18-inch
masonry wall. The piles are spaced 3 feet center to center, i. e. , as
shown in Fig. 478, and driven with a
1,000-pound hammer, until a fall of 15
feet causes a penetration of one-fourth
inch. What height of wall can be safely
carried by the piles ?

SOLUTION. By formula 1O9, L =
r, we have Z, safe load in tons; /,




weight of hammer = .5 ton; h, height
of fall of hammer = 15 feet ; S, last pene-
tration = inch. Substituting these
values in the formula, we have L = FIG. 478.

2^ = = y-oF= 12 tons, i.e., each pile will safely support 12 tons.

Each yard in length of the wall is supported by two piles, which
together can safely carry 24 tons. Taking the average weight of
masonry at two tons per cubic yard, such a foundation would support
an 18-inch wall 72 feet in height.. Ans.

Modern depot buildings often carry roof trusses, which
tax foundation piles to their safe limit.

1583. Trestle Loads. In computing loads for pile
trestles it is not too great an allowance to assume that the
entire weight of the driving wheel base falls upon each
bent, or row of piles, in succession. Suppose, for example,
a bent of four piles is driven in building a trestle for heayy
railroad traffic. In driving, a hammer weighing 3,000
pounds is given a free fall of 30 feet, and suppose the average
penetration for the last three blows for the different piles is
as follows:



1008 RAILROAD CONSTRUCTION.

First pile, $ inch; second pile, f inch; third pile, f inch;
fourth pile, inch.

Applying formula 1O9, L = ^ . , we have

, , .. ,, 2 X 1-5 X 30 90 tons

Safe load for 1st pile, L = = = 60.0 tons.

. o ~\~ 1 1. o

Cf . , c .. . 2X1.5X30 90 tons

Safe load for 2d pile, L = = = 65. 5 tons.

. OV ~j~ 1 1. Oi

T 2 X 1.5 X 30 90 tons
Safe load for 3d pile, L = = = oo. 4 tons.

, 2 X 1.5 X 30 90 tons

Safe load for 4th pile, L = = =51.4 tons.

. 75 -pi 1. 7o

Total safe load for four piles 232.3 tons.

Taking the weight on wheel base of a consolidation engine
at 48 tons, which load each bent must successively carry, and
dividing the combined safe load of the four piles, viz., 232.3
tons, by 48 tons, the weight on the wheel base, we have a
quotient of 4.84, i. e., the bent is able to safely carry 4.84
times as great a load as it will ever be required to carry.
The above values of 5 are much smaller than can be obtained
in many soils. Often the penetration from the last blow is
several inches. If, however, the piles are allowed to stand
24 hours and the earth to settle firmly about them before
being tested with the hammer, it will usually require two or
three heavy blows to start them. Supposing the average
penetration for the last three blows on the above given
piles had been, respectively, 2 in., 3 in., 3 in., and 2f in.,
the safe loads would have been the following, viz., 30 tons,
22.5 tons, 20 tons, and 24 tons, and the aggregate safe load
96.5 tons, which, divided by 48 tons, the weight on wheel
base of locomotive, gives a quotient of 2.00 -4- , i. e., the
trestle can safely carry twice as great a load as will ever be
required of it.

1584. Piles Acting as Columns. Piles penetrating
through soft, yielding material into a comparatively hard,
unyielding material act as columns, and should be given a



RAILROAD CONSTRUCTION. 1009

factor of safety not less than six. Assuming the weight of
hammer at 3,000 pounds and the fall 20 feet, we have a blow
of 3,000 X 20 = GO, 000 ft.-lb., and for penetration of 1 in.,
2 in., 3 in., 4 in., 5 in., and G in., the safe load in pounds by
our formula is GO, 000, 40,000, 30,000, 24,000, 20,000, 17,143
Ib. , respectively, which is about - of the ultimate breaking
load of a 10-inch column of wood of a height of 8 feet, 14
feet, 18 feet, 21 feet, 24 feet, and 26 feet, respectively. Where
the length of the column without side support is greater
than this and the safe load by the formula is less, in the
same proportion will the safe load given by the formula ex-
ceed the safe load of the column, i. e., the safe load indi-
cated by the penetration will be in excess of the load which
an unsupported column can carry.

1585. Pile-Driving Machines. Pile-driving ma-
chines are of two general classes, viz.. land machines and
floating machines. In both classes the framework of
the pile driver is essentially the same. This framework
consists of the upright timbers called the guides or leaders
which hold the pile in position and between which the ham-
mer rises and falls, the wooden bracing of the leaders, and
the iron stayrods for the same.

