Structural
Engineering,
comprises
1.
The
theory
of
girders, with
an extended
succeeding
from
making
the
student
do
does
its
work
thoroughly.
can
formulae,
and
show
vocationalizing
education
and
making
a
man
a
machine
which
performs
certain
motions
without
understanding
the
reason
is
not
true
education.
True
education
is
drawing
out,
or
developing
the
innate
powers
is
con-
cerned
no
human
OF Inertia.
XXII. Retaining Walls
of this
work, the
latter supplemented
volume and
Most
structures,
however,
it studies
various
ways,
as,
instance,
according
to
constructed
are
being
gradually
requires
consider-
able
study,
investigation,
and
inquiry,
factor
not necessary
it is
determination of
given
later.
upon a railway
therefore always
load
beforehand,
by
experience,
necessary to redesign
structure,
respect
with
respect
the
inner
forces
may
is
termed
statically
determined
structure is statically
should
be
computed
and
assumption
of
the
will
be
and their
much
judgment.
of wind.
a
crowd
of
people,
of
earth.
of
and reactions,
the
paper.
namely,
two
components
and
Si
completely
fixes
structure
reaction
second
condition,
being
otherwise
fulfilled,
a
force,
we
mean
that
sense,
i.e.,
we
say
hinge must
in
some
similar
makes an
given.
lacking, and this
the
statical
equations.
Here
the
usual
practice
be
either
vertical
or
parallel
unless
the
system
of
found by
in
the
center
reactions,
if
statically
circufn-
—
in
which
both
com-
ponents
about
any
point
Since
exert a
force is
such
problems
is held
nearest
tenth.
nearest
tenth.
Case
solve
as
many
mastery of
the method.
They may
all be
whether
the
be considered to
reaction
or from it.
rollers
shown,
but
acts
statically
tion, and the condition
obvious
that
if
a
horizontal,
other words,
soHd
body
Ri)
conditions will be
under
a
particular
combination
in
any
the table may be
given regarding each
have
no
fixed leg. A struc-
a
line
perpendicular
thereto).
at
More
the plane through
The
same
vals,
it
may
not
exact
are
assumed
were
with the
to 30 per cent
a structure;
C, and
so on,
loads it
be
known.
Thus,
the
string-
assumed loads and
a
truss
or
beam
is
foot
of
span,
will
be
nearly
constant.
foot,
including
floor,
will
be
approximately
Ci
in
in
pounds
per
yard;
to
this
a, its weight per foot of
length
will
structure
able
should be
those which
assumed that
vorable
position,
are
in
motion,
is uneven.
is moving,
highway
and
elec-
R.
E.
A.
the
allowance
is
for,
though
a
is
to
snow
being
generally
per foot,
of
snow will
remain, though
a layer
per foot,
per
foot,
a
vertical
acting
together
or
separately.
The
maximum
wind
pressure,
futility of
—The
On floors,
the live
loads are
the merchandise,
and
high-
way
long
and
that
even
is
reasonable
to
assume.
though
it
should
be
remembered
that
some staircases, and some assembly
rooms,
a
carry
more
before
assumed
uniformly
is
1
Trans.
Am.
Soc.
C.
a
building
(see Art.
be
from
a
crowd,
it
and 75
The
New
columns
in
buildings
more
than
the top
gives
it is not necessary to assume that the entire area
tributary to it
seem eminently
for
the
next
columns,
and,
for
and
storage
or
manufacturing
and
to
some
floor in
loads
of
less
than
be
assumed
that
be
small.
12.
often specified for
of gravel or
depending
upon
the
degree
a
quarter
of
a
by
frequently
changed.
1
See
pp.
300-303,
edition
allowable floor loads
the
materials
or
foot, 4
Code
Committee
taken,
i.e.,
for
floor,
however, that building
requirement
that
changes
in
and the
should
specify
notice, stating
that
of
those
prescribed
members, but
considered, for
equal
to
1,600
pounds
-
=
Cars
Fig.
17.
10 feet
toward
lighter
weights.
The
beams, it may be necessary to cover the part of
the adjacent panels
electric
be
each
direction.
Also,
for
Bureau
feet, the
to
arrange
vehicles
only
a
uniform
load
from
a
crowd
of
produce the same stress
load on the
pounds
50
See also
in Art.
to
the
floor
of
a
larger
area
below.
It
to say, a
of
fill;
a
the
rail,
distributed
on
the
inches
apart;
i.e.,
one or two
will seldom, if
the future,
the heaviest
but
simpler
method
by
assuming
either
(a)
an
equivalent
uniform
load,
or
{h)
a
uniform
over
the
uniform
used, there should be,
that the locomotive excess
middle of
point
the
uni-
form
various
typical
/j
^0
that to equal them the ^-loading
will require
E-l^, or
2. The
1924;
also
great
part
on
driving
wheels.
This
tractive
monster
the
heaviest
train
of the
Jones and
service
railroad, some, like
making
engine
loads
and
train
doubtful.
Predictions
are
5
per
load capacity
for plate
assumed, considering
sively
ings will
ilf-loading
is
advocated
by
influence lines,
made
up to
the longest
shown.
Tables
loads for
excesses
load,
that
the
most
striking
characteristic
of
vol.
XXVI,
concrete,
objective,
and
same
results,
it
may
be
all
shown, if
necessary, as
and
train.
32.
Relations
Equiva-
lent
point
or
many
by
the
AJ)B. The
shorter segment
which
the
influence
line
has
lie
SP,
and
according to
the criteriod.
Then the
of
the
forward
wheels
 
author
presents
three
alternatives:
1.
The
typical
Af-diagram
(Fig.
22).
90,000
pounds
each,
spaced
diagram,
and
then
from
the same
uniform load
stress
maximum
using Eq.
those equivalents,
indicated
-12
k-^'8-->is-
W moving
C
d is the ''degree of the curve, or the angle
subtended
and
the
mass
This
is large,
a
momentum
air is larger than the plate.
If the
as
intensity of pressure,
to
only
partly
deflected
of
to it. This reduces the value of P and of
p.
In
It has
known as
of
weight
and the
for
measuring
wind
velocity.
It
of a cup and the
convex side
the
average
velocity
in
are record-
Wiley
surface, the
is not very satisfactory, because it is uncertain whether the
hori-
zontal
force
will
be
p,
and
this
way,
p
difficult to make, and that they may be
entirely wrong if the wind
should
direction.
the
a
the
know that
the wind does not always blow horizontally, in fact, that it
rarely does. For
may be very
ical
justification,
is
Pn
Pn
and
p
windward
to
be
correct
for
the
as
the
pressure
on
the
true.
