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UNIVERSITY OF CALIFORNIA.
The D. Van NoSlrand Company
intend this book to be sold to the Public
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THEORY AND PRACTICE
THEORY AND PRACTICE
FREDERICK RINGS, M.S.A.,
Architect and Consulting \Engineer
B. T. BATSFORD, 94 HIGH HOLBORN
D. VAN NOSTRAND CO., 27 WARREN SIT.
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MUCH has been written upon the subject of reinforced
concrete, and the design of structures in this material no
doubt still affords opportunity for invention and improve-
ment. New systems, new bars, new details of various
kinds are constantly being patented in many countries, but
the leading features and ideas remain the same. Generally
speaking, one may say that there are as many systems as
there are specialists, each naturally insisting upon the
superiority of his own favourite ideas.
The Author had occasion to see reinforced concrete
constructions designed and executed for many years, and
has closely followed its development. His principal object
in writing this book was not to put forward any particular
method of construction, but to collect in a concise form
what seemed to him best of the many formulae and systems
used in various countries, and to deal with the subject in
such a manner as to be intelligible to average students of
architecture who have not been required to devote that
amount of study to the theory of construction which is
demanded of the young engineer. At the same time, it is
hoped that the present volume may be useful also to the
As no mere series of unexplained formulae can give any
useful idea of the subject to a beginner, and as, as has
been indicated, the intention is to treat the subject in aa
elementary manner, an effort has been made to afford brief
explanations of the calculations given and to further eluci-
date them by numerical examples. Thus it is hoped the
reader will be enabled to acquire a methodical knowledge
of the principles upon the application of which all the
varied systems alike depend.
No doubt the design and execution of reinforced con-
crete work will always remain to a great extent in the
hands of specialists, but the average architect or engineer
should have sufficient knowledge of the subject to himself
decide where this form of construction can be most usefully
employed and what kind of reinforcement is most suitable
to the particular case in hand. Each patent bar and
system has its advantages, and after a careful study of
the principles set forth in the following pages it should be
possible for the designer to himself decide which is the
most suitable for use in any special case, and to hand over
to the specialist only the task of properly working out the
details upon general lines already laid down. Thus will be
avoided the risks inherent in having to leave the whole
design in the hands of one whose financial interests may
incline him to use methods not quite the best for the
special work under consideration.
The formulae are based on the assumption that ordinary
round bars, such as are obtainable everywhere from stock,,.
are used. Some tables and extracts are reproduced from
the R. I. B. A. Report on Reinforced Concrete, by kind per-
mission of the Institute. The history of reinforced concrete
is partly compiled from the data given in Tozer's Handbook
on the Lock Woven Mesh System, and facts relating to the
manufacture and qualities of Portland cement and its use
are chiefly from Everyday Uses of Portland Cement, pub-
lished by the Associated Portland Cement Manufacturers
(1900) Ltd. The author is indebted to the various special-
ists mentioned for the loan of interesting photographs, etc.,
dealing with work executed in reinforced concrete.
The Figs, marked 1 are reproduced from Kersten's Der
Eisenbetonbau, except where otherwise stated.
It is hoped that the tables at the end of the book,
together with the Ready Reckoner, will be a help to
designers and others for reference, calculation, and the
checking of designs.
LONDON, March, 1910.
LIST OF SYMBOLS
BASED ON THE STANDARD NOTATION SUGGESTED BY THE
SCIENCE STANDING COMMITTEE OF THE
a Area of the couple formed by compressive and tensile forces
in a beam.
a c Area of compressive force measured from neutral axis in
a t Area of tensile reinforcement measured from neutral axis.
b Breadth generally in inches.
b r Breadth of rib in a tee-beam in inches.
b s Effective breadth of slab in tee-beam in inches.
c Compressive stress intensity on concrete.
c s Compressive stress intensity on steel.
c * \ Stresses in concrete of columns eccentrically loaded.
d Depth generally in rectangular sections.
d Effective depth of beam or slab from top to axis of tensile
reinforcement in inches.
d Diameter in circular sections in inches.
d c Depth or distance of centre of compressive reinforcement
from compressed edge of beams in inches.
d c Diameter of core of pillars in inches.
d c Depth of arch ring at crown of arch in inches.
d d Distance of bottom of reinforcement of rib from centre of
gravity of reinforcement in inches.
d]. Diameter of a helical reinforcing rod in any compression
piece in inches.
