William Macfarland Patton.

A treatise on civil engineering online

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to the breaking of joints in all directions without the expenditu
of any special labor for this purpose. It, however, requires a gre
deal of mortar and special care in filling perfectly all interstice
which is absolutely necessary to be done. It will cost much le
than ashlar masonry. It is advantageous to have a great varie
in the shapes and dimensions of the stones that they may interloc
or bond in every direction.

Many large dams are, however, built of rather small stones-
such that one or two men can handle; the only advantage in th
class of construction is to avoid the expense of derricks, engine
and other kinds of machinery; or they may be built of large stone
one, two, or more cubic yards in volume, and weighing many ton

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require strong and expensive machinery to handle them,
aller interstices between the stones may be filled with rub-

ither class of masonry all facing stones should be set with
t Portland cement mortar; the filling or hearting between
an be laid in ordinary cement mortar. The mortar for
iug should be composed of 1 cement to 2 of sand, but for
Me or concrete filling 1 cement, 3 sand may be used,
of this kind should not be grouted under any circumstances.
, Concrete Dams, — The same distrust of concrete that has
its use for other eugineering purposes has also resulted in
imited use in the construction of dams, the more so on
i of the general belief that it is impracticable to make it
ous. But with the more uniform product now obtained, a
acquaintance with its valuable properties, and the improved
s of thoroughly incorporating its ingredients, there would
1 be no valid objection to its use on the score of suitableness
purpose, and the controlling factor in its selection should be
economy. It is doubtless a less difficult matter to construct
mass free, certainly, from any large or continuous open
[s or interstices than it is with rubblework. The greatest
d the closest inspection is required to secure good rubble-
hen built in large masses. Mechanics and laborers will not
e pains necessary; each gang or shift of men try to make
t record for a day in prder to please their employer, eyen at
^ of slurring over the work. The same causes, however,
in the use of concrete, but not to the same extent, as mix-
machinery is more lijcely to produce a uniform product; and
ae may be said of hand mixing. The main source of a
re product in making concrete is the use of inferior mate-
The broken ston« should be thoroughly washed to remove^
d dirt; the sand should be clean and sharp; the water should
clean (dirty water will not make good concrete: but little
m is given to this matter). Too much water should not be
\ it will always result in a porous mass; if too wet, the con-
tnnot be properly consolidated. A layer of concrete should
e deposited on another layer whose surface has a skim of
y set cement, which leaves the surface smooth. Such a skim
exists where the mixing and ramming have been properly
In such case the surface should be roughened before placing
r layer, ' It is not necessary that any layer should be exactly

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of the same thickness throughout; a few breaks, resembling
steps, will prevent any continuous seams through the mass.

607. One or two illustrations of masonry and concrete dan
given below. It should be noted that a cross-section of a di



designed simply to be stable under the pressure of the ^
against its inner slope, whatever may be the depth of the sustj
water; whereas a weir has not only to be stable under this w
pressure, but its outer slope has to be formed in such a mt
that the fall of the overflowing water shall neither destroy the
by the shocks and vibrations produced by it, nor undermine
the action of the same forces. The entire length of the stru
may be designed as a dam proper or as a weir, or partly dam
partly weir. The construction and design must be regu

In Fig. 254 is shown a cross-section of a part weir and
^dam constructed across the Colorado River at Austin, T
The section shown is that of the weir portion. The stru<
wiis only recently completed at a cost of $300,000. It was
posed to have been founded on solid rock, but owing to tli
isteiice of some undiscovered underlying seams of earthy mat
a portion of the dam, or more accurately the walls of the ]
gates, wSSsiindermined, resulting in its destruction. This ne-
tated the construction of a coffer-dam around this portion o
wall, and the further excavation of the underlying bed, in ord
get below the seams of loose material. This work is now 1
prosecuted; the additional cost will amount to 150,000, or moi