The
most
is
an
excess
retical curve
without
serious
error.
The
pressure
on
a
cylinder
is
of
suspension
for
a
cylinder
by
integrating
from
Eq.
(22),
is
corrugated,
with
twisted
in
other
words,
p
cannot
be
taken
as
singular
result
is
obtained
that
if
Eq.
(22)
accurate.
I
to
be
partially
as great,
the pres-
sure on the leeward girder was 25 per cent of that
on the
of
the
structure.
leeward truss back of the train, and the pressure on
the
For unloaded
bridge it
or
girder
The
English
Commission
leeward truss
or girder,
the windward
to
three-fourths
of
the
total
area,
three-fourths
the
the ground,
that the average
is because
the greatest
less
on the large
not
always
reliable.
a span
apart,
the
other
ten or more oscillations in 1 second,
and less
 
exceeded,
though
gusts
British India it is said that maximum
gusts
have
Tamalpais,
have reached
14 feet wide by
110 feet high, these
on a
in cities, partially sheltered,
30 pounds per square
paper of
for
many
probably not be
unloaded
ever be
should be assumed.
forces
The
1925
specifications
of
of
over the whole length
be
pushing
to
wheels
of
the
train
were
would
structure.
lifted, carried
be
be
weight
b^ho
pins.
It
follows
are
applied
acting along
must
therefore
may
a
bow,
and
acting
action
curved, or
chords
and
may
be
arranged
in
many
of computing
a
truss,
with
not, may
all be
be
removed,
ditions
2/7
the stresses
can be
the three
stresses
equation
ZV
are
more
the other two;
forces
an
=
two
parallel
bars,
ends of
bars can be
members
section,
then
consider
then see clearly
is not
a stress
curve for
stresses
by
taking
and
inclined
41,
the
reaction,
right
abutment.
The part going to the left will be the shear just to
the left of
splits
will
always
be
the
load,
consider
by
one
to
get
the left
stress being
the number
written on
reaction omitting
meeting at that
two trusses, the
The
chord
stresses
are
that they must be
are written
down at
chords,
partial loading.
joint,
Ui
the
second,
and
5.
Maximum
Web
be a
support,
and
from
neutral point.
A similar
construction in
be
with live
stress
may
shear only in the
under
a
given
loading.
It
must
be
remembered
therefore no
carry
all
the rigidity
of some
determined
or
not
with
reference
1,
others?
us that
in equilibrium; therefore they
do
outer forces in
the structure is
this is not
numbers
of
that
that has
center is
any point
to the
load at
not appear
to sag,
below
the
horizontal.
This
camber
panels
e
is
computed
thus
a
different panels.
were lying
initial
tension.
Assuming
that
a
to put
by
a
turnbuckle
is
produced
by
diagonal
has
initial
stresses,
and
these
may
be
minds
of
adjusted
action, the
statical
indetermination
is necessary
stress,
stress, and the
It
truck is
considered.
cal joints the
between
correct.
The
loaded
chord,
dead load
at each
cases, namely, 10 panels
be
used,
has
been
fully
discussed
in
all
the
chord
excess
stresses
will
be:
UoUi:
40
X
at L4 and
•
this panel is
would be needed if
added
48.9,
and
in
of
the
real
be
provided
for.
Suppose
the
be 60,000
6,000,
of
16,000,
as
often
specified.
Now
the
stress, there should
the
have counters in
by
of
80,
36,600
a rod
l}/^ inches
the
counters
is
not
The
writer
believes
that
in
fact
up
to
the
first
load.
The
above
computations
left of that
the
give
maximum
in
be
on
the
safe
side,
to
the
left,
zero from the vertical loads, the
truss
could
not
be
that a
19.
Compression
in
Bottom
Chords.
rusted, or
due to
expansion may
make
will
be
less
a
horizontal
and Sway
but
bars
UqLo
and
LoLi
are
omitted.
Such
a
may,
be
will
be
Fig.
48c.
In
supported
at
Ui,
at
in
should
never
a
details.
entire width
dimensions
to
sticks passing
upon
the
chords,
a
fact
which
panels. Hence
or
even
For
this point.
be
ilfl
Loads.
Diagonals.
of
Us
added
at
the
chord,
members
added
the
Thus the
either old joint
the truss is so
same
for instance, bars he and he could not be in
action at the
they
are
shortened
by
This is
h,
shown
in
Fig.
bisects the
*Si;
a
Si
greater
middle of
Fig.
52a.
the present truss
load
of
by
diagonals
tension
pieces.
In
writing
the
like
M1U2,
all
always be
forces
position (at
are
at
Li
and
L3,
the
UJJ2,
the
maximum
positive
to
it
L2 would merely
load
at
Li,
for
Fig.
55.
If
put
in,
L2M3
should
a
tension
piece.
If
not
put
is
1
feet,
tion
to
maximum
The maximum V.
meeting it at
double panel
the
following
chord
is
the
maximum
this case is
the
maximum
-\-S
in
L2L3
minus
extending
to
L3
and
excesses,
sit-
uation
greater
than
and numericalhj
be
easy
to
-(-
the safe
to use
=
4. Maximum
A
truss
of
the
Warren
as
two
chords.
Each
short
are obvious.
For
the
actual
same general form
(not dimensions) as
c
on
a
simple
of truss
but one
is
considered
a
chord
diagonals should
shear in
the center
Li,
m is
and 2m
of the
posts
long spans,
the panels
form,
inclined ; it
was so
used in
know
are easily found.
equal slopes, their
are and each carries
stresses are
as follows:
to
the
abutments.
This
than the
other. Figures
69, 70,
end
of
the
span
may
rest
and
bar may
uniform Live load is
span.
3,600
bridge), and let the total dead load
of
floor
the stringers
lower truss will
l)e as follows:
dead
load
of
equally divided
stringers to project
joints of the trusses;
stringer
lengths
need ot be found,
see the principles
stress.
The
the
Counters.
action
the influence
differ
from
the
74).
line for the
a
unit
load
influence
line
influence line for
act
singly;
the
possibilities:
in
action.
3.
Main
and the
C.
E.,
1887.
LgkR.
be
that joint
the
fourth
cannot
be
see
maximum stress for
bars being
in action.
In this
determined, but
static-
ally
truss, and was
and
also
likely
usually
followed.
the loads
at
n really
both systems,
k
this truss?
last
assump-
But
load
eight-tenths,
the
entire
more (including some that
cannot be truly independent,
etc., and
these results
must
if
there
were
loads
only
on
divided
between
the
case
of
the
Warren
the
with
as it offers
are given
dot-and-dash
system
to end.
index
a
stress
of
the
opposite
kind.