d\ Diameter of a longitudinal reinforcing rod of a pillar in
d n Deflection of a beam in inches.
d r Distance of rods centre to centre in inches.
d s Total depth of slab in tee-beam in inches.
d t Total depth in inches.
e Eccentricity of load in inches.
e Distance of centre of rod from axis of column in inches.
f Friction or adhesion of concrete and steel.
h Height generally in inches.
i Inset of centre of reinforcement from bottom of slab or rib
/ Inset of rod centres from outer edge of column section in
/ Inset of centre of gravity of column section from outer edge
/" Distance of eccentric load from outer edge of column
section in inches. / =* d - e (diameter - eccentricity).
/ Length generally in inches.
/ Effective length or span of beam or arch.
m Modular ratio, i.e. the ratio between the elastic moduli of
steel and concrete
n Distance of neutral axis from compressed edge in inches
p Intensity of pressure per unit of length or area.
r Radius in inches.
3 Shearing stress intensity.
Sh Spacing of hoops round columns in inches.
s r =~ Stress ratio in ribbed slabs.
/ Tensile stress intensity on steel.
t c Tensile stress intensity on concrete.
x \ Stresses in steel in columns eccentrically loaded.
v Versine or camber of a curve or rise of an arch in inches.
w Weight or load generally, per unit of length or area.
w Superimposed load uniformly distributed on arch.
w d Dead load above arch ring at crown.
Co-ordinates in arch calculations in inches.
x Distance of hangers or bending up of rods from support in
y Height of shear triangle.
ft Distance of compressive force from neutral axis in ribbed
slabs in inches.
y = - In ribbed slabs.
TT Ratio of circumference of a circle to its diameter.
O Perimeter of steel rods in inches.
A Total cross-sectional area of beam or pillar in inches.
AC Area of compressive reinforcements of beams in inches.
A L Cross-sectional area of longitudinal steel rods of pillar in
A r Sectional area of one rod in ins. 2
AS Area of shear reinforcement in ins. 2
AT Area of tensile reinforcement in beams in ins. 2
B Bending moment generally.
B Maximum bending moment of the external forces or loads
on a beam.
B Bending moment at crown of arch.
BC Bending moment at centre of beam.
B E Bending moment at end of beam,
B L Bending moment left half of arch.
BR Bending moment right half of arch.
C Total compressive force or stress.
Cc Total compression on concrete.
Cs Total compression on steel.
EC Elastic modulus of concrete in compression in lbs./in. 2
E s Elastic modulus of steel in lbs./in. 2
G Centre of gravity of column section.
Ic Moment of inertia for concrete.
Is Moment of inertia for steel.
N rf Number of divisions in one half of arch.
N r Number of rods.
PH Horizontal pressure.
PV Vertical pressure.
R Moment of resistance of internal stresses in a beam at a
RL Left reaction.
RR Right reaction.
Total shearing force across a section.
Sc Shear at crown of arch.
S c Total shear taken up by concrete.
S s Total shear taken up by steel.
Sp Safety factor.
T Total tensile force.
T c Thrust at crown of arch.
VV Weight or load.