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Ls seen in the drawing, the weir is constructed with a facing of
t)locks of coursed granite. Its interior filling is of rubble ma-
y. Its length is 1375 feet along the crest-line; of this 1125
is designed as a weir, and 150 feet as a dam. Its maximum
ht is 66 feet. Its upper face is vertical. The lower face has
jasy ogee-shaped curve, calculated to pass the overflow water

such ease as will reduce the erosive action at its base to a
[mum. The maximum flood to be passed is estimated at
}00 cubic feet per second from a drainage area of 50,000 square
s. The cross-section is heavier than required by theory, if the
3ture be regarded simply as a dam. The lower curve is ex-
ed to deliver the flood- water away from the toe of the dam and
nst the back-water below. The top width is 5.0'. The total
B^ridth is 16.0', and maximum width at bottom 68.0'.
Inhere has been considerable and acrimonious discussion in re-

to the design and construction of this dam or weir. It is
a as a good type of this kind of construction and as one of the
latest. Its purpose is both for water-supply and water-power
le city. See Supplement for additional facts.
i08. In Fig. 255 is shown a cross-section (a) of a concrete dam
(b) of a weir. The elevation of the water surface is shown at
feetabove the bottom ; the total height of the dam is 173 feet,
g built across a valley, the height decreases as the sides of the
ly rise. The weir portion being on the higher ground, its
imum height is 40 feet above its bed. Its top is shown as on
el with the water surfaqe of the reservoir. The vertical scales
le two sections are not the same. The dam and weir are both
ded on rock, into which longitudinal trenches were cut and
I with concrete, thereby bonding the dam into the rock, so as
•event leakage between the two.

?his structure was built throughout of concrete. Its lengtlT
5 its crest is 1230 feet. A parapet 5 feet high is built on the

The top width is 12 feet and bottom, width 138 feet 9 inches,
dther end are waste ways cut through the solid rock, their
egate length being 920 feet.

?he maximum capacity of the reservoir is 300,000 acre-feet;
vailable capacity 157,000 acre-feet, the acre-foot being equiva-
to 43,560 cubic feet.

^he inner face of the dam is almost vertical, having only a very
it batter. The outer or lower slope has the form shown in the
ring. This is one of the many theoretical sections adopted in

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the construction of very high dams. The ah
is to make the inner face nearly vertical, (
very slight inclination. This may be straig
up-stream. Sometimes a more decided batt<
bottom of the wall. The outer or lower slop
curves, depending on the formulae used, whi
in a somewhat arbitrary manner to suit su
tions. All, however, approximate to a contii
torn to top, concave down-stream, the curve
the top and flattening as it approaches the oi

Theoretically, the thickness at the top m
cross-section of the dam is approximately t
triangle: but in fact the top width is alwaj
quently the upper section of almost all dan
certain distance below the top, and then it

609. At all points the three conditions
565, 566, 567 must be fulfilled, namely: (1
not give way by the sliding of one portion c
dition is satisfied when equation (350) is sat
tal joints, equation (358). (2) That the wall
crushing of the materials with which it
this condition be fulfilled it is necessary thai
(365) and (366) shall not exceed the safe crui
material. The safe resistance to crushing fo
is taken as follows, per square inch: Grani
stone, 150 pounds; sandstone, 130 pounds; h
per square foot, respectively, 22,320, 21,600,
(See Wilson, " Irrigation Engineering,")

These are limiting pressures within one i
viasonry. In the heart of the wall it should :
per square inch, or 28,800 per square foot,
inspection of Figs. 254 and 255, that when
the resultant pressure, which is simply th(
passes nearer the inner edge B than the out
the reservoir is full the resultant pressure ii
weight of the wall and the pressure of the
nearer the outer edge A than the inner edge
safety against crushing must then be f ulfille<
voir is empty and when it is full. Up to a
may be safely stated that, with any well-desi

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of masonry, there is little danger of the dam giving way by cruah-
ing; and although it is well to apply the formula, that the actual
pressure on the base may be known, it is not necessary.

The resistance to crushing of concrete is taken anywhere be-
tween 60 and 150 pounds per square inch, or 8640 to 21,600 pounds
per square foot.