The machinery for hoisting the hammer may be either a
simple crab-winch or a stationary engine, or horse power
may be used. For all important modern work a hoisting
engine is used. The land machine (see Fig. 479) rests on
longitudinal sills A, A, which in turn rest on rollers/). The
hoisting machinery, contained in the house C, and the coal
and water supply D and E are well to the rear of the frame-
work. When a row of piles is driven, they are cut off at a
fixed elevation and capped and temporary or permanent
stringers laid. The pile driver is then moved forwards on
its rollers, the leaders F projecting far enough beyond the
last bent to reach the line of the next row of piles. Tfee
engine, boiler, coal and water supply, resting on the rear end
of the framework of the machine, serve as a counterweight.
The side braces G, G extend nearly to the heads of the



1010



RAILROAD CONSTRUCTION.



leaders, and foot upon the cross timber //, where they are
securely braced with timber knees K, K. The back braces
Z, M, and N are bolted at top to the leaders and at bottom
to the sills O and P and to the cross timber Q. The main
back braces L are fitted with rounds, forming a ladder, by




FIG. 479.



means of which ascent is made to the hammer sheave R.
Stayrods 5 and T y fitted with turnbuckles, extend from
the heads of the leaders to anchorages in the sills at the
rear end of the framework. The hammer rope U winds on
a drum not shown in the drawing. The brackets V and W



RAILROAD CONSTRUCTION. 1011

support cross-bars upon which the hammer rests when not
working. The sizes of the timbers will depend upon the
character of the work to be done and upon the length of the
piles to be driven.

The floating machine (see Fig. 480) is carried on a power-
fully built scow A of light draught. The machine shown is
of the latest model, and the heaviest in New York harbor.
The hull is 56 feet 6 inches long and 23 feet G inches wide
over all ; each of the sides of the hull is made of four pieces
of yellow pine, the two lower 8x1-4 inches, the third 7 X 14
inches, the top piece 6 X 14 inches, all securely tied by
through bolts.

The bow planking is oak 5 inches thick; the bottom and
end plank, yellow pine 3 inches thick. The bow is further
strengthened by a 16 X 16-inch cross timber at top, and at
the stem is an 8 X 12-inch cross timber of yellow pine. Oak
is used on the bow as being better adapted to stand the con-
stant wear of the piles hauled against it. To prevent knots
or inequalities on the piles from interfering with their posi-
tion under the hammer, the bow planking overhangs 6 inches
in its total height.

The hull is especially designed to obtain longitudinal stiff-
ness so that the strain between the bow and engine may be
properly distributed. To attain this end the hull is strength-
ened lengthwise by four longitudinal bulkheads, or keelsons
f, each 6 inches thick and braced laterally by four sets of X
braces g, made of 6 X 6-inch timber. The hull is further
braced in the center by two 3 X 12-inch yellow pine braces
h, and tie-rods or " log chains" k of iron If inches in diam-
eter. Wale pieces and fender plank / 3 inches thick protect
the outside of the hull against chafing; the deck has a crown
of about 6 inches in its total width.

The leaders ;//, m are made of two pieces of 12" X 12* yel-
low pine 67 feet long from out to out, with inside guides n
of 4 X 5-inch stuff protected by plate iron one-fourth inch
thick; five-eighths inch bolts with countersunk heads fas-
ten the inner guides to the main sticks and at the same time
secure the iron work to the same. The bottoms of the leaders



1012



RAILROAD CONSTRUCTION.



are connected with the 12 X 12-inch bed pieces o by two
timber knees not shown, and are tied at the top by the cap/.
The arrangement of the back braces q, r, and. s is clearly
shown in the elevation. Their dimensions are, respectively,
6 X 12, 5 X 10, and 5x12 inches. They are of yellow pine




and securely bolted at the top and bottom with seven-eighths
inch bolts.

The side braces u and v are of round timber 16 inches in
diameter at butt, and each anchored to the hull by two heavy
timber knees. The bed pieces o are fastened down to the
hull by four bolts each one inch in diameter, the forward
bolt passing through the 16 X 16-inch oak piece iv on the



RAILROAD CONSTRUCTION.



1013



bow, and the after bolts passing through a cross timber x,
6 X 14 inches. The bottoms of the back braces are secured
to the bed timbers by 1-inch strap bolt in each timber, the
strap portion of the bolt being 2 inches X i inch in section.
A seven-eighths inch through bolt ties the three braces
together. The iron stayrods running from heads of lead-
ers to the after part of hull are two in number, and each one
inch in diameter.

The hoisting sheaves on top are two in number, placed
side by side. They are 12 inches in working diameter,
15 inches from out to out, and 3 inches wide, and the pin
passing through them is 2 inches in diameter at the sheaves
and 2 inches in diameter in the boxes. These dimensions
are none too great to stand the severe work frequently put
upon the sheaves in hoisting heavy weights and tearing out
timber. The fall or hammer rope is 2 inches in diameter,
and the "runner" used in hoisting up piles is If inches in
diameter.