I. INTRODUCTORY . . . . . :. i
HISTORY OF REINFORCED CONCRETE AND ITS AD-
VANTAGES OVER OTHER SYSTEMS OF BUILDING 5
II. MATERIALS . , . . . ' . V . 12
A. PORTLAND CEMENT. ITS MANUFACTURE
AND QUALITIES, STRENGTH, TESTING, ETC. . 12
B. CONCRETE. THE AGGREGATE, SAND AND
WATER, PROPORTIONS, DENSITY, MIXING,
TESTING . , . . 'v V . 14
C. STEEL. ITS PROPERTIES, CONNEXIONS,
CUTTING AND BENDING, DISTRIBUTION OF
RODS .,, . . . -'. . 30
III. EXECUTION OF WORK . . " .. . '. 36
STORING OF MATERIALS, CENTERING, CONCRETING,
WORK DURING FROSTY WEATHER, STRIKING
OF CENTERING, PLASTERING, TESTS . . 36
IV. LOADS, MOMENTS, STRESSES, AND VARIOUS
APPLICATIONS OF REINFORCED CON-
A. FLOOR SLABS . . . . . 47
B. RIBBED CEILINGS . 52
C. STANCHIONS AND COLUMNS .'' . -54
D. WALLS . . ... . -54
E. ARCHES, VAULTS, AND BRIDGES . . -57
F. FOUNDATIONS AND PILES . . . . 61
G. STAIRS . . . .V . . . 61
H. PIPES, WATER MAINS, SEWERS, ETC. .; . 62
I. ROOFS . ... . . - . : '.- -. 65
V. RESISTANCE AND SAFE STRESSES . . 67
VI. FORMULA FOR SLABS . . .* . - , 75
EXAMPLES. . . . ~. . . . 82
VII. FORMULA FOR DOUBLE REINFORCED
SLABS . . . . ., . .'. . 87
EXAMPLE . . ... . . ... ^ . 89
VIII. FORMULAE FOR RIBBED CEILINGS. . ; ..' 91
EXAMPLE . .. . '. , . v . . 98
IX. FORMULA FOR DOUBLE REINFORCED
RIBBED CEILINGS . . .. . . _ . 102
EXAMPLE . . . . . ^ -. . .^ v . 103
X. SHEARING STRESSES AND ADHESION . 105
EXAMPLE . , . . . . A .~ 1 06
CALCULATION OF STIRRUPS . . . .. . 108
CALCULATION OF BEND UP RODS . * '. " . in
EXAMPLE . . ^. . \. . . in
TORMUL^E FOR COLUMNS
AXIALLY LOADED . . . . . '. 112
XL-! EXAMPLES . . . . '*. , . 116
ECCENTRICALLY LOADED . .. . 117
EXAMPLE . . . . . . . 121
XII. FORMULA FOR ARCHES ., . / . 123
XIII. PATENT BARS AND SYSTEMS . , . 127
MEMORANDA AND TABLES . . . . .' 148
TABLE FOR CALCULATING SLABS AND T BEAMS . 148
TABLE FOR CALCULATING COLUMNS . . . 149
STOCK SIZES AND WEIGHTS, ETC., OF BARS, WIRE,
ETC. . . * ...... . 150
STOCK SIZES OF PATENT BARS, ETC. . .' . 151
SUNDRY USEFUL MEMORANDA AND PRICES . . 155
ROOTS, SQUARES, CUBES, ETC. . * . . 158
SYMBOLS .... . . . . .181
INDEX . . -. -.., I . . ' . : , . 185
READY RECKONER (IN POCKET).
THEORY AND PRACTICE
REINFORCED concrete, although considered a modern building
construction, is really very old in principle, and it has been proved
that the Romans, many years before Christ, used it, naturally
only in a very crude form, but evidently fully understanding the
principle of the combination of metal and concrete. There are
examples of Roman reinforced concrete in many parts, the rein-
forcement consisting as a rule of bronze rods placed crossing each
other in the centre of the slab. The concrete consisted of lime
with occasionally other additions of hydraulic materials and
aggregate, which latter was, as a rule, rather coarse. The Roman
system of strengthening concrete with tiles is well known, and
there are still many samples of their work in existence. The
reinforced concrete of old times cannot, of course, be compared
at all with our modern concrete as regards properties of strength
and resistance, as the manufacture of Portland cement was not
then known. In the Middle Ages concrete of lime mortar and
stones was also used to a certain extent, but it was not before
about the middle of the nineteenth century that the idea was more
fully explored. About this time we trace various patents relating
to the construction, like Louis Leconte's patent protecting the use
of iron plate trusses for floors. He suspended iron rods from
these plates, the rods carrying a mesh work of wire, which in its
turn supported the ceiling plaster. Other patents of this period
are the Vaux and Thuasne systems. Vaux used round rods,
hooked on flat iron bars placed edgewise in the concrete slabs.
Thuasne's system consisted of small iron joists having hangers
placed over them, with round iron bars suspended through a hole
in the hanger. In these systems plaster of Paris was used. This
material does, however, not protect the iron from rusting, and
consequently the constructions were not lasting.
In these specimens of reinforcement no attention was paid to
what is now the leading principle of reinforced concrete construc-
tions, namely, to use the iron reinforcement to resist the tensile
stresses while the concrete resists the compressive stresses.
No substantial improvement can be recorded before the in-
vention of Portland cement. This was discovered in 1824 by
Joseph Aspdin of Leeds, and improved by William Aspdin, who
took out a patent relating to the manufacture of Portland cement
in 1852. Wilkinson in 1854 used a layer of wet sand on the
surface of fresh concrete, keeping the sand wet in order to get the
concrete as hard as possible. The same inventor also took out a
patent for hollow partition blocks and for fireproof floors. These
latter he reinforced with flat iron bars placed on edge, and he de-
scribed these bars as taking the tensile stresses, thus coming nearer
to our modem ideas of reinforced concrete.