6.
Treble
System.
The top
zontal
projection
two at
These facts must not be forgotten in writing index figures
on the chords;
verticals,
would
have
12
joints,
and
22
verticals
must
be
considered
as
apparent
figures will be
portal
and
transverse
frames
of
b any
unbalanced horizontal
when
bridge
^
3
members
cut.
Such
bridges
are,
a
that in
by
toward the
and the
by inspec-
already
explained.
at
4,
the
u
and
v
with
A
be
3^
X
Sp/Zi,
and
the
point
similarly
to
the
heavy
system
half
and
half.
To
find the loading causing the maximum stress in a, it is evident that the
heaviest
tracing
cloth,
the
loading
to
stringers
at
execution.
is
best
illustrated
systems,
at the
used without
at one end,
symmetrical.
The
method
by
it is
position
assumed.
is,
that is
to say,
it is
must
be
Fig.
88,
if
track,
with
and
stringers,
and
in computing the
resulting
therefrom.
that in the left-
in
com-
out
numerically
the
two
tion.
and
Joint 5:
necessary except
to
find
the stresses in
It
is
of the method.
ex-plained
is, the
pure method
of moments,
be,
and
bar,
if
a
in
finding
as tension, and
the
by arrows.
this
by the method
Fig. 91.
—7.4
(compression)
Z,
obtained
from
the
equation
The
above
computations
necessary
to
a panel;
or other shapes,
certain plates if
or
the joint
order to
the left
5
of
Chap.
 
supports
and
through
these
the panel
meet on the vertical
will
be
CT
top
chord
to
C
and
as before.
shape A 'P'8'B', shown
impossible; hence there
precise
For
a
the
counter
when
it
extends
but
may
be
of the section, divided
left
a
moment
about
reaction,
and,
as
load
Pi
is
at
S.
Then,
if
„ai
Example.
negative,
panel CD, and the
and dividing it
Great
the stress
Ml
Ml
neutral point
In
Fig.
A in
the panel
to
would
is obvious.
This is
not so
If
there
is
a
Art.
42,
it would be
case
provided this load
In
be
action,
and
should
be
able
to
solve
all
the
verticals.
Europe large
and
vertex
at
Since
A
and
which,
Fig.
102.
through
vertical
carry concentrated loads
In Fig. 102
is
The
joints
or
angles
cord
will
be
103
Ml
and
Mi
the
moments
for
diagonal
=
^-^
parabolas,
verticals must be
parabolic
top
chord,
and
the
verticals
are
point.
truss,
when
are
In
the
This can be checked
a panel,
feet
When the main diagonal on its left is in action,
it
has
a
action, it has
found.
in the trusses
practice of sub-
practice
to
done above.
It is
only desirable
peculiarity,
above
from
Fig. 112.
disadvantage that no
each end.
built
as
 pony
inclined end
But
be portal bracing
explained in Arts.
end
to
end,
while
the
web
increases
as
parabolic
truss
with
stress
in
maximum
stress
the
ends.
It
is
parabolic truss and with the same center height, increasing the
other
the
straight
little
chord
constant
straight
chord.
With
a
double
parabolic
or
in each of the
of stress,
minimum stress
or
else
as
much
of
the
given
height
be
20
tons,
the
dead
of
material,
material
alone.
Many
the
most
important
which, alone,
the mind
only
to
a
question
one
mathematical
principle
be familiar
which
course the
equipment will be
piers
n
it
is
based
are
discussion
of
a
varies
as
cost
of
a
per
foot
be
6
-f
cost
the
cost
of
ratios
is
of
4. Later
spans
economical
or ties be vertical?
view taken
must be
two parts,
divided
into
or to resist
the web horizontal
then,
in
up
c,
and
so
number-
less
wasteful
of
floor.
It
the stresses are
web members
same
(h) is
for then
varies
inversely
with
the
height.
I,
Qr.
panels of the
Hence it would
the column formula
of
55°,
however,
per
foot,
in
a
pendent
of
the
height,
if
formula.
Practically,
the
material
in
the
web
to use greater
For long
economical, and generally
lie
on
a
the
curved chord increases
through
bridges
curved
was
largely
built
by
the
It is
long-span trusses, both in
sinners
in
used
by
In Europe, more systems
were used in the
12.
Economy
of
inclined
end
stress but
OF
STRUCTURAL
FORMS
nineteenth
1728,
1728,
be
made
entirely
wooden
keys
or
treenails.
In
1840
5.
not understood
was
the
Bollman, and largely used between 1840 and 1850 on the
Baltimore
and
analyzed
and finally
tures,
they
and
did
as
all
engineers
with
such
Howe
Hermann Haupt wrote his
Whipple's
book.
His
methods
suspension bridges
have
entirely
flanges
were
widened
and
made
up
culminating
steel,
panel length, economical
height of truss,
prevailing type in
rebuilt in 1909,
the direction
been designed
The stresses,
been
abandoned.
The prevailing form of steel truss in this country is now the
Pratt
truss
or
Pettit truss). The
tically
feet; and
were
by
within the
much
longer
European
bridges
had
riveted
connec-
of
erection.
to sudden
to
of
ing
systems.^
pin bridge the stresses
appreciable bending moments in the bars at
the
is well
Soc.
C.
E.,
Briickcnbau
im
XIX
Jahrhundcrt,
Julius
chapter
on
bridges,
and
atlas.
Merriman
for
units,
any
beginning
force is
designated by
the numbers
always
show
in
Straight
Line.—
If
resultant
be determined
by
the
use
of
the
principle
Pi
are o'l'2'3'4' and
of
immaterial; for
the
order
o3, as
by
R
i-^;
it
gives
also
Thus
in
Fig.
141,
o2
is
may
be
in
equilibrium,
zero,
replaces
at a
condition being that
143,
into
repre-
senting
the
given
force,
two
lines
having
intersection of
sides parallel to
of action of the
Further
n\
and
10
represent
two
forces,
having
the
given
one of the
solved
by
exercise
the
imagination.
1-
3
but
of
Pi
known,
while
hence the
all acting
to
Pi
figure,
determine
such
a
point
by
pro-
longing
a;
of
oO,
01,
10,
and
02,
acting
as
are
equal
and
opposite;
hence
12,
and
also
of oO and 02. In the same manner, P3 is resolved
at
and
03;
hence
R2-Z
is
Ri-3
intersection
of
sa
and
dc,
as
oO
and
04,
it
acts
through
the
point
of
intersection
Ri-a
would
be
dt);
also
that
Pi
P1P2P3P4
by
ones
a
on the
lines sa,
ab, be,
polygon
funicular
or
the strings; the
to
polygon.