As already stated, there is no danger of a dam giving way by
sliding if it is safe against overturning. The form of cross-section
is therefore determined mainly with reference to its stability
against overturning. This condition requires that the moment of
the pressure tending to overturn the wall shall be less than the
moment of the weight which resists this overturning. Therefore
for all depths the equations (349) and (357) or (362) must be satis-
fied at any and all horizontal sections of the wall.

Since theoretically the thickness at the top should be zero,
while practically it is many feet, it is not necessary to apply the
formula until a depth is reached requiring a greater base than the
top width. Then as the depth increases the resultant pressure
will be more and more inclined, requiring an increased and increas-
ing width of base in order that the centre of pressure shall not be
outside of the outer edge, which is the position, theoretically, of
the axis of rotation; but, as often stated, this axis should be taken
at from one eighth to one third of the thickness of the wall from
the outer edge. The absolute thickness of the wall will then de-
pend upon this distance of the axis from the outer edge. Many
theories and formulae have been worked out, based upon certain
conditions and assumptions, and while no two agree, the general
cross-sections obtained are somewhat similar.

The authors of the formulae are Krantz, Rankine, Wegmaun,
Molesworth, Delvere, and others. For full discussion of these sub-
jects the reader is referred to the works of these authors.

It is necessary to increase the heights of the dams from 1 to 10
feet to prevent the waves from dashing over them. The top width
varies from 5 to 15 feet.

610. Weirs Classified. — Weirs are classified, according to their
construction, as follows: (1) With clear overfall to the bed of the
stream; (2) with clear overfall to a water-cushion ; (3) with clear
overfall to aprons constructed to resist and break the fall; (4) with
roUerway in lower faces; (5) with heavy profile and ogee-shaped

(1) With clear overfall the danger and objections arise from

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erosive and scouring action, which will undern
dam if the material upon which the weir is
earthy or gravelly character; and even solid ]
greatly affected, though it may not result in
to the weir.

(3) With water-cushion the erosive action i
the overflow falling into a water-basin.

What should be the relation between the V(
overflow and the depth of the water-cushion
out of loose material, is probably not known,
structions are made to form these pools or ci
They can be made entirely effective for the pu

(3) With aprons the overflow water is made
platform, usually of timber, which may rest oi
the river, or upon beds constructed of broken st
receive the force of the fall, and they are made
with a gentle slope or horizontally, so as to gi
locity of the water, and at the same time lead i
weir. They are sometimes inclined or curved
further retards or breaks the velocity.

(4) With rollerways the weirs are constn
slopes, or series of steps, by which means the ^
is retarded and at the same time the water is c
the weir. These require the use of large qu
and consequently great expenditure of money,
rollerways are often used.

The ogee curve may be considered as a m

way construction. It reduces the material req

and produces about the same effect as the rol

of the ogee-curved face is to cause the water

fall over and clear of the weir. So long as the

serves a bluish color, and when it commences

whitish or milky. The following is the const

curve: In Fig. 259 make GB = — ^^ and A£


sect AE with a perpendicular HC^ which pr<
sects the normal from A to GBy at the point
prolong it until it intersects the normal to 1
point By at the point D ; and with C and D as
DE 08 radii, describe the respective curves
construction is simply that of two connected j

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h a reverse curve. Fig. 260 shows a good example of this form
outer face of a weir used in tjonnectiou with the Croton Dam,
B^ York, the construction of which is novel and somewhat

611. The Croton dam and weir were constructed for water-
rage purposes. It is one of the largest masonry weirs, and was
nded on unstable material for a portion of its length and on
d rock for the remaining portion.

As seen in the drawing, the weir portion of the dam is com-
ed of a series of cribs of different widths, forming a series of

Fig. 259.




pa. These cribs are filled with broken stone; between the several
3 of cribs there are masses or columns of concrete. The cribs
I concrete are built on a stratum of alluvial soil containing
vlders. Upon the cribs and columns of concrete the masonry is
istructed. The hearting of the masonry is laid in courses, gen-
lly horizontal, over which, on the curved outer face, cut granite
Jar is laid.