Frangois Coignet of Paris invented about the same period his
" Be"ton-Coignet," a concrete composed of hydraulic lime and
aggregates mixed mechanically in certain proportions. In con-
structing slabs he put rods crosswise, similar to the Monier system.
A good specimen of his work is the aqueduct of the River Vanne,
which still exists at the present day.
In 1857 Dennett, a Nottingham contractor, introduced con-
crete arch floors between JL iron joists.
In 1867 Scott took out a patent for a fireproof floor consisting
of a lacework of rods, hoop irons or wire embedded in the concrete,
and he states in his specification that the concrete takes the com-
pression while the ironwork resists the tension in the slab.
FIG. i. AQUEDUCT j
This remarkable Aqueduct for the Paris Water Supply was executed by the late Fran
has a span oi
:i HE RIVER VANNE.
(Reproduced from Coignets Handbook.)
in moulded concrete. The principal arch shown in the above photograph
[To come between pages 2 and 3.]
The introduction of reinforced concrete is usually attributed to
Monier, who patented in France in 1867 a method for making large
tubs for shrubs, using a meshwork of wires and rods embedded
in concrete. Later on he took out further protection for other
applications of his idea, and, on exhibiting his inventions at the
Antwerp Exhibition, 1879, he came in touch with Wayss of Berlin,
a civil engineer, who took Monier's patents up and worked them
extensively. Wayss and his partner Koenen are responsible for
the first method of calculating the strength of reinforced concrete
floors. In these calculations they assumed the neutral axis to lie
half-way up the beam and that the steel rods are equivalent to
the bottom flange of an ordinary steel girder, while the concrete
was considered to take the place of the top flange.
Lascelles in 1877 erected a number of cottages, the walls of
which consisted of concrete slabs reinforced with iron rods placed
The first reinforced concrete building in America was built by
Ward of New York in 1875, the whole of the walls, floors and
roof being composed of concrete reinforced with metal rods.
Further important inventions are the patents of Golding (1884)
for expanded metal, Ransome (1884) for a twisted bar, and
Lindsay's patent (1885) for reinforced concrete floors consisting of
passing rods over and under the iron joists to form a continuous
In 1894 Edmond Coignet published a booklet setting forth
a theory of the distribution of stresses based on the different
moduli of elasticity of iron and concrete, thus establishing the
modern theory of calculating the stresses of reinforced concrete.
A further important advance was made by Wayss and Koenen
of Berlin in 1892, who patented a reinforced concrete floor having
the rods cranked up at the point of contraflexure.
About the same time Hennebique patented a construction of
reinforced beams having stirrups to resist shear, and later, in 1897,
the same inventor introduced the system of rods cranked up placed
one above the other to reduce the width of the beam.
Further important patents were taken out in quick succession
in various countries like the Ast patent largely in use on the
Continent and many others ; and the introduction of various patent
bars, mention of which will be made later, rapidly put the import-
ant subject of reinforced concrete on strong bases, and the engin-
eering and architectural professions of almost every civilized country
were induced to look upon reinforced concrete as what it really
means, viz., an ideal building construction tending to sound
stability and, if properly designed, considerable economy as com-
pared with solid brick and iron buildings, the most important
feature being its fireproof properties.
It naturally became necessary for the building authorities in
the various countries to safeguard the public against improper
usage of the new method of building, and the German Government
passed some very stringent building laws dealing with the calculat-
ing of stresses and the execution of the work, mention of which
will be made in due course.
The Royal Institute of British Architects, recognising the great im-
portance of the subject, appointed a committee who in 1907 issued
a report laying down various recommendations and suggestions for
the calculation of stresses, to which reference is made hereafter.
The leading idea of the construction is to use the concrete, the
tensile resistance of which is considerably less than its compres-
sive resistance, to take the compressive stresses of the com-
bined material while the steel work resists the tensile and shearing
stresses. Consequently round or square rods are placed in the
concrete in such positions and in such dimensions as is necessary
to resist the tensile and shearing stresses at the various points of
stress, while the concrete is left to take the compression.