We
number of forces
choose
forces is given
^3-2=02
be very
equilibrium polygon
the
equilibrium
not
also,
if
Go
and
10;
hence
=
shows
P
constant,
a
result
the
force
the
same
way,
if
c
is
the theorem:
will
not
be
force polygon closes. If the force polygon
does not
close, the resultant of all the forces is the resultant of the two
parallel
forces
in
polygon, and these
strings will not
of
action
be
avoided
of the
in Art.
shows
a
resultant
polygon
ol,
12,
23,
etc.,
there
were
a
different
Pi,
a
second
result-
ant
polygon
Po
Ps
that
they
would
and
0'
were
two
Fig.
152.
poles,
with
Ol
and
Oj
horizontal
and
04 passes through
may
be
point a,
continue to
as
polygon
on
a
line
through
0
ing
the
relation
between
two
equilibrium
for all equilib-
the polygon passing
(Fig.
155)
be
through
C.
and 01.
Draw lines
through A
the
given
forces.
O2O
parallel
to
BC\
to AB and BC.
O3
a
line
parallel
to
AC,
G\,
force
polygon
of
the
forces
which
necessary
to
draw
compo-
nents
along
and
12
is
Pi,
direction as
P12. In
Three
point
(Fig.
158),
along
I
balance
three forces
reactions is merely that
to those
must
be
equal
at
two
reactions
must fulfil are that
forces, and
reaction is given, and
except
when
the
If
the
direction
these
the
The problem is merely this: The
equilibrium
will
be
made
to
close
by
force
polygon
directions of the reactions.
prolofig the
end string, and the
of
both,
if
they
are
be
produced
string
in
order
to
solve
the
problem.
of
applica-
tion
of
the
the closing line
Oko,
and
ko
named
because
were
not
in
known outer force.
the
left
abutment,
and
the
are drawn
as before,
and the
represent a
acting
along
the
strings
shown
find the
vertical
between the right-hand
supports were
of
placing
the
a
new
of the span
Uh',
then
f \\
f
r*
Fig.
172.
closing
line
^3/3;
then
azhz
The
may
be
and each
aa'b'h.
loads
are
treated
concentrated
loads
be
tangent
loads between
h',
for the loads
between a' and
for
such
a
with vertical
may
be
found
graphically,
in
magnitude
shear
>Si
between
8z
between
now, we make
first
load
In
other
words,
words,
same
directly
the
shear
at
every
to
If
Pi
is
when
Pi
is
at
continued till
find
the
reaction
and
horizontal,
and
o'a'
spaces between bars
of
the
frame,
and
the
spaces a
and h is the bar ah, and the stress in it, in
the
gram,
is the distance
ab, the letter a being at one end of the line
and h
reason that
the different
stress
no
value,
since
it
involves finding many stresses besides the particular one sought, these
others, however,
being of
determine the
(3)
wind
on
the
right-hand
roof (provided it is symmetrical)
for
in
Fig.
177,
the
stress
in
DE
of the wind, the diagram
must be drawn
position
neously
in
the
case
of
fiat
roofs,
a
total
easily
be
decided
upon,
and
shown in the
parallel
c
will
be
located
tance xo; the force
chord joint,
the
bars
PA
and
OA
op;
therefore
draw
from
p
a
line
acts
from
p
to
find
the
a
diagram
bar
can
be
found;
statically determined, may
parallel
c
RS;
p'
load.
The
stress
will
carry.
be altered.
5. The
single load at
in ekch
at
the
end there is a check on the work in the closure
of
the
last
polygon.
On
the
by
accurate than
graphical methods.
The student
tures
for
to
It is
student
mind,
in it found, independent
of moments; except
graphical method of
R,
the
resultant
of
R
and
S
goes
the outer
bar, except
methods
are.
Figure
the lower chord bar
of
lax
R^-h
about t
is found
in x
forces to
about / is
In.
In
general,
H
times
the
practice in this method,
each bar
That principle makes
b
are
distances,
and
anything else. It is
of
2. Center
areas
whose
each,
first
through
the
intersection.
Now
227
line
the areas of its parts each multiplied
by
the
square
'LAx^.
where its
A acts,
convenient to
force acting at the
equilibrium polygons,
184,
extreme string.
polygon and the two extreme strings, as the reader will
see
to some even
however, since the results may be obtained so much more
easily and quickly
The writer, in a long experience, has never had occasion
to use
the two end
Suppose
now
to find the
Clearly
such
a
frame
really
an
arch
is normal
The
polygon
will
be
held
in
equilibrium
by
any
set
broken
line,
03;
then
depend
upon
the
magnitude
of
relative
enabling
us
carrying
a
bending
moment;
Fio.
185.
/;
similar
to
yy',
which
has
the
load
equilibrium
polygon
without
a
concen-
trated
load
at
that
point,
it
should
that factor
the
bridges,
and
(1)
by
using
a
variable
factor
the
live
dead
load.
3.
The
recognition
an equivalent
dead stress.
the dead stress to
be
should
be,
live
stress
be
multiplied
proper for
a dead
stress. This
necessary in
in workmanship.
5. Defects
load
and
are
themselves
based
on
untrue
assumptions.
The
as
small
as
practicable,
straightening
of
bent
With
the
improvements
and
tons in
or
library
carrying
much
heavier
loads.
an increase
16,000
pounds
per
an
excellent
provision,
but
for
steel
by
the
following
requirement:^
Allowance
for
Increase
of
Live
Load.
heavier
designing
be all
right for
counters and
overload will
generally have
in the different
to
^^^{^8(1
the
live
load
50
per
cent
will
the
designing
stresses.
This
a
piece
of
almost
any
from
tension
to
to
break
on
it;
Although
Fairbairn,
in
England,
a
of
stress,
determines
becomes
less.
1. If
fracture
will
the smaller
minimum.
Thus
of
the
allowable
stress
when
removed each
time, then
instead
of
u,
railroad, Mr.
Wilson, dealing
9,000
pounds
for
zero,
the
following
formulae
/
=
and
where
the
same
kind,
a
maximum
not depend on the
was
the range, the
allowable stress must
vary with the range if the factor is based on
the
on
is
reversals,
or
the
the
effect
of
as shown
by tests;
of
''Strength
of
Commissioners of Massachu-
multiplying
reversals of
stresses of
elastic limit.
correct,
about
right
is
a
=
the
investigations
material
used,
that
is,
a
diagram
in
which
flowing
slowly
strain
repeated
stress.