The hoisting engine is double-drummed and of nominally
25 H. P. The detail of the hammer, shown at E, gives a
clear idea of its general design. The weight is 3,300 pounds.

1586. Sheet Piles. In building cofferdams for
foundations and often in protection work, piles are driven
in close contact to prevent leakage. Such piles are called




FIG. 481.



FIG. 482.



sheet piles. Sheet piles are always of sawed timber.
Where the water is shallow and without a current, 2-inch
planks will be sufficient. As the depth of water and pressure



1014



RAILROAD CONSTRUCTION.



increase, the dimensions of sheet piles increase. Usually
they are thinner than they are wide, but frequently they
are of square timber and as large as bearing piles, and are
then called close piles.

To make sheet piles drive close together at foot, the points
are sharpened as shown at fin Fig. 481. Any lateral move-
ment is prevented by the wales o, o.

To keep the edges at top .close to those already driven, a
dog iron, such as shown at a in Fig. 482, is often used.

A cut of a standard sheet pile driver is given in Fig.
483. A general plan of cofferdam illustrating the use of





sheet piling was given in Fig. 465, Art. 1 554. The frame
is light, and readily shifted by hand. The hammer A is
oak. It is raised by the rope B, which works in the single
pulley C. The hammer is usually worked by hand, three or
four laborers generally being sufficient.

1587. Cost of Pile Driving. The following figures
on the cost of pile driving are taken from reports published
in the Engineering News :



RAILROAD CONSTRUCTION.



1015





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RAILROAD CONSTRUCTION.

Cost of Piles. At Chicago, and points on the Mississippi
river at and above St. Louis, pine piles cost from 10 to
15 cents per lineal foot, according to length and location.
Soft wood piles, including cottonwood, rock elm, etc., can
be had at any point for from 8 to 10 cents per lineal foot.
Oak piles 20 to 30 feet long cost from 10 to 12 cents per foot ;
30 to 40 feet long, from 12 to 14 cents; 40 to 60 feet long,
from 20 to 30 cents per foot.

The tables of cost which follow are for various classes of
work.

Railroad Construction. The accompanying table of cost is
exclusive of first cost of piles and of the expense of hauling.
Piles used in construction of the Chicago branch of the
Atchison, Topeka and Santa Fe Railroad. Piles were
driven ahead of the track by a horsepower drop hammer
weighing 2,200 pounds. Average depth driven, 13 feet.
Table includes cost of driving piles for foundations of Howe
truss bridge, and for false work used in the erection of
same. The contractor received the same price for all
classes of work. The work was varied, the piles being
driven into all kinds of soil. Wages for labor were high,
and as follows: Foreman, $4 per day; six laborers, at $2;
two teams at $3.50; total cost for labor, $23 per day. Work
in progress in the year 1887.

Number of piles included in report 4,409

Number of lineal feet included in report 109,578

Average length of piles in feet 24.8

Number of days employed in driving 491

Number of lineal feet driven per day 223.2

Cost of driving, per pile $2.53

Cost of driving, per foot 10.2 cents

Bridge construction, Northern Pacific Railroad bridge
over Red River, at Grand Forks, Dakota, constructed in
1887. Soil, sand and clay. The penetration under a 2,250
pound hammer, falling 30 feet, was 2 to 4 inches. The
foreman received $5 per day, stationary engineer $3.50 per
day, and laborers $2 per day.



RAILROAD CONSTRUCTION.



lOlt



In the construction of a railroad in Southern Wisconsin
during 1885- 87, the contract price the lowest competitive
bid for piles in place under the piers of several large
bridges, averaged as in the following table. The piles were
driven in a strong current and sawed off under water; hence,
the comparatively great expense:



CONTRACT PRICE FOR FOUNDATION PILES.



Material of Pile.


Kind of
Driving.


Contract Price per Lineal Foot.


For Part
Remaining in
Structure.


For Pile Heads
Sawed Off.


Rock Elm
Pine
Oak
Oak


Ordinary
Ordinary
Ordinary
Hard


40 cents.
40 cents.
48 cents.
50 cents.


15 cents.
20 cents.
25 cents.
30 cents.



ESTIMATES.

1 588. Calculating Cross-Sections. Cross-sections
are the basis of most calculations employed in determining
the amount of material handled in grading the roadway.
A full description of the method of taking and recording
cross-sections was given in Arts. 1457 and 1458. The
cross-section notes are copied into a Quantity Book, and the
total end areas of the cross-sections, together with the
partial areas representing the classification of the material
as determined by the excavations, are placed in regular
order. On the same line, under their proper headings, are
placed the quantities of the different materials excavated
between the two points of the line where the cross-sections
are taken.