The three principal qualities of the two materials making it
possible to gain the particular result are :
1. The adhesion of the concrete to the steel is considerable
(100 Ibs. per square inch : see later).
2. The coefficient of expansion of concrete has been shown to
be practically the same as that of steel.
3. The protection of the steel is such, that the formation of
rust is quite impossible.
ADVANTAGES OF REINFORCED CONCRETE.
Reinforced concrete has been used so frequently and for so
many purposes that practical conclusions can be arrived at,
and it is now universally granted that the construction possesses
many advantages over the method of building as used heretofore.
There is hardly a branch of construction where reinforced concrete
has not been used to decided advantage.
The principal recommendation is the fact that it is highly fire-
The vast expansion of our big cities, the huge factories, where
hundreds of people work in close proximity, the massing of people
in theatres, schools, churches, and public buildings, make it im-
perative to study the prevention and spreading of fire and to use
every possible means to this end in designing a building. Steel
in itself, as used for stanchions, columns and girders, does not
guarantee a protection at all ; in fact, the contrary effect is more
likely to happen, as the destruction by fire of a beam does not only
involve the collapse of a floor or other superincumbent load, but
very often the demolition of the walls as well. The heated steel
loses its power of resistance and bends and fails altogether, bring-
ing down everything with it. Various big fires have repeatedly
shown this, where heavy girders were bent to all sorts of fantastic
shapes. The failing naturally makes the extinction of the fire and
the salvage almost impossible. It is absolutely necessary to con-
sider the fire danger, even if everything in a room or building is
carried by steel constructions. The only remedy is reinforced
concrete, as the protection afforded by the concrete does away
with the danger of the steel failing, and even if the whole build-
ing is burnt out, the carrying frame remains unhurt and re-
building can start at once, be carried on at a greater speed, and
the cost of rebuilding is reduced to the reconstruction of the
fittings and decorations. The danger of collapse during a
fire is almost entirely removed and thus salvage operations made
It is consequently necessary to protect all steel stanchions and
girders with a fire-resisting material, and cement concrete has
for some considerable time past been used for this purpose. In
ordinary steel constructions, however, this is rather costly, as the
concrete mantel does not take any stresses, and, therefore, does
not make it possible to reduce the thicknesses and weights of the
protected stanchions or girders. In fact, the material used is simply
superfluous and only of use in case of a fire which may never
occur. Reinforced concrete, on the other hand, does away with
all heavy steel work and the concrete is made to do part of the
duty of the member protected, thus effecting a considerable saving
in cost, while at the same time affording full protection against
The concrete does not crack nor split under the influence of
fire, nor when water is thrown on while heated, thus effectively
protecting the embedded steel from all dangerous influences.
It must be admitted 'that when exposed to great heat the con-
crete loses somewhat of its strength. The hardening of the material
took place under the influence of water, and it is obvious that, if
this is lost under fire, the concrete must become a little less com-
pact and perfect, but this shortcoming is easily outbalanced by the
advantage of keeping the whole structure intact, and as the in-
fluence of the heat can only be destructive to a very little depth,
the various parts are easily repaired at small cost.
Furthermore, it has been repeatedly proved that the fire does
not affect the complete adhesion of the concrete to the steel, so
that, as far as the strength of the structure is concerned, little need
be feared in consequence of a fire.
Objections .have been raised repeatedly that the moisture con-
tained in the concrete during construction would cause the steel
work to rust. But this supposition has been proved wrong over
and over again. The famous French architect, Viollet le Due,
removed some iron clamps that had been built into the stonework
[To face page 6.]
of the church of Notre Dame at Paris, and they were found to be
as bright as when they were put in some 500 years ago. Some
reinforced concrete mortar pipes (if in. thick) were constructed in
Grenoble twenty-two years ago. After fifteen years two lengths
of pipe were raised for inspection, and it was found that, although
the water had been flowing through them and they had been em-
bedded in soil for these fifteen years with only f in. of Portland
cement concrete protecting the steel, the metal was as bright as on
the day it had been put in. Many other instances could be men-
tioned, and we might take it for granted that experience has
shown how perfect is the protection afforded by the concrete.
The mixing of the concrete should be as perfect as possible with
a sufficiency but not superabundance of water, as the latter has a
weakening effect on the strength of the concrete. The proportion
should be i part of water to 3 or 4 parts of solids ; in no case less.
It is very important that the reinforcements should be fully pro-
tected against rust. Painting with oil would seriously interfere