For,
if
and
dead
stresses,
c
fa
r
10
12
, 000
Bearing
legs
of
stiffener
apply
flanges, but the
between lateral connections
than 70 per
portion
of
the
denominator
should
their
least
radius
2.0
Dense
Douglas
fir
1.5
and
spruce
1.2
204.
Allowable
30
lengths.
(d)
chords,
be
seventeen
thousand
(17,000)
pounds
least
width,
nor
direction,
except-
by the
20,000
rollers or rockers, cast
swing bridges,
supposed to
to
the
centers
of
the
bearing
surfaces
24 ,
000
On
rollers,
the
roller
in
inches
600f/
On
rollers
of
drawbridges,
per
recommended
Special
Committee
on
flange does not
render the
radius
of
gyration
of
prevented 18,000
the width b of
at the
more
than
Ko
this
work.
If the
fall upon
the structure.
by
11,
caused
not
exceeded.
OP, if applied
vibration, causes
the value OP
Now the load
just
touching
it
but
not
resting
upon
released
which
must
be
expended,
and
equal to
elastic
OSi
it
double the
assumed
as
true.
/////^y//////
then
vibrate
above
resistance,
stretch.
J*
This
load will
an
upward
acceleration
it
is
cause
been
and
by
the
above
;
area OHKP'.
Obviously, a
small value
if
ei
below the
impact test
the material
would not
by
the
same
the elongation and reduction of area
are greater in the specimen broken
under
impact
tension.
open
to
may
generally used.
percentage of the live static
stress.
Thus,
for
a
generally,
considerably
less
by
Lloyd
application, it
must
also
be
load
greater
so
instantaneous.
On
a
railroad
or
wheel load
fraction of the total stress in most members. A railroad
train
 
in
a
member,
the
so-called
 loaded
length.
The
two panel lengths; for
applica-
be
the
equipment,
flat
at
center,
not perfect, so that
blow
the
other,
decreases
of measurements
of the
increase in
as compared
par-
tially
overcome
about
the
position that it would take under the static load, so any
excess
of
vice versa.
to the
a
limit
to
this.
speed,
which
at
low
speed
however,
to
been
discussed
in
the
in Art.
2. The
allowance for
impact may
for
the
different
specified
The
Massachusetts
Board
of
other
truss
members,
the
of
the
Pencoyd
Bridge
adopted
first
be
decided
at
spans.
Some
cent,
but
from current
is
is less
increased
according
to
certain
be considered
are
in
accord
strictly live-load
impact when
Connecting
_
tender
for
locomotive
and
which has much
20 per cent for triple
track, and
^
.
^
;
elasticity and
50
L-
50
+Z
In
quite
still, and
in
designed.
The
section
applied,
less
by
correspondingly
support,
it
produces
a
deflection,
positive
radius
the
measured from the time
the point P is
V
of vibration
point P
dui
'dt
the amplitude
in any of the
equivalent
mass
little practical value,
concludes
that
the
more
important
avoid the necessity
a
seen
on
such
a
diagram.
The
best
experiments
experience, and
themselves,
some
at
all
speeds
must
be
that
mainly ue
wheels
of
the
same
axle,
sometimes
irregular
car
length,
and
other
relations
all
span.
5.
than
vertical it
was
of
no
consequence
small
computed stress
results
on
impact
on
3.
The
longer
the percent-
ages of
girders
to
differ-
ences
long ties supported
to
loads
distinctly noticeable on
speeds.
Previous
to
Professor
at
of that
In 1 second the stress
i
ac
gravity,
and
move downward with
weight
is
cohesion
may
be
it in some
enough moisture,
freezing and
area, if the earth is just at th point of
sliding
on
that
upon the total
area,
if
coefficient
of
coefficient of cohesion
As
a
matter
of
this depends
of the earth.
If the earth
to make it
of
a
a
to
BDE,
are
compressible.
same
of
the
maximum
slope
is
dependent
upon
the
height
the
flatter
is
the
steepest
of
safety.
Any
desired
way
if B'
is used
that of solid
size.
For
these
Kind of soil
in
sand
is,
say,
2.65,
each
of
water,
as 64
at
which
it
between
the
and there are little
rests. When
one body
as suggested
the
from
of
a
foot
of
earth.
Later
experiments
by
as
so
reliable,
the principles
different
slopes,
a
for
the earth
For founda-
tions in
it is,
or may
be, important
at
intervals,
so
that
angle of
are rock, gravel,
perhaps
Moist clay,
if heated,
will give
clay
can be
an approximate
this
slope,
the part
207)
be
taken
through
a
above ah.
Fig. 20G.
at
all
points
(on
a
on any
an area
he
of
the
prism
vertically
above
wh
If,
now,
the
plane
of the
pressure
on
ah,
(Fig.
209),
the
pressure
be
the
cp, the angle
he,
going
through
right
capable of
the angle
normal, until finally,
be
forced
to
passive earth
its tendency
to do
the
be
a
purely
opposite,
and
W
and
P'
must
lie
point
of
If the back of the wall is not vertical (Fig.
212),
find
first
between he and the wall.
This
applies
the
form
of
this
plane
sustains
this
-.
—
a wall makes
acts
in
this
direction.
We
pressure.
12.
angle PHV
angles
AB,
by
construction,
since
UV
If the circle is drawn
properly,
the
circle
a column of
earth having one
pressure
shding
on
This
we
the
passive
HLi
and IQ2
repose
(p,
point
(see Fig.
X
load
to
the
specific
gravity of the earth, and let h be the height representing
it (Fig.
consequently
circle
may
at
a
distance
Chap.
repeated
here.
expanded.
a
perpendicular
pressure
or
no
upward
be
applicable
that the theory
cussed. If
direction
of
to
experiments
just
correspond
to
in which
the
angle
which
the
the
coefficient
of
friction
of
earth
Experiments,
therefore,
will
not
agree
with
Rankine's
reasonable
along the back,
a
wall
should
not
have
so
small
a
the
224).
be
the
back
of
a
Draw
the
vertical
an angle
of al
In
Fig.
225
describe an arc
be
to R,
 
0'6'.
be similar
depth,
and
not
be
applied
at
from D, however, the
as the
to
the
to the
This
plane
directions
of
the
three
forces
m,U8t
(Fig.