All of the masonry is laid with hydraulic cement mortar. As
>wn, the up-stream face is vertical for a depth of 23 feet from
J top, at which point the masonry rests on a concrete column
ween two sets of cribs. The upper of the two cribs is above
» masonry face, and forms two steps. This face is backed by

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earth having a long, flat stope, which is j

The crest of the dam is formed on a coi
radius of 10 feet, and the outer slope is formed
having a radius of 55 feet, thus forming an oj
that which will be taken by the water flowing <
total depth along the inner face is 50 feet. Tl
ness at the base is 76 feet. The lowest point c
at B is only 38 feet below the line of the crest

Extending outwards from B a series of ci
so as to give a rising surface, by which a watei
in depth is formed. Of these the two cri
masonry are filled with concrete; the other t]


which the water falls to the bed of the stream,
feet. This construction, therefore, combines t
tages: (1) The water slides along the ogee curve
fall and consequent shock; (2) the shock and
reduced by the water-cushion and upward i
together with its great length ; (3) the total fall
falls of less heiglit, namely, 38 and 15 feet, re
by this arrangement the timbers of the crib ar
water at all times.

612. The new Croton dam will have a total
divided as follows: An earthen dam 530 feet lo
above foundation-bed 120 feet; top width 30 j
high water. The upper or water slope is 2 to

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► 2 feet of cobblestone laid on 1| feet of broken stone. The
r or lower slope is 2 to 1, broken by three benches 5 feet wide;
intire slope sodded. The core of this dam is rubble masonry,
iding below the base of the dam to solid rock, having a total
lit of 225 feet, with a thickness at top of 6 feet and at base of

^he main dam, 630 feet long, has ^ maximum height above its
dation-bed of 248 feet, and 163 feet above the river-bed; its
vidth is 18 feet and its bottom width 185 feet. It is built of
le masonry, and faced above ground with coursed work bedded
jrtland cement. This dam is connected with the core wall of
earthen dam, and the earthen dam itself with heavy masonry

walls. The crests of these two. portions are straight,
'he weir portion, 1020 feet long, curves up-stream from the
>nry dam nearly at right angles to it. The maximum height
feet, and its extreme width at base will be 195 feet. Its up-
m slope is nearly vertical, while its outer slope conforms to an

curve, but is broken into a series of steps varying from 2 to 10
in height. It is constructed of uncoursed rubble backing and
sed facing. The crest of the weir is about 14 feet lower than
jrest of the dam.

^oth the masonry dam and weir are founded on solid rock,
capacity of the reservoir is 92,000 acre- feet,
'he overflow water passes over the weir into a canal or channel
eated in the hillside, and returns into the river well below the
•f the dam.

13. In Fig. 261 is shown a weir constructed of logs and square
ers forming a large crib, which is filled with broken stone or
b1, the entire upper surface enclosed in a sheeting of plank,
necessary, when such dams are built on earth, gravel, or soft
, to carry the water some distance below the toe of the dam by
IS of a rollerway, as shown on the drawing, from which the
r should fall either into a water-cushion of back or dead water,

this cannot be secured, it should fall on a timber or masonry

b is unadvisable to let the water have a clear fall over the
, even when the weir is founded on solid rock, unless it can
nto a water-cushion. There are many designs of timber dams.
Fig. 261 shows both the usual design and character of con-
Fnless there is a constant overflow of water, and all the timbers

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and slow approaches they may be smothered or choked down.

tendency will be to collect these different channels into one

flow^ which^ seeking an escape along the line of least resistance,

>ften cause much trouble in closing a dam.

pringy soils are always sources of great difficulty, cost, and

sr; and where practicable it is better to change the site if by

ing such uncertain foundations can be avoided.

16. Curved Dams, — The dams heretofore considered have been

jsed to provide stability by their weight and sufficient spread

fie. As is readily seen, they require krge quantities of ma-

and consequent cost. There has been much theorizing on
jubject of reducing the weight and quantity of material by
g the form of a large horizontal arch to the dam convex up-
m, thereby transmitting the pressures and strains along and
id the dam to natural or artificial abutments at its ends.
;he true theory of the arch being so little understood, few cu-
ts have been bold enough to attempt to apply the principles
e arch to the construction of curved dams,
ince the pressure of water is normal to the up-stream face of a

the advantage to be derived from the curved plan arises from
act that we can decompose the. pressure into two components,
)erpendicular to the span and the other parallel to it. The
ness and weight can therefore be reduced by proportioning

on the basis of the component perpendicular to the span,
J the parallel component produces a compression on the up-
m face tending to bring all parts of the dam to act as a unit,
evident that it would be safe to give a lighter cross -section to
lam when built on a curve than when in a straight line; but
lat extent this can be done with safety is uncertain, if not im-
ble to determine.