The common practice in calculating quantities from
cross-sections is to multiply the mean or average area in



1018 RAILROAD CONSTRUCTION.

square feet of two consecutive sections by the distance in
feet between them.

Thus, let A represent the area in square feet of one sec-
tion ; >, the area in square feet of the next section ; C, the
number of feet between the sections, and D, the total num-
ber of cubic feet in the prismoid lymg between these sections.
Then, by common practice,

''D=^lxc. (no.)

id

EXAMPLE. Two consecutive cross-sections are 50 feet apart. The
area of one is 150.4 square feet, and of the other is 191.3 square feet.
What is the volume of the included prism ?

SOLUTION. Substituting the given quantities in the above formula,



we have volume = 150 - 4 + 191 - 3 x 50 _ g,542.5 cu. ft. = 316.39 cu. yd.

Ans.

1589. The Prismoidal Formula. A more accurate
result is obtained by the use of the prismoidal formula. In
applying the prismoidal formula to the calculation of cubic
contents, it is requisite to know the middle cross-section
between each two that are measured on the ground. The
dimensions of this middle section are the mean of the
dimensions of the end sections.

Calling one of the given sections A, the other B, the
average or mean section M, the distance between the sec-
tions L, and the required contents S, we have, by the
prismoidal formula,

S = ~(A+M+). (111.)

In calculating the cubical contents of the prismoid in-
cluded between the following sections, both methods of cal-
culation will be used and the two results compared. The
sections are represented by Figs. 484 and 485, and are
denoted by the letters^ and B. The perpendicular distance
between them is 50 feet. The section given in Fig. 484 is
composed of the four triangles , b, r, and d. 'The triangles



RAILROAD CONSTRUCTION.



1019



a and b have equal bases of Q feet, the half width of the
roadway; hence, if we take half the sum of their altitudes
and multiply it by the common base we shall have the sum
of the areas of the triangles a and b.

The triangles c and d have a common base 8 feet, the
center cut of the section, and if we take the half sum of the
side distances and multiply it by 8 feet, we shall obtain




FIG. 485.



the areas of the triangles c and d. Taking the dimensions
of section A given in Fig. 484, we have



Area of triangles a + b =



X 9 = 80. 1 sq. ft.



21 8 -I- 14
Area of triangles c + d - X 8 = 143.2 sq. ft.



Total area of section A = 223.3 sq. ft.

Taking the dimensions of the section B given in Fig. 485,
we have



1020



RAILROAD CONSTRUCTION.



Area of triangles a'-\- b'



Area of triangles c'+ d'



-i o f



- X 9 = 53.55 sq. ft.
x 5= 74. 75 sq.ft.



Total area of section B = 128.3 sq. ft.

, _ 223.3 + 128.3
Mean area of sections A and B = ! = 175. 8

sq. ft.

Contents of the included prismoid = 175.8 x 50 = 8,790
cu. ft. = 325.6 cu. yd.

In apolying the prismoidal formula we calculate the area
of a section midway between the given sections, and for its
dimensions we take the mean of the dimensions of the given
sections. These dimensions will be as follows:



Center cut,

Right side distance,



= 6.5 ft.
= 12.6 ft.



Left side distance, 2L8 + 18 - 7 _ 20 .25 ft.
&

With these dimensions, construct the section M shown in
Fig. 486.



203-




The area of section M is computed by the same method
as that used with sections A and B in Figs. 484 and 485,
and is as follows:



RAILROAD CONSTRUCTION. 1021

Area of triangles a" + b" = 1L2 + 3 ' 6 X 9 = 66.6 sq. ft.

a

on 2 I 1 9. fi
Area of triangles c' +d" = - X 6. 5 = 106. 6 -sq. ft.



Total area of section M 173. 2 sq. ft.

Denoting the distance between the sections by Z, and the
cubical contents of the prismoid by S, we have, by applying
the prismoidal formula 111,



Substituting known values in the formula, we have S =

Kf\

y (223.3 + 4 X 173.2 + 128.3) = 8,703 cu. ft. = 322.3 cu. yd.
Ans.

Comparing the results, we have

By averaging end areas, contents = 325.6 cu. yd.
By prismoidal formula, contents = 322.3 cu. yd.
A difference of about 1 per cent.

Fig. 487 represents a mixed section of which the part
a b c is solid rock, the part cdef is loose rock and the
part d e g h is earth. The slope a c in solid rock is ^ hori-
zontal to 1 vertical. In a section where the excavated



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