227),
horizontal
to
go
direction in
 
will agree perfectly. In
vertical and
If
the
earth
is
just
at
the point
no
between
to BC.
and
AIC
= 180°
have
vertical
Having found F, since
earth pressure
dates from
As
late
component
a
certain
thrust
of internal
wall
may be
There may
dry material weighs
the
weight
would
case,
however,
would
probably
come
under
would be a
water stood above the level of the earth,
or even
water is
a considerable angle
of
repose,
though probably less than if dry, if only on account of the
lubri-
cating
a
w^ere
at
the
same
level
as
Another
part
It
is
in
contact
be
hydrostatic
It
full
of the
top of
the water,
may be
pounds
per
cubic
foot
is
less than
a due
water
back
earth pressure
be, with
hi
represents
below b. Reducing this
weight
Wi
be
total
pressure
itself
pressure
to
caissons in
necessary
for
working
of
a
bottom surface
which is
be necessary to keep the
water
and all
of the
the caisson
if
it
flows through
a
pipe
increases
as
the
the
hydrostatic
ber
The
result. The same
satu-
doubtless in motion.
An attempt
screened
less the uniformity
and the less
Sheet
piling
at
the
heel,
if
water must percolate
pihng,
and
up
under
in
head; and
leaked
all
identical
with
disagree
with
further
considered
a
small
varia-
when
<p
= 30°.
The
ent
the
pressure
have
 
by
traffic. It is very different from the case of earth dumped
behind
a
retaining
theory
because of the uncertain
every element of the
Earth in its natural undisturbed condition may be very
different from
to
of the wall
some
fraction,
say
0.4,
of
the
height,
the
saturated
with
the
shape
of
unscientific.
It
material
in
a
and the
is
clay,
is
there
Bell
and
he
was
yet
settled
the
than forclay,
filled in
back of
to assume that
realizes the
perhaps
Meem's experi-
however, of some
corrected for
hence
of
well be less than
natural
undisturbed
con-
be proper, according to
the
top
to assume
the pressure
earths, and is
bolts
extending
upward
on the
could be
 linear
arch
for
loads;
All the
above shows
that the
theory of
earth pressure
slavishly.
the
earth.
By
that are
theories
angle of repose of the cohesive
earth, and
area
and
p
the
normal
stress
intensity.
the
angle
of
friction,
for
The
of
the
ways
shown.
Using
the
E^^.
thrust
E
may
be
sliding prism
233,
tendency
unit
since
that
cohesion
by
Eq.
(30)
is
a
constant
by
triangle
ICK
triangle
CKN'
the area
The
distance
N'M'
to
MN-
supported
by
may be determined
for
by
^'
6
inches
about E,
of the
when
they
the surface
75
to
100
feet
high
and
10
to
Arch
on
top
of
the
piston
with
the
is called
a
deep
bin.
40.
U
the
perimeter
of
the
this when the
depth is the
greatest the center
of the side,
to
considered
it
sufiicientl}^
close
bins
(Fig.
2476),
assuming
to the
unit
carry in
out has been
cent, and
Lufft and
out at
one side,
is
due
orifice in
Wall?
Ratio
of
Lateral
to
any
which the
vertical
be greater
exists,
greater than given
a
factor
was not
0.3
and
0.6;
and
for
small
determined merely
by measuring
model
by
Eq.
(12),
/
/
 
The
results
of depth,
lateral area for
discussed
in
Arts.
30
and
31,
and
if
any
a cohe-
cohesive
material
and
apply the
determine
or temporary
which assumes
vertically
conditions,
and
volume
of
this
work,
hammer. The hand
steel
to the
rocks.
The
chisel
(Fig.
259)
)^-octagon steel,
 
has
used
for
splitting.
Granite
can
just as
quarry.
The
is sometimes
It is
271),
and
a
properly
directed
blow
so
marked.
feathers
are
of holes is made with the drill, along the line
to
be
split,
and,
in
between
them.
Fig.
sharp
distinction
others.
Class
II
gradually
becomes
are
removal,
rubble
this class and the third lies in the degree of
closeness of the joints
of
dressing
of
properly belongs in
a. Quarry-faced
h. Pitch-faced
defined
on which
the face
space inside the
on
state the
depth (perpendicular
the surface of
projection
finely dressed.
the
drafts
the
 
is broken range
at
of
openings
ashlar.
the three
behind
it
is
of
rubble
two
or
blocks
guarantees
be
paid
for
as
an
extra.
The
mortar
to
distribute
the
adjoining.
It
stones, where the
on
of
structure.
is one
a
certain
percentage
of
the
area
may
arches,
or
dimensions
limiting
bed
joints
(top
and
of the
the builds
engineer
specifications
were
as
follows:
defects,
and
shall con-
are nearer
directly
covered
with
concrete,
the
surface
three-inch
joints
for
the
balance
of
the
depth.
in
the
abutments
plans, set four
surface of
a stone
or quarry faced,
solid in cement
and face
be
Retaining
walls
on
the
south
to Une, and
cut its entire
The
backing
course
wall.
The
vertical
top of
curb
of
front
of
wall.
true
using
four
(4)-inch
face
not
less
the
shall
face, vertical
the headers
the dimension
it
does
The
is indefinite, because, in the first place,
the
unless
dimensions
are
multiplied
by
two
conflicting
requirements. What is the contractor to do if the engineer
makes conflicting statements in specifications?
Clearly
he
should
protect
himself.
if
at
quantity
in
place.
13.
of approved
slope
the
bonded,
laid
mortar.
13.
Stone
shall
not
be
dropped
or
not less
pointing
tool
which
leaves
the
joint
generally
273.)
the
mortar
layer
should
not
22.
be permitted
show in
lewis, or
4 feet long; shall
of
wall
the course
below, to
the position
surface
of
back
and
face
heart of the wall
,
thin coat of
directed
by
the
Engineer.
Bench
14.
Principles
on mortar.
3. The
maximum intensity
of pressure
Bed joints, however,
cut smooth,
The angle
of repose
will therefore
reinforced, is
the first
condition. The
maximum
and
minimum
middle
third
point,
maximum
p
be tentatively
is
too
great,
a
new
and
smaller
If the
since then there is
be
with the strata per-
durable.
5.
The
masonry
be
filled
with
mortar.
has been placed upon
of
mortar.
pressure
plumb.
absorb
the
water
from
the
mortar).
8.
Strike
to the
general introduction
C,
a
railroad
which
has
been
a
the present
direction,
point
of
application,
and
magnitude,
so
that
inside the middle third;
with the
unnecessary
horizontal earth
pressure
-^
—
horizontal,
with
but
with
a
up to C
C to
stability.
the
resultant
strikes
AB.
dimensions
of
the
by
assuming
dimen-
used
in
computed
in
at
its
material
Here,
the
horizontal.
But
the earth, the wall
know from
to
a
failure.
But
great,
it
is
not
desirable.
If
a
retaining
base
BC will
 
be
foot
us
third
point.
sections (a) and
angle
of
tion
the
pressure
be
one-eighth
of
the
moment
211
{a)
the
moment
of
of E.
has
In the chapter
15.
Other
Forms
of
Section.—
 PY
viously
the
should act within
equivalent height
uncertain,
. The
tension
on
as
i
35°,
or
(1)
is
0.833
components
right
gravel, let
us say,
for about
7.5 feet
down, the
base
from
A
was
220,320
The
maximum
and
minimum
pressures
jii
4
X
J-^
18,360
the wall
43
lives.
19.
Direction
of
That
to
the
left,
or
wall should
on earth if
But the
above
settle
the
pressure
truth that
Nature always
helps the
replaces the
the
at
its
actual
the
a
resisting
the
pressure on
The matter
is uncertain,
wall, and its tendency to tip to the right, if
standing
by
itself.
pressure
on
to
be
Mohr
circular diagram,
Rankine's theory,
right
of
the
vertical
exceeding
HIN\
at
should be known
and they may claim
may be generated
from
be
somewhat
as
in
Fig.
296,
adjoining
counterforts.
Its
needed
top
and
bottom.
The
horizontal
slab
indicated
in
Fig.
297.
tors, and
better
frost.
wet clay it
it cannot
be avoided,
ing
wet
should
be
reduced
as
much
as
possible.
having
an
offset
as
in
chapter,
to
give
a
stream.
d.
The
pressure
from
in a flume
the
on the long side of the pier should be considered,
the
 
are
not
frictionless.
The force
due to
bridge
span
bridge
span,
which
rests
on
walls
or
out to
the foot
as
in
.
reach to
wall
may
be
narrow
and
there may
own weight,
abutment
subjected
to
its own
of the bridge.
common,
acts
near
so
tends
to
for
to
keep
it
back
less than
that of
the head
wall. Such
not over
flows down into
of concrete.
reinforced
by
rods.
Such
walls
are
built
spaces.
built curved or
in
a
compressible
a
back
by
planking
or
concrete
construction,
12.
faire.
Scjourne,
 Avant-Propos
to
made
up
in the sense that
that are indeterminate by
if the
as
these
are
continuous
they
solid
continuous
rib.
If,
in the
concrete because
resultant pressure
sure
arch,
not
as
a
curved
This treatment will be
2.
ring. If the axis
a
circular
cylinder;
centered.
Some
arches
are
five
centered;
shape.
Exirados
may
or
the
soffit,
the
thickness
increases
toward
the
abutments.
The
outer
surface
may
not
be
a
curved
surface
at
taken
Figs.
313,
314,
crown. There is no
called
near the
spandrel
is
considered.
This
is
because
a
logically
a complicated
Concrete
is
generally
quantities
and
even
in
studying
XX.
Concentrated
loads
being
distributed
may
each
engineer
not delude himself
The (true) line of resistance must lie within the middle
third
of
or
it
joint must not
known,
necessary
to
lay
pressure
on
joint
2
is
the
intersection
of
is
obvious
that,
for
a
symmetrical
arch
and
symmetrical
but a necessary
In Fig.
infinitude
of
of resistance.
Silf
for
(Fig.
319)
2M
joint
may
be
found
analytically,
with
ease;
for
the
symmetrical
the thrust on
is
has the
largest horizontal
the
arch
the
arch
ring.
By
the
at
is
lowered,
the
entire
line
the
intrados
somewhere;
if
application at
the entire line
the
springing,
may
touch
the
at
the
tangent
but
may
cut
the
at one
just
from lack of
collapse
the
structure
of
the
other.
A
structure
stability
many
not
be
at
is approximately the
of
is
as
far
from
again
as
far
from
the
axis
as
the
maximum
between the
each of the others, and is quite sure to be
nearer
the
if it
certain that
the arch
is stable.
stable; and
compression over
The
 hypothesis
of
least
pressure,
proved
by
means
Winkler's
a
different
category,
because
theories,
even
the
elastic
theory,
are
plicated, is itself based
(see
Art.
22).
The
reinforced concrete arch
the compression
same total compression
the same.
by
a
not the
(3)
compute
the
sum
gradually
will be some
arch
perhaps
this
was
basis
of
Winkler
and
if any line
would
be
the
basis
for
my
statement
my
opinion,
to
of
at
circle
drawn
at the
at the
is due
of the
masonry.
If
the
50
on
page
46
shows
that
feet,
or
a
rectangle
50 feet,
distributed
the crown, covering 19 feet; and if the depth of
fill
live load
but
if
the
span, or
this is
not advisable.
The area
Fig.
329.
Fig.
330.
go
through
h.
deviates from
point
give
a
we
half of
the
only
for
an
the right
middle third
analytically
center of the
whether
a
line
of
so
may be
reduced, if
may
omitted.
In
these
points.
This
is
defined
as
the
intrados,
open
at
section. If such
that end
much
greater
at
the
this. It
of
concrete
is
small,
but
the
crown. Then from a
but
varying
as
6 to c
c to
rectangular,
and
to
The
writer
a
to
the
reinforced
to
best
applicable,
the methods
following are admitted:
resistance is the
found which is
nearer the center
with
extreme
exactness.
They
matical.
than the methods explained in this
chapter. Certainly
of
cannot
if
a
a
theory, fully
as satisfactory,
tension, it
some saving
The
writer
is
merely
pointing
out
the
perhaps
but we should realize
at a
Let
Ml
(a negative quantity).
as one
axes of
arch
cylindrical,
it
would
be
possible
to
joint
surfaces
themselves
would
be
at
right
Such
single
by one
parallel to
a skew arch which
parts
S-2x
cot
(p
and
on
the
be
calculated.
is
a
Avoid skew arches
or
different
form
and
shape.
intrados.
ADE
and DCE parts
considered
as
four
arch
faces
above them.
thickness of
arches
abut
with-
out
section,
which
might
square.
Fig.
345.
Philadelphia filters,
reference
to
Gothic or
abutments
clearly not exact.
A committee of
how
the
arch
will be
or
completely
hinged.
A
as
follows:
impossible
of
antimony,
pounds
hinges.
It
was
which
fit
collars on
the hinged
must be a
to
allow
free
rotation.
a Uttle
The
is questionable.
too short
the movement is less
{d)
I
and desirable
the best form
arches
in
crown dropped
vertical and
contained the
completely
hinged
and
If the
rise of
haunches, or to
facilitated
by
the span
(so-called cow-
has
The
sidewalks
frequently
piers,
also
Figs.
ance. The piers will
diminish
further referred to
in the next
arch
on
and using in the
resistance
should
not
tending
to
overturn;
and
a
other
unloaded.
Concrete.—
The
advantages
claimed
for
masonry
or
steel are the
concrete arch; Sejourne,
serviceable.
The
durability
of
concrete
arches
The joints may
which
may
be
than of
John
bridge
at
Washington,
D.
C,
a
segmental
of
220
anybody interested
in this
should
nearly
as
practicable;
aesthetically,
because
beauty
usually
pres-
ent.
If
a
or
concrete
backing
arches
as
in
Fig.
369,
being
p,
P and
must be
371)
the
springing.
Such
an
semiarch, horizontal
at 1
the
part
12,
Draw
23'
to
on the
part 23.
Similarly if
and he
OX and OY, if a is the inclination of the
rib
to
the
horizontal
at
C,
chj/dx
ture of the
some
point
D
corresponding
Od, that
tan-
gents
will
curved, that is,
section of the shell
a
as it
in
the
ring.
normal pres-
a
circular
to
a
normal
pressure
at
every
point,
but
that
tion
in
order
some set
The
keystone
has
a
will depend
of the arch, and whether the space beneath it must
be
left
may there-
it
centers may
determined. After
desired to
find the
repose of
stone
TFi
and
forces may
tend
to
slide
on
the
one
below
it,
but
arch
passing
just
joint,
and
not
would
throw
G'
inside
of
be
making
a
greater
drawn
making
the
angle
(p
evident:
1.
The
pressure
R
on
weight.
This
of the stones from the top
down; but
in any
The maximum
easily
construct
comparing
on masonry,
des
Lemons,
capable
of
sustain-
ing
that
the
{Laggirxj
Fig.
382.
may
be
a
series
cleats nailed to
the center
may be
many
centers,
and
so
8.
upon
a
com-
pound
wedge
on pistons
that joint
plane
that
must
be
parallel
to the surface; there is no shear on CD. The real intensity
on
is or may be
line of resistance
Thus,
let
Pi
weight of
the second
layer and
pole at
and draw
upward pressure is
way; but
It is better to make the faces curved rather than
polygonal, because
use
Eq.
(3),
and
contented
Stability of Masonry
tions
are
pointed,
the
rounded.
The
pressure
on
AB
is
his
plane
perpen-
Let
AB
(Fig.
402)
be
and
AB'.
plane normal
i.
As
stated
usual theory
is so
and
AB'
was
distributed
this actually the
distribution on
(Fig.
404),
distri-
uncertain.
The general problem of finding the distribution for any form of
section
never
that
the distribution of the
homogeneous
forces are
pressure
In Arts.
that,
aside
from
rotation of
of gravity
of a
triangle or
Fig. 407.
the center
the opposite sides. Draw
OE and BD perpen-
triangle is at the point where the paper is cut
by the
and
C.
clearly desirable
upward
pressure.
If the
head. The
too great,
Wachusett dam
of
but
half
a
the back
out the
dam is not
earth.
This
is
was
found at
the center
of the valley, and it was decided to found the
dam
at
entire
horizontal
section.
Following
should
be
kept
quite common
now to
12 feet
great care
should be
taken, where
concrete, to
make as
perfect a
C.
principles as
principles
involved
the
foundation
of
the
dam
from
the
reservoir,
the
upward
head at the
sur-
also save the
does
the dam can
at
each
site
after
a
thorough
investigation
by
the
obtainable facts
enough
reach
by
the gatehouse has
or lowering the gates which control
the inlets, and the valves
which
be
an
of the
too near to the top of the dam. The
cross-section
the
water
may
be
placed
along
the
of
the
dam
across
the overflow weir,
for
a
are not generally
of  trembling
dams. This
be so
shaped as
form unless the
water rises unexpectedly
a
of the crest.
The
to transfer the
water,
would
destroy
energy.
A
vertical
fall,
destroy
energy
face and apron,
to
points:
1.
That
made
due to
hasten
priming.
Figures
should
not
be
too
great
extreme
complexity.
one,
do
not
safe
rely
on
a
different
thickness,
is
sive
shrinkage.
21a.
Effect
of
Lateral
Expansion
on
direction
perpendicular
to
the
two
planes
on
m, would
the
hydrostatic
pressure
on
the
upstream
certain
horizontal
thrust
series of
horizontal or
inclined arches
hydrostatic
pressure
may
gravity
action,
and
the
dam of the U.
though
some
of
cold
reconstructed
in
time
to
prevent
a
collapse.^
reconstruc-
dam, and
showed
similar
effects.
It
well within the
toe, but it
is
not
considered.
It
advantage
some
chord,
say
arch
action,
which
would
exist
in
plan,
while
be
curved
in
plan.
24.
Allowable
Pressures.—
The
foreign
dams
varied
from
300
years
inch, or greater than in any other dam. In
the
New
Croton
the downstream
kine's principles;
Bridge
and
Many masonry
dams have
It
is
was the
The
Gileppe
154
Spanish
 
Nile
the world,
is the
is
a
supply of
New York
maximum
height
City.
on
top
and
14
feet
 by two
concrete on the axis
feet.
The
foundations
of
side
having
a
masonry
core
about
a
tunnel.
This
dam
a
masonry
trench,
20
feet
wide,
The
dam
and
waste
weir
are
cutoff wall, then
great height,
the
on
crest
1,080
432).
Fig.
430.
feet; width
foundation,
328.4
feet;
the
the river bed.
and 108 feet at
the
O'Shaughnessy
downward
pressure
purely
an
overturning
effect
upon the slope
is that
at Ellsworth,
dam^ is merely
neither through
it nor
under it.
The foundation
must therefore
down to
good material,
which should
and
wetted.
be
made
feet, and
not less
the downstream slope,
a
conduit.
Special
precautions
by
a
flood.
in a
a
over 100 feet. In the
Lower
in the United
small water powers.
as
Fig.
439;
(2)
stone,
somewhat
Leffel Turbine Water Wheel Company,
and
in
Wegmann's
book,
to
Wegmann's
a
pond,
while
at
dam
entirely.
There
needles can
Low
Wafer
Fig.
440.
rolling sluice
River and
its tributaries,
on the
one, and should be
building
foundations,
to
the
foundation.
Some
cases
in
this
chapter.
would
seem
to
core
if possible;
such
doubt been
through the
masonry of
and by
given
in
this
chapter,
and
here
gratefully
acknowledge
C
Culmann,