'here have been built but few dams on the curved plan. Expe-
e has proved that their construction is safe, but with what
[in or factor of safety is not known. Figs. 256, 257, and 258

the elevation, plan, and vertical cross-section of one of the
3st designs of the curved dam, namely, the Bear Valley Dam,
•ornia. It is not given as an example to be followed, though it
proved its efficiency, but to show that at least a very great
Qce can be placed on the stability of curved dams. As shown
le drawing, the top width is 3.2 feet, at 48 feet below it is 8.4
and at the extreme base it is only 20 feet, while its extreme
bt is 64 feet. The length of its crest is 450 feet. The radius

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of curvatare is 300 feet. It is built of ur
lines of pressure fall from 13 to 15 feet outsi
The Zola dam has a maximum height of
19 feet and at base 41.8 feet. It is only 205


of curvature is 158 feet. It is built of uncoi
bility depends upon its arched form and the
struction, as is the case with the Bear ValL
mended to increase the thickness near the en


617. The following discussion of severa
introduced in this place on account of the re
pies and the formulae expressive of them to t
The principles are, however, directly applica
connection with other and useful engineering

Equilibruim of a Cord. — Referring to
funicular polygon and to Figs. 68 and 09, ii
number of sides of the polygon is increased,
number of loaded points, the more nearly doe
mil forces approximate to a continuous line, i
the more nearly does the funicular polygon a
of a cord continuously loaded. Also, the nun
representing the stresses on the several bars
ular polygon, increase accordingly.

In Fig. 26:.', let RABR^ be a cord or chi

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polygon of an indefinite number of small sides; A and B
bs on this cord, AF and BF the directions of the two
hiose points, and CF the resultant of the forces between
B A and B, Since the portion of the cord between A and


Fig. 262.

Fig. 263.

quilibrium under the action of the forces AF, BF, and
must meet at one point and be proportional to the sides
gle respectively parallel to their lines of action, and the
3 AF and BF must be tangents to the cord. If, then, in
we draw lines tangent to the cord at the points B, R^ , Ay
hey will be the directions of the pulls at those points.
Fig. 263, from a point draw lines OR, OB, OA, and
king their lengths proportional to the magnitudes of the
i join the extremities of these lines by a straight, broken,
I Hne : the straight line joining A and B will represent the
and magnitude of the resultant of the forces on the por-
le cord (Fig. 262) between A and B, since the three forces
)rtional to the sides of a triangle.

w the points A and B are taken nearer and nearer together,
AB (Fig. 263) approaches nearer and nearer a tangent to
e, and when they become consecutive points the straight
be tangent to the curve; and hence, as this line is the
of the forces between A and B, the direction of the force
at any point B is represented by a tangent to the line
(Fig. 263), which is called the line of loads,
en, a line of loads be drawn such that while its radius
parallel to a tangent to a loaded cord at a given point its
^ent is parallel to the direction of the load at the given
the cord, the radius vector from the fixed and common
will represent the pull on the cord at the given point,
•aight line drawn between any two points on the line of
1 represent in magnitude and direction the resultant load

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between the corresponding points on t
pulls or forces at the points R and R^ i
treme radii OR and OR^.

A loaded cord is stable^ but permits o
618. If the forces are parallel and vei
becomes the straight Hue RR^ in Fig. 26
points A' and B' of this line; CP bee
Fig. 262. If, then, A be taken as the lo
that ^P is horizontal, the following wi]
sion of this condition:

Let H := OA' = horizontal pull or t

" P = OB' = pull or tension on 1

Online LibraryWilliam Macfarland PattonA treatise on civil engineering → online text (page 56 of